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import pandas as pd
import numpy as np
import symengine
import pathlib
#WATCH OUT! All abs have been removed!!!
#Results only appliclable for real wilson coefficients
mN = 0.938272 #nucleon mass in GeV
mpi = 138.0/1000 #pion mass in GeV
mAMU = 931.494/1000 #atomic mass unit
sigma = 10**(-46) #WIMP-nucleon cross section in cm^2
cvel = 299792458 #speed of light in m/s
#Dirac WIMP (zeta=1) or Majorana WIMP (zeta=2).
#For spin-0 WIMPs for a complex scalar particle zeta=1
#and zeta=2 for a real scalar particle.
zeta = 1
#approximate WIMP velocity
#v=10**(-3)
#xi_ud
xiud = 0.37
#scalar radii
sigdot = 0.27 #GeV^-1
sigdots = 0.3 #GeV^-1
#magnetic moments
kappap = 1.792847356
kappan = -1.91304272
kappaNs = 0.006
#charge radii
r2Ep = 18.1597 #GeV^-2 = 0.7071 fm^2
r2En = -2.9817 #GeV^-2 = -0.1161 fm^2
r2EsN = 30.8183*10**(-3) #GeV^-2 = 0.0012 fm^2
#nucleon masses
mp = 938.272 * 10**(-3) #GeV
mn = 939.565 * 10**(-3) #GeV
#couplings to quarks/gluons
#scalar
fpu = 20.8 * 10**(-3)
fnu = 18.9 * 10**(-3)
fpd = 41.1 * 10**(-3)
fnd = 45.1 * 10**(-3)
fps = 43 * 10**(-3)
fns = fps
fpQ = 68 * 10**(-3)
fnQ = fpQ
fpiu=0.32
fpid=0.68
#spin-2
fpi2u = 0.298
fpi2d = 0.298
fpi2s = 0.055
fpi2g = 0.341
fp2u = 0.346
fp2d = 0.192
fp2s = 0.034
fp2c = 0.0088
fp2b = 0
fp2t = 0
fp2g = 0.419
fn2u = 0.192
fn2d = 0.346
fn2s = 0.034
fn2c = 0.0088
fn2b = 0
fn2t = 0
fn2g = 0.419
#tensor
fTpu = 0.784
fTpd = -0.204
fTps = -0.0027
fTpc = 0
fTpb = 0
fTpt = 0
fTnd = 0.784
fTnu = -0.204
fTns = -0.0027
fTnc = 0
fTnb = 0
fTnt = 0
kappatilTpu = -1.3
kappatilTpd = -0.7
kappatilTps = 0.0
kappatilTpc = 0.0
kappatilTpb = 0.0
kappatilTpt = 0.0
kappatilTnu = -0.7
kappatilTnd = -1.3
kappatilTns = 0.0
kappatilTnc = 0.0
kappatilTnb = 0.0
kappatilTnt = 0.0
r21p = r2Ep - 3*kappap/(2*mp**2)
r21n = r2En - 3*kappan/(2*mn**2)
def set_param(mchi,lam, **kwargs):
muN = (mchi * mN)/(mchi + mN) #WIMP-nucleon reduced mass
mupi = (mchi * mpi)/(mchi + mpi) #WIMP-pion reduced mass
names = [
#WILSON coefficients
#scalar-scalar
'CSSu',
'CSSd',
'CSSs',
'CSSc',
'CSSb',
'CSSt',
'CSg',
'CSgtil',
#pseudoscalar-scalar
'CPSu',
'CPSd',
'CPSs',
'CPSc',
'CPSb',
'CPSt',
#vector-vector
'CVVu',
'CVVd',
'CVVs',
'CVVc',
'CVVb',
'CVVt',
#axial-vector-vector
'CAVu',
'CAVd',
#spin-2
'C2u',
'C2d',
