1. Studies of  + and  (1520) photoproductions [ TN46 and TN47 (will be released soon)] Norihito Muramatsu RCNP, Osaka University LEPS Collaboration Meeting in Taiwan, 1 May 2008

2. 4.2 Before/after inclusion of new ntag=1 So far, tagger reconstruction was updated twice by Kato. First a part of ntag=2 events was saved by tightening true tagger hit requirement, and statistics of K - p events was increased by 15.7% (11391  13179 events). Then, a part of ntag.ge.3 events was further saved, and the statistics was increased by 2.4% (13179  13495 events), which resulted in18.5% increase in total. Background spectra were simply scaled by these factors, and overlaid to the updated missing mass spectra as shown in Fig.16-18. Width of the  + peak got wider after inclusion of new ntag=1 events. E  resolution was slightly changed from 11.74 MeV to 12.69 MeV after the update of tagger reconstruction, but it is not large as the observations. (This resolution was re-smeared to the background spectra at the first update, and the individual back- ground was rescaled depending on small change of #events, which passed the same event selection.) Also, it was confirmed that this width change was not caused by the new photon energy calibration, simultaneously released by Kato. The increase of the statistics must have forced the peak width wider in direction of the mass resolution. Statistical significance was not so changed (rather increased a bit) by improving the tagger reconstruction as shown in Table 3. This is a signal-like behavior of the peak structure, and not likely a fluctuation. Table 3. Comparison of statistical significances depending on tagger reconstruction. old new1 new2 narrow gate S/sqrt(B)=4.75 S/sqrt(S+B)=4.15 S/sqrt(B)=5.04 S/sqrt(S+B)=4.41 S/sqrt(B)=5.24 S/sqrt(S+B)=4.57 wide gate S/sqrt(B)=3.18 S/sqrt(S+B)=2.97 S/sqrt(B)=3.49 S/sqrt(S+B)=3.25 S/sqrt(B)=4.15 S/sqrt(S+B)=3.83 2 Fig.16 MMd( ,K - p) spectrum in the  (1520) region of the LD 2 data with the original tagger reconstruction. Fig.17 MMd( ,K - p) spectrum in the  (1520) region of the LD 2 data with the first update of tagger reconstruction. Fig.18 MMd( ,K - p) spectrum in the  (1520) region of the LD 2 data with the second update of tagger reconstruction.

3. 3 After adopting the second update of tagger reconstruction, photon energy resolution was re-estimated to be 12.58 MeV with the same calculation method. (See Fig.28.) Since this value was consistent with the previous estimate, 12.69 MeV was retained to smear the resolution in the MC simulations. Photon energy resolution for original ntag=1 events and newly reconstructed events by the two updates were also measured to be 12.31 MeV and 13.41 MeV, respectively. (See Fig.29 -30.) Since the new events do not have too worse resolution, these events are kept in the analysis. Fig.28 Difference of tagger energy measurement from photon energy calculated by assuming MMp( ,K - p) gives K + mass in the LH 2 data, after the second update of tagger reconstruction. Fig.29 Same as Fig.28, but for events which were saved by the updated tagger reconstruction. Fig.30 Same as Fig.28, but for events which were retained from the original tagger reconstruction. 5.1 Photon energy resolution

4. 4.3 Dependence on gate width of  (1520) selection Table 4. Number of signal events and statistical significances depending on width of  selection cut. 1.51<M(K - p)<1.53 GeV/c 2 narrow gate: data= 238  15.4 bg= 164.4  2.7 sig= 73.6  15.7 s/sqrt(b)=5.74 s/sqrt(s+b)=4.77 wide gate : data= 415  20.4 bg= 327.1  3.9 sig= 87.9  20.7 s/sqrt(b)=4.86 s/sqrt(s+b)=4.32 1.50<M(K - p)<1.54 GeV/c 2 narrow gate: data= 364  19.1 bg= 276.9  3.6 sig= 87.1  19.4 s/sqrt(b)=5.24 s/sqrt(s+b)=4.57 wide gate : data= 653  25.6 bg= 555.2  5.2 sig= 97.8  26.1 s/sqrt(b)=4.15 s/sqrt(s+b)=3.83 1.47<M(K - p)<1.57 GeV/c 2 narrow gate: data= 721  26.9 bg= 567.0  5.4 sig=154.0  27.4 s/sqrt(b)=6.47 s/sqrt(s+b)=5.74 wide gate : data=1284  35.8 bg=1122.3  7.6 sig=161.7  36.6 s/sqrt(b)=4.83 s/sqrt(s+b)=4.51 1.42<M(K - p)<1.62 GeV/c 2 narrow gate: data=1127  33.6 bg= 954.1  7.1 sig=172.9  34.3 s/sqrt(b)=5.60 s/sqrt(s+b)=5.15 wide gate :data=2069  45.5 bg=1881.6  10.0 sig=187.4  46.6 s/sqrt(b)=4.32 s/sqrt(s+b)=4.12  10 MeV  20 MeV (standard)  50 MeV  100 MeV 4 Fig.19 Distribution of K - p missing mass from a deuteron depending on width of  (1520) selection cut in the LD 2 data.

