TMD Collaboration Meeting

15 Jun 2022, 08:00 → 17 Jun 2022, 17:00 America/Denver

Canyon (Hilton Santa Fe Historic Plaza)

The 5th and final Collaboration Meeting of the TMD Topical Collaboration will be held in-person in Santa Fe, NM, at the Hilton Santa Fe Historic Plaza hotel, June 15-17, 2022. Hybrid (virtual) participation will be available.

This meeting aims not only at recapping research accomplishments since the last TMDc meeting but taking stock of the progress that TMDc has made over its > 5 year span. As such we will have sessions discussing final reports regarding the various milestones that TMDc set out to achieve, as well as finalizing the TMD Handbook we have worked so hard to produce, taking account of student input from the Jan 2022 TMD Winter School.

There will a be a $100 registration fee for attending the meeting in-person to cover onsite costs. Payment will be through the New Mexico Consortium, you must register and pay on this website: NMC's TMD Collaboration Meeting website.

Registration will include lodging during the Meeting dates. Funds for reimbursing other travel expenses will be extremely limited. Please inquire with clee@lanl.gov if you are genuinely in need of such support.

Lodging registration and abstract submission deadline is May 13, 2022. We cannot guarantee a hotel room after this date. (Submit the dates you need lodging on your registration form, the organizers will reserve the room for you.)

Wednesday, 15 June

08:00 Breakfast & check-in

Talks I

1 Welcome

Speaker: Christopher Lee (LANL)

2 Intro

Speaker: Jianwei Qiu

TMD-2022-Qiu.pdf

3 The Drell-Yan q_T Spectrum and Its Uncertainty at N3LL'

We provide state-of-the art SCETlib predictions for the $W$ and $Z/\gamma^∗$ transverse-momentum ($q_T$) distributions at the LHC at complete three-loop order in resummed perturbation theory (N$^3$LL$'$) and matched to available fixed order. We compare our predictions to high-precision measurements by the ATLAS and CMS experiments. We pay particular attention to the estimation of perturbative theory uncertainties via profile scale variation and the parametric uncertainty from the collinear PDF set and the value of the strong coupling, in turn allowing us to assess to what extent they may compensate the impact of the nonperturbative TMD structure of the proton and its evolution at small $q_T$. We find intriguing evidence that the normalized ATLAS and CMS $Z$ $q_T$ spectra may prefer a lower strong coupling than the PDG value, with important implications for the extraction of TMD PDFs from LHC data.

Speaker: Johannes Klaus Ludwig Michel (Center for Theoretical Physics)

Michel_TMD_Workshop_2022-06-15.pdf

4 Axial Gauge and Wilson Lines of Infinite Extent

Two gluon TMDs with different Wilson line configurations have been studied intensively at small-x: the Weizsacker-Williams type and the dipole type. They have different transverse momentum dependences and thus they will correspond to two different integrated gluon distributions. However, these two distributions have exactly the same expressions in light-cone gauge. In this talk, I will discuss the subtlety when using axial gauge (light-cone gauge is one kind of axial gauge) to study correlation functions of non-Abelian field strengths dressed with Wilson lines of infinite extent. I will explain the breakdown of naive axial gauge by showing an explicit example of perturbative calculations and discussing the issue from a path integral perspective. I will also illuminate under what conditions naive application of axial gauge will lead to unreliable results.

Speaker: Xiaojun Yao (Massachusetts Institute of Technology)

tmd_XY.pdf

10:30 Coffee break

Talks II

5 Independent amplitudes in the quark and antiquark correlators and TMDs in the covariant parton model

Covariant parton model (CPM) is a generalization of the Feyman's parton
model which does not prefer any special reference system. Within the
framework of covariant parton model, we study the properties of the quark
and antiquark correlators determined by the equations of motion of the
free partons, and derive the polarization vectors for quarks and
antiquarks in mixed-spin and pure-spin states. We show that for partons in
the pure-spin state, there is only one polarized and one unpolarized
amplitude in each of the quark and antiquark correlator.

Speaker: Fatma Aslan (JLab/UConn)

TMD_2022.pdf

6 Global Analysis of Worm-Gear Function g_1T

We report on the first global QCD analysis of the worm gear function g_1T, based on data from COMPASS, HERMES and Jefferson Lab. The results are compared to the Wandzura-Wilczek approximation, the large-Nc approximation, and information from lattice QCD. The talk is based on the preprint arXiv:2110.10253.

Speaker: Shohini Bhattacharya

TMD_Collab_Meeting2022_Shohini-1.pdf

7 Global Analysis of Single Transverse-Spin Asymmetries

I will discuss the latest results from a global analysis of single transverse-spin asymmetries that includes data from SIDIS, electron-positron annihilation, Drell-Yan, and single-inclusive proton-proton collisions as well as constraints on transversity from lattice QCD and the Soffer bound. This aligns with Milestone 6 of the TMD Collaboration.

