TMDs: Towards a Synergy between Lattice QCD and Global Analysis

21 Jun 2023, 08:00 → 23 Jun 2023, 19:00 US/Eastern

Center for Frontiers in Nuclear Science, Stony Brook University

Shohini Bhattacharya (BNL), Xiangdong Ji (University of Maryland), Swagato Mukherjee (Brookhaven National Laboratory), Alexei Prokudin (Penn State Berks), Yong Zhao (member@anl.gov)

The workshop "TMDs: Towards a Synergy between Lattice QCD and Global Analyses" is supported by the BNL EIC Theory Institute and Center for Frontiers in Nuclear Science, Stony Brook University. The workshop will take place from June 21 to 23, 2023 at Stony Brook University at Stony Brook, NY, USA. This workshop aims at bringing the lattice, phenomenology and experimental communities together to make advances in the extraction of TMDs. The topics of interest include how to incorporate the lattice results into the Collins-Soper-Sterman factorization framework to help improve the global fits, identify the TMD observables for lattice studies, and benchmark the precision for each observable.

The scientific goals of this workshop align well with the Electron-Ion Collider (EIC), which is expected to provide the most precise measurement of the 3D structure of the proton and nuclei. Lattice QCD calculations can determine: the non-perturbative Collins-Soper kernel, the spin-dependent TMDs, light-flavor separation of TMDs, for both quarks and gluons. These will help the global analyses for the unpolarized, helicity and transiversity TMDs at the EIC, thus improving the extraction of the 3D proton structure. In particular, the lattice calculation of time-reversal-odd TMDs such as the Sivers and Boer-Mulders function will offer useful insight on the test of universality, spin-orbit correlations, and multi-parton correlations, which are of great interest to the single transverse spin experiments at the EIC.

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This meeting is intended as an in-person event, and talks are by invitation only. The presentations will be broadcasted via Zoom (password via email to registered participants).

This event is part of the CFNS workshop/ad-hoc meeting series. See the CFNS conferences page for other events.

 

Wednesday, 21 June

Welcome

Welcome_CFNS.pdf

Session I

1 TMDs at Hadron Colliders

The turn-on of high energy hadron colliders, such as RHIC and the LHC, have created a new arena for the study of TMDs. The collisions of protons over a wide range of center-of-mass energies allow for tests of universality and factorization as well as the study of evolution effects. The wide-acceptance and variety of technologies featured in typical collider detectors have paved the way for the simultaneous measurement of a variety of observables, including inclusive hadrons, jets and W/Z bosons. This talk will provide a broad survey of TMD results, focusing on the most recent spin-dependent and spin-integrated TMD measurements from RHIC and the LHC. Special attention will be paid to opportunities for future measurements in the forward region at RHIC and their connection to the TMD program at the future EIC.

Speaker: Renee Fatemi (University of Kentucky)

Fatemi_CNFS_TMD.pdf

2 TMDs from Collins-Soper-Sterman Resummation

In this talk, I will summarize the TMDs from the Collins-Soper-Sterman Resummation formalism. Phenomenological results from recent global analysis of ResBos approach will also be presented, including the TMDs and the associated Collins-Soper evolution kernel.

Speaker: Feng Yuan (Lawrence Berkeley National Laboratory)

TMD_Lattice_2023_Yuan.pdf

3 TMDs from Various Avenues

In this talk, we will provide different ways of exploring TMDs, both the standard processes (SIDIS, Drell-Yan, and e+e- collisions) and those beyond which have been developed in recent years, such as the ones via jets, jet substructures, and energy-energy correlators. We will provide some recent progress on the (polarized) TMD phenomenology and global analysis, in connection with the theme of the workshop.

Speaker: Zhongbo Kang (UCLA)

Kang_CFNS_workshop.pptx

10:30 Break

Session II

4 Global extraction of unpolarized Transverse Momentum Distributions

We present a global extraction of unpolarized Transverse Momentum Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) from two different types of processes: Semi-Inclusive Deep Inelastic Scattering (SIDIS) and Drell–Yan (DY). The analysis is performed in the TMD factorization framework and is based on data from several experiments and kinematic ranges.
The extraction reaches the state-of-the art perturbative accuracy of N$^3$LL$^-$.

