the standard model and scale symmetrytheo.phys.sci.hiroshima-u.ac.jp/~soken/schedule/...the standard...
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William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 1!
The Standard Model and Scale Symmetry
William A. Bardeen Fermilab!
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 2!
The Standard Model • The Standard Model of Particle Physics is remarkable!
• Forces – nonablelian gauge dynamics: SU(3)Cx(SU(2)xU(1))EW
• Matter - fermions in chiral representations
• Role of the Higgs field and EWSB:
€
H =V10⎛
⎝ ⎜ ⎞
⎠ ⎟
• Higgs Kinetic -> W and Z masses
• Higgs Yukawa -> fermion masses and mixing
• No explicit mass terms for forces and matter fields
• All coupling constants are dimensionless
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 3!
The Standard Model
• Classically Conformal - except for the Higgs mass term, the cosmological constant (and possibly neutrino masses)
€
• Higgs Potential : V = λ H+H( )2
• λ > 0, only symmetric vacuum state, H = 0 - , conformal phase, all particles massless
• λ -> λc = 0, critical point, flat potential - dynamical symmetry breaking with <H> = v - all Standard Model particles are massive: top, W, Z, etc - Higgs particle remains massless, the Goldstone mode of the dynamically broken scale symmetry
• W. Bardeen, On Naturalness in the Standard Model 1995 Ontake Summer Institute, FERMILAB-CONF-95-391-T (1995)
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 4!
The Standard Model • Explicit symmetry breaking and the Higgs particle mass
• Classical Higgs Potential
€
V = λ H+H - v2( )2, v ≈ 173 GeV
mh2 = 4λv2, mh = 126 GeV ⇒ λ ~ 1
8, small
• Higgs particle can be viewed as a pseudo-Goldstone boson of the dynamical breaking of an approximate scale symmetry
• analogue to magnetic field used to align magnet
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 5!
The Standard Model
• Quantum Corrections – infrared divergences from matter loops
• Coleman-Weinberg - one loop effective potential - S. Coleman and E. Weinberg, Phys.Rev. D7, 1888(1973)
€
ΔV =14
A4π( )2 H+H( )2
ln H+Hev2
⎛
⎝ ⎜
⎞
⎠ ⎟ ,
A =mv
⎛
⎝ ⎜
⎞
⎠ ⎟ b
4
−mv
⎛
⎝ ⎜
⎞
⎠ ⎟ f
4⎡
⎣ ⎢
⎤
⎦ ⎥
dof∑ = 6 m
v⎛
⎝ ⎜
⎞
⎠ ⎟ W
4
+ 3 mv
⎛
⎝ ⎜
⎞
⎠ ⎟ Z
4
−12 mv
⎛
⎝ ⎜
⎞
⎠ ⎟ top
4
+ ...
H+H( )2ln H+H
ev2
⎛
⎝ ⎜
⎞
⎠ ⎟ → H+H - v2( )2
+C, H →v
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 6!
The Standard Model
• Known quantum corrections (W, Z, top): A ~ -11.5
• Wrong sign, gives small correction to classical term, -13%
• No classical term would require, A ~ +80
€
mh2 /4v2 = λ0 +
14
A4π( )2
~ 18
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 7!
UV Behavior of the Standard Model
• Running couplings at high energies remains perturbative
• SM Higgs coupling appears to be metastable
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 8!
UV Behavior of the Standard Model
• No evidence for higher dimension operators, S-T plot
• Curious behavior of SM beta functions – opposite expectations – compensated running, λHiggs, ytop, g2
color – UV or IR?
• Possible significance of UV boundary conditions: λ -> 0, βλ -> 0 - fixed point gravity, asymptotic safety - Shaposhnikov and Wetterich (2010); Holthausen, Lim and Lindner (2011)
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 9!
IR Behavior of the Standard Model
• IR Running of SM Couplings
0.000
0.500
1.000
1.500
2.000
2.500
0.00 50.00 100.00 150.00 200.00
lambda
ytop
alpha3
• little evidence for nonperturbative effects before QCD scale
• QCD provides mechanism for EWSB – too small for physics
• Possible nonperturbative SM effects – pert. Th us asymptotic
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 10!
