Today's Progress 24. July. 2006

Energy loss correction and Kstop->PA TOF calculation for PA-PB-detected velocity for proton

Method

We modify the Iwasaki's LEPS energy-loss correction code originally prepared dedicated to E471 proton measurement to relevant form to E549. The Iwasaki's correction procedure after E549-dedicated modification is as follows:

0. Prepare the virtual setup, in which protons are transported, to be identical to the realistic one.

1. Reaction vertex (BLC-PDC detected), direction vector of proton motion (PDC-detected), and PAPB-detected TOF are inputted.

2. Simulate the proton emission with given generation point and direction vector of motion. Search for the momentum value by which inputted PAPB-TOF is reproduced within an accuracy. The momentum value is indeed the corrected momentum.

3. Simulate the TOF from the generation to PA with the corrected momentum.

Production of dummy data

In order to confirm tha proper work of the correction code, the E549 proton measurement is simulated by GEANT 3.21. The assumed virtual setup, which is identical to that on the correction code, is shown below.

Virtual setup for the dummy data production.

On the Monte-Carlo, we simulate

A. TOF from PA to PB,

B. TOF from the proton creation to PA,

and they are recorded with

C. Generation point (exact value),

D. Direction vector of proton motion (at the creation - i.e. exact value) ,

E. Momentum at the generation.

We generate proton events from 180 to 720 MeV/c with the uniform distribution on the unit sphere about the initial motion. Inputting A, C, and D, we get expectation values for B and E by the correction code (B' and E'). Comparing them to the exact ones, we can study the performance of the energy loss correction. The conditions of the Monte-Carlo are tablatted below.

Conditions for the dummy data sets.
	set 1	set 2	set 3/4
momentum range	180-720 (MeV/c)	180-720 (MeV/c)	180-720 (MeV/c)
momentum distribution	uniform	uniform	uniform
angler distribution	uniform on unit sphare	uniform on unit sphare	uniform on unit sphare
x/y generation point distribution	4.0 cm sigma Gaussian	4.0 cm sigma Gaussian	4.0 cm sigma Gaussian
z generation point distribution	uniform	uniform	uniform
multiple scattering	on(Moliere)	on(Moliere)	on(Moliere)
energy loss straggling	on(Gauss/Landau/Vavilov)	on(Gauss/Landau/Vavilov)	on(Vavilov)
PA resolution	0 psec	60 psec (Gaussian responce)	0/60 psec
PB resolution	0 psec	80 psec (Gaussian responce)	0/80 psec
software	GEANT 3.21	GEANT 3.21	LEPS(g77 compilation)

Performance study

Here we compare the performance of the correction code for the dummy data sets described above. For a certain fraction of the events, the correction is not feasible, by following reasons:

1. No PB hit on the correction due to the absence of the multiple scattering process (2.6 %),

2. No PA hit on the correction due to the absence of the multiple scattering process (0.7 %),

3. Large angle scattering inside the target system on the dummy data (0.03 %).

The resulting correction efficiency was 96.6 % for the dummy data set 1.

Distribution of the momentum residual with 0 (black) and 60 + 80 psec (red) TOF resolution for 100,000 proton incident events on PAPB.

Correlation between momentum residual (horizontal) and exact momentum value at the generation (vertical) with 0 (top) and 60 + 80 psec (bottom) TOF resolution for 100,000 proton incident events on PAPB

Distribution of the residual of TOFA, with 0 (black) and 60 + 80 psec (red) TOF resolution for 100,000 proton incident events on PAPB.

Correlation between the residual of TOFA (horizontal) and exact momentum value at the generation (vertical) with 0 (top) and 60 + 80 psec (bottom) TOF resolution for 100,000 proton incident events on PAPB

Correlation between the residual of TOFA (horizontal) and x vertex (vertical) if proton are with positive x component of their direction vector. The top is when proton momentum at the generation is more than 500 MeV/c, while the bottom is less than 400 MeV/c .

Substantial deviation was found for lower momentum side, especially penetrating larger amount of material. For the event over 500 MeV/c, systematic difference is around 2 ~ 3 psec, which is accurate enough. The origin of the difference may be attributed to the difference of the behaviour of the simulaters (LEPS and GEANT3.21) for the low-momentum region. To confirm the hypothesis, data set 3 has been produced and now examined.

Saying conclusion firstly, energy-loss correction works completely for LEPS-originated dummy data .

Correlation between momentum residual (horizontal) and exact momentum value at the generation (vertical) with 0 psec TOF resolution for 100,000 proton incident events on PAPB. Dummy data set 3 was used.

Correlation between the residual of TOFA (horizontal) and exact momentum value at the generation with 0 psec TOF resolution for 100,000 proton incident events on PAPB. Dummy data set 3 was used.

Correlation between the residual of TOFA (horizontal) and x vertex (vertical) if proton are with positive x component of their direction vector. The top is when proton momentum at the generation is more than 500 MeV/c, while the bottom is less than 400 MeV/c . Dummy data set 3 was used.

Distribution of the residual of TOFA, with 0 (black) and 60 + 80 psec (red) TOF resolution for 100,000 proton incident events on PAPB. Dummy data set 3/4 were used.

Missing mass/momentum resolution as the function of missing mass/momentum

The resolution is defined by the Gaussian sigma value to fit the obtained momentum/missing mass residuals,

Delta p = p_gen_calc - p_gen ,

and

Delta M = M(p_gen_calc) - M(p_gen) ,

where M(p) is the missing mass expression as the function of proton momentum. The resulting momentum/missing mass resolution with 0/100 psec TOF resolution is shown below. It is dominated by the statistical future of the energy loss up to 400 MeV/c, while it is dominated by the TOF uncertainty at the region over 450 MeV/c. The broadenning of the TOFsec is ~ 20psec by sigma for proton with 1/beta smaller than ~ 2.0 .