Collinear Factorization Research Articles

Modified TMD Factorization and Sub-leading Power Corrections

Collinear factorization and transverse-momentum-dependent (TMD) factorization are two complementary approaches to perform QCD calculations of Drell-Yan differential cross sections. The former is designed to correctly describe the behavior of the observable at large values of the gauge boson transverse momentum qT, while the latter accounts for non-perturbative effects relevant at small qT. We present basic features and first numerical results of a novel factorization formalism which is related to both previous frameworks and allows for an improved description of the intermediate-qT region.

Modified TMD Factorization and Sub-leading Power Corrections

Collinear factorization and transverse-momentum-dependent (TMD) factorization are two complementary approaches to perform QCD calculations of Drell-Yan differential cross sections. The former is designed to correctly describe the behavior of the observable at large values of the gauge boson transverse momentum qT, while the latter accounts for non-perturbative effects relevant at small qT. We present basic features and first numerical results of a novel method which is related to both previous frameworks and allows for an improved description of the intermediate-qT region.

The high-energy limit of perturbative QCD: Theory and phenomenology

After a brief introduction of formal and phenomenological progresses in the study of the high-energy limit of perturbative QCD, we present arguments supporting the statement that the inclusive emission of Higgs bosons or heavy-flavored hadrons acts as fair stabilizer of high-energy resummed differential distributions. We come out with the message that the hybrid high-energy and collinear factorization, built in term of the next-to-leading logarithmic resummation à la BFKL and supplemented by collinear parton distributions and fragmentation functions, is a valid and powerful tool to gauge the feasibility of precision analyses of QCD in its high-energy limit.

Celestial OPEs and w1+\u221e algebra from worldsheet in string theory

Celestial operator product expansions (OPEs) arise from the collinear limit of scattering amplitudes and play a vital role in celestial holography. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celestial CFT. We also derive the celestial OPEs from the collinear factorization of string amplitudes and the results derived in these two different methods are in perfect agreement with each other. Our final formulae of celestial OPEs are applicable to general dimensions, corresponding to Einstein-Yang-Mills theory supplemented by some possible higher derivative interactions. Specializing to 4D, we reproduce all the celestial OPEs for gluon and graviton in the literature. We consider various string theories, including the open and closed bosonic string, as well as the closed superstring theory with mathcal{N} = 1 and mathcal{N} = 2 worldsheet supersymmetry. In the case of mathcal{N} = 2 string, we also derive all the overline{mathrm{SL}left(2,mathbb{R}right)} descendant contributions in the celestial OPE; the soft sector of such OPE just yields the w1+∞ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the microscopic realization of celestial CFT dual to string theory in flat spacetime.

Bottom-flavored inclusive emissions in the variable-flavor number scheme: A high-energy analysis

We propose the inclusive semi-hard production, in proton-proton collisions, of two bottom-flavored hadrons, as well as of a single bottom-flavored hadron accompanied by a light jet, as novel channels for the manifestation of stabilization effects of the high-energy resummation under next-to-leading-order corrections. Our formalism relies on a hybrid high-energy and collinear factorization, where the BFKL resummation of leading and next-to-leading energy logarithms is used together with collinear factorization. We present results for cross sections and azimuthal correlations differential in rapidity, which are widely recognized as standard observables where to hunt for distinctive signals of the BFKL dynamics. We propose the study of double differential distributions in the transverse momenta of final-state particles as a common basis to investigate the interplay of different kinds of resummation mechanisms.

Collinear factorization of diphoton photoproduction at next to leading order

We calculate in the framework of collinear factorization the amplitude for the photoproduction of a near forward large mass diphoton at leading twist and next to leading order (NLO) in $\alpha_s$. We demonstrate the validity of factorization at this order, which was never achieved for such a reaction where the coefficient function describes a $2 \to 3$ hard process. While the Born order amplitude was purely imaginary and only probed the $x=\pm \xi$ cross-over line of generalized parton distributions (GPD) domain, the NLO result contains both a real and an imaginary part and probes the whole domain of definition of quark GPDs. The phenomenology of our results for medium (JLab) and higher energy (EIC) experiments will be developed in a future study.

