baryon spectroscopy in the sextet gauge model · baryon spectroscopy in the sextet gauge model chik...

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopyin the Sextet Gauge Model

Baryon Spectroscopyin the Sextet Gauge Model

Chik Him (Ricky) Wong

Lattice Higgs Collaboration (LatHC):Zoltán Fodor $, Kieran Holland ∗,Julius Kuti †, Santanu Mondal −,

Dániel Nógrádi −, Chik Him Wong $

†: University of California, San Diego *: University of the Pacific $: University of Wuppertal -: Eötvös University

SCGT 2015

1 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

OutlineOutline

Review: Sextet Model as a Composite Higgs candidate modelBaryon Spectroscopy in the Sextet Model

Operator ConstructionPreliminary Lattice Simulation Results

Sextet Baryons as Dark Matter Candidates?Conclusion

2 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Goal: Look for a Composite Higgs model:An infrared fixed point almost exists + Confining⇒ models at theedge of conformal windowAfter Higgs boson discovery : Light 0++ Higgs + reproducedetected phenomenologyParameter Space:NC, Nf , Representations of SU(NC)

Focus of this talk: SU(3) Nf = 2 Sextet(Two-index symmetric)Model

3 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Goal: Look for a Composite Higgs model:An infrared fixed point almost exists + Confining⇒ models at theedge of conformal windowAfter Higgs boson discovery : Light 0++ Higgs + reproducedetected phenomenologyParameter Space:NC, Nf , Representations of SU(NC)

Focus of this talk: SU(3) Nf = 2 Sextet(Two-index symmetric)Model

3 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Goal: Look for a Composite Higgs model:An infrared fixed point almost exists + Confining⇒ models at theedge of conformal windowAfter Higgs boson discovery : Light 0++ Higgs + reproducedetected phenomenologyParameter Space:NC, Nf , Representations of SU(NC)

Focus of this talk: SU(3) Nf = 2 Sextet(Two-index symmetric)Model

3 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Goal: Look for a Composite Higgs model:An infrared fixed point almost exists + Confining⇒ models at theedge of conformal windowAfter Higgs boson discovery : Light 0++ Higgs + reproducedetected phenomenologyParameter Space:NC, Nf , Representations of SU(NC)

Focus of this talk: SU(3) Nf = 2 Sextet(Two-index symmetric)Model

3 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelSU(3) gauge theory with Nf = 2 fermions in Two-index symmetricrepresentation: (a,b = 0,1,2)

ψLab = ψ

Lba ≡

uLab

dLab

, ψRab = ψ

Rba ≡

(uR

ab dRab)

Flavor symmetry:SU(2)L×SU(2)R×U(1)“Minimal” Composite Higgs Theory:SU(2)L×SU(2)R → SU(2)V ⇒ SU(2)W ×U(1)Y → U(1)em

*taken and modified from a post by FLIP TANEDO in Quantum Diaries http://www.quantumdiaries.org/2012/02/14/why-do-we-expect-a-higgs-boson-part-ii-unitarization-of-vector-boson-scattering/

U(1) remains unbroken⇒ Baryon number conservation

4 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelSU(3) gauge theory with Nf = 2 fermions in Two-index symmetricrepresentation: (a,b = 0,1,2)

ψLab = ψ

Lba ≡

uLab

dLab

, ψRab = ψ

Rba ≡

(uR

ab dRab)

Flavor symmetry:SU(2)L×SU(2)R×U(1)“Minimal” Composite Higgs Theory:SU(2)L×SU(2)R → SU(2)V ⇒ SU(2)W ×U(1)Y → U(1)em

*taken and modified from a post by FLIP TANEDO in Quantum Diaries http://www.quantumdiaries.org/2012/02/14/why-do-we-expect-a-higgs-boson-part-ii-unitarization-of-vector-boson-scattering/

U(1) remains unbroken⇒ Baryon number conservation

4 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelSU(3) gauge theory with Nf = 2 fermions in Two-index symmetricrepresentation: (a,b = 0,1,2)

