Ac correlation Estimate ======================= It is not clear to me how to deal with background events. So I will only count the real signal overlaps and ignore background events. Also when getting to the true signal overlaps, we assume all tags have them 100% right signed. These are conservative assumptions which should give a slightly larger correlation. ***************************************************** A) Basic characteristics of individual measurements: ***************************************************** K+Vtx D*,D Muon Data sample 96-98 93-98 93-98 cos(theta) <0.7 <0.87 <0.63 K+Vtx sample: ------------- Yhem<0.4 & Pvtx>5 has ~22% hemisphere efficiency. ~12% total efficiency including Vtx+K sign tag After the Yhem tag, 42% hemispheres have Qvtx sign ! reading Q plots 27% " K+- sign ! The total final Ac fit sample is 9970 events, with ~92% correct charge tag => signal ~9170 events (which includes accidental right tags e.g. D0 tagged as D+ by vtx charge). The cc D vertex reconstruction is ~80% exactly correct as D0 or D+; while the other 20% mostly wrong by +-1 in charge - so that D0 mistagged as D+ still gets 50:50. K-:K+ D+ 24%:5.8% D0 53%:3.4% Ds 13%:20% (large error) To estimate what fraction of the reconstructed D*,D or muon are also part of the K+Vtx tag, I have taken a look at the c tag variation vs many oberservables and actually learned quite a few things: http://www.slac.stanford.edu/~sudong/sld/rbrc/ctag-eff-variations.ps a) c-tag efficiency for very high D momentum is not higher, and efficiency even drops for long decay length higher raw mass prosumably because NN thinks that makes it too much like b's. b) There is a balancing point for tagging efficiency vs D decay mode. High multiplicity makes easier vertexing, but lower track momentum blur the resolution. So it looks like the efficiency is best for modes with 3-4 tracks. Unfortunately, the ntp doesn't have more info to allow looking at e.g. eff vs No. of neutrals. D*,D sample: ------------ All 93-98 D*+ -> D0pi+ cc signal D0 -> K-pi+ 413 D0 -> K-pi+pi-pi+ 601 D0 -> K-pi+pi0 418 D0 -> K-l+nu 296 inclusive ~940* D+ ->K-pi+pi+ 698 D0 ->K-pi+ 403 ----- 3768 * the inclusive pi* analysis has a 25% weight in the overall sample so that we convert that to an equivalent exclusive signal. Most modes have some level of decay length / impact significance cuts. First two D*+ exclusive modes also have some pure kinematic x>0.4 subsample. Lepton Ac sample ---------------- 93-95 electron has 7.7% weight 93-95 muon has 24.4% weight 96-98 muon has 68.0% weight P>2 GeV muon ID efficiency = 81% with 68% purity. 21199 total muon sample, including ~2700 true c->l. ************************************ B) Compare analyses in pairs: ************************************ K+Vtx vs D*,D ------------- K+Vtx D*,D 1) Data sample 96-98 93-98 ->80% The 93-95 sample has 20% weight for D*,D. 2) cos(theta) thrust <0.7 <0.87 ->76% Given the D*,D efficiency slopes down beyond 0.8, we can put the effect cth cut for D*,D as 0.83. Making the Ac costheta weighted overlap fraction: int(cth/(1+cth**2))[0-0.7]/[0-0.83] = 0.76 So the starting effective event fiducial selection max overlap is 80%*76% = 0.61 Now we look at individual D*,D mode to see their overlap with K+Vtx: Mode Qmode c-tag K-prod K/Vtx-Overlap total D*+ D0->K-pi+ 0 1.50* 0.240 1.00 0.1230 0.0220 59 D*+ D0->K-pi+pi-pi+ 0 1.50* 0.290 1.00 0.1486 0.0265 105 D*+ D0->K-pi+pi0 0 1.50* 0.240 1.00 0.1230 0.0220 60 D*+ D0->K-lnu 0 1.50* 0.240 1.00 0.1230 0.0220 42 D*+ D0->inclusive 0 1.20* 0.280 0.53 0.0608 0.0205 76 D+ ->K-pi+pi- 1 1.50* 0.500 1.00 0.0640 0.3660 300 D0 ->K-pi+ 0 1.50* 0.240 1.00 0.1230 0.0220 58 Total D*,D signal sample = 3769 ----- Total K+Vtx signal sample = 9170 700 Signal Overlap = 700 Correlation coeff = 11.9% <=== The c-tag factors are based on the tag eff vs D decay multiplicity. Because the full reco D*,D are picking on longer decay length, high momentum decays already, we give a boost factor of 1.5 for D reco bias. We will not give degrading factors for containing a pi0 or neutrino, since the raw mass bias work in the opposite direction so that two effects may cancel. The inclusive pi*, has a bit of impact parameter requirement, so just give it a boost of 1.2. K+Vtx vs Lepton --------------- K+Vtx lepton 1) Data sample 96-98 93-98 ->68% The 96-98 muon sample has 68% weight. 2) cos(theta) thrust <0.7 <0.63 ->76% Making the Ac costheta weighted overlap fraction: int(cth/(1+cth**2))[0-0.63]/[0-0.7] = 0.84 So the starting effective event fiducial selection max overlap is 68%*84% = 0.57 The semileptonic mode tag is probably close to the average inclusive c-tag and K+Vtx charge tag. Although the semileptonic mode boost up the D+ fraction with longer lifetime, it also tends to yield more lepton+K0 single prong mode making it harder to tag so that the average effect make cancel. However, the pure c->l sample gets some weight up for vertexing c->l tag in the lepton analysis once there is a c-vertex tag, so we give that a 1.5 weigh up. The effective weight of fiducial lepton sample tagged by K+Vtx is then 12%*1.5 = 18%; x fiducial selection (0.57)=0.103. correlation coeff = 0.103*2700/sqrt(2700*9710) = 5.4% <=== D*D vs lepton ------------- 1) Data samples are both full 93-98 for D*,D and muons, but electron sample only goes from 93-95. The electron sample only has 8% of weight so that the data period overlap mismatch can be ignored. 2) cos(theta) thrust D*D <0.87 but effectively more like 0.83 lepton <0.63 int(cth/(1+cth**2))[0-0.63]/[0-0.83] = 0.64 So the total effective fiducial overlap is 64%. Only two D*,D modes are relevant: fiducial lepton-sel D*->D0pi+ D0->K-l+nu 0.64 * 1.0 *296 = 189 D*->D0pi+ D0->inclusive 0.64 * 7%*0.8 *940 = 33 correlation coeff = (189+33)/sqrt(2700*3768) = 7.0% <=== *********************** C) Summary of results *********************** D*,D vs K+Vtx 11.9% D*,D vs lepton 7.0% K+vtx vs lepton 5.4%