Today's Progress 9. June. 2006

PA-NT TOF analysis with (K^+, X)

NT slewing correction with NT-PA TOF

Since we have already performed the PA-PB analysis for (K^+, X), PA-NT analysis for (K^+, X) can be performed extremely easily, because:

We have sophisticated PA slewing functions and offsets,

Kmu2 selection is very easily done with high-resolution PA-PB-detected velocity with 100% coverage,

Hence we do not need to iterate the procedure.

However, substantial correlation between z-vs-time residual was found, as shown below. Therefore, we do need to invoke Eta-term in segment-dependent way.

Time-residual vs z correlation

z (cm unit, vertical)-vs-time residual (nsec), i.e. Tnt - Tpa -TOFmu, for Kmu2 events selected by beta-inverse measuered by PA-PB. PA slewing correction factors are fixed by those obtained with PB. The layer increase from left to light, namely, top->1,2,3,4 bottom -> 5,6,7 from left to right. Significant z-correlation is found. Note that NT slewing correction is not done at this stage (we do not know how to do that).

Larm row 1

Larm row 2

Larm row 3

Larm row 4

Larm row 5

Larm row 6

Larm row 7

Larm row 8

Rarm row 1

Rarm row 2

Rarm row 3

Rarm row 4

Rarm row 5

Rarm row 6

Rarm row 7

Rarm row 8

Procedure of NT slewing correction

Below, the correction process is exhibitted step-by-step. Now, the definition of NT-detected-time, Tnt, is

Tnt = (Tu+Td)/2 - f(sqrt(phu*phd))*g(xi) - h(eta) + offset.

Note that this is an assumption, at least at the moment. The validity can be confirmed only with the result from the formulation. Then, we find

f(x): Energy term,

g(x): xi term (y on NT),

h(x): eta term (z on NT),

offset: NT offset with respect to PA wall,

in order to tune Tnt to be

Tnt = Tpa + TOFkmu2,

with Kmu2 decay events tagged by PAPB-detected inverse velocity. Note that Tpa is fixed with those obtained by PAPB analysis.

Event selection with PA-PB TOF

Energy vs time residual correlation and its fit with a 3rd order polinomial

Xi vs time residual correlation after energy correlation removal

Eta vs time residual correlation after energy correlation removal

Determination of Xi/Eta correcation term after energy correlation removal

Correlation between sqrt(phu*phd) and time residual after the overall correction

Correlation between Top-bottom time difference and PDC-measured y position

We, however, cannot study the NC behavior at the high-energy-deposit region, as is for PB. It will be checked T0-NC, with (K^-,gamma) data. Here, we just go ahead, adopting the new slewing correction procedure. It is also important to obtain the conversion function from time difference to y position for the future (K^-, n) analysis. It will be also performed here.

Results

row-by-row inverse beta spectrum for stopped K^+ on 4He events are shown below.

L row 1

L row 2

L row 3

L row 4

L row 5

L row 6

L row 7

L row 8

R row 1

R row 2

R row 3

R row 4

R row 5

R row 6

R row 7

R row 8

It is very important whether strange correlation remains after the correction. Hence, we check the correlation between 1/beta and i)NT-related variables and ii) PA-related variables as follows:

Below, all results are tabulatted.

