LHC Phenomenology andLattice Strong Dynamics

KMI Inauguration ConferenceNagoya, Japan

25 October 2011

George T. Fleming(Yale U.)

What is Technicolor?

• http://en.wikipedia.org/wiki/Technicolor_(physics)

• Gedanken world: If EW symmetry SU(2)L×U(1)Y were unbroken at GeV energies, QCD would break it via strongly-coupled Higgs mechanism.

• Pions eaten to give mass to W and Z bosons of O(30 MeV).

• No Yukawa mechanism, so no fermion masses, plus much stronger EW couplings: many new phenomena. [Quigg-Shrock 2009]

• Basic Idea: Break EW symmetry at TeV scales by adding new fermions (Q̅,Q) with new strong interactions. [Weinberg, Susskind 1979]

• SM fermion mass: New gauge interactions broken at high scale ΛETC couple SM fermions to techniquarks. [Dimopoulis-Susskind, Eichten-Lane 1979]

Masses:(QQ)(qq)

Λ2ETC

FCNC’s:(qq)(qq)Λ2

ETC

ΛETC � 1000 TeV

Why did Technicolor fall out of favor?

• QCD-like strong interactions at the TeV scale can drive the Higgs mechanism, but face phenomenological challenges:

• Either flavor changing neutral currents (FCNC) are too large or generated SM fermion masses are too small.

• Precision EW oblique corrections (S parameter) in tension with experiment.

• A resolution: TeV strong interactions are not like QCD.

• A problem: How well do we really understand generic strongly interacting theories other than QCD?

• A solution: Lattice field theory is only now powerful enough to begin the study of strongly-coupled theories beyond QCD.

Where to look for non-QCD theories?

2 3 �0

11

16.5

�

Nc

Nf

QCD Large Nc

AF lost

Conformal (α*<1)

(Ethan Neil, Yale U.)

• Phenomenological success of large Nc calculations suggest QCD-like theories for Nf = 2–3 and Nc ≥ 3.

• Simplest search strategy: start from QCD and increase Nf.

• For Nf = 0–1, confinement but no NG bosons.

• For Nc = 2, enhanced chiral symmetry means special case: Pattern of symmetry breaking yet to be determined.

• Pert. theory indicates IRFP for Nf ≲ 5.5⋅Nc.

Can the running coupling be our guide?• In QCD, g(L) is asympotically free and runs

rapidly until SSB and confinement: g(Lc)=gc.

• As Nf increases, the running slows down.

• For large Nf, g(L) flows to g* at IR fixed point(IRFP). No SSB, no Technicolor.

• Walking theories may exist nearby theories with strongly-coupled IRFP: g* ≲ gc .

• Unlike QCD, walking theories would have two dynamically generated scales: LI and Lc, and in rare cases LI ≪ Lc.

• In Walking Technicolor, LI-1 = ΛETC ~ 1000 TeV and Lc-1 = ΛTC ~ 1 TeV.

• How does walking help Technicolor’s FCNC problem?

Current Status on Running Coupling

g2(Tc-1)

g2(r0)

L/a=24

Nf = 0

Nf = 2

Nf = 4

Nf = 6

Nf = 8

Nf = 10

Nf = 12

Nf = 20

(Ethan Neil, Yale U.)

5 10 15 20 25

0

2

4

6

8

10

12

14

Log�L�L0�

g2�L�

3�loop SF running coupling with Nf light fermions

Nf = 0

Nf = 2

Nf = 4

Nf = 6

Nf = 8

Nf = 10

Nf = 12

Nf = 20

5 10 15 20 250

2

4

6

8

10

12

14

Log�L�L0�

g2�L�

3�loop SF running coupling with Nf light fermionsNon-perturbative SF running coupling

L/a=32

PRD 83, 07

4509 (

2011)

NPB

840

,114

(20

10)

• Nf=10-12 still unclear. New work by E. Itou et al. arXiv:1109.5806 [hep-lat].

Walking Dynamics• The relevant scale for mass generation is ΛETC, so the relevant condensate is

renormalized at that scale: 〈Q ̅Q〉at ΛETC.

• The condensate is renormalized using the anomalous dimension γ(μ). In QCD-like theories, γ(μ) ≪ 1 for μ ≫ ΛTC. Leads to log(ΛETC / ΛTC) enhancement.

• Walking dynamics (γ∼1) leads to power-enhanced condensates.

�QQ

�ΛETC

=�QQ

�ΛTC

exp

�� ΛETC

ΛTC

γ(µ)µ

dµ

�

�QQ

�

F 3πT

∼ �qq�f3

π

�ΛETC

ΛTC

�γ

Masses:(QQ)(qq)

Λ2ETC

FCNC’s:(qq)(qq)Λ2

ETC

ΛETC � 1000 TeV

• Now, a hierarchy of SM fermion masses can be generated while suppressing FCNC.