ψLab = ψ

Lba ≡

uLab

dLab

, ψRab = ψ

Rba ≡

(uR

ab dRab)

Flavor symmetry:SU(2)L×SU(2)R×U(1)“Minimal” Composite Higgs Theory:SU(2)L×SU(2)R → SU(2)V ⇒ SU(2)W ×U(1)Y → U(1)em

*taken and modified from a post by FLIP TANEDO in Quantum Diaries http://www.quantumdiaries.org/2012/02/14/why-do-we-expect-a-higgs-boson-part-ii-unitarization-of-vector-boson-scattering/

U(1) remains unbroken⇒ Baryon number conservation

4 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelSU(3) gauge theory with Nf = 2 fermions in Two-index symmetricrepresentation: (a,b = 0,1,2)

ψLab = ψ

Lba ≡

uLab

dLab

, ψRab = ψ

Rba ≡

(uR

ab dRab)

Flavor symmetry:SU(2)L×SU(2)R×U(1)“Minimal” Composite Higgs Theory:SU(2)L×SU(2)R → SU(2)V ⇒ SU(2)W ×U(1)Y → U(1)em

*taken and modified from a post by FLIP TANEDO in Quantum Diaries http://www.quantumdiaries.org/2012/02/14/why-do-we-expect-a-higgs-boson-part-ii-unitarization-of-vector-boson-scattering/

U(1) remains unbroken⇒ Baryon number conservation

4 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Review:Sextet Model as Composite Higgs candidate

Review:Sextet Model as Composite Higgs candidate

Sextet ModelIntrinsically close to Conformal Windowβ function investigation is ongoing (Fodor et al, PoS (LATTICE 2014) 419)

Consistent evidence of χSBChiral Condensate: non-zero (Fodor et al, PoS (LATTICE 2013) 089)

Potential: Confining(Fodor et al, PoS (Lattice 2012) 025)

Hadron Spectrum: consistent with χSB (Fodor et al, Phys.Lett B 718, p. 657-666 )

Meson Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 419 )

f0 seems to be light⇒ Composite Higgs ImpostorMasses of a0, a1 and ρ’s are within LHC reach

Baryon Spectroscopy: (Fodor et al, PoS (LATTICE 2014) 281 )

What are the predictions from the Baryon Spectrum?Can the Sextet Baryons serve as Dark Matter candidates?

5 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Color structureIn fundamental representation (QCD), the baryon color singlet isgiven by three fermions:

3⊗3⊗3 = 1⊕2×8⊕10,

where ψa transforms as ψa′ → Ua′a ψa, and the constructed colorsinglet is Anti-symmetric:

εabc ψa ψb ψc

In the sextet representation, a color singlet can also be obtained bythree fermions:

6⊗6⊗6 = 1⊕2×8⊕10⊕10⊕3×27⊕28⊕2×35,

where ψab transforms as ψa′b′ → Ua′a ψab UTbb′ , and the constructed

color singlet is Symmetric, in sharp contrast with QCD:

εabc εa′b′c′ ψaa′ ψbb′ ψcc′ ≡ TABCΨAΨBΨC,

where A,B,C = 0,1,2,3,4,5

6 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Color structureIn fundamental representation (QCD), the baryon color singlet isgiven by three fermions:

3⊗3⊗3 = 1⊕2×8⊕10,

where ψa transforms as ψa′ → Ua′a ψa, and the constructed colorsinglet is Anti-symmetric:

εabc ψa ψb ψc

In the sextet representation, a color singlet can also be obtained bythree fermions:

6⊗6⊗6 = 1⊕2×8⊕10⊕10⊕3×27⊕28⊕2×35,

where ψab transforms as ψa′b′ → Ua′a ψab UTbb′ , and the constructed

color singlet is Symmetric, in sharp contrast with QCD:

εabc εa′b′c′ ψaa′ ψbb′ ψcc′ ≡ TABCΨAΨBΨC,

where A,B,C = 0,1,2,3,4,5

6 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Color structureIn fundamental representation (QCD), the baryon color singlet isgiven by three fermions:

