Module flavio.physics.quarkonium.Sll

$S\to ll^\prime$ branching ratio

Functions

def Sll_br(wc_obj, par, S, l1, l2, CeGGij, CeGGji)

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def Sll_br(wc_obj, par,S, l1,l2,CeGGij,CeGGji):
    r"""Branching ratio for the lepton-flavour violating leptonic decay P -> l l' """
    #####branching ratio obtained from 2207.10913#####
    flavio.citations.register("Calibbi:2022ddo")
    mP = par['m_'+S]   
    tauP = par['tau_'+S]  
    ml1 = par['m_'+l1]
    ml2 = par['m_'+l2]
    y1=ml1/mP
    y2=ml2/mP
    y1s=y1**2
    y2s=y2**2
    SL,SR = getS_lfv(wc_obj,par,S,l1,l2,CeGGij,CeGGji)
    return  tauP*mP/(16.*np.pi) * np.sqrt(lambda_K(1,y1s,y2s)) * ((1-y1s-y2s)*(np.abs(SL)**2+np.abs(SR)**2) -4*y1*y2 *(SL*SR.conjugate()).real)

Branching ratio for the lepton-flavour violating leptonic decay P -> l l'

def Sll_br_comb_func(S, l1, l2)

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def Sll_br_comb_func(S,  l1, l2):
    def fct(wc_obj, par,CeGGij=0,CeGGji=0):
        return Sll_br(wc_obj, par, S,  l1, l2,CeGGij,CeGGji)+ Sll_br(wc_obj, par, S,  l2, l1,CeGGij,CeGGji)
    return fct

def Sll_br_func(S, l1, l2)

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def Sll_br_func(S,  l1, l2):
    def fct(wc_obj, par,CeGGij=0,CeGGji=0):
        return Sll_br(wc_obj, par, S,  l1, l2,CeGGij,CeGGji)
    return fct

def getS_lfv(wc_obj, par, S, l1, l2, CeGGij, CeGGji)

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def getS_lfv(wc_obj,par,S,l1,l2,CeGGij,CeGGji):
    # renormalization scale
    scale = flavio.config['renormalization scale'][S]
    alphas = running.get_alpha_s(par, scale)
    # Wilson coefficients
    wc = wc_obj.get_wc(wc_sector[(l1,l2)], scale, par)

    mS = par['m_'+S]   
    # The form factor in the parameters_uncorrelated.yml file follows 1607.00815. Thus we have to include an additional factor of "-i" which drops out in the absence of an anomaly term.
    fS=par['f_'+S]*(-1j) 
    aS=par['a_'+S]
    qq=meson_quark[S]
    aPfac=1j*aS*4.*np.pi/alphas
    SR= aPfac * CeGGij +  (mS*fS/2.)*(wc['CSRR_'+l1+l2+qq]+wc['CSRL_'+l1+l2+qq])  
    SL= aPfac * CeGGji + (mS*fS/2.)*(wc['CSRL_'+l2+l1+qq]+wc['CSRR_'+l2+l1+qq]).conjugate() 
    return SL,SR