Abstract
In this paper, we study the fragmentation of a heavy quark into a jet near threshold, meaning that final state jet carries most of the energy of the fragmenting heavy quark. Using the heavy quark fragmentation function, we simultaneously resum large logarithms of the jet radius R and 1 − z, where z is the ratio of the jet energy to the initiating heavy quark energy. There are numerically significant corrections to the leading order rate due to this resummation. We also investigate the heavy quark fragmentation to a groomed jet, using the soft drop grooming algorithm as an example. In order to do so, we introduce a collinear-ultrasoft mode sensitive to the grooming region determined by the algorithm’s zcut parameter. This allows us to resum large logarithms of zcut/(1 − z), again leading to large numerical corrections near the endpoint. A nice feature of the analysis of the heavy quark fragmenting to a groomed jet is the heavy quark mass m renders the algorithm infrared finite, allowing a perturbative calculation. We analyze this for EJR ∼ m and EJR » m, where EJ is the jet energy. To do the latter case, we introduce an ultracollinear-soft mode, allowing us to resum large logarithms of EJR/m. Finally, as an application we calculate the rate for e+e− collisions to produce a heavy quark jet in the endpoint region, where we show that grooming effects have a sizable contribution near the endpoint.
Highlights
Jets that contain a heavy quark [6]
We show the comparison between fragmentation function to a jet (FFJ) and fragmentation function to a groomed jet (FFGJ) for top quark jets when there is a large difference between EJ R and heavy quark mass mt
We studied the process of a heavy quark fragmenting into a jet in the endpoint region where the jet carries almost all of the energy of the initiating heavy quark, i.e., z ∼ 1 where z is the jet energy fraction of the fragmenting parton
Summary
If we consider a jet with a small radius (R), the relevant dynamics are in general described by collinear interactions. At one loop the splitting of a heavy quark to a jet is divided into two processes, Q → JQ + g and Q → Jg + Q, where Ji denotes the jet containing the parton i. The fragmenting function can be described by the dominant process Q → JQ + g In this case the jet JQ takes most of the energy of the mother parton Q, while radiation out of the jet will be carried by gluons with energy ∼ EJ (1 − z). Similar to with the massless parton case [20], the heavy quark FFJ can be factorized into the collinear and the csoft parts as z goes to 1
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