# Resonance scan

by nakulphy
Tags: breit wigner, resonance, scan
 P: 323 The Breit-Wigner distribution is a particular factor appearing in the expression for the scattering cross section when this scattering happens via an intermediate particle. Consider for example the scattering $a+b\to A\to X+Y$. The expression for the cross section is given by: $$\frac{d\sigma(a+b\to X+Y)}{d\vec pd s_X}=\frac{d\Gamma(A\to X)}{\Gamma(A\to all)}\frac{d\sigma(a+b\to A+Y)}{d\vec pd s_A} W(s_A)\sqrt{\frac{\vec p^2+m_A^2}{\vec p^2+s_A}},$$ where the Breit-Wigner distribution is given by: $$W(s_A)=\frac{1}{\pi}\frac{m_A\Gamma}{(s_A-m_A^2)^2+m_A^2\Gamma^2}.$$ As you can see, such a distribution gives an enhancement of the cross section (i.e. of the number of particles produced) when $s_A\simeq m_A^2$, provided that the width $\Gamma$ of the intermediate particle is not too large.