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<p>Hi Wally,</p>
<p><br>
</p>
<p>Thanks! I think it's settled now that the factor 2 gain in the
ratio is indeed there, I'm just glad it goes in the right
direction :)</p>
<p><br>
</p>
<p>I'll have a look at the NLO calculations.</p>
<p><br>
</p>
<p>Best,</p>
<p>Jan<br>
</p>
<p><br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 8/11/2020 9:44 AM, Wally Melnitchouk
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:BL0PR0901MB30115100A868C8D2F67A307EA8450@BL0PR0901MB3011.namprd09.prod.outlook.com">
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Hi Jan,</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);">
The leading order (in á_s) formula for F2 is F2(x,Q) = <span
style="caret-color: rgb(0, 0, 0); font-family: Calibri, Arial,
Helvetica, sans-serif; background-color: rgb(255, 255, 255);
display: inline !important">
Ó_q<span class="Apple-converted-space"> </span></span>e_q^2 *
<span style="caret-color: rgb(0, 0, 0); font-family: Calibri,
Arial, Helvetica, sans-serif; background-color: rgb(255, 255,
255); display: inline !important">
x *<span class="Apple-converted-space"> </span></span>[q(x,Q)
+ qbar(x,Q)], without a factor 2 in front. Definitions like this
you can check with the PDG, which I try to use as much as
possible to standardize notations/conventions [see e.g. Eq.
(18.18) of the online PDG].</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);">
If you are interested in quantitive, or even semi-quantitative,
calculations of F2, I would however use at least NLO PDFs with
the corresponding NLO formula, which just involves a convolution
of the (NLO) PDF with the hard scattering function [see e.g. Eq.
(18.21) of PDG]. Also for standardization, you should probably
use LHAPDF for any PDF set (which sounds like you have
implemented already).</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);">
As far as cuts implemented in the code, I cannot tell you
anything reliable because I didn't work on the latest version of
the code, so I can't really help with 2).</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);">
It's a good confirmation at least that the two independent codes
give similar results, with the factor 2 correction you found.</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);">
Let me know if you have further questions.</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);">
Wally</div>
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<br>
</div>
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font-size: 12pt; color: rgb(0, 0, 0);">
<br>
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<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> Jan C.
Bernauer <a class="moz-txt-link-rfc2396E" href="mailto:jan.bernauer@stonybrook.edu"><jan.bernauer@stonybrook.edu></a><br>
<b>Sent:</b> Tuesday, August 11, 2020 9:19 AM<br>
<b>To:</b> Wally Melnitchouk <a class="moz-txt-link-rfc2396E" href="mailto:wmelnitc@jlab.org"><wmelnitc@jlab.org></a><br>
<b>Cc:</b> <a class="moz-txt-link-abbreviated" href="mailto:tdis@jlab.org">tdis@jlab.org</a> <a class="moz-txt-link-rfc2396E" href="mailto:tdis@jlab.org"><tdis@jlab.org></a>; Hobbs, Timothy
<a class="moz-txt-link-rfc2396E" href="mailto:TJHobbs@mail.smu.edu"><TJHobbs@mail.smu.edu></a><br>
<b>Subject:</b> Re: [Tdis] [EXTERNAL] Inconsistencies in the
TDIS proposal: Some things I found</font>
<div> </div>
</div>
<div>
<p style="margin-top: 0px; margin-bottom: 0px;">Hi Wally,</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">Thank you for
looking into this. <br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">Your suggestion
to write my own implementation is a very good one, and exactly
what I did. This is where I found the discrepancies to the
proposal (except the ones in the proposal itself). I think
there are two questions left for that:</p>
<p style="margin-top: 0px; margin-bottom: 0px;">1) Is my formula
for F2p correct, or the one in the code I attached. I.e, is F2
= x * Sum quarkcharge_i^2 quarkdistributionfunction_i(x,Q^2)
(what I think) or is there an additional factor 2 (what the
old code says).</p>
<p style="margin-top: 0px; margin-bottom: 0px;">2) Are there
some other cuts I didn't realize</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">I think all
other points I raised are simple mistakes in the original
proposal or otherwise understood artifacts.
<br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;"> Other than
that, your code + my code produce the same results. Q2 can
probably only be answered by the person who originally came up
with the table in the proposal. But if you could write down
what you think the formula for F2p is, it would be a good
cross check that I didn't just misunderstand the textbooks.