CW Symmetry Breaking
• require new physics to trigger EWSB via CW mechanism
• physical Higgs mass requires ACW(new physics) ~ 91.5
• new heavy bosons that get their mass from the Higgs VeV - singlet scalars, Higgs partners, etc -Silveira&Zee(1985); Patt&Wilczek(2006); Hambye&Tytgat(2007)
• Higgs portal coupling:
€
L =12G2ϕ2H+H, mϕ ~ GV Anew ~ 91.5 →G ~ 3
• all masses from dimensional transmutation from running couplings
• natural dark matter, accidental parity symmetry in 4d
• produced via Higgs portal: h -> ϕϕ, possible couplings to νR
• constrained by missing energy search, possible UV Landau poles
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 11!
Darkside CW Mechanisms
• Negative SM Higgs mass term can be generated through a Higgs portal to IR symmetry breaking on the darkside
• requires dark Higgs and negative portal coupling
€
Vhiggs portal = −κφ +φH+H, µH2 = −κVφ
2 ~ − 90GeV( )2
• physical states will be mixtures of the dark and SM Higgs bosons - for small κ (large Vϕ), the mixings are suppressed - production and decay through this mixing
• Dark Higgs scalar potential may be generated in infrared
• many possibilities discussed in recent literature
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 12!
Darkside CW Mechanisms – B-L Model • Gauged B-L Model
- Iso, Okada, Orikasa, Hashimoto, Aoki (2009-2013) - Chun, Jung, Lee, Barenboim (2013) - Baek, Ko, Park (2013)
• Ingredients - U(1) gauge boson coupled to B-L current - dark Higgs scalar, charged under B-L symmetry - Majorana couplings to νR - portal coupling between dark and visible Higgs
• CW instability generates dark side symmetry breaking - massive gauge boson, Z’B-L, mZ’ ~ few to many TeV - triggers visible side symmetry breaking through portal - νR masses, mixings (possible dark matter candidates) - mixing between dark and visible Higgs states - leptogensis
• UV Evolution -dynamical generation of IR Higgs couplings
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 13!
Darkside CW Mechanisms – Dark SU(2) Model
• Gauged SU(2)D Model - Hambye & Strumia, arXiv:1306.2329 [hep-ph] 10 Jun 2013
• Ingredients - dark SU(2) gauge boson - dark Higgs doublet - portal coupling between dark and visible Higgs - vector dark matter candidate
• CW instability generates dark side symmetry breaking - massive gauge boson multiplet - triggers visible side symmetry breaking through portal
• Dark Matter constraints
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 14!
Darkside CW Mechanisms – Dark SU(2) Model
• Smooth UV Evolution of all coupling constants (Hambye et al)
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 15!
Darkside CW Mechanisms – Dark SU(2)xU(1) Model
• Gauged (SU(2)xU(1))D Model - Altmannhofer, Bardeen, Bauer, Carena, Lykken, in preparation - Davoudiasl, Lewis (2013)
• Ingredients - dark SU(2)xU(1) gauge bosons - dark Higgs doublet - two generations of chiral fermions - portal coupling between dark and visible Higgs - fermionic dark matter
• Dark Matter constraints
• Full Higgs potential generated by running below Planck scale - at MPl, λi ->0, βλ ->0
• Higgs boson mixing important for IR boundary conditions
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 16!
Conclusions • A light Higgs boson may result from the approximate scale invariance of the Standard Model – the Higgs particle can be viewed as pseudo-Goldstone boson / dilaton.
• The explicit breaking of the scale symmetry by the classical SM Higgs potential is IR stable against loop corrections
• Novel running in UV – possible that running from UV creates IR potential
• Dynamical Generation of electroweak scale via Coleman- Weinberg mechanism and dimensional transmutation
• Requires Higgs Portal and new physics on Dark Side
• Many models including dark and not-so-dark physics
• Connections to Planck scale boundary conditions, asymptotic gravity
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 17!
