itr_corr

The virtual proton velocity was set to v_p = pfer/sqrt(pfer**2+Mp**2). The results, which do not contain Pauli blocking, N-N FSI or missing mass shifts, and can be compared to the two tables in the entry below are:

New missing mass (missmass) plots - Proton on-shell

¹H

²H

Obviously, the strange peaks appear to have been reduced. They were most likely due to the iteration parameterization, which does not work very well far from the region where it was iterated. The large velocities that rarely occurred with the old method may have produced large, unphysical weights that messed up some of the plots. These missing mass plots compared to the new missing mass plots below are not very different for both deuterium and gold.

Results with the new iteration procedure 05/05/06

The SIMC missing mass plots shifted toward the data with the new procedure. The plots below do not contain missing mass shifts, Pauli blocking or the Jost function FSI. The shift can be seen by opening the plots in tabs and flipping back and forth.

New missing mass (missmass) plots - Proton off-shell

¹H

²H

Old missing mass (missmass) plots- Proton stationary

¹H

²H

It is very strange that missing mass plots with the new procedure occasionally has strange behavior at large missing mass. See, for example, this plot for Carbon.

Correction to the iteration procedure 05/05/06

After working through the cross section code, I worked out how to improve our iteration procedure. The previous method was
1) Iterate the cross section for hydrogen in the variables Q2, nu, thetapq, phipq
2) Insert the correction function into event.f, applied as a multiplicative factor to main.sigcc
3) Run the nuclear targets with the same correction factor as hydrogen

The problem with this procedure is that nu, thetapq and phipq are not invariant. For a hydrogen target, these quantities are evaluated in a frame where the proton is at rest. For a nuclear target, these quantities were still evaluated in the lab frame, but the proton was not at rest.

The solution was to boost q, P_pi, and P_m to the frame where the proton was at rest, and then calculate nu, thetapq and phipq in this new frame. I checked many parts of my work, but among the checks were that various invariants were the same before and after the boost. Also, there was no change in the nu, thetapq and phipq for hydrogen targets.

It was found that the boosted quantities could change by large amounts! (See below)

To make the boost to the new frame, I needed the virtual proton velocity. This is calculated as follows:

momentum = pfer, or, P_m
M^*_{A-1} = M_A - M_p + E_m
energy = efer = M_A - sqrt[ (M^*_{A-1})^2 + pfer^2 ]
proton velocity = pfer/efer

Is this correct? For some reason, the virtual proton velocity can be greater than 1 (very rarely), but under these conditions, there is no way to do the boost to the frame where the proton is at rest! Notes:

efer is not E_m from the spectral function.
Another solution might be to use momentum = pfer and virtual proton mass = M_p and forget about efer (?!?)
Using pfer/efer is a correction used in the flux factor to correct for the motion of the proton, and there is no check to make sure that the velocity is not greater than 1 (!)

Here are some results for carbon at Q2=1.1 GeV2. Thetapq was calculated before and after the boost, and is printed side-by-side. The same was then done for phipq and then nu. This was just one Monte Carlo particle. Other particles are then listed below.

VARIABLE BEFORE AFTER

thetapq 6.072335294338550E-002 4.858364088528884E-002
phipq    2.65745279147250 2.61981003145746
nu       2.94538349956946 3.51153916316651

thetapq 9.928626563773456E-003 7.820363241004024E-003
phipq    0.541918894784569 3.08381936579284
nu       2.92441198166300 2.40819195109334

thetapq 4.438411519833172E-002 4.120584720126879E-002
phipq    1.04757180339921 0.818073266117937
nu       2.86525463730085 3.14522661680204

thetapq 6.192974104221763E-002 4.440285582729206E-002
phipq    3.75743031385741 3.63776246592981
nu       2.99029529930342 4.13700466646847

thetapq 1.810345956823101E-002 1.317909938582621E-002
phipq    3.29413618414512 3.97702873628008
nu       2.82411901502650 3.02282755716168

thetapq 4.083450311819703E-002 5.085725381298543E-002
phipq    5.30585866709761 5.22421150397362
nu       2.70690245324035 2.32128441339374

thetapq 3.737150589481579E-002 2.993158028778295E-002
phipq    5.16026069521372 4.67332421893457
nu       2.68401218992335 2.75088086146345

New event.f with the changes to boost nu, thetapq and phipq to the frame where the proton is stationary (Search for 5/5/06 in the file).