Longitudinal part of the resonanceW-boson propagator

Abstract

We prove that the coefficient of the longitudinal part of the W-boson propagator close to resonance is equal to 1 /( M& + i e , ), where eL is proportional to squares of masses of those fermions that the W can decay to. Consequently, the full propagator has a non-gGV part that differs from the commonly used form, even in the limit of vanishingly small fermion masses.PACS number(s): 14.70.Fm, 13.38.+BeThe resonance Breit-Wigner propagator of vector bosons has been repeatedly discussed in the literature [I].Most, but not all [2], studies concentrate on the part proportional to -gpv which is Discussions concentrate on renormalization, renormalization schemes, pole position, and whether one should use a 4 2-dependent or 4 2-independent width, E,=T~'/M, or e T = r M W , respectively. We will not dwell upon the above issues here, but rather prove that the commonly written form [3] for the full propagator in the unitary gauge, which is an obvious generalization of the nonresonance W propagator (E,=O), treats the longitudinal part incorrectly. Our main concern is the situation near resonance, where we find that the correct form of the propagator is where the "longitudinal width" is proportional to squares of fermion masses to which the W decays:Eq. (3) differs significantly from Eq. (2). The discussion will also be valid for Z bosons up t o complications due t o y -Z mixing.In most cases one is not sensitive to the qpqv part of the propagator in view of its coupling t o light fermion masses on at least one end, i.e., either at the production or the decay vertex. However, one can encounter a scenario which depends crucially on a knowledge of that part. Let us now describe such a situation, in which an observable is proportional t o ImG,, where the propagator is decomposed into its transverse and longitudinal parts with G, given by Eq. (1). Let us consider [4,5] the CPviolating partial rate asymmetry (PRA) between t +br+v, and i-67-3, with the Weinberg model [6] (WM) of CP violation. A t the lowest order in the weakcoupling constant, and assuming for simplicity that the lowest-mass charged Higgs boson obeys M H + > m , , the P R A is given by the interference between Figs. l(a) and l(b). That interference for t -b T ' V , equals [the integration is from m 2, to ( m, -mb )' I It is interesting t o note that even in the limit E~ <<E,, *present address: SLAC, Stanford, CA 94309. (a (b) +permanent address: Department of Physics, Technion, 32000 FIG. 1. (a) The resonance W diagram for t -b~v . (b) The Haifa, Israel. H + tree diagram for the same process. 0556-282 1/94/49( 1)/289(4)/%06.00 -49 289

Width effects on near threshold decays of the top quarkt→cWW,cZZand of neutral Higgs bosons

“…are the absorptive parts of the transverse and longitudinal vacuum polarization tensor (see e.g., [4,21]). …”

Usingt→bb¯cto search for new physics

“…In particular, if an exchanged particle in the process has a resonance, there is a strong phase associated with the width of that particle. Strong phases originating from particles' widths have been used to generate PRAs in many different systems, including t → bbc [2,24], t → bτ + ν [2,[4][5][6][7]9], and various supersymmetric decays [25][26][27]. In the present calculation, the width of the W provides the required strong phase.…”

“…Other top decays where NP effects have been examined include t → bτ + ν [2][3][4][5][6][7][8][9] and t → W + d k [10].…”

CP violation in top physics

“…only ℑm G L will appear in A τ [158,159]. In fact A τ , obtained from the interference between diagrams (a) and (c) in Fig.…”