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

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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. 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: Rigidity of the model provides bona fide testable firm predictions due to symmetries: 9 sterile ν R for anomaly freedom – new global U(3) sterility symmetry 9 sterile ν R for anomaly freedom – new global U(3) sterility symmetry Dynamics implies 12 massive Majorana neutrinos (3 active) Dynamics implies 12 massive Majorana neutrinos (3 active) There is the massless composite Nambu-Goldstone majoron There is the massless composite Nambu-Goldstone majoron There is the light Weinberg-Wilczek axion There is the light Weinberg-Wilczek axion

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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 ν R : New global U(3) S =U(1) S x SU(3) S sterility symmetry. Theory is AF but not vector-like (not QCD-like)

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QCD and electroweak SU(2) L x U(1) Y can be introduced at will by gauging in L f the corresponding indices of chiral fermion fields and by adding the corresponding pure gauge terms. GLOBAL SYMMETRIES GLOBAL SYMMETRIES Gauge and global non-Abelian symmetries tie together different chiral fermion fields. Only 6 Abelian symmetries corresponding to 6 common phases of l L, ν s R, e R, q L, u R, d R survive. Gauge and global non-Abelian symmetries tie together different chiral fermion fields. Only 6 Abelian symmetries corresponding to 6 common phases of l L, ν s R, e R, q L, u R, d R 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. 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. There are 4 distinct gauge forces, hence 4 distinct anomalies. Therefore, one current remains exactly conserved at quantum level: B-(L+S) 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 Divergences of linear combinations of remaining 4 currents can be ordered according to strengths of anomalies

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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(p 2 ) Chirality changing fermion self energy Σ(p 2 ) is a R-L bridge : all important is a R-L bridge : all important Fermion mass is then the position of the pole of the full fermion propagator, m=Σ(p 2 =m 2 ). Fermion mass is then the position of the pole of the full fermion propagator, m=Σ(p 2 =m 2 ). 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. 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 M C ~10 6 GeV. FCNC by flavor gluons imply M C ~10 6 GeV. Arbitrary smallness of fermion masses is attributed to the proximity of the fixed point. Arbitrary smallness of fermion masses is attributed to the proximity of the fixed point. Knowledge of at low momenta is the necessity. Knowledge of at low momenta is the necessity.

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

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Charged fermion mass generation Poor guy illustration Poor guy illustration With M=10 6 GeV the ‘neutrino’ mass m ν =10 -9 GeV is obtained for h ν =2π/15 ln 10 ~ 0.18 and the ‘top quark’ mass m t =10 2 GeV is obtained for h t =2π/4 ln 10 ~ With M=10 6 GeV the ‘neutrino’ mass m ν =10 -9 GeV is obtained for h ν =2π/15 ln 10 ~ 0.18 and the ‘top quark’ mass m t =10 2 GeV is obtained for h t =2π/4 ln 10 ~ All masses related All masses related

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Neutrino mass (Majorana) generation canonical warm dark matter candidate

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

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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 Spontaneously broken by fermion self energies Σ

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Massless Abelian majoron J Exact anomaly free U(1) B-(L+S) is spontaneously broken by Σ ν Exact anomaly free U(1) B-(L+S) is spontaneously broken by Σ ν There is a massless neutrino-composite majoron 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/r 3 fall off For interaction strength weak enough no phenomenological danger : exchange of massless NG boson leads only to a spin-dependent tensor potential with a 1/r 3 fall off BUT: If there are neutrino oscillations, there is the classical majoron field ! (L. Bento, Z. Berezhiani) BUT: If there are neutrino oscillations, there is the classical majoron field ! (L. Bento, Z. Berezhiani)

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Weinberg-Wilczek axion a Symmetry generated by B 5 -4S or B 5 -(L 5 -L) has QCD anomaly (i.e. is explicitly broken) and is spontaneously broken by both lepton and quark masses Symmetry generated by B 5 -4S or B 5 -(L 5 -L) has QCD anomaly (i.e. is explicitly broken) and is spontaneously broken by both lepton and quark masses Canonical dark matter candidate Canonical dark matter candidate Axion mass is m a ~ m π f π / Λ g.f.d. Axion mass is m a ~ m π f π / Λ g.f.d. Invisibility requires Λ g.f.d. > 10 6 TeV Invisibility requires Λ g.f.d. > 10 6 TeV

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

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