Progress and opportunities in backward angle (u-channel) physics

Backward angle (u-channel) scattering provides complementary information for studies of hadron spectroscopy and structure, but has been less comprehensively studied than the corresponding forward angle case. As a result, the physics of u-channel scattering poses a range of new experimental and theoretical opportunities and questions. We summarize recent progress in measuring and understanding high energy reactions with baryon charge exchange in the u-channel, as discussed in the first backward angle (u-channel) Physics Workshop. In particular, we discuss backward angle measurements and their theoretical description via both hadronic models and the collinear factorization approach, and discuss planned future measurements of u-channel physics. Finally, we propose outstanding questions and challenges for u-channel physics.

Production and polarization of direct J/ψ to O(αs3) in the improved color evaporation model in collinear factorization

We calculate the production and polarization of direct $J/\psi$ in the improved color evaporation model at $\mathcal{O}(\alpha_s^3)$ in the collinear factorization approach. We present the first calculation of polarization parameters $\lambda_\vartheta$, $\lambda_{\phi}$, and $\lambda_{\vartheta \phi}$ in the helicity and the Collins-Soper frames, as well as the frame-invariant polarization parameter $\tilde{\lambda}$ as a function of transverse momentum. We find agreement with both $J/\psi$ cross sections and the invariant polarization parameters at small and moderate $p_T$.

Three-photon productions within the k_t-factorization at the LHC

Recently, the ATLAS data of isolated three-photon production showed that the next-to-leading order (NLO) collinear factorization is not enough to describe experimental data. Therefore, one needs to calculate the cross section beyond the NLO, and as showed later, these data can be well described by the NNLO calculation within the collinear factorization framework. However, it is shown that the k_t-factorization can be quite successful in describing exclusive and high energy collision processes, henceforth we decided to calculate isolated three-photon production within this framework. In this work we use the Martin, Ryskin, and Watt unintegrated parton distribution functions (MRW UPDFs) at LO and NLO levels, in addition to parton branching (PB) UPDFs in order to calculate cross section which we utilize the KATIE parton level event generator. It will be shown that in contrast to collinear factorization, the k_t-factorization can describe quiet well the three-photon production ATLAS data. Interestingly our results using the NLO-MRW and PB UPDFs can cover the data within their uncertainty bands, similar to the NNLO collinear results.

Matching of fracture functions for SIDIS in target fragmentation region

In the target fragmentation region of Semi-Inclusive Deep Inelastic Scattering, the diffractively produced hadron has small transverse momentum. If it is at order of ΛQCD, it prevents to make predictions with the standard collinear factorization. However, in this case, differential cross-sections can be predicted by the factorization with fracture functions, diffractive parton distributions. If the transverse momentum is much larger than ΛQCD but much smaller than Q which is the virtuality of the virtual photon, both factorizations apply. In this case, fracture functions can be factorized with collinear parton distributions and fragmentation functions. We study the factorization up to twist-3 level and obtain gauge invariant results. They will be helpful for modeling fracture functions and useful for resummation of large logarithm of the transverse momentum appearing in collinear factorization.

A new approach to semi-inclusive deep-inelastic scattering with QED and QCD factorization

We present the details of a new factorized approach to semi-inclusive deep-inelastic scattering which treats QED and QCD radiation on equal footing, and provides a systematically improvable approximation to the extraction of transverse momentum dependent parton distributions. We demonstrate how the QED contributions can be well approximated by collinear factorization, and illustrate the application of the factorized approach to QED radiation in inclusive scattering. For semi-inclusive processes, we show how radiation effects prevent a well-defined “photon-nucleon” frame, forcing one to use a two-step process to account for the radiation. We illustrate the utility of the new method by explicit application to the spin-dependent Sivers and Collins asymmetries.