Result of slewing correction for NT segments obtained with NT-PA TOF analysis. "Order" is the order of the polinomial to fit the 1/sqrt(phu*phr) correlation, and "fit region" is the 1/sqrt(phu*phd) region used for the global fit. Time / 1/beta resolution is defined as the time-residual / 1/beta width for Kmu2 events selected by PAPB-detected 1/beta value. Position resolution is defined by the width of the position residual of the f(t) - y(PDC). Here, f(t) is defined as a linear function to fit the y(PDC) VS top-bottom time difference correlation.
NT arm	Layer	Row	Order/fit region	Time / 1/beta Resolution (psec/-)	Position Resolution (cm)	Light velocity (cm/nsec)	Used/Total Event Number
L	1	1	3/0.041-0.174	129.6/0.0213	2.79/3.69	14.6	31809/51740
L	2	1	3/0.051-0.189	125.9/0.0200	2.75/3.65	14.7	31533/48712
L	3	1	3/0.061-0.199	134.0/0.0206	2.88/3.70	14.7	31015/46319
L	4	1	3/0.051-0.199	134.3/0.0199	3.13/3.84	15.1	30419/43844
L	5	1	3/0.051-0.184	143.6/0.0206	3.41/4.05	15.1	29318/40597
L	6	1	3/0.061-0.189	137.1/0.0191	3.48/4.45	14.9	28698/34340
L	7	1	3/0.051-0.199	151.2/0.0205	3.86/4.74	15.2	28032/32822
L	1	2	3/0.041-0.189	125.2/0.0212	2.67/3.48	14.6	42607/68338
L	2	2	3/0.036-0.184	131.9/0.0214	2.73/3.52	14.6	40824/62176
L	3	2	3/0.041-0.199	133.6/0.0201	2.81/3.65	15.0	39253/57825
L	4	2	3/0.061-0.199	142.8/0.0216	3.19/3.95	15.2	37338/53125
L	5	2	3/0.051-0.179	141.3/0.0207	3.29/4.02	15.0	35344/48534
L	6	2	3/0.051-0.179	135.5/0.0192	3.44/4.39	15.1	33727/40208
L	7	2	3/0.051-0.199	142.6/0.0196	3.98/4.80	15.4	32186/37226
L	1	3	3/0.036-0.184	124.9/0.0216	2.56/3.44	14.5	46146/73716
L	2	3	3/0.036-0.199	121.8/0.0203	2.57/3.41	14.6	43636/66175
L	3	3	3/0.041-0.199	134.4/0.0215	2.86/3.68	14.9	41362/60904
L	4	3	3/0.041-0.184	140.3/0.0216	3.04/3.80	15.1	39155/55786
L	5	3	3/0.061-0.179	131.7/0.0196	3.15/3.91	15.0	36973/50730
L	6	3	3/0.051-0.169	132.1/0.0190	3.45/4.34	15.0	35193/42057
L	7	3	3/0.051-0.199	145.7/0.0203	3.86/4.61	15.6	33557/38639
L	1	4	3/0.041-0.179	129.6/0.0225	2.78/3.60	14.5	46628/74017
L	2	4	3/0.036-0.199	132.0/0.0220	2.75/3.66	14.6	43982/66217
L	3	4	3/0.036-0.199	127.2/0.0205	2.75/3.65	14.9	41738/60872
L	4	4	3/0.036-0.199	145.5/0.0226	3.04/3.87	15.2	39657/56075
L	5	4	3/0.041-0.164	132.0/0.0197	3.17/3.94	15.1	37384/50952
L	6	4	3/0.061-0.179	135.2/0.0195	3.42/4.58	15.0	35390/42282
L	7	4	3/0.056-0.199	129.2/0.0181	3.77/4.64	15.6	33728/38673
L	1	5	3/0.036-0.194	137.5/0.0239	2.60/3.49	14.6	46865/74185
L	2	5	3/0.036-0.199	129.0/0.0215	2.57/3.38	14.7	44349/66520
L	3	5	3/0.031-0.199	128.7/0.0208	2.68/3.51	14.9	42016/61069
L	4	5	3/0.041-0.199	141.6/0.0219	3.10/3.87	15.3	39623/56015
L	5	5	3/0.046-0.169	130.1/0.0195	3.16/4.06	15.0	37386/51087
