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| Original file line number | Diff line number | Diff line change |
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@@ -4,3 +4,4 @@ | |
| from . import b_p | ||
| from . import b_gamma | ||
| from . import lambdab_12 | ||
| from . import lambdab_32 | ||
63 changes: 63 additions & 0 deletions
63
flavio/physics/bdecays/formfactors/lambdab_32/LatticeQCD.py
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,63 @@ | ||
| from math import sqrt, exp | ||
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| def omega(q2, mLb, mLst): | ||
| # eq. (73) in arXiv:2009.09313v1 | ||
| return (mLb*mLb + mLst*mLst - q2)/(2*mLb*mLst) | ||
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| def F(q2, Ff, Af, Omega): | ||
| # eq. (75) | ||
| return Ff + Af*(Omega - 1) | ||
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| _process_dict = {} | ||
| _process_dict['Lambdab->Lambda(1520)'] = {'X': 'Lambda(1520)'} | ||
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| def formfactors(process, par, q2): | ||
| r"Formfactors for $\Lambda_b\to L(1520)$ from Lattice QCD as in arXiv:2009.09313v1" | ||
| pd = _process_dict[process] | ||
| mL = par['m_'+pd['X']] | ||
| mLb = par['m_Lambdab'] | ||
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| Omega = omega(q2, mLb, mL) | ||
| FList = ['f0', 'fplus', 'fperp', 'fperpPrim', | ||
| 'g0', 'gplus', 'gperp', 'gperpPrim', | ||
| 'hplus', 'hperp', 'hperpPrim', 'hTplus', 'hTperp', 'hTperpPrim'] | ||
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| FormDict = {} | ||
| for e in FList: | ||
| Ff = par[process+' '+e+' F'] | ||
| Af = par[process+' '+e+' A'] | ||
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| FormDict[e] = F(q2, Ff, Af, Omega) | ||
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| return FormDict, mL, mLb | ||
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| def ff_equiv(process, q2, par): | ||
| # eq. (A21) - (A34) and (6) | ||
| FD, mLst, mLb = formfactors(process, par, q2) | ||
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| splus = (mLb + mLst)**2 - q2 | ||
| sminus = (mLb - mLst)**2 - q2 | ||
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| ff = {} | ||
| ff['fVt'] = ( mLst/splus )*FD['f0'] | ||
| ff['fV0'] = ( mLst/sminus )*FD['fplus'] | ||
| ff['fVperp'] = ( mLst/sminus )*FD['fperp'] | ||
| ff['fVg'] = FD['fperpPrim'] | ||
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| ff['fAt'] = ( mLst/sminus )*FD['g0'] | ||
| ff['fA0'] = ( mLst/splus )*FD['gplus'] | ||
| ff['fAperp'] = ( mLst/splus )*FD['gperp'] | ||
| ff['fAg'] = -FD['gperpPrim'] | ||
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| ff['fTt'] = 0 | ||
| ff['fT0'] = ( mLst/sminus )*FD['hplus'] | ||
| ff['fTperp'] = ( mLst/sminus )*FD['hperp'] | ||
| ff['fTg'] = ( mLb + mLst )*FD['hperpPrim'] | ||
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| ff['fT5t'] = 0 | ||
| ff['fT50'] = ( mLst/splus )*FD['hTplus'] | ||
| ff['fT5perp']= ( mLst/splus )*FD['hTperp'] | ||
| ff['fT5g'] = -( mLb - mLst )*FD['hTperpPrim'] | ||
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| return ff |
101 changes: 101 additions & 0 deletions
101
flavio/physics/bdecays/formfactors/lambdab_32/QuarkModel_MCN.py