<br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">Best,</p>
<p style="margin-top: 0px; margin-bottom: 0px;">Jan<br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<div class="x_moz-cite-prefix">On 8/11/2020 12:30 AM, Wally
Melnitchouk wrote:<br>
</div>
<blockquote type="cite">
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;
font-size:12pt; color:rgb(0,0,0)">
Hi Jan,</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)">
Thanks for your emails, and apologies for the delay.</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)">
The programs you appended look familiar -- I think I wrote
the core of them back in the 1990s -- and Tim developed them
some half dozen years ago (and possibly other people before
and since) when we were working on some related
applications.</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)">
The best suggestion I would give anyone interested in
implementing the meson exchange contributions to the DIS
structure functions would be to write some script yourself
from scratch. The formulas are actually very simple, if you
look at the analytic expressions. The original ancient
Fortran could probably now be written in a few lines of
python code and done much more efficiently, and writing it
yourself would give you a much clearer idea of what is being
computed.</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)">
I am happy to discuss the formulas with you or anyone else
if you have any questions -- maybe more efficiently over
bluejeans/zoom.</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)">
Best regards,</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif;
font-size:12pt; color:rgb(0,0,0)">
Wally</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)">
<br>
</div>
<hr tabindex="-1" style="display:inline-block; width:98%">
<div id="x_divRplyFwdMsg" dir="ltr"><font
style="font-size:11pt" face="Calibri, sans-serif"
color="#000000"><b>From:</b> Jan C. Bernauer
<a class="x_moz-txt-link-rfc2396E"
href="mailto:jan.bernauer@stonybrook.edu"
moz-do-not-send="true"><jan.bernauer@stonybrook.edu></a><br>
<b>Sent:</b> Monday, August 10, 2020 2:03 PM<br>
<b>To:</b> <a class="x_moz-txt-link-abbreviated"
href="mailto:tdis@jlab.org" moz-do-not-send="true">tdis@jlab.org</a>
<a class="x_moz-txt-link-rfc2396E"
href="mailto:tdis@jlab.org" moz-do-not-send="true"><tdis@jlab.org></a>;
Hobbs, Timothy
<a class="x_moz-txt-link-rfc2396E"
href="mailto:TJHobbs@mail.smu.edu"
moz-do-not-send="true"><TJHobbs@mail.smu.edu></a>;
Wally Melnitchouk
<a class="x_moz-txt-link-rfc2396E"
href="mailto:wmelnitc@jlab.org" moz-do-not-send="true"><wmelnitc@jlab.org></a><br>
<b>Subject:</b> Re: [Tdis] [EXTERNAL] Inconsistencies in
the TDIS proposal: Some things I found</font>
<div> </div>
</div>
<div>
<p style="margin-top: 0px; margin-bottom: 0px;">Hi all,</p>
<p style="margin-top: 0px; margin-bottom: 0px;">An update
from the trenches of the generator writing:</p>
<p style="margin-top: 0px; margin-bottom: 0px;">1) G4SBS
seems to agree on the definition of F2. Would be nice if
somebody who knows what they are doing (Tim, Wally?) can
double check though. So if there is no other effect, I'm
pretty sure we see ~5 times more than we thought.<br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">2) G4SBS
also agrees with my estimate of the total DIS rate. It's
actually slightly higher, but I think that's because the
simulated e-arm acceptance is slightly bigger. I'll update
my analysis with that. I'm pretty sure it's very close to
2 times what the proposal has, so I'd hazard a guess and a
factor of 2 comes from the number of molecules to the
number of protons. It's also assuming that we run at 77K
-- I think we talked about running at room temperature,
that makes it 4 times worse of course. (2 times worse
than what is in). Can somebody (Carlos?) run g4sbs in DIS
configuration and see the total rate between x 0.05 and
0.2? I assume a particle is accepted if
Harm.SBSGem.Track.P[0]>1 (for very few it's not track
0).</p>
<p style="margin-top: 0px; margin-bottom: 0px;">So I think,
if we run room temp, we'll get half the DIS rate we
assumed, but about 2.5 times the TDIS rate (but in a
different distribution, as far as I can tell). I'll make
some updated reach plots, but I don't have background
numbers. Does anyone have those for all bins? <br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;">Best,</p>
<p style="margin-top: 0px; margin-bottom: 0px;">Jan<br>
</p>
<p style="margin-top: 0px; margin-bottom: 0px;"><br>
</p>
<div class="x_x_moz-cite-prefix">On 8/6/2020 11:43 AM, Jan
C. Bernauer wrote:<br>
</div>
<blockquote type="cite">Hi Tim, Hi Wally, Hi TDIS, <br>
<br>
Sorry for the lengthy email. <br>
<br>
Some updates and questions to my talk: <a
class="x_x_moz-txt-link-freetext"
href="https://hallaweb.jlab.org/wiki/images/2/2f/TDIS_sim.pdf"
moz-do-not-send="true">
https://hallaweb.jlab.org/wiki/images/2/2f/TDIS_sim.pdf</a>
where I found what I believe are internal inconsistencies,
and differences to my own implementation of F_2, f_\pi,
and a full MC.
<br>
<br>
Wally, Tim, I also send this to you, because I believe you
might have additional insight to the source of some of
these figures/values.
<br>
<br>
<br>
0) Does anybody have the exact bins used for the projected
result figures? Especially the one as a function of t.
That would be very helpful!
<br>
<br>
1) I do see about a factor of 2 more inclusive CS than in
the proposal. I think it's likely that this error is on my
end, I have to verify with g4SBS. In any case, the code
version I got from Carlos (Thanks!), authored from Tim and
Wally, do not calculate that as far as I can tell. It's
not helping us in any case, we would just need less
current I'd assume.
