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## /distributions [ Modules ]

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NAME

module distributions

PURPOSE

This module contains various distribution functions:

## distributions/gauss [ Functions ]

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NAME

real function gauss(x, x0, w)

PURPOSE

Returns the value of the Gaussian distribution at x.

INPUTS

• real :: x --- the argument (where the function is evaluated)
• real :: x0 --- pole parameter
• real :: w --- width parameter

## distributions/novo [ Functions ]

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NAME

real function novo(x, x0, s, t)

PURPOSE

Returns the value of the Novosibirsk distribution at x.

INPUTS

• real :: x --- the argument (where the function is evaluated)
• real :: x0 --- pole parameter
• real :: s --- width parameter sigma
• real :: t --- skewness parameter tau

## distributions/woods_saxon [ Functions ]

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NAME

real function woods_saxon(x, f0, x0, dx)

PURPOSE

Returns the value of the Woods-Saxon distribution at x.

INPUTS

• real :: x --- the argument (where the function is evaluated)
• real :: f0 --- normalization constant, approximately equals the value at x=0
• real :: x0 --- 'radius' parameter
• real :: dx --- 'diffuseness' parameter

## distributions/Sigmoid [ Functions ]

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NAME

real function Sigmoid(x, x0, dx)

PURPOSE

Returns the value of the sigmoid function, which used for smooth turning on and off of individual subprocesses, smooth approximation to Heaviside function:

• Sigm -> 1 for x -> infty, Sigm -> 0 for x -> -infty for dx > 0
• Sigm -> 0 for x -> infty, Sigm -> 1 for x -> -infty for dx < 0

INPUTS

• real :: x --- the argument (where the function is evaluated)
• real :: x0 --- cutoff point
• real :: dx --- 'diffuseness' parameter, width of cutoff

## distributions/Fermi [ Functions ]

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NAME

real function Fermi(E, mu, T)

PURPOSE

Returns the value of the Fermi distribution for the energy E, chemical potential mu and temperature T.

INPUTS

• real :: E --- energy in GeV
• real :: mu --- chemical potential in GeV
• real :: T --- temperature in GeV

## distributions/bW [ Functions ]

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NAME

real function bW(x,pole,width)

PURPOSE

Returns the value of the non-relativistic Breit-Wigner distribution at x with a given pole and width.

INPUTS

## distributions/RelBW [ Functions ]

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NAME

real function RelBW(x,pole,width)

NOTES

Returns the value of the relativistic Breit-Wigner distribution at x with a given pole and width.

INPUTS

• real :: x --- invariant mass sqrt(p_nu*p^nu) [GeV]
• real :: pole --- pole mass [GeV]
• real :: width --- width [GeV]

NOTES

Evaluates the spectral function of a particle with given mass and gamma at p^nu p_nu= x**2. Normalized to Integral(RelBW) from p**2=(0,infinity)GeV**2 = 1

## distributions/BlattWeisskopf [ Functions ]

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NAME

real function BlattWeisskopf(x,l)

NOTES

Returns the function value of the Blatt-Weisskopf-Functions, which govern the momentum dependence of the width of a resonance decaying into AB. See e.g. Effenberger Dr. thesis, page 28

INPUTS

• real :: x -- = p_ab *R with p_ab = Relative Momentum of outgoing particles AB and R = Interaction-Radius
• integer :: l -- angular Momentum of outgoing particles AB

## distributions/markusPostFormFactor [ Functions ]

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NAME

real function markusPostFormFactor(mass, pole, srts0, lambda)

PURPOSE

See Post's Phd thesis, page 35, eq. (3.22).