Idea
B(inivisible)/B(normalization)={N(upper limit)/efficiency(invisible)}/{N(normalization)/efficiency(normalization)} * {1/(1-sigma)}
- B(inivisible): branching ratio of the invisible decay
- B(normalization): branching ratio of the reference channel
- N(upper limit): upper limit of the yield of the invisible decay
- N(normalization): yield of the reference channel
- efficiency(invisible): acceptance of the invisible decay
- efficiency(normalization): acceptance of the reference channel
- sigma: systematic uncertainty
What applies here:
The channel we are using is : gamma p -> p eta_prime -> p pi+ pi－ （eta). The invisible decay of eta is eta -> xx. x is something like U boson, which could be dark photon or heavy photon.
B(normalization) is 1 when we obtain eta by requiring the missing mass.
efficiency(invisible)=efficiency(normalization) * efficiency (invisible decay of eta). efficiency(normalization) is the detection efficiency of p pi+ pi-. efficiency(invisible) is the product of efficiency(normalizaiton) and efficiency(invisible decay of eta). efficiency(invisible decay) is the detection efficiency of at least one photon from eta decay.
photon detection efficeincy
procedure
- collection events of p, pi+, pi- and one or two photons
- requiring the missing mass of p pi+ pi- to be pi0
- requiring the missing mass of p to be eta or omega
- events passing the above three conditions are called "all" events
- two-photon events are called "good" events
-
- the ratio of "good" events to "all" events is the detection efficiency of photon
- the ratio is binned in energy, theta, and phi angle in lab frame
result
Error creating thumbnail: File missing efficiency of photon in cosine theta vs. phi |
Error creating thumbnail: File missing efficency of photon in momentum vs. phi after selection cosine theta between 0.7 and 0.98 |
Eta acceptance
File:Eta efficiency.pdf
partial statistics
The following is from 2% of the data.
Different efficiency
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Compare expected and no-photon detected
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance with acceptance larger than 0.5 |
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance for all events |
Error creating thumbnail: File missing Ratio of the events of no photon detected to all events (red) and expected events to all events (blue) |
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance for all events with PART bank |
Error creating thumbnail: File missing Ratio of the events of no photon detected to all events (red) and expected events to all events (blue) with PART bank |
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance larger than 50% with PART bank |
Error creating thumbnail: File missing Ratio of the events of no photon detected (red) and expected events (blue) to acceptance larger than 50% with PART bank |
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance for all events with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Ratio of the events of no photon detected to all events (red) and expected events to all events (blue) with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance larger than 50% with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Ratio of the events of no photon detected (red) and expected events (blue) to acceptance larger than 50% with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Study of the difference
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance for all events with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Ratio of the events of no photon detected to all events (red) and expected events to all events (blue) with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance larger than 50% with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Ratio of the events of no photon detected (red) and expected events (blue) to acceptance larger than 50% with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance larger than 60% with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Ratio of the events of no photon detected (red) and expected events (blue) to acceptance larger than 60% with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Compare the events of no photon detected with expected from acceptance larger than 70% with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Error creating thumbnail: File missing Ratio of the events of no photon detected (red) and expected events (blue) to acceptance larger than 70% with PART bank and validating photon with missing mass squre between [-0.1,0.1] |
Three-pion acceptance is considered
File:First try study eta acceptance.pdf
File:Compare seen expected.pdf
File:Second try study eta acceptance.pdf
This results yield 3e-3 upper limit.
Compare events from CMU and JLab
First line is JLab data, second line is CMU kinfit result
run# event# proton.px py pz pip.px py pz pim.px py pz photon.eid photon.energy
43634 7520 -0.218356 0.252237 0.850728 0.219179 -0.719475 1.00864 0.099808 -0.17973 0.341651 23 3.75253
43634 7520 0.219289 -0.723163 1.01175 -0.22012 0.247369 0.848749 0.0987671 -0.179789 0.342487 23 3.76824
43634 14658 0.0711455 -0.20281 0.597634 -0.104869 0.152357 0.275508 -0.199497 -0.0941665 0.0464326 638 1.35182
43634 14658 0.0715849 -0.204999 0.602069 -0.105456 0.151199 0.276457 -0.199497 -0.094166 0.0464326 275 2.79164
43634 14953 0.176975 -0.487071 1.02445 -0.228198 -0.0155644 0.203839 0.176574 0.267612 0.14746 485 1.9536
43634 14953 0.178628 -0.490327 1.02955 -0.228806 -0.0163596 0.204688 0.177539 0.268025 0.149043 225 2.9897
Limited statistics with timing cut
timing cut at ± 1 ns
All statistics
Error creating thumbnail: File missing 50% efficiency;Red: no decay detected; Blue: expected |
Error creating thumbnail: File missing Difference between no decay detected and expected divided by all eta events of 50% efficiency |
No Kin Fit
Assign the Q value of each event
Assign Q value of each event according to the missing mass and missing mass of proton.
Error creating thumbnail: File missing Missing mass of proton vs. missing mass |
The events are separated into 9 groups according to the missing mass of proton between 0.9 and 1.8 GeV.
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 0.9 and 1.0 GeV |
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 1.0 and 1.1 GeV |
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 1.1 and 1.2 GeV |
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 1.2 and 1.3 GeV |
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 1.3 and 1.4 GeV |
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 1.4 and 1.5 GeV |
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 1.5 and 1.6 GeV |
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 1.6 and 1.7 GeV |
Error creating thumbnail: File missing Missing mass w/ missing mass of proton between 1.7 and 1.8 GeV |
The result after applying this value:
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Finer binning
The events are separated into 75 groups according to the missing mass of proton between 0.9 and 1.8 GeV and 12 MeV per group.
The fitting results are in fitting missing mass with p pi+ pi- detected only, and fitting missing mass with all events of eta included
Binning adjustment
The fitting itself looks good and the result from fitting is good too. The problem must come from the binning is too fine. Therefore, the number of binning changed from 75 to 30 for events with p pi+ pi- detected only.
fitting missing mass of eta with all events included (p pi+ pi- AT LEAST)
fitting missing mass of eta with p pi+ pi- detected Only
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Event-based Q value
Check the validity of Q value
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Accidental Photon
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Reference
arxiv:1209.2469
