Searcharxiv⌕ Search

arXiv subjects

T. C. Rogers

Publications and source records attributed to T. C. Rogers.

At least 19 recordsLinked to original sources
arXiv2026

What are the consequences of independent factorization and renormalization scales?

It is common for separate factorization and renormalization scales to be discussed in connection with phenomenological applications of QCD factorization theorems. We observe that simultaneously preserving renormalization group invariance, Ward identities, and the basic sum rules in the definitions of parton densities forces these scales to be equal. The statement applies to generalized pole subtraction schemes that use dimensional regularization and to collinear factorization theorems for basic processes like deep inelastic scattering. We discuss implications for estimating the effects of scale sensitivity in phenomenological calculations, consistent extractions of Standard Model parameters alongside parton densities in global QCD analyses, and generally connecting phenomenologically extracted parton densities to first principles non-perturbative techniques like lattice QCD.

hep-ph↗
arXiv2024

QCD factorization with multihadron fragmentation functions

Important aspects of QCD factorization theorems are the properties of the objects involved that can be identified as universal. One example is that the definitions of parton densities and fragmentation functions for different types of hadrons differ only in the identity of the nonperturbative states that form the matrix elements, but are otherwise the same. This leads to independence of perturbative calculations on nonperturbative details of external states. It also lends support to interpretations of correlation functions as encapsulations of intrinsic nonperturbative properties. These characteristics have usually been presumed to still hold true in fragmentation functions even when the observed nonperturbative state is a small-mass cluster of $n$ hadrons rather than simply a single isolated hadron. However, the multidifferential aspect of cross sections that rely on these latter types of fragmentation functions complicates the treatment of kinematical approximations in factorization derivations. That has led to recent claims that the operator definitions for fragmentation functions need to be modified from the single hadron case with nonuniversal prefactors. With such concerns as our motivation, we retrace the steps for factorizing the unpolarized semi-inclusive $e^+e^-$ annihilation cross section and confirm that they do apply without modification to the case of a small-mass multihadron observed in the final state. In particular, we verify that the standard operator definition from single hadron fragmentation, with its usual prefactor, remains equally valid for the small-mass $n$-hadron case with the same hard parts and evolution kernels, whereas the more recently proposed definitions with nonuniversal prefactors do not. Our results reaffirm the reliability of most past phenomenological applications of dihadron fragmentation functions.

hep-ph↗
arXiv2024

Phenomenology of TMD parton distributions in Drell-Yan and $Z^0$ boson production in a hadron structure oriented approach

We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to TMD phenomenology applied to Drell-Yan like processes, including lepton pair production at moderate $Q^2$ and $Z^0$ boson production. We compare and contrast general features of our methodology with other common practices and emphasize the improvements derived from our approach that we view as essential for applications where extracting details of nonperturbative transverse hadron structure is a major goal. These include the HSO's preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution, explicit preservation of the integral relationship between TMD and collinear pdfs, and the ability to meaningfully compare different theoretical models of nonperturbative TMD parton distributions. In our examples, we show that there is significant sensitivity at moderate $Q^2$ to both the form of the nonperturbative transverse momentum dependence and the parametrization of collinear parton densities. However, we also find that evolving to $Q^2 = M_Z^2$, without fitting, results in a satisfactory postdiction of existing data for $Z^0$ production, nearly independently of the modeling of nonperturbative transverse momentum behavior. We argue that this demonstrates that moderate $Q$ measurements should be given greater weight than high $Q$ measurements in extractions of nonperturbative transverse momentum dependence. We also obtain new extractions of the nonperturbative Collins-Soper kernel within the HSO approach. We discuss its features and compare with some earlier extractions.

hep-ph↗
arXiv2023

The resolution to the problem of consistent large transverse momentum in TMDs

Parametrizing TMD parton densities and fragmentation functions in ways that consistently match their large transverse momentum behavior in standard collinear factorization has remained notoriously difficult. We show how the problem is solved in a recently introduced set of steps for combining perturbative and nonperturbative transverse momentum in TMD factorization. Called a ``bottom-up'' approach in a previous article, here we call it a ``hadron structure oriented'' (HSO) approach to emphasize its focus on preserving a connection to the TMD parton model interpretation. We show that the associated consistency constraints improve considerably the agreement between parametrizations of TMD functions and their large-$k_T$ behavior, as calculated in collinear factorization. The procedure discussed herein will be important for guiding future extractions of TMD parton densities and fragmentation functions and for testing TMD factorization and universality. We illustrate the procedure with an application to semi-inclusive deep inelastic scattering (SIDIS) structure functions at an input scale $Q_0$, and we show that there is improved consistency between different methods of calculating at moderate transverse momentum. We end with a discussion of plans for future phenomenological applications.