5. Fig. 19 shows MMd( ,K - p) distributions depending on width of  (1520) selection cut. A clear peak at the  + mass was observed in all the mass spectra. Table 4 summarizes statistical significances of the 4 different conditions to select  (1520). 5.24 to 6.47 sigmas (4.15 to 4.86 sigmas) of enhancement was observed in the missing mass region of 1.520<MMd( ,K - p)<1.545 GeV/c 2 (1.510<MMd( ,K - p)<1.560 GeV/c 2 ). S/N ratio at the  + mass region was increased by tightening the  (1520) selection cut. Fig.20 shows M(K - p) distribution in case that 1.525<MMd( ,K - p)<1.540 GeV/c 2 is tagged in the LD 2 sample. It is clear that the  + photoproduction is associated with  (1520). Fig. 21 shows #signal / [width of  (1520) selection cut] as a function of the width. Solid line indicates relative number of events from quasi- free  (1520) photoproduction with the  (1520) selection cut indicated in x axis. The number of events were counted in the filtered sample of the K  (1520) MC, and normalized to the measurement at the standard  (1520) selection cut. Again,  (1520) association of the  + signals is clear. 5 Fig.20 K - p invariant mass distribution after tagging  + signal region in the LD 2 data. Background estimates are overlaid with the same selection cuts. Fig.21 Number of  + signals divided by width of  (1520) selection cut depending on the width. Data points correspond to four panels of Fig.19.

6. 4.4  + photoproduction in sidebands Table 5. Number of signal events and statistical significances in sidebands. Narrow gate: data=576  24.0 BG=479.1  5.1 signal=96.9  24.5 sig/sqrt(bg)=4.43 sig/sqrt(sig+bg)=4.04 Wide gate : data=1027  32.0 BG=937.8  7.2 signal=89.2  32.8 sig/sqrt(bg)=2.91 sig/sqrt(sig+bg)=2.78 Fig.24 MMd( ,K - p) spectrum in 1.450<M(K - p)<1.500 GeV/c 2 and 1.540<M(K - p)<1.590 GeV/c 2. This spectrum is the same as sum of Fig.22 and Fig.23. 6 Fig.25 Number of  + signals divided by M(K - p) mass range to count it. Two data points correspond to the standard  (1520) selection (Fig.14) and the sideband selection (Fig.24). A curve made from quasi-free K  (1520) MC was fitted to them.

7. 5.3 Unbinned fit to the  + mass spectrum Since usual  2 fitting to a binned histogram is affected by a way of binning incase of limited signal statistics, unbinned fit was adopted to examine the  + peak. The unbinned fit defines a probability density function with free parameters, and maximizes a product of the probability densities of individual events. A ‘RooFit’ package, which ran on ROOT and was prepared for BABAR experiment, was used to perform the unbinned fit. (Basic programming scheme for our purpose was prepared by Matsumura.) 7 Fig.33 Unbinned fit of a Voigt function to MMd( ,K - p) spectrum over the MC-based background estimate in the LD 2 data. Mass resolution was fixed in the Voigt function. Fig.34 Unbinned fit of a Gaussian function to MMd( ,K - p) spectrum over the MC-based background estimate in the LD 2 data.

8. 5.4 Probability to observe a peak with sigma=7.3 MeV 5.5 Probability to observe a 5.24 sigma peak Methods were updated, and number of toy MC trials were increased. Fig.35  distribution of unbinned Gaussian fits in 1000 toy MC simulations. The  got below 7.3 MeV (a vertical line) 121 times, which gave a probability of the downward fluctuation to be 12.1  0.7 %. 8 Fig.36 Distribution of statistical significances of the maximum fluctuation in 25 MeV mass window around the  + mass. Measurement was performed in 1,000,000 MC trials, and two trials exceeded 5.24 sigma, indicated by a vertical line.