'C2s',
'C2c',
'C2b',
'C2t',
'Cg2',
#tensor
'CTTu',
'CTTd',
'CTTs',
'CTTc',
'CTTb',
'CTTt',
'CtilTTu',
'CtilTTd',
'CtilTTs',
'CtilTTc',
'CtilTTb',
'CtilTTt',
#dipole
'eCF',
'eCFtil'
]
param = {name:0 for name in names}
for key, value in kwargs.items():
param[key] = value
#------------------------------------------------------------------------------
CSgp = param['CSg']-1/(12*np.pi)*(param['CSSc']+param['CSSb']+param['CSSt'])
CSgptil = param['CSgtil']-1/(12*np.pi)*(param['CPSc']+param['CPSb']+param['CPSt'])
#nucleon/pion form factors------------------------------------------------------------------------------
fp = mp/lam**3*(param['CSSu']*fpu+param['CSSd']*fpd+param['CSSs']*fps-12*np.pi*fpQ*CSgp)
fn = mn/lam**3*(param['CSSu']*fnu+param['CSSd']*fnd+param['CSSs']*fns-12*np.pi*fnQ*CSgp)
ftilp = mp/lam**3*(param['CPSu']*fpu+param['CPSd']*fpd+param['CPSs']*fps-12*np.pi*fpQ*CSgptil)
ftiln = mn/lam**3*(param['CPSu']*fnu+param['CPSd']*fnd+param['CPSs']*fns-12*np.pi*fnQ*CSgptil)
fdotp = 1/lam**3*(param['CSSu']*(1-xiud)/2*sigdot + param['CSSd']*(1+xiud)/2*sigdot+param['CSSs']*sigdots)
fdotn = fdotp
fVp1 = 1/lam**2*(2*param['CVVu'] + param['CVVd'])
fVn1 = 1/lam**2*(2*param['CVVd'] + param['CVVu'])
fVp2 = 1/lam**2*((2*param['CVVu']+param['CVVd'])*kappap \
+ (param['CVVu']+2*param['CVVd'])*kappan \
+(param['CVVu']+param['CVVd']+param['CVVs'])*kappaNs)
fVn2 = 1/lam**2*((2*param['CVVd']+param['CVVu'])*kappap \
+ (param['CVVd']+2*param['CVVu'])*kappan\
+(param['CVVd']+param['CVVu']+param['CVVs'])*kappaNs)
ftilVp1 = 1/lam**2*(2*param['CAVu'] + param['CAVd'])
ftilVn1 = 1/lam**2*(2*param['CAVd'] + param['CAVu'])
fdotVp1 = 1/lam**2*((2*param['CVVu']+param['CVVd'])*(r2Ep/6-kappap/(4*mp**2)) \
+(param['CVVu']+2*param['CVVd'])*(r2En/6-kappan/(4*mn**2)) \
+(param['CVVu']+param['CVVd']+param['CVVs'])*(r2EsN/6-kappaNs/(4*mN**2)))
fdotVn1 = 1/lam**2*((2*param['CVVd']+param['CVVu'])*(r2Ep/6-kappap/(4*mp**2)) \
+(param['CVVd']+2*param['CVVu'])*(r2En/6-kappan/(4*mn**2)) \
+(param['CVVu']+param['CVVd']+param['CVVs'])*(r2EsN/6-kappaNs/(4*mN**2)))
fp2 = mchi*mp/lam**4*(param['C2u']*fp2u + param['C2d']*fp2d + param['C2s']*fp2s \
+ param['C2c']*fp2c + param['C2b']*fp2b+param['C2t']*fp2t + param['Cg2']*fp2g)
fn2 = mchi*mn/lam**4*(param['C2u']*fn2u + param['C2d']*fn2d + param['C2s']*fn2s \