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,101 @@ | ||
| from math import sqrt, exp | ||
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| def p_Lambda(q2, mL, mLb): | ||
| # daughter baryon momentum in the Lb rest frame | ||
| s = q2/mLb**2 | ||
| r = (mL/mLb)**2 | ||
| return mLb/2*sqrt((1-r)**2 - 2*(1+r)*s + s**2) | ||
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| def m_Lambda(m_q, m_s): | ||
| return 2*m_q + m_s | ||
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| def alpha_ll(alpha_l1, alpha_l2): | ||
| return sqrt((alpha_l1**2 + alpha_l2**2)/2) | ||
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| def F(a0, a2, a4, p_L, m_q, m_L, alpha): | ||
| return (a0 + a2*p_L**2 + a4*p_L**4)*exp(-3*(m_q*p_L)**2/(2*(m_L*alpha)**2)) | ||
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| _process_dict = {} | ||
| _process_dict['Lambdab->Lambda(1520)'] = {'X': 'Lambda(1520)'} | ||
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| def formfactors(process, par, q2): | ||
| r"Functions for $\Lambda_b\to X_{3/2}$ form factors where $X_{3/2} is a spin-3/2 baryon$ using the Quark Model and the MCN approach treated in arXiv:1108.6129 [nucl-th]" | ||
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| # experimental masses because of small difference to model masses, differences will be covered by uncertainties | ||
| pd = _process_dict[process] | ||
| mL = par['m_'+pd['X']] | ||
| mLb = par['m_Lambdab'] | ||
| m_q = par[process + ' m_q'] | ||
| m_s = par[process + ' m_s'] | ||
| alpha_l1 = par[process +' alpha_Lambdab'] | ||
| alpha_l2 = par[process +' alpha_'+pd['X']] | ||
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| FList = ['F1', 'F2', 'F3', 'F4', | ||
| 'G1', 'G2', 'G3', 'G4', | ||
| 'H1', 'H2', 'H3', 'H4', 'H5', 'H6'] | ||
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| p_L = p_Lambda(q2, mL, mLb) | ||
| mL_tilde = m_Lambda(m_q, m_s) | ||
| alpha_LL = alpha_ll(alpha_l1, alpha_l2) | ||
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| FormDict = {} | ||
| for e in FList: | ||
| a0 = par[process+' '+e+' a0'] | ||
| a2 = par[process+' '+e+' a2'] | ||
| a4 = par[process+' '+e+' a4'] | ||
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| FormDict[e] = F(a0, a2, a4, p_L, m_q, mL_tilde, alpha_LL) | ||
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| return FormDict, mL, mLb | ||
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| def ff_equiv(process, q2, par): | ||
| # transform FormDict in form factors used in arXiv:1903.00448 | ||
| FD, mL, mLb = formfactors(process, par, q2) | ||
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| e_fVt = par[process+' fVt uncertainty'] | ||
| e_fVperp = par[process+' fVperp uncertainty'] | ||
| e_fV0 = par[process+' fV0 uncertainty'] | ||
| e_fVg = par[process+' fVg uncertainty'] | ||
| e_fAt = par[process+' fAt uncertainty'] | ||
| e_fAperp = par[process+' fAperp uncertainty'] | ||
| e_fA0 = par[process+' fA0 uncertainty'] | ||
| e_fAg = par[process+' fAg uncertainty'] | ||
| e_fTt = par[process+' fTt uncertainty'] | ||
| e_fTperp = par[process+' fTperp uncertainty'] | ||
| e_fT0 = par[process+' fT0 uncertainty'] | ||
| e_fTg = par[process+' fTg uncertainty'] | ||
| e_fT5t = par[process+' fT5t uncertainty'] | ||