Some References Naturalness
• W. Bardeen, FERMILAB-CONF-95-391-T (1995) On Naturalness in the Standard Model • K. Meissner and H. Nicolai, Phys.Lett. B648, 312(2007) Conformal Symmetry and the Standard Model • M. Farina, M. Perelstein and N. Rey-LeLorier, arXiv:1305.6068 [hep-ph] Higgs Couplings and Naturalness F. Jegerlehner, arXiv:1305.6652 [hep-ph] 14 Sep 2013 The Hierarch Problem of the electroweak Standard Model Revisited
Coleman-Weinberg Mechanism
• S. Coleman and E. Weinberg, Phys.Rev. D7, 1888(1973) Radiative Corrections as the Origin of Spontaneous Symmetry Breaking • E. Gildner and S. Weinberg, Phys.Rev. D13, 3333(1976) Symmetry Breaking and Scalar Bosons • K. Meissner and H. Nicolai, arXiv:0809.1338 [hep-th] Renormalization Group and Effective Potential in Classically Conformal Theories
SVZ
• M. Shifman, A. Vainshtein, V. Zakharov, Phys.Lett. 78B, 443(1978) Remarks on Higgs-Boson Interactions with Nucleons • A. Vainshtein, M. Voloshin, V. Zakharov, M. Shifman, Sov.J.Nucl.Phys. 30, 711(1979) Low Energy Theorems for Higgs Meson Interaction with Photons • A. Vainshtein, V. Zakharov and M. Shifman, Sov.Phys.Usp. 23, 429(1980) Higgs Particles
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 18!
Some References Darkside Standard Models
• M. Hashimoto, S. Iso and Y. Orikasa, arXiv:1310.4304 [hep-ph] 16 Oct 2013 Electroweak Symmetry Breaking in the Flatland • E.-J. Chun, S. Jung and H.-M. Lee, arXiv:1304.5815 [hep-ph] 22 Apr 2013 Radiative Generation of the Higgs Potential • T. Hambye and A.Strumia, arXiv:1306.2329 [hep-ph] 10 Jun 2013 Dynamical Generation of the Weak and Dark Scale Matter Scale • M. Holthausen, J. Kubo, K.S. Lim and M. Lindner, arXiv:1310.4423 [hep-ph] 16 Oct 2013 Electroweak and Conformal Symmetry Breaking by a Strongly Coupled Hidden Sector • H. Davoudiasl and I. Lewis, arXiv:1309.6640 [hep-ph] 11 Oct 2013 Dark Matter from Hidden Forces • Y. Bai and P. Schwaller, arXiv:1306.4676 [hep-ph] 19 Jun 2013 The Scale of Dark QCD • S. Baek, P. Ko and Wan-II Park, arXiv:1303.4280 [hep-ph] 18 Mar 2013 Singlet Portal Extensions of the Standard Seesaw Model to a Dark Sector with Local Dark Symmetry • X. Chu, T. Hambye, M. Tytgat, arXiv:1112.0493 [hep-ph] 24 May 2012 Four Basic Ways of Creating Dark Matter Through a Portal • Y. Farzan and A. Rezaei Akbarieh, arXiv:1207.4272 [hep-ph] 18 Jul 2012 VDM: A Model for Vector Dark Matter • S. Iso, N. Okada and Y. Orikasa, Phys.Lett. B676, 81(2009) Classically Conformal B-L extended Standard Model • S. Iso, N. Okada, and Y. Orikasa, Phys.Rev. D80, 115007(2009) The minimal B-L model naturally realized at TeV scale • L. Anchordoqui et al, arXiv:1208:2821 [hep-ph] 23 Jan 2013 Vacuum Stability of the Standard Model • W. Altmannshofer, W. Bardeen, M. Carena and J. Lykken, in preparation The Radiative Origins of Electroweak Scale, Dark Matter and Vacuum Instability
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 19!
