Rb final results Summer-04 Jul/07/04 Su Dong ========================== Analysis updates since summer-01: 1) Analyses ntuples rerun with latest tracking resolution (Aaron's triplet based) corrections and all MC samples utilized including cc only MC. 2) Default MC is now with both tracking resolution and efficiency correction. Previous analysis used only resolution correction and tracking eff was not appplied by default and only used as variation for systematics. We were previously not sure the apparant tracking eff correction needed to make data and MC track multiplicity agree a real efficiency issue or generator over production. The b, c vertex charge distributions finally broke the ambiguity to clearly implying there is real tracking inefficiency to be corrected. 3) Gluon splitting effect study reperformed and uncovered an extra correction. The gluon splitting recommended by LEPEWWP based on measurements are ~x2 higher than JETSET MC. We previously only corrected the g->QQ effect on uds efficiency. It turns out the g->QQ effect on cc efficiency is also significant, and there is also a slight effect on the correlations. The g->QQ scaling is now applied to all efficiencies and correlations. 4) Extensive checks are made on b/c tag hemisphere correlations and reasonably good agreement found between component sums and MC total correlations. Various effects of the tag behavior previously unnoticed are observed. Systematic effects for 2b in same hemisphere reexamined. 5) Detector systematic was previous using 1/2 of resolution correction and the full tracking eff correction as variations. Given that we are a bit more confident about the origin of the track efficiency correction, its error is now also half the correction. However, there are two ways of estimating the systematics depending on the combination of tracking eff and resolution. We take the larger of the two estimates then /2. 6) IP tail effect studied by Sean with YT distributions and concluded no visible beam spot tail for 97-98, but 96 is consistent with having 0.5% tail at 100 microns. This systematics is added for 96. 7) Our charm MC is slightly different in some respect compared to the LEPEWWG central values. This was previously uncorrected and only the variations was looked at for systematics. The Rb central value is now corrected for two of the most significant effects: cc hadron production spiecies (our MC had a bit more c-baryon) and D decay multiplicity (our MC D+ 1-prong fraction low). 8) Majority of the physics systematics are untouched as was for Summer-01. Central value corrections: -------------------------- This was what we had for summer-01: 93-95 96 97-98 Raw Rb measured 0.21626 0.21793 0.21907 Event selection bias -0.00176 -0.00176 -0.00176 running b mass correction +0.00026 +0.00026 +0.00026 gamma/Z +0.00030 +0.00030 +0.00030 g->QQ correction -0.00046 -0.00103 -0.00105 tracking resolution correction -0.00096 -0.00044 tracking efficiency correction +0.00035 +0.00032 -------- -------- -------- Fully corrected 0.21460 0.21509 0.21670 Updated analysis: 93-95 96 97-98 Raw Rb measured 0.21626 0.21795 0.21913 Event selection bias -0.00176 -0.00176 -0.00176 running b mass correction +0.00026 +0.00026 +0.00026 gamma/Z +0.00030 +0.00030 +0.00030 cc production/decay corr +0.00015 +0.00012 g->QQ correction -0.00046 -0.00139 -0.00150 tracking corrections -0.00110 -0.00022 -------- -------- -------- Fully corrected 0.21460 0.21441 0.21633 Notes: 1) For the tracking corrections, there is a choice on how to combine the tracking eff and res effects. Take 97-98 as example: Tracking resolution corr only -0.00041 Tracking efficiency corr only +0.00026 -------- linear sum -0.00015 Combined res+eff corr -0.00022 The difference is most likely stat fluctuations associated with the smearing/track tossing. For the convenience of analysis, we take the combined res+eff result as default. 