Erratum: Collinear factorization in wide-angle hadron pair production in e+e− annihilation [Phys. Rev. D 100 , 094014 (2019)

Received 24 August 2021DOI:https://doi.org/10.1103/PhysRevD.104.059904Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFragmentation into hadronsPerturbative QCDQuantum chromodynamicsTechniquesLepton collidersParticles & Fields

Twist-3 gluon fragmentation contribution to polarized hyperon production in unpolarized proton-proton collision

Understanding the origin and mechanism of the transverse polarization of hyperons produced in unpolarized proton-proton collision, $pp\to \Lambda^\uparrow X$, has been one of the long-standing issues in high-energy spin physics. In the framework of the collinear factorization applicable to large-$p_T$ hadron productions, this phenomenon is a twist-3 observable which is caused by multi-parton correlations either in the initial protons or in the process of fragmentation into the hyperon. We derive the twist-3 gluon fragmentation function (FF) contribution to this process in the leading order (LO) with respect to the QCD coupling constant. Combined with the known results for the contribution from the twist-3 distribution function and the twist-3 quark FF, this completes the LO twist-3 cross section. We also found that the model independent relations among the twist-3 gluon FFs based on the QCD equation of motion and the Lorentz invariance property of the correlation functions guarantee the color gauge invariance and the frame-independence of the cross section.

Validity check of the KATIE parton level event generator in the kt -factorization and collinear frameworks

In the present paper, we check and study the validity of the \textsc{KaTie} parton level event generator, by calculating the inclusive electron-proton (ep) dijet and the Proton-proton (p-p) Drell-Yan electron-pair productions differential cross sections in the $k_t$- and collinear factorization frameworks. The Martin-Ryskin-Watt (MRW) unintegrated parton distribution functions (UPDFs) are used as the input UPDFs. The results are compared with those of ZEUS ep inclusive dijet and ATLAS p-p Drell-Yan electron-pair productions, experimental data. The \textsc{KaTie} parton level event generator can directly calculate the cross sections in the $k_t$-factorization framework. It is noticed that the lab to the Breit transformation in this generator is not correctly implemented by its author, so the produced output does not cover the ep ZEUS experimental data in which the mentioned transformation is applied. By fixing the above transformation in the \textsc{KaTie} generator code, we could appropriately produce the ep inclusive dijet differential cross section, in comparison with those of ZEUS data. It is also shown that the MRW at the NLO level, with the angular ordering constraint can successfully predict the ATLAS p-p Drell-Yan data. Finally, as it is expected, we conclude that the $k_t$-factorization is an appropriate tool for the small longitudinal parton momenta and high center of mass energies, with respect to the collinear one.

Transverse momentum dependent gluon distribution within high energy factorization at next-to-leading order

We discuss transverse momentum dependent (TMD) gluon distributions within high energy factorization at next-to-leading order in the strong coupling within the framework of Lipatov's high energy effective action. We provide a detailed discussion of both rapidity divergences related to the TMD definition and its soft factor on the one hand, and rapidity divergences due to high energy factorization on the other hand, and discuss common features and differences between Collins-Soper (CS) and Balitsky-Fadin-Kuarev-Lipatov (BFKL) evolution. While we confirm earlier results which state that the unpolarized and linearly polarized gluon TMD agree in the BFKL limit at leading order, we find that both distributions differ, once next-to-leading order corrections are being included. Unlike previous results, our framework allows us to recover the complete anomalous dimension associated with the Collins-Soper-Sterman (CSS) evolution of the TMD distribution, including also single-logarithmic terms in the CSS evolution. As an additional result, we provide a definition of ${k}_{T}$ factorization, i.e., matching of off shell coefficients to collinear factorization at next-to-leading order within high energy factorization and the effective action framework. We furthermore establish a link between the QCD operator definition of the TMD gluon distribution and a previously derived off shell TMD gluon-to-gluon splitting function, which is within the present framework obtained as the real one-loop correction.