9. 6. Measurement of differential cross sections 6.1 Luminosity Number of photons in LEP beam tagger counts w/ dead time correction depending on filling pattern, DAQ live time, upveto efficiency, and #photon normalization based on #proton/#photon ratio (See miho:/np1b/v01/mura/leps/ana/temp2/ngamma- [lld2/llh2]-corr-[mylist/missing].dat, which was made based on tables from Kohri / Sumihama and TN43.) LD 2 : 4.587*10 12, LH 2 : 2.803*10 12 w/ all the above corrections (LD 2 : 5.142*10 12, LH 2 : 3.205*10 12 w/o #photon normalization) (LD 2 : 5.01 *10 12, LH 2 : 3.13 *10 12 before the above corrections) transmission : 0.526  0.017(  0.007[stat]  0.016[sys]) (See ~sp8lep/HTMLpub/leps_notes/ana_meeting/2004may28/index.html.) ntag=1 prob. : LD 2 : 15954/19677=0.8108  0.0006, LH 2 : 5049/6127=0.8241  0.0011 Ratio of ntag(the newest reconstruction)=1 was measured by the real data samples selected with K - p detection, |ytof|>50 mm, vertex requirement, and 1.75<E  (calculated backwardly from K - p missing mass=M K+ )<2.40 GeV. tagger reconstruction eff. * Ratio of E  >1.75 GeV (See miho:/np1b/v01/mura/leps/ana/temp2/weightcc_ [ld2/llh2]_term*.20.1.50001, which were made based on tables from Sumihama.) LD 2 r24095-r24231: 0.780 (0.60*10 12 photons) + r24241-r24398:0.753 (0.43*10 12 photons) + r24443-r26338: 0.748 (3.99*10 12 photons) ---> weighted efficiency: 0.752 Note that there was a tagger SSD problem in r24241-r24398 and that this period was specially treated as described in the next section. LH 2 r23690-r24058: 0.792 (1.14*10 12 photons) + r25453-r25968: 0.747 (1.99*10 12 photons) ---> weighted efficiency: 0.763 -----> #photon(LD 2 ) = (1.471  0.049)*10 12, #photon(LH 2 ) = (0.927  0.030)*10 12 Number of target particles density LD 2 :0.169 g/cm 3, LH 2 :0.0708 g/cm 3 thickness: 16 cm due to pressure difference between target cell and vacuum (The information came from Kohri.) Avogadro number : 6.022*10 23 & mass number LD 2 : 2, LH 2 : 1 -----> #deuteron = 8.14 * 10 -13 /pb, #proton = 6.82 * 10 -13 /pb Luminosity (Its error is dominated by a systematic error of the transmission.) LD 2 : #photon * #deuteron = 1.197  0.040 /pb LH 2 : #photon * #proton = 0.632  0.020 /pb 9

10. 6.3 Differential cross section of  + photoproduction assuming a constant matrix element As shown in Fig.39, there is no acceptance of  + detection in case of K - p polar angle at  d-CMS greater than 35 . Therefore, differential cross section was measured in the polar angle region less than 35 . Table 6 summarizes number of signals and significance in this region. Number of signals in wide signal gate (1.51<MMd( ,K - p)<1.56 GeV/c 2 ) was used to calculate differential cross section because it covers 2  region of the expected mass resolution with some statistics: #signal(0-35 degree, wide gate) = 96.6  26.0 events & solid angle of 0-35 degree = 1.136 sr Acceptance was measured by generating  d   +  (1520) events flatly at  d-CMS. Energy dependence of the yield just followed a E  spectrum of backward Compton scattering of the multi-line UV laser. The event generation was done by G3LEPS with options of DCAY=1, HADR=1, LOSS=2, MULS=1, dc_eff.00009. (Note influence by a possible update of DC efficiency map is discussed in the next page.) Acc.(E  >1.75 GeV, 0-35 degree) = 0.04153  0.00075 As a result, differential cross section of  d  + K - p in 1.50<M(K - p)<1.54 GeV/c 2 was calculated to be: d  /d  (  d  + K - p) = 96.6  26.0 events / 0.04153  0.00075 / (1.197  0.040 /pb) / 1.136 sr = 1.71  0.46 nb/sr In case of assuming that most of the observed signals come from  d  +  (1520), total acceptance further includes acceptance of  (1520) resonance within 1.50-1.54 GeV/c 2, and branching ratio of  (1520)  K - p decay (0.225) must be also taken into account. Acc.(E  >1.75 GeV, 0-35 degree) = 0.03156  0.00059 Differential cross section of  d  +  (1520) was calculated to be: d  /d  (  d  +  * ) = 96.6  26.0 events / 0.03156  0.00059 / 0.225 / (1.197  0.040 /pb) / 1.136 sr = 10.00  2.72 nb/sr 10 Table 6. Number of signal events and statistical significances in K - p polar angle smaller than 35 degree at  d-CMS. Narrow gate: data = 362  19.0, BG = 275.1  3.6 signal =86.9  19.4 events sig/sqrt(bg) = 5.24, sig/sqrt(sig+bg) = 4.57 Wide gate: data = 647  25.4, BG = 550.4  5.1 signal = 96.6  26.0 events sig/sqrt(bg) = 4.12, sig/sqrt(sig+bg) = 3.80 Fig.39 MMd( ,K - p) spectra of the LD 2 data in K - p polar angle at  d-CMS smaller than 35 degree (upper panel) and larger than 35 degree (lower panel).