We discuss the introduction of (pre-computed) normalization coefficients for SIDIS data.
The fit is performed taking into account correlated and uncorrelated uncertainties and we found that present data are very well described by our choice of non-perturbative functions.

Speaker: Chiara Bissolotti (Argonne National Laboratory)

2023-CNFSworkshopTMDs.pdf

5 Tomography of pions and protons via transverse momentum dependent distributions

I will present our work, https://inspirehep.net/literature/2628962, on the first simultaneous extraction of parton collinear and transverse degrees of freedom from low-energy fixed-target Drell-Yan data in order to compare the transverse momentum dependent (TMD) parton distribution functions (PDFs) of the pion and proton. We demonstrate that the transverse separation of the quark field encoded in TMDs of the pion is more than $\sim$5 $\sigma$ smaller than that of the proton. We also consider the nuclear modification of TMDs, we find clear evidence for a transverse EMC effect. We comment on possible explanations for these intriguing behaviors, which call for a deeper examination of tomography in a variety of strongly interacting quark-gluon systems.

Speaker: Leonard Gamberg (Penn State)

Gamberg_SB_23.pdf

6 Three dimensional imaging in Nuclei

In this talk, I'll discuss our recent work where we perform the first simultaneous global QCD extraction of the transverse momentum dependent (TMD) parton distribution functions and the TMD fragmentation functions in nuclei. We have considered the world set of data from semi-inclusive electron-nucleus deep inelastic scattering and Drell-Yan di-lepton production. In total, this data set consists of 90 data points from HERMES, Fermilab, RHIC and LHC. Working at next-to-leading order and next-to-next-to-leading logarithmic accuracy, we achieve a $\chi^2/dof = 1.196$. In this analysis, we perform the first extraction of nuclear modified TMDs and compare these to those in free nucleons. We also make predictions for the ongoing JLab 12 GeV program and future EIC measurements.

Speaker: John Terry (UCLA)

Terry.pdf

12:30 Lunch

Session III

7 Accessing TMDs from single pion and kaon SIDIS with CLAS12

Semi inclusive deep inelastic scattering is a well established tool to study TMDs and fragmentation functions. With the CLAS12 detector at Jefferson Laboratory (JLab) precise, multidimensional measurements of cross sections and asymmetry observables become possible in the valence quark regime, for the first time.
As a first observable, the structure function ratio $F_{LU}^{\sin\phi}/F_{UU}$ was studied based on beam single spin asymmetries from pion and kaon SIDIS. The talk will present a comprehensive multidimensional study for all pions, as well as charged kaons, and discuss the connection of the observable to TMDs and the impact of the new data on our understanding of the involved TMDs. Furthermore, an overview on ongoing and planed studies to extract the cos($\phi$) and cos(2$\phi$) moments of the SIDIS cross section, as well as an LT separation of the $\phi$ integrated cross section, will be provided.

Speaker: Dr Stefan Diehl (JLU Giessen and UCONN)

Diehl_TMD_workshop_2023.pdf

8 A Better Angle on Hadron Transverse Momentum Distributions at the EIC

We propose an observable $q_*$ sensitive to transverse momentum dependence (TMD) in
$e N \to e h X$, with $q_*/E_N$ defined purely by lab-frame angles. In 3D measurements of confinement and hadronization this resolves the crippling issue of accurately reconstructing small transverse momentum $P_{hT}$. We prove factorization for $\mathrm{d} \sigma_h / \mathrm{d}q_*$ for $q_*\ll Q$ with standard TMD functions, enabling $q_*$ to substitute for $P_{hT}$. A double-angle reconstruction method is given which is exact to all orders in QCD for $q_*\ll Q$. $q_*$ enables an order-of-magnitude improvement in the expected experimental resolution at the EIC.

