Observable effects of gauge flavor dynamics

1. Observable effects of gauge flavor dynamics J. Hošek, in “Strong Coupling Gauge Theories in LHC Era”, World Scientific 2011 (arXiv: 0909.0629) P. Beneš, J. Hošek, A. Smetana, arXiv: 1101.3456 A. Smetana, arXiv.1104.1935

2. Plan of the talk • Dynamical mass generation by gauge SU(3)f (f=1,2,3) flavor dynamics. Having just one free parameter (gauge coupling h or the scale Λ) it is either right or plainly wrong. Reliable computation of the spectrum is, however, a formidable task. • Rigidity of the model provides bona fide testable firm predictions due to symmetries: • 9 sterile νR for anomaly freedom – new global U(3) sterility symmetry • Dynamics implies 12 massive Majorana neutrinos (3 active) • There is the massless composite Nambu-Goldstone majoron • There is the light Weinberg-Wilczek axion

3. We pretend to replace the Higgs sector with its ‘twenty-some’ parameters by gauge flavor dynamics (g.f.d.). For anomaly freedom there must be 3 triplets of νR : New global U(3)S=U(1)S x SU(3)Ssterility symmetry. Theory is AF but not vector-like (not QCD-like)

4. QCD and electroweak SU(2)L x U(1)Y can be introduced at will by gauging in Lf the corresponding indices of chiral fermion fields and by adding the corresponding pure gauge terms. • GLOBAL SYMMETRIES • Gauge and global non-Abelian symmetries tie together different chiral fermion fields. Only 6 Abelian symmetries corresponding to 6 common phases of lL, νsR, eR, qL, uR, dR survive. • 6-1=5: U(1)Y is gauged. 5 global Abelian U(1) currents generated by B, B5, L, L5, S charges are classically conserved for massless fermions. • There are 4 distinct gauge forces, hence 4 distinct anomalies. • Therefore, one current remains exactly conserved at quantum level: B-(L+S) • Divergences of linear combinations of remaining 4 currents can be ordered according to strengths of anomalies

5. We argue that g.f.d. completely self-breaks: At low momenta g.f.d. is strongly coupled and lepton, quark and flavor gluon masses are generated. There must be, unlike in QCD, the nontrivial non-perturbative fixed point. • Chirality changing fermion self energy Σ(p2) is a R-L bridge : all important • Fermion mass is then the position of the pole of the full fermion propagator, m=Σ(p2=m2). • If different fermion masses are generated, the ‘would-be’ composite NG bosons of completely broken S(U3) f give rise to the flavor gluon masses. There should be also other (massive) bound states. • FCNC by flavor gluons imply MC~106 GeV. • Arbitrary smallness of fermion masses is attributed to the proximity of the fixed point. • Knowledge of at low momenta is the necessity.

6. Momentum-dependent sliding coupling and non-perturbative IR fixed point • In PT • For П~ln q 2 we get the formula of asymptotic freedom • For П=M2/q2 we get the massive gluon propagator (Schwinger mechanism). • For q2 -> 0 we get erroneously zero. • We suggest to use • Postulate at low momenta : the way to the fixed point is matrix-fold

7. Charged fermion mass generation • Poor guy illustration • With M=106 GeV the ‘neutrino’ mass mν=10-9 GeV is obtained for hν=2π/15 ln 10 ~ 0.18 and the ‘top quark’ mass mt=102 GeV is obtained for ht=2π/4 ln 10 ~ 0.68. • All masses related

8. Neutrino mass (Majorana) generation canonical warm dark matter candidate

9. Intermediate boson mass generation • Fermion proper self energies Σ break spontaneously also the ‘vertical’ SU(2)LxU(1)Y . Schwinger mechanism at work: • WT identities, ‘would-be’ NG bosons, … • No generic Fermi (electroweak) scale-remnant of the top quark mass

10. Spontaneously broken global symmetries: generic predictions(We assume that there are nontrivial solution Σ with no accidental symmetries) • Spontaneously broken by fermion self energies Σ

11. Massless Abelian majoron J • Exact anomaly free U(1) B-(L+S)is spontaneously broken by Σν • There is a massless neutrino-composite majoron • For interaction strength weak enough no phenomenological danger : exchange of massless NG boson leads only to a spin-dependent tensor potential with a 1/r3 fall off • BUT: If there are neutrino oscillations, there is the classical majoron field ! (L. Bento, Z. Berezhiani)

12. Weinberg-Wilczek axion a • Symmetry generated by B5-4S or B5-(L5-L) has QCD anomaly (i.e. is explicitly broken) and is spontaneously broken by both lepton and quark masses • Canonical dark matter candidate • Axion mass is ma ~ mπ fπ / Λg.f.d. • Invisibility requires Λg.f.d. > 106 TeV

13. Conclusions • One free parameter: Either right or plainly wrong • Hard to solve (1st Weinberg’s law: “You will get nowhere by churning equations.” ) • Nobody knows how to put the model on the lattice • Dynamical (shining or dark) mass generation (all masses in principle related) • Fixed neutrino pattern • Massless NG majoron • Fixed pattern of pseudo-Goldstone bosons • Find other robust low-energy manifestation(s) of the model ???