3⊗3⊗3 = 1⊕2×8⊕10,

where ψa transforms as ψa′ → Ua′a ψa, and the constructed colorsinglet is Anti-symmetric:

εabc ψa ψb ψc

In the sextet representation, a color singlet can also be obtained bythree fermions:

6⊗6⊗6 = 1⊕2×8⊕10⊕10⊕3×27⊕28⊕2×35,

where ψab transforms as ψa′b′ → Ua′a ψab UTbb′ , and the constructed

color singlet is Symmetric, in sharp contrast with QCD:

εabc εa′b′c′ ψaa′ ψbb′ ψcc′ ≡ TABCΨAΨBΨC,

where A,B,C = 0,1,2,3,4,5

6 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Spin-Flavor structureSymmetric Color Structure⇒ Anti-symmetric Spin-Flavor StructureIn non-relativistic limit, a spin-up Sextet Nucleon is given byanti-symmetrizing | ↑ u ↑ d ↓ u 〉:

| ↑ N〉= | ↑ u ↑ d ↓ u 〉+ | ↓ u ↑ u ↑ d 〉+ | ↑ d ↓ u ↑ u 〉− | ↓ u ↑ d ↑ u 〉− | ↑ d ↑ u ↓ u 〉− | ↑ u ↓ d ↑ d 〉

The lattice operators that respect the Spin-flavor structure belong to asuitable multiplet of taste SU(4)(H. Kluberg-Stern et al, Nucl. Phys. B 220, 447 (1983), M. F. L. Golterman et al, Nucl. Phys. B 255, 328 (1985))

The lattice Sextet Nucleon operator that respect the overallstructure, in Dirac basis, takes the form

Nαi(2y) = TABC uαiA (2y)

[uβ j

B (2y) (Cγ5)βγ (C∗γ∗5 )ij dγj

C (2y)],

C : charge conjugation matrix, y : elementary staggered hypercubes

7 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Spin-Flavor structureSymmetric Color Structure⇒ Anti-symmetric Spin-Flavor StructureIn non-relativistic limit, a spin-up Sextet Nucleon is given byanti-symmetrizing | ↑ u ↑ d ↓ u 〉:

| ↑ N〉= | ↑ u ↑ d ↓ u 〉+ | ↓ u ↑ u ↑ d 〉+ | ↑ d ↓ u ↑ u 〉− | ↓ u ↑ d ↑ u 〉− | ↑ d ↑ u ↓ u 〉− | ↑ u ↓ d ↑ d 〉

The lattice operators that respect the Spin-flavor structure belong to asuitable multiplet of taste SU(4)(H. Kluberg-Stern et al, Nucl. Phys. B 220, 447 (1983), M. F. L. Golterman et al, Nucl. Phys. B 255, 328 (1985))

The lattice Sextet Nucleon operator that respect the overallstructure, in Dirac basis, takes the form

Nαi(2y) = TABC uαiA (2y)

[uβ j

B (2y) (Cγ5)βγ (C∗γ∗5 )ij dγj

C (2y)],

C : charge conjugation matrix, y : elementary staggered hypercubes

7 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Spin-Flavor structureSymmetric Color Structure⇒ Anti-symmetric Spin-Flavor StructureIn non-relativistic limit, a spin-up Sextet Nucleon is given byanti-symmetrizing | ↑ u ↑ d ↓ u 〉:

| ↑ N〉= | ↑ u ↑ d ↓ u 〉+ | ↓ u ↑ u ↑ d 〉+ | ↑ d ↓ u ↑ u 〉− | ↓ u ↑ d ↑ u 〉− | ↑ d ↑ u ↓ u 〉− | ↑ u ↓ d ↑ d 〉

The lattice operators that respect the Spin-flavor structure belong to asuitable multiplet of taste SU(4)(H. Kluberg-Stern et al, Nucl. Phys. B 220, 447 (1983), M. F. L. Golterman et al, Nucl. Phys. B 255, 328 (1985))

The lattice Sextet Nucleon operator that respect the overallstructure, in Dirac basis, takes the form

Nαi(2y) = TABC uαiA (2y)