Speaker: Daniel Pitonyak (Lebanon Valley College)

Pitonyak_TMDc2022.pdf

12:30 Lunch

8 Handbook Discussions

15:30 Coffee break

9 Milestones & Final Report

18:30 Dinner

Thursday, 16 June

08:00 Breakfast

Talks III

10 Lattice QCD Determination of the Bjorken-x Dependence of PDFs at Next-to-next-to-leading Order

The large-momentum effective theory (LaMET) is a systematic approach to calculate parton physics from Euclidean approaches such as lattice QCD. With major improvements in the non-perturbative renormalization and perturbative matching, the lattice calculation of PDFs with LaMET is now entering the stage of precision control. In this talk, I will present a state-of-the-art lattice QCD calculation of pion valence quark distribution with the hybrid scheme and the first-time implementation of next-to-next-to-leading order matching correction, which is done using two fine lattices with spacings a=0.04 fm and 0.06 fm and valence pion mass 300 MeV at boost momentum as large as 2.42 GeV. I will demonstrate that the renormalization and the perturbative matching in Bjorken-$x$ space yields a reliable determination of the valence quark distribution for moderate x with controlled systematic uncertainties, which is in nice agreement with the most recent global analyses.

Speaker: Yong Zhao (Argonne National Laboratory)

TMD_2022_yzhao.pdf

11 Improving Lattice QCD calculations of the Collins-Soper Kernel

Collins-Soper (CS) evolution kernel is critical to relate transverse-momentum-dependent parton distribution functions (TMDPDFs) at different scales. When the parton transverse momentum is small, q_T \sim \Lambda_{QCD}, the CS kernel is non-perturbative; the determination of the CS kernel in the non-perturbative regime can only be done through experiment or first-principles calculations. I will review how lattice QCD can be used to compute the CS kernel through Large-Momentum Effective Theory, how results from lattice calculations compare with phenomenological fits, and provide an update on ongoing efforts to improve the precision of current lattice QCD results from forward matrix elements with a complementary approach via quasi-TMD wavefunctions.

Speaker: Artur Avkhadiev (Massachusetts Institute of Technology)

Avkhadiev_Improving_LQCD_CS_Kernel.pdf

12 Quark spin-orbit correlations in the proton from lattice QCD

Generalized transverse momentum-dependent parton distributions (GTMDs)
provide a comprehensive framework for imaging the internal structure of
the proton. In particular, by encoding the simultaneous distribution of
quark transverse positions and momenta, they allow one to directly access
longitudinal quark orbital angular momentum, and, moreover, to
correlate it with the quark helicity. The relevant GTMD is evaluated
through a lattice calculation of a proton matrix element of a quark
bilocal operator (the separation in which is Fourier conjugate to the
quark momentum) featuring a momentum transfer (which is Fourier conjugate
to the quark position), as well as the Dirac structure appropriate for
capturing the quark helicity. The weighting by quark transverse position
requires a derivative with respect to momentum transfer, which is obtained
in unbiased fashion using a direct derivative method. The lattice
calculation is performed directly at the physical pion mass, using
domain wall fermions to mitigate operator mixing effects. Both the
Jaffe-Manohar as well as the Ji quark spin-orbit correlations are
extracted, yielding evidence for a strong quark spin-orbit coupling
in the proton.

Speaker: Michael Engelhardt

talk_sf.pdf

10:30 Coffee

Talks IV

13 Lattice-to-continuum factorization for TMDs

Non-perturbative parton distributions that arise in the factorization of cross-sections are inaccessible to direct lattice QCD calculations, as their lightcone-dominated dynamics induce a real-time sign problem. One may circumvent this issue by constructing a lattice-calculable distribution that shares the same IR physics as the desired physical distribution, and then connecting the two distributions with a factorization formula. In this talk, I prove such a relation for quasi (lattice) and Collins (physical) TMDs that holds at leading power to all orders in α_s, for all spins and parton flavors.

Speaker: Stella Schindler (MIT)

schindler-tmd.pdf

14 Simultaneous extraction of collinear and transverse momentum dependent parton densities using Drell-Yan data

Drell-Yan production data have been used to extract transverse momentum dependent parton distribution functions (TMDPDFs). The evolution of these non-perturbative objects is conveniently described in $b_T$ space, which is the Fourier conjugate to transverse momentum. Both perturbative QCD calculations and non-perturbative TMD functions comprise the Drell-Yan cross section at low and high regions of the $b_T$ spectrum, respectively. The perturbative QCD description includes the operator product expansion, which has dependence on collinear PDFs. We particularly focus on the $\pi A$ Drell-Yan experimental data and the effects on pion parton distributions. We also show progress in the nucleon sector with high-energy Drell-Yan and $Z$-boson production data.

