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kopplung.py
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kopplung.py
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import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit, fmin
import uncertainties.unumpy as unp
from uncertainties.unumpy import (nominal_values as noms,
std_devs as stds)
from uncertainties import ufloat
def beta():
N_f = 5
return(11 - 2/3 * N_f)
def alpha(alpha_mz, mass_Z, mu):
alf = alpha_mz/(1 + alpha_mz/(4*np.pi) * beta()
* unp.log((mu**2)/(mass_Z**2)))
return(alf)
def plotalpha(alpha_mz, mass_Z):
mu = np.logspace(-1, 30, 10000)
alf = alpha(alpha_mz, mass_Z, mu)
plt.fill_between(mu, noms(alf)+stds(alf), noms(alf) - stds(alf),
color='red', label='1$\sigma$-Intervall')
plt.plot(mu, noms(alf), label='Kurve')
d = np.zeros(len(alf))
d = noms(alf) - 1/128
print(d)
for i in range(len(d) - 1):
if d[i] == 0. or d[i] * d[i + 1] < 0.: # crossover at i
print('Grafische Lösung:', alf[i])
plt.xlim(0.1, 1000)
plt.xlabel(r'$\mu \:/\: \si{\giga\electronvolt}$')
plt.ylabel(r'$\alpha_S$')
plt.legend(loc='best')
plt.xscale('log')
# in matplotlibrc leider (noch) nicht möglich
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.savefig('build/plotalpha.pdf')
plt.close()
def diverg(alpha_mz, mass_Z):
mu = unp.sqrt(unp.exp((-1)*4*np.pi/(alpha_mz*(11-(10/3))))*mass_Z**2)
return mu
def sbeta(Nf):
return (11 - (2/3) * Nf)
def ebeta(Nu):
return (-16/3 * (1 + Nu/3))
def muvfunc(Nu, Nf, alpha_mz, ealpha_mz, mass_Z):
muv = unp.exp(((ealpha_mz - alpha_mz)/(ealpha_mz*alpha_mz))*(2*np.pi/(ebeta(Nu) - sbeta(Nf))))*mass_Z
return muv
if __name__ == '__main__':
# z, b = np.genfromtxt('daten/magnetfeld.txt', unpack='True')
mass_Z = ufloat(91.1876, 0.0021)
alpha_mz = ufloat(0.1182, 0.0016)
ealpha_mz = ufloat(127.950, 0.017)
# ealpha_mz = ufloat(137, 0.014)
ealpha_mz = 1/ealpha_mz
Nf = np.array([5, 6, 10])
Nu = np.array([2, 3, 3])
plotalpha(alpha_mz, mass_Z)
print('Skala divergent bei mu=', diverg(alpha_mz, mass_Z), 'GeV')
print('muv =', muvfunc(Nu, Nf, alpha_mz, ealpha_mz, mass_Z), 'GeV')
print(sbeta(Nf), ebeta(Nu))