construction of the models of the dynamical electroweak symmetry breaking using the ideas that come...
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Construction of the models of the dynamical Electroweak symmetry breaking using the ideas that come from the effective field model of Helium - 3 superfluid. 1. Nambu sum rule 2. Lorentz group as a source of DESB. . G.E.Volovik (Aalto U& ITP, Moscow) M.A.Zubkov (ITEP, Moscow) - PowerPoint PPT PresentationTRANSCRIPT
Construction of the models of the Construction of the models of the dynamical Electroweak symmetry dynamical Electroweak symmetry
breaking using the ideas that breaking using the ideas that come from the effective field come from the effective field
model of Helium - 3 superfluid.model of Helium - 3 superfluid.
1. Nambu sum rule
2. Lorentz group as a source of DESB.
The Nambu sum rule and the relation between the masses of composite Higgs bosons
G.E.Volovik (Aalto U& ITP, Moscow)M.A.Zubkov (ITEP, Moscow)ArXiv:1302.2360, to appear in JETP lett.arXiv:1209.0204
abstractabstract It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. The masses of
the Higgses may be related to the mass of t — quark as
(The sum is within a group of the scalar excitations.) This rule is the analogue of the sum rule in He3-B
(for the excitations of the same total momentum J). It was originally proposed by Nambu for He3-B. We call it the Nambu sum rule.
Plan 1. Introduction: experimental situation; accidents;
the essence of the Nambu sum rule.
2. Review of bosonic excitations in He3-B,A and thin films He3-a,b.
3. Consideration of the toy model for the top — quark condensation
4. Review of bosonic excitations in dense QCD
5. Conclusions
Nambu Sum rule
QCD
He3-B
AccidentsExcess of events at the Tevatron and CMS in 2011 at
325 GeV
"A 325 GeV scalar resonance seen at CDF?", Krzysztof A. Meissner,
Hermann Nicolai, arXiv:1208.5653
"Probing Minimal Supersymmetry at the LHC with the Higgs Boson Masses", L. Maiani, A. D. Polosa, V. Riquer, arXiv:1202.5998
Excess of events at ATLAS in 2011 at 245 GeV
He-3
Bosons
He3-B
derivation
He3-b thin film
He3-a thin film
Triply degenerated
He3-A
Goldstones:hidden symmetry: there are three terms that depend on with definite these terms are transformed to each other by
New massless modes:
He3-A
Bosonic modes (triply degenerated):
and six massless models
Relativistic models of top quark condensation
Particular case
bosons
C is diagonal
T-anti t and q — anti q channels
Channels with different quarks
Nambu Sum Rule
If one of the quarks dominates
Veltman identity vs Nambu Sum Rule
The number of colors is important
Hadronic phasediquarks:
Color superconductivity, CFL phase
Conclusions1. The notion of the Nambu Sum rule is introduced. It works in:
- Helium superfluid 3-B, 3-A, in thin films 3-b,3-a
- QCD at finite chemical potential (normal phase, small T, small mu),
- color superconductor (CFL phase)
- the considered models of top — quark condensation
2. Lessons for the TeV — scale physics:
- The 125 GeV Higgs cannot be the Nambu partner of the neutral
Goldstone boson
- If there are two twice degenerated Higgs bosons, then the Namby partner of the 125 GeV Higgs should have mass 210 GeV
-If there are only two states, then the second Higgs should have mass 325 GeV
-If there are two Higgs bosons of equal masses, these masses are around 245 GeV
M. ZubkovM. Zubkov
ITEP Moscow 2010-2013ITEP Moscow 2010-2013
1.1.M.A.Zubkov, arXiv:1301.69712. G.E. Volovik, M.A. Zubkov, arXiv:1302.2360, To appear in
JETP lett.3. 3. M.A.Zubkov, M.A.Zubkov, Mod. Phys. Lett. A, Vol. 25, Mod. Phys. Lett. A, Vol. 25,
No. 34 (2010) pp. 2885-2898No. 34 (2010) pp. 2885-2898
Lorentz Group as the source of dynamical Lorentz Group as the source of dynamical electroweak symmetry breaking electroweak symmetry breaking
3030
AbstractAbstract
1. Dynamics of torsion degrees of freedom in Poincare 1. Dynamics of torsion degrees of freedom in Poincare gravity can be considered as the gauge theory of gravity can be considered as the gauge theory of Lorentz group. Lorentz group.
2. Suppose this theory is coupled in a nonminimal way 2. Suppose this theory is coupled in a nonminimal way to spinors. The effective four - fermion interactions to spinors. The effective four - fermion interactions appear that may lead to the condensation of fermions. appear that may lead to the condensation of fermions.
3. The given construction may provide the dynamical 3. The given construction may provide the dynamical Electroweak symmetry breaking. Electroweak symmetry breaking.
3131
PlanPlan1. From Superconductivity to Technicolor2. Fermions in Riemann – Cartan space.3. 4 – fermion interactions. 4. Condensation of fermions.5. Fermion masses.
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Corrections to the effective action are taken into account
Lattice discretization
Gauge field action
4949
ConclusionsConclusions1. The dynamical SO(3,1) gauge theory with the scale >1000
TeV and the torsion mass ~ this scale is coupled in a nonminimal way to fermions.
2. Due to the effecitve 4 – fermion interactions fermions are condensed and provide the DEWSB.
3. In zero order approximation all fermions acquire equal masses.
4. When the corrections due to the other gauge fields are taken into account, the hierarchy of fermion masses appears.
5. The given gauge theory is unusual since it should provide chiral symmetry breaking but cannot be confining.
Summary of two talks:1. Nambu sum rules in the NJL models: from Helium-3 to top
quark condensation. G.E. Volovik, M.A. Zubkov, ArXiv:1302.2360, to appear in JETP lett.; arXiv:1209.0204.
2. Numerical investigation of the effective field model of graphene monolayer using lattice field theory technique.M.V.Ulybyshev, M.A. Zubkov, Solid State Comm. http://dx.doi.org/10.1016/j.ssc.2012.12.030
3. Calculation of Euler — Heisenberg effective lagrangian for the effective field model of multilayer graphene.
M.I. Katsnelson, G.E. Volovik, M.A. Zubkov, Annals Phys. 331 (2013) 160
4. Momentum space topology in 4D relativistic quantum field theory.M.A. Zubkov, G.E. Volovik, Nucl.Phys. B860 (2012) 295-309, M.A. Zubkov, Phys.Rev. D86 (2012) 034505
5. Numerical investigation of Weinberg — Salam model in lattice regularization. M.A. Zubkov, Phys.Rev. D85 (2012) 073001.
6. Gauge theory of Lorentz group as a source of the dynamical Electroweak symmetry breaking. M.A. Zubkov. arXiv:1301.6971