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Tool_Normalisation.py
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#Roman Sultanov
#Imports
from Form import *
#-----------------------------------------------------------------------------------------------------------------------
#Data (GeV)
mΛ=2.4677 #Xi_c^+ mass
mp=0.9383 #proton mass
mK=0.4937 #kaon- mass
mπ=0.1396 #pion+ mass
mR=1.519 #Lambda(1520) peak mass
ΓR=0.016 #Lambda(1520) width
mS=1.232 #Delta++(1232) peak mass
ΓS=0.117 #Delta++(1232) width
mU=0.896 #K*(892) peak mass
ΓU=0.047 #K*(892) width
dr = 1.5
di = 5
#-----------------------------------------------------------------------------------------------------------------------
@njit
def DecayrateDist(m2pK, m2Kπ, cosθp, φp, χ, Px, Py, Pz, HRpr, HRpi, HRmr, HRmi, HSpr, HSpi, HSmr, HSmi, HUp0r, HUp0i, HUpmr, HUpmi, HUmpr, HUmpi, HUm0r, HUm0i):
Es2 = (m2pK - mp ** 2 + mK ** 2) / (2 * np.sqrt(m2pK))
Es3 = (mΛ ** 2 - m2pK - mπ ** 2) / (2 * np.sqrt(m2pK))
sqrt_term1 = np.sqrt(np.maximum(Es2 ** 2 - mK ** 2, 0))
sqrt_term2 = np.sqrt(np.maximum(Es3 ** 2 - mπ ** 2, 0))
sq_term = (Es2 + Es3) ** 2
if m2pK <= (mp + mK) ** 2 or m2pK >= (mΛ - mπ) ** 2 or m2Kπ <= sq_term - (sqrt_term1 + sqrt_term2) ** 2 or m2Kπ >= sq_term - (sqrt_term1 - sqrt_term2) ** 2:
return 0.0
P1, P2, P3 = FinalStateMomenta(m2pK, m2Kπ, mΛ, mp, mK, mπ)
θR, θR1, aR, θS, θS1, aS, θbU2 = FinalStateAngles(P1, P2, P3)
HRp=HRpr+HRpi*1j
HRm=HRmr+HRmi*1j
HSp=HSpr+HSpi*1j
HSm=HSmr+HSmi*1j
HUpm=HUpmr+HUpmi*1j
HUp0=HUp0r+HUp0i*1j
HUmp=HUmpr+HUmpi*1j
HUm0=HUm0r+HUm0i*1j
HRpC=np.conjugate(HRp)
HRmC=np.conjugate(HRm)
HSpC=np.conjugate(HSp)
HSmC=np.conjugate(HSm)
HUp0C=np.conjugate(HUp0)
HUpmC=np.conjugate(HUpm)
HUmpC=np.conjugate(HUmp)
HUm0C=np.conjugate(HUm0)
WdR_12pp=np.cos(θR/2)
WdR_12pm=-np.sin(θR/2)
WdR_12mp=np.sin(θR/2)
WdR_12mm=np.cos(θR/2)
WdR1_32pp=0.5*(3*np.cos(θR1)-1)*np.cos(θR1/2)
WdR1_32pm=-0.5*(3*np.cos(θR1)+1)*np.sin(θR1/2)
WdR1_32mp=0.5*(3*np.cos(θR1)+1)*np.sin(θR1/2)
WdR1_32mm=0.5*(3*np.cos(θR1)-1)*np.cos(θR1/2)
AR=θR+θR1+aR
