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wilson-eft / wilson

A Python package for the running and matching of Wilson coefficients above and below the electroweak scale
https://wilson-eft.github.io
MIT License
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Running of CVLR and CSLR in Bq-mixing #91

Closed girishky closed 2 years ago

girishky commented 2 years ago

Hello, In sbsb operator basis, CVLR_bsbs and CSLR_bsbs mix during QCD running. Executing the following

w = Wilson({'CVLR_bsbs': 1}, scale=160, eft='WET', basis='flavio')
wc = w.match_run(scale=4.2, eft='WET', basis='flavio', sectors=('sbsb',))

yield, CVLR_bsbs = 0.91, CSLR_bsbs= -0.82

But, if start with:

w = Wilson({'CSLR_bsbs': 1}, scale=160, eft='WET', basis='flavio')
wc = w.match_run(scale=4.2, eft='WET', basis='flavio', sectors=('sbsb',))

I get, CSLR_bsbs = 2.142085e+00, CVLR_bsbs = 5.551115e-17 I am doubtful of negligible CVLR in this case.

I cross-checked the above running case using results of hep-ph/0112303. The paper utilizes a different basis, but their C4 and C5 are related to CVLR and CSLR of flavio-basis after Fierz (CVLR = C5/2, CSLR =-C4). Using their eq.9 and 10, If I start with, say, C4=1 at 300 GeV, running induces C5 roughly close to 0.05 at mb scale. I find finite mixing reasonable as operators (O4, O5) (or OVLR, OSLR in flavio basis) should mix under QCD as they only differ via color structure.

I also note similar issue in case of Bd mixing as well.

Is there a bug or I am doing something wrong?

Thanks.

Best regards,

DavidMStraub commented 2 years ago

The ADM matrix in the SLR, VLR basis should have a form like [[*, 0], [*, *]], so they do mix, but only in one direction, if you know what I mean. If you carefully check the basis transformations, I'm pretty sure you'll find Wilson is correct.

girishky commented 2 years ago

Dear David, Thanks for the quick response. You are correct. I also checked evolution matrices of the concerning operators given in 1704.06639, finding agreement with what you said (and Wilson). Somehow, hep-ph/0112303 results indicate mixing in these two operators in both direction. Note that B-mixing operator basis is exactly same in 1704.06639 and hep-ph/0112303. To further check that I am not doing something silly in using their results, I found one paper (eq. 70 therein) which also uses hep-ph/0112303 and finds mixing in both ways. So it is more likely that there is some issue in results of hep-ph/0112303.

Anyways, thanks again. ~Before I close this issue, can you please tell me about the following two things:~ ~1. is there any method in Wilson to access ADMs? I couldn't find anything in API docs~ ~2. is it logical to set, say 300 GeV, in WET eft in Wilson instance, and use match_run afterwards? (iirc, Dsix Tools does not even allow it). In some scenarios, where NP scale is above but very close to EW scale, I would prefer to use WET eft instead of smeft.~

MJKirk commented 2 years ago

To jump in: regarding the mixing between CVLR and CSLR, the difference is because wilson only includes the 1-loop ADMs, while hep-ph/0112303 includes the NLO ADMs (which come from 2-loop diagrams) and at this order the ADM matrix structure David described is broken.

girishky commented 2 years ago

@MJKirk the response much appreciated. Silly enough, I did not realize hep-ph/0112303 includes NLO. This solves my issue. Thanks again. I will close this now. Happy new year everyone!