[uβ j

B (2y) (Cγ5)βγ (C∗γ∗5 )ij dγj

C (2y)],

C : charge conjugation matrix, y : elementary staggered hypercubes

7 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Spin-Flavor structureSymmetric Color Structure⇒ Anti-symmetric Spin-Flavor StructureIn non-relativistic limit, a spin-up Sextet Nucleon is given byanti-symmetrizing | ↑ u ↑ d ↓ u 〉:

| ↑ N〉= | ↑ u ↑ d ↓ u 〉+ | ↓ u ↑ u ↑ d 〉+ | ↑ d ↓ u ↑ u 〉− | ↓ u ↑ d ↑ u 〉− | ↑ d ↑ u ↓ u 〉− | ↑ u ↓ d ↑ d 〉

The lattice operators that respect the Spin-flavor structure belong to asuitable multiplet of taste SU(4)(H. Kluberg-Stern et al, Nucl. Phys. B 220, 447 (1983), M. F. L. Golterman et al, Nucl. Phys. B 255, 328 (1985))

The lattice Sextet Nucleon operator that respect the overallstructure, in Dirac basis, takes the form

Nαi(2y) = TABC uαiA (2y)

[uβ j

B (2y) (Cγ5)βγ (C∗γ∗5 )ij dγj

C (2y)],

C : charge conjugation matrix, y : elementary staggered hypercubes

7 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Spin-Flavor structureSymmetric Color Structure⇒ Anti-symmetric Spin-Flavor StructureIn non-relativistic limit, a spin-up Sextet Nucleon is given byanti-symmetrizing | ↑ u ↑ d ↓ u 〉:

| ↑ N〉= | ↑ u ↑ d ↓ u 〉+ | ↓ u ↑ u ↑ d 〉+ | ↑ d ↓ u ↑ u 〉− | ↓ u ↑ d ↑ u 〉− | ↑ d ↑ u ↓ u 〉− | ↑ u ↓ d ↑ d 〉

The lattice operators that respect the Spin-flavor structure belong to asuitable multiplet of taste SU(4)(H. Kluberg-Stern et al, Nucl. Phys. B 220, 447 (1983), M. F. L. Golterman et al, Nucl. Phys. B 255, 328 (1985))

The lattice Sextet Nucleon operator that respect the overallstructure, in Dirac basis, takes the form

Nαi(2y) = TABC uαiA (2y)

[uβ j

B (2y) (Cγ5)βγ (C∗γ∗5 )ij dγj

C (2y)],

C : charge conjugation matrix, y : elementary staggered hypercubes

7 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Substituting qαi(2y) = 18 ∑η Γαi

η χq(2y+η) and combiningparity-opposite channels for locality in time:

Nαi(2y) =− 183 TABC ∑

~η ′Γ

αi~η ′ χ

Au (2y+~η ′)

·∑~η

S(~η) χBu (2y+~η) χ

Cd (2y+~η),

where Γ = γη11 γ

η22 γ

η33 γ

η44 and S(η) =±1

Local terms vanish due to symmetric color structureSurviving terms have the u quark and the diquark at diagonallyopposite corners, e.g.:

Set a:

Set b:

IVxy IVyz IVzx VIII

: χu : χd

8 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Substituting qαi(2y) = 18 ∑η Γαi

η χq(2y+η) and combiningparity-opposite channels for locality in time:

Nαi(2y) =− 183 TABC ∑

~η ′Γ

αi~η ′ χ

Au (2y+~η ′)

·∑~η

S(~η) χBu (2y+~η) χ

Cd (2y+~η),

where Γ = γη11 γ

η22 γ

η33 γ

η44 and S(η) =±1

Local terms vanish due to symmetric color structureSurviving terms have the u quark and the diquark at diagonallyopposite corners, e.g.:

Set a:

Set b:

IVxy IVyz IVzx VIII

: χu : χd

8 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy - Operator ConstructionBaryon Spectroscopy - Operator Construction

Substituting qαi(2y) = 18 ∑η Γαi

η χq(2y+η) and combiningparity-opposite channels for locality in time:

Nαi(2y) =− 183 TABC ∑

~η ′Γ

αi~η ′ χ

Au (2y+~η ′)

·∑~η

S(~η) χBu (2y+~η) χ

Cd (2y+~η),

where Γ = γη11 γ

η22 γ

η33 γ

η44 and S(η) =±1

Local terms vanish due to symmetric color structureSurviving terms have the u quark and the diquark at diagonallyopposite corners, e.g.:

Set a:

Set b:

IVxy IVyz IVzx VIII

: χu : χd

8 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Action: Tree-level Symanzik-Improved gauge action withStaggered Nf = 2 Sextet SU(3) fermionsRHMC algorithm with multiple time scales and Omelyan integratorLattices used: ( ∼ 1000−1500 Trajectories each)

β ≡ 6/g2 L T mq

3.20 48 96 0.00332 64 0.004, 0.005, 0.006, 0.007, 0.008

Comparison of operators:(V = 323×64, mq = 0.007, 1000 trajectories, tmax = 20)

12 13 14 15 16tmin

0.5

0.55

0.6

0.65

MN

VIIIIV

xy

IVyz

IVzx

Set a

12 13 14 15 16tmin

0.5

0.55

0.6

0.65

MN

VIIIIV

xy

IVyz

IVzx

Set b

9 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Action: Tree-level Symanzik-Improved gauge action withStaggered Nf = 2 Sextet SU(3) fermionsRHMC algorithm with multiple time scales and Omelyan integratorLattices used: ( ∼ 1000−1500 Trajectories each)

β ≡ 6/g2 L T mq

3.20 48 96 0.00332 64 0.004, 0.005, 0.006, 0.007, 0.008

Comparison of operators:(V = 323×64, mq = 0.007, 1000 trajectories, tmax = 20)

12 13 14 15 16tmin

0.5

0.55

0.6

0.65

MN

VIIIIV

xy

IVyz

IVzx

Set a

12 13 14 15 16tmin

0.5

0.55

0.6

0.65

MN

VIIIIV

xy

IVyz

IVzx

Set b

9 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Action: Tree-level Symanzik-Improved gauge action withStaggered Nf = 2 Sextet SU(3) fermionsRHMC algorithm with multiple time scales and Omelyan integratorLattices used: ( ∼ 1000−1500 Trajectories each)

β ≡ 6/g2 L T mq

3.20 48 96 0.00332 64 0.004, 0.005, 0.006, 0.007, 0.008

Comparison of operators:(V = 323×64, mq = 0.007, 1000 trajectories, tmax = 20)

12 13 14 15 16tmin

0.5

0.55

0.6

0.65

MN

VIIIIV

xy

IVyz

IVzx

Set a

12 13 14 15 16tmin

0.5

0.55

0.6

0.65

MN

VIIIIV

xy

IVyz

IVzx

Set b

9 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Action: Tree-level Symanzik-Improved gauge action withStaggered Nf = 2 Sextet SU(3) fermionsRHMC algorithm with multiple time scales and Omelyan integratorLattices used: ( ∼ 1000−1500 Trajectories each)

β ≡ 6/g2 L T mq

3.20 48 96 0.00332 64 0.004, 0.005, 0.006, 0.007, 0.008

Comparison of operators:(V = 323×64, mq = 0.007, 1000 trajectories, tmax = 20)

12 13 14 15 16tmin

0.5

0.55

0.6

0.65

MN

VIIIIV

xy

IVyz

IVzx

Set a

12 13 14 15 16tmin

0.5

0.55

0.6

0.65

MN

VIIIIV

xy

IVyz

IVzx

Set b

9 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Operator IVxy in set a is chosenChiral extrapolation at β = 3.20

0 0.002 0.004 0.006 0.008m

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

F

Fπ=F + p

F m

F=0.02422(45)

pF=4.07(10)

Χ2/dof=1.28

0 0.002 0.004 0.006 0.008m

0

0.1

0.2

0.3

0.4

0.5

0.6

MN

MN

=c0 + c

1 m

c0=0.332(13)

c1=38.8(2.1)