WdAR_12pp=np.cos(AR/2)
WdAR_12pm=-np.sin(AR/2)
WdAR_12mp=np.sin(AR/2)
WdAR_12mm=np.cos(AR/2)
pmR = TwoBodyMomenta(np.sqrt(m2pK), mp, mK)
p0R = TwoBodyMomenta(mR, mp, mK)
qmR = TwoBodyMomenta(mΛ, np.sqrt(m2pK), mπ)
q0R = TwoBodyMomenta(mΛ, mR, mπ)
FrR = np.sqrt((9 + 3 * (p0R * dr) ** 2 + (p0R * dr) ** 4) / (9 + 3 * (pmR * dr) ** 2 + (pmR * dr) ** 4))
ΓmR = ΓR * (pmR / p0R) ** 5 * (mR / np.sqrt(m2pK)) * (FrR) ** 2
BWR=(qmR / q0R) * (pmR / p0R) ** 2 * np.sqrt((1 + (q0R * di) ** 2) / (1 + (qmR * di) ** 2)) * FrR / \
(mR ** 2 - m2pK - ΓmR * mR * 1j)
WdS_12pp=np.cos(θS/2)
WdS_12pm=-np.sin(θS/2)
WdS_12mp=np.sin(θS/2)
WdS_12mm=np.cos(θS/2)
WdS1_32pp=0.5*(3*np.cos(θS1)-1)*np.cos(θS1/2)
WdS1_32pm=-0.5*(3*np.cos(θS1)+1)*np.sin(θS1/2)
WdS1_32mp=0.5*(3*np.cos(θS1)+1)*np.sin(θS1/2)
WdS1_32mm=0.5*(3*np.cos(θS1)-1)*np.cos(θS1/2)
AS=θS+θS1-aS
WdAS_12pp=np.cos(AS/2)
WdAS_12pm=-np.sin(AS/2)
WdAS_12mp=np.sin(AS/2)
WdAS_12mm=np.cos(AS/2)
m2=mΛ**2 + mp**2 + mK**2 + mπ**2 - m2pK - m2Kπ
pmS = TwoBodyMomenta(np.sqrt(m2), mp, mπ)
p0S = TwoBodyMomenta(mS, mp, mπ)
qmS = TwoBodyMomenta(mΛ, np.sqrt(m2), mK)
q0S = TwoBodyMomenta(mΛ, mS, mK)
FrS = np.sqrt((1 + (p0S * dr) ** 2) / (1 + (pmS * dr) ** 2))
ΓmS = ΓS * (pmS / p0S) ** 3 * (mS / np.sqrt(m2)) * (FrS) ** 2
BWS = (qmS / q0S) * (pmS / p0S) * np.sqrt((1 + (q0S * di) ** 2) / (1 + (qmS * di) ** 2)) * FrS / \
(mS ** 2 - m2 - ΓmS * mS * 1j)
WdbU2_1p0=-1/np.sqrt(2)*np.sin(θbU2)
WdbU2_100=np.cos(θbU2)
WdbU2_1m0=1/np.sqrt(2)*np.sin(θbU2)
pmU = TwoBodyMomenta(np.sqrt(m2Kπ), mK, mπ)
p0U = TwoBodyMomenta(mU, mK, mπ)
FrU = np.sqrt((1 + (p0U * dr) ** 2) / (1 + (pmU * dr) ** 2))
ΓmU = ΓU * (pmU / p0U) **3 * (mU / np.sqrt(m2Kπ)) * (FrU) ** 2
BWU = (pmU / p0U) * FrU / (mU ** 2 - m2Kπ - ΓmU * mU * 1j)
θp = np.arccos(cosθp)
cWDE_12pp=np.exp(1j/2*φp)*np.cos(θp/2)*np.exp(1j/2*χ)
cWDE_12pm=-np.exp(1j/2*φp)*np.sin(θp/2)*np.exp(-1j/2*χ)
cWDE_12mp=np.exp(-1j/2*φp)*np.sin(θp/2)*np.exp(1j/2*χ)
cWDE_12mm=np.exp(-1j/2*φp)*np.cos(θp/2)*np.exp(-1j/2*χ)