+ param['C2c']*fn2c + param['C2b']*fn2b+param['C2t']*fn2t + param['Cg2']*fn2g)
fTp1 = 1/lam**2*(fTpu*param['CTTu'] + fTpd*param['CTTd'] + fTps*param['CTTs'] \
+ fTpc*param['CTTc'] + fTpb*param['CTTb'] + fTpt*param['CTTt'])
fTn1 = 1/lam**2*(fTnu*param['CTTu'] + fTnd*param['CTTd'] + fTns*param['CTTs'] \
+ fTnc*param['CTTc'] + fTnb*param['CTTb'] + fTnt*param['CTTt'])
ftilTp1 = 1/lam**2*(fTpu*param['CtilTTu'] + fTpd*param['CtilTTd'] + fTps*param['CtilTTs'] \
+ fTpc*param['CtilTTc'] + fTpb*param['CtilTTb'] + fTpt*param['CtilTTt'])
ftilTn1 = 1/lam**2*(fTnu*param['CtilTTu'] + fTnd*param['CtilTTd'] + fTns*param['CtilTTs'] \
+ fTnc*param['CtilTTc'] + fTnb*param['CtilTTb'] + fTnt*param['CtilTTt'])
fTp2 = 1/lam**2*(kappatilTpu*param['CTTu'] + kappatilTpd*param['CTTd'] + kappatilTps*param['CTTs'] \
+ kappatilTpc*param['CTTc'] + kappatilTpb*param['CTTb'] + kappatilTpt*param['CTTt'])
fTn2 = 1/lam**2*(kappatilTnu*param['CTTu'] + kappatilTnd*param['CTTd'] + kappatilTns*param['CTTs'] \
+ kappatilTnc*param['CTTc'] + kappatilTnb*param['CTTb'] + kappatilTnt*param['CTTt'])
ftilTp2 = 1/lam**2*(kappatilTpu*param['CtilTTu'] + kappatilTpd*param['CtilTTd'] + kappatilTps*param['CtilTTs'] \
+ kappatilTpc*param['CtilTTc'] + kappatilTpb*param['CtilTTb'] + kappatilTpt*param['CtilTTt'])
ftilTn2 = 1/lam**2*(kappatilTnu*param['CtilTTu'] + kappatilTnd*param['CtilTTd'] + kappatilTns*param['CtilTTs'] \
+ kappatilTnc*param['CtilTTc'] + kappatilTnb*param['CtilTTb'] + kappatilTnt*param['CtilTTt'])
fpi = mpi/lam**3 *((param['CSSu']+8*np.pi/9*CSgp) \
*fpiu+(param['CSSd']+8*np.pi/9*CSgp)*fpid)
fpitheta = -mpi/lam**3*8*np.pi/9*CSgp
fpi2 = mchi*mpi/lam**4*(param['C2u']*fpi2u+param['C2d'] \
*fpi2d+param['C2s']*fpi2s+param['Cg2']*fpi2g)
#hadronic matrix elements for the different responses-------------------------------------------------------
cform = {
'cMp': zeta/2*(fp + fn + fVp1 + fVn1 + 3/4*(fp2 + fn2)) \
+ (2-zeta)*param['eCF']/(2*mchi*lam),
'cMm': zeta/2*(fp - fn + fVp1 - fVn1 + 3/4*(fp2 - fn2)) \
+ (2-zeta)*param['eCF']/(2*mchi*lam),
'cdotMp': zeta*mN**2/2*(fdotp + fdotn + fdotVp1 + fdotVn1 \
+ 1/(4*mN**2)*(fVp2 + fVn2) \
+ 1/(2*mchi*mN)*(fTp1 + fTn1) \
+ 1/(mchi*mN)*(fTp2 + fTn2)) \
+ (2-zeta)*param['eCF']/(2*mchi*lam)*mN**2/6*(r21p + r21n),
'cdotMm': zeta*mN**2/2*(fdotp - fdotn + fdotVp1 - fdotVn1 \
