Resummed mass distribution for jets initiated by massive quarks

AbstractWe resum the invariant mass distribution of jets initiated by massive quarks in next-to-leading logarithmic approximation and beyond in heuristic way. We find that the inclusion of mass terms, in the N-moment space, results in the universal factor δN(Q2;m2)=exp[∫01dzzm2Q2(N−1)−11−z{−∫m2(1−z)2m2(1−z)dk⊥2k⊥2A[αS(k⊥2)]−B[αS(m2(1−z))]+D[αS(m2(1−z)2)]}], taking into account dead-cone effects and soft radiation characteristic of massive charges. This factor multiplies the massless jet distribution function JN(Q2). In the above equation the variable N is rescaled by the mass correction parameter m2/Q2≪1 with respect to the standard massless case, being m the quark mass and Q the hard scale. The functions A(αS) and B(αS) appear with a minus sign suppressing collinear effects at very large N≳Q2/m2, as expected. In the same region, soft radiation not collinearly enhanced, characteristic of on-shell massive charges, makes its appearance with the function D(αS). Phenomenological applications, such as the resummation of b→clν decay spectra or the inclusion of beauty mass effects in t→bW decays, are briefly sketched