Lattice Strong Dynamics (LSD) Collaboration

Tom AppelquistGeorge Fleming

Meifeng LinGennady Voronov

Joe Kiskis

Michael BuchoffJoe Wasem

Pavlos Vranas

Heechang NaJames OsbornRich BrowerMichael ChengClaudio RebbiOliver Witzel

Ron BabichMike Clark

David Schaich

Ethan Neil Saul CohenSergey Syritsyn

LSD Program Overview• SU(2) and SU(3) gauge theories with Nf domain wall

fundamental fermions.

• Initial focus on SU(3): code readiness and QCD experience.

• Preparing SU(2) code for production.

• Majority of flops so far spent on SU(3) with Nf=2,6,10.• Exploration of IR: QCD-like, conformal or “walking”.

• Phenomenology: S parameter, condensate enhancement/mass anomalous dimension, WW scattering, dark matter form factors.

• Published results: PRL 104, 071601 (2010); PRL 106, 231601(2011).

• Four new publications in draft.

LSD: Comparing Nf = 2 and Nf = 6

• Lattice scales chosen to match confinement scale physics to ~10%.

• Usual caveats (finite L, m, a) expected to get worse with increasing Nf.

• Why Nf = 6? It’s very unlikely to walk...

• On largest computers, calculations still limited to lattices where L / a ≤ 64.

• A walking theory should be studied on lattices where L / a ~ 256–1024.

• Can precursors to walking be seen in slowly running theories?

LSD: Condensate Enhancement• Tricky to compare scale dependent

quantities in two different theories.

• Definition of Enhancement:

• GMOR Ratios

• Chiral extrapolation

• Perturbative estimates of enhancement:

• Enhancement bigger than expected. Is this a precursor to walking?

R =

CF� �� ��ψψ

�

F 3π

=

CM� �� �M3

π�(2m)3

�ψψ

� =

FM� �� �M2

π

2mFπas m→ 0

R(5Mρ) ∼ 1.2–1.3 (lat scheme)

RXY, em =R(Nf )

R(2)[1 + �m (αXY 10 + α11 log �m)] , �m =

�m(Nf )m(2)

�ψψ

�(Nf )

�ψψ

�(2)

�����5Mρ

≡ R(5Mρ) ≈exp

�� α(Mρ)α(5Mρ)

γ(α)πβ(α)

���Nf

dα

�

exp�� α(Mρ)

α(5Mρ)γ(α)

πβ(α)

���Nf =2

dα

�

S Parameter for Scaled-Up QCD

• χPT for Polarization Tensor

• T=0 in lattice calculations due to isospin symmetry.

• Vertical bands based on JLQCD PRL 101, 242001; RBC-UKQCD PRD 81, 014504; LSD PRL 106, 231601.

LSD: Polarization Tensor for S Parameter• S for Nf / 2 EW doublets

• χPT for Polarization Tensor

• Pade(1,2) fit of ΠV-A(Q2) assumes Q-2 scaling as Q2→∞ [1st WSR].

• Slope shows decreasing trend with decreasing mass for Nf = 6.

• n.b. smaller S for fewer EW doublets.

S = 4πNf

2[Π�

VV(0)−Π�AA(0)] + ∆SSM

=13π

� ∞

0

ds

s

�Nf

2[RV (s)−RA(s)]

−14

�1−

�1− m2

h

s

�3

Θ(s−m2h)

��

D. Schaich & E. Neil

!

!

!

!

!

!

!

"!!"

!

!

!

!

!

!

!

"!!"

!"#$%&

!"#$'&

LSD: Flavor dependence of Π′V-A(0)

• χPT for Polarization Tensor

• Polarization tensor computed for one EW doublet.

• Filled symbols MP⋅L≥4.

• Plot vs. MP2 instead of m, in units of MV0.

• Π′∼log MP2 as MP2→0.

• Free field value for Π′=1/2π=0.159…

Nf=6

Nf=2

0.0 0.5 1.0 1.5 2.00.0

0.1

0.2

0.3

0.4

0.5

MP2�MV0

2

4Π�' V�A�0�

Flavor dependence of S Parameter• Very naïve scaling for S

• χPT for Polarization Tensor

S ∝ Nf

2Nc

3• Walking conjectured to

reduce S by parity doubling, e.g. single-pole dominance:

• After ΔSSM subtraction, S reduced relative to naïve scaling for Nf=6. Is it a precursor of walking behavior?

• n.b. S for Nf=6 still log divergent until spectrum of PNGB’s fixed.

Nf=6

Nf=2S ∼ 4π

�Nf

2

� �F 2

V

M2V

− F 2A

M2A

�0.0 0.5 1.0 1.5 2.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

MP2 �MV0

2

S�4Π�N f�2

��' V�A�0���

S SM

Updated!

naïve scaling?

