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    Created: 2020-03-28 Sat 11:30

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    Validate

    -
    - - \ No newline at end of file diff --git a/prog/python/qqgg/analytical_xs.org b/prog/python/qqgg/analytical_xs.org index 40715e2..869d4cb 100644 --- a/prog/python/qqgg/analytical_xs.org +++ b/prog/python/qqgg/analytical_xs.org @@ -142,11 +142,19 @@ charge = 1/3 esp = 200 # GeV #+END_SRC +Set up the integration and plot intervals. +#+begin_src ipython :session :exports both :results raw drawer +interval_η = [-η, η] +interval = η_to_θ([-η, η]) +interval_cosθ = np.cos(interval) +interval_pt = η_to_pt([0, η], esp/2) +plot_interval = [0.1, np.pi-.1] +#+end_src + #+RESULTS: 7e62918a-2935-41ac-94e0-f0e7c3af8e0d :RESULTS: :END: - *** Analytical Integratin And now calculate the cross section in picobarn. #+NAME: cf853fb6-d338-482e-bc55-bd9f8e796495 @@ -175,19 +183,7 @@ Compared to sherpa, it's pretty close. I had to set the runcard option ~EW_SCHEME: alpha0~ to use the pure QED coupling constant. -*** Numerical Integration and Sampling -Set up the integration and plot intervals. -#+begin_src ipython :session :exports both :results raw drawer -interval_η = [-η, η] -interval = η_to_θ([-η, η]) -interval_cosθ = np.cos(interval) -interval_pt = η_to_pt([0, η], esp/2) -plot_interval = [0.1, np.pi-.1] -#+end_src - -#+RESULTS: -:RESULTS: -:END: +*** Numerical Integration Plot our nice distribution: #+begin_src ipython :session :exports both :results raw drawer @@ -257,6 +253,7 @@ print(tex_value(xs_pb_mc, unit=r'\pico\barn', prefix=r'\sigma = ', prec=5)) [[file:results/xs_mc.tex]] :END: +*** Sampling and Analysis Now we monte-carlo sample our distribution. #+begin_src ipython :session :exports both :results raw drawer cosθ_sample = sample(lambda x: diff_xs_cosθ(x, charge, esp), interval_cosθ)
    - - -
    -

    1 Init

    -
    -
    -
    -

    1.1 Required Modules

    -
    -
    -
    import numpy as np
    -import matplotlib.pyplot as plt
    -
    -
    -
    -
    - -
    -

    1.2 Utilities

    -
    -
    -
    %run ../utility.py
    -
    -
    -
    -
    -
    - -
    -

    2 Implementation

    -
    -
    -
    """
    -Implementation of the analytical cross section for q q_bar ->
    -gamma gamma
    -
    -Author: Valentin Boettcher <hiro@protagon.space>
    -"""
    -
    -import numpy as np
    -from scipy.constants import alpha
    -
    -# NOTE: a more elegant solution would be a decorator
    -def energy_factor(charge, esp):
    -    """
    -    Calculates the factor common to all other values in this module
    -
    -    Arguments:
    -    esp -- center of momentum energy in GeV
    -    charge -- charge of the particle in units of the elementary charge
    -    """
    -
    -    return charge**4*(alpha/esp)**2/6
    -
    -
    -def diff_xs(theta, charge, esp):
    -    """
    -    Calculates the differential cross section as a function of the
    -    azimuth angle theta in units of 1/GeV^2.
    -
    -    Arguments:
    -    theta -- azimuth angle
    -    esp -- center of momentum energy in GeV
    -    charge -- charge of the particle in units of the elementary charge
    -    """
    -
    -    f = energy_factor(charge, esp)
    -    return f*((np.cos(theta)**+1)/np.sin(theta)**2)
    -
    -def diff_xs_eta(eta, charge, esp):
    -    """
    -    Calculates the differential cross section as a function of the
    -    pseudo rapidity of the photons in units of 1/GeV^2.
    -
    -    Arguments:
    -    eta -- pseudo rapidity
    -    esp -- center of momentum energy in GeV
    -    charge -- charge of the particle in units of the elementary charge
    -    """
    -
    -    f = energy_factor(charge, esp)
    -    return f*(2*np.cosh(eta)**2 - 1)
    -
    -def total_xs_eta(eta, charge, esp):
    -    """
    -    Calculates the total cross section as a function of the pseudo
    -    rapidity of the photons in units of 1/GeV^2.  If the rapditiy is
    -    specified as a tuple, it is interpreted as an interval.  Otherwise
    -    the interval [-eta, eta] will be used.
    -
    -    Arguments:
    -    eta -- pseudo rapidity (tuple or number)
    -    esp -- center of momentum energy in GeV
    -    charge -- charge of the particle in units of the elementar charge
    -    """
    -
    -    f = energy_factor(charge, esp)
    -    if not isinstance(eta, tuple):
    -        eta = (-eta, eta)
    -
    -    if len(eta) != 2:
    -        raise ValueError('Invalid eta cut.')
    -
    -    def F(x):
    -        return np.tanh(x) - 2*x
    -
    -    return 2*np.pi*f*(F(eta[0]) - F(eta[1]))
    -
    -
    -
    -
    - -
    -

    3 Calculations

    -
    -
    -
    -

    3.1 XS qq -> gamma gamma

    -
    -

    -First, set up the input parameters. -

    -
    -
    eta = 2.5
    -charge = 1/3
    -esp = 200  # GeV
    -
    -
    - -

    -And now calculate the cross section in picobarn. -

    -
    -
    xs_gev = total_xs_eta(eta, charge, esp)
    -xs_pb = gev_to_pb(xs_gev)
    -print(tex_value(xs_pb, unit=r'\pico\barn', prefix=r'\eta = '))
    -
    -
    - -

    -../../../results/xs/xs.tex -

    - -

    -Compared to sherpa, it's pretty close. -

    -
    -
    sherpa = 0.0538009
    -xs_pb/sherpa
    -
    -
    - -

    -0.9998585425137037 -

    - - - -

    -I had to set the runcard option EW_SCHEME: alpha0 to use the pure -QED coupling constant. -

    -
    -
    -
    -

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