Χ2/dof=0.506

10 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Operator IVxy in set a is chosenChiral extrapolation at β = 3.20

0 0.002 0.004 0.006 0.008m

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

F

Fπ=F + p

F m

F=0.02422(45)

pF=4.07(10)

Χ2/dof=1.28

0 0.002 0.004 0.006 0.008m

0

0.1

0.2

0.3

0.4

0.5

0.6

MN

MN

=c0 + c

1 m

c0=0.332(13)

c1=38.8(2.1)

Χ2/dof=0.506

10 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Chiral extrapolation at β = 3.20

0 0.002 0.004 0.006 0.008m

0

0.1

0.2

0.3

0.4

0.5

0.6M

MN

Ma

1

Mρ

Mπ

3.2

β

0

2

4

6

8

10

12

14

16

18

20

22

M /

F

0

0.49

0.98

1.5

2

2.5

3

3.4

3.9

4.4

4.9

5.4

M /

TeV

MN

Ma

1

Mρ

11 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

β = 3.25 is being investigatedPreliminary results:(with ∼ 250 trajectories of V = 483×96 at m = 0.002,0.003)

0 0.002 0.004 0.006 0.008m

0

0.1

0.2

0.3

0.4

0.5

0.6

MN

MN

=c0 + c

1 m

c0=0.2471(33)

c1=33.23(65)

Χ2/dof=1.92

12 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Baryon Spectroscopy -Preliminary Lattice Simulation Results

Baryon Spectroscopy -Preliminary Lattice Simulation Results

β = 3.25 is being investigatedPreliminary results:(with ∼ 250 trajectories of V = 483×96 at m = 0.002,0.003)

0 0.002 0.004 0.006 0.008m

0

0.1

0.2

0.3

0.4

0.5

0.6

MN

MN

=c0 + c

1 m

c0=0.2471(33)

c1=33.23(65)

Χ2/dof=1.92

12 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?

Lightest Sextet Baryon as we know so far:Mass could be in the range of 3 TeVStable

If the Sextet model is a viable composite Higgs candidate,Can the Sextet Baryons be Dark Matter candidates?

if Yes→ Can any predictions be made?if No→ Look for variants and extensions (or find a better model)

Embedding Electroweak interaction:ABJ Anomaly Free⇒ Tr Y = Tr Y3 = 0Hypercharge generator: Y ≡ 2(Q−T3)⇒ QuL = QuR = 1

2 , QdL = QdR =− 12 is a consistent choice

⇒ YuL = YdL = 0, YuR = 1, YdR =−1The Lightest Sextet Baryons : Sextet Nucleons (uud and udd)Quud = 1

2 , Qudd =− 12 as Dark Matters

⇒ Fractionally CHArged Massive Particle (FCHAMP) Category*Background picture taken and modified fromhttp://www.cita.utoronto.ca/ dubinski/iya2009/gallery/images/Simulation_dubinski_cosmoslice_blue.jpg

13 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

Dark Matter Candidates?Dark Matter Candidates?Sakharov’s Conditions for Baryogenesis: (J. M. Cline, hep-ph/0609145)

B-violation: Possible by non-Abelian non-perturbative anomaliesLoss of Thermal Equilibrium

Sextet baryons and antibaryons are produced in the Electroweak phasetransition (expected to be of second order with two fermion flavors inthe chiral limit)Charge symmetric sextet baryon and sextet antibaryon densities inthermal equilibrium will continue to decrease well below the criticaltemperature Tc until at freeze-out temperature T∗Expansion rate sets the density to its relic abundance level from thesolution of the Boltzmann equationT∗ and the related relic abundance level are very sensitive to theannihilation rate of Sextet Baryons and Sextet AntibaryonsExperimental Constraints & Theoretical Requiem prefer tiny FCHAMPrelic abundance (P. Langacker and G. Steigman, Phys. Rev. D 84, 065040 (2011)

Boltzmann suppression from ∝ e−MB/T∗ is expectedC, CP violation: Undetermined

The lightest Baryons of the “Minimal” Sextet model cannot beDark Matter candidates⇒ Possible extensions:

