DYNAMICAL GENERATION OF FERMION MASSES AND ITS CONSEQUENCES

Jiří Hošek

Department of Theoretical Physics

Nuclear Physics Institute Rez (Prague) Czech Republic

with important departures from 1401.7503

and to appear soon

MIAMI 2015

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In the Standard model the fermion masses come out as the scale v = 246 GeV multiplied by independently

renormalized i.e., theoretically arbitrary, numerically vastly different, Yukawa couplings. This is the phenomenological

description of fermion masses by construction.

SUGGESTION: Replace the essentially classical Higgs sector with its ‘twenty-some’ parameters (T.D.Lee) by

genuinely quantum SU(3) flavor dynamics (q.f.d.): GAUGE THE FLAVOR (FAMILY) SYMMETRY

one triplet of sterile right-handed neutrinos (anomaly ) one octet of flavor gluons C,

one coupling constant h or by dimensional transmutation arbitrary scale Λ below which the dynamics is strong

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Lagrangian of q.f.d. is formally identical with the Lagrangian of QCD. This is highly suspicious: ‘In QCD we trust’, and it is the firm experimental fact that the flavor symmetry is not

confining but badly broken.

CARDINAL DIFFERENCE: QUANTUM FLAVOR DYNAMICS LIKES TO GENERATE

THREE DIFFERENT MAJORANA MASSES OF νR. INEVITABLE CONSEQUENCE IS THAT THE COMPOSITE ‘WOULD-BE’ NG BOSONS MAKE ALL EIGHT FLAVOR

GLUONS MASSIVE. GAUGE SU(3)f COMPLETELY SPONTANEOUSLY BROKEN

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FERTILE STERILE NEUTRINOS spontaneous (dynamical) breakdown of SU(3)f

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• The (matrix) fermion self-energy is a bridge between left- and right-handed fermion fields:

• In the case of sterile neutrinos the left-handed components are the charge conjugates of the right-handed ones, and transform as antitriplets: Q.F.D. IS CHIRAL

In vertices there is the momentum –dependent coupling matrix entirely unknown in the strong-coupling low-momentum region

• To proceed we integrate in the Schwinger-Dyson equation only up to Λ: the resulting model is thus not asymptotically, but strictly free above the scale Λ:

• For unknown kernel we use separable symmetry breaking Ansatz • the matrix SD equation is immediately solved (σ is a

numerical matrix to be found by solving an algebraic nonlinear gap equation)

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• Neglect the fermion mixing and consider only

g33 ,g88 , g38 different from zero

In general the proper self energy ∑ defines the fermion mass m: Consequently:

where

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Fertile sterile neutrinos: Conclusion

• Spontaneous emergence of MR (3* x 3* = 3 + 6*) THERE ARE NINE NG BOSONS (EIGHT ‘WOULD-BE’) ALL EIGHT FLAVOR GLUONS MASSIVE (Ma ) • Λ is theoretically arbitrary, later fixed to ~ 1010 GeV MR and Ma ARE HUGE (MR ~ 1017 GeV)

• With mixing MR is a complex symmetric matrix NEW CP VIOLATING PHASES IN THE MODEL • Dual (Higgs) description of the same phenomenon: Higgs field

in complex sextet representation : 2 x 6 = 1 + 8 + 3 • THREE HIGGS-LIKE SUPERHEAVY SCALARS χ • Separable Ansatz for illustration – we would love to do better

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ELECTROWEAK SYMMETRY BREAKING: mi(f)

Dirac fermion masses generated by the same SD equation

Ta(R) = Ta(L) =

λa

For electroweak corrections switched off mi(f), f = u, d, e, ν come out equal – opposite sign in comparison with MR

In reality weak hypercharges (exchanges of the B boson) distinguish between different fermion types: Yu = 4/3, Yd = --2/3, Ye = -2, Yν = 0

No new parameters

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ELECTROWEAK SYMMETRY BREAKING: mW, mZ

• Spontaneous SU(2)L x U(1)Y breakdown by dynamically generated fermion masses generates three composite ‘would-be’ NG bosons with calculable pseudoscalar couplings P with fermions visualized by WT identities

• Composite ‘would-be’ NG bosons become the longitudinal

polarization states of W, Z: Masses mW and mZ expressed in terms of fermion masses by sum rules

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WHERE IS THE CERN HIGGS ?

• Dual (Higgs) description of the same phenomenon: Higgs in DOUBLET representation ONE HIGGS-LIKE HEAVY SCALAR

• Replace m by ∑(p2) and v by the weighted sum of the fermion masses F: Composite Higgs interacts with fermions as in SM

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INTERACTION OF COMPOSITE HIGGS WITH γ GENERIC DIFFERENCE FROM SM

In SM: W and fermion loops separately UV finite

• In this model: no tree-level hWW coupling absent also in Higgs production only the fermion (top quark) loop

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INTERACTIONS OF COMPOSITE HIGGS WITH W, Z: GENERIC DIFFERENCES FROM SM

• in SM

• In this model Analogously for h2 WW

TRUE ELECTROWEAK UNIFICATION: ALL FOUR GAUGE BOSONS TREATED ON THE SAME FOOTING

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FATE OF SIX ABELIAN SYMMETRIES generated by six Abelian chiral fermion currents

There are 4 gauge forces in the game, hence 4 anomalies 1. Anomaly-free current of weak hypercharge (Q=T3 + ½Y) corresponds to a gauged vectorial symmetry: no NG boson 2. Second anomaly-free current can be gauged: massive Z’ - one ‘would-be’ NG boson 3. Anomalous baryon (vectorial) current – no NG boson 4. Three anomalous currents – three pseudo NG bosons, AXIONS massive due to three non-Abelian instantons: - Weinberg-Wilczek QCD axion a(x) (strong CP problem) - Anselm-Uraltsev electroweak axion b(x) - new q.f.d. axion c(x) Some like them as hot candidates for cold dark matter

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PROPERTIES OF STRONGLY COUPLED Q.F.D.

• Mass spectrum of leptons and quarks is calculable by q.f.d. as are the energy spectra of other quantum systems (oscillators, hydrogen atom, hadron masses in QCD,…). The Higgs mechanism is essentially classical.

• There is no genuine electroweak symmetry scale ~246 GeV • The only particle physics scale is much higher Λ~1010 GeV. • Composite Higgs is similar to but different from SM Higgs . • There are three superheavy neutrino-composite inflatons χ. • There are new CP violating phases in sterile neutrino sector • There are decent candidates for dark matter – axions. • There is a (wishfull) understanding of the origin of seesaw. • There are (presumably) other heavy composites.

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THANK YOU FOR YOUR ATTENTION

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