+ 1/(4*mN**2)*(fVp2 - fVn2) \
+ 1/(2*mchi*mN)*(fTp1 - fTn1) \
+ 1/(mchi*mN)*(fTp2 - fTn2)) \
+ (2-zeta)*param['eCF']/(2*mchi*lam)*mN**2/6*(r21p - r21n),
'cpi': zeta * (fpi + 2 * fpitheta - 1/2 * fpi2),
'cb': zeta * (fpitheta + 1/4 * fpi2),
'cPhip': zeta/2*(fVp2 + fVn2 + (1 + muN/mchi)/2 * (fVp1 + fVn1) \
+ mN/mchi * (1 + muN/mN)*(fTp1 + fTn1)),
'cPhim': zeta/2*(fVp2 - fVn2 + (1 + muN/mchi)/2 * (fVp1 - fVn1) \
+ mN/mchi * (1 + muN/mN)*(fTp1 - fTn1)),
'cM5p': zeta/2 * ((1 + mN/(2*mchi)) * (fVp1 + fVn1) \
+ (1 + 2*mchi/mN)*(fTp1 + fTn1) \
+ 4*mchi/muN*(fTp2 + fTn2)) \
+ (2-zeta)*2*param['eCF']*(mchi+mN)/6/lam*(r21p + r21n),
'cM5m': zeta/2 * ((1 + mN/(2*mchi)) * (fVp1 - fVn1) \
+ (1 + 2*mchi/mN)*(fTp1 - fTn1) \
+ 4*mchi/muN*(fTp2 - fTn2)) \
+ (2-zeta)*2*param['eCF']*(mchi+mN)/6/lam*(r21p - r21n),
'cM8p': zeta/2 * (ftilVp1 + ftilVn1),
'cM8m': zeta/2 * (ftilVp1 - ftilVn1),
'cM11p': zeta/2*(ftilp + ftiln - 2*mchi/mN*(ftilTp1 + ftilTn1) \
- 4*mchi/mN*(ftilTp2 + ftilTn2)) \
- (2-zeta)*2*param['eCFtil']*mchi/6/lam*(r2Ep + r2En),
'cM11m': zeta/2*(ftilp - ftiln - 2*mchi/mN*(ftilTp1 - ftilTn1) \
- 4*mchi/mN*(ftilTp2 - ftilTn2)) \
- (2-zeta)*2*param['eCFtil']*mchi/6/lam*(r2Ep - r2En),
#part of the dipole terms that come with 1/q^2
'DcM5_1p': -(2-zeta)*2*param['eCF']*(mchi+mN)/lam,
'DcM5_1m': -(2-zeta)*2*param['eCF']*(mchi+mN)/lam,
'DcM11_1p': (2-zeta)*2*param['eCFtil']*mchi/lam,
'DcM11_1m': (2-zeta)*2*param['eCFtil']*mchi/lam,
}
return cform
def fit(u,c):
y = 0
for i in range(len(c)):
y += c[i] * u**i
return np.exp(-u/2)*y
def ufunc(q,b):
return (1000*q)**2*b**2/2
def bosc(A):
m = 938.919
return 1/np.sqrt(m*(45*A**(-1.0/3.0)-25*A**(-2.0/3.0)))
def sf0(q,ds,A,cform,mchi):
#structure factors that come with no additional powers of v
muN = (mchi * mN)/(mchi + mN) #WIMP-nucleon reduced mass
mupi = (mchi * mpi)/(mchi + mpi) #WIMP-pion reduced mass
eps = 10**(-16)
mA = A * mAMU #nucleus mass in GeV
mu = (mchi * mA)/(mchi + mA) #WIMP-nucleus reduced mass
vT = q/(2*mu)
#kinematic factors
xi5 = muN*q*vT/(2*mchi*mN)
xi8 = vT
xi11 = -q/(2*mchi)
#check if the dipole terms contribute
if (cform['DcM5_1p'] > eps or cform['DcM5_1m'] > eps \
or cform['DcM11_1p'] > eps or cform['DcM11_1m'] > eps):
if q < eps:
print("WARNING: For q=0 the dipole term 1/q^2 diverges.")
print("sf0(q=0) set to 0.")
