[Hybrid baryons] Proposal to demonstrate the hybrid baryon manifestation in KY data

[Viktor Mokeev]

Dear Colleagues,

We want to make suggestions on the strategy to demonstrate the feasibility
of the hybrid baryon state extraction from the exclusive KY
electroproduction off protons. In our view we should address the following
two major issues:

A) demonstrate the statistical significance of the hybrid signal in
differential dsigma/domega cross sections for the hybrid electrocouplings
above certain values as a function of Q^2;

B) demonstrate the capability of accessing hybrid parameters (mass, widths,
electrocouplings) if hybrid electrocouplings are above certain values in
each bin of Q^2.


The proposal made at the last Friday meeting addressed the bullet A) only.
Now we want to propose possible ways of attacking the problem B).

The simplest way to address problem B) can be the evaluation of the
j-moments of unpolarized KY differential cross sections, which were
presented by E.Golovach last Friday meeting. The computations of j-moments
are described in the attachment. The moment for a given j should isolate
the contribution from the resonance of spin J. Therefore, we propose:
-E.Golovach will provide Annalisa and Lucilla the code for the computation
of dsigma/d(-cos\theta) with hybrid electrocouplings as the input variable
parameters;
-our Italian colleagues evaluate the moment C(W) for different values of
hybrid electrocouplings including zero values (no hybrid contribution).
They will find the values of A1/2, A3/2 S1/2 at different Q^2 bins above
which the W-dependence of C(W) (W from 2.1 GeV to 2.5 GeV) with/without
hybrid will be significantly different.

The best hope is that the C(W)-dependence with hybrid can be fit by:
 BW curve (Gamma=Gamma_hybrid, M= M_hybrid) + polynomial background of the
second order.

It will demonstrate our sensitivity to establish the hybrid baryon
existence and to determine the hybrid mass and width.

We also see a more complex, but the more convincing way to demonstrate the
capability of accessing the hybrid parameters from the fit of the expected
experimental data.

The dsigma/d(-cos\theta) cross sections, computed by E. Golovach, are
treated as the "data" with an uncertainty of 5% and should be fit within
the framework of the following model:

Resonant hybrid amplitude from JM + (Non-resonant amplitudes and known N* contributions)  from Ghent
model.

The resonant parameters, electrocouplings and KY decay widths of hybrid baryon, should be
sampled randomly around the start values shifted with respect to the values
for which cross sections were computed. Random multiplicative factor(s) in
the interval [0.7-1.3] should be applied to the aforementioned Ghent model amplitudes.
For each trial set of the aforementioned parameters,
differentialDsigma/d(cos\theta) cross sections should be computed in entire
area of W and Q^2. From the comparison with the E.Golovach quasi-data the
chi^2/d.p. should be evaluated. In the fit we will select the computed
cross sections with chi^2/d.p. < chi^2/d.p._thresh, so that all computed
cross sections selected in the fit are spread inside the "data"
uncertainties for most data points. The hybrid parameters, so selected in
the fit, should be averaged. Their mean values will be treated as extracted
results from the data fit, while dispersions of their distributions will be
considered as the extracted parameter uncertainties.

We then have to demonstrate that extracted hybrid parameters are consistent
with those hybrid parameters from which cross sections were computed.

Of course, the final extraction of hybrid parameters should be done
employing the amplitude analysis methods. Our area of W is perfect for the
Regge theory. We need to ask Adam for possible contribution from him to the
proposal outlining the methods used in an amplitude analysis which can be
used in order to establish the existence of a new state (hybrid)  and to
access its mass, width, and electrocouplings.

We appreciate your opinions on this proposal.

With Best Regards,


                                       Ralf and Victor

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