hep-ph↗
arXiv2022

Basics of factorization in a scalar Yukawa field theory

The factorization theorems of quantum chromodynamics (QCD) apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler theories is convenient for stress-testing the limits of the factorization program and for examining general properties of the parton density functions (pdfs) or other correlation functions that might be necessary for a factorized description of a process. With this view in mind, we review the steps of factorization in a real scalar Yukawa field theory for both deep inelastic scattering (DIS) and semi-inclusive deep inelastic scattering (SIDIS) cross sections. In the case of SIDIS, we illustrate how to separate the small transverse momentum region, where transverse momentum dependent (TMD) pdfs are needed, from a purely collinear large transverse momentum region, and we examine the influence of subleading power corrections. We also review the steps for formulating TMD factorization in transverse coordinate space, and we study the effect of transforming to the well-known $b_*$-scheme. Within the Yukawa theory, we investigate the consequences of switching to a generalized parton model (GPM) approach, and compare with a fully factorized approach. Our results highlight the need to address similar or analogous issues in QCD.

hep-ph↗
arXiv2022

Combining nonperturbative transverse momentum dependence with TMD evolution

Central to understanding the nonpertubative, intrinsic partonic nature of hadron structure are the concepts of transverse momentum dependent (TMD) parton distribution and fragmentation functions. A TMD factorization approach to the phenomenology of semi-inclusive processes that includes evolution, higher orders, and matching to larger transverse momentum, is ultimately necessary for reliably connecting with phenomenologically extracted nonperturbative structures, especially when widely different scales are involved. In this paper, we will address some of the difficulties that arise when phenomenological techniques that were originally designed for very high energy applications are extended to studies of hadron structures, and we will solidify the connection between standard high energy TMD implementations and the more intuitive, parton model based approaches to phenomenology that emphasize nonperturbative hadron structure. In the process, we will elaborate on differences between forward and backward TMD evolution, which in the context of this paper we call "bottom-up" and "top-down" approaches, and we will explain the advantages of a bottom-up strategy. We will also emphasize and clarify the role of the integral relations that connect TMD and collinear correlation functions. We will show explicitly how they constrain the nonperturbative "$g$-functions" of standard Collins-Soper-Sterman (CSS) implementations of TMD factorization. This paper is especially targeted toward phenomenologists and model builders who are interested in merging specific nonperturbative models and calculations (including lattice QCD) with TMD factorization at large $Q$. Our main result is a recipe for incorporating nonperturbative models into TMD factorization, and for constraining their parameters in a way that matches to perturbative QCD and evolution.

hep-ph↗
arXiv2021

Simultaneous Monte Carlo analysis of parton densities and fragmentation functions

We perform a comprehensive new Monte Carlo analysis of high-energy lepton-lepton, lepton-hadron and hadron-hadron scattering data to simultaneously determine parton distribution functions (PDFs) in the proton and parton to hadron fragmentation functions (FFs). The analysis includes all available semi-inclusive deep-inelastic scattering and single-inclusive $e^+ e^-$ annihilation data for pions, kaons and unidentified charged hadrons, which allows the flavor dependence of the fragmentation functions to be constrained. Employing a new multi-step fitting strategy and more flexible parametrizations for both PDFs and FFs, we assess the impact of different data sets on sea quark densities, and confirm the previously observed suppression of the strange quark distribution. The new fit, which we refer to as "JAM20-SIDIS", will allow for improved studies of universality of parton correlation functions, including transverse momentum dependent (TMD) distributions, across a wide variety of process, and the matching of collinear to TMD factorization descriptions.

hep-ph↗
arXiv2021

QCD Factorization and Quantum Mechanics

It is unusual to find QCD factorization explained in the language of quantum information science. However, we will discuss how the issue of factorization and its breaking in high-energy QCD processes relates to phenomena like decoherence and entanglement. We will elaborate with several examples and explain them in terms familiar from basic quantum mechanics and quantum information science.

quant-ph↗
arXiv2019

Collinear Factorization in Wide-Angle Hadron Pair Production in $e^+e^-$ Annihilation

We compute the inclusive unpolarized dihadron production cross section in the far from back-to-back region of $e^+ e^-$ annihilation in leading order pQCD using existing fragmentation function fits and standard collinear factorization, focusing on the large transverse momentum region where transverse momentum is comparable to the hard scale (the center-of-mass energy). We compare with standard transverse-momentum-dependent (TMD) fragmentation function-based predictions intended for the small transverse momentum region with the aim of testing the expectation that the two types of calculation roughly coincide at intermediate transverse momentum. We find significant tension, within the intermediate transverse momentum region, between calculations done with existing non-perturbative TMD fragmentation functions and collinear factorization calculations if the center-of-mass energy is not extremely large. We argue that $e^+ e^-$ measurements are ideal for resolving this tension and exploring the large-to-small transverse momentum transition, given the typically larger hard scales ($\gtrsim 10$ GeV) of the process as compared with similar scenarios that arise in semi-inclusive deep inelastic scattering and fixed-target Drell-Yan measurements.