Speaker: Patrick Barry (Jefferson Lab)

Barry_TMDc.pdf

15 Medium modifications in the initial and final states to heavy-flavor production in $pA$ and $AA$ collisions

Speaker: Weiyao Ke (Los Alamos National Laboratory)

TMD22-WK.pdf

12:30 Lunch

16 Handbook Feedback and Discussion

15:30 Coffee break

17 Handbook Publication Discussion

18:30 Dinner

Friday, 17 June

08:00 Breakfast

Talks V

18 Factorization for Subleading Power TMD Observables

TMD distributions depending on the azimuthal angle provide a non-trivial example of observables that start at subleading order in the power expansion. They also have a long history, for example in 1978 Cahn showed that quark transverse momentum gives rise to an azimuthal cos(phi) asymmetry of the outgoing hadrons in semi-inclusive DIS (SIDIS). Such subleading distributions also are an interesting probe of the spin structure of hadrons. In this talk I study the full set of such subleading TMD distributions in SIDIS, Drell-Yan (DY), and e+e- to back-to-back hadrons. Under the assumption that leading power Glauber interactions do not spoil factorization at this power, I provide a complete derivation of factorization for these structure functions using soft-collinear effective theory. This yields generalized definitions of the TMDs that depend on two longitudinal momentum fractions (one of them only relevant beyond tree level), and a complete proof that only the same leading power soft function appears and can be absorbed into the TMD distributions at this order. We also show that perturbative corrections can be accounted for with only one new hard coefficient. Factorization formulae are given for all spin dependent structure functions which start at next-to-leading power. Prospects for improved subleading power predictions that include resummation are discussed.

Speaker: Anjie Gao (Massachusetts Institute of Technology)

Anjie_TMDc.pdf

19 TMD Factorization at subleading Twist

We will present our results for TMD factorization at sub-leading power and focus on the matching of the large and small transverse momentum contribution in semi-inclusive deep inelastic scattering process (SIDIS and Drell Yan). We investigate their connection, paying special attention to azimuthal distributions such as the Cahn effect. Our results have consequences for the extension of transverse momentum-dependent factorization beyond leading twist.

Speaker: Leonard Gamberg (Penn State University)

Gamberg_TMDc_0622-ff.pdf

20 Toward TMD Resummation at NLL+NLP

In this talk, I will discuss our ongoing work in establishing a factorization and resummation formalism in Drell-Yan and Semi-Inclusive DIS which takes into consideration the evolution of TMDs at sub-leading power.

Speaker: John Terry (UCLA)

talk.pdf

10:30 Coffee break

Talks VI

21 nucleon charges and moments of PDFs from lattice QCD

I will review results for nucleon charges and moments of momentum fraction, helicity and transversity obtained from lattice QCD and discuss systematics using the results obtained by the LANL lattice QCD team as benchmarks.

Speaker: Rajan Gupta (Los Alamos National Lab)

TMD_LQCD_2022June.pdf

22 Observables for Longitudinal and Transverse Orbital Angular Momentum

Speaker: Simonetta Liuti (University of Virginia)

liuti_INT22_2.pdf

23 Energy-Energy Correlators in Deep inelastic Scattering

Event shape observables have been widely used for precision QCD studies at various lepton and hadron colliders. We present recent calculations of the (transverse) energy-energy correlation event shape variable distributions in deep-inelastic scattering. In the framework of soft-collinear effective theory the cross section can be factorized as the convolution of the hard function, beam function, jet function and soft function in the back-to-back limit. A close connection to TMD factorization is established, as the beam function when combined with part of the soft function is identical to the conventional TMD parton distribution function, and the jet function is the second moment of the TMD fragmentation function matching coefficient. We validate our framework by comparing the obtained LO and NLO leading singular distributions to the full QCD calculations in the back-to-back limit. Results are obtained in the laboratory frame and the Breit frame (albeit with somewhat different observable definitions). In both cases we report the resummed (transverse) energy-energy correlation distributions up to N3LL accuracy matched with the NLO cross section. The Breit frame observable is shown to be insensitive to experimental pseudorapidity cuts, often imposed in the laboratory frame due to detector acceptance limitations. Non-perturbative effects are also discussed. The (T)EEC distributions provide a new way to precisely study TMD physics at the future Electron-Ion Collider.

Speaker: Ivan Vitev

EIC_TEEC-TMD-Vitev.pdf

12:30 Lunch

24 Final Report and Future Plans

TMD-2022-Qiu.pdf