The relativistic Breit–Wigner distribution is a continuous probability distribution with the following probability density function : <math> f(E) \sim \frac{1}{\left(E^2-M^2\right)^2+M^2\Gamma^2}. \!</math> (This equation is written using natural units, <math>\hbar=c=1</math>. ) It is most often used to model resonances (i.e. , unstable particles) in high energy physics.

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  • The relativistic Breit–Wigner distribution is a continuous probability distribution with the following probability density function : <math> f(E) \sim \frac{1}{\left(E^2-M^2\right)^2+M^2\Gamma^2}. \!</math> (This equation is written using natural units, <math>\hbar=c=1</math>. ) It is most often used to model resonances (i.e. , unstable particles) in high energy physics. In this case E is the center-of-mass energy that produces the resonance, M is the mass of the resonance, and <math>\Gamma</math> is the resonance's width (or decay width), related to its mean lifetime according to <math>\tau=1/\Gamma</math>. (With units included, the formula is <math>\tau = \hbar/\Gamma</math>. ) The probability of producing the resonance at a given energy E is proportional to f(E), so that a plot of the production rate of the unstable particle as a function of energy traces out the shape of the relativistic Breit-Wigner distribution. In general, <math>\Gamma</math> can also be a function of E; this dependence is typically only important when <math>\Gamma</math> is not small compared to M (i.e. , when the particle has a large width relative to its mass) and the phase-space dependence of the width needs to be taken into account. This occurs, for example, for the decay of the rho meson into a pair of pions. The factor of M that multiplies <math>\Gamma^2</math> should also be replaced with E (or E/M, etc. ) when the resonance is wide . The form of the relativistic Breit-Wigner distribution arises from the propagator of an unstable particle, which has a denominator of the form <math>(p^2-M^2+iM\Gamma)</math>. Here p is the square of the four-momentum carried by the particle. The propagator appears in the quantum mechanical amplitude for the process that produces the resonance; the resulting probability distribution is proportional to the absolute square of the amplitude, yielding the relativistic Breit-Wigner distribution for the probability density function as given above. The form of this distribution is similar to the solution of the classical equation of motion for a damped harmonic oscillator driven by a sinusoidal external force.
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  • The relativistic Breit–Wigner distribution is a continuous probability distribution with the following probability density function : <math> f(E) \sim \frac{1}{\left(E^2-M^2\right)^2+M^2\Gamma^2}. \!</math> (This equation is written using natural units, <math>\hbar=c=1</math>. ) It is most often used to model resonances (i.e. , unstable particles) in high energy physics.
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  • Relativistic Breit–Wigner distribution
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