Exclusive heavy vector meson electroproduction to NLO in collinear factorisation

We compute the exclusive electroproduction, γ*p → Vp, of heavy quarkonia V to NLO in the collinear factorisation scheme, which has been formally proven for this process. The inclusion of an off-shell virtuality Q2 carried by the photon extends the photoproduction phase space of the exclusive heavy quarkonia observable to electroproduction kinematics. This process is relevant for diffractive scattering at HERA and the upcoming EIC, as well as at the proposed LHeC and FCC.

Reweighted nuclear PDFs using heavy-flavor production data at the LHC

We present the reweighting of two sets of nuclear parton distribution functions (PDFs), nCTEQ15 and EPPS16, using a selection of experimental data on heavy-flavor meson [${D}^{0}$, $J/\ensuremath{\psi}$, $B\ensuremath{\rightarrow}J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}(1S)$] production in proton-lead collisions at the LHC which were not used in the original determination of these nuclear PDFs. The reweighted PDFs exhibit significantly smaller uncertainties thanks to these new heavy-flavor constraints. We present a comparison with another selection of data from the LHC and relativistic heavy ion collider (RHIC) which were not included in our reweighting procedure. The comparison is overall very good and serves as a validation of these reweighted nuclear PDF sets, which we dub $\mathrm{nCTEQ}{15}_{\mathrm{rwHF}}$ and $\mathrm{EPPS}{16}_{\mathrm{rwHF}}$. This indicates that the LHC and forward RHIC heavy-flavor data can be described within the standard collinear factorization framework with the same (universal) small-$x$ gluon distribution. We discuss how we believe such reweighted PDFs should be used as well as the limitations of our procedure.

Parton interpretation and twist-4 parton distributions

Through explicit examples we show that twist-4 parton distributions have no parton interpretation in the sense that parton or partons inside a hadron can carry the momentum fraction x of the hadron with x>1 or x<−1. The studied twist-4 parton distributions of collinear factorization are power-divergent for |x|>1. The corresponding transverse momentum dependent parton distributions have finite contributions for |x|>1 and they have hence no parton interpretation. Parton distributions are defined with products of field operators. In the case of twist-4, different orderings give different results. The differences are determined by commutation relations of field operators. This has been explicitly checked in the studied case. The implications of our results are discussed.

Inclusive production of a heavy-light dijet system in hybrid high-energy and collinear factorization

We propose the study of the inclusive hadroproduction of a heavy-flavored jet in association with a light jet, as a probe channel of strong interactions at high energies. We build up a hybrid factorization that encodes genuine high-energy effects, provided by a partial next-to-leading BFKL resummation, inside the standard collinear structure of the cross section. We present a detailed analysis of different distributions, shaped on kinematic ranges typical of experimental analyses at the Large Hadron Collider, and differential in rapidity, azimuthal angle and transverse momentum. The fair stability that these distributions exhibit under higher-order corrections motivates our interest toward future studies. Here, the hybrid factorization could help to deepen our understanding of heavy-flavor physics in wider kinematic ranges, like the ones accessible at the Electron-Ion Collider.

CASCADE3 A Monte Carlo event generator based on TMDs

The Cascade3 Monte Carlo event generator based on Transverse Momentum Dependent (TMD) parton densities is described. Hard processes which are generated in collinear factorization with LO multileg or NLO parton level generators are extended by adding transverse momenta to the initial partons according to TMD densities and applying dedicated TMD parton showers and hadronization. Processes with off-shell kinematics within k_{{t}}-factorization, either internally implemented or from external packages via LHE files, can be processed for parton showering and hadronization. The initial state parton shower is tied to the TMD parton distribution, with all parameters fixed by the TMD distribution.