Chiral freedomChiral freedomand the and the scale ofscale of

weak interactionsweak interactions

proposal for solution of proposal for solution of gauge hierarchy problemgauge hierarchy problem model without fundamental scalarmodel without fundamental scalar non-local interaction in chiral tensor non-local interaction in chiral tensor

channelchannel no mass termsno mass terms chiral couplings to quarks and leptonschiral couplings to quarks and leptons chiral couplings are asymptotically freechiral couplings are asymptotically free weak scale by dimensional transmutationweak scale by dimensional transmutation

Non-local interaction inNon-local interaction inchiral tensor channelchiral tensor channel

non – local interaction

f : chiral coupling for top and bottom quarks

non-local interactions in non-local interactions in chiral tensor channelchiral tensor channel

Lorentz invariantLorentz invariant Could be generated by exchange of chiral Could be generated by exchange of chiral

tensor fields – not necessary and not used tensor fields – not necessary and not used herehere

Chiral coupling Chiral coupling ff is dimensionless is dimensionless Generalization to chiral couplings for lighter Generalization to chiral couplings for lighter

quarks : chiral couplings described by 3x3 quarks : chiral couplings described by 3x3 matrices , similar to Yukawa couplings in SMmatrices , similar to Yukawa couplings in SM

convenient for graphicalrepresentation ofchiral vertex

f f f f

classical dilatation classical dilatation symmetrysymmetry

action has no parameter with action has no parameter with dimension massdimension mass

all couplings are dimensionlessall couplings are dimensionless

flavor and CP violationflavor and CP violation chiral couplings can be made chiral couplings can be made

diagonal and real by suitable phases diagonal and real by suitable phases for fermionsfor fermions

Kobayashi – Maskawa MatrixKobayashi – Maskawa Matrix

same flavor violation and CP same flavor violation and CP violation as in standard modelviolation as in standard model

asymptotic freedomasymptotic freedom

evolution equations for top evolution equations for top couplingcoupling

fermion anomalous dimension

tensor anomalous dimension

no vertex correction

asymptotic freedom !Similar observation in abelian model for chiral tensors :Avdeev,Chizhov ‘93

dimensional dimensional transmutationtransmutation

Chiral coupling for top grows large Chiral coupling for top grows large at chiral scale at chiral scale ΛΛchch

This sets physical scale : dimensional This sets physical scale : dimensional transmutation -transmutation -

similar to similar to ΛΛQCD QCD in strong QCD- gauge interactionin strong QCD- gauge interaction

spontaneous electroweakspontaneous electroweaksymmetry breakingsymmetry breaking

top – anti-top condensatetop – anti-top condensate large chiral coupling for top leads to large large chiral coupling for top leads to large

effective attractive interaction for top effective attractive interaction for top quarkquark

this triggers condensation of top – anti-top this triggers condensation of top – anti-top pairspairs

electroweak symmetry breaking : effective electroweak symmetry breaking : effective Higgs mechanism provides mass for weak Higgs mechanism provides mass for weak bosonsbosons

effective Yukawa couplings of Higgs give effective Yukawa couplings of Higgs give mass to quarks and leptonsmass to quarks and leptons

cf : Miranski ,Tanabashi, Yamawaki; Bardeen, Hill, Lindner

Induced interactions in Induced interactions in scalar channelscalar channel

NJL – type interaction

effective interactionseffective interactions

introduce composite field for top- introduce composite field for top- antitop bound stateantitop bound state

plays role of Higgs fieldplays role of Higgs field new effective interactions involving new effective interactions involving

the composite scalar the composite scalar φφ effective scalar-top Yukawa couplingeffective scalar-top Yukawa coupling

Running effective Running effective couplingscouplings

fh

scalar mass term m2

Ratio between top quark mass and W-boson mass is predictable in this model

phenomenologyphenomenology

chironschirons possibility of observable bound states in possibility of observable bound states in

chiral tensor channelchiral tensor channel irreducible representation for anti-irreducible representation for anti-

symmetric tensor fields has three symmetric tensor fields has three componentscomponents

in presence of mass : little group SO(3)in presence of mass : little group SO(3) with respect to SO(3) : anti-symmetric with respect to SO(3) : anti-symmetric

tensor equivalent to vectortensor equivalent to vector massive chiral tensors = massive spin massive chiral tensors = massive spin

one particles : chironsone particles : chirons

new resonances at LHC ?new resonances at LHC ?

production of massive chirons at LHC ?production of massive chirons at LHC ? signal : massive spin one resonancessignal : massive spin one resonances rather broad : decay into top quarksrather broad : decay into top quarks relatively small production cross section : relatively small production cross section :

small chiral couplings to lowest generation small chiral couplings to lowest generation quarks , no direct coupling to gluonsquarks , no direct coupling to gluons

perhaps no resonances – just additional perhaps no resonances – just additional effective interactions in chiral tensor channeleffective interactions in chiral tensor channel

composite scalarscomposite scalars

two composite Higgs doublets expectedtwo composite Higgs doublets expected mass 400 -500 GeVmass 400 -500 GeV loop effects ?loop effects ?

conclusionsconclusions chiral tensor model interactions chiral tensor model interactions

offer interesting solution of gauge offer interesting solution of gauge hierarchy problemhierarchy problem

phenomenology needs to be phenomenology needs to be explored !explored !

less couplings than in standard less couplings than in standard model predictivity !model predictivity !