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 weak scale by dimensional
transmutationtransmutation
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
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
top – anti-top condensatetop – anti-top condensate
large chiral coupling for top leads to large chiral coupling for top leads to large effective attractive interaction for large effective attractive interaction for top quarktop quark
this triggers condensation of top – anti-this triggers condensation of top – anti-top pairstop pairs
electroweak symmetry breaking : electroweak symmetry breaking : effective Higgs mechanism provides mass effective Higgs mechanism provides mass for weak bosonsfor weak bosons
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
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
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 effective interactions in chiral tensor channelchannel
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 !