Breit-Wigner Distribution: What is it & How is it Used?

[nakulphy]

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

 

[Einj]

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.

 

[nakulphy]

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

 

[Einj]

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.

 

[nakulphy]

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

 

[Einj]

Do you mean the X(3872) or resonances in general?

 

[nakulphy]

for the basic of Breit-Wigner and the distribution function.

 

[Einj]

One of the best books is De Wit - Field theory in particle physics. In particular the chapter on decay rates