JJ. Hošek, . Hošek, in “Strong Coupling Gauge Theories in LHC in “Strong Coupling Gauge Theories in LHC Era”, World Scientific 2011 (Era”, World Scientific 2011 (arXiv: 0909.0629arXiv: 0909.0629))

P. Beneš, J. Hošek, A. Smetana, P. Beneš, J. Hošek, A. Smetana, arXiv: 1101.3456 arXiv: 1101.3456 A. A. Smetana, Smetana, arXiv.1104.1935arXiv.1104.1935

Observable effects of gauge flavor dynamicsObservable effects of gauge flavor dynamics

Plan of the talkPlan of the talk

Dynamical mass generation by gauge SU(3)Dynamical mass generation by gauge SU(3)ff (f=1,2,3) flavor (f=1,2,3) flavor

dynamics. Having just one free parameter (gauge coupling h or the dynamics. Having just one free parameter (gauge coupling h or the scale scale ΛΛ) it is either right or plainly wrong. Reliable computation of ) it is either right or plainly wrong. Reliable computation of the spectrum is, however, a formidable task.the spectrum is, however, a formidable task.

Rigidity of the model provides bona fide testable firm predictions Rigidity of the model provides bona fide testable firm predictions due to symmetries:due to symmetries:

9 sterile 9 sterile ννR R for anomaly freedom – new global U(3) sterility for anomaly freedom – new global U(3) sterility

symmetrysymmetry Dynamics implies 12 massive Majorana neutrinos (3 active)Dynamics implies 12 massive Majorana neutrinos (3 active) There is the massless composite Nambu-Goldstone majoronThere is the massless composite Nambu-Goldstone majoron There is the light Weinberg-Wilczek axionThere is the light Weinberg-Wilczek axion

We pretend to replace the Higgs sector with its ‘twenty-some’ We pretend to replace the Higgs sector with its ‘twenty-some’ parameters by gauge flavor dynamics (g.f.d.). For anomaly freedom parameters by gauge flavor dynamics (g.f.d.). For anomaly freedom there must be 3 triplets of there must be 3 triplets of ννR R : New global U(3): New global U(3)SS=U(1)=U(1)SS x SU(3) x SU(3)SS

sterility symmetry.sterility symmetry. Theory is AF but not vector-like (not QCD-like) Theory is AF but not vector-like (not QCD-like)

QCD and electroweak SU(2)QCD and electroweak SU(2)LL x U(1) x U(1)YY can be introduced at will by can be introduced at will by

gauging in Lgauging in Lf f the corresponding indices of chiral fermion fields and by the corresponding indices of chiral fermion fields and by

adding the corresponding pure gauge terms. adding the corresponding pure gauge terms.

GLOBAL SYMMETRIESGLOBAL SYMMETRIES Gauge and global non-Abelian symmetries tie together different Gauge and global non-Abelian symmetries tie together different

chiral fermion fields. Only 6 Abelian symmetries corresponding to 6 chiral fermion fields. Only 6 Abelian symmetries corresponding to 6 common phases of lcommon phases of lLL, , ννss

RR, e, eRR, q, qLL, u, uRR, d, dRR survive. survive.

6-1=5: U(1)6-1=5: U(1)YY is gauged. 5 global Abelian U(1) currents generated by is gauged. 5 global Abelian U(1) currents generated by

B, B5, L, L5, S charges are classically conserved for massless B, B5, L, L5, S charges are classically conserved for massless fermions.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: Therefore, one current remains exactly conserved at quantum level:

B-(L+S)B-(L+S) Divergences of linear combinations of remaining 4 currents can be Divergences of linear combinations of remaining 4 currents can be

ordered according to strengths of anomalies ordered according to strengths of anomalies

We argue that g.f.d. completely self-breaks: At low momenta g.f.d. is 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 strongly coupled and lepton, quark and flavor gluon masses are generated. There must be, unlike in QCD, the generated. There must be, unlike in QCD, the nontrivial non-nontrivial non-perturbative fixed pointperturbative fixed point. .

Chirality changing fermion self energy Chirality changing fermion self energy ΣΣ(p(p22) ) is a R-L bridge is a R-L bridge : : all importantall important

Fermion mass is then the position of the pole of the full fermion propagator, Fermion mass is then the position of the pole of the full fermion propagator, m=m=ΣΣ(p(p22=m=m22).).

If different fermion masses are generated, the ‘would-be’ If different fermion masses are generated, the ‘would-be’ compositecomposite NG NG bosons of completely broken S(U3)bosons of completely broken S(U3) f f give rise to the flavor gluon masses. give rise to the flavor gluon masses. There should be also other (massive) bound states.There should be also other (massive) bound states.

