Abstract:We consider the class of jet shapes known as angularities in dijet production at hadron colliders. These angularities are modified from the original definitions in e + e − collisions to be boost invariant along the beam axis. These shapes apply to the constituents of jets defined with respect to either k T -type (anti-k T , C/A, and k T ) algorithms and conetype algorithms. We present an SCET factorization formula and calculate the ingredients needed to achieve next-to-leading-log (NLL) accuracy in kinematic regions where nonglobal logarithms are not large. The factorization formula involves previously unstudied "unmeasured beam functions," which are present for finite rapidity cuts around the beams. We derive relations between the jet functions and the shape-dependent part of the soft function that appear in the factorized cross section and those previously calculated for e + e − collisions, and present the calculation of the non-trivial, color-connected part of the soft-function to O(α s ). This latter part of the soft function is universal in the sense that it applies to any experimental setup with an out-of-jet p T veto and rapidity cuts together with two identified jets and it is independent of the choice of jet (sub-)structure measurement. In addition, we implement the recently introduced soft-collinear refactorization to resum logarithms of the jet size, valid in the region of non-enhanced non-global logarithm effects. While our results are valid for all 2 → 2 channels, we compute explicitly for the qq → qq channel the color-flow matrices and plot the NLL resummed differential dijet cross section as an explicit example, which shows that the normalization and scale uncertainty is reduced when the soft function is refactorized. For this channel, we also plot the jet size R dependence, the p cut T dependence, and the dependence on the angularity parameter a.

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We analyze the recent LHCb measurement of the distribution of the fraction of the transverse momentum, z(J/ψ), carried by the J/ψ within a jet. LHCb data is compared to analytic calculations using the fragmenting jet function (FJF) formalism for studying J/ψ in jets. Logarithms in the FJFs are resummed using DGLAP evolution. We also convolve hard QCD partonic cross sections, showered with PYTHIA, with leading order Non-Relativistic Quantum Chromodynamics (NRQCD) fragmentation functions and obtain consistent results. Both approaches use Madgraph to calculate the hard process that creates the jet initiating parton. These calculations give reasonable agreement with the z(J/ψ) distribution that was shown to be poorly described by default PYTHIA simulations in the LHCb paper. We compare our predictions for the J/ψ distribution using various extractions of nonperturbative NRQCD long-distance matrix elements (LDMEs) in the literature. NRQCD calculations agree with LHCb data better than default PYTHIA regardless of which fit to the LDMEs is used. LDMEs from fits that focus exclusively on high transverse momentum data from colliders are in good agreement with the LHCb measurement.The production of quarkonium is a challenging test of Quantum Chromodynamics due to the mutiple length scales involved. The LHCb collaboration [1] published the first study of J/ψ produced within jets. The distribution of the fraction of the jet's transverse momentum, p T , carried by the J/ψ, z(J/ψ), was found to disagree significantly with predictions from the PYTHIA monte carlo [2, 3] using leading order calculations of J/ψ production in the Non-Relativistic Quantum Chromodynamics (NRQCD) factorization formalism [4]. This letter is provides improved theoretical calculations of the z(J/ψ) distribution and to discuss the implications of the LHCb results for the NRQCD factorization formalism.Production of quarkonium in hadron colliders has been the subject of experimental and theoretical studies for decades. The problem is challenging because it involves several disparate scales. These include p T , which can be much larger than the mass of the bound state, ≈ 2m Q , where m Q is the mass of the heavy quark, as well as scales that are much smaller: the relative momenta, m Q v (v is the typical velocity of the heavy quarks in the bound state), the kinetic energy, m Q v 2 , and the nonperturbative scale Λ QCD .The most common approach to calculating quarkonium production is the NRQCD factorization formalism [4]. In this formalism, the cross section for J/ψ in a pp collision is written aswhere dσ[pp → cc(n)X] is the short distance cross section for producing the cc pair in a state n with definite color and angular momentum quantum numbers and O J/ψ (n) is a long distance matrix element (LDME) that describes the nonperturbative transition of the cc pair in the state n into a final state containing J/ψ. X denotes other possible particles in the final state. The quantum numbers n will be denoted 2S+1 L [i]J where the notation for angular momentum is st...

We present the transverse momentum spectrum of groomed jets in di-jet events for e + e − collisions and semi-inclusive deep inelastic scattering (SIDIS). The jets are groomed using a soft-drop grooming algorithm which helps in mitigating effects of non-global logarithms and underlying event. At the same time, by reducing the final state hadronization effects, it provides a clean access to the non-perturbative part of the evolution of transverse momentum dependent (TMD) distributions. In SIDIS experiments we look at the transverse momentum of the groomed jet measured w.r.t. the incoming hadron in the Breit frame. Because the final state hadronization effects are significantly reduced, the SIDIS case allows to probe the TMD parton distribution functions. We discuss the sources of non-perturbative effects in the low transverse momentum region including novel (but small) effects that arise due to grooming. We derive a factorization theorem within SCET and resum any large logarithm in the measured transverse momentum up to NNLL accuracy using the ζ-prescription as implemented in the artemide package and provide a comparison with simulations. arXiv:1907.05896v1 [hep-ph]

We present the framework for obtaining precise predictions for the transverse momentum of hadrons with respect to the thrust axis in e+e− collisions. This will enable a precise extraction of transverse momentum dependent (TMD) fragmentation functions from a recent measurement by the Belle Collaboration. Our analysis takes into account, for the first time, the nontrivial interplay between the hadron transverse momentum and the cut on the thrust event shape. To this end, we identify three different kinematic regions, derive the corresponding factorization theorems within Soft Collinear Effective Theory, and present all ingredients needed for the joint resummation of the transverse momentum and thrust spectrum at NNLL accuracy. One kinematic region can give rise to non-global logarithms (NGLs), and we describe how to include the leading NGLs. We also discuss alternative measurements in e+e− collisions that can be used to access the TMD fragmentation function. Finally, by using crossing symmetry, we obtain a new way to constrain TMD parton distributions, by measuring the displacement of the thrust axis in ep collisions.