Inelastic Channels in the Electroweak Symmetry-Breaking Sector

نویسنده

  • S. G. Naculich
چکیده

It has been argued that if light Higgs bosons do not exist then the self– interactions of W ’s become strong in the TeV region and can be observed in longitudinal WW scattering. We present a model with many inelastic channels in the WW scattering process, corresponding to the creation of heavy fermion pairs. The presence of these heavy fermions affects the elastic scattering of W ’s by propagating in loops, greatly reducing the amplitudes in some charge channels. Consequently, the symmetry–breaking sector cannot be fully explored by using, for example, the WW mode alone; all WW → WW scattering modes must be measured. If light Higgs bosons do not exist, it is believed that elastic longitudinal WW scattering will be enhanced, indicating the presence of new strong interactions at or above 1 TeV. (We useW to denote either theW or Z boson.) It has been claimed that the energy and luminosity of the SSC are large enough that, whatever form the new interactions take, they would be observable inWW two–body interactions via leptonic decays of W ’s. [1] This is called the “no–lose theorem.” Study of the WW mode has been particularly promoted [2] in the context of observing these strong interactions because the standard model background for this mode is small. Recently, Chivukula and Golden have emphasized the possible existence of inelastic channels in the WW scattering process. [3] They studied an O(4) × O(n) model in which the WW interactions are almost entirely inelastic (to n species of pseudo–Goldstone bosons). Consequently, the elastic WW amplitude is reduced, the more so for a larger number n of inelastic channels. (The total event rate for elastic scattering, however, does not decrease as n increases. [4] ) In that model, inelastic scattering leads to a very broad low–energy resonance in the elastic WW scattering amplitudes. In this letter, we present a model with many inelastic channels in the electroweak sector and which has no resonances. In general, the presence of inelastic channels corresponds to additional particles in the theory. Even if the production of these particles is not directly observed, they affect the elastic scattering of W ’s by propagating in loops. These loops necessarily contribute to the imaginary part of the elastic scattering amplitude, which is related by the optical theorem to the total cross section. The loops also contribute to the real part of the elastic amplitude, interfering with the Born contribution. This interference may dramatically reduce the signal in some charge channels, e.g. the WW channel. Other channels may be enhanced, however, both by real and imaginary loop corrections. The model we present below has precisely this behavior. The moral is that to be certain of detecting the symmetry– breaking sector it will be necessary to measure scattering in all the final stateWW modes. 2 The no–lose theorem, with its prediction of strong WW scattering in the absence of a light Higgs resonance, is based on the low–energy theorems for a theory with spontaneously–broken symmetry. The pattern of symmetry breaking for the electroweak sector is SU(2)L × SU(2)R −→ SU(2)V if we assume that it respects a custodial SU(2) symmetry. At energies s≫ M W , the longitudinal vector bosons W correspond, via the equivalence theorem, to the three Goldstone bosons φ resulting from this broken symmetry. The interactions of these Goldstone bosons are described by low–energy theorems, which emerge automatically when we describe this broken symmetry using chiral Lagrangians. In this approach, the Goldstone bosons are parametrized by the matrix Σ = exp ( iτφ f ) , a = 1, 2, 3, (1) where τ are the Pauli matrices. The lowest energy term of the chiral Lagrangian is L = f 2 4 Tr (

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تاریخ انتشار 1992