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Add translators for the sbcu and dbcu sectors #116

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Feb 20, 2025
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Add translators for the sbcu and dbcu sectors #116

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b12c177
Update wcxf-bases submodule reference
MJKirk Nov 13, 2024
3abaaa4
Add translator between JMS and flavio for sbcu and dbcu sectors
MJKirk Aug 12, 2024
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220 changes: 220 additions & 0 deletions wilson/translate/wet.py
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Original file line number Diff line number Diff line change
Expand Up @@ -871,6 +871,206 @@ def _Fierz_to_EOS_III(Fqqqq, qqqq, p):
return {k: v * pf_ckm for k, v in d.items()}
raise ValueError(f"Case not implemented: {qqqq}")

def _JMS_to_Flavio_III(C, qqqq, parameters):
p = parameters
V = ckmutil.ckm.ckm_tree(p["Vus"], p["Vub"], p["Vcb"], p["gamma"])
if qqqq in ('sbcu', 'dbcu', 'sbuc', 'dbuc'):
d1 = dflav[qqqq[0]]
d2 = dflav[qqqq[1]] # Will always be b = 2
u1 = uflav[qqqq[2]]
u2 = uflav[qqqq[3]]
xi = V[u1, d2] * V[u2, d1].conj()
else:
raise ValueError("Unexpected flavours: {}".format(qqqq))
pf = -sqrt(2) / p['GF'] / xi / 4
qqqq_fl = qqqq[1:4] + qqqq[0] # Indices flipped for flavio (sbcu -> bcus, etc)
Nc = 3
if qqqq == 'sbcu':
indices_ud = (1,0,1,2)
indices_ud_conj = (0,1,2,1)
indices_uddu = (1,2,1,0)
indices_uddu_conj = (0,1,2,1)
indices_du = (1,2,1,0)
elif qqqq == 'dbcu':
indices_ud = (1,0,0,2)
indices_ud_conj = (0,1,2,0)
indices_uddu = (1,2,0,0)
indices_uddu_conj = (0,0,2,1)
indices_du = (0,2,1,0)
else:
raise ValueError(f"Sector not implemented: {qqqq}")
return {
f'CVLL_{qqqq_fl}': pf * ( C["V8udLL"][*indices_ud_conj].conj()/2 ),
f'CVLR_{qqqq_fl}': pf * ( C["V1udduLR"][*indices_uddu] - C["V8udduLR"][*indices_uddu]/(2*Nc) ),
f'CVRL_{qqqq_fl}': pf * ( C["V1udduLR"][*indices_uddu_conj].conj() - C["V8udduLR"][*indices_uddu_conj].conj()/(2*Nc) ),
f'CVRR_{qqqq_fl}': pf * ( C["V8udRR"][*indices_ud_conj].conj()/2 ),
f'CSLL_{qqqq_fl}': pf * ( C["S1udduRR"][*indices_uddu_conj].conj() - C["S8udduRR"][*indices_uddu_conj].conj()/(2*Nc) - C["S8udRR"][*indices_ud_conj].conj()/4 ),
f'CSLR_{qqqq_fl}': pf * ( -C["V8duLR"][*indices_du] ),
f'CSRL_{qqqq_fl}': pf * ( -C["V8udLR"][*indices_ud_conj].conj() ),
f'CSRR_{qqqq_fl}': pf * ( C["S1udduRR"][*indices_uddu] - C["S8udduRR"][*indices_uddu]/(2*Nc) - C["S8udRR"][*indices_ud]/4 ),
f'CTLL_{qqqq_fl}': pf * ( -C["S8udRR"][*indices_ud_conj].conj()/16 ),
f'CTRR_{qqqq_fl}': pf * ( -C["S8udRR"][*indices_ud]/16 ),
f'CVLLt_{qqqq_fl}': pf * ( C["V1udLL"][*indices_ud_conj].conj() - C["V8udLL"][*indices_ud_conj].conj()/(2*Nc) ),
f'CVLRt_{qqqq_fl}': pf * ( C["V8udduLR"][*indices_uddu]/2 ),
f'CVRLt_{qqqq_fl}': pf * ( C["V8udduLR"][*indices_uddu_conj].conj()/2 ),
f'CVRRt_{qqqq_fl}': pf * ( C["V1udRR"][*indices_ud_conj].conj() - C["V8udRR"][*indices_ud_conj].conj()/(2*Nc) ),
f'CSLLt_{qqqq_fl}': pf * ( -C["S1udRR"][*indices_ud_conj].conj()/2 + C["S8udduRR"][*indices_uddu_conj].conj()/2 + C["S8udRR"][*indices_ud_conj].conj()/(4*Nc) ),
f'CSLRt_{qqqq_fl}': pf * ( -2*C["V1duLR"][*indices_du] + C["V8duLR"][*indices_du]/Nc ),
f'CSRLt_{qqqq_fl}': pf * ( -2*C["V1udLR"][*indices_ud_conj].conj() + C["V8udLR"][*indices_ud_conj].conj()/Nc ),
f'CSRRt_{qqqq_fl}': pf * ( -C["S1udRR"][*indices_ud]/2 + C["S8udduRR"][*indices_uddu]/2 + C["S8udRR"][*indices_ud]/(4*Nc) ),
f'CTLLt_{qqqq_fl}': pf * ( -C["S1udRR"][*indices_ud_conj].conj()/8 + C["S8udRR"][*indices_ud_conj].conj()/(16*Nc) ),
f'CTRRt_{qqqq_fl}': pf * ( -C["S1udRR"][*indices_ud]/8 + C["S8udRR"][*indices_ud]/(16*Nc) ),
}

