Abstract
We present the transverse momentum spectrum for a heavy hadron at threshold in a groomed jet initiated by a heavy quark. The cross section is doubly differential in the energy fraction of an identified heavy hadron in the jet and its transverse momentum measured with respect to the groomed (recoil free) jet axis. The grooming is implemented using a soft-drop grooming algorithm and helps us in mitigating the effects of Non-Global logarithms and pile up. For the particular case of a B meson, we identify two distinct regimes of the transverse momentum spectrum and develop an EFT within the formalisms of Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) for each of these regions. We show how each region can be matched smoothly into the other to provide a prediction for the perturbative transverse momentum spectrum. The EFT also predicts the scaling behavior of the leading non-perturbative power corrections and implements a simple shape function to account for hadronization. We work in the threshold region where the heavy hadron carries most of the energy of the jet since in this regime, we have a very good discriminating power between heavy quark and gluon initiated jets. We observe that the shape of the spectrum is independent of the energy of the jet over a large range of transverse momentum. We propose that this spectrum can be used as a probe of evolution for heavy quark TMD fragmentation function. At the same time, it can be treated as a jet substructure observable for probing Quark-Gluon Plasma (QGP).
Highlights
Functions (PDFs) [5,6,7,8] to what are referred to as Transverse Momentum Dependent PDF’s or TMDPDF’s
We present the transverse momentum spectrum for a heavy hadron at threshold in a groomed jet initiated by a heavy quark
When the color-singlet state is within a final state jet not aligned with the beam, we can likewise extend the notion of collinear Fragmentation Functions (FFs) to include the relative motion of the hadron with respect to all of the other jet constituents in the form of TMDFF’s
Summary
Consider the simple case of e+e− collisions where the hard annihilation creates a heavy quark, anti-quark pair. The center of mass energy is much larger than the mass of the quark so that we get two highly boosted partons moving back to back. We isolate a hemisphere jet initiated by heavy quark using a suitable jet algorithm. The heavy quark showers and eventually hadronizes. The jet is groomed with a soft-drop grooming algorithm. The heavy hadron is identified and we measure the energy fraction, z, of the hadron with respect to the jet energy. We measure its transverse momentum (q⊥) with respect to the axis of the groomed jet (which is recoil free). We are interested in the regime where the heavy hadron carries most of the jet energy (z ∼ 0.8)
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