return 0
else:
sf = abs((cform['cMp']-q**2/mN**2*cform['cdotMp'])*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cMm']-q**2/mN**2*cform['cdotMm'])*fit(ufunc(q,bosc(A)), ds[1][str(A)]) \
+q**2/(2*mN**2)*(cform['cPhip']*fit(ufunc(q,bosc(A)), ds[2][str(A)]) \
+cform['cPhim']*fit(ufunc(q,bosc(A)), ds[3][str(A)])) \
+cform['cb']*fit(ufunc(q,bosc(A)), ds[4][str(A)]) \
+cform['cpi']*fit(ufunc(q,bosc(A)), ds[5][str(A)]) \
)**2 \
-abs(xi5*((cform['cM5p']+cform['DcM5_1p']/(q**2))*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cM5m']+cform['DcM5_1m']/(q**2))*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
-abs(xi8*(cform['cM8p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM8m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
+abs(xi11*((cform['cM11p']+cform['DcM11_1p']/(q**2))*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cM11m']+cform['DcM11_1m']/(q**2))*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2
return sf
else:
sf = abs((cform['cMp']-q**2/mN**2*cform['cdotMp'])*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cMm']-q**2/mN**2*cform['cdotMm'])*fit(ufunc(q,bosc(A)), ds[1][str(A)]) \
+q**2/(2*mN**2)*(cform['cPhip']*fit(ufunc(q,bosc(A)), ds[2][str(A)]) \
+cform['cPhim']*fit(ufunc(q,bosc(A)), ds[3][str(A)])) \
+cform['cb']*fit(ufunc(q,bosc(A)), ds[4][str(A)]) \
+cform['cpi']*fit(ufunc(q,bosc(A)), ds[5][str(A)]) \
)**2 \
-abs(xi5*(cform['cM5p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM5m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
-abs(xi8*(cform['cM8p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM8m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
+abs(xi11*(cform['cM11p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM11m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2
return sf
def sf2(q,ds,A,cform,mchi):
#structure factors that come with an additonal v^2
eps = 10**(-16)
muN = (mchi * mN)/(mchi + mN) #WIMP-nucleon reduced mass
mupi = (mchi * mpi)/(mchi + mpi) #WIMP-pion reduced mass
#kinematic factors
xi5 = muN*q/(2*mchi*mN)
xi8 = 1
#check if the dipole terms contribute
if (cform['DcM5_1p'] > eps or cform['DcM5_1m'] > eps):
if q < eps:
print("WARNING: For q=0 the dipole term 1/q^2 diverges.")
print("sf2(q=0) set to 0.")
return 0
else:
sf = abs(xi5*((cform['cM5p']+cform['DcM5_1p']/(q**2))*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cM5m']+cform['DcM5_1m']/(q**2))*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
+abs(xi8*(cform['cM8p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM8m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2
return sf
else:
sf = abs(xi5*(cform['cM5p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM5m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
+abs(xi8*(cform['cM8p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM8m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2
return sf
def sf0_wo_abs(q,ds,A,cform,mchi):
muN = (mchi * mN)/(mchi + mN) #WIMP-nucleon reduced mass
mupi = (mchi * mpi)/(mchi + mpi) #WIMP-pion reduced mass
#structure factors that come with no additional powers of v
eps = 10**(-16)
mA = A * mAMU #nucleus mass in GeV
mu = (mchi * mA)/(mchi + mA) #WIMP-nucleus reduced mass
vT = q/(2*mu)
#kinematic factors
xi5 = muN*q*vT/(2*mchi*mN)
xi8 = vT
xi11 = -q/(2*mchi)
#check if the dipole terms contribute
if (cform['DcM5_1p'] > eps or cform['DcM5_1m'] > eps \
or cform['DcM11_1p'] > eps or cform['DcM11_1m'] > eps):
if q < eps:
print("WARNING: For q=0 the dipole term 1/q^2 diverges.")
print("sf0(q=0) set to 0.")
return 0
else:
sf = ((cform['cMp']-q**2/mN**2*cform['cdotMp'])*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cMm']-q**2/mN**2*cform['cdotMm'])*fit(ufunc(q,bosc(A)), ds[1][str(A)]) \
+q**2/(2*mN**2)*(cform['cPhip']*fit(ufunc(q,bosc(A)), ds[2][str(A)]) \
+cform['cPhim']*fit(ufunc(q,bosc(A)), ds[3][str(A)])) \
+cform['cb']*fit(ufunc(q,bosc(A)), ds[4][str(A)]) \
+cform['cpi']*fit(ufunc(q,bosc(A)), ds[5][str(A)]) \
)**2 \
-(xi5*((cform['cM5p']+cform['DcM5_1p']/(q**2))*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cM5m']+cform['DcM5_1m']/(q**2))*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
-(xi8*(cform['cM8p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM8m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
+(xi11*((cform['cM11p']+cform['DcM11_1p']/(q**2))*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cM11m']+cform['DcM11_1m']/(q**2))*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2
return sf
else:
sf = ((cform['cMp']-q**2/mN**2*cform['cdotMp'])*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cMm']-q**2/mN**2*cform['cdotMm'])*fit(ufunc(q,bosc(A)), ds[1][str(A)]) \
+q**2/(2*mN**2)*(cform['cPhip']*fit(ufunc(q,bosc(A)), ds[2][str(A)]) \
+cform['cPhim']*fit(ufunc(q,bosc(A)), ds[3][str(A)])) \
+cform['cb']*fit(ufunc(q,bosc(A)), ds[4][str(A)]) \
+cform['cpi']*fit(ufunc(q,bosc(A)), ds[5][str(A)]) \
)**2 \
-(xi5*(cform['cM5p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM5m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
-(xi8*(cform['cM8p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM8m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
+(xi11*(cform['cM11p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM11m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2
return sf
def sf2_wo_abs(q,ds,A,cform,mchi):
muN = (mchi * mN)/(mchi + mN) #WIMP-nucleon reduced mass
mupi = (mchi * mpi)/(mchi + mpi) #WIMP-pion reduced mass
#structure factors that come with an additonal v^2
eps = 10**(-16)
#kinematic factors
xi5 = muN*q/(2*mchi*mN)
xi8 = 1
#check if the dipole terms contribute
if (cform['DcM5_1p'] > eps or cform['DcM5_1m'] > eps):
if q < eps:
print("WARNING: For q=0 the dipole term 1/q^2 diverges.")