FCNC by flavor gluons imply MFCNC by flavor gluons imply MCC~10~1066 GeV. GeV. Arbitrary smallness of fermion masses is attributed to the proximity of the Arbitrary smallness of fermion masses is attributed to the proximity of the

fixed point.fixed point. Knowledge of at low momenta is Knowledge of at low momenta is the necessitythe necessity. .

Momentum-dependent sliding coupling and Momentum-dependent sliding coupling and non-perturbative IR fixed pointnon-perturbative IR fixed point

In PTIn PT

For For ПП~ln q~ln q 2 2 we get the formula of asymptotic freedom we get the formula of asymptotic freedom For For ПП=M=M22/q/q2 2 we get the massive gluon propagator (Schwinger we get the massive gluon propagator (Schwinger

mechanism). mechanism). For qFor q2 2 -> 0 we get erroneously zero. -> 0 we get erroneously zero. We suggest to use We suggest to use

Postulate at low momenta : Postulate at low momenta : the way to the fixed point is matrix-fold the way to the fixed point is matrix-fold

Charged fermion mass generationCharged fermion mass generation

Poor guy illustrationPoor guy illustration

With M=10With M=1066 GeV the ‘neutrino’ mass m GeV the ‘neutrino’ mass mνν=10=10-9-9 GeV is GeV is obtained for hobtained for hνν=2=2ππ/15 ln 10 ~ 0.18 and the ‘top quark’ /15 ln 10 ~ 0.18 and the ‘top quark’ mass mmass mtt=10=1022 GeV is obtained for h GeV is obtained for htt=2=2ππ/4 ln 10 ~ 0.68./4 ln 10 ~ 0.68.

All masses relatedAll masses related

Neutrino mass (Majorana) generation Neutrino mass (Majorana) generation canonical warm dark matter candidatecanonical warm dark matter candidate

Intermediate boson mass generation Intermediate boson mass generation

Fermion proper self energies Fermion proper self energies ΣΣ break spontaneously also the break spontaneously also the ‘vertical’ SU(2)‘vertical’ SU(2)LLxU(1)xU(1)Y Y . Schwinger mechanism at work: . 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 massNo generic Fermi (electroweak) scale-remnant of the top quark mass

Spontaneously broken global symmetries: Spontaneously broken global symmetries: generic predictionsgeneric predictions

((We assume that there are nontrivial solution We assume that there are nontrivial solution ΣΣ with no accidental symmetries)with no accidental symmetries)

Spontaneously broken by fermion self energies Spontaneously broken by fermion self energies ΣΣ

Massless Abelian majoron JMassless Abelian majoron J

Exact anomaly free U(1) Exact anomaly free U(1) B-(L+S)B-(L+S) is spontaneously broken is spontaneously broken

by by ΣΣνν

There is a There is a massless neutrino-composite majoronmassless neutrino-composite majoron For interaction strength weak enough For interaction strength weak enough no no

phenomenological dangerphenomenological danger : exchange of massless NG : exchange of massless NG boson leads only to a spin-dependent tensor potential boson leads only to a spin-dependent tensor potential with a 1/rwith a 1/r33 fall off fall off

BUT: If there are neutrino oscillations, there is the BUT: If there are neutrino oscillations, there is the classical majoron field ! (L. Bento, Z. Berezhiani)classical majoron field ! (L. Bento, Z. Berezhiani)

Weinberg-Wilczek axion aWeinberg-Wilczek axion a

Symmetry generated by BSymmetry generated by B55-4S or B-4S or B55-(L-(L55-L) has -L) has QCD QCD

anomalyanomaly (i.e. is explicitly broken) and is spontaneously (i.e. is explicitly broken) and is spontaneously broken by both lepton and quark massesbroken by both lepton and quark masses

Canonical dark matter candidateCanonical dark matter candidate

Axion mass is Axion mass is mmaa ~ m ~ mππ f fππ / / ΛΛg.f.d.g.f.d.

Invisibility requires Invisibility requires ΛΛg.f.d. g.f.d. > 10> 1066 TeV TeV

ConclusionsConclusions

One free parameter: Either right or plainly wrongOne free parameter: Either right or plainly wrong Hard to solve (1Hard to solve (1stst Weinberg’s law: “You will get Weinberg’s law: “You will get

nowhere by churning equations.” )nowhere by churning equations.” ) Nobody knows how to put the model on the latticeNobody knows how to put the model on the lattice Dynamical (shining or dark) mass generation (all masses Dynamical (shining or dark) mass generation (all masses

in principle related)in principle related) Fixed neutrino patternFixed neutrino pattern Massless NG majoronMassless NG majoron Fixed pattern of pseudo-Goldstone bosonsFixed pattern of pseudo-Goldstone bosons Find other robust low-energy manifestation(s) of the Find other robust low-energy manifestation(s) of the

model ???model ???