def _Flavio_to_JMS_III(C, qqqq, parameters):
p = parameters
V = ckmutil.ckm.ckm_tree(p["Vus"], p["Vub"], p["Vcb"], p["gamma"])
if qqqq in ('sbcu', 'dbcu', 'sbuc', 'dbuc'):
d1 = dflav[qqqq[0]]
d2 = dflav[qqqq[1]] # Will always be b = 2
u1 = uflav[qqqq[2]]
u2 = uflav[qqqq[3]]
xi = V[u1, d2] * V[u2, d1].conj()
else:
raise ValueError("Unexpected flavours: {}".format(qqqq))
pf = -4 * p['GF'] * xi / sqrt(2)
Nc = 3
qqqq_fl = qqqq[1:4] + qqqq[0] # Indices flipped for flavio (sbcu -> bcus, etc)
if qqqq == 'sbcu':
indices_ud = "2123"
indices_ud_conj = "1232"
indices_uddu = "2321"
indices_uddu_conj = "1232"
indices_du = "2321"
elif qqqq == 'dbcu':
indices_ud = "2113"
indices_ud_conj = "1231"
indices_uddu = "2311"
indices_uddu_conj = "1132"
indices_du = "1321"
else:
raise ValueError(f"Sector not implemented: {qqqq}")
return {
f"V1udLL_{indices_ud_conj}": pf * ( C[f"CVLL_{qqqq_fl}"].conjugate()/Nc + C[f"CVLLt_{qqqq_fl}"].conjugate() ),
f"V8udLL_{indices_ud_conj}": pf * ( 2*C[f"CVLL_{qqqq_fl}"].conjugate() ),
f"V1udRR_{indices_ud_conj}": pf * ( C[f"CVRR_{qqqq_fl}"].conjugate()/Nc + C[f"CVRRt_{qqqq_fl}"].conjugate() ),
f"V8udRR_{indices_ud_conj}": pf * ( 2*C[f"CVRR_{qqqq_fl}"].conjugate() ),
f"V1udLR_{indices_ud_conj}": pf * ( -C[f"CSRL_{qqqq_fl}"].conjugate()/(2.*Nc) - C[f"CSRLt_{qqqq_fl}"].conjugate()/2. ),
f"V8udLR_{indices_ud_conj}": pf * ( -C[f"CSRL_{qqqq_fl}"].conjugate() ),
f"V1duLR_{indices_du}": pf * ( -C[f"CSLR_{qqqq_fl}"]/(2.*Nc) - C[f"CSLRt_{qqqq_fl}"]/2. ),
f"V8duLR_{indices_du}": pf * ( -C[f"CSLR_{qqqq_fl}"] ),
f"V1udduLR_{indices_uddu_conj}": pf * ( C[f"CVRL_{qqqq_fl}"].conjugate() + C[f"CVRLt_{qqqq_fl}"].conjugate()/Nc ),
f"V8udduLR_{indices_uddu_conj}": pf * ( 2*C[f"CVRLt_{qqqq_fl}"].conjugate() ),
f"V1udduLR_{indices_uddu}": pf * ( C[f"CVLR_{qqqq_fl}"] + C[f"CVLRt_{qqqq_fl}"]/Nc ),
f"V8udduLR_{indices_uddu}": pf * ( 2*C[f"CVLRt_{qqqq_fl}"] ),
f"S1udRR_{indices_ud_conj}": pf * ( (-8*C[f"CTLL_{qqqq_fl}"]).conjugate()/Nc - 8*C[f"CTLLt_{qqqq_fl}"].conjugate() ),
f"S8udRR_{indices_ud_conj}": pf * ( -16*C[f"CTLL_{qqqq_fl}"].conjugate() ),
f"S1udduRR_{indices_uddu_conj}": pf * ( C[f"CSLL_{qqqq_fl}"].conjugate() + C[f"CSLLt_{qqqq_fl}"].conjugate()/Nc - 4*C[f"CTLL_{qqqq_fl}"].conjugate() - (4*C[f"CTLLt_{qqqq_fl}"]).conjugate()/Nc ),
f"S8udduRR_{indices_uddu_conj}": pf * ( 2*C[f"CSLLt_{qqqq_fl}"].conjugate() - 8*C[f"CTLLt_{qqqq_fl}"].conjugate() ),
f"S1udRR_{indices_ud}": pf * ( (-8*C[f"CTRR_{qqqq_fl}"])/Nc - 8*C[f"CTRRt_{qqqq_fl}"] ),
f"S8udRR_{indices_ud}": pf * ( -16*C[f"CTRR_{qqqq_fl}"] ),
f"S1udduRR_{indices_uddu}": pf * ( C[f"CSRR_{qqqq_fl}"] + C[f"CSRRt_{qqqq_fl}"]/Nc - 4*C[f"CTRR_{qqqq_fl}"] - (4*C[f"CTRRt_{qqqq_fl}"])/Nc ),
f"S8udduRR_{indices_uddu}": pf * ( 2*C[f"CSRRt_{qqqq_fl}"] - 8*C[f"CTRRt_{qqqq_fl}"] ),
}