print("sf2(q=0) set to 0.")
return 0
else:
sf = (xi5*((cform['cM5p']+cform['DcM5_1p']/(q**2))*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+(cform['cM5m']+cform['DcM5_1m']/(q**2))*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
+(xi8*(cform['cM8p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM8m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2
return sf
else:
sf = (xi5*(cform['cM5p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM5m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2 \
+(xi8*(cform['cM8p']*fit(ufunc(q,bosc(A)), ds[0][str(A)]) \
+cform['cM8m']*fit(ufunc(q,bosc(A)), ds[1][str(A)])))**2
return sf
def Heaviside(*args):
return symengine.Symbol("Heaviside"+str(args))
def g(vmin, v0, vE, vesc):
k = symengine.erf(vesc/v0) \
- 2/np.sqrt(np.pi)*vesc/v0*np.exp(-(vesc/v0)**2)
prefac = 1/(k*vE*np.sqrt(np.pi))
xmin = vmin/v0
z = vesc/v0
neta = vE/v0
res = 0
res =(prefac * (np.sqrt(np.pi)/2 \
*(symengine.erf(xmin+neta)-symengine.erf(xmin-neta)) \
-2*neta*np.exp(-z**2)))*Heaviside(z-neta-xmin)
res =res+(prefac * (np.sqrt(np.pi)/2 \
*(symengine.erf(z)-symengine.erf(xmin-neta)) \
-np.exp(-z**2)*(z+neta-xmin)))*Heaviside(xmin-(z-neta),z+neta-xmin)
return res
def gv2(vmin,v0, vE, vesc):
cvel = 299792458 #speed of light in m/s
k = symengine.erf(vesc/v0) \
- 2/np.sqrt(np.pi)*vesc/v0*np.exp(-(vesc/v0)**2)
prefac = 1/(k*vE*np.sqrt(np.pi))
xmin = vmin/v0
z = vesc/v0
neta = vE/v0
res = 0
res = (prefac/4*(-2*np.exp(-(xmin+neta)**2)*(xmin-neta) \
+2*np.exp(-(xmin-neta)**2)*(xmin+neta) \
-8/3*np.exp(-z**2)*neta*(3+3*z**2+neta**2) \
+np.sqrt(np.pi)*(1+2*neta**2) \
*(-symengine.erf(xmin-neta)+symengine.erf(xmin+neta))))*Heaviside(z-neta-xmin)
res = res+(prefac/4*(2*np.exp(-(xmin-neta)**2)*(xmin+neta) \
-2*np.exp(-z**2)*(z+2*neta) \
+1/3*np.exp(-z**2)*(4*xmin**3-4*(z+neta)**3) \
+np.sqrt(np.pi)*(1+2*neta**2) \
*(symengine.erf(z)-symengine.erf(xmin-neta))))*Heaviside(xmin-(z-neta),z+neta-xmin)
return res *v0**2/(cvel/1000)**2
def Fv0MB(eta, xmin):
return (symengine.erf(xmin + eta) - symengine.erf(xmin - eta)) / (2 * eta)
def FvsqMB(eta, xmin):
return (
np.exp(-((-xmin + eta) ** 2)) * (xmin + eta)
- np.exp(-((xmin + eta) ** 2)) * (xmin - eta)
) / (2 * np.sqrt(np.pi) * eta) + (
(1 + 2 * eta ** 2) * (symengine.erf(xmin + eta) - symengine.erf(xmin - eta))
) / (
4 * eta
)
def WC_name_converter(directdm3f_dict, lam):
chiraleft4dm_dict = {}
chiraleft4dm_dict['CVVu']=directdm3f_dict['C61u']*lam**2
