-
Notifications
You must be signed in to change notification settings - Fork 60
/
mueconversion.py
96 lines (90 loc) · 4.08 KB
/
mueconversion.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
import flavio
from flavio.classes import Observable, Prediction
import numpy as np
from flavio.physics.edms.common import proton_charges
r"""Functions for neutrinoless $\mu - e$ conversion in different target nuclei"""
def CR_mue(wc_obj, par, nucl):
r"""Conversion rate independent of the target nucleus"""
mm = par['m_mu']
scale = flavio.config['renormalization scale']['mudecays']
#####overlap integrals and other parameters#####
pc = proton_charges(par, scale)
GuSp = (pc['gS_u+d'] + pc['gS_u-d']) / 2
GdSp = (pc['gS_u+d'] - pc['gS_u-d']) / 2
GsSp = pc['gS_s']
GuSn = GdSp
GdSn = GuSp
GsSn = GsSp
D = par['D ' +nucl]*mm**(5/2)
Sp = par['Sp '+nucl]*mm**(5/2)
Vp = par['Vp '+nucl]*mm**(5/2)
Sn = par['Sn '+nucl]*mm**(5/2)
Vn = par['Vn '+nucl]*mm**(5/2)
omega_capt = par['GammaCapture '+nucl]
#####Wilson Coefficients######
#####Conversion Rate obtained from hep-ph/0203110#####
flavio.citations.register("Kitano:2002mt")
wc = wc_obj.get_wc('mue', scale, par, nf_out=3)
prefac = -np.sqrt(2)/par['GF']
AL = prefac / ( 4 * mm ) * wc['Cgamma_emu']
AR = prefac / ( 4 * mm ) * wc['Cgamma_mue'].conjugate()
gRV = {
'u': prefac * ( wc['CVRR_mueuu'] + wc['CVLR_uumue'] ) / 2,
'd': prefac * ( wc['CVRR_muedd'] + wc['CVLR_ddmue'] ) / 2,
's': prefac * ( wc['CVRR_muess'] + wc['CVLR_ssmue'] ) / 2,
}
gLV = {
'u': prefac * ( wc['CVLR_mueuu'] + wc['CVLL_mueuu'] ) / 2,
'd': prefac * ( wc['CVLR_muedd'] + wc['CVLL_muedd'] ) / 2,
's': prefac * ( wc['CVLR_muess'] + wc['CVLL_muess'] ) / 2,
}
gRS = {
'u': prefac * ( wc['CSRR_emuuu'] + wc['CSRL_emuuu'] ).conjugate() / 2,
'd': prefac * ( wc['CSRR_emudd'] + wc['CSRL_emudd'] ).conjugate() / 2,
's': prefac * ( wc['CSRR_emuss'] + wc['CSRL_emuss'] ).conjugate() / 2,
}
gLS = {
'u': prefac * ( wc['CSRR_mueuu'] + wc['CSRL_mueuu'] ) / 2,
'd': prefac * ( wc['CSRR_muedd'] + wc['CSRL_muedd'] ) / 2,
's': prefac * ( wc['CSRR_muess'] + wc['CSRL_muess'] ) / 2,
}
lhc = (
AR.conjugate() * D
+ ( 2 * gLV['u'] + gLV['d'] ) * Vp
+ ( gLV['u'] + 2 * gLV['d'] ) * Vn
+ ( GuSp * gLS['u'] + GdSp * gLS['d'] + GsSp * gLS['s'] ) * Sp
+ ( GuSn * gLS['u'] + GdSn * gLS['d'] + GsSn * gLS['s'] ) * Sn
)
rhc = (
AL.conjugate() * D
+ ( 2 * gRV['u'] + gRV['d'] ) * Vp
+ ( gRV['u'] + 2 * gRV['d'] ) * Vn
+ ( GuSp * gRS['u'] + GdSp * gRS['d'] + GsSp * gRS['s'] ) * Sp
+ ( GuSn * gRS['u'] + GdSn * gRS['d'] + GsSn * gRS['s'] ) * Sn
)
omega_conv = 2 * par['GF']**2 * ( abs(lhc)**2 + abs(rhc)**2 )
return omega_conv / omega_capt
def CR_mueAu(wc_obj, par):
r"""Conversion rate for $\phantom k^{197}_{79} \mathrm{Au}$"""
return CR_mue(wc_obj, par, 'Au')
def CR_mueAl(wc_obj, par):
r"""Conversion rate for $\phantom k^{27}_{13} \mathrm{Al}$"""
return CR_mue(wc_obj, par, 'Al')
def CR_mueTi(wc_obj, par):
r"""Conversion rate for $\phantom k^{48}_{22} \mathrm{Ti}$"""
return CR_mue(wc_obj, par, 'Ti')
CRAu = Observable('CR(mu->e, Au)')
Prediction('CR(mu->e, Au)', CR_mueAu)
CRAu.tex = r"$CR(\mu - e)$ in $\phantom k^{197}_{79} \mathrm{Au}$"
CRAu.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{197}_{79} \mathrm{Au}$"
CRAu.add_taxonomy(r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRAu.tex)
CRAl = Observable('CR(mu->e, Al)')
Prediction('CR(mu->e, Al)', CR_mueAl)
CRAl.tex = r"$CR(\mu - e)$ in $\phantom k^{27}_{13} \mathrm{Al}$"
CRAl.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{27}_{13} \mathrm{Al}$"
CRAl.add_taxonomy(r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRAl.tex)
CRTi = Observable('CR(mu->e, Ti)')
Prediction('CR(mu->e, Ti)', CR_mueTi)
CRTi.tex = r"$CR(\mu - e)$ in $\phantom k^{48}_{22} \mathrm{Ti}$"
CRTi.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{48}_{22} \mathrm{Ti}$"
CRTi.add_taxonomy(r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRTi.tex)