<br>
<br>
2) It would be great to figure out in which configuration
the code was for the generation of table 6 and 7. I assume
it was this code I attach here? Is that the code version
after a factor 2 has already been found? I believe so,
because I can get the F_2^{\pi p} plots out that are in
the new proposal, which are higher than the old proposal.
<br>
<br>
Some things which I found in the code which do not match
the experiment: <br>
<br>
Theta_e is ~12, not 35 degrees. That only affects the
calculation of Q^2, which is slightly affecting the proton
PDFs. Can't explain a big difference.
<br>
<br>
The code was set up for pi^+, I'm looking at pi^0, so I
changed the isospin factor to 1. I changed some other
integration ranges (ymax=1, xmax=0, km1, km2 ), and also
implemented a cosph cut (proton theta<70)
<br>
<br>
With these changes, I match exactly (on a log scale :) )
my own implementation and the plots in the new proposal.
<br>
<br>
3) BUT the ratio was still off. I traced it down to
F_2^p. The relevant lines are here:
<br>
<br>
CALL SETCTQ6(1) ! CTEQ 'MS-bar' SCHEME. <br>
u_pro = CTQ6PDF (1, REAL(x), SQRT(REAL(Q2))) <br>
ubar_pro = CTQ6PDF (-1, REAL(x), SQRT(REAL(Q2)))
<br>
d_pro = CTQ6PDF (2, REAL(x), SQRT(REAL(Q2))) <br>
dbar_pro = CTQ6PDF (-2, REAL(x), SQRT(REAL(Q2)))
<br>
<br>
F2neu = 2.*x * ((4./9.)*(d_pro + dbar_pro) <br>
& + (1./9.)*(u_pro + ubar_pro)) <br>
<br>
<br>
a) LHAPDF 6 and this code has a different definition for
what PID=1 and 2 are. That stumped me for a while, but I'm
pretty sure u_pro is indeed the proton u PDF.
<br>
<br>
b) For the neutron, d_neu=u_pro and vice versa, so the
line actually reads 2 *x * ( 4/9 ( u_neu +ubar_neu) + 2/9
( d_neu +dbar_neu)). I changed it back to be correct for
the proton.
<br>
<br>
c) BUT: I do not have the 2 there. Where does that come
from? I'm not super versed in PDFs, but it is my
understanding that that shouldn't be there. If not, can
anybody please explain?
<br>
<br>
( d) There is also a small difference in the code here and
LHAPDF for x<0.1. 10% or so. That must be in the
underlying PDF or Q^2 evolution)
<br>
<br>
In any case, without the 2, my code and this code
essentially agree on F_2^p (with Q^2=1, very close to the
plots in the proposal. With Q^2 changing, slightly
different from the proposal, maybe 30% at most, but both
codes the same way. Makes me think that the proposal line
comes from a different program, which might explain the
discrepancy with the 2).
<br>
<br>
<br>
4) Going back to table 6. We already know that it was not
updated from the first proposal, so it likely already has
a factor of 2 missing in the F/F ratio. With this
additional factor 2, we are getting very close to what my
program has, 4 is close enough to 5 that I would believe
the rest is acceptance, slightly different cuts, etc, or
the first factor 2 was actually 2.5 or something.
<br>
<br>
With these changes, both my code as well as the code I got
from Carlos, modified as described above, gives a ratio
F/F of 550 for the first line in the text. This assumes we
accept k between 60 and 500 Mev, x between 0.05 and 0.2,
at around 12 degrees, with 30 to 70 deg proton angle.
This is also the number my MC gets, and roughly what I
would get looking at the plots. Or is there some other
cut that should be applied? Cut on z (y in the code)?
<br>
<br>
TLDR: If all my assumptions are correct, we see indeed 5.5
times more TDIS events (per DIS event) than we thought!
<br>
<br>
Let me know what you think! <br>
<br>
Best, <br>
<br>
Jan <br>
<br>
<br>
Attached: TDIS_orig.f, code I got from Carlos. TDIS.f:
Code with my modifications.
<br>
<br>
<br>
<br>
<br>
<br>
<fieldset class="x_x_mimeAttachmentHeader"></fieldset>
<pre class="x_x_moz-quote-pre">_______________________________________________
Tdis mailing list
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</pre>
</blockquote>
<pre class="x_x_moz-signature" cols="72">--
Dr. Jan C. Bernauer
Assistant Professor
Department of Physics and Astronomy
Stony Brook University
Stony Brook, NY 11794-3800 </pre>
</div>
</blockquote>
<pre class="x_moz-signature" cols="72">--
Dr. Jan C. Bernauer
Assistant Professor
Department of Physics and Astronomy
Stony Brook University
Stony Brook, NY 11794-3800 </pre>
</div>
</blockquote>
<pre class="moz-signature" cols="72">--
Dr. Jan C. Bernauer
Assistant Professor
Department of Physics and Astronomy
Stony Brook University
Stony Brook, NY 11794-3800 </pre>
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