[Hadstruct] [EXTERNAL] Collaboration Meeting....

Tue Sep 15 11:11:42 EDT 2020

Dear David, Anatoly and All,

You might have seen the chain of email exchange on the topic of threshold resummation during last week's workshop.  I think, the issue is effectively settled.  Of course, I might have missed some emails about this.

To simplify our future discussion on all-order QCD factorization of quasi-PDF, if we are going to have one, I summarize below the key points from the discussion that we had with LaMET people on this issue following the last week’s workshop.

Please let me know if you have any questions.

Best,

Jianwei
==================
Points that people more or less agree:
(1) The equal-time quark-quark operator that defines the quasi-PDF is not a physical observable, like DIS/Drell-Yan cross section, and requires additional UV renormalization beyond that defines pQCD;

(1’) The renormalization can be achieved by many different approaches, and their perturbative differences should be reflected in the differences in perturbatively calculated matching coefficients;

(2) This operator is NOT leading twist, and is proved to be multiplicative renormalizable in position-space to all orders in pQCD, as presented in Eq. (16) of [arXiv:1706.08962] or Eq. (27) of [arXiv:1707.03107] with a position ($z$) dependent renormalization factor;

(3) With the multiplicative renormalizability in position space, hadron matrix elements of this operator in position-space can be factorized in terms of PDFs in momentum space to all orders in pQCD, with corrections at $O(z^2\Lambda_{QCD}^2)$, as argued in [arXiv:1404.6860];

(3’) The same all-order factorization has also been proved by applying OPE, as done in  [arXiv:1709.03018], and [arXiv:1801.03917].

(4) Fourier transform of this renormalized and factorized matrix elements with respect to $pz\cdot z$ (Ioffe time), while holding $z^2$ small, one gets corresponding pseudo-PDF and its all-order factorized expression in terms of normal PDF in momentum space [arXiv:1705.01488];

(4’) Fourier transform of the same renormalized and factorized matrix elements with respect to $z$, while holding $pz$ large, one gets corresponding quasi-PDF, which should have a formally factorized term in terms of the PDF in momentum space, plus a non-perturbative correction sensitive to the matrix elements at large $z$ and corresponding non-perturbative renormalization at large $z$ (due to the (1) above), which is sensitive to “cancellation” in exponential;

Points of disagreement:
(1) LaMET people believe that there is a multiplicative renormalization for quasi-PDF in momentum space, and then, the argument given in [arXiv:1404.6860] should carry through to prove the factorization of quasi-PDF in momentum space, without the need to go to position space;

(1’) The Fourier transform of the position ($z$) dependent multiplicative renormalization constant in position space does not lead to a multiplicative renormalizability in momentum-space (unique feature of equal-time operator).

What is needed:
(1) Need a well-justified proof of multiplicative renormalizability of the parton-parton operators that define quasi-PDFs in momentum-space.
==================

________________________________
From: Hadstruct <hadstruct-bounces at jlab.org> on behalf of David Richards <dgr at jlab.org>
Sent: Tuesday, September 15, 2020 10:15 AM
To: Anatoly Radyushkin <radyush at jlab.org>
Cc: hadstruct at jlab.org <hadstruct at jlab.org>
Subject: Re: [Hadstruct] [EXTERNAL] Collaboration Meeting....

Hi Anatoly,

Fair enough…. …threshold resummation is another topic in the same category!

David

On Sep 15, 2020, at 9:43 AM, Anatoly Radyushkin <radyush at jlab.org<mailto:radyush at jlab.org>> wrote:

My experience is that discussions on this topic are endless.
We are not working with coordinate space,
so factorization in qPDF is not a primary topic.
So, I personally would prefer if we start with discussion of new results,
if any.  Then, maybe,to discussion of  the last-week workshop .
If there will be no time left for factorization in qPDF, so be it.

________________________________
From: Hadstruct <hadstruct-bounces at jlab.org<mailto:hadstruct-bounces at jlab.org>> on behalf of David Richards <dgr at jlab.org<mailto:dgr at jlab.org>>
Sent: Tuesday, September 15, 2020 9:30 AM
To: jmkarpie at email.wm.edu<mailto:jmkarpie at email.wm.edu> <jmkarpie at email.wm.edu<mailto:jmkarpie at email.wm.edu>>
Cc: hadstruct at jlab.org<mailto:hadstruct at jlab.org> <hadstruct at jlab.org<mailto:hadstruct at jlab.org>>
Subject: Re: [Hadstruct] [EXTERNAL] Collaboration Meeting....

Hi Joe,

I think that Anatoly has to leave at around 10am, so we should probably open with that discussion?

David

On Sep 14, 2020, at 6:24 PM, Joseph Karpie <jmkarpie at email.wm.edu<mailto:jmkarpie at email.wm.edu>> wrote:

Can I suggest that we spend a, preferably limited, amount of time on the issue of factorization of the quasi-PDF? I have had some back and forth with Anatoly on this topic this afternoon. I believe it would be good if all of HadStruc can be in agreement on the existence or lack there of this issue. If we can all be convinced by Jianwei's comments, then it would be stronger if we can have a common list of arguments that we can use to appear unified while discussing with others.

On Mon, Sep 14, 2020 at 1:46 PM David Richards <dgr at jlab.org<mailto:dgr at jlab.org>> wrote:
Hi All,

We decided not to have a meeting last week, but left it open as to whether to meet this Wednesday (9am) or Friday (11am), and indeed Savvas asked me about that this morning.   So…. ….I think it would be very timely to meet this Wednesday at 9am - there is a conflict with EIC YR workshop on both days, but looking at the agenda, I suspect Wednesday AM may be less critical for members of our community.  DOES STARTING THIS WEEK AS THE “WEDNESDAY” WEEK MAKE SENSE?

Lots of stuff to talk about, it seems to me….

- followup from LaMET
- updates on running, and in particular distillation.
- ….

Regards,
David

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