2pi

Results with the new multi-pion cut 07/25/06

The multi-pion cut was placed at the point where the contribution from multi-pion events were not more than 3% (1.5% for deuterium). The uncertainties due to the multi-pion contribution are approximately
copper 0.86 %
carbon 0.53 %
deuterium 1.0 %
gold 0.64 %
dummy 0.5 %
These numbers are based on the observed variation in Y_2pi/Y_1pi when no missing mass cuts were used (data file). Mostly the fitting of the multi-pion contribution was ok, however, there was some problems at low Q2. See, for example the plots below for the gold target. The variable plotted is the nuclear missing mass. Fortunately, the statistics are not a problem for the low Q2 settings, and the cut was placed at 183.57. This was based on the point where there is very close to zero contribution from multi-pion events.

Plots for all targets and missing mass variables are here

The yields in the single pion simulation were multiplied by (Y_2pi+Y_1pi)/Y_1pi in the calculation of the nuclear transparency. The results using nucleon missing mass cuts are on the LHS in the plots below, while the results using nuclear missing mass cuts are on the RHS. The error bars are the statistical uncertainty. The aluminum results using the nucleon cut (LHS) needed to be analyzed with the same cuts used for the LH2 and LD2 targets for proper dummy target subtraction, and had significantly larger multi-pion contributions than 3%.

Full results
Results with old missing mass cuts

***** PREVIOUS WORK ********

Simulation of multi-pion production 07/21/06

Multi-pion production code was written for SIMC. One must be careful to increase the hadron generation windows (in the infiles) when using this code, as will be described below.

There is no physics describing the cross section as a function of the multi-pion kinematics.

The code (here) was put at the end of generate() in event.f. After the single pion event has been generated and radiated in event.f, the kinematics are stored in the "orig" record. I modify the orig record with multi-pion production just before the single-arm monte carlo is called.

The nucleon where the multi-pion production takes place is given random
Fermi motion.

The outgoing pion from the multi-pion production is generated uniformly
over the acceptance.

The missing mass of the recoiling nucleon plus undetected pion(s) is
calculated and the event is thrown away if the missing mass is below the
threshold of 2-pi production.

A larger generation window is needed because the pion produced from the quasifree reaction does not need to be close to the acceptance of the spectrometers. This is because the multi-pion production can scatter the event into the acceptance. I found that approximately doubling all of the acceptance edges in the infiles increases the multipion yield, but does not change the missing mass distribution significantly. The missing mass distributions shifted slightly to larger missing mass.

The simulation with the larger generation window required much more time, and so was run with less generated particles. This does not, however, affect the normalization mentioned earlier, as the histograms were normalized by the number of generated particles.
Multi-pion simulation plots

Next the missing mass histograms from the multi-pion simulation were added to the missing mass histograms from the single-pion simulation. The multi-pion contribution was given an arbitrary normalization to match the data, and was adjusted independently at each Q2. The results for carbon at all Q2 are shown in the plots below.

As the multi-pion yields change with the widths of the generation windows, the normalization assigned to the multi-pion contribution has no physical significance. However, the yield from the multi-pion events was divided by the yield from the single-pion events, and the ratio was very flat with Q2:

 4acarbon  Q2=1.1   Y2pi/Y1pi=0.135985
 1acarbon  Q2=2.15  Y2pi/Y1pi=0.176651
 3acarbon  Q2=3     Y2pi/Y1pi=0.20212
 8acarbon  Q2=4     Y2pi/Y1pi=0.164774
 7acarbon  Q2=4.8   Y2pi/Y1pi=0.170575

CARBON, NUCLEON MISSING MASS, RED=DATA, BLUE=SINGLE PION SIMC, BLACK=MULTI-PION

CARBON, NUCLEAR MISSING MASS, RED=DATA, BLUE=SINGLE PION SIMC, BLACK=MULTI-PION

The same plots for the W vs.kpi and low epsilon settings are below
Nuclear missing mass
Nucleon missing mass

Estimate of multi-pion production 07/16/06

The contribution from multi-pion prodction was estimated using the data at Q2=1.1 GeV2. This is shown in the plots of missing mass (GeV) below. The data histogram (red) was subtracted from the SIMC histogram (blue) in the first plot. The bump in the data near missing mass=11.45 GeV was assumed to be the multi-pion contribution. The histogram showing the bin-by-bin subtracted histogram is shown in the second plot (red). The green histogram that is superimposed is set to zero below the double-pion threshold.

CARBON, MISSMASS (GeV), Q2=1.1 GeV2

The green histogram is assumed to be the contribution from multi-pion events at low Q2. This distribution is assumed to have a Q^-4 dependence. The green histogram was scaled by Q^-4 and then added to SIMC at higher Q2. This is shown in the plots below.

CARBON, MISSMASS (GeV), Q2>1.1 GeV2, RED=DATA, BLUE=SIMC, BLACK=SIMC+MULTIPION

The same procedure was also performed for copper.

COPPER, MISSMASS (GeV), Q2=1.1 GeV2

COPPER, MISSMASS (GeV), Q2>1.1 GeV2, RED=DATA, BLUE=SIMC, BLACK=SIMC+MULTIPION