L	6	5	3/0.046-0.174	125.2/0.0181	3.36/4.32	15.1	35424/42463
L	7	5	3/0.046-0.194	132.9/0.0186	3.71/4.57	15.5	33614/38653
L	1	6	3/0.036-0.179	123.2/0.0212	2.51/3.46	14.6	44916/70849
L	2	6	3/0.031-0.189	126.3/0.0209	2.59/3.41	14.7	42578/63856
L	3	6	3/0.036-0.199	126.7/0.0202	2.73/3.54	15.0	40561/58946
L	4	6	3/0.041-0.199	129.1/0.0198	2.95/3.83	15.2	38604/54407
L	5	6	3/0.061-0.184	136.1/0.0202	3.24/4.06	15.0	36615/49976
L	6	6	3/0.061-0.179	132.4/0.0190	3.42/4.44	15.0	34874/41536
L	7	6	3/0.056-0.189	131.5/0.0183	3.64/4.47	15.3	33205/37925
L	1	7	3/0.036-0.184	134.6/0.0228	2.65/3.58	14.5	34154/53303
L	2	7	3/0.036-0.184	142.9/0.0233	2.62/3.53	14.5	33468/49418
L	3	7	3/0.036-0.199	153.0/0.0241	2.72/3.59	14.9	32709/46837
L	4	7	3/0.031-0.199	158.6/0.0240	2.99/3.77	15.1	31471/43902
L	5	7	3/0.041-0.179	143.0/0.0210	3.28/4.04	15.1	30150/40776
L	6	7	3/0.041-0.179	146.6/0.0208	3.71/4.51	15.2	29063/34293
L	7	7	3/0.041-0.199	142.8/0.0196	3.96/4.80	15.4	28015/31902
L	1	8	3/0.036-0.164	152.3/0.0250	2.69/3.57	14.6	21674/33930
L	2	8	3/0.036-0.169	146.5/0.0232	2.83/3.64	14.5	21813/32521
L	3	8	3/0.056-0.199	178.2/0.0273	2.80/3.59	14.9	21973/31757
L	4	8	3/0.056-0.199	168.1/0.0249	3.16/3.82	15.3	21722/30445
L	5	8	3/0.036-0.174	154.2/0.0221	3.34/4.01	14.9	21257/28850
L	6	8	3/0.041-0.179	159.2/0.0221	3.54/4.43	15.1	21028/24813
L	7	8	3/0.041-0.199	171.5/0.0232	3.97/4.73	15.3	20827/23867
R	1	1	3/0.041-0.199	214.6/0.0349	3.53/4.33	14.8	31852/50192
R	2	1	3/0.036-0.199	188.8/0.0296	3.29/4.05	14.9	31444/47110
R	3	1	3/0/036-0.199	145.3/0.0222	2.85/3.72	14.9	30881/44806
R	4	1	3/0.041-0.199	145.7/0.0215	3.16/3.94	15.2	30151/42247
R	5	1	3/0.041-0.199	154.3/0.0221	3.42/4.17	15.3	29625/39849
R	6	1	3/0.061-0.189	162.2/0.0226	3.59/4.72	15.4	28985/33742
R	7	1	3/0.051-0.199	160.1/0.0216	4.07/4.98	15.5	28119/31182
R	1	2	3/0.041-0.199	212.0/0.0355	4.89/4.93	14.4	43484/67759
R	2	2	3/0.036-0.199	177.3/0.0287	4.07/4.44	14.9	41839/61758
R	3	2	3/0.041-0.189	138.2/0.0217	3.03/4.05	14.5	39786/56543
R	4	2	3/0.041-0.199	137.0/0.0208	3.03/3.86	15.2	38214/52634
R	5	2	3/0.041-0.199	148.0/0.0216	3.30/4.09	15.2	36473/48496
R	6	2	3/0.041-0.199	143.7/0.0204	3.59/4.75	15.4	34788/40141
R	7	2	3/0.046-0.199	147.0/0.0202	4.01/4.98	15.6	33140/36983
R	1	3	3/0.041-0.199	166.7/0.0286	3.39/4.06	14.7	47976/74307
R	2	3	3/0.041-0.199	195.2/0.0319	3.72/4.36	14.9	45251/66594
R	3	3	3/0.036-0.199	116.4/0.0186	2.80/3.62	15.0	42644/60756
R	4	3	3/0.041-0.199	125.9/0.0194	3.02/3.86	15.1	40319/55552
R	5	3	3/0.036-0.199	120.3/0.0179	3.21/4.16	15.5	38161/50648
R	6	3	3/0.061-0.199	130.0/0.0186	3.49/4.57	15.4	36199/42152
R	7	3	3/0.056-0.199	132.2/0.0184	3.73/4.99	15.2	34320/38329
R	1	4	3/0.041-0.199	169.8/0.0295	3.16/3.99	14.8	48564/75210
