We use the framework of a relativistic constituent quark model to study the semileptonic transitions of the Bc meson into (cc) charmonium states where (cc) = ηc (We compute the q 2 -dependence of all relevant form factors and give predictions for their semileptonic Bc decay modes including also their τ -modes. We derive a formula for the polar angle distribution of the charged lepton in the (lν l ) c.m. frame and compute the partial helicity rates that multiply the angular factors in the decay distribution. For the discovery channel Bc → J/ψ(→ µ + µ − )lν we compute the transverse/longitudinal composition of the J/ψ which can be determined by an angular analysis of the decay J/ψ → µ + µ − . We compare our results with the results of other calculations.
The analytic expressions for the production cross sections of polarized bottom and top quarks in e + e − annihilation are explicitly derived at the one-loop order of strong interactions. Chirality-violating mass effects will reduce the longitudinal spin polarization for the light quark pairs by an amount of 3%, when one properly considers the massless limit for the final quarks. Numerical estimates of longitudinal spin polarization effects in the processes e + e − → bb(g) and e + e − → tt(g) are presented. * supported in part by the BMFT, Germany under contract 06MZ730. † e-mail address: pilaftsis@vax2.rutherford.ac.uk ‡ e-mail address: tung@evalvx.ific.uv.es 1 Precision tests at LEP have so far shown great agreement with electroweak theory giving strong experimental support for the Standard Model (SM ) [1]. However, quantum chromodynamics (QCD), though being non-convergent or weakly convergent in the perturbative expansion at low energies, provides an interesting testing ground at the Z peak to probe many field-theoretical aspects of this asymptotically free theory. In this note, we will study the longitudinal polarization asymmetry P L of the bottom quark (b) and top quark (t) produced through the e + e − annihilation reaction at LEP and future colliders. A suprising outcome of our calculations is that the O(α s ) correction of P L in the limit m q → 0 differs substancially from the corresponding result of a theory where m q was originally set to zero. In the following, we will call such a theory a naive massless theory, since it leads to the wrong result for the O(α s ) contributions to P L for the processAt the one-loop QCD level, thefunctions relevant for the production of massive quarks can be written down as follows:whereand the form factors A, B, C and D have been calculated by using dimensional regularization. These form factors are given by2The function F (v) given in Eqs. (3) and (5) is defined aswhere v = √ 1 − ξ with ξ = 4m 2 q /q 2 . To remove the UV divergences in the vertex functions Eqs. (1) and (2), we have considered the wave-function renormalization constant of the final quarksand renormalized the form factors A and C according the prescriptionOur final result is also valid when employing dimensional reduction methods for the calculation of QCD quantum corrections [2]. In addition to the UV divergences, one encounters in Eqs. (3)-(6) infrared (IR) singularities due to the soft-gluon part of the one-loop contributions, which will exactly cancel with those of the real-gluon emission graphs at the same order of strong interaction.Decomposing the hadronic tensors in terms of their Lorentz structure and considering the one-loop QCD corrections, one getswhere the superscripts refer to the parity-parity combination of the corresponding squared amplitudes. A straightforward computation of the hadronic tensors involving real-gluon emission gives3where y = 1 − 2p 1 · q/q 2 and z = 1 − 2p 2 · q/q 2 are kinematical variables. Note that gluon-mass effects can safely be neglected in the computation...
Using the helicity method we derive complete formulas for the joint angular decay distributions occurring in semileptonic hyperon decays including lepton mass and polarization effects. Compared to the traditional covariant calculation the helicity method allows one to organize the calculation of the angular decay distributions in a very compact and efficient way. In the helicity method the angular analysis is of cascade type, i.e. each decay in the decay chain is analyzed in the respective rest system of that particle. Such an approach is ideally suited as input for a Monte Carlo event generation program. As a specific example we take the decay Ξ 0 → Σ + + l − +ν l (l − = e − , µ − ) followed by the nonleptonic decay Σ + → p + π 0 for which we show a few examples of decay distributions which are generated from a Monte Carlo program based on the formulas presented in this paper. All the results of this paper are also applicable to the semileptonic and nonleptonic decays of ground state charm and bottom baryons, and to the decays of the top quark.
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases of their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology with an irreducible loop addition.
We calculate the electroweak and finite width corrections to the decay of an unpolarized top quark into a bottom quark and a W -gauge boson where the helicities of the W are specified as longitudinal, transverse-plus and transverse-minus. Together with the O(αs) corrections these corrections may become relevant for the determination of the mass of the top quark through angular decay measurements.
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