2) The 96 MC generated tracking efficiency correction was actually very close to be right (may be even slightly overshot), so that there is no tracking efficiency correction for 96 MC. The correction is entirely resolution correction. 3) For 93-95, the 'raw' result already had tracking corrections applied. I don't think I have enough info to guess on the extra effect of gQQ on cc efficiency which we now added to the 96-98 (the main change from summer-01). It's also too tedious to uncover R12 MC cc production/decay info to make that correction and in any case their effects multiplied by the 93-95 weights will be negligible. So 93-95 are left as it was. The MC cc production/decay correction ------------------------------------- Using 97-98 all flav + cc MC cc events: Charm production/decay LEPEWWG/MC c efficiency scales: c hadron production species : 1.0048 D meson decay multiplicity : 0.9753 Combine cc eff scale factor : 0.9799 -> dRb +0.00012 This correction has rather small effect at nominal b tag cut, but is showing more effect at looser b-tags when examinging Rb variation vs cuts. Event selection statistics -------------------------- 97-98 Event statistics: Sample All ntp skim cth<0.7 Njet=2,3 Trigger Data 555541 250233 211581 192189 191770 MCZH All 1572513 1090886 920105 845382 844538 uds 666923 561881 515578 515066 c 187368 158110 144792 144642 b 236595 200114 185012 184830 MCBB b 1577784 1097279 927289 856403 855526 MCCC c 933372 649098 547211 501954 501468 96 Event statistics: Sample All ntp skim cth<0.7 Njet=2,3 Trigger Data 102699 39042 33105 30122 29996 MCZH All flav 260948 179810 151911 139861 139732 uds 109964 92976 85358 85277 c 30745 25868 23790 23776 b 39101 33067 30713 30679 MCBB b 262992 181911 153780 142211 142062 MCCC c 155591 107699 90788 83454 83377 Rb, tag-stat, efficiencies and correlations at each step -------------------------------------------------------- Standard cbsel cut = 0.75 Data raw event tag statistics: All 0-tag 1-tag 2-tag 97-98 191770 154984 20738 16048 96 29996 24590 3315 2091 RAWM = raw vanilla MC TRES = tracking resolution corrections only TEFF = tracking efficiency corrections only TALL = both tracking res+eff corrections ccorr= cc production/decay correction a) 97-98: Hemisphere Double Correlation Correlation Sample tag eff(%) tag evt lambda (%) (Cx-1) uds RAWM 0.0733+-0.0027 0 uds TRES 0.0784+-0.0028 0 uds TEFF 0.0717+-0.0026 0 uds TALL 0.0774+-0.0027 0 uds + g->QQ wt 0.134 c RAWM 1.1363+-0.0093 102 0.256+-0.137 0.22272+-0.11897 c TRES 1.1913+-0.0095 118 0.346+-0.140 0.28690+-0.11623 c TEFF 1.0936+-0.0091 96 0.268+-0.138 0.24245+-0.12465 c TALL 1.1450+-0.0094 109 0.332+-0.140 0.28678+-0.12100 c + ccorr 1.122 c + g->QQ wt 1.187 0.361 b RAWM mc 62.9106+-0.0335 411919 0.071+-0.080 0.00042+-0.00047 b TRES mc 62.8372+-0.0335 410929 0.059+-0.080 0.00035+-0.00048 b TEFF mc 61.9230+-0.0337 399097 0.072+-0.080 0.00044+-0.00049 b TALL mc 61.8519+-0.0337 398009 0.002+-0.080 0.00001+-0.00049 b + g->QQ wt 61.78 -0.020 MC corr Rb meas b-eff meas b-eff MC RAWM raw 0.21913+-0.00104 0.6177+-0.0024 0.6291 RAWM+ccorr 0.21925+-0.00104 0.6176+-0.0024 0.6291 TRES+ccorr 0.21884+-0.00104 0.6182+-0.0024 0.6284 TEFF+ccorr 0.21951+-0.00104 0.6172+-0.0024 0.6192 TALL+ccorr 0.21903+-0.00104 