hep-ph↗
arXiv2019

Mapping the Kinematical Regimes of Semi-Inclusive Deep Inelastic Scattering

We construct a language for identifying kinematical regions of transversely differential semi-inclusive deep inelastic scattering cross sections with particular underlying partonic pictures, especially in regions of moderate to low $Q$ where sensitivity to kinematical effects outside the usual very high energy limit becomes non-trivial. The partonic pictures map to power law expansions whose leading contributions ultimately lead to well-known QCD factorization theorems. We propose methods for estimating the consistency of any particular region of overall hadronic kinematics with the kinematics of a given underlying partonic picture. The basic setup of kinematics of semi-inclusive deep inelastic scattering is also reviewed in some detail.

hep-ph↗
arXiv2019

Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering Beyond Lowest Order

Motivated by recently observed tension between $O\left(α_s^2\right)$ calculations of very large transverse momentum dependence in both semi-inclusive deep inelastic scattering and Drell-Yan scattering, we repeat the details of the calculation through $O\left(α_s^2\right)$ transversely differential cross section. The results confirm earlier calculations, and provide further support to the observation that tension exists with current parton distribution and fragmentation functions.

hep-ph↗
arXiv2019

What does kinematical target mass sensitivity in DIS reveal about hadron structure?

We study the role of purely external kinematical approximations in inclusive deep-inelastic lepton--hadron scattering within QCD factorization, and consider factorization with an exact treatment of the target hadron mass. We discuss how an observed phenomenological improvement obtained by accounting for target mass kinematics could be interpreted in terms of general properties of target structure, and argue that such an improvement implies a hierarchy of nonperturbative scales within the hadron.

hep-ph↗
arXiv2018

Challenges with Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering

We survey the current phenomenological status of semi-inclusive deep inelastic scattering at moderate hard scales and in the limit of very large transverse momentum. As the transverse momentum becomes comparable to or larger than the overall hard scale, the differential cross sections should be calculable with fixed order pQCD methods, while small transverse momentum (TMD factorization) approximations should eventually break down. We find large disagreement between HERMES and COMPASS data and fixed order calculations done with modern parton densities, even in regions of kinematics where such calculations should be expected to be very accurate. Possible interpretations are suggested.

hep-ph↗
arXiv2017

What are the low-$Q$ and large-$x$ boundaries of collinear QCD factorization theorems?

Familiar factorized descriptions of classic QCD processes such as deeply-inelastic scattering (DIS) apply in the limit of very large hard scales, much larger than nonperturbative mass scales and other nonperturbative physical properties like intrinsic transverse momentum. Since many interesting DIS studies occur at kinematic regions where the hard scale, $Q \sim$ 1-2 GeV, is not very much greater than the hadron masses involved, and the Bjorken scaling variable $x_{bj}$ is large, $x_{bj} \gtrsim 0.5$, it is important to examine the boundaries of the most basic factorization assumptions and assess whether improved starting points are needed. Using an idealized field-theoretic model that contains most of the essential elements that a factorization derivation must confront, we retrace the steps of factorization approximations and compare with calculations that keep all kinematics exact. We examine the relative importance of such quantities as the target mass, light quark masses, and intrinsic parton transverse momentum, and argue that a careful accounting of parton virtuality is essential for treating power corrections to collinear factorization. We use our observations to motivate searches for new or enhanced factorization theorems specifically designed to deal with moderately low-$Q$ and large-$x_{bj}$ physics.

hep-ph↗
arXiv2017

Combining TMD factorization and collinear factorization

We examine some of the complications involved when combining (matching) TMD factorization with collinear factorization to allow accurate predictions over the whole range of measured transverse momentum in a process like Drell-Yan. Then we propose some improved methods for combining the two types of factorization. (This talk is based on work reported in arXiv:1605.00671.)

hep-ph↗
arXiv2017

Kinematics of Current Region Fragmentation in Semi-Inclusive Deeply Inelastic Scattering

Different kinematical regimes of semi-inclusive deeply inelastic scattering (SIDIS) processes correspond to different underlying partonic pictures, and it is important to understand the transition between them. This is particularly the case when there is sensitivity to intrinsic transverse momentum, in which case kinematical details can become especially important. We address the question of how to identify the current fragmentation region --- the kinematical regime where a factorization picture with fragmentation functions is appropriate. We distinguish this from soft and target fragmentation regimes. Our criteria are based on the kinematic regions used in derivations of factorization theorems. We argue that, when hard scales are of order a few GeVs, there is likely significant overlap between different rapidity regions that are normally understood to be distinct. We thus comment on the need to take this into account with more unified descriptions of SIDIS, which should span all rapidities for the produced hadron. Finally, we propose general criteria for estimating the proximity to the current region at large Q.

hep-ph↗
arXiv2016

Relating Transverse Momentum Dependent and Collinear Factorization Theorems in a Generalized Formalism

We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard $W+Y$ prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and $Q$-dependence of the cross sections at lower $Q$ are largely governed by the matching to the $Y$-term.

hep-ph↗