ppC1=(WdAR_12pp*WdR_12pp*WdR1_32pp*BWR-WdAR_12pm*WdR_12pp*WdR1_32pm*BWR)*cWDE_12pp+(WdAR_12pp*WdR_12mp*WdR1_32pp*BWR-WdAR_12pm*WdR_12mp*WdR1_32pm*BWR)*cWDE_12pm
ppC2=(WdAR_12pp*WdR_12pm*WdR1_32mp*BWR-WdAR_12pm*WdR_12pm*WdR1_32mm*BWR)*cWDE_12pp+(WdAR_12pp*WdR_12mm*WdR1_32mp*BWR-WdAR_12pm*WdR_12mm*WdR1_32mm*BWR)*cWDE_12pm
ppC3=(WdAS_12pp*WdS_12pp*WdS1_32pp*BWS+WdAS_12pm*WdS_12pp*WdS1_32pm*BWS)*cWDE_12pp+(WdAS_12pp*WdS_12mp*WdS1_32pp*BWS+WdAS_12pm*WdS_12mp*WdS1_32pm*BWS)*cWDE_12pm
ppC4=(WdAS_12pp*WdS_12pm*WdS1_32mp*BWS+WdAS_12pm*WdS_12pm*WdS1_32mm*BWS)*cWDE_12pp+(WdAS_12pp*WdS_12mm*WdS1_32mp*BWS+WdAS_12pm*WdS_12mm*WdS1_32mm*BWS)*cWDE_12pm
ppC5=WdbU2_100*cWDE_12pp*BWU
ppC6=WdbU2_1m0*cWDE_12pm*BWU
ppC7=0
ppC8=0
App = HRp*ppC1 + HRm*ppC2 +HSp*ppC3 + HSm*ppC4 + HUp0*ppC5 + HUpm*ppC6 + HUmp*ppC7 + HUm0*ppC8
pmC1=(WdAR_12mp*WdR_12pp*WdR1_32pp*BWR-WdAR_12mm*WdR_12pp*WdR1_32pm*BWR)*cWDE_12pp+(WdAR_12mp*WdR_12mp*WdR1_32pp*BWR-WdAR_12mm*WdR_12mp*WdR1_32pm*BWR)*cWDE_12pm
pmC2=(WdAR_12mp*WdR_12pm*WdR1_32mp*BWR-WdAR_12mm*WdR_12pm*WdR1_32mm*BWR)*cWDE_12pp+(WdAR_12mp*WdR_12mm*WdR1_32mp*BWR-WdAR_12mm*WdR_12mm*WdR1_32mm*BWR)*cWDE_12pm
pmC3=(WdAS_12mp*WdS_12pp*WdS1_32pp*BWS+WdAS_12mm*WdS_12pp*WdS1_32pm*BWS)*cWDE_12pp+(WdAS_12mp*WdS_12mp*WdS1_32pp*BWS+WdAS_12mm*WdS_12mp*WdS1_32pm*BWS)*cWDE_12pm
pmC4=(WdAS_12mp*WdS_12pm*WdS1_32mp*BWS+WdAS_12mm*WdS_12pm*WdS1_32mm*BWS)*cWDE_12pp+(WdAS_12mp*WdS_12mm*WdS1_32mp*BWS+WdAS_12mm*WdS_12mm*WdS1_32mm*BWS)*cWDE_12pm
pmC5=0
pmC6=0
pmC7=WdbU2_1p0*cWDE_12pp*BWU
pmC8=WdbU2_100*cWDE_12pm*BWU
Apm = HRp*pmC1 + HRm*pmC2 +HSp*pmC3 + HSm*pmC4 + HUp0*pmC5 + HUpm*pmC6 + HUmp*pmC7 + HUm0*pmC8
mpC1=(WdAR_12pp*WdR_12pp*WdR1_32pp*BWR-WdAR_12pm*WdR_12pp*WdR1_32pm*BWR)*cWDE_12mp+(WdAR_12pp*WdR_12mp*WdR1_32pp*BWR-WdAR_12pm*WdR_12mp*WdR1_32pm*BWR)*cWDE_12mm
mpC2=(WdAR_12pp*WdR_12pm*WdR1_32mp*BWR-WdAR_12pm*WdR_12pm*WdR1_32mm*BWR)*cWDE_12mp+(WdAR_12pp*WdR_12mm*WdR1_32mp*BWR-WdAR_12pm*WdR_12mm*WdR1_32mm*BWR)*cWDE_12mm
mpC3=(WdAS_12pp*WdS_12pp*WdS1_32pp*BWS+WdAS_12pm*WdS_12pp*WdS1_32pm*BWS)*cWDE_12mp+(WdAS_12pp*WdS_12mp*WdS1_32pp*BWS+WdAS_12pm*WdS_12mp*WdS1_32pm*BWS)*cWDE_12mm
