what is breit wigner distribution function ? it is used in resonance scan means it decides the no of events for any specific channel. i am also giving the link of the paper where i found this http://pos.sissa.it/archive/conferences/160/018/Bormio2012_018.pdf please help me out thank you
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 [itex]a+b\to A\to X+Y[/itex]. 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 [itex]s_A\simeq m_A^2[/itex], provided that the width [itex]\Gamma[/itex] of the intermediate particle is not too large.
thank you very much i will try to understand this and also try to correlate with the paper and will come back to you soon. thank you
The paper itself is about the exotic hadron X(3872). It is a perfect example of resonance. Namely it doesn't appear as a final state of the reaction but as an intermediate particle. It is, for example, produced ad LHC via the reaction: p+p -> X(3872) -> D0 + antiD0*. As you can see this is exactly as the reaction I showed you before.
thank you very much. can you please suggest me the reference book to study this ? actually I understood the things but still I want to understand in more detail. thank you Nakul Soni
One of the best books is De Wit - Field theory in particle physics. In particular the chapter on decay rates