<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=Windows-1252">
<style type="text/css" style="display:none;"> P {margin-top:0;margin-bottom:0;} </style>
</head>
<body dir="ltr">
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Dear David, Anatoly and All,</div>
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
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.</div>
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
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.<br>
<div><br>
</div>
<div>Please let me know if you have any questions.</div>
<div><br>
</div>
<div>Best,</div>
<div><br>
</div>
<div>Jianwei<br>
</div>
<div>==================<br>
</div>
<div><i>Points that people more or less agree:</i></div>
<div>(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;</div>
<div><br>
</div>
<div>(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;</div>
<div><br>
</div>
<div>(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; </div>
<div><br>
</div>
<div>(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];</div>
<div><br>
</div>
<div>(3’) The same all-order factorization has also been proved by applying OPE, as done in [arXiv:1709.03018], and [arXiv:1801.03917].</div>
<div><br>
</div>
<div>(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];</div>
<div><br>
</div>
<div>(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;</div>
<div><br>
</div>
<div><i>Points of disagreement:</i></div>
<div>(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;</div>
<div><br>
</div>
<div>(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).</div>
<div><br>
</div>
<div><i>What is needed</i>:</div>
<div>(1) Need a well-justified proof of multiplicative renormalizability of the parton-parton operators that define quasi-PDFs in momentum-space.<br>
</div>
==================<br>
<br>
</div>
<div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div id="appendonsend"></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
</div>
<hr tabindex="-1" style="display:inline-block; width:98%">
<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Hadstruct <hadstruct-bounces@jlab.org> on behalf of David Richards <dgr@jlab.org><br>
<b>Sent:</b> Tuesday, September 15, 2020 10:15 AM<br>
<b>To:</b> Anatoly Radyushkin <radyush@jlab.org><br>
<b>Cc:</b> hadstruct@jlab.org <hadstruct@jlab.org><br>
<b>Subject:</b> Re: [Hadstruct] [EXTERNAL] Collaboration Meeting....</font>
<div> </div>
</div>
<div class="" style="word-wrap:break-word; line-break:after-white-space">Hi Anatoly,
<div class=""><br class="">
</div>
<div class="">Fair enough…. …threshold resummation is another topic in the same category!</div>
<div class=""><br class="">
</div>
<div class="">David<br class="">
<div class="">
<div><br class="">
<blockquote type="cite" class="">
<div class="">On Sep 15, 2020, at 9:43 AM, Anatoly Radyushkin <<a href="mailto:radyush@jlab.org" class="">radyush@jlab.org</a>> wrote:</div>
<br class="x_Apple-interchange-newline">
<div class="">
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt">
My experience is that discussions on this topic are endless.</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt">
We are not working with coordinate space,</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt">
so factorization in qPDF is not a primary topic.<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt">
So, I personally would prefer if we start with discussion of new results,</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt">
if any. Then, maybe,to discussion of the last-week workshop .</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt">
If there will be no time left for factorization in qPDF, so be it.</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div id="x_appendonsend" class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
</div>
<hr tabindex="-1" class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; display:inline-block; width:866.3125px">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important"></span>
<div id="x_divRplyFwdMsg" dir="ltr" class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<font class="" style="font-size:11pt" face="Calibri, sans-serif"><b class="">From:</b><span class="x_Apple-converted-space"> </span>Hadstruct <<a href="mailto:hadstruct-bounces@jlab.org" class="">hadstruct-bounces@jlab.org</a>> on behalf of David Richards <<a href="mailto:dgr@jlab.org" class="">dgr@jlab.org</a>><br class="">
<b class="">Sent:</b><span class="x_Apple-converted-space"> </span>Tuesday, September 15, 2020 9:30 AM<br class="">
<b class="">To:</b><span class="x_Apple-converted-space"> </span><a href="mailto:jmkarpie@email.wm.edu" class="">jmkarpie@email.wm.edu</a><span class="x_Apple-converted-space"> </span><<a href="mailto:jmkarpie@email.wm.edu" class="">jmkarpie@email.wm.edu</a>><br class="">
<b class="">Cc:</b><span class="x_Apple-converted-space"> </span><a href="mailto:hadstruct@jlab.org" class="">hadstruct@jlab.org</a><span class="x_Apple-converted-space"> </span><<a href="mailto:hadstruct@jlab.org" class="">hadstruct@jlab.org</a>><br class="">
<b class="">Subject:</b><span class="x_Apple-converted-space"> </span>Re: [Hadstruct] [EXTERNAL] Collaboration Meeting....</font>
<div class=""> </div>
</div>
<div class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; word-wrap:break-word; line-break:after-white-space">
Hi Joe,
<div class=""><br class="">
</div>
<div class="">I think that Anatoly has to leave at around 10am, so we should probably open with that discussion?</div>
<div class=""><br class="">
</div>
<div class="">David<br class="">
<div class=""><br class="">
<blockquote type="cite" class="">
<div class="">On Sep 14, 2020, at 6:24 PM, Joseph Karpie <<a href="mailto:jmkarpie@email.wm.edu" class="">jmkarpie@email.wm.edu</a>> wrote:</div>
<br class="x_x_Apple-interchange-newline">
<div class="">
<div dir="ltr" class="">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. </div>
<br class="">
<div class="x_x_gmail_quote">
<div dir="ltr" class="x_x_gmail_attr">On Mon, Sep 14, 2020 at 1:46 PM David Richards <<a href="mailto:dgr@jlab.org" class="">dgr@jlab.org</a>> wrote:<br class="">
</div>
<blockquote class="x_x_gmail_quote" style="margin:0px 0px 0px 0.8ex; border-left-width:1px; border-left-style:solid; border-left-color:rgb(204,204,204); padding-left:1ex">
Hi All,<br class="">
<br class="">
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?<br class="">
<br class="">
Lots of stuff to talk about, it seems to me….<br class="">
<br class="">
- followup from LaMET<br class="">
- updates on running, and in particular distillation.<br class="">
- ….<br class="">
<br class="">
Regards,<br class="">
David<br class="">
<br class="">
_______________________________________________<br class="">
Hadstruct mailing list<br class="">
<a href="mailto:Hadstruct@jlab.org" target="_blank" class="">Hadstruct@jlab.org</a><br class="">
<a href="https://mailman.jlab.org/mailman/listinfo/hadstruct" rel="noreferrer" target="_blank" class="">https://mailman.jlab.org/mailman/listinfo/hadstruct</a></blockquote>
</div>
</div>
</blockquote>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<br class="">
</div>
</div>
</div>
</body>
</html>