The Standard Model and Scale Symmetrytheo.phys.sci.hiroshima-u.ac.jp/~soken/schedule/...The Standard...

William A. Bardeen, Fermilab! Hiroshima University, December 9, 2013 1!

The Standard Model and Scale Symmetry

William A. Bardeen Fermilab!


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


The Standard Model

• Classically Conformal - except for the Higgs mass term, the cosmological constant (and possibly neutrino masses)

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• 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)


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


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


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


UV Behavior of the Standard Model

• Running couplings at high energies remains perturbative

• SM Higgs coupling appears to be metastable


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)


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


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:

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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


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


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


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


Darkside CW Mechanisms – Dark SU(2) Model

• Smooth UV Evolution of all coupling constants (Hambye et al)


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


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


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


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


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


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


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

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