WC JSON vs WC in SPheno output

[innes]

Hi,

I'm working on a Leptoquark model with Sarah+Spheno, and whilst it appears that the Wilson coefficients in the SPheno.spc are evolving in the expected way with changes in my model parameters, this doesn't appear to be true of the WCs in the json files. In particular, I am looking at C9 for b \to s mu mu. This is nonzero for the SPheno.spc, but the corresponding contributions in the json file operator basis are writing out to be zero. I have attached the relevant SPheno input/output.

Thanks in advance for your time!

Innes

[FStaub]

Hi,

looking at the file FlavorKit/WCXF_WilsonCoefficients.m it seems to me that some definitions are missing:

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Table[{"EVLL_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllVLL[2,3,i,i]-OddllVLLSM[2,3,i,i], Complex},{i,1,3}],
Table[{"EVRR_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllVRR[2,3,i,i]-OddllVRRSM[2,3,i,i], Complex},{i,1,3}],
Table[{"EVLR_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllVLR[2,3,i,i]-OddllVLRSM[2,3,i,i], Complex},{i,1,3}],
Table[{"EVRL_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllVRL[2,3,i,i]-OddllVRLSM[2,3,i,i], Complex},{i,1,3}],
Table[{"ESRR_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllSRR[2,3,i,i]-OddllSRRSM[2,3,i,i], Complex},{i,1,3}],
Table[{"ESRR_"<>ToString[3]<>ToString[2]<>ToString[i]<>ToString[i],OddllSRR[3,2,i,i]-OddllSRRSM[3,2,i,i], Complex},{i,1,3}],

For VLL, VRR, VLR, VRL the combinations with (3,2) are missing. Could you try if adding

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Table[{"EVLL_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllVLL[2,3,i,i]-OddllVLLSM[2,3,i,i], Complex},{i,1,3}],
Table[{"EVLL_"<>ToString[3]<>ToString[2]<>ToString[i]<>ToString[i],OddllVLL[3,2,i,i]-OddllVLLSM[3,2,i,i], Complex},{i,1,3}],
Table[{"EVRR_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllVRR[2,3,i,i]-OddllVRRSM[2,3,i,i], Complex},{i,1,3}],
Table[{"EVRR_"<>ToString[3]<>ToString[2]<>ToString[i]<>ToString[i],OddllVRR[3,2,i,i]-OddllVRRSM[3,2,i,i], Complex},{i,1,3}],
Table[{"EVLR_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllVLR[2,3,i,i]-OddllVLRSM[2,3,i,i], Complex},{i,1,3}],
Table[{"EVLR_"<>ToString[3]<>ToString[2]<>ToString[i]<>ToString[i],OddllVLR[3,2,i,i]-OddllVLRSM[3,2,i,i], Complex},{i,1,3}],
Table[{"EVRL_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllVRL[2,3,i,i]-OddllVRLSM[2,3,i,i], Complex},{i,1,3}],
Table[{"EVRL_"<>ToString[3]<>ToString[2]<>ToString[i]<>ToString[i],OddllVRL[3,2,i,i]-OddllVRLSM[3,2,i,i], Complex},{i,1,3}],
Table[{"ESRR_"<>ToString[2]<>ToString[3]<>ToString[i]<>ToString[i],OddllSRR[2,3,i,i]-OddllSRRSM[2,3,i,i], Complex},{i,1,3}],
Table[{"ESRR_"<>ToString[3]<>ToString[2]<>ToString[i]<>ToString[i],OddllSRR[3,2,i,i]-OddllSRRSM[3,2,i,i], Complex},{i,1,3}],

Solve the problem?

Best,
Florian

[innes]

Hi Florian,

Now when I try and use the Wilson package to load the json file for use in Flavio the following error:

"Wilson coefficients do not exist in this basis: " + str(unknown_keys)
AssertionError: Wilson coefficients do not exist in this basis: {'EVLR_3233', 'EVLR_3211', 'EVLL_3211', 'EVLL_3222', 'EVLR_3222', 'EVRR_3211', 'EVRR_3233', 'EVLL_3233', 'EVRR_3222', 'EVRL_3222', 'EVRL_3233', 'EVRL_3211'}"

I have attached the newly written json WC file.

[FStaub]

Hi sorry,

I had to refresh my memory about the operator basis in the WcXF. It's correct that these operators are not needed because they are related by the other by a hermitian conjugation. Now, the issue seems to be that SPheno and Wcxf use slightly different conventions concerning that h.c. Therefore, the correct way should be to use

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conj[OddllVLL[3,2,i,i]-OddllVLLSM[3,2,i,i]]

instead of

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OddllVLL[2,3,i,i]-OddllVLLSM[2,3,i,i]

and so on. I'll try to patch that before the next release of SARAH, but it will take some time because of many other things these days...

Cheers,
Florian

[innes]

Hi Florian

That worked! Thank you so much

Innes

[innes]

Hi Florian

Is there a similar issue with the definition of couplings contributing to b to c tau nu?

I am inputting effective interactions that should be contributing to the cbtaunu effective operators but these are only ever writing out as zero:

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  "GVLL_3213": {
       "Re":    0.0000000000000000      ,
       "Im":    0.0000000000000000     
     },
     "GVLL_3223": {
       "Re":    0.0000000000000000      ,
       "Im":    0.0000000000000000     
     },
     "GVLL_3233": {
       "Re":    0.0000000000000000      ,
       "Im":    0.0000000000000000     
     },
     "GVRL_3213": {
       "Re":    0.0000000000000000      ,
       "Im":    0.0000000000000000     
     },

I am unfamiliar with the SPheno basis so am unsure if there is any issue with the definitions in the WCXF definitions .m file.



Innes

[Avelino]

Hi,

the basis for the FlavorKit and SPheno codes can be found here:

https://wcxf.github.io/assets/pdf/WET.FlavorKit.pdf

Does that clarify the issue for the b -> c tau nu processes?

[innes]

Hi,

the basis for the FlavorKit and SPheno codes can be found here:

https://wcxf.github.io/assets/pdf/WET.FlavorKit.pdf

Does that clarify the issue for the b -> c tau nu processes?

Hi Avelino,

It's not a misunderstanding of the basis, but rather that I am never able to obtain a nonzero value for these vector operator contributions to b->c tau nu. My misunderstanding is in the correspondence between the SPheno internal basis and that which is written out in the WCXF.

I was wondering if there was a similar issue to that with the vector contribution to b to s mumu that Florian noted above, but my unfamiliarity with the flavorkit files means that I haven't been able to find an easy fix.

Thank you so much for your help

[innes]

To clarify, this b-> c vector coupling issue is still unsolved.

[FStaub]

Hi,

yes, there is a problem with the vector operators. The reason is that FlavorKit spits out the coefficients for (\tau P_(L,R) \gamma_\mu \nu) while the Wcxf format uses (\tau \gamma_\mu P_(L,R) \mu). Thus, left-right is exchanged and one needs to put dulvVLR instead of dulvVLL in GVLL.
Sorry for the trouble. The WCxF file SARAH was set up in a rush during my parental leave and seems to be quite buggy. We need to revise it carefully.

Cheers,
Florian