11. 6.4 Differential cross section of  + photoproduction assuming Titov’s theoretical prediction Instead of the isotropic generation of  d  +  *, another MC set following Titov’s theoretical differential cross section, shown in Fig.40, was generated to measure a variation of the acceptance. This measurement gives a hint of systematic error to the cross section measurement. Titov’s cross section is peaked around 22  in polar angle of  (1520) at  d-CMS, where a momentum of a nucleon reacting with an exchanged kaon becomes the minimum.  + production yield is significantly lower in the other polar angle region because of a deuteron form factor. This may explain a negative result in CLAS experiment. The strength in a region less than 10 degree slightly depends on spin-parity of  +, but the peaking structure is unchanged. A region of 0-35 degree was used for the differential cross section measurement as done in the previous section: Acc(  d  + K - p) = 0.04692  0.00026 = 1.13 * Acc.(flat) ===> d  /d  (  d  + K - p) = 1.51  0.41 nb/sr Acc(  d  +  * ) = 0.03548  0.00020 = 1.12 * Acc.(flat) ===> d  /d  (  d  +  * ) = 8.90  2.41 nb/sr The results are well close to the case with a constant matrix element, which only differs by ~10%. Fig.40 Titov’s theoretical calculation of differential cross section for  d  +  (1520) depending on  * polar angle at  d-CMS. A calculation for E  = 2.0 GeV and spin-parity = 3/2- is shown. 11

12. 7. Kinematic dependences of the  + yield 7.1 Polar angle dependence at  d-CMS 12 Since CLAS have not observed the  + peak in their acceptance region, where extremely forward going K - p system cannot be covered, polar angle dependence of the  + yield may exist. Interestingly, Titov’s theoretical calculation of differential cross section (Fig.40) shows such dependence, which supports  + photoproduction associates with extremely forward going  (1520). Fig.47 shows  (1520) polar angle at  d-CMS vs. missing K + momentum in the quasi-free K +  (1520) MC simulation. At the polar angle of ~25 degree, the K + momentum reaches ~420 MeV/c, which can produce  + with a rest neutron. In the other angle region, a neutron must have larger Fermi momentum to produce  +, and the reaction rate will decrease by a deuteron form factor. Unfortunately, LEPS experiment has no acceptance for  (1520) polar angles larger than 35 degree, but peaking behavior around 25 degree was examined by dividing the LD 2 sample to two angle regions (0-15 degree and 15-35 degree). Since statistics with the standard  (1520) selection was not large, the width of the selection cut was extended to  40 MeV/ c 2 of the  (1520) pole.(  d  + K - p may be contaminated in the sample, but it is assumed that reaction mechanism is not so different.) Fig.47  (1520) polar angle at  d-CMS vs. K + momentum in quasi-free  p  K +  (1520) MC simulation.

13. 13 Table 7. Number of signal events and statistical significances depending on K - p polar angle in 1.520<MMd( ,K - p)<1.545 GeV/c 2. 0<   d-CMS (K - p)<15 degree data= 135  11.6 bg=106.1  2.3 sig=28.9  11.9 s/sqrt(b)=2.81, s/sqrt(s+b)=2.49 15<   d-CMS (K - p)<35 degree data=463  21.5 bg=363.4  4.3 sig=99.6  21.9 s/sqrt(b)=5.22, s/sqrt(s+b)=4.63 35<   d-CMS (K - p)<90 degree data= 4  2.0 bg= 3.7  0.4 sig= 0.3  2.0 s/sqrt(b)=0.16, s/sqrt(s+b)=0.15 0  <   d-CMS (K - p)<15  15  <   d-CMS (K - p)<35  Fig.49 Relative yield of  d  +  * depending on  (1520) polar angle at  d-CMS. Fig.48 MMd( ,K - p) spectra depending on  (1520) polar angle in LD 2 data.

