mirror of
https://github.com/vale981/bachelor_thesis
synced 2025-03-07 02:21:40 -05:00
281 lines
7.9 KiB
Python
281 lines
7.9 KiB
Python
"""
|
||
Implementation of the analytical cross section for q q_bar ->
|
||
γγ in the lab frame.
|
||
|
||
Author: Valentin Boettcher <hiro@protagon.space>
|
||
"""
|
||
|
||
import numpy as np
|
||
import monte_carlo
|
||
import lhapdf
|
||
from numba import jit, vectorize, float64, boolean
|
||
import lab_xs.lab_xs as c_xs
|
||
|
||
|
||
@vectorize([float64(float64, float64, float64, float64)], nopython=True)
|
||
def energy_factor(e_proton, charge, x_1, x_2):
|
||
"""Calculates the factor common to all other values in this module.
|
||
|
||
:param e_proton: proton energy per beam
|
||
:param charge: charge of the quark
|
||
:param x_1: momentum fraction of the first quark
|
||
:param x_2: momentum fraction of the second quark
|
||
|
||
"""
|
||
return charge ** 4 / (137.036 * e_proton) ** 2 / (24 * x_1 * x_2)
|
||
|
||
|
||
def momenta(e_proton, x_1, x_2, cosθ, φ=None):
|
||
"""Given the Energy of the incoming protons `e_proton` and the
|
||
momentum fractions `x_1` and `x_2` as well as the cosine of the
|
||
azimuth angle of the first photon the 4-momenta of all particles
|
||
are calculated.
|
||
"""
|
||
x_1 = np.asarray(x_1)
|
||
x_2 = np.asarray(x_2)
|
||
cosθ = np.asarray(cosθ)
|
||
|
||
if φ is None:
|
||
φ = 0
|
||
cosφ = np.ones_like(cosθ)
|
||
sinφ = 0
|
||
|
||
else:
|
||
if φ == "rand":
|
||
φ = np.random.uniform(0, 2 * np.pi, cosθ.shape)
|
||
else:
|
||
φ = np.asarray(φ)
|
||
sinφ = np.sin(φ)
|
||
cosφ = np.cos(φ)
|
||
|
||
assert (
|
||
x_1.shape == x_2.shape == cosθ.shape
|
||
), "Invalid shapes for the event parameters."
|
||
|
||
sinθ = np.sqrt(1 - cosθ ** 2)
|
||
|
||
ones = np.ones_like(cosθ)
|
||
zeros = np.zeros_like(cosθ)
|
||
|
||
q_1 = e_proton * x_1 * np.array([ones, zeros, zeros, ones,])
|
||
q_2 = e_proton * x_2 * np.array([ones, zeros, zeros, -ones,])
|
||
g_3 = (
|
||
2
|
||
* e_proton
|
||
* x_1
|
||
* x_2
|
||
/ (x_1 + x_2 - (x_1 - x_2) * cosθ)
|
||
* np.array([1 * np.ones_like(cosθ), sinθ * sinφ, cosφ * sinθ, cosθ])
|
||
)
|
||
g_4 = q_1 + q_2 - g_3
|
||
|
||
q_1 = q_1.reshape(4, cosθ.size).T
|
||
q_2 = q_2.reshape(4, cosθ.size).T
|
||
g_3 = g_3.reshape(4, cosθ.size).T
|
||
g_4 = g_4.reshape(4, cosθ.size).T
|
||
|
||
return np.array([q_1, q_2, g_3, g_4])
|
||
|
||
|
||
@vectorize([float64(float64, float64, float64, float64, float64)], nopython=True)
|
||
def diff_xs_η(e_proton, charge, η, x_1, x_2):
|
||
"""Calculates the differential cross section as a function of the
|
||
cosine of the pseudo rapidity η of one photon in units of 1/GeV².
|
||
|
||
Here dΩ=dηdφ
|
||
|
||
:param e_proton: proton energy per beam [GeV]
|
||
:param charge: charge of the quark
|
||
:param x_1: momentum fraction of the first quark
|
||
:param x_2: momentum fraction of the second quark
|
||
:param η: pseudo rapidity
|
||
|
||
:return: the differential cross section [GeV^{-2}]
|
||
"""
|
||
|
||
rap = np.arctanh((x_1 - x_2) / (x_1 + x_2))
|
||
f = energy_factor(e_proton, charge, x_1, x_2)
|
||
|
||
return f * ((np.tanh(η - rap)) ** 2 + 1)
|
||
|
||
|
||
class Cut:
|
||
def __init__(self):
|
||
self._other = None
|
||
self._current_comb = self._call
|
||
|
||
self._greater_than = 0
|
||
self._lower_than = np.inf
|
||
|
||
def __gt__(self, greater_than):
|
||
self._greater_than = greater_than
|
||
|
||
return self
|
||
|
||
def __lt__(self, lower_than):
|
||
self._lower_than = lower_than
|
||
|
||
return self
|
||
|
||
def _or_comb(self, event):
|
||
return self._call(event) or self._other(event)
|
||
|
||
def _and_comb(self, event):
|
||
return self._call(event) and self._other(event)
|
||
|
||
def _call(self, event):
|
||
return self._greater_than < self._calculate(event) < self._lower_than
|
||
|
||
def _calculate(self, event):
|
||
raise NotImplementedError('"_calulate" must be implemented.')
