Relativistic Breit–Wigner distribution

The relativistic Breit–Wigner distribution (after the 1936 nuclear resonance formula of Gregory Breit and Eugene Wigner) is a continuous probability distribution with the following probability density function, f ( E ) = k ( E 2 − M 2 ) 2 + M 2 Γ 2 , {\displaystyle f(E)={\frac {k}{(E^{2}-M^{2})^{2}+M^{2}\Gamma ^{2}}},} where k is a constant of proportionality, equal to k = 2 2 M Γ γ π M 2 + γ , γ = M 2 ( M 2 + Γ 2 ) . {\displaystyle k={\frac {2{\sqrt {2}}\,M\Gamma \gamma }{\pi {\sqrt {M^{2}+\gamma }}}},\quad \gamma ={\sqrt {M^{2}(M^{2}+\Gamma ^{2})}}.} (This equation is written using natural units, ħ = c = 1.) It is most often used to model resonances (unstable particles) in high-energy physics.

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Relativistic Breit–Wigner distribution

The relativistic Breit–Wigner distribution (after the 1936 nuclear resonance formula of Gregory Breit and Eugene Wigner) is a continuous probability distribution with the following probability density function, f ( E ) = k ( E 2 − M 2 ) 2 + M 2 Γ 2 , {\displaystyle f(E)={\frac {k}{(E^{2}-M^{2})^{2}+M^{2}\Gamma ^{2}}},} where k is a constant of proportionality, equal to k = 2 2 M Γ γ π M 2 + γ , γ = M 2 ( M 2 + Γ 2 ) . {\displaystyle k={\frac {2{\sqrt {2}}\,M\Gamma \gamma }{\pi {\sqrt {M^{2}+\gamma }}}},\quad \gamma ={\sqrt {M^{2}(M^{2}+\Gamma ^{2})}}.} (This equation is written using natural units, ħ = c = 1.) It is most often used to model resonances (unstable particles) in high-energy physics.

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Source: Wikipedia "Relativistic Breit–Wigner distribution" · CC BY-SA 4.0

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