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Exclurad

1.   Copied the EXCLURAD code from the JLab Radiation Corrections helpdesk.   The paper on EXCLURAD is in Phys.Rev.D66:074004,2002.

2.   Modified code so that
                     a.  Can use tables of multipoles from MAID 2003 for (pi0,p) and (pi+,n) final states and from Eta-MAID( MAID web page.)
                      b.  Plot for sig_t, sig_l sig_tt and sig_lt and a  plot of  the total center-of-mass cross sections for p(e,ep)pi0 versus W from EXCLURAD and MAID2003 web page at Q2 = 4 and theta_cm_pi = 30 degrees and phi_cm_pi = 210 ( for the total cross section plot).
                      c. Plot for sig_t, sig_l sig_tt and sig_lt and a  plot of  the total center-of-mass cross sections for p(e,epi+)n versus W from EXCLURAD and MAID2003 web page at Q2 = 4 and theta_cm_pi = 30 degrees and phi_cm_pi = 30 ( for the total cross section plot).
                      d. Plot for sig_t, sig_l sig_tt and sig_lt and a  plot of  the total center-of-mass cross sections for p(e,ep)eta versus W from EXCLURAD and etaMAID web page at Q2 = 4 and theta_cm_eta = 150 degrees and phi_cm_eta = 210 ( for the total cross section plot).
                       e. The multipoles from MAID go to Q2 = 5. To go to higher Q2, the center-of-mass response functions are multipled by square of G_d(Q2 = 6.3)/G_d(Q2=5) with G_d = 1/(1-Q2/.71)/(1-Q2/.71).

2a.   Found bug in exclurad.  In calculating the sig_t,sig_l, sig_tt and sig_lt needed for the  cross section there is a missing factor of 2W*p_pi_cm/(W2-M2).

3.  The radiated cross section, sig_rad = sig_born*t1 + t2 . This is only the internal radiation correction. The external radiation correction has to be done separately.  t1 = exp(del_inf)*(1 + del_VR + del_vac). del_inf  is the radiation of soft photons. del_vac is the effects of vacuum polarization. del_VR is the infrared-free sum of the factorized parts of the real and virutal photon radiation. t2 is the infrared-free contribution from the bremsstrahlung process.

4. Comparing the ratio of the radiated cross section to the Born cross section.
                                      a.  The code has the choice of the full calculations ( which is time consuming because an integration over all angles is done) or the leading log (  "peaking  approximation"). The t1 calculation is the same for full or leading log, but the t2 part is different.
                                       b.  One can also place a cut on  Vcut = (missing mass squared) - (mass of meson squared) to simulate the cut that is applied to the data.
                                       c. At Q2 = 5 , W = 1232 and pion production, plot  of  sig_rad/sig_born versus phi_cm for different Vcut < 0.01,  0.02 and 0.04 for cos(theta_cm_pi) = 0.9 and -0.9 using the full calculation of sig_rad .
                                        d. At Q2 = 6.3 and pion production, plot of  sig_rad/sig_born versus W for Vcut < 0.04 comparing full and leading log calculation and cos(theta_cm_pi) = 1.
                                        e. At Q2 = 6.3 and eta productions, plot of  sig_rad/sig_born versus W for Vcut < 0.04 comparing full and leading log calculation and cos(theta_cm_pi) = 1.
                                         f.  Plots  comparing internal radiative correction from SIMC to internal radiative correction of EXCLURAD.  SIMC has been run for all kinematic setting of the experiment and chained together into one ntuple. SIMC was run without radiation and with internal radiation only. The table below has links to plots of the ratio of radiated cross section to the Born ( unradiated) cross section. The black line in the plot is from EXCLURAD for leadiing log, the green is the full EXCLURAD calcuation and the red points are from SIMC. The SIMC points are determined by the ratio of the yield for no radiation input file to yield from internal radiation input file. Each plot link is for a given W and has 6 plots centered on six different cos(thcm) = -0.83, -0.50, -0.16, +0.16,+0.50, + 0.83 showing the cross section ratio versus phi center of mass.