Speaker: Johannes K. L. Michel (MIT CTP)

Johannes_Michel_CFNS_Workshop_A_Better_Angle.pdf

9 Understanding TMD structure using jets

In this talk, I will discuss how jets provide powerful new processes to understand both the TMD distributions and TMD fragmentation functions. In this talk, I will discuss three different processes involving jets that are useful to studying TMD functions at the EIC:

i) back-to-back production of e+jet

ii) TMD hadron distribution inside an inclusive jet production process

iii) TMD hadron distribution inside an inclusive jet produced back-to-back with e.

Speaker: Kyle Lee (MIT)

TMDusingJets.pdf

15:30 Break

Session IV

10 Disentangling long and short distances in momentum-space TMDs

The extraction of nonperturbative TMD physics is made challenging by prescriptions that shield the Landau pole, which entangle long- and short-distance contributions in momentum space. The use of different prescriptions then makes the comparison of fit results for underlying nonperturbative contributions not meaningful on their own. We propose a model-independent method to restrict momentum-space observables to the perturbative domain. This method is based on a set of integral functionals that act linearly on terms in the conventional position-space operator product expansion (OPE). Artifacts from the truncation of the integral can be systematically pushed to higher powers in $\Lambda_\mathrm{QCD} / k_T$. We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over $k_T \leq k_T^\mathrm{cut}$ in terms of collinear PDFs, accounting for both radiative corrections and evolution effects. This yields a systematic way of correcting the naive picture where the TMD PDF integrates to a collinear PDF, and for unpolarized quark distributions we find that when renormalization scales are chosen near $k_T^\mathrm{cut}$, such corrections are a percent-level effect. We also show that, when supplemented with experimental data and improved perturbative inputs, our integral functionals will enable model-independent limits to be put on the non-perturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.

Speaker: Zhiquan Sun (MIT)

CFNS2023_ZS.pdf

11 the role of fragmentation measurements for TMD extractions

TMD extractions of Semi-inclusive DIS measurements and in part hadronic collision measurements rely on the knowledge of (TMD) fragmentation functions in order to successfully obtain TMD distribution functions. There exists some access to unpolarized TMD fragmentation functions via SIDIS measurements, but the cleanest approach is via electron-positron annihilation. It is also the only current venue to cleanly obtain polarized fragmentation functions.
The recent TMD related fragmentation function measurements in electron-positron annihilation, most notably at the B factories will be reported.

Speaker: Ralf Seidl (RIKEN)

2023_06_21_TMDFF_Seidl.pdf

12 Transverse $\Lambda$ polarization in $e^+e^−$ annihilation and SIDIS processes within a TMD framework

We present an updated analysis of Belle data for the transverse $\Lambda$ polarization in $e^+e^−$ annihilation processes within a TMD factorization approach. $SU(2)$ isospin symmetry and charm quark contribution, with their impact on the description of the experimental data as well as on the extraction of the polarizing fragmentation functions, will be discussed.
Predictions for SIDIS processes within different scenarios, at typical energies of the future EIC, will be presented.

Speaker: Prof. Umberto D'Alesio (University and INFN Cagliari)

TMD_Lattice_PTLambda_DAlesio.pdf

TMD_Lattice_PTLambda_DAlesio.pptx

Thursday, 22 June

Session I

13 A journey through the heavy-light Sudakov universality class in LaMET: from quasi-TMDPDF at large Pz to quasi-PDFmatching kernel in the threshold limit

In this talk we will provide a survey of three fundamental objects: quasi-TMDPDF, quasi-LFWF amplitudes and (quark non-singlet) quasi-PDF matching kernel that appears naturally in the application of LaMET to lattice calculation of various parton distribution functions. We demonstrate how TMD factorization or threshold factorization works for the corresponding objects with a common perturbative hard kernel: the universal heavy-light Sudakov form factor. We show how the universal TMDPDF/LFWF amplitudes can be extracted by combining factorization theorems for the quasi-TMD quantities with an auxiliary space-like form factor. Finally, we explain how the NNLO heavy-light Sudakov form factor can be extracted through the threshold limit of quasi-PDF matching kernel.

