Re: Comment on Resonances

[Matthew Shepherd <mashephe@indiana.edu>]

Hi Curtis,

I agree with your statements regarding broad resonances.  In general  
it isn't meaningful to talk about a particle coming from a parent  
resonance since there is the potential for many interfering  
amplitudes.  It is impossible to even try to figure out how one would  
write such a decay tree in the Monte Carlo.

I think the most important thing is for narrow particles like eta,  
pi, etc. to have "tagged" decays.  This is most useful when it comes  
to understanding issues regarding backgrounds and signal selection  
efficiency

I'm not sure how kinematically separated excited baryon production is  
either, but perhaps this is another place where some MC tagging could  
help in understanding backgrounds.

Cheers,

-Matt


On Jun 6, 2007, at 7:47 AM, Curtis A. Meyer wrote:

> Dear Offline Colleagues -
>
>    durning the offline meeting yesterday (June 5, 2007), there
> was a comment about being able to know the history of particles
> coming from broad resonaces such as the b1 and rho in the
> Monte Carlo. During the meeting, I commented that in doing
> Partial Wave Analysis, one would not put these broad resonances
> into the Monte Carlo sample, rather one would throw the appropriate
> n-body phase space and then let the fit decide what the relevant  
> physics
> was (including resonances).
>
>    There is one situation where one might want to put the resonances
> in. That would be when we are testing fits on Monte Carlo Data. In  
> that
> case, we would need to weight the "data set" by the appropriate  
> physics
> weights. However, these weights WOULD INCLUDE all possible decay
> chains through the data---that is what the physics would say. As an  
> example,
> consider the production of a neutral eta_2 (spin2 isospin zero)  
> state X
> which then decays to an a2 and a pi
>
>      gamma p -> X(0) p
>                           X(0) -> a2 pi_1
>                                   a2 -> rho pi_2
>                                             rho -> pi_3 pi_4
>
>       So the final state is four pions. Let us for simplicity  
> assume that we
> have pi+ pi- pi0 pi0. There are actually four ways that the event  
> could
> have been produced.
>
>                          [a2-zero   pi-zero]      rho+ pi-
>                                                             rho- pi+
>                          [a2-plus   pi-minus]    rho+ pi0
>                          [a2-minus pi-plus]      rho-  pi0
>
> The physics weight for this event would include all four possible  
> decay chains
> with appropriate isospin factor and resonance weights (e.g. Breit  
> Wigner). It
> doe not make sense to say that a particular pion came from the a2  
> or from the
> rho, there is only a probability that one of them did.  These also  
> interfere with
> each other, so even the probability is not overly meaningful. There  
> is an amplitude
> that includes all of these and that has to be right.
>
>
> If we go to the situation of narrow resonances---the pi0, eta,  
> omega, etaprime and phi,
> then we can in some sense treat these as final state particles and  
> to first order ignore
> the combinatorics. However, this may not be true for the omega in  
> all situations. In Crystal
> Barrel when we looked at
>
>    p-bar p -> omega pi0 pi0  and omega -> pi0 gamma
>
> we actually had to write the amplitudes with all three pi0s having the
> possibility of coming from the omega. There were regions where this
> was ambigious.
>
>    Finally, the fact that genr8 allows one to impose a particular  
> resonance path
> does not meant that is true physics.  So, I come back to my  
> statement from
> yesterday in that narrow resonances (as defined above) can have a  
> history.
> In general, nothing else does.
>
>    -- Curtis
> -- 
> Professor Curtis A. Meyer        Department of Physics
> Phone:  (412) 268-2745          Carnegie Mellon University
> Fax:    (412) 681-0648            Pittsburgh PA 15213-3890
> cmeyer@ernest.phys.cmu.edu  http://www.curtismeyer.com/
>