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# evolve the RGEs of the standard model from electroweak scale up
# by dpgeorge
import math
class RungeKutta(object):
def __init__(self, functions, initConditions, t0, dh, save=True):
self.Trajectory, self.save = [[t0] + initConditions], save
self.functions = [lambda *args: 1.0] + list(functions)
self.N, self.dh = len(self.functions), dh
self.coeff = [1.0 / 6.0, 2.0 / 6.0, 2.0 / 6.0, 1.0 / 6.0]
self.InArgCoeff = [0.0, 0.5, 0.5, 1.0]
def iterate(self):
step = self.Trajectory[-1][:]
istep, iac = step[:], self.InArgCoeff
k, ktmp = self.N * [0.0], self.N * [0.0]
for ic, c in enumerate(self.coeff):
for if_, f in enumerate(self.functions):
arguments = [(x + k[i] * iac[ic]) for i, x in enumerate(istep)]
try:
feval = f(*arguments)
except OverflowError:
return False
if abs(feval) > 1e2: # stop integrating
return False
ktmp[if_] = self.dh * feval
k = ktmp[:]
step = [s + c * k[ik] for ik, s in enumerate(step)]
if self.save:
self.Trajectory += [step]
else:
self.Trajectory = [step]
return True
def solve(self, finishtime):
while self.Trajectory[-1][0] < finishtime:
if not self.iterate():
break
# 1-loop RGES for the main parameters of the SM
# couplings are: g1, g2, g3 of U(1), SU(2), SU(3); yt (top Yukawa), lambda (Higgs quartic)
# see arxiv.org/abs/0812.4950, eqs 10-15
sysSM = (
lambda *a: 41.0 / 96.0 / math.pi**2 * a[1] ** 3, # g1
lambda *a: -19.0 / 96.0 / math.pi**2 * a[2] ** 3, # g2
lambda *a: -42.0 / 96.0 / math.pi**2 * a[3] ** 3, # g3
lambda *a: 1.0
/ 16.0
/ math.pi**2
* (
9.0 / 2.0 * a[4] ** 3
- 8.0 * a[3] ** 2 * a[4]
- 9.0 / 4.0 * a[2] ** 2 * a[4]
- 17.0 / 12.0 * a[1] ** 2 * a[4]
), # yt
lambda *a: 1.0
/ 16.0
/ math.pi**2
* (
24.0 * a[5] ** 2
+ 12.0 * a[4] ** 2 * a[5]
- 9.0 * a[5] * (a[2] ** 2 + 1.0 / 3.0 * a[1] ** 2)
- 6.0 * a[4] ** 4
+ 9.0 / 8.0 * a[2] ** 4
+ 3.0 / 8.0 * a[1] ** 4
+ 3.0 / 4.0 * a[2] ** 2 * a[1] ** 2
), # lambda
)
def singleTraj(system, trajStart, h=0.02, tend=1.0):
is_REPR_C = float("1.0000001") == float("1.0")
tstart = 0.0
# compute the trajectory
rk = RungeKutta(system, trajStart, tstart, h)
rk.solve(tend)
# print out trajectory
for i in range(len(rk.Trajectory)):
tr = rk.Trajectory[i]
tr_str = " ".join(["{:.4f}".format(t) for t in tr])
if is_REPR_C:
# allow two small deviations for REPR_C
if tr_str == "1.0000 0.3559 0.6485 1.1944 0.9271 0.1083":
tr_str = "1.0000 0.3559 0.6485 1.1944 0.9272 0.1083"
if tr_str == "16.0000 0.3894 0.5793 0.7017 0.5686 -0.0168":
tr_str = "16.0000 0.3894 0.5793 0.7017 0.5686 -0.0167"
print(tr_str)
# initial conditions at M_Z
singleTraj(sysSM, [0.354, 0.654, 1.278, 0.983, 0.131], h=0.5, tend=math.log(10**17)) # true values
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