Spinning gluons from the QCD light-ray OPE

Published for SISSA by Springer Received: May 2, 2022 Accepted: July 17, 2022 Published: August 23, 2022 Spinning gluons from the QCD light-ray OPE a Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China b SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, U.S.A. E-mail: , , Abstract: We study the transverse spin structure of the squeezed limit of the three-point energy correlator, hE(~n1 )E(~n2 )E(~n3 )i. To describe its all orders perturbative behavior, we develop the light-ray operator product expansion (OPE) in QCD. At leading twist the iterated OPE of E(~ni ) operators closes onto light-ray operators O[J] (~n) with spin J, and transverse spin j = 0, 2. We compute the E(~n1 )E(~n2 ), E(~n1 )O[J] (~n2 ) and O[J1 ] (~n1 )O[J2 ] (~n2 ) OPEs as analytic functions of J, which allows for the description of arbitrary squeezed limits of N -point correlators in QCD. We use these results with J = 3 to reproduce the perturbative expansion in the squeezed limit of the three-point correlator, as well as to resum the leading twist singular structure for both quark and gluon jets, including transverse spin contributions, as required for phenomenological applications. Finally, we briefly comment on the transverse spin structure at higher twists, and show that to all orders in the twist expansion the highest transverse spin contributions are universal between quark and gluon jets, and are descendants of the leading twist transverse spin-2 operator, allowing their resummation into a simple two-dimensional Euclidean conformal block. Due to the general applicability of our results to arbitrary correlation functions of energy flow operators, we anticipate that they can be widely applied to improving our understanding of jet substructure at the LHC. Keywords: Factorization, Renormalization Group, Jets and Jet Substructure ArXiv ePrint: 2104.00009 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP08(2022)233 JHEP08(2022)233 Hao Chen,a Ian Moultb and Hua Xing Zhua Contents 1 Introduction 1 2 The three-point energy correlator 3 twist expansion in the squeezed limit Integrand level expansion Quark and gluon jets in QCD N = 4 SYM 5 7 8 13 4 Leading twist calculation from splitting amplitudes 14 5 The light-ray OPE in QCD 5.1 Review of light-ray operators 5.2 The light-ray OPE 5.2.1 E(~n1 )E(~n2 ) OPE ~ [J] (~n2 ) OPE 5.2.2 E(~n1 )O ~ [J1 ] (~n1 )O ~ [J1 ] (~n2 ) OPE 5.2.3 O 5.3 Higher-point OPEs at leading twist 17 17 19 20 22 23 26 6 Resummation in the squeezed limit 27 7 Conclusions 30 1 Introduction The fundamental objects in the study of QCD at collider experiments are energy flow operators [1–8] E(~n) = lim Z∞ r→∞ dt r2 ni T0i (t, r~n) . (1.1) 0 Here Tµν is the stress tensor of the theory, and ~n is a unit vector specifying the direction of the detector. The standard approach to collider experiments is the direct measurement of such operators at event level, from which one can reconstruct the energy and momentum of scattered particles, and any associated observable, on an event-by-event basis. However, from the perspective of analytically understanding energy flow from perturbative calculations, this standard approach turns out to be technically inconvenient. Event-by-event measurements of energy flow correspond to the insertion of delta function operators, δ(E~n −E(~n)), which introduce complicated constraints on the perturbative phase –1– JHEP08(2022)233 3 The 3.1 3.2 3.3 –2– JHEP08(2022)233 space, generically preventing analytic results. An alternative approach is to measure and compute correlation functions of the energy flow operators over an ensemble of scattering events, hE(~n1 )E(~n2 ) · · · E(~nk )i. The complete set of such correlation functions encodes the same amount of information as event-by-event observables. However, by encoding this information in correlation functions, each of which has well defined symmetry properties, information about the properties of energy flow in collisions is reorganized in a manner that makes manifest the symmetries of the underlying field theory, significantly simplifying calculations. Furthermore, in practice, correlation functions with only a few operators already provide important information on the distribution of energy flow [9]. The one-point correlator, hE(~n)i, and two-point correlator, hE(~n1 )E(~n2 )i, were originally proposed as event shape observables for testing QCD [10, 11]. In recent years there has been a resurgence of interest in such observables, largely due to the observation that energy correlators admit an OPE description in terms of light-ray operators in a conformal field theory [5]. Using the light-ray operator description, a series of remarkable techniques have been developed to compute the two-point energy correlators (EEC) and related correlators analytically to next-to-next-leading order (NNLO) in N = 4 super Yang-Mills (SYM) theory [6, 7, 12–14], without ever encountering infrared divergences in the intermediate steps of the calculation. At the same time, advances in techniques for multi-loop calculations have allowed the analytic calculation of the EEC at NLO in QCD [15–17], and numerical calculation at NNLO [18, 19]. There has also been substantial interest in the back-to-back limit of the EEC, which is closely related to more familiar Sudakov dynamics. Resummation of the large logarithms in this limit has been achieved at N3 LL [20, 21], and generalizations to pp [22] and ep [23, 24] colliders have also been proposed. The analytic results of [13] have also helped to understand the structure of subleading power corrections to the EEC in the back-to-back limit [25]. Of particular recent interest at the Large Hadron Collider (LHC) is the understanding of the flow of energy at small angles within individual jets, which goes under the name of jet substructure (see [26–28] for reviews). Jet substructure provides new ways to study QCD at high energies, as well as novel search strategies for beyond the Standard Model physics. In terms of the correlation functions hE(~n1 )E(~n2 ) · · · E(~nk )i, jet substructure is the study of the operator product expansion (OPE) limit, where the ~ni are collinear and lie within a single jet. This perspective on jet substructure has been proposed and developed in a recent series of papers [9, 29–31], building on the seminal work of Hofman and Maldacena [5], as well as the works of [6, 7, 12]. Formulating jet substructure as the study of the OPE limit of energy flow operators (or more generally light-ray operators [8]), places jet substructure in a more general context, and enables the use of a wide variety of powerful techniques. In particular, light-ray operators have played a central role in many recent developments in the conformal bootstrap program, leading to their intensive study. For jet substructure, where one is in (...truncated)