[Hadstruct] [EXTERNAL] Draft lattice abstract

Tue Sep 30 14:28:49 EDT 2025

Hey,

I think these strange results look great. I am not positive about the renormalization with the light quarks. Ultimately, there are two competing statements.

The renormalization constants in our ideal scheme should be flavor independent and multiplicative. This is perhaps a little idealistic and disagrees with some issues other groups run into.

The ideal setting perhaps is just simply different than Rajan's implementation of RIMom using ensembles which doesn't have flavor symmetry (ie strange mass =/= light mass). This is the sort of mixing effect Mike Wagman was worrying about at QCD Evolution where the renormalization goes

M^s_R = (1+alpha_s ...) M^s_b + (alpha_s....) M^l_v

Since M^l_b is 10x larger than M^s_b, the supposedly alpha_s suppressed contribution is still large enough to be a problem. Maybe doing RIMom in the massless limit while controlling flavor symmetry this can be avoided which is what RBC does because SU(N_f) gets harder when you care about left vs right.

I'm sketchy on all this but if you show this strange result people might ask questions about it. The Schrodinger Functional is a way around this, but it's non-trivial amount of work.

As for the ratio shown, as you say the normalization might be off. The bare l=u+d matrix elements you use are M^l_b(0,z) = Z M^l_R(0,z) where M^l_R(0,z)=3 in the small z^2 limit. On the other hand, you want the normalization as if it were just giving Z, that is M_R(0,z)=1. This implies you need to multiply all your results by 3.

Now this is the problem. In the attached, I have a notebook which reads in the data from https://drive.google.com/file/d/1wxbnWK6-sf6lL3gV-sDSs2al2VxxwroN/view?usp=drive_link and plots the imaginary ITD. It looks like you are 3x too large not 3x too small.

My other hacky idea which is a million times easier to test than SF which is to assume flavor symmetry. u+d+s and u+d-2s would be in different SU(3) irreps and renormalize multiplicatively and you form their double ratio. Then you take the linear combination to isolate s from u+d. I think this also makes the issues with normalization clear too since both combinations approach 3 at nu=0. Chris, have you tried this yet? If you share bare matelem jackknife samples for u+d (conn + disco combined) and s, then I can try it easy enough.

Best,
Joe

________________________________
From: Hadstruct <hadstruct-bounces at jlab.org> on behalf of David Richards via Hadstruct <hadstruct at jlab.org>
Sent: Tuesday, September 30, 2025 9:04 AM
To: Christopher Monahan <cmonahan2024 at ColoradoCollege.edu>
Cc: Joseph Karpie via Hadstruct <hadstruct at jlab.org>
Subject: Re: [Hadstruct] [EXTERNAL] Draft lattice abstract

Hi Chris,

I think this looks good.  I’ll circulate an abstract tomorrow, though with the shutdown I suspect my attendance might be shutdown also since it is waiting on the CFO for approval.

David

On Sep 29, 2025, at 9:41 PM, Christopher Monahan via Hadstruct <hadstruct at jlab.org> wrote:

Hi Savvas,

Thank you. I am happy to share strange disco results if those are ready, but I was not planning to mention that in the abstract, in case they aren't. I figured just leaving "isoscalar quark" is broad enough to cover both cases.

Regards
Chris

---

Chris Monahan
Pronouns: he/his
Department of Physics
Colorado College
(719) 389-6236
________________________________
From: Savvas Zafeiropoulos <savvaslz at gmail.com<mailto:savvaslz at gmail.com>>
Sent: 29 September 2025 13:42
To: Christopher Monahan <cmonahan2024 at coloradocollege.edu<mailto:cmonahan2024 at coloradocollege.edu>>
Cc: Joseph Karpie via Hadstruct <hadstruct at jlab.org<mailto:hadstruct at jlab.org>>
Subject: Re: [Hadstruct] [EXTERNAL] Draft lattice abstract

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Hi Chris,

looks very good. Are you planning only to show the disco results for light quarks or strange too (if we manage to have these results ready)?

Best,
Savvas
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