Two-loop QCD corrections to top quark decay

It is well-known that the top quark is the heaviest fermion in the Standard Model. An immediate consequence of that fact is its very short lifetime which turns out to be shorter than the characteristic timescale of nonperturbative QCD effects. Thanks to this feature, the top behaves almost like a free quark, which is really a unique situation in QCD. Moreover, the process t → bW is an absolutely dominant decay channel. Additional decay channels arise in various extensions of the present Standard Model (like t → bH or t → supersymmetric particles). For these reasons, top physics seems to be a particularly clean laboratory for new physics searches but two complementary pieces of information are necessary. First, we need an accurate experimental determination of the top decay rate, which will be feasible in the future, e.g. at the Next Linear Collider. Also, to fully utilize this measurement it is incredibly important to have theoretical predictions in the framework of the present Standard Model with accuracy matching the experimental precision. Much effort has been invested into studies of radiative corrections to the top quark decay width. The one-loop QCD contribution was computed in [1]. It decreases the tree-level rate by about 8.4%. The electroweak NLO part was evaluated in [2] but its effect turned out to be much smaller — it increases the decay rate by about 2%. Moreover, the electroweak contribution is almost entirely canceled when one takes into account the finite W width [3]. The NNLO QCD contribution has been studied so far in various kinematical limits. For example, there exists a result in zero recoil kinematics with mW set to zero [4], as well as a numerical study done by means of Padé approximations [5]. All these calculations estimate the NNLO QCD contribution at about −2% but, for comparison with planned measurements, a precise and preferably analytical result would be of interest. In the present study we start with the limit of a mas-