Discussion 11-04-24

Speakers and participants, please review the guidance provided on the main page. This agenda page is editable by anyone that has a Jefferson Lab computing account. Feel free to log in and post comments, questions, or answers to questions in the section below.

Meeting Location

The 22 GeV Open Discussions will be held here:

• Date/Time: Monday, November 4 at 12:30 PM Jefferson Lab Local Time
• Physical Location: CEBAF Center F224/5
• Virtual Location: Zoom Meeting Number 161 111 8017 (The password is the two-digit number that appears before "GeV" in the first sentence of this section.)

Agenda

• Phenomenology of helicity TMD PDF: status and challenges (Matteo Cerutti)

Comments and Questions

• (Add content here)

Minutes/Notes (D.S. Carman)

Local participants at JLab: 10; Remote participants: 25

Goal – To extract details on the internal structure of the proton from the helicity-dependent Transverse Momentum Distribution (TMD) functions.

Note: This discussion is based on the paper, A. Bacchetta, A. Bongallino, M. Cerutti, M. Radici, and L. Rossi, “Exploring the 3D Momentum Distribution of Longitudinally Polarized Quarks in the Proton”, arXiv: 2409.18078, Sep. 26, 2024.

Presentation points:

• The main questions to address from this program include:
  • How does the polarization of the proton reflect its internal structure in three dimensions?
  • How does the polarization of the quarks distort their transverse momentum?
  • Do quarks with spin parallel to the proton’s spin have smaller or larger transverse momentum?
• The helicity-dependent TMD g₁^q is a function of both x (the struck quark fractional momentum) and k_T (the struck quark transverse momentum).
• Access to the helicity-dependent TMDs is typically through either SIDIS measurements with a longitudinally polarized target or also Drell-Yan processes. The focus of this discussion for JLab @ 22 GeV is on SIDIS. The experimental quantity that is extracted is the double-spin asymmetry A₁. This asymmetry can be written in terms of the helicity-independent TMDs (f₁^q) and the helicity-dependent TMDs (g₁^q).
  • To access the TMDs from A₁ relies on a factorization theorem that is valid for Q² >> M² and q_T² << Q² (where q_T = k_T/z = k_T/E_had/ν).
  • In the regime where the factorization assumptions are valid, the experimental observables can be written in terms of “universal” objects (i.e. process independent quantities).
• The assumption made to access the helicity-dependent TMDs in this work is that the unpolarized TMDs are already known from previous phenomenological analysis (the MAP22 extraction is assumed).
  • MAP is the Multi-Dimensional Analysis of Partonic Distribution Collaboration.
• The evolution of the TMDs in this phenomenological analysis is assumed to follow from the CSS approach (Collins, Soper, Sterman, Nucl. Phys. B 261, 104 (1985)).
• The available data (mainly) come from HERMES – K+/ K- production from deuterons, K+/ K- and π+/π- production from protons – but there are less than 300 data points surviving the kinematical cuts (for TMD factorization) and the uncertainties are relatively large. Thus new, precise data would be very welcome from JLab @ 22 GeV.
  • Data from JLab @ 22 GeV would be important as target-mass corrections and higher-twist corrections are expected to be smaller at higher energies. Thus, data at 22 GeV is preferred over data from the JLab12 program.
• Phenomenology challenges:
  • There are not many constraints on the fitted parameters based on the available data. This is mainly due to the lack of constraining power from the HERMES data, and from the non-trivial correlations between the helicity and the unpolarized TMDs;
  • The HERMES data at large x violate the positivity constraint |A₁|> 1, but they have large uncertainties. New data in that region are needed (data at 22 GeV is preferred over data from the JLab12 program to avoid small-Q effects).

Questions/comments from discussion:

• The form of the non-perturbative part of g₁ relies on the assumption of a parameterization in terms of a simple Gaussian times the MAP12 functional. This is an important assumption whose implications should be detailed. It is needed to apply a reliable prescription to impose the positivity constraint |g₁| < f₁ a priori.
• The assumption of the so-called positivity constraint g₁/f₁ * 1/k_norm(x) ≤ 1 was also questioned and should be better detailed. With the MAP parameterization, that inequality is needed to impose the positivity constraint at k_T = 0, above all in the region of x where the collinear helicity PDF is of the same size of the unpolarized PDF.
• There was quite some discussion about what happens to the helicity-dependent TMDs at large x. In fact, there was quite some focus on measurements at high x when JLab22 is mainly relevant in the SIDIS regime at high p_TT (the hadron transverse momentum). This point needs to be clarified to make the argument less ambiguous. The problem for the high-p_T region is that it cannot be described in terms of TMDs, because the TMD factorization theorem is not valid. The high-p_T tail will be very useful to understand when the TMD formalism breaks down and the perturbative regime is reached.
• The assumption of factorization that q_T/Q << 1 is questionable in the case of ρ production. This needs to be considered and expanded upon. However, there are no theoretical results on the modification of TMD factorization up to now.
• Need to make projections for the helicity-dependent TMDs for JLab22 based on the planned programs with CLAS22 and SoLID.
• A general caution was provided about putting the phenomenological results for π and K on the same footing due to possible differences in the applicability of the factorization assumption – this should be clarified/considered. However, a phenomenological proof of the reliability of the factorization is shown by the good quality of the simultaneous fit of kaons and pion, in both the unpolarized and the polarized analyses of the MAP collaboration.
• The phenomenology developed in this work is limited to k_TT < 0.6 – it cannot be pushed to higher k_TT (up to >1 GeV) without additional development. However, the higher k_TT (or p_TT) range is most relevant for JLab @ 22 GeV.