14. Fig. 48 shows MMd( ,K - p) spectra in the two different polar angle regions with the extended  (1520) selection cut. A clearer  + peak was observed in 15<   d-CMS (K - p)<35 degree. Numbers of signal and background events are summarized in Table 7 with angle region of 35<   d-CMS (K - p)<90 degree.  + yields were compared by correcting number of signals with K - p detection acceptance and solid angle: #signal acceptance solid angle 0-15 deg 28.9  11.9 0.0807  0.0020 0.214 15-35 deg 99.6  21.9 0.0322  0.0007 0.922 Number of signals were counted in the narrow signal region (1.520<MMd( ,K - p)<1.545 GeV/ c 2 ) since S/N ratio must be better giving smaller influence of background fluctuation. The acceptance was measured by using  d  +  (1520) MC generated in flat phase space. Fig. 49 shows relative  + yields with the above corrections. Enhancement was observed in  (1520) polar angle region of 15-35 degree. Fig. 50 shows missing mass resolutions for  + in the three polar angle regions described above. The mass resolutions are consistent in all angle regions. Therefore, the polar angle dependence of the  + yields is not caused by the mass resolution. 14 0  <   d-CMS (K - p)<15  15  <   d-CMS (K - p)<35  35  <   d-CMS (K - p)<90  Fig.50 Mass resolutions of  + depending on  (1520) polar angle in  d  +  * MC.

15. 7.2 Photon energy dependence 15 1.75<E  <2.06 GeV 2.06<E  GeV Fig. 51 shows MMd( ,K - p) spectra in two photon energy region: 1.75 2.06 GeV. In order to increase statistics, width of the  (1520) selection cut was extended to  40 MeV/ c 2 of the  (1520) pole.  + peak was observed in both energy regions. Numbers of signal and background events are summarized in Table 8.  + yields were compared by correcting number of signals with acceptance and ratio of number of photons in the two energy regions: #signal acceptance #photon 1.75-2.06 GeV 73.3  16.3 0.00255  0.00010 0.308 2.06-~2.4 GeV 55.6  19.0 0.00475  0.00011 0.443 As done in the measurement of polar angle dependence, number of signals were counted in the narrow signal region (1.520<MMd( ,K - p)<1.545 GeV/ c 2 ), and the acceptance was measured by using  d  +  (1520) MC generated in flat phase space. Fig.52 shows relative  + yields with the above corrections. Since the acceptance and the number of photons in the higher energy region are larger, relative  + yield is further enhanced in the lower energy region. This may be connected with the fact that many high energy experiments have not observed  +. Fig.51 MMd( ,K - p) spectra depending on photon energy in LD 2 data.

16. 16 Table 8. Number of signal events and statistical significances depending on photon energy in 1.520<MMd( ,K - p)<1.545 GeV/c 2. 1.75<E  <2.06 GeV data=256  16.0 bg=182.7  3.0 sig=73.3  16.3 s/sqrt(b)=5.42, s/sqrt(s+b)=4.58 2.06<E  GeV data=346  18.6 bg=290.4  3.8 sig=55.6  19.0 s/sqrt(b)=3.26, s/sqrt(s+b)=2.99 Fig.52 Relative yield of  d  +  * depending on photon energy.

17. As a result, differential cross sections were calculated as follows: Luminosity=0.632  0.020 /pb, BR(  (1520)  K - p)=0.225 0  <  CMS (K - p)< 30  (0.84 sr) #events=3903.3  275.1 d  /d  =32.7  2.5 nb/sr d  /dcos  =205  16 nb 30  <  CMS (K - p)< 60  (2.30 sr) #events=8279.0  581.5 d  /d  =25.3  1.9 nb/sr d  /dcos  =159  12 nb 60  <  CMS (K - p)< 90  (3.14 sr) #events=7868.6  1333.8 d  /d  =17.6  3.0 nb/sr d  /dcos  =111  19 nb Order of the differential cross sections is consistent with Nam’s calculation, which are shown in Fig.43 and 44. Note that the acceptance measurement may depend on polar angle distribution at t-channel helicity frame, which is currently studied with Jia-Ye. Updates related with this point will be described in a separate note later. From Nam et. al., hep-ph/053149 Note definition of angle is vice-versa. 17 Fig.43 Fig.44