Speaker: Yizhuang Liu (Jagiellonian University)

TMDCFNS.pptx

14 Determination of Collins-Soper kernel from lattice and global analysis

I review the latest progress in the determination of Collins-Soper kernel. There are two main subjects to be discussed. The first one is the recent N4LL global analysis of the Drell-Yan data, which provides a very precise control of the evolution due a huge span of energies (from 4 GeV to 1000 GeV). The second one is the determination of the Collins-Soper kernel from the twist-three TMD distributions.

Speaker: Alexey Vladimirov (Universidad Complutense de Madrid)

Vladimirov.pdf

15 Unpolarized TMDPDFs of the Nucleon from Lattice QCD

We present a first calculation of the unpolarized proton’s isovector transverse-momentumdependent parton distribution functions (TMDPDFs) from lattice QCD, which are essential to predict observables of multi-scale, semi-inclusive processes in the standard model. We use a Nf = 2 + 1 + 1 MILC ensemble with valence clover fermions on a highly improved staggered quark sea (HISQ) to compute the quark momentum distributions in large-momentum protons on the lattice. The state-of-the-art techniques in renormalization and extrapolation in correlation distance on the lattice are adopted. The one-loop contributions in the perturbative matching kernel to the light-cone TMDPDFs are taken into account, and the dependence on the pion mass and hadron momentum is explored. Our results are qualitatively comparable with phenomenological TMDPDFs, which provide an opportunity to predict high energy scatterings from the first principles.

Speaker: Jinchen He (University of Maryland, College Park)

TMD_workshop_pre.pdf

10:30 Break

Session II

16 Lattice QCD calculations of transverse momentum-dependent (TMD) observables

The status of an ongoing program of evaluating TMD observables
within Lattice QCD is reviewed. These lattice calculations are
based on a definition of TMDs through hadronic matrix elements
of quark bilocal operators containing staple-shaped gauge
connections. A parametrization of the matrix elements in terms
of invariant amplitudes serves to cast them in the Lorentz frame
preferred for a lattice calculation. A survey of the twist-2 TMD
sector as well as selected twist-3 TMD results are presented, and
advances in establishing control over systematic uncertainties
are exhibited.

Speaker: Michael Engelhardt (New Mexico State University)

talk (1).pdf

17 Lattice calculation of the Collins-Soper kernel

The Collins-Soper (CS) kernel is a nonperturbative function that characterizes the rapidity evolution of transverse-momentum-dependent parton distribution functions and wave functions. In this talk, we show the determination of the CS kernel using lattice QCD in two different strategies. We compare the results obtained from these two methods and also those from literature using various methods.

Speaker: Dr Hai-Tao Shu

Hai-Tao_Shu (1).pdf

18 Collins-Soper kernel from lattice QCD at the physical pion mass

This work presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions (TMDs) at different rapidity scales, using lattice Quantum Chromodynamics (QCD). This is the first lattice QCD calculation of the kernel at quark masses corresponding to a close-to-physical value of the pion mass, with next-to-next-leading order matching to TMDs from the corresponding lattice-calculable distributions, and includes a complete analysis of systematic uncertainties arising from operator mixing. The kernel is extracted at transverse momentum scales $ 240\,\rm{MeV} < q_{T} < 1.7 \,\rm{GeV}$ with a precision sufficient to discriminate between different phenomenological models in the non-perturbative region.

Speaker: Artur Avkhadiev (Massachusetts Institute of Technology)

Avkhadiev_CS_noon.pdf

12:30 Lunch

Session III

19 Transversity PDFs and GPDs from lattice QCD

Generalized parton distributions (GPDs) are important quantities that characterize the 3-D structure of hadrons, and complement the information extracted from TMDs. They provide information about the partons’ momentum distribution and also on their distribution in position space. Most of the information from lattice QCD is on the Mellin moments of GPDs, namely form factors and their generalizations. Recent developments in calculations of matrix elements of boosted hadrons coupled with non-local operators opened a new direction for extracting the x dependence of GPDs.