R	2	4	3/0.041-0.199	159.5/0.0267	3.08/3.90	14.9	45829/67333
R	3	4	3/0.041-0.199	121.8/0.0196	2.85/3.68	14.8	43212/61321
R	4	4	3/0.061-0.199	144.2/0.0224	3.02/3.93	15.2	40997/56628
R	5	4	1/0.041-0.199	120.9/0.0181	3.00/3.85	15.3	38709/51510
R	6	4	3/0.061-0.199	128.1/0.0185	3.28/4.58	15.4	36647/42907
R	7	4	3/0.056-0.199	135.7/0.0190	3.87/4.95	15.7	34691/38730
R	1	5	3/0.041-0.199	203.0/0.0351	3.39/4.14	14.8	49247/76124
R	2	5	3/0.041-0.199	203.5/0.0337	3.25/4.02	15.2	46270/67782
R	3	5	3/0.036-0.199	129.7/0.0209	2.62/3.55	15.0	43604/61854
R	4	5	3/0.041-0.199	132.8/0.0206	2.86/3.79	15.3	41214/56835
R	5	5	3/0.061-0.199	127.8/0.0191	3.00/3.89	15.4	38911/51973
R	6	5	3/0.051-0.199	136.2/0.0197	3.26/4.53	15.6	36975/43657
R	7	5	3/0.056-0.199	133.5/0.0187	3.53/4.75	15.6	34982/39264
R	1	6	3/0.036-0.199	198.0/0.0339	3.17/4.00	14.7	48352/74211
R	2	6	3/0.036-0.199	177.7/0.0294	3.18/3.97	14.8	45873/66568
R	3	6	3/0.041-0.199	124.4/0.0199	2.95/3.78	14.9	43200/60683
R	4	6	3/0.041-0.199	124.5/0.0192	2.94/3.85	15.3	41214/56307
R	5	6	3/0.041-0.199	121.5/0.0181	3.09/4.02	15.4	39278/51907
R	6	6	3/0.041-0.199	121.7/0.0176	3.36/4.48	15.4	37212/43191
R	7	6	3/0.041-0.199	135.5/0.0189	3.78/5.11	15.5	35543/39331
R	1	7	3/0.036-0.199	183.4/0.0309	3.07/3.87	14.9	37879/58817
R	2	7	3/0.036-0.189	130.1/0.0213	2.54/3.50	14.9	36128/53105
R	3	7	3/0.036-0.199	134.1/0.0212	2.64/3.59	15.0	35413/50146
R	4	7	3/0.041-0.199	135.2/0.0206	2.88/3.76	15.3	34062/46781
R	5	7	3/0.036-0.199	136.8/0.0201	3.23/4.12	15.4	32752/43803
R	6	7	3/0.041-0.199	145.8/0.0207	3.63/4.71	15.3	31377/46835
R	7	7	3/0.046-0.199	133.3/0.0184	3.83/4.91	15.3	30111/33959
R	1	8	3/0.041-0.199	222.0/0.0366	3.61/4.41	14.8	24535/38521
R	2	8	3/0.041-0.199	193.6/0.0307	3.26/3.97	14.9	24067/36089
R	3	8	3/0.036-0.164	165.4/0.0257	3.08/3.82	14.8	23387/34157
R	4	8	3/0.041-0.199	140.0/0.0209	3.10/3.84	15.2	23306/33051
R	5	8	3/0.036-0.199	141.2/0.0203	3.28/3.96	15.2	23010/31613
R	6	8	3/0.061-0.199	146.6/0.0205	3.46/4.31	15.3	22593/27149
R	7	8	3/0.061-0.199	172.5/0.0233	3.83/4.51	15.3	22242/25787

Segment-by-segment PA-NT TOF resolution

Segment-by-segment position resolution

Resulting NTsegemnt-by-segment correlations between inverse beta and NT/PA-related quantities

Here, correlations between inverse beta and NT/PA-related quantities are exhibitted, for NT Larm 1st row 1st layer segment as an example. For all 112 segments, same correlations are checked as the minimum requirement.

sqrt(phu*phd) on NT vs 1/beta

PDC-detected y on NT vs 1/beta

PDC-detected z on NT vs 1/beta

PDC-detected direction cos y vs 1/beta

PDC-detected direction cos z vs 1/beta

sqrt(phu*phd) on PA vs 1/beta

PDC-detected y on PA vs 1/beta

PDC-detected z on PA vs 1/beta