corrections to m_z and m_w

[certik]

from math import pi, sin, cos, sqrt, log
eV = 1
KeV = 1e3
MeV = 1e6
GeV = 1e9
g = 0.631
theta_W = 28.67 * pi / 180
v = 246.218 * GeV
h_e = 2.935 * 1e-6 * eV
h_mu = 6.065 * 1e-4 * eV
h_tau = 1.021 * 1e-2 * eV
alpha = 1/137.035999


m_t = 180 * GeV
m_w = g*v/2
m_z = g*v/2/cos(theta_W)
s_w = sin(theta_W)   # Same as: s_w = sqrt(1-m_w**2/m_z**2)
# I think that s_0 and s_w is the same
#s_0 = sqrt(0.2307)
s_0 = s_w
print s_0**2

# from the graph:
#s_w = sqrt(0.226)
#s_star = sqrt(0.231)
#print s_star**2

m_h = 1000 * GeV
rhs = -3*alpha/(16*pi*(cos(theta_W)**2 - sin(theta_W)**2)) * m_t**2 / m_z**2
rhs += alpha * (1+9*sin(theta_W)**2)/(48*pi * (cos(theta_W)**2 - sin(theta_W)**2)) * log(m_h**2/m_w**2)
s_star = sqrt(s_0**2 + rhs)

rhs = -3*alpha/(16*pi*sin(theta_W)**2) * m_t**2 / m_z**2
rhs += alpha * 5./(24*pi) * log(m_h**2/m_w**2)
s_w = sqrt(s_star**2 + rhs)
print s_star**2
print s_w**2

This prints:

bash-3.2$ python a.py 
0.230173648241
0.228245381646
0.222897377383

Which agrees with P & S at least a little bit, page 772, Figure 21.14

[certik]

A better script is:

from math import pi, log, sqrt, sin, cos, asin

eV = 1.
KeV = 1e3 * eV
MeV = 1e6 * eV
GeV = 1e9 * eV

M = 76500 * MeV
M0 = 87640 * MeV
m_u = 250 * MeV
m_d = 250 * MeV
m_e = 0.511 * MeV
m_mu = 105.6 * MeV
m_tau = 1777 * MeV
g = sqrt(0.039 * pi**2)
theta = asin(sqrt(0.238))
s_t = sin(theta)
c_t = cos(theta)
#m_H = 3 * GeV
#m_H = 200 * GeV
m_H = 1000 * GeV

#print g**2/(384*pi**2) * M * log(m_H**2) / MeV
#print g**2/(384*pi**2) * M0 * (1 + 10*s_t**2/c_t**2)* log(m_H**2) / MeV

delta_M_e = - g**2 * M**2 / pi**2 * (5./36 + 1./48 * \
                (2*log(m_u**2/M**2) + log(m_d**2/M**2) + log(m_e**2/M**2)))
#delta_M_mu = - g**2 * M**2 / pi**2 * (5./36 + 1./48 * \
#                (2*log(m_u**2/M**2) + log(m_d**2/M**2) + log(m_mu**2/M**2)))
#delta_M_tau = - g**2 * M**2 / pi**2 * (5./36 + 1./48 * \
#                (2*log(m_u**2/M**2) + log(m_d**2/M**2) + log(m_tau**2/M**2)))
delta_M0 = - g**2 * M0**2 / (pi**2 * c_t**2) *  ( \
        1./108 * (40*c_t**4 - 50*c_t**2 + 25  ) + \
        1./72  * (8 *c_t**4 - 10*c_t**2 + 5   ) * log(m_u**2/M0**2) + \
        1./72  * (2 *c_t**4 -    c_t**2 + 1./2) * log(m_d**2/M0**2) + \
        1./48  * (4 *c_t**4 - 6 *c_t**2 + 3   ) * log(m_e**2/M0**2))

M_higgs = 120 * MeV
M0_higgs = 140 * MeV

print 0.5 * delta_M_e / M / MeV
print 0.5 * delta_M0 / M0 / MeV

print "bare masses:"
print M / GeV
print M0 / GeV
print "shifted masses:"
print (M + 0.5 * delta_M_e / M + M_higgs) / GeV
print (M0 + 0.5 * delta_M0 / M0 + M0_higgs) / GeV

print "shifted masses (correct):"
print (M + 3080 * MeV) / GeV
print (M0 + 3310 * MeV) / GeV

print "experimental values:"
print 80.399
print 91.1876

Which produces:

1600.76296787
1702.62148258
bare masses:
76.5
87.64
shifted masses:
78.2207629679
89.4826214826
shifted masses (correct):
79.58
90.95
experimental values:
80.399
91.1876