Traditionally, lattice QCD computations of GPDs have been carried out in a frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. However, such frames are inconvenient for lattice QCD calculations since each value of the momentum transfer requires a separate calculation, increasing the computational cost. Here, we present results extracted through a new Lorentz invariant parametrization that leads to more effective calculations of GPDs applicable for any frame, with freedom in the transferred momentum distribution. We demonstrate the efficacy of the formalism through numerical calculations using one ensemble of $𝑁_f=2+1+1$ twisted mass fermions with a clover improvement. The value of the light-quark masses lead to a pion mass of about 260 MeV. Concentrating on the proton and zero skewness, we extract the invariant amplitudes from matrix element calculations in both the symmetric and asymmetric frame, and obtain results for the twist-2 light-cone GPDs for unpolarized quarks, 𝐻 and 𝐸, as well as polarized quarks, $\widetilde{H}$.

Speaker: Martha Constantinou (Temple University)

CFNS_TMDs_June_2023_Constantinou.pdf

20 Transversely Polarized Distribution from Lattice QCD

We report an ongoing analysis of the lattice-QCD calculation of the isovector quark transversity distribution of the proton at physical pion mass at lattice spacing 0.06~fm using large-momentum effective theory. We compare our results with previous lattice calculations and discuss potential synergies with global analysis.

Speaker: Huey-Wen Lin (member@msu.edu;faculty@msu.edu;employee@msu.edu)

Transversely Polarized Distribution from Lattice QCD

21 Transversity PDF of the proton from lattice QCD with physical quark masses

The transversity PDFs, which describe the difference between probabilities to find a parton spin aligned and anti-aligned to the transversely polarized parent nucleon, is considerably less constrained from experiments due to their chiral-odd nature. Complementary information from lattice QCD is desired. In this talk, we report a calculation using a $N_f = 2 +1$ HISQ ensemble with physical-mass quarks and a lattice spacing of $a = 0.076$ fm. Applying short distance factorization to the ratio-scheme renormalized bi-local matrix elements of nucleon boosted up to 1.5 GeV, we extract the first few Mellin moments and reconstruct the Bjorken-x dependence using a deep neural network (DNN).  We also present the results from large-momentum effective theory approach utilizing a hybrid renormalization scheme.

Speaker: Xiang Gao

Transversity_XG.pdf

15:30 Break

Session IV

22 QCD Global Analysis of (Single-Hadron Fragmentation) Transverse Single-Spin Asymmetries: the Role of Lattice QCD in Phenomenology

I will report on a recent QCD global analysis of single-spin asymmetries involving observables where single-hadron fragmentation is relevant. This includes measurements of the Sivers, Collins, and \sin(\phi_S) effects in SIDIS, Collins effect in electron-positron annihilation, Sivers effect in Drell-Yan, and AN in single-inclusive proton-proton collisions, which are sensitive to important TMD and collinear twist-3 (quark-gluon-quark) functions. In particular, I will focus on the transversity function, which then can be used to calculate the tensor charges of the nucleon, and discuss the role of lattice QCD in the phenomenological analysis.

Speaker: Daniel Pitonyak (Lebanon Valley College)

Pitonyak_CFNS_2023.pdf

23 Simultaneous Global Analysis of Dihadron Fragmentation Functions and Transversity PDFs

We propose a new definition of unintegrated dihadron fragmentation functions (DiFFs) which is compatible with the probability interpretation of collinear DiFFs and derive the leading-order evolution equations for these DiFFs. With these new definitions, we perform the first simultaneous extraction of DiFFs and transversity PDFs using data from semi-inclusive annihilation (SIA) in electron-positron collisions, semi-inclusive DIS, and proton-proton collisions. In particular, we include new SIA data from Belle that provides, for the first time, experimental constraints on the unpolarized DiFFs, as well as proton-proton data from STAR at center of mass energy 500 GeV. We present results for the transversity PDFs and tensor charge and explore the impact of theoretical constraints such as the Soffer bound and lattice computations of the tensor charge.

