We calculate the rate for the decay B u → lνγ using the light cone QCD sume rules. We find Br(B u → lνγ) ≃ 2 · 10 −6 . The results are used to test the applicability of the constituent quark model approximation to the same process.The latter estimate is proportional to 1/m 2 u , where m u ≃Λ u is the "constituent quark mass", indicating that the process is of long distance type. We find that the two approaches yield similar results for the total rate with the choice m u ≃ 480 MeV . This indicates that the constituent quark model may be used for estimates of the radiative "annihilation" contribution to this and other radiative decays. We point out that this decay may be useful for the measurement of |V ub |.

We calculate all radiative corrections to one-loop order for the main decay of the top quark, t-+ b + W y in the standard model, retaining exact dependence on all masses. For m t -150 GeV and MH = 100 GeV we find a -2.9% ( -6.9%) correction with a very weak dependence on the Higgs-boson mass, in renormalization schemes that use a, GF, and Mz (GF, MW, and Mz) as input parameters. Out of the above results, -8.5% is due to QCD. The m t and MH dependence is given up to 300 and 1000 GeV, respectively. The inadequacy of a leading m t calculation is pointed out.PACS numbers: 14.80.Dq, ll.10.Gh, 12.15Ji, 12.38.Bx The top quark, according to recent analyses, is around the corner. From Collider Detector at Fermilab experiments, x m t > 89 GeV, and a maximum-likelihood analysis of recent data 2 has given the most likely value of m t -150 GeV. Other studies 3 prefer m t~~ 130 GeV, while a most recent analysis 4 of some-but not all -higher-order (beyond one-loop) effects shows reasonable probability distributions up to m, --300 GeV. Within the framework of the standard model (SM) discussed here, the main decay of the top quark is t-+ bW, with a tree-level width given byGo s =mb+m l f -2Mjy-\ z , M w and the square of the Weinberg angle is defined as s w = 1 -Mw/Mz.Once the top quark is discovered more accurate experiments will search for radiative corrections to the tree-level width. We present here the full radiative corrections to one-loop order to the main decay mode t-+ bW.The motivation for this work should be clear. Since the top quark has a unique mass scale, being (very likely) the heaviest in the SM, precise tests of its properties against the predictions of the SM represent a unique opportunity to search for the effects of mass scales beyond the SM. Radiative corrections are, of course, powerful tests of gauge theories. Furthermore, the mixing angle V t b must be deduced from experiments by studying the decays of the top quark. At this point we remark that while the quantum chromodynamics (QCD) part of our calculation confirms previous results, 5,6 the electroweak (EW) component of the radiative corrections has not been presented in full. Only leading results valid in the limit ra, ^>A/V,M// have been previously presented. 6 The leading m t calculation fails to describe the correct dependence on the relevant masses, and does not reproduce the exact results even for high m t and low A///, as is shown below.Before the current lower limit on m t was established, a complete first-order calculation of W + -+tb had been presented in Ref. 7. We have independently done that calculation and will adopt the notation of Ref. 7, hereafter referred to as DS (Denner and Sack), and emphasize all the necessary modifications needed for the transformation from W-* tb to t -* Wb, Define the relative correction a-(r-r 0 )/ro,where F is the width including first-order, i.e., one-loop, corrections. Then, the total correction can be separated asThe EW correction is further given aswith contributions from fermion and W-boson wavefunction...

%'e study CP asymmetries in 8 -h~-decays, where the hadronic states h = p p, KKvr, vr+7r K+K, etc. , and h = m+vr, K+K, 2(vr+7r ), etc. , are taken on the resonances 71, and y,o, respectively. The relatively large g, and g,o decay widths, of aboot 10 -15 MeV, provide the necessary absorptive phase in the interference between the resonance (going through b~ccd) and the background (through b~uud) contributions to the amplitude.Large asymmetries of order 10% or more are likely in some modes.

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~ <

We find a large CP violation effect within the two-Higgs-doublet model for the reaction e+e-+ tUf" at future linear colliders. The CP asymmetry arises already at the tree level as a result of interference between diagrams with Ho emission from t (and q and its emission from a 2' and can be about lo-20 %. In the best case one needs a few hundred tEHO events to observe CP violation at the 3c, level.PACS number(s): 12.6O.Fk, 11.30.Er, 13.65.+i