Transverse Momentum Spectra at Threshold for Groomed Heavy Quark Jets

TL;DR

The paper develops a two-region EFT description (SCET+HQET) of the heavy-hadron transverse momentum spectrum inside a soft-drop groomed jet initiated by a heavy quark, focusing on the threshold region where the hadron carries most of the jet energy. It derives factorization theorems and performs resummation of large logarithms in region 2 ($q_{\perp} \gg m(1-z)$) and region 1 ($q_{\perp} \sim m(1-z)$), then smoothly matches the two regimes to predict the perturbative $q_{\perp}$ spectrum. Non-perturbative effects are incorporated via a simple shape-function model, predicting leading power corrections and a hadronization shift in the energy fraction $z$, with parameters fitted to simulations. Comparisons with Pythia show good agreement in the EFT-valid regions, reinforcing the result that the spectrum shape is largely jet-energy independent over a wide range and offering a potential probe of heavy-quark TMD fragmentation evolution and a jet-substructure observable for QGP studies. The work lays groundwork for higher-order refinements and broader applications in heavy-flavor jet phenomenology.

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 Collineat 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).

Figures (5)

• Figure 3: Profiles in the collinear soft scale $\mu_S$, which smoothly turn off the resummation going from region 2 to region 1. The variation in the profiles probes the error band due to missing higher order corrections
• Figure 4: Comparison of the analytical result(with error bands) at LL+LO accuracy with parton level Pythia with a jet energy $E_J =Q/2 \sim 50 GeV$.
• Figure 5: Comparison with parton level Pythia for different values of jet energy $E_J =Q/2$. As the jet energy increases, the EFT is valid till a higher value of $q_{\perp}$. This plot vividly demonstrates the Q independence of the shape at low $q_{\perp}$.
• Figure 6: Hadronization effects in Pythia versus the simplified prescription of Eq.(\ref{['eq:hadronizationeffects']}). The results are shown for various values of the momentum fraction, particularly we choose $z=0.7,0.75,0.8,$ and $0.85$. We find that, as expected, the simple shift works better for values away from the energy threshold, $1-z_{cut}$.
• Figure 7: One loop diagrams for the HQET jet function.