Physics PDFs

Physics PDFs are PDFs that are often used in high energy physics. They are in the zfit-physics package, which needs to be installed separately (for example, via pip install zfit-physics) and accessed via the zfit_physics.pdf module.

Physics PDFs are specialized probability density functions commonly used in particle physics for modeling signal and background distributions. These PDFs are designed to capture specific physical phenomena observed in experimental data.

Below are visualizations of physics PDFs with different parameter values to help understand their shapes and choose appropriate initial parameter values.

CrystalBall PDF

The CrystalBall function is a Gaussian with a power-law tail, commonly used to model energy loss and detector resolution effects in particle physics.

zfit.pdf.CrystalBall(mu, sigma, alpha, n, obs, *)

Crystal Ball shaped PDF.

GaussExpTail PDF

The GaussExpTail combines a Gaussian core with an exponential tail, useful for modeling detector resolution effects with asymmetric tails.

zfit.pdf.GaussExpTail(mu, sigma, alpha, obs, *)

GaussExpTail shaped PDF.

GeneralizedCB PDF

The GeneralizedCB extends the Crystal Ball function with additional parameters for more flexible modeling of asymmetric peaks with power-law tails.

zfit.pdf.GeneralizedCB(mu, sigmal, alphal, ...)

Generalized asymmetric double-sided Crystal Ball shaped PDF.

GeneralizedGaussExpTail PDF

The GeneralizedGaussExpTail extends the GaussExpTail function with additional parameters for more flexible modeling of asymmetric distributions.

zfit.pdf.GeneralizedGaussExpTail(mu, sigmal, ...)

GeneralizedGaussedExpTail shaped PDF which is Generalized assymetric double-sided GaussExpTail shaped PDF.

DoubleCB PDF

The DoubleCB function extends the Crystal Ball by having power-law tails on both sides of the Gaussian core, providing more flexibility for modeling asymmetric peaks.

zfit.pdf.DoubleCB(mu, sigma, alphal, nl, ...)

Double-sided Crystal Ball shaped PDF.

The following PDFs are available in the separate zfit_physics package:

Argus

The Argus PDF is commonly used to model background distributions in B physics, particularly for describing the kinematic threshold behavior.

zfit_physics.pdf.Argus(*args[, obs])

ARGUS shape describing the invariant mass of a particle in a continuous background.

RelativisticBreitWigner

The RelativisticBreitWigner PDF describes the mass distribution of unstable particles, taking into account relativistic effects.

zfit_physics.pdf.RelativisticBreitWigner(*args)

Relativistic Breit-Wigner distribution.

CMSShape

The CMSShape PDF is used to model background distributions in CMS analyses.

zfit_physics.pdf.CMSShape(m, beta, gamma, obs, *)

CMSShape PDF.

Cruijff

The Cruijff PDF is an asymmetric Gaussian with different widths and tails on each side, often used to model detector resolution effects.

zfit_physics.pdf.Cruijff(mu, sigmal, alphal, ...)

Cruijff PDF, a Gaussian with two width, left and right, and non-Gaussian tails.

ErfExp

The ErfExp PDF combines an error function with an exponential, useful for modeling backgrounds with a turn-on effect.

zfit_physics.pdf.ErfExp(mu, beta, gamma, n, ...)

ErfExp PDF, the product of a complementary error function and an exponential function.

Novosibirsk

The Novosibirsk PDF is used to model asymmetric peaks with a Gaussian-like core and exponential tails.

zfit_physics.pdf.Novosibirsk(mu, sigma, ...)

Novosibirsk PDF.

Tsallis

The Tsallis PDF is used in high-energy physics to model particle production spectra.

zfit_physics.pdf.Tsallis(m, t, n, obs, *[, ...])

Tsallis-Hagedorn PDF.

zfit.pdf.CrystalBall(mu, sigma, alpha, n, obs, *)	Crystal Ball shaped PDF.
zfit.pdf.DoubleCB(mu, sigma, alphal, nl, ...)	Double-sided Crystal Ball shaped PDF.
zfit.pdf.GeneralizedCB(mu, sigmal, alphal, ...)	Generalized asymmetric double-sided Crystal Ball shaped PDF.
zfit.pdf.GaussExpTail(mu, sigma, alpha, obs, *)	GaussExpTail shaped PDF.
zfit.pdf.GeneralizedGaussExpTail(mu, sigmal, ...)	GeneralizedGaussedExpTail shaped PDF which is Generalized assymetric double-sided GaussExpTail shaped PDF.

zfit_physics.pdf.Argus(*args[, obs])	ARGUS shape describing the invariant mass of a particle in a continuous background.
zfit_physics.pdf.RelativisticBreitWigner(*args)	Relativistic Breit-Wigner distribution.
zfit_physics.pdf.CMSShape(m, beta, gamma, obs, *)	CMSShape PDF.
zfit_physics.pdf.Cruijff(mu, sigmal, alphal, ...)	Cruijff PDF, a Gaussian with two width, left and right, and non-Gaussian tails.
zfit_physics.pdf.ErfExp(mu, beta, gamma, n, ...)	ErfExp PDF, the product of a complementary error function and an exponential function.
zfit_physics.pdf.Novosibirsk(mu, sigma, ...)	Novosibirsk PDF.
zfit_physics.pdf.Tsallis(m, t, n, obs, *[, ...])	Tsallis-Hagedorn PDF.