Difference between revisions of "Discussion 11-04-24"
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** Do quarks with spin parallel to the proton’s spin have smaller or larger transverse momentum? | ** Do quarks with spin parallel to the proton’s spin have smaller or larger transverse momentum? | ||
* The helicity-dependent TMD g<sub>1</sub><sup>q</sup> is a function of both x (the struck quark fractional momentum) and k<sub>T</sub> (the struck quark transverse momentum). | * The helicity-dependent TMD g<sub>1</sub><sup>q</sup> is a function of both x (the struck quark fractional momentum) and k<sub>T</sub> (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 | + | * 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 A<sub>1</sub>. This asymmetry can be written in terms of the helicity-independent TMDs (f<sub>1</sub><sup>q</sup>) and the helicity-dependent TMDs (g<sub>1</sub><sup>q</sup>). |
| − | ** | + | ** To access the TMDs from A<sub>1</sub> relies on a factorization theorem that is valid for Q<sup>2</sup> >> M<sup>2</sup> and q<sub>T</sub><sup>2</sup> << Q<sup>2</sup> (where q<sub>T</sub> = k<sub>T</sub>/z = k<sub>T</sub>/E<sub>had</sub>/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). | ** 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). | * 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). | ||
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Questions/comments from discussion: | Questions/comments from discussion: | ||
| − | * The form of the non-perturbative part of | + | * The form of the non-perturbative part of g<sub>1</sub> 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 |g<sub>1</sub>| < f<sub>1</sub> a priori. |
| − | * The assumption of the so-called positivity constraint g<sub>1</sub>/f<sub>1</sub> * 1/k<sub>norm</sub>(x) | + | * The assumption of the so-called positivity constraint g<sub>1</sub>/f<sub>1</sub> * 1/k<sub>norm</sub>(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<sub>T</sub> = 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<sub>T</sub> | + | * 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<sub>T</sub> (the hadron transverse momentum). This point needs to be clarified to make the argument less ambiguous. The problem for the high-p<sub>T</sub> region is that it cannot be described in terms of TMDs, because the TMD factorization theorem is not valid. The high-p<sub>T</sub> 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<sub>T</sub>/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. | * The assumption of factorization that q<sub>T</sub>/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. | * 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. | * 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<sub>T</sub> | + | * The phenomenology developed in this work is limited to k<sub>T</sub> < 0.6 – it cannot be pushed to higher k<sub>T</sub> (up to >1 GeV) without additional development. However, the higher k<sub>T</sub> (or p<sub>T</sub>) range is most relevant for JLab @ 22 GeV. |
Latest revision as of 15:28, 5 November 2024
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 g1q is a function of both x (the struck quark fractional momentum) and kT (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 (f1q) and the helicity-dependent TMDs (g1q).
- To access the TMDs from A1 relies on a factorization theorem that is valid for Q2 >> M2 and qT2 << Q2 (where qT = kT/z = kT/Ehad/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/knorm(x) ≤ 1 was also questioned and should be better detailed. With the MAP parameterization, that inequality is needed to impose the positivity constraint at kT = 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 pT (the hadron transverse momentum). This point needs to be clarified to make the argument less ambiguous. The problem for the high-pT region is that it cannot be described in terms of TMDs, because the TMD factorization theorem is not valid. The high-pT tail will be very useful to understand when the TMD formalism breaks down and the perturbative regime is reached.
- The assumption of factorization that qT/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 kT < 0.6 – it cannot be pushed to higher kT (up to >1 GeV) without additional development. However, the higher kT (or pT) range is most relevant for JLab @ 22 GeV.