[Gpdtc] Wednesday....

[Jianwei Qiu]

Dear David and all,

Thanks for your effort of putting this together.  I agree with Wally's comments, and have one more for discussion.

I noticed a potential confusion or contradiction.  We said on slide #4, "First-principle lattice calculations of ... x-dependent GPDs ...", while we also said on slide #5 -bullet 3, "Global ... to extract ... GPDs ...".  We would not need to "extract" GPDs from global analysis if we were able to calculate them from the "first-principle lattice calculations".

As we all know, such potential confusion or contradiction is caused by the fact that we cannot calculate GPDs directly from "first-principle lattice calculations".  What we can calculate are matrix elements that have good information on GPDs, while they contain contributions beyond the GPDs, such as high twist contributions that could be related to multi-parton correlations.

In some senses, what we can calculate on lattice likes the inclusive DIS cross section that we can measure from experiment.  Inclusive DIS cross section carries a good information on PDFs, but, has high twist contributions that cannot be represented by PDFs.  When $Q^2$ and $\sqrt{S}$ are asymptotically large, while in the scaling regime, the leading power and leading order contribution dominates and the inclusive DIS cross section is directly proportional to the quark-pdf at $x_{Bj}$, like what Feynman told us many years ago in terms of his parton model.  But, for any realistic $Q^2$ and $\sqrt{S}$, we have to rely on QCD factorization and worry about the high-twist or power corrections, and need QCD global analysis to help extract PDFs.

As pointed by Xiangdong, when $P\to\infnty$, the F.T. of the hadron matrix element with space separated parton-parton correlator can be approached to PDFs (or GPDs).  More precisely, when $P\to\infty$ (like the $\sqrt{S}\to\infty$) and $z^2\to 0$ (like $1/Q^2\to 0$), while $P\cdot z$ is finite, the F.T. of the lattice QCD calculated hadron matrix element approaches to the PDF.  For any realistic $P$ and $z$, like the inclusive DIS cross section, we will have to rely on QCD factorization and worry about the high-twist or power corrections, and need QCD  global analysis to help extract PDFs, which applies to GPDs as well.

Of course, in Euclidean space, $z^2$ small is the same as $z$ small, different from inclusive DIS where $1/Q^2$ small is not necessary meaning $1/q$ is small.

To get reliable full GPDs with $x,\xi, t$ dependence, or special case for 3D spatial imaging when we need F.T. of GPDs in $t_T$ at $\xi\to 0$, QCD global analyses are necessary.  A three-prong approach, as I mentioned in my previous message, (1) Theory - factorization, (2) lattice QCD - generate data complementary to experimental data, and (3) Phenomenology - QCD global analyses to extract full GPDs from both lattice and experimental data, could be a good selling point of this proposal for our joint effort.

With this said, I would suggest not over emphasize the term "first-principle LQCD calculation of x-dependent GPDs".  Instead, we state the "first-principle calculation of lattice observable" that gives good information on GPDs, complementary to experimentally measured observable.  This approach does not weaken in any way of the importance of LQCD calculations, since we never said it is not important to spend a lot of money and manpower to measure Drell-Yan, jet, DVCS, ... cross sections although they do not directly give the PDFs, GPDs ...

I am confident that we can put together a very strong TC proposal.  Please let me know if you have any questions on what I wrote here.

Best,

Jianwei








We might think of a better way to say this

________________________________
From: Gpdtc <gpdtc-bounces at jlab.org> on behalf of Wally Melnitchouk <wmelnitc at jlab.org>
Sent: Monday, January 10, 2022 11:02 PM
To: David Richards <dgr at jlab.org>
Cc: gpdtc at jlab.org <gpdtc at jlab.org>
Subject: Re: [Gpdtc] Wednesday....

Thanks, David, for putting this together.

On slide 4, 3rd bullet: a suggestion for alternative wording for the is "Development of global QCD analysis methods with uncertainty quantification for PDFs and TMDs, and their extension to (3D) GPDs."

Slide 5, point #1: there might be potential uncertainty about what exactly "QCD-inspired descriptions of GPDs and CFFs" refers to. If it is some other than model calculations of GPDs and CFFs, perhaps this should be specified a bit more explicitly?

Slide 5, point #2: is it just the x dependence of GPDs that is of interest, or also the ξ (skewedness) dependence, along with the t dependence?

Slide 5, point #3: "Global QCD analysis with uncertainty quantification to extract..." Again, I would like to be careful about how "QCD-inspired descriptions" would be used to extract GFFs and GPDs, as we don't want to imply that models will be used to help determine these from data (since we may want to "test" models rather than assume them).

Slide 5, point #5: what is the significance of this point being in parentheses?

Slide 6: maybe put dots after a bullet below "William and Mary" to suggest other institutions may be involved too?

Wally


________________________________
From: Gpdtc <gpdtc-bounces at jlab.org> on behalf of David Richards <dgr at jlab.org>
Sent: Monday, January 10, 2022 5:06 PM
To: gpdtc at jlab.org <gpdtc at jlab.org>
Subject: [Gpdtc] Wednesday....

Hi All,

Before I go too far down writing something for Wednesday, please find attached some first thoughts - without figures.


The first couple of slides are basically some observations about the call, and what are likely to be the criteria (NB I could have also included diversity in all its interpretations…).
The real issue is how much should we discuss about our discussions and aims in the context of this meeting (transparency 5), and should I say (verbally or on paper) who is currently in our discussions (page 6) - I’ve listed institutions + (incomplete) names.  I make the point on page 3 that the creation of long-term positions is an important task, but I’m not sure I would want to say in writing where those positions might be.

I’ve taken the Executive Summary document, and page 5 is basically the extraction of that.  But we had some discussion before the break as to what the focus should be - for example, purely to extract GPDs, or aim to learn something more about the internal dynamics of hadrons (ie as Christian was discussing).  Similarly, Global Fitting or are there some better words we can use?


Regards,
David
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