18. 18 3.2 K - polar angle distribution at t-channel helicity frame LH2LD2

19. 3.3 Differential cross sections of forward  (1520) photoproduction from proton Differential cross sections were measured depending on photon energy (2 bins) and  (1520) polar angle at CMS (3 bins). Number of signals were divided by acceptance, branching ratio (BR[  (1520)  K-p]=0.225), lumnosity in each energy bin, and solid angle (or cos  range). Since K- polar angle distribution at t-channel helicity was consistent with isotropic generation, acceptances were measured without applying any filters to phase space MC. Therefore, number of signals and acceptances are basically the same as TN46. (Only re-smearing of photon energy resolution was updated.) Differential cross sections were evaluated in two photon energy regions, although this energy division was not done in TN46. In polar angle region less than 60 degree, cross sections became higher in lower energy region. This behavior is seen in forward  (1520) photoproduction of Nam’s theoretical calculation, while not seen in Titov’s calculation. The energy dependence of  (1520) photoproduction would partly explain energy dependence of  d  +  (1520) reaction in TN46. *** 2.04<Ecms<2.18 GeV (1.75<Eg<2.06 GeV) *** 0-30 degree data:118  10.863 BG:21.652  0.788 #signal:96.348  10.891 Acc.:0.0551717  0.0015925 d  /d  :35.81  4.32 nb/sr d  /dcos  :224.55  27.11 nb 30-60 degree data:195  13.964 BG:53.584  1.258 #signal:141.416  14.021 Acc.:0.0335178  0.0007592 d  /d  : 31.60  3.36 nb/sr d  /dcos  :198.57  21.11 nb 60-90 degree data: 91  9.539 BG:53.451  1.237 #signal: 37.549  9.619 Acc.:0.0122138  0.0003955 d  /d  : 16.87  4.39 nb/sr d  /dcos  :105.92  27.55 nb *** 2.18<Ecms GeV (2.06<Eg GeV) *** 0-30 degree data:283  16.823 BG:92.581  1.616 #signal:190.419  16.900 Acc.:0.0881741  0.0016560 d  /d  : 30.55  2.94 nb/sr d  /dcos  :191.56  18.43 nb 30-60 degree data:275  16.583 BG:107.442  1.741 #signal:167.558  16.674 Acc.:0.0413323  0.0007065 d  /d  : 20.95  2.22 nb/sr d  /dcos  :131.61  13.94 nb 60-90 degree data: 69  8.307 BG:31.556  0.943 #signal: 37.444  8.360 Acc.:0.0077876  0.0002662 d  /d  : 18.20  4.15 nb/sr d  /dcos  :114.28  26.07 nb 19

20. 3.4 Differential cross sections of forward  (1520) photoproduction from deuteron *** 2.04<Ecms<2.18 GeV (1.75<Eg<2.06 GeV) *** 0-30 degree data:261  16.155 BG:113.265  2.558 #signal:147.735  16.357 Acc.:0.0448652+-0.0014849 d  /d  : 35.48  4.26 nb/sr d  /dcos  :222.49  26.71 nb 30-60 degree data:313  17.692 BG:118.791  2.590 #signal:194.209  17.880 Acc.:0.0188388+-0.0005937 d  /d  : 40.57  4.16 nb/sr d  /dcos  :254.94  26.16 nb *** 2.18<Ecms GeV (2.06<Eg GeV) *** 0-30 degree data:593  24.352 BG:345.428  4.403 #signal:247.572  24.746 Acc.:0.0774524  0.0015879 d  /d  : 23.96  2.58 nb/sr d  /dcos  :150.20  16.15 nb 30-60 degree data:311  17.635 BG:191.667  3.283 #signal:119.333  17.938 Acc.:0.0165916  0.0004650 d  /d  : 19.69  3.08 nb/sr d  /dcos  :123.70  19.38 nb 20

21. 21 LD 2 data 1.525-1.540 GeV/c 2 was tagged. LD 2 data - BG sum MC simulation of  d  +  * K + mass Fig.54 MMp( ,K - p) spectrum of LD 2 data by tagging  + peak. Upper panel shows an original spectrum with background estimates and lower panel shows a spectrum after the sub- traction. Fig.55 MMp( ,K - p) spectrum of  d  +  (1520) MC. 7.3 Dependence on MMp( ,K - p) Off-shell component of kaon exchange does not look negligible.