Some References Higgs and Planck Scale Boundary Conditions • M. Shaposhnikov and C. Wetterich, arXiv:0912.0208 [hep-th] 12 Jan 2010 Asymptotic Safety of Gravity and the Higgs Boson Mass • M. Shaposhnikov, arXiv:0708.3550 [hep-th] 27 Aug 2007 Is there new physics between electroweak and Planck scales? • O. Antipin, M. Gillioz, J. Krog, E. Mølgaard and F. Sannino et al, arXiv:1306.3234 [hep-ph] 13 Jun 2013, Standard Model Vacuum Stability and Weyl Consistence Conditions • Y. Hamada, H. Kawai and K. Oda, arXiv:1210.2538 [hep-ph] 21 Jan 2013 Bare Higgs Mass at Planck Scale • M. Holthausen, K. Lim and M. Lindner, arXiv:1112.2415 [hep-ph] 2 Mar 2012 Planck Scale Boundary Conditions and the Higgs Mass • G. Barenboim, E-J Chun and H-M Lee, arXiv:1309.1695 [hep-ph] 6 Sep 2013 Coleman-Weinberg Inflation in light of Planck
Dilatons • K. Haba, S. Matsuzaki and K. Yamawaki, arXiv:1003.2841 [hep-ph] 15 Mar 2010 Holographic Techni-dilaton, or Conformal Higgs? • S. Matsuzaki and K. Yamawaki, arXiv:1209.2017 [hep-ph] Holographic techni-dilaton at 125 GeV • B. Bellazzini et al, arXiv:1209.3299 [hep-ph] A Higgslike Dilaton • W. Goldberger, B. Grinstein and W. Skiba, arXiv:0708:1463 [hep-ph] 10 Aug 2007 Light Scalar LHC: the Higgs or the Dilaton? •Z. Chacko et al, arXiv:1209.3022 [hep-ph] Effective Theory of a Light Dilaton •Z. Chacko et al, arXiv:1209.3259 [hep-ph] Resonance at 125 GeV: Higgs or Dilaton/Radion
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 20!
Some References Additional IR Higgs Papers
• S. Iso, N. Okada and Y. Orikasa, arXiv:0902.4050 [hep-ph] 17 Apr 2009 Classically Conformal B-L extended Standard Model • S. Iso and Y. Orikasa, arXiv:1210.2848 [hep-ph] 10 Oct 2012 TeV Scale B-L Model with a flat Higgs Potential at the Planck Scale • F. Sannino et al, arXiv:1306.3234 [hep-ph] 13 Jun 2013 Standard Model Vacuum Stability and Weyl Consistency Conditions • G. Wouda, arXiv:1306.6855 [hep-ph] 28 Jun 2013 Higgs Properties in the Stealth Doublet Model • Y. Hamada, H. Kawai and K. Oda, arXiv:1210.2538 [hep-ph] 21 Jan 2013 Bare Higgs Mass at Planck Scale • Michel Tytgat, Heidelber Dark Matter Conference (2011) The Higgs Portal to the Dark Universe • T. Hambye and M. Tytgat, arXiv:0707.0633 [hep-ph] 4 Jul 2007 Electroweak Symmetry Breaking induced by Dark Matter • V. Silveira and A. Zee, Phys.Lett. B161, 136(1985) Scalar Phantoms • B. Patt and F. Wilczek, arXiv:hep-ph/0605188 16 May 2006 Higgs Field Portal into Hidden Sectors • W. Chao, M. Gonderinger, M. Ramsey-Musolf, arXiv:1210.0491 [hep-ph] 1 Oct 2012 Higgs Vacuum Stability, Neutrino Mass and Dark Matter • Y. Farzan and A. Rezaei Akbarieh, arXiv:1207.4272 [hep-ph] 18 Jul 2012 VDM: A Model for Vector Dark Matter • A. Farzinnia, H-J He and J. Ren, arXiv:1308.0295 [hep-ph] 1 Oct 2013 Natural Electroweak Symmetry Breaking for Scale Invariant Higgs Mechanism • C. Burgess, M. Pospelov and T. der Veldhius, arXiv:hep-ph/0011335v3 11 Jul 2001 The Minimal Model of Nonbaryonic Dark Matter: A Singlet Scalar
William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 21!
Some References BEH
• F. Englert and R. Brout, Phys.Rev.Lett. 13, 321(1964) Broken Symmetry and the Mass of Gauge Vector Bosons
• F. Englert, R. Brout and M. Thiry, NuovoCim. A43, 244(1966) Vector Mesons in the presence of broken symmetry
• P. Higgs, Phys.Rev.Lett. 13, 508(1964) Broken Symmetries and the Masses of Gauge Bosons
• P. Higgs, Phys.Lett. 12, 132(1964 Broken Symmetries, massless particles and gauge fields
• P. Higgs, Phys.Rev. 145, 1156(1966)
• G. Guralnik, C. Hagen and T. Kibble, Phys.Rev.Lett. 13, 585(1964) Global Conservation Laws and Massless Particles