Optimization of f exclusion cut for the Q+ and L(1520) analysis Takashi NakanoBased on Draft version of Technical Note 42

What are the optimization criteria?Large signal acceptanceGood S/N ratioNo bias, no kinematical reflection

Photon energy in rest frame of the struck nucleon,

MKK (GeV)a)b)c)Eg (GeV)MKK (GeV)MKK (GeV)Eg (GeV)Eg (GeV)KK invariant mass distribution vs. photon energy: a) for a proton target, b) for a deuteron target in respect to the lab photon energy, and c) for a proton target in respect to the reconstructed photon energy in the nucleon rest frame.

MKK (GeV)MKK (GeV)MKK (GeV)MNK (GeV)MNK (GeV)MNK (GeV)a))) MKK vs. MNK for non-resonant events (MC) at = 2 GeV (a), 2.2 GeV (b), and 2.4 GeV (c).f exclusion cut point must be as close to the f peak as possible in the low energy region.

Eg (GeV)a)b)Eg (GeV)MnK+ (GeV)MnK+ (GeV)Rejection of f exclusion cut can be refined by using Eg in the nucleon frame. f exclusion can be tight in the high energy regionEg in nrest frameEg in lab frame

Optimization procedureconsistency check in the wide parameter region is very important

Eg (GeV)MKK (GeV)Mibes f exclusion cutCut was designed to keep N(f)/N(f) constant (energy independent).Signal acceptance nor the S/N ratio was not optimized. The cut line is almost linear in the energy region above 2.2 GeV.The acceptance for 2-track KK events was about 14 %.

Definition of cut parametersslopeoffsetMKK> slope(Eg-2.0) + offsetoffsetslopeThe slope parameter was changed from 0 to 0.15.The acceptance was kept at 15% for 2-track KK events.Other conditions with Acc=13% and 17% were also tested.Cuts with two lines were also tested.

ACC = 15 %

NSPeak fittingSpectrum is fitted with a gaussian + linear background.Significance is calculated from the peak height (S) divided by its error.Signal to noise ratio (S/N) is defined at the peak position.Background level (N or BG) is defined at the peak position.

Fitting result: L(1520)in this 2x2 presentation, a fitted line is not correctly drawn.PAWs bug? But the quality of the actual fit was fine!

Significance and S/N: L(1520)Both significance and S/N are the highest at slope=0.09

Fitting result: Q+

Significance and S/N: Q+Both significance and S/N are the highest at slope=0.09

The best cutEg (GeV)MKK (GeV)significance: 6.83S/N: 1.38

Peak height and BG level

Check by LH2 data analysisnarrower peakless backgroundless affected by change of BG level and shape.

Yield and BG ratios Both peak height and BG level ratios are stable against change of the cut parameters. The yield ratio of Q+ to L(1520) is0.5 x 0.5 x (11/16) = 0.17yield ratiobackground ratio

Changing the slopeThe best fitting result was obtained with slope=0.09 and offset=1.02.Now, anchor the offset at 1.02 and change the slope parameter from 0 to 0.15.Signal acceptance is bigger for smaller slope.Background level (mainly due to f) is bigger for smaller slope.

Fitting result: L(1520)

Fitting result: Q+

Peak heights of L(1520) and Q+L*Q+BGPeak heights become lower with a smaller value of the slope parameter.Note: acceptance should not decrease

Check by LH2 data analysisLH2LD2slope=0.02L(1520) yield does not drop at small slope for LH2.

Effect of f backgroundABCDA slope=0.09B slope=0.02-0.09 (f MC)C slope=0.02D A+BSharp rise of the f BG around 1.55 GeV dilutes the signal peak structure.

f BG subtraction at slope=0.04Peak structure with a correct magnitude was reproduced by subtracting f contributions.

f BG subtraction at slope=0.02

Changing the low energy limitThe low energy limit was varied from 2.0 to 1.9 GeV.The f exclusion cut parameters were kept at slope=0.09 and offset=1.02.Signal acceptance is bigger for a smaller energy limit.Background level (mainly due to f) is bigger for a smaller energy limit.

Fitting results: Q+

Pmin Cut dependence for Elimit=1.9 and 2.0 GeVElimit=1.9 GeVElimit=2.0 GeVTotal # ofevents(normalized)Q+ yield saturates in the large Pmin region for Elimit=2.0 GeV, but it gradually increases for Elimit=1.9 GeV, which is almost proportional to the total number of the events.

Comparison of Fermi motion corrected and uncorrected spectra at Elimit=2.0 GeVDifference is about 20 counts at the center of the peak, 2/3 of the peak height.- consistent with MC study

Comparison of Fermi motion corrected and uncorrected spectra at Elimit=1.9 GeVreal dataMC(f)

Difference between Fermi motion corrected and uncorrected spectraReal dataMC (f) (not normalized)About 1/3 of the excess can be due to f BG. Need refined MC study to improve the accuracy.

f BG subtraction at Elimit=1.9 and 2.0 GeV The peak height dropped from 46 to 31 for Elimit=1.9.The peak height is stable (29 to 28) for Elimt = 2.0.To get the cross-section below 2.0 Gev, we need a refined MC study.

Comparison of peak heightsElimit dependence

3 track events3-track (a proton track in addition to a kaon pair) is a clear indication that the struck nucleon is a proton.

no ntrk cutntrk=2variationL(1520) LH247.043.3-8%L(1520) LD254.649.9-9%Q+29.329.7+1%BG L(1520)30.829.0-6%BG Q+22.721.5-5%

SummaryThe f exclusion cut was optimized by keeping the cut acceptance constant and maximizing the L(1520) significance and S/N ratio.The both significance and S/N ratio for the Q+ peak was turned out be maximum with the same cut.The heights and BG levels depend on the cut parameters very similarly for L(1520) and Q+.The yield ratio is about 0.17.The effects of f contamination was studied: The background dilutes the signal peaks in the high energy region and causes a possible kinematical reflection in the low energy region. The effects can be simulated, but need more refined study to make it quantitative. Q+ events seems to come from a neutron.

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