1. 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. 1

2. 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 2

3. 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 ν R. INEVITABLE CONSEQUENCE IS THAT THE COMPOSITE ‘WOULD-BE’ NG BOSONS MAKE ALL EIGHT FLAVOR GLUONS MASSIVE. GAUGE SU(3) f COMPLETELY SPONTANEOUSLY BROKEN 3

4. FERTILE STERILE NEUTRINOS spontaneous (dynamical) breakdown of SU(3) f 4 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

5. 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) 5

6. Neglect the fermion mixing and consider only g 33,g 88, g 38 different from zero In general the proper self energy ∑ defines the fermion mass m: Consequently: where 6

7. Fertile sterile neutrinos: Conclusion Spontaneous emergence of M R (3* x 3* = 3 + 6*) THERE ARE NINE NG BOSONS (EIGHT ‘WOULD-BE’) ALL EIGHT FLAVOR GLUONS MASSIVE (M a ) Λ is theoretically arbitrary, later fixed to ~ 10 10 GeV M R and M a ARE HUGE (M R ~ 10 17 GeV) With mixing M R 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 7

8. ELECTROWEAK SYMMETRY BREAKING: m i (f) 8

9. ELECTROWEAK SYMMETRY BREAKING: m W, m Z 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 m W and m Z expressed in terms of fermion masses by sum rules 9

10. WHERE IS THE CERN HIGGS ? Dual (Higgs) description of the same phenomenon: Higgs in DOUBLET representation ONE HIGGS-LIKE HEAVY SCALAR Replace m by ∑(p 2 ) and v by the weighted sum of the fermion masses F: Composite Higgs interacts with fermions as in SM 10

11. 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 11

12. INTERACTIONS OF COMPOSITE HIGGS WITH W, Z: GENERIC DIFFERENCES FROM SM in SM In this model Analogously for h 2 WW TRUE ELECTROWEAK UNIFICATION: ALL FOUR GAUGE BOSONS TREATED ON THE SAME FOOTING 12

13. 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=T 3 + 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 13

14. 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~10 10 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. 14

15. THANK YOU FOR YOUR ATTENTION 15

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