chiraleft4dm_dict['CVVd']=directdm3f_dict['C61d']*lam**2
chiraleft4dm_dict['CVVs']=directdm3f_dict['C61s']*lam**2
chiraleft4dm_dict['CAAu']=directdm3f_dict['C64u']*lam**2
chiraleft4dm_dict['CAAd']=directdm3f_dict['C64d']*lam**2
chiraleft4dm_dict['CAAs']=directdm3f_dict['C64s']*lam**2
chiraleft4dm_dict['CAVu']=directdm3f_dict['C62u']*lam**2
chiraleft4dm_dict['CAVd']=directdm3f_dict['C62d']*lam**2
chiraleft4dm_dict['CAVs']=directdm3f_dict['C62s']*lam**2
chiraleft4dm_dict['CSSu']=directdm3f_dict['C75u']*lam**3
chiraleft4dm_dict['CSSd']=directdm3f_dict['C75d']*lam**3
chiraleft4dm_dict['CSSs']=directdm3f_dict['C75s']*lam**3
chiraleft4dm_dict['CPSd']=directdm3f_dict['C76d']*lam**3
chiraleft4dm_dict['CPSu']=directdm3f_dict['C76u']*lam**3
chiraleft4dm_dict['CPSs']=directdm3f_dict['C76s']*lam**3
chiraleft4dm_dict['CSg']=directdm3f_dict['C71']*lam**3/(12*np.pi)
chiraleft4dm_dict['CSgtil']=directdm3f_dict['C72']*lam**3/(12*np.pi)
#+chiraleft4dm_dict['eCF']=directdm3f_dict['C51']*lam*(0.30282212088)/(8*np.pi**2)
#chiraleft4dm_dict['eCFtil']=directdm3f_dict['C52']*lam*(0.30282212088)/(8*np.pi**2)
return chiraleft4dm_dict
def get_eventrate(
target_isotope,
dm_particle,
coeff,
num_target_nuclei: float,
dm_density: float,
q: float,
v_earth: float,
v_0: float,
lam: float,
v_esc: float,
halo: str = "MBcutoff",
) -> float:
if halo != "MBcutoff":
raise Exception("Halo must be of type Maxwell-Boltzmann with cutoff if you want to use ChiralEFT4DM")
mchi= dm_particle.m
chiraleft4dm_dict = WC_name_converter(coeff, lam)
cform=set_param(mchi,lam, **chiraleft4dm_dict)
rho = dm_density
elem = target_isotope.isotope_short_name #element
A = target_isotope.A #mass number
directory = str(pathlib.Path(__file__).parent.resolve())+r"/fit_data/"
ds = []
reslist = ["m+","m-","phi+","phi-","eb","pi"]
for res in reslist:
name = directory + elem + "_wimps_" + res + "_fit.dat"
#print("Directory: ", name)
ds.append(pd.read_csv(name, sep='\s+'))
mA = A * mAMU #nucleus mass in GeV
mu = (mchi * mA)/(mchi + mA) #WIMP-nucleus reduced mass
vmin = q/(2*mu)/1000*cvel
v_0_nu = v_0*1000/cvel
sf0_0=sf0_wo_abs(q,ds,A,cform,mchi)
sf2_2=sf2_wo_abs(q,ds,A,cform,mchi)
eventrate = rho/(2*np.pi*mchi) \
*(sf0_0*g(vmin, v_0, v_earth,v_esc)+sf2_2*gv2(vmin, v_0, v_earth, v_esc)) \
/1000*100/(10**9*1.602*10**(-19))*60**2 \
*24*cvel**4/10**6 \
*0.197327**2 *10**(-26)#this is 1/cm^2 to natural units
eventrate = eventrate*10**6#go from 1/keV to 1/GeV
return eventrate