22. 8.1 LD 2 extra events  d  K - pK + n MC As seen in Fig. 11, extra events were observed in higher side of  (1520) resonance peak in the LD 2 data. They can not be figured out by non-resonant KKp, K  (1520), and  p productions, whose kinematics was extracted from the LH 2 data. In order to understand nature of the extra events, M(K - p)>1.54 GeV/c 2 region was tagged in the LD 2 data. Fig. 56 shows MMp( ,K - p) distribution of the tagged sample. Non-resonant KKp background spectrum (blue) was scaled twice as in Fig. 11, and it was added to K  (1520) and  p background spectra (red). MMp( ,K - p) spectrum after subtracting the summed background spectrum is well peaked at K + mass. Fig. 57 shows momentum of spectator nucleon vs. MMp( ,K - p) in  d  K - pK + n MC simulation. It is clear that MMp( ,K - p) is peaked at K + mass when the spectator momentum is close to 0. The LD 2 extra events are likely due to contribution from  n photoreaction. That is why background spectrum for the extra events were estimated by making kinematic filters for non-resonant KKN MC simulation. LD 2 data (KKp x2) LD 2 data - BG sum 22 Fig.56 MMp( ,K - p) spectrum of LD 2 data by tagging LD 2 extra events. Upper panel shows an original spectrum with background estimates and lower panel shows a spectrum after the subtraction. Sum of K  *,  p, and twice of non-resosnt KKp MCs were taken for BG estimates. Fig.57 Spectator momentum vs. MMp( ,K - p) of  d  K - pK + n MC.

23. 23 LD 2 data w/ BG estimates LD 2 data - BG sum  d  K +  (1520)n MC  n  K  (1520) MC  d  K +  (1520)n  is not likely a source of the bump structure, since MMp( ,K - p) distribution is skewed toward high mass side and the maximum of MMd( ,K - p) spectrum differs from 1.6 GeV/c 2. By comparing MMp( ,K - p) distributions of  d  K +  (1520)n and  n  K  (1520), the former spectrum is closer to the LD 2 spectrum. Since a ‘shoulder’ of the maximum region in the LD 2 spectrum is slightly lower than the  d  K +  (1520)n MC, momentum of a spectator nucleon may be soft. Also, a possibility of new particle states like  + cannot be excluded. Fig.63 MMp( ,K - p) spectrum of  d  K +  (1520)n MC. Fig.62 MMp( ,K - p) spectrum of LD 2 data by tagging 1.6 GeV bump. Upper panel shows an original spectrum with background estimates and lower panel shows a spectrum after the subtraction. Fig.64 MMp( ,K - p) spectrum of  n  K  (1520) MC. 8.2 1.6 GeV bump

24. 24 Table 10. Number of signal events and statistical significances by sideband method. Narrow gate: 1.520-1.545 GeV/c 2 (5 bins) ~ 1 sigma of mass resolution data = 364  19.1 events BG = 279.0  6.9 events signal = 85.0  20.3 events sig/sqrt(bg) = 5.09 sig/sqrt(sig+bg) = 4.46 Wide gate: 1.510-1.560 GeV/c 2 (10 bins) ~ 2 sigma of mass resolution data = 653  25.6 events BG = 535.1  9.6 events signal = 117.9  27.3 events sig/sqrt(bg) = 5.10 sig/sqrt(sig+bg) = 4.61 Note: In calculation of errors in background estimates, an improvement factor by 10 MeV smearing (0.4), a normalization factor of sideband average to the  (1520) region (0.4), and a scaling factor of K  (1520) component (1.336) were used. The improvement factor came from Nakano’s study. In order to test existence of  + peak, the K  (1520) spectrum estimated by the sideband subtraction in the LH 2 sample was fitted to MMd( ,K - p)<1.51 GeV/c 2 of the LD 2 missing mass spectrum over the sideband averaged background components. Fig. 76 shows the MMd( ,K - p) spectra obtained after the fitting.  + peak and 1.6 GeV bump were observed as seen in the filtering method. Number of signals and statistical significances are summarized in Table 10. The statistical significances were at the same level as the filtering method. Fig.76 MMd( ,K - p) spectra of LD 2 data with background estimates by sideband method. Appendix A. Background estimation based on sideband method

25. 25 Fig.1 MMp( ,K + ) distribution with M(KK)>cutmkk2(20,egamma) in LH 2 data. 2.2 Results of training by LH 2 Fig.4 MMp( ,K - ) distribution with M(KK)>cutmkk2(20,egamma) in LH 2 data.

26. 26 Fig.7 MMp( ,K + K - ) distribution without phi exclusion cut in LH 2 data. Fig.8 M(K + K - ) distribution without phi exclusion cut in LH 2 data.