|
||
|
||
def __call__(self, event):
|
||
return self._current_comb(event)
|
||
|
||
def __and__(self, other):
|
||
self._other = other
|
||
self._current_comb = self._and_comb
|
||
|
||
return self
|
||
|
||
def __or__(self, other):
|
||
self._other = other
|
||
self._current_comb = self._or_comb
|
||
|
||
return self
|
||
|
||
def apply(self, function):
|
||
@wraps(function)
|
||
def wrapper(event):
|
||
if self(event):
|
||
return function(event)
|
||
|
||
return 0
|
||
|
||
return wrapper
|
||
|
||
|
||
@vectorize([float64(float64, float64, float64)], nopython=True)
|
||
def averaged_tchanel_q2(e_proton, x_1, x_2):
|
||
return 2 * x_1 * x_2 * e_proton ** 2
|
||
|
||
|
||
class CutpT(Cut):
|
||
def __init__(self):
|
||
super().__init__()
|
||
|
||
def _calculate(self, event):
|
||
e_hadron, eta, x_1, x_2 = event
|
||
return c_xs.pT(e_hadron, eta, x_1, x_2)
|
||
|
||
|
||
class CutOtherEta(Cut):
|
||
def __init__(self):
|
||
super().__init__()
|
||
|
||
def _calculate(self, event):
|
||
_, η, x_1, x_2 = event
|
||
return c_xs.second_eta(η, x_1, x_2)
|
||
|
||
def cached_pdf(pdf, q, points, e_hadron):
|
||
x_min = pdf.xMin
|
||
x_max = pdf.xMax
|
||
Q2_max = 2 * e_hadron ** 2
|
||
|
||
cache = np.array(
|
||
[
|
||
[
|
||
pdf.xfxQ2(
|
||
q, xx := x_min + (x_max - x_min) * x / points, Q2_max / 100 * Q2
|
||
)
|
||
/ xx
|
||
for Q2 in range(100)
|
||
]
|
||
for x in range(points)
|
||
]
|
||
)
|
||
|
||
def cached(x, q2):
|
||
return cache[int((x - x_min) / (x_max - x_min) * points - 1)][
|
||
int(q2 * 100 / Q2_max - 1)
|
||
]
|
||
|
||
return cached
|
||
|
||
|
||
def get_xs_distribution_with_pdf(
|
||
xs,
|
||
q,
|
||
e_hadron,
|
||
quarks=None,
|
||
pdf=None,
|
||
cut=None,
|
||
num_points_pdf=1000,
|
||
vectorize=False,
|
||
):
|
||
"""Creates a function that takes an event (type np.ndarray) of the
|
||
form [angle_arg, impulse fractions of quarks in hadron 1, impulse
|
||
fractions of quarks in hadron 2] and returns the differential
|
||
cross section for such an event. I would have used an object as
|
||
argument, wasn't for the sampling function that needs a vector
|
||
valued function. Angle_Arg can actually be any angular-like parameter
|
||
as long as the xs has the corresponding parameter.
|
||
|
||
:param xs: cross section function with signature (energy hadron, angle_arg, x_1, x_2)
|
||
:param q2: the momentum transfer Q^2 as a function with the signature
|
||
(e_hadron, x_1, x_2)
|
||
:param quarks: the constituent quarks np.ndarray of the form [[id, charge], ...],
|
||
the default is a proton
|
||
:param pdf: the PDF to use, the default is "NNPDF31_lo_as_0118"
|
||
:param cut: cut function with signature (energy hadron, angle_arg, x_1,
|
||
x_2) to return 0, when the event does not fit the cut
|
||
|
||
:returns: differential cross section summed over flavors and weighted with the pdfs
|
||
:rtype: function
|
||
"""
|
||
|
||
pdf = pdf or lhapdf.mkPDF("NNPDF31_lo_as_0118", 0)
|
||
quarks = (
|
||
quarks
|
||
if quarks is not None
|
||
else np.array([[5, -1 / 3], [4, 2 / 3], [3, -1 / 3], [2, 2 / 3], [1, -1 / 3]])
|
||
) # all the light quarks
|
||
|
||
supported_quarks = pdf.flavors()
|
||
for flavor in quarks[:, 0]:
|
||
assert flavor in supported_quarks, (
|
||
"The PDF doesn't support the quark flavor " + flavor
|
||
)
|
||
|
||
xfxQ2 = pdf.xfxQ2
|
||
|
||
def distribution(angle_arg, x_1, x_2) -> float:
|
||
if cut and not cut([e_hadron, angle_arg, x_1, x_2]):
|
||
return 0
|
||
|
||
q2_value = q(e_hadron, x_1, x_2)
|
||
|
||
xs_value = xs(e_hadron, 1 / 3, angle_arg, x_1, x_2)
|
||
pdf_values = (
|
||
xfxQ2(quarks[:, 0], x_1, q2_value),
|
||
xfxQ2(-quarks[:, 0], x_1, q2_value),
|
||
xfxQ2(quarks[:, 0], x_2, q2_value),
|
||
xfxQ2(-quarks[:, 0], x_2, q2_value),
|
||
)
|
||
|
||
result = 0
|
||
xs_value = xs(e_hadron, 1, angle_arg, x_1, x_2)
|
||
|
||
for (quark, charge), q_1, qb_1, q_2, qb_2 in zip(quarks, *pdf_values):
|
||
|
||
result += ((q_1 * qb_2) + (qb_1 * q_2)) * (charge ** 4)
|
||
|
||
return result * xs_value / (x_1 * x_2) # identical protons
|
||
|
||
def vectorized(angle_arg, x_1, x_2):
|
||
results = np.empty_like(angle_arg)
|
||
for a, x__1, x__2, i in zip(angle_arg, x_1, x_2, range(len(results))):
|
||
results[i] = distribution(a, x__1, x__2)
|
||
return results
|
||
|
||
return vectorized if vectorize else distribution, (pdf.xMin, pdf.xMax)
|