Jet substructure using semi-inclusive jet functions within SCET

TL;DR

The paper introduces the semi-inclusive fragmenting jet function within Soft Collinear Effective Theory to describe hadron-in-jet observables in inclusive jet measurements. It establishes NLO expressions, a renormalization group framework with timelike DGLAP evolution, and a systematic ln R resummation to NLL_R, enabling NLO+NLL_R predictions. The framework is validated against LHC data, showing excellent agreement and improved description over previous exclusive-jet approaches, while maintaining controlled scale uncertainties. This inclusive, RG-improved approach broadens jet substructure studies and paves the way for extensions to e+e−, ep, and heavy-ion contexts, as well as combining with other resummations.

Abstract

We propose a new method to evaluate jet substructure observables in inclusive jet measurements, based upon semi-inclusive jet functions in the framework of Soft Collinear Effective Theory (SCET). As a first example, we consider the jet fragmentation function, where a hadron $h$ is identified inside a fully reconstructed jet. We introduce a new semi-inclusive fragmenting jet function ${\mathcal G}^h_i(z= ω_J/ω,z_h=ω_h/ω_J,ω_J, R,μ)$, which depends on the jet radius $R$ and the large light-cone momenta of the parton `$i$' initiating the jet ($ω$), the jet ($ω_J$), and the hadron $h$ ($ω_h$). The jet fragmentation function can then be expressed as a semi-inclusive observable, in the spirit of actual experimental measurements, rather than as an exclusive one. We demonstrate the consistency of the effective field theory treatment and standard perturbative QCD calculations of this observable at next-to-leading order (NLO). The renormalization group (RG) equation for the semi-inclusive fragmenting jet function ${\mathcal G}_i^h(z,z_h, ω_J, R,μ)$ are also derived and shown to follow exactly the usual timelike DGLAP evolution equations for fragmentation functions. The newly obtained RG equations can be used to perform the resummation of single logarithms of the jet radius parameter $R$ up to next-to-leading logarithmic (NLL$_R$) accuracy. In combination with the fixed NLO calculation, we obtain NLO+NLL$_R$ results for the hadron distribution inside the jet. We present numerical results for $pp\to(\mathrm{jet}\,h)X$ in the new framework, and find excellent agreement with existing LHC experimental data.

Figures (6)

• Figure 1: Feynman diagrams that contribute to the semi-inclusive quark fragmenting jet function. The quark initiating the jet has momentum $\ell = (\ell^+, \ell^- = \omega, 0_\perp)$, with $\omega = \omega_J/z=\omega_h/(zz_h)$ and $\omega_J$, $\omega_h$ are the jet and hadron energies respectively. Note that the dashed (curly) lines correspond to collinear quarks (gluons).
• Figure 2: The three contributions that need to be considered for the semi-inclusive quark fragmenting jet function: (A) both the quark and the gluon are inside the jet, (B) only the quark is inside the jet, (C) only the gluon is inside the jet.
• Figure 3: Comparison of our numerical calculations (solid blue lines) to the ATLAS experimental data Aad:2011sc (red circles) in proton-proton collisions at $\sqrt{s} = 7$ TeV. Jets are reconstructed using the anti-k$_{\rm T}$ algorithm with $R=0.6$ and $|\eta|<1.2$. The numbers in the square brackets correspond to different jet transverse momentum bins in the range of $25-500$ GeV.
• Figure 4: Comparison of our numerical calculations (solid blue lines) to LHC data in proton-proton collisions at $\sqrt{s} = 2.76$ TeV. The solid red circles correspond to the preliminary ATLAS data form Ref. ATLAS:2015mla and the green triangles are the CMS data from Ref. Chatrchyan:2012gw.
• Figure 5: Ratio of the NLO+NLL$_R$ resummed cross section to the fixed NLO calculation as a function of $z_h$ for two bins of the jet transverse momentum $60<p_T<80$ GeV (left panel) and $260<p_T<310$ GeV (right panel). We choose $\sqrt{s}=7$ TeV, $|\eta|<1.2$ and two phenomenologically relevant values of the jet radius parameter $R=0.6$ (red line) and $R=0.3$ (blue line). In addition, we show the result for $R=0.99$ (black line) illustrating that our new result indeed converges to the NLO result in the limit $R\to 1$.