[Hybrid baryons] s-p-wave interference

[Viktor Mokeev]

Sorry! I fixed two typos.

 Best Regards,
                   Victor

----- Original Message -----
From: "Viktor Mokeev" <mokeev at jlab.org>
To: "hybrid baryons" <hybrid_baryons at jlab.org>
Sent: Sunday, July 19, 2015 2:56:49 PM
Subject: Re: [Hybrid baryons] s-p-wave interference

Hi All,


 Considering compelling examples presented by Volker on the importance of interference, I would suggest to modify a way to investigate the hybrid state contribution in the MC simulation of KY channels.

 I would suggest to carry-out 3 MC simulations:

A) KY Gent model without extra resonances;
B) KY Gent model adding 1/2+ hybrid state incoherently summing up the resonant cross section from BW anstanz of JM model with 1 hybrid-baryon resonance and Gent model cross sections;
C) KY Gent model plus cross section from resonance contributions from two resonances: a) hybrid state and b)conventional PDG state of spin 1/2 and opposite parity ``-" (known 1/2^- resonance closest in mass to 1/2^+ hybrid). Resonant amplitude represents a coherent superposition of two resonances of spin 1/2 and opposite parities ``-" and "+". Interference between both resonances will be taken into account explicitly.

 Difference between the results of the computations C and B will elucidate the impact of the interference effects between resonances. Difference between the results from C and A will show the overall resonance contribution plus all interferences between resonances and between resonances and background.

As it is proposed in LOI, the hybrid mass should be in the range between 2.1 and 2.3 GeV.


According to PDG, the state of 1/2^- spin-parity, which is the most overlapping with the modeled hybrid state is the \Delta(1900)1/2^-
with the status **

                Bonn-Gatchina                                      Kent U.
  
Mass BW, MeV       1840+/-30                                       1920+/-24     
Width BW, MeV      300+/-45                                        263+/-39

Sigma K inelastic pole residue 7+/-2 % 

 So we have overlap between this resonance and hybrid state with mass from 2.1 to 2.3 GeV considering 250-300 MeV hybrid width.

I also suggest to repeat the step C with the known resonance of 3/2^+ spin-parity, which is N(1900)3/2^+ of *** status

                                          Bonn-Gatchina                                Kent U

Mass BW, MeV                                1905+/-30                                   1879+/-17
Width BW, MeV                               250+120-50                                  498+/-78

BF(\Sigma K)=5.0+/-2%
BF(Lambda K)=0-10%

Analytical expressions for the resonant cross sections with two contributing resonances will be available next Meeting.

 Could we proceed with this plan? I appreciate any comments and further suggestions.

   Thank you!


                 Best Regards,
                                           Victor 

----- Original Message -----
From: "burkert" <burkert at jlab.org>
To: "hybrid baryons" <hybrid_baryons at jlab.org>
Sent: Sunday, July 19, 2015 10:16:57 AM
Subject: [Hybrid baryons] s-p-wave interference

Hi all, 

At the last hybrid meeting we had some discussion on s-p-wave interference. 
I attached a slide that hopefully helps clarifying this aspect. 

Any J P =1/2 + and J P =1/2 - terms that overlap in energy will interfere and generate in the Legendre expansion shown on the slide a term that is proportional to cos(theta). In the example shown (from our CLAS publication Phys.Rev. C78 (2008) 045209; arXiv:0804.0447 [nucl-ex] ; Phys.Rev. C77 (2008) 015208 , arXiv:0709.1946 ) 
the interference of the Roper P11 p-wave multipoles (S1-, M1-) with s-wave multipoles (E0+, S0+) from the N(1535) and non-resonant terms generates a strong cos(theta) term, half of which is due to the resonant Roper contribution (difference between solid and dotted lines). Of course, at this Q 2 the Roper is a large amplitude and contributes to the total cross section also strongly, but that is not the case at some smaller Q 2 where the interference term is essential in extracting the Roper contribution. 

Any comments on this are appreciated. 

Cheers, 
Volker 



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