CKM factor in K -> pi nu nu amplitude

Hi,
Flavio basis convention (https://wcxf.github.io/assets/pdf/WET-3.flavio.pdf) for s -> d nunu transition has CKM factor (Vts* Vtd) in operators' definition. But in flavio implementation, amplitude for K -> pi nu nu has xi('t', 'sd') which is basically (Vts Vtd*)

flavio/flavio/physics/kdecays/kpinunu.py

Line 11 in 3d11de0

xi_t = flavio.physics.ckm.xi('t', 'sd')(par)

Shouldn't it be xi('t', 'ds') in the above to be consistent with flavio operator definition?

In the observables, only the absolute value or the square of the imaginary part of the amplitude enters. so it shouldn't matter whether it's the d->s or the s->d amplitude. Do you agree?

Hi David, Thanks for reply. I agree with what you said. But my point is that in K -> pi nunu amplitude function, X is basically WC for s -> d transition

flavio/flavio/physics/kdecays/kpinunu.py

Line 20 in 3d11de0

X = -( wc['CL_'+label] + wc['CR_'+label] ) * s2w

but the CKM factor that is multiplied by WC here

flavio/flavio/physics/kdecays/kpinunu.py

Line 24 in 3d11de0

amp = xi_t * X # top contribution

is related to conjugate (d->s) transition.

For absolute value, I agree this won't matter. But imaginary part of amplitude (even square of it) would be different if X also contain complex phase due to NP. So shouldn't amplitude be amp = xi_t.conj() * X or amp = xi_t * X.conj() ?

I agree with @girishky. Simply taking imaginary part for different neutrino species is inappropriate. It is the same kind of error that has been reported in #138 for K0->ll'.

But that's a different issue...

Hi @hoodyn , even in cases where nu flavor is conserved, so that NP contribution can only rescales X function, the current flavio implementation has issue (imo).
The operator $(\bar s d )_{V-A} (\bar nu nu)_{V-A}$ comes with VtdVts* in the normalization but its WC (i.e. X) is being multiplied with VtsVtd*; but this ckm factor appears in normalization of conjugate operator $(\bar d s)_{V-A} (\bar nu nu)_{V-A}$ . The results of this is that even a CP conserving NP will affect KL decay mode which it shouldn't.
people can crosscheck the above observation.

best,

In the observables, only the absolute value or the square of the imaginary part of the amplitude enters. so it shouldn't matter whether it's the d->s or the s->d amplitude. Do you agree?

I agree with this as long as in

flavio/flavio/physics/kdecays/kpinunu.py

Line 24 in 3d11de0

amp = xi_t * X # top contribution

the X is strictly real. However, I agree with @girishky that if X also has an imaginary part, then it does matter whether xi('t', 'sd') or xi('t', 'ds') is used.

I suggest to simply replace

flavio/flavio/physics/kdecays/kpinunu.py

Lines 11 to 12 in 3d11de0

    
           xi_t = flavio.physics.ckm.xi('t', 'sd')(par) 
        
           xi_c = flavio.physics.ckm.xi('c', 'sd')(par)

by

 xi_t = flavio.physics.ckm.xi('t', 'ds')(par) 
 xi_c = flavio.physics.ckm.xi('c', 'ds')(par)

@DavidMStraub @girishky do you both agree with this solution?

@peterstangl Yes. This is better. Thanks.

best,

This issue has been fixed in PR #189.

	xi_t = flavio.physics.ckm.xi('t', 'sd')(par)
	xi_c = flavio.physics.ckm.xi('c', 'sd')(par)