Speaker: Christopher Cocuzza (Temple University)

CFNS2023 2 (1).pdf

18:00 Group dinner

Friday, 23 June

Session I

24 Small-x TMD factorization at NLO

Two-particle azimuthal correlations provide valuable insights into the dynamics of gluon saturation in collider experiments. In the kinematic regime where the two particles are produced sufficiently forward in rapidity but back-to-back in the transverse plane, the differential cross-section computed in the Color Glass Condensate (CGC) EFT, admits a small-x Transverse Momentum Dependent (TMD) factorization. This so-called TMD-CGC correspondence was shown to hold at leading order (LO) in [1] where TMD operators are related to correlators of Wilson lines in the CGC. At next-to-leading order (NLO), one encounters two types of potentially large contributions: high-energy (small-x) logs and Sudakov (soft) logs, which must be jointly resummed in order to attain reliable theoretical predictions. Their simultaneous resummation was proposed in [2] based on TMD factorization arguments. However, a complete NLO calculation justifying this correspondence has been missing in the literature. The subject of this talk is to elucidate this correspondence.

By examining the back-to-back limit of semi-inclusive dijet production in deep inelastic scattering (DIS) computed in the CGC EFT at NLO [3], we demonstrate that a kinematic constraint on the non-linear small-x evolution equation of the Weizsäcker Williams (WW) gluon distribution [4, 5] is essential for properly separating the phase space of small-x gluons and soft gluons. Remarkably, this kinematic constraint allows us to establish the first proof of small-x TMD factorization at NLO, as we show that all remaining NLO corrections can be fully factorized in terms of an NLO perturbative factor and the WW gluon distribution [6].

I will present preliminary results [6] for the differential cross-section of back-to-back dijets in DIS at small-x kinematics in the CGC EFT at NLO.

[1] F. Dominguez, C. Marquet, B-W. Xiao, and F. Yuan. Phys.Rev.D 83 (2011) 105005
[2] A. Mueller, B-W. Xiao, and F. Yuan. Phys.Rev.D 88 (2013) 11, 114010
[3] P. Caucal, F. Salazar and R. Venugopalan, JHEP 11 (2021) 222

[4] P. Caucal, F. Salazar, B. Schenke and R. Venugopalan. JHEP 11 (2022) 169
[5] P. Taels, T. Altinoluk, G. Beuf, C. Marquet. JHEP 10 (2022) 184

[6] P. Caucal, F. Salazar, T. Stebel, B. Schenke and R. Venugopalan (arXiv: 2304.03304).

Speaker: Farid Salazar (UCLA/UCB/LBNL)

CFNS_TMD_Salazar.pdf

25 Semi-inclusive diffractive deep inelastic scattering at small-x

We propose semi-inclusive
diffractive deep inelastic scattering (SIDDIS) to investigate the gluon tomography in the nucleon and
nuclei at small-x. The relevant diffractive quark and gluon parton distribution functions (DPDF) are computed in terms of the color dipole S-matrices in the fundamental and adjoint representations. respectively.

Speaker: Yoshitaka Hatta (BNL)

CFNS_TMD.pdf

26 Rapidity-only TMD factorization

Typically, a production of a particle with a small transverse momentum in hadron-hadron collisions is described
by CSS-based TMD factorization at moderate Bjorken $x_B\sim 1$ and by $k_T$-factorization at small $x_B$.
A uniform description valid for all $x_B$ is provided by rapidity-only TMD factorization developed in a series
of recent papers. In this talk, I will discuss two applications: power
corrections to DY hadronic tensor and one-loop result for
particle (Higgs) production by gluon fusion.