New Lepton doublets and singlets: φ L ≡

νL

eL

, φ R ≡(νR eR)

QCD-like Q assignment⇒ Lightest Sextet Baryon expected to be neutralThird fermion flavor which is massive and electroweak singlet 14 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

ConclusionConclusionBaryon Spectroscopy is studied in the Sextet model, a compositeHiggs candidate modelSextet baryon operators are constructed differently from QCD dueto the symmetric color structurePreliminary Lattice results are shown

Mass of the lightest Sextet Baryon: ∼ 3 TeVMore comprehensive studies on extended dataset are undergoing

The Possibility of Sextet Baryons being Dark Matter candidates isexplored

*taken from http://cdn.thewestsidestory.net/wp-content/uploads/2014/12/Scientists-detect-possible-pragmatic-existence-of-dark-matter.jpg

15 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

ConclusionConclusionBaryon Spectroscopy is studied in the Sextet model, a compositeHiggs candidate modelSextet baryon operators are constructed differently from QCD dueto the symmetric color structurePreliminary Lattice results are shown

Mass of the lightest Sextet Baryon: ∼ 3 TeVMore comprehensive studies on extended dataset are undergoing

The Possibility of Sextet Baryons being Dark Matter candidates isexplored

*taken from http://cdn.thewestsidestory.net/wp-content/uploads/2014/12/Scientists-detect-possible-pragmatic-existence-of-dark-matter.jpg

15 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

ConclusionConclusionBaryon Spectroscopy is studied in the Sextet model, a compositeHiggs candidate modelSextet baryon operators are constructed differently from QCD dueto the symmetric color structurePreliminary Lattice results are shown

Mass of the lightest Sextet Baryon: ∼ 3 TeVMore comprehensive studies on extended dataset are undergoing

The Possibility of Sextet Baryons being Dark Matter candidates isexplored

*taken from http://cdn.thewestsidestory.net/wp-content/uploads/2014/12/Scientists-detect-possible-pragmatic-existence-of-dark-matter.jpg

15 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

ConclusionConclusionBaryon Spectroscopy is studied in the Sextet model, a compositeHiggs candidate modelSextet baryon operators are constructed differently from QCD dueto the symmetric color structurePreliminary Lattice results are shown

Mass of the lightest Sextet Baryon: ∼ 3 TeVMore comprehensive studies on extended dataset are undergoing

The Possibility of Sextet Baryons being Dark Matter candidates isexplored

*taken from http://cdn.thewestsidestory.net/wp-content/uploads/2014/12/Scientists-detect-possible-pragmatic-existence-of-dark-matter.jpg

15 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

ConclusionConclusionBaryon Spectroscopy is studied in the Sextet model, a compositeHiggs candidate modelSextet baryon operators are constructed differently from QCD dueto the symmetric color structurePreliminary Lattice results are shown

Mass of the lightest Sextet Baryon: ∼ 3 TeVMore comprehensive studies on extended dataset are undergoing

The Possibility of Sextet Baryons being Dark Matter candidates isexplored

*taken from http://cdn.thewestsidestory.net/wp-content/uploads/2014/12/Scientists-detect-possible-pragmatic-existence-of-dark-matter.jpg

15 / 15

BaryonSpectroscopyin the SextetGauge Model

Chik Him (Ricky)Wong

Outline

Review

BaryonSpectroscopy

Operator Construction

Simulation Results

Dark Mattercandidates?

Conclusion

ConclusionConclusionBaryon Spectroscopy is studied in the Sextet model, a compositeHiggs candidate modelSextet baryon operators are constructed differently from QCD dueto the symmetric color structurePreliminary Lattice results are shown

Mass of the lightest Sextet Baryon: ∼ 3 TeVMore comprehensive studies on extended dataset are undergoing

The Possibility of Sextet Baryons being Dark Matter candidates isexplored

*taken from http://cdn.thewestsidestory.net/wp-content/uploads/2014/12/Scientists-detect-possible-pragmatic-existence-of-dark-matter.jpg

15 / 15