27. 27 Fig.19 K - polar angle distribution at t-channel helicity frame [KK mode in LH 2 data]. sin 2  was fitted. Fig.20 K - polar angle distribution at t-channel helicity frame [same as Fig.19]. a*sin 2  +b*(1/3+cos 2  ) was fitted. Fig.19 and Fig.20 have the same data points, but sin 2  and a*sin 2  +b*(1/3+cos 2  ) were fitted, respectively. Better  2 was obtained in Fig.20 (  2 /ndf=0.3697/1) than Fig.19 (  2 /ndf=4.844/2). In Fig.20, ratio of sin 2  [a/(a+b)] was calculated to be 0.7829  0.0943, which resulted in sin 2  dominance. In calculations of differential cross sections described below, the fitting result of Fig.20 was adopted to estimate detector acceptance. (The observed dependence means K - p pair tends to fly to side direction, and the detector acceptance of KK mode must be lower than the case with isotropic generation at t-channel helicity frame.) This fit will at least give a phenomenological correction to the detector acceptance.

28. 2.5 Luminosity in K + K - detection mode 28 Procedure to calculate luminosity is similar to TN46, but a few calculations were updated as indicated blue characters. Number of photons in LEP beam tagger counts (same as TN46) LD 2 : 4.587*10 12, LH 2 : 2.803*10 12 transmission (same as TN46) 0.526  0.017(  0.007[stat]  0.016[sys]) ntag=1 prob. (re-estimated by using real events with K + K - detection) LD 2 : 18861/22712=0.8304  0.0025, LH 2 : 6408/7668=0.8461  0.0041 Ratio of ntag(the newest reconstruction)=1 was measured by the real data samples selected with K + K - detection, |ytof|>50 mm, vertex requirement, and 2.00<E  (calculated backwardly from K + K - missing mass=M p )<2.40 GeV. Note these probabilities are slightly higher than Kp mode because higher energy region (E  >2.0 GeV) is selected. tagger reconstruction eff. * Ratio of E  >2.00 GeV (See miho:/np1b/v01/mura/leps/ana/temp2/weightcc_ [ld2/llh2]_term*.20.1.50001.qfkk, which were made based on tables from Sumihama.) LD 2 r24095-r24231: 0.5328 (0.60*10 12 photons) + r24241-r24398:0.5328 (0.43*10 12 photons) + r24443-r26338: 0.5056 (3.99*10 12 photons) ---> weighted efficiency: 0.5112 Note that a tagger SSD problem in r24241-r24398 does not affect this ratio because E  >2.0 GeV is required. LH 2 r23690-r24058: 0.5411 (1.14*10 12 photons) + r25453-r25968: 0.5068 (1.99*10 12 photons) ---> weighted efficiency: 0.5193 -----> #photon(LD 2 ) = (1.0242  0.0332)*10 12, #photon(LH 2 ) = (0.6478  0.0212)*10 12 Number of target particles (same as TN46) -----> #deuteron = 8.1417 * 10 -13 /pb, #proton = 6.8217 * 10 -13 /pb Luminosity LD 2 : #photon * #deuteron = 0.8339  0.0270 /pb LH 2 : #photon * #proton = 0.4419  0.0145 /pb

29. Fig.21 shows MMp( ,K + ) distributions depending on K + polar angle at CMS. Number of  (1520) signals were counted in 1.48<MMp( ,K + )<1.56 GeV/c 2, and was divided by detector acceptance, branching ratio (BR[  (1520)  K - p]=0.225), lumnosity, and solid angle (or cos  range) to calculate differential cross sections. The acceptances were measured by applying 0.7829*sin 2  +0.2171*(1/3+cos 2  ) dependence to  p  K +  (1520) MC at t-channel helicity frame. Calculations of differential cross sections are summarized below: 0- 30 degree Data: 141  11.874, BG: 65.310  1.561 #signal: 75.690  11.976 Acc.: 0.0076038  0.0005343 d  =0.84179 sr  d  /d  =118.93  20.96 nb/sr dcos  =0.13397  d  /dcos  =747.30  131.68 nb 30- 60 degree Data: 208  14.422, BG: 151.479  2.249 #signal: 56.521  14.597 Acc.: 0.0048083  0.0002582 d  =2.29981 sr  d  /d  = 51.41  13.67 nb/sr dcos  =0.36603  d  /dcos  = 322.99  85.86 nb 60- 90 degree Data: 31  5.568, BG: 22.900  0.845 #signal: 8.100  5.632 Acc.: 0.0004087  0.0000646 d  =3.14159 sr  d  /d  = 63.45  45.29 nb/sr dcos  =0.50000  d  /dcos  =398.66  284.56 nb 2.6 Differential cross sections of backward  (1520) photoproduction 29 Fig.21 MMp( ,K + ) distributions depending on K + polar angle at CMS. Four panels correspond to 0  -30 , 30  - 60 , 60  -90 , and 90  -180  from upper-left to lower-right.