Module flavio.physics.quarkonium.Vll

$V\to ll^\prime$ branching ratio

Functions

def Vll_br(wc_obj, par, V, Q, l1, l2)

Expand source code

def Vll_br(wc_obj, par,V,Q, l1,l2):
    r"""Branching ratio for the lepton-flavour violating leptonic decay J/psi-> l l'"""
    #####branching ratio obtained from 2207.10913#####
    flavio.citations.register("Calibbi:2022ddo")
    mV = par['m_'+V]   
    tauV = par['tau_'+V]  
    ml1 = par['m_'+l1]
    ml2 = par['m_'+l2]
    y1=ml1/mV
    y2=ml2/mV
    y1s=y1**2
    y2s=y2**2
    if l1==l2:
        VL,VR,TL,TR = getVT_lfc(wc_obj,par,V,Q,l1)
    else:
        VL,VR,TL,TR = getVT_lfv(wc_obj,par,V,Q,l1,l2)


    ampSquared_V = (np.abs(VL)**2+np.abs(VR)**2 )/12. *(2-y1s-y2s-(y1s-y2s)**2)+y1*y2*(VL*VR.conjugate()).real
    ampSquared_T= 4./3.*(np.abs(TL)**2+np.abs(TR)**2) * (1+y1s+y2s-2*(y1s-y2s)**2) +16.*y1*y2*(TR*TL.conjugate()).real
    ampSquared_VT = 2*y1*(1+y2s-y1s)*(VR*TR.conjugate()+VL*TL.conjugate()).real + 2*y2*(1+y1s-y2s)*(VL*TR.conjugate()+VR*TL.conjugate()).real
    
    return tauV*mV/(16.*np.pi) * np.sqrt(lambda_K(1,y1s,y2s)) * (ampSquared_V+ampSquared_T+ampSquared_VT)

Branching ratio for the lepton-flavour violating leptonic decay J/psi-> l l'

def Vll_br_comb_func(V, Q, l1, l2)

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def Vll_br_comb_func(V, Q, l1, l2):
    def fct(wc_obj, par):
        return Vll_br(wc_obj, par, V, Q, l1, l2)+ Vll_br(wc_obj, par, V, Q, l2, l1)
    return fct

def Vll_br_func(V, Q, l1, l2)

Expand source code

def Vll_br_func(V, Q, l1, l2):
    def fct(wc_obj, par):
        return Vll_br(wc_obj, par, V, Q, l1, l2)
    return fct

def Vll_ratio_comb_func(V, Q, l1, l2)

Expand source code

def Vll_ratio_comb_func(V, Q, l1, l2):
    def fct(wc_obj, par):
        BRee=Vll_br(wc_obj,par,V,Q,'e','e')
        return (Vll_br(wc_obj, par, V, Q, l1, l2)+ Vll_br(wc_obj, par, V, Q, l2, l1))/BRee
    return fct

def Vll_ratio_func(V, Q, l1, l2)

Expand source code

def Vll_ratio_func(V, Q, l1, l2):
    def fct(wc_obj, par):
        BRee=Vll_br(wc_obj,par,V,Q,'e','e')
        return Vll_br(wc_obj, par, V, Q, l1, l2)/BRee
    return fct

def getVT_lfc(wc_obj, par, V, Q, l)

Expand source code

def getVT_lfc(wc_obj,par,V,Q,l):
# add contribution from photon exchange and then activate LFC channels

    # renormalization scale
    scale = flavio.config['renormalization scale'][V]
    # Wilson coefficients
    wc = wc_obj.get_wc(wc_sector[(l,l)], scale, par)
    ll=l+l
    alphaem = running.get_alpha_e(par, scale)
    ee2=4.*np.pi*alphaem
    ee=np.sqrt(ee2) 

    norm=4*par['GF']/np.sqrt(2)
    normDipole=norm*ee/(16*np.pi**2)*par['m_'+l]

    mV = par['m_'+V]   
    fV=par['f_'+V] 
    fV_T=par['fT_'+V]
    qq=meson_quark[V]

    VL=fV*mV*(wc['CVLL_'+ll+qq]*norm + wc['CVLR_'+ll+qq]*norm - 2*Q* ee2/mV**2 ) 
    VR=fV*mV*(wc['CVRR_'+ll+qq]*norm + wc['CVLR_'+qq+ll]*norm  - 2*Q* ee2/mV**2 )
    TR=fV_T*mV*wc['CTRR_'+ll+qq]*norm - ee*Q *fV*wc['C7_'+ll]*normDipole 
    TL=TR.conjugate()
    
    return VL,VR,TL,TR

def getVT_lfv(wc_obj, par, V, Q, l1, l2)

Expand source code

def getVT_lfv(wc_obj,par,V,Q,l1,l2):
    # renormalization scale
    scale = flavio.config['renormalization scale'][V]
    # Wilson coefficients
    wc = wc_obj.get_wc(wc_sector[(l1,l2)], scale, par)

    alphaem = running.get_alpha_e(par, scale)
    ee=np.sqrt(4.*np.pi*alphaem) 

    mV = par['m_'+V]   
    fV=par['f_'+V] 
    fV_T=par['fT_'+V]
    qq=meson_quark[V]
    # for emu and taue the name of the Wilson coefficient sector agrees with the ordering of leptons in the vector bilinear
    # This is not the case for mutau. Thus distinguish between the two cases here.
    if wc_sector[(l1,l2)]=="mutau":
        ll="taumu"
    else:
        ll=wc_sector[(l1,l2)]
    VL=fV*mV*(wc['CVLL_'+ll+qq] + wc['CVLR_'+ll+qq]) 
    VR=fV*mV*(wc['CVRR_'+ll+qq] + wc['CVLR_'+qq+ll]) 
    TR=fV_T*mV*wc['CTRR_'+l1+l2+qq] - ee*Q *fV*wc['Cgamma_'+l2+l1] 
    TL=(fV_T*mV*wc['CTRR_'+l2+l1+qq] - ee*Q *fV*wc['Cgamma_'+l1+l2]).conjugate()
    if ll==l2+l1: 
        VL=VL.conjugate()
        VR=VR.conjugate()
    return VL,VR,TL,TR