Speaker: Prof. Ian Balitsky (JLab/ODU)

30mintalk.pdf

10:30 Break

Session II

27 Proton spin at small-x

Resolution of the proton spin puzzle, which is inability of the constituent quark model to explain discrepancy between the spin-$1/2$ of the proton and the amount of spin carried by its quarks and gluons, as measured in experiment, is an outstanding problem in modern hadronic physics. One possibility is that ‘’missing” spin of the proton may be found at small values of Bjorken-x. I’ll give an overview of the current status of the theory of spin at small-x. Starting with a conventional approach which is based on a high-energy expansion in the shock-wave background, I’ll discuss the small-x evolution of the gluon and flavour-singlet quark helicity distributions. The evolution contains mixing between different types of operators appearing as sub-eikonal corrections to the leading order shock-wave approximation. The evolution is consistent with the spin-dependent DGLAP evolution at small-x. At the same time, I’ll show that the helicity evolution doesn’t provide a complete picture of the problem since it lacks the anomaly contribution. I’ll demonstrate that there is a class of spin-dependent observables which are dominated by the triangle anomaly in both Bjorken ($Q^2\rightarrow \infty)$ and Regge ($x_B\rightarrow 0$) asymptotics. The anomaly manifests itself as an infrared pole which appears in both limits. The cancellation of this pole involves a subtle interplay of perturbative and nonperturbative physics that is deeply related to the $U_A(1)$ problem in QCD. I’ll demonstrate the fundamental role played by a Wess-Zumino-Witten term, coupling the topological charge density to a “primordial” isosinglet meson, both in the cancellation of the infrared pole and topological mass generation of the eta prime meson. I’ll argue that such topological effects can be measured in polarized DIS at a future Electron-Ion Collider.

Speaker: Andrey Tarasov (North Carolina State University)

Tarasov. CFNS workshop.pdf

28 TMD Factorization and Renormalization at Next-to-Leading Power

Since shortly after the discovery of partons, people have thought about probing their transverse momentum inside hadrons. For example, in 1978 it was shown to give rise to an azimuthal cos(phi) asymmetry of the outgoing hadrons in the process of semi-inclusive DIS (SIDIS), known as the Cahn effect. The cos(phi) distribution, as well as a number of other asymmetries in both SIDIS and Drell-Yan, are difficult to study since in QCD they first appear at subleading order in the small transverse momentum expansion. These observables have traditionally been studied at tree level using the parton model. In this talk I show that the use of effective field theory makes it possible to treat these observables systematically. Utilizing the soft-collinear effective theory formalism we completely determine the structure of contributions to all orders in perturbation theory. Interestingly, we find that dynamical soft gluon contributions remains simple at this power. We show that the only new ingredients are a set of the quark-gluon-quark (qgq) correlators, which come along with only one new Wilson coefficient. Perturbative matching calculations for the qgq correlators reveal novel additive rapidity divergences as well as endpoint divergences in the convolution of energy fractions, thus making the renormalization and factorization nontrivial and interesting. I discuss our solution to removing these divergences to define renormalized qgq correlators. Our results for the subleading power azimuthal asymmetries, establish them as useful observables within QCD, and enable higher precision predictions.

Speaker: Anjie Gao (MIT)

talk_CFNS.pdf

29 Transverse Momentum Distributions of Heavy Hadrons and Polarized Heavy Quarks

We initiate the study of transverse momentum-dependent (TMD) fragmentation functions for heavy quarks, demonstrate their factorization in terms of novel nonperturbative matrix elements in heavy-quark effective theory (HQET), and prove new TMD sum rules that arise from heavy-quark spin symmetry. We discuss the phenomenology of heavy-quark TMD FFs at $B$ factories and find that the Collins effect, in contrast to claims in the literature, is not parametrically suppressed by the heavy-quark mass. We further calculate all TMD parton distribution functions for the production of heavy quarks from polarized gluons within the nucleon and use our results to demonstrate the potential of the future EIC to resolve TMD heavy-quark fragmentation in semi-inclusive DIS, complementing the planned EIC program to use heavy quarks as probes of gluon distributions.

Speaker: Johannes K. L. Michel (MIT CTP)

Johannes_Michel_CFNS_Workshop_Heavy_TMDs.pdf