mpC4=(WdAS_12pp*WdS_12pm*WdS1_32mp*BWS+WdAS_12pm*WdS_12pm*WdS1_32mm*BWS)*cWDE_12mp+(WdAS_12pp*WdS_12mm*WdS1_32mp*BWS+WdAS_12pm*WdS_12mm*WdS1_32mm*BWS)*cWDE_12mm
mpC5=WdbU2_100*cWDE_12mp*BWU
mpC6=WdbU2_1m0*cWDE_12mm*BWU
mpC7=0
mpC8=0
Amp = HRp*mpC1 + HRm*mpC2 +HSp*mpC3 + HSm*mpC4 + HUp0*mpC5 + HUpm*mpC6 + HUmp*mpC7 + HUm0*mpC8
mmC1=(WdAR_12mp*WdR_12pp*WdR1_32pp*BWR-WdAR_12mm*WdR_12pp*WdR1_32pm*BWR)*cWDE_12mp+(WdAR_12mp*WdR_12mp*WdR1_32pp*BWR-WdAR_12mm*WdR_12mp*WdR1_32pm*BWR)*cWDE_12mm
mmC2=(WdAR_12mp*WdR_12pm*WdR1_32mp*BWR-WdAR_12mm*WdR_12pm*WdR1_32mm*BWR)*cWDE_12mp+(WdAR_12mp*WdR_12mm*WdR1_32mp*BWR-WdAR_12mm*WdR_12mm*WdR1_32mm*BWR)*cWDE_12mm
mmC3=(WdAS_12mp*WdS_12pp*WdS1_32pp*BWS+WdAS_12mm*WdS_12pp*WdS1_32pm*BWS)*cWDE_12mp+(WdAS_12mp*WdS_12mp*WdS1_32pp*BWS+WdAS_12mm*WdS_12mp*WdS1_32pm*BWS)*cWDE_12mm
mmC4=(WdAS_12mp*WdS_12pm*WdS1_32mp*BWS+WdAS_12mm*WdS_12pm*WdS1_32mm*BWS)*cWDE_12mp+(WdAS_12mp*WdS_12mm*WdS1_32mp*BWS+WdAS_12mm*WdS_12mm*WdS1_32mm*BWS)*cWDE_12mm
mmC5=0
mmC6=0
mmC7=WdbU2_1p0*cWDE_12mp*BWU
mmC8=WdbU2_100*cWDE_12mm*BWU
Amm = HRp*mmC1 + HRm*mmC2 +HSp*mmC3 + HSm*mmC4 + HUp0*mmC5 + HUpm*mmC6 + HUmp*mmC7 + HUm0*mmC8
#return np.real(ppC1*np.conjugate(ppC1)+pmC1*np.conjugate(pmC1)+mpC1*np.conjugate(mpC1)+mmC1*np.conjugate(mmC1))
return np.imag(ppC1*np.conjugate(mpC1)+pmC1*np.conjugate(mmC1))
import vegas
@vegas.lbatchintegrand
def I(x):
return np.array([DecayrateDist(x1, x2, x3, x4, x5, 0.3, 0.5, -0.2, 0.29, 0.04, -0.16, 1.5, -6.8, 3.1, -13.0, 4.5, 1, 0, 1.19, -1.03, -3.1, -3.3, -0.7, -4.2) for x1, x2, x3, x4, x5 in zip(x[:,0], x[:,1], x[:,2], x[:,3], x[:,4])])
def main():
import time
start_time = time.time()
integ = vegas.Integrator([[(mp + mK)**2, (mΛ - mπ)**2], [(mπ + mK)**2, (mΛ - mp)**2], [-1, 1], [-np.pi, np.pi], [-np.pi, np.pi]], nproc=8)
integ(I, nitn=10, neval=30000000)
intt=integ(I, nitn=15, neval=30000000)
print(intt.summary())
print(intt.mean)
end_time = time.time()
totalseconds=end_time - start_time
print(f"Time taken: {totalseconds//60} m, {totalseconds%60} s.")
if __name__ == '__main__':
main()