# CUSTODIAL SYMMETRY IN THE STANDARD MODEL AND BEYOND V. Pleitez Instituto de Física Teórica/UNESP Modern Trends in Field Theory João Pessoa ─ Setembro 2006.

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CUSTODIAL SYMMETRY IN THE STANDARD MODEL AND BEYOND V. Pleitez Instituto de Física Teórica/UNESP Modern Trends in Field Theory João Pessoa ─ Setembro 2006

OUTLINE  What is the Custodial Symmetry?  Standard Model  3-3-1 Models ...  Conclusions

Automatic or Accidental (Global) Symmetry, are not imposed, consequence of:  Lorentz invariance  Gauge invariance  Renormalizability  Representation content of the model Examples: Baryon number, Lepton number, and approximate chiral symmetries:

STANDARD MODEL’s THREE GENERATIONS:

The fermion mass problem:  Why do weak isospin partners have different masses?  Why are quark and lepton masses split?  Why there is a mass hierarchy between generations, and  Why is there a mixing angle hierarchy in quarks but not in leptons?

PDG 2004 Weak isospin partners u d

The SM answer: the gauge group permits a different Yukawa coupling constantto set each fermion mass and mixing angle. The SM accomodates the problem but does not explain it. this suggests that it should be correlated with the breakdown of a larger symmetry. Weak isospin partners have different masses because the left- and right-handed fields are not related by any symmetry. Before SSB: After SSB: ? u,d generic quarks

a few percent (At the tree level) (Radiative corrections)  -parameter in the SM

a few percent The first is a clear violation of isospin The second one is a consequence of isospin [SU(2)] conservation can be made compatible ? How the following experimental facts The accidental SU(2) (global) symmetry, for its protective functions is called: CUSTODIAL SYMMETRY. (It may, or not, be the isospin.)

STANDARD MODEL’s GAUGE SYMMETRIES: SSB

SSB: ONE SCALAR DOUBLET SCALAR POTENTIAL: 2-doublet:

Global and local: g’=0 (sin  W =0) Global

g’=0

(broken) (conserved) When g’≠0 At the tree level this is a zero order correction: g 0,g’ 0 W 1,W 2,W 3  Z are in a triplet of SU(2) L+R

Fermion loops Radiative correction due to gauge and Higgs bosons are proportional to g’ 2 (or sin 2  W ). For instance, loops of Higgs Due to unbroken SU(2) L+R in the limit g’→0 (sin 2  W =0) the custodial symmetry protects the tree level relation  =1. This correction vanishes in the limit m t =m b

Quark masses in the SM (Yukawa couplings) (we have omitted summation symbols) If all Yukawa couplings  ’s are different the generated Dirac masses in eachcharge sector (weak isospin partners) are different and arbitrary.

Defining the 2-doublets: in the quark sector and in the lepton sector Right-handed neutrinos are needed Extending the custodial symmetry to the Yukawa sector

The Yukawa interactions are now, manisfestly invariant under SU(2) L  SU(2) R, This is a consequence of the custodial SU(2) L+R symmetry

g’≠0 (sin  W ≠0), i.e, turn on the electromagnetic interactions and, as usual

or it is possible that the source of the breakdown of the SU(2) L+R symmetry in the gauge-Higgs bosons system is different from the breakdown of that symmetryin the fermion-Higgs sector. In the latter one, NEW PHYSIC may be at work. M&P (hep-ph/0607144 ): Assume that

New Physics:  New quark singlets of SU(2) L  U(1) Y (generalized seesaw mechanism)  Multi-Higgs doublet extensions  Radiative corrections of a Z’ vector boson  The seesaw mechanism for neutrinos is mandatory (for details see hep-ph/0607144 )

 generalized seesaw mechanism

 Multi-Higgs doublet extensions

Radiative corrections of a Z’ vector boson Breaks the deneracy of charged lepton and neutrino masses

Also in the context of the SM, multi-Higgs extensions The most general scalar structure which naturally (follows from the group structure and representation content... (Glashow-Weinberg)Added for unification at 10 15 GeV Manohar & Wise, hep-ph/0606172 And...

BEYOND THE STANDARD MODEL

In the context of the standard model: No attempt is made to explain the number of fermion generations from the viewpoint of anomaly cancelation: each generation is anomaly free. Also sin 2  W is a completely arbitrary parameter Among other open problems, the SM does not give an answer to the questions: Why three generations? Why sin 2  W is near ¼?

There are only three active sequential generations (LEP):

PDG 2004 sin 2  W (M Z )=0.231 20(15) The history of the value of sin 2  W until 1989 Just an accident?

If sin 2  W  1/4 is not na accident there must be an SU(3) symmetry at the TeV scale sin 2  W (µ)=1/4 but sin 2  W (M Z )=0.23120(15) By choosing appropriately the representation content of the model: The anomaly cancelation plus the property of asymptotic freedom of QCD the number of generations allowed is three and only three Both problems have answers in the so called 3-3-1 models. SU(3) C  SU(2) L  U(1) Y  SU(3) C  SU(3) L  U(1) X STANDARD MODEL3-3-1 MODELS SU(3) L symmetry at an energy scale v  of the order of TeV

New quarks have masses proportional to v  The neutral vector boson Z’ has a mass proportional to v  and also Z’ prime has a mixing with Z of the SM  v  at the TeV scale Goldberger-Treimam Relation valid in the m 2  =0 (chiral limit) D&M&P: PRD73, 113004 (2006); PL B637, 85 (2006) v   G F at the Fermi scale (weak interactions) 3-3-1 models have an approximate SU(2) L+R custodial symemtry

Ths condition is valid if, and only if, At the tree level (v  >1 TeV), sin  <<1

ILC e+e-  H 1 H 2 (Cieza Montalvo-Tonasse, PRD71, 095015) ?

Little Higgs, 5D composite Higgs Higgsless models,Little Higgs and 5D composite models: SU(2) that protects  from radiative corrections can also protect the Zbbbar coupling. Agashe et al. hep-ph/0605341....in a Randall-Sundrum scenarios the SU(2) L  SU(2) R and left-right symmetries can be used to make the tree level contributions to the T parameter and the anomalous couplings of the b-quark to the Z very small... M. Carena, et al., hep-ph/0607106

Conclusions  The difference on the weak isospin partners’s masses may be a signal of NEW PHYSICS  Right-handed neutrinos have to added  The seesaw mechanism have to be implemented  Custodial symmetry is important, both in the SM and beyond