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Dear Volker:<br>
<br>
Now that we agree that there are \bar{C} terms in Eq. (6),
take the trace of the GFF in the rest frame, one<br>
has the expression <T_{\mu\mu}> = [(A_q(0) + A_g(0)]M +
Tr-Anomaly + chiral condensate - [(A_q(0) + A_g(0)]M = Tr-Anomaly <br>
+chiral condensate which is the correct expression. The last three
terms come from \bar{C} which is zero (for a good reason because<br>
it is the stability condition). If one drops them first, one ends up
with the expression of [(A_q(0) + A_g(0)]M. Please explain why<br>
it is acceptable and not wrong with an expression where the trace of
EMT does not contain trace anomaly. \bar{C} exists in many<br>
publications in the literature, I don't understand the rationale for
dropping it in this document. It leads to (unintended) consequences.<br>
<br>
Best,<br>
Keh-Fei<br>
<br>
<br>
<div class="moz-cite-prefix">On 8/12/22 4:07 PM, Volker Burkert
wrote:<br>
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Dear Keh-Fei,</div>
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<ol>
<li><span>There is agreement for eq.(6) which deals with quark
and gluon EMT separately, and the \bar{C} is needed (with
opposite sign for q and g). </span></li>
<li><span>For eq.(19), which deals with the full EMT (quark +
gluons} the \bar{C} terms should cancel out to zero, and
the term \bar{C} should not appear. </span></li>
<li style="display:block"><br>
</li>
<li style="display:block"><br>
</li>
<li style="display:block">Volker</li>
<li style="display:block"> <br>
</li>
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<hr style="display:inline-block;width:98%" tabindex="-1">
<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt"
face="Calibri, sans-serif" color="#000000"><b>From:</b>
Keh-Fei Liu <a class="moz-txt-link-rfc2396E" href="mailto:liu@g.uky.edu"><liu@g.uky.edu></a><br>
<b>Sent:</b> Friday, August 5, 2022 8:35 AM<br>
<b>To:</b> Volker Burkert <a class="moz-txt-link-rfc2396E" href="mailto:burkert@jlab.org"><burkert@jlab.org></a>;
<a class="moz-txt-link-abbreviated" href="mailto:psqateic-request@jlab.org">psqateic-request@jlab.org</a> <a class="moz-txt-link-rfc2396E" href="mailto:psqateic-request@jlab.org"><psqateic-request@jlab.org></a><br>
<b>Cc:</b> Lorcé Cédric (M.)
<a class="moz-txt-link-rfc2396E" href="mailto:cedric.lorce@polytechnique.edu"><cedric.lorce@polytechnique.edu></a><br>
<b>Subject:</b> [EXTERNAL] Re: [Psqateic] PSQ@EIC White Paper</font>
<div> </div>
</div>
<div>Dear Volker and Latifa:<br>
<br>
Thank you for your tremendous effort in organizing
this valuable whitepaper for the community.
<br>
<br>
I now have a firm argument to show that one cannot
drop the \bar{C} term in Eqs. (6) and (19). Take the<br>
forward FF of the trace T_{\mu\mu}, they give (A_q(0) +
A_g(0))M. This is a trivial and meaningless result. It relates<br>
the matrix element of the trace to the mass via a sum rule of
traceless matrix elements. It does not have the anomaly.<br>
Only when the \bar{C} is retained, do you get the correct
expression with the anomaly. We should put the \bar{C} term back<br>
in these equations.<br>
<br>
Best,<br>
Keh-Fei<br>
<br>
<br>
<br>
<br>
<div class="x_moz-cite-prefix">On 8/3/22 4:33 PM, Volker Burkert
wrote:<br>
</div>
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<p style="margin:0px 0in; font-size:medium;
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high-impact science requiring high integrated luminosity
at the low-to-medium center-of-mass energy of the U.S.
Electron-Ion Collider project. </span></p>
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