def _Bern_to_Flavio_III(C, qqqq, parameters):
p = parameters
V = ckmutil.ckm.ckm_tree(p["Vus"], p["Vub"], p["Vcb"], p["gamma"])
if qqqq in ('sbcu', 'dbcu', 'sbuc', 'dbuc'):
d1 = dflav[qqqq[0]]
d2 = dflav[qqqq[1]] # Will always be b = 2
u1 = uflav[qqqq[2]]
u2 = uflav[qqqq[3]]
xi = V[u1, d2] * V[u2, d1].conj()
else:
raise ValueError("Unexpected flavours: {}".format(qqqq))
pf = -sqrt(2) / p['GF'] / xi / 4
qqqq_fl = qqqq[1:4] + qqqq[0] # Indices flipped for flavio (sbcu -> bcus, etc)
Nc = 3
CBern = [C[f"{i}{qqqq}"] if i <= 10 else C[f"{i-10}p{qqqq}"] for i in range(1,21)]
dic = {
f'CVLL_{qqqq_fl}': CBern[2-1]/2+8*CBern[4-1],
f'CVLR_{qqqq_fl}': -(CBern[16-1]/4)-4*CBern[20-1],
f'CVRL_{qqqq_fl}': -(CBern[6-1]/4)-4*CBern[10-1],
f'CVRR_{qqqq_fl}': CBern[12-1]/2+8*CBern[14-1],
f'CSLL_{qqqq_fl}': -(CBern[16-1]/4)-3*CBern[18-1]+32*CBern[20-1],
f'CSLR_{qqqq_fl}': -CBern[2-1]-4*CBern[4-1],
f'CSRL_{qqqq_fl}': -CBern[12-1]-4*CBern[14-1],
f'CSRR_{qqqq_fl}': -(CBern[6-1]/4)-3*CBern[8-1]+32*CBern[10-1],
f'CTLL_{qqqq_fl}': -(CBern[16-1]/16)+CBern[18-1]/4-8*CBern[20-1],
f'CTRR_{qqqq_fl}': -(CBern[6-1]/16)+CBern[8-1]/4-8*CBern[10-1],
f'CVLLt_{qqqq_fl}': -(CBern[2-1]/(2*Nc))-(8*CBern[4-1])/Nc+CBern[1-1]+16*CBern[3-1],
f'CVLRt_{qqqq_fl}': CBern[16-1]/(4*Nc)+(4*CBern[20-1])/Nc-CBern[15-1]/2-8*CBern[19-1],
f'CVRLt_{qqqq_fl}': CBern[6-1]/(4*Nc)+(4*CBern[10-1])/Nc-CBern[5-1]/2-8*CBern[9-1],
f'CVRRt_{qqqq_fl}': -(CBern[12-1]/(2*Nc))-(8*CBern[14-1])/Nc+CBern[11-1]+16*CBern[13-1],
f'CSLLt_{qqqq_fl}': CBern[16-1]/(4*Nc)+(3*CBern[18-1])/Nc-(32*CBern[20-1])/Nc-CBern[15-1]/2-6*CBern[17-1]+64*CBern[19-1],
f'CSLRt_{qqqq_fl}': CBern[2-1]/Nc+(4*CBern[4-1])/Nc-2*CBern[1-1]-8*CBern[3-1],
f'CSRLt_{qqqq_fl}': CBern[12-1]/Nc+(4*CBern[14-1])/Nc-2*CBern[11-1]-8*CBern[13-1],
f'CSRRt_{qqqq_fl}': CBern[6-1]/(4*Nc)+(3*CBern[8-1])/Nc-(32*CBern[10-1])/Nc-CBern[5-1]/2-6*CBern[7-1]+64*CBern[9-1],
f'CTLLt_{qqqq_fl}': CBern[16-1]/(16*Nc)-CBern[18-1]/(4*Nc)+(8*CBern[20-1])/Nc-CBern[15-1]/8+CBern[17-1]/2-16*CBern[19-1],
f'CTRRt_{qqqq_fl}': CBern[6-1]/(16*Nc)-CBern[8-1]/(4*Nc)+(8*CBern[10-1])/Nc-CBern[5-1]/8+CBern[7-1]/2-16*CBern[9-1],
}
return {k:v*pf for k,v in dic.items()}