| e_fT5perp = par[process+' fT5perp uncertainty'] | ||
| e_fT50 = par[process+' fT50 uncertainty'] | ||
| e_fT5g = par[process+' fT5g uncertainty'] | ||
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| ff = {} | ||
| ff['fVt'] = ( FD['F2']*mL*(mL**2 - mLb**2 - q2) + mLb*(2*FD['F1']*mL*(mL - mLb) - 2*FD['F4']*mL*mLb + FD['F3']*(mL**2 - mLb**2 + q2)) )/( 2*mL*(mL-mLb)*mLb**2 ) * e_fVt | ||
| ff['fVperp'] = ( FD["F1"]/mLb - FD["F4"]*mL/(mL**2 - 2*mL*mLb + mLb**2 - q2) )*e_fVperp | ||
| ff['fV0'] = ( FD["F2"]*mL*(mL**4 + (mLb**2 - q2)**2 - 2*mL**2*(mLb**2 + q2)) + mLb*(2*FD["F1"]*mL*(mL + mLb)*(mL**2 - 2*mL*mLb + mLb**2 - q2) - 2*FD["F4"]*mL*mLb*(mL**2 - mLb**2 + q2) + FD["F3"]*(mL**4 + (mLb**2 - q2)**2 - 2*mL**2*(mLb**2 + q2))) )/( 2*mL*mLb**2*(mL+mLb)*(mL**2 - 2*mL*mLb + mLb**2 - q2) )*e_fV0 | ||
| ff['fVg'] = FD["F4"]*e_fVg | ||
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| ff['fAt'] = ( FD["G2"]*mL*(mL**2 - mLb**2 - q2) + mLb*(-2*FD["G4"]*mL*mLb + 2*FD["G1"]*mL*(mL + mLb) + FD["G3"]*(mL**2 - mLb**2 + q2)) )/( 2*mL*mLb**2*(mL + mLb) )*e_fAt | ||
| ff['fAperp'] = ( FD["G1"]/mLb - (FD["G4"]*mL)/(mL**2 + 2*mL*mLb + mLb**2 - q2) )*e_fAperp | ||
| ff['fA0'] = ( FD["G2"]*mL*(mL**4 + (mLb**2 - q2)**2 - 2*mL**2*(mLb**2 + q2)) + mLb*(2*FD["G1"]*mL*(mL - mLb)*(mL**2 + 2*mL*mLb + mLb**2 - q2) - 2*FD["G4"]*mL*mLb*(mL**2 - mLb**2 + q2) + FD["G3"]*(mL**4 + (mLb**2 - q2)**2 - 2*mL**2*(mLb**2 + q2))) )/( 2*mL*(mL - mLb)*mLb**2*(mL**2 + 2*mL*mLb + mLb**2 - q2) )*e_fA0 | ||
| ff['fAg'] = -FD["G4"]*e_fAg | ||
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| ff['fTt'] = 0*e_fTt | ||
| ff['fTperp'] = ( 2*FD["H5"]*mL - ((FD["H3"]+FD["H6"])*mL**2)/mLb + FD["H3"]*mLb + 2*FD["H1"]*mL*(mL + mLb)/mLb - 2*(FD["H5"] + FD["H6"])*mL**2*(mL - mLb)/((mL - mLb)**2 - q2) - FD["H3"]*q2/mLb + FD["H2"]*mL*(-mL**2 + mLb**2 + q2)/mLb**2 )/( 2*mL*(mL + mLb) )*e_fTperp | ||
| ff['fT0'] = ( (FD["H1"] + FD["H2"] - FD["H3"] - FD["H6"])/mLb - 2*((FD["H5"] + FD["H6"])*mL)/((mL - mLb)**2 - q2) + FD["H4"]*((mL + mLb)**2 - q2)/(2*mL*mLb**2) )*e_fT0 | ||
| ff['fTg'] = ( FD["H5"]*(mL- mLb) - FD["H6"]*(-mL**2 + mLb**2 + q2)/(2*mLb) )*e_fTg | ||
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| ff['fT5t'] = 0*e_fT5t | ||
| ff['fT5perp'] = ( -1/(2*mL*(mL-mLb)*mLb**2*(mL**2 + 2*mL*mLb + mLb**2 - q2)) * (FD["H2"]*mL*(mL**4 + (mLb**2 - q2)**2 - 2*mL**2*(mLb**2 + q2)) + mLb*(mL*(2*FD["H5"]*mLb*(mL*mLb + mLb**2 - q2) + FD["H6"]*mL*(mL**2 + 2*mL*mLb + mLb**2 -q2)) - 2*FD["H1"]*mL*(mL - mLb)*(mL**2 + 2*mL*mLb + mLb**2 -q2) + FD["H3"]*(mL**4 + (mLb**2 - q2)**2 - 2*mL**2*(mLb**2 + q2)))) )*e_fT5perp | ||
| ff['fT50'] = ( FD["H1"]/mLb + 2*FD["H5"]*mL/(mL**2 + 2*mL*mLb + mLb**2 - q2) )*e_fT50 | ||
| ff['fT5g'] = ( -FD["H5"]*(mL + mLb) - FD["H6"]*(mL**2 + 2*mL*mLb + mLb**2 - q2)/(2*mLb) )*e_fT5g | ||
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| return ff | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,5 @@ | ||
| r"""Functions for $\Lambda_b\to X_{3/2}$ form factors where $X_{3/2}$ is a spin-3/2 baryon.""" | ||
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| from . import lambdab | ||
| from . import QuarkModel_MCN | ||
| from . import LatticeQCD |
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