Flavor dependence of parity partners

• χPT for Polarization Tensor

0.2

0.3

0.4

0.5

0.6

MV

, MA

Nf=2, Axial-VectorNf=6, Axial-VectorNf=2, VectorNf=6, Vector

0 0.5 1 1.5 2 2.5MP

2/MV2

11.21.41.61.8

MA

/ M

V

Nf=2Nf=6

0 0.5 1 1.5 2 2.5MP

2/MV2

0.030.040.050.060.07

F A

0.04

0.05

0.06

0.07

F V

Nf=2Nf=6

PRL 106, 231601 (2011)

• Note slope of MV vs. MP2 roughly independent of Nf, not true for MV vs. m.

Conclusions• For SU(3) running coupling studies for various Nf suggest a

walking theory may exist for 10 ≤ Nf ≤ 12 flavors.

• Direct study of walking theories beyond the current capabilities of largest computers, best algorithms, ...

• Searches for precursors of walking behavior as the running slows with increasing Nf support the vision that a walking theory can solve Technicolor’s phenomenological problems.

• For Nf = 6, non-perturbative condensates are enhanced and S parameter reduced relative to perturbative expectations.

• Technicolor remains a viable option for physics at the TeV scale.

• Last week: “Lattice Meets Experiment for BSM”, www.usqcd.org

Backup Slides

A Dozen Lattice BSM Efforts Worldwide

Del Debbio et al.

Catteral et al.

Hietanen et al.

LHC

Yamada et al.

Deuzeman et al.

Aoyama et al. DeGrand et al.

LSD

A. Hasenfratz

Jin-Mawhinney

Kogut-Sinclair

How can the lattice address Technicolor?

• Technicolor scenario has Higgs mechanism driven by TeV-scale strong interactions with spontaneous symmetry breaking (SSB)and Nambu-Goldstone (NG) bosons.

• QCD has these features and been studied on the lattice for decades, recently with much success.

• Other strongly-coupled gauge theories likely have these features, i.e. other flavors (Nf), colors (Nc), etc.

• Lattice studies can search for the right combination that enables Technicolor to satisfy phenomenological constraints.

• Unfortunately, other theories are usually computationally more expensive than QCD for calculation: ∝ N3/2

f , N3c , d(R)3

Technicolor on the Lattice (II)

• Tools developed for study of Lattice QCD:

• Non-perturbative Running Coupling

• Non-perturbative Renormalization of Operators

• Light Hadron and Glueball Spectrum

• Chiral Observables (condensate, Dirac eigenvalues)

• Thermodynamic Observables (Tc , EoS)

• Are tools optimized for QCD useful for non-QCD studies?

• Exception: Monte Carlo methods using Wilsonian RG?

• Can finite-size scaling methods be adapted from stat. mech.?

Flavor dependence of NLO ChiPT

• The leading non-analytic terms are enhanced in the condensate and fπ but suppressed in (Mπ)2.

• The αi∼O(1) low energy constants.

• η2∼O(a-2) contact term: UV-sensitive slope for condensate.

M2π = 2mB

�1 +

2mB

(4πF )2

�2α8 − α5 + Nf (2α6 − α4) +

1Nf

log2mB

(4πF )2

��

Fπ = F

�1 +

2mB

(4πF )2

�12

(α5 + Nfα4)−Nf

2log

2mB

(4πF )2

��

�qq� = F 2B

�1 +

2mB

(4πF )2

�12

(2α8 + η2) + 2Nfα6 −N2

f − 1Nf

log2mB

(4πF )2

��

Non-analytic flavor factors in NNLO ChiPT

• J. Bijnens and J. Lu, JHEP11(2009)116 [arXiv:0910.5424]

• Small NLO coeff for Mπ2 is not generic and doesn’t persist to higher orders.

• Can NNLO formulae help us extrapolate Nf ≫ 2 results?

m log(m) m2 log2(m)

Mπ2

Fπ

〈qq〉

Nf-1 -3/8 Nf2 + 1/2 - 9/2 Nf-2

-1/2 Nf 3/16 Nf2 + 1/2

-Nf + Nf-1 3/2 - 3/2 Nf-2

Preliminary: Basic Chiral Observables

• NNLO ChiPT fits work fine for Nf=2.

• NNLO expression for general Nf recently derived by Bijnens and Lu [JHEP11(2009)116].

Preliminary: χPT Radius of Convergence

• Smaller quark masses needed for reliable NNLO extrapolation for Nf>2 [E.T. Neil et al., PoS(CD09)088].

• On 323×64, m≅0.01: Mπ⋅L~4 and Fπ⋅L~1. 483×64 lattices needed to reach smaller quark masses.

0.000 0.002 0.004 0.006 0.008 0.010 0.012�1.0

�0.5

0.0

0.5

1.0

m

FmNLO,NNLO

FmLO

Nf=6 NLO, NNLO

Nf=2 NLO, NNLO