def _Flavio_to_Bern_III(C, qqqq, parameters):
### Overall sign fixed, but messily
p = parameters
V = ckmutil.ckm.ckm_tree(p["Vus"], p["Vub"], p["Vcb"], p["gamma"])
if qqqq in ('sbcu', 'dbcu', 'sbuc', 'dbuc'):
d1 = dflav[qqqq[0]]
d2 = dflav[qqqq[1]] # Will always be b = 2
u1 = uflav[qqqq[2]]
u2 = uflav[qqqq[3]]
xi = V[u1, d2] * V[u2, d1].conj()
else:
raise ValueError("Unexpected flavours: {}".format(qqqq))
pf = -4 * p['GF'] * xi / sqrt(2)
Nc = 3
qqqq_fl = qqqq[1:4] + qqqq[0] # Indices flipped for flavio (sbcu -> bcus, etc)
CVLL = C[f"CVLL_{qqqq_fl}"]
CVLR = C[f"CVLR_{qqqq_fl}"]
CVRL = C[f"CVRL_{qqqq_fl}"]
CVRR = C[f"CVRR_{qqqq_fl}"]
CSLL = C[f"CSLL_{qqqq_fl}"]
CSLR = C[f"CSLR_{qqqq_fl}"]
CSRL = C[f"CSRL_{qqqq_fl}"]
CSRR = C[f"CSRR_{qqqq_fl}"]
CTLL = C[f"CTLL_{qqqq_fl}"]
CTRR = C[f"CTRR_{qqqq_fl}"]
CVLLt = C[f"CVLLt_{qqqq_fl}"]
CVLRt = C[f"CVLRt_{qqqq_fl}"]
CVRLt = C[f"CVRLt_{qqqq_fl}"]
CVRRt = C[f"CVRRt_{qqqq_fl}"]
CSLLt = C[f"CSLLt_{qqqq_fl}"]
CSLRt = C[f"CSLRt_{qqqq_fl}"]
CSRLt = C[f"CSRLt_{qqqq_fl}"]
CSRRt = C[f"CSRRt_{qqqq_fl}"]
CTLLt = C[f"CTLLt_{qqqq_fl}"]
CTRRt = C[f"CTRRt_{qqqq_fl}"]
dic = {
f'1{qqqq}': -2*CSLR/(3*Nc)-2*CSLRt/3-CVLL/(3*Nc)-CVLLt/3,
f'2{qqqq}': -4*CSLR/3-2*CVLL/3,
f'3{qqqq}': CSLR/(24*Nc)+CSLRt/24+CVLL/(12*Nc)+CVLLt/12,
f'4{qqqq}': CSLR/12+CVLL/6,
f'5{qqqq}': CSRR/(6*Nc)+CSRRt/6+(2*CTRR)/Nc+2*CTRRt-8*CVRL/(3*Nc)-8*CVRLt/3,
f'6{qqqq}': CSRR/3+4*CTRR-16*CVRL/3,
f'7{qqqq}': -7*CSRR/(24*Nc)-7*CSRRt/24-3*CTRR/(2*Nc)-3*CTRRt/2+(2*CVRL)/(3*Nc)+(2*CVRLt)/3,
f'8{qqqq}': -7*CSRR/12-3*CTRR+(4*CVRL)/3,
f'9{qqqq}': -CSRR/(96*Nc)-CSRRt/96-CTRR/(8*Nc)-CTRRt/8+CVRL/(24*Nc)+CVRLt/24,
f'10{qqqq}': -CSRR/48-CTRR/4+CVRL/12,
f'1p{qqqq}': -2*CSRL/(3*Nc)-2*CSRLt/3-CVRR/(3*Nc)-CVRRt/3,
f'2p{qqqq}': -4*CSRL/3-2*CVRR/3,
f'3p{qqqq}': CSRL/(24*Nc)+CSRLt/24+CVRR/(12*Nc)+CVRRt/12,
f'4p{qqqq}': CSRL/12+CVRR/6,
f'5p{qqqq}': CSLL/(6*Nc)+CSLLt/6+(2*CTLL)/Nc+2*CTLLt-8*CVLR/(3*Nc)-8*CVLRt/3,
f'6p{qqqq}': CSLL/3+4*CTLL-16*CVLR/3,
f'7p{qqqq}': -7*CSLL/(24*Nc)-7*CSLLt/24-3*CTLL/(2*Nc)-3*CTLLt/2+(2*CVLR)/(3*Nc)+(2*CVLRt)/3,
f'8p{qqqq}': -7*CSLL/12-3*CTLL+(4*CVLR)/3,
f'9p{qqqq}': -CSLL/(96*Nc)-CSLLt/96-CTLL/(8*Nc)-CTLLt/8+CVLR/(24*Nc)+CVLRt/24,
f'10p{qqqq}': -CSLL/48-CTLL/4+CVLR/12,
}
return {k:v*pf for k,v in dic.items()}

def _Fierz_to_Flavio_V(Fqqqq, qqqq, parameters):
p = parameters
V = ckmutil.ckm.ckm_tree(p["Vus"], p["Vub"], p["Vcb"], p["gamma"])
Expand Down Expand Up @@ -1784,6 +1984,11 @@ def JMS_to_flavio(Cflat, scale, parameters=None, sectors=None):
qq+'l_'+l+'nu_'+lp),
qq+'l_'+l+'nu_'+lp, p))

# Class III
for qqqq in ['sbcu', 'dbcu']: # 'sbuc', 'dbuc' not implemented yet
if sectors is None or qqqq in sectors:
d.update(_JMS_to_Flavio_III(C, qqqq, p))

# Class V semileptonic
for l in lflav.keys():
for lp in lflav.keys():
Expand Down Expand Up @@ -1880,6 +2085,11 @@ def Bern_to_flavio(C_incomplete, scale, parameters=None, sectors=None):
for qq in ['cb', 'ub', 'us', 'cs', 'cd', 'ud']:
d.update(_BernII_to_Flavio_II(C, qq+'l_'+l+'nu_'+lp, p))

# Class III
for qqqq in ['sbcu', 'dbcu']: # 'sbuc', 'dbuc' not implemented yet
if sectors is None or qqqq in sectors:
d.update(_Bern_to_Flavio_III(C, qqqq, p))

# Class V semileptonic
for l in lflav.keys():
for lp in lflav.keys():
Expand Down Expand Up @@ -1943,6 +2153,11 @@ def flavio_to_Bern(C_incomplete, scale, parameters=None, sectors=None):
for qq in ['cb', 'ub', 'us', 'cs', 'cd', 'ud']:
d.update(_FlavioII_to_BernII(C, qq+'l_'+l+'nu_'+lp, p))

# Class III
for qqqq in ['sbcu', 'dbcu']: # 'sbuc', 'dbuc' not implemented yet
if sectors is None or qqqq in sectors:
d.update(_Flavio_to_Bern_III(C, qqqq, p))

# Class V semileptonic
for l in lflav.keys():
for lp in lflav.keys():
Expand Down Expand Up @@ -2144,6 +2359,11 @@ def flavio_to_JMS(C_incomplete, scale, parameters=None, sectors=None):
qq+'l_'+l+'nu_'+lp, p),
qq+'l_'+l+'nu_'+lp))

# Class III
for qqqq in ['sbcu', 'dbcu']: # 'sbuc', 'dbuc' not implemented yet
if sectors is None or qqqq in sectors:
d.update(_Flavio_to_JMS_III(C, qqqq, p))

# Class V semileptonic
for l in lflav.keys():
for lp in lflav.keys():
Expand Down
2 changes: 1 addition & 1 deletion wilson/wcxf/bases
Open in desktop
Submodule bases updated 3 files
+4 −1 util/convert.py
+124 −0 wet.flavio.basis.json
+82 −0 wet.flavio.basis.yml