0.6180+-0.0024 0.6185 + gQQ wt 0.21753 0.6201 0.6178 b) 96: Hemisphere Double Correlation Correlation Sample tag eff(%) tag evt lambda (%) (Cx-1) uds RAWM 0.0651+-0.0062 0 uds TRES 0.0704+-0.0064 0 uds TEFF 0.0651+-0.0062 0 uds TALL 0.0704+-0.0064 0 uds + g->QQ wt 0.113 c RAWM 1.0458+-0.0220 9 -0.245+-0.268 -0.23196+-0.25244 c TRES 1.2076+-0.0236 17 0.107+-0.317 0.08789+-0.25847 c TEFF 1.0458+-0.0220 9 -0.245+-0.268 -0.23196+-0.25244 c TALL 1.2076+-0.0236 17 0.107+-0.317 0.08789+-0.25847 c + ccorr 1.180 c + g->QQ wt 1.238 0.206 b RAWM mc 57.0611+-0.0842 56661 0.985+-0.192 0.00741+-0.00145 b TRES mc 56.9567+-0.0842 56442 0.953+-0.192 0.00721+-0.00146 b TEFF mc 57.0611+-0.0842 56661 0.985+-0.192 0.00741+-0.00145 b TALL mc 56.9567+-0.0842 56442 0.953+-0.192 0.00721+-0.00146 b + g->QQ wt 56.91 0.890 MC corr Rb meas b-eff meas b-eff MC RAWM raw 0.21795+-0.00290 0.5633+-0.0067 0.5706 RAWM+ccorr 0.21810+-0.00290 0.5632+-0.0067 0.5706 TRES+ccorr 0.21700+-0.00289 0.5646+-0.0067 0.5696 TEFF+ccorr 0.21810+-0.00290 0.5632+-0.0067 0.5706 TALL+ccorr 0.21700+-0.00289 0.5646+-0.0067 0.5696 + g->QQ wt 0.21561 0.5663 0.5691 Gluon splitting effect ---------------------- Gluon->cc (%) Gluon->bb (%) JETSET 1.357 0.142 LEPEWWG-2001 2.96+-0.38 0.254+-0.051 Use all 97-98 MC sample with detector corrections: g->QQ event statistics: g->cc uds tag 0/1/2= 6026 315 0 all= 6341 frac= 0.01231 g->cc c tag 0/1/2= 6827 636 6 all= 7469 frac= 0.01156 g->cc b tag 0/1/2= 2110 5707 3426 all= 11243 frac= 0.01081 g->bb uds tag 0/1/2= 223 270 0 all= 493 frac= 0.00096 g->bb c tag 0/1/2= 250 346 10 all= 606 frac= 0.00094 g->bb b tag 0/1/2= 91 416 409 all= 916 frac= 0.00088 The following tests starts with nominal MC without g->QQ weighting to investigate the effect of apply g->cc, g->bb, g->cc & g->bb to first uds eff, then also include c eff, and finally include correlations accumulatively to see the effect step by step: Sample Rb diffRb ebmeas effuds effc effb lamb lamc No g->QQ wt 0.21903 0.6180 0.00077 0.01122 0.6185 0.00002 0.00332 g->cc wt uds 0.21833 -0.00070 0.6190 0.00113 g->cc wt effc 0.21810 -0.00094 0.6190 0.00113 0.01165 g->cc wt all 0.21807 -0.00097 0.6193 0.00113 0.01165 0.6177 -0.00018 0.00307 g->bb wt uds 0.21863 -0.00041 0.6186 0.00098 g->bb wt effc 0.21851 -0.00052 0.6186 0.00098 0.01143 g->bb wt all 0.21851 -0.00052 0.6187 0.00098 0.01143 0.6186 0.00001 0.00388 g->QQ wt uds 0.21791 -0.00112 0.6196 0.00134 g->QQ wt effc 0.21756 -0.00147 0.6196 0.00134 0.01187 g->QQ wt all 0.21753 -0.00150 0.6201 0.00134 0.01187 0.6178 -0.00020 0.00361 the overall correction therefore changed from -0.00112 to -0.00150 largely due to the extra effect on cc efficiency. To calculate the g->QQ systematic: g->cc systematic/correction = 0.38/(2.96-1.357) = 0.237 g->bb " = 0.051/(0.254-0.142) = 0.455 97-98 96 g->cc correction -0.00097 -0.00080 g->cc systematics -0.00023 -0.00019 g->bb correction -0.00052 -0.00057 g->bb systematic -0.00024 -0.00026 MC statistics ------------- dRb 97-98 96 uds eff 0.00007 0.00018 c eff 0.00005 0.00014 Lambda b 0.00011 0.00032 Lambda c 0.00001 0.00002 ------- ------- Total MC stat 0.00014 0.00039 The MC cc stats dropped from using the cc MC. but uds came up due to large weighting up for g->QQ. Detector systematics: --------------------- Similar to Nicolo's scheme for Rc. Two schemes of estimating the error. Take the larger of the two then x50%. 96 TEFF corr=0 so that there is only resolution correction. dRb 97-98 96 Resolution effect TALL-TEFF -0.00048 -0.0110 TRES-RAWM -0.00041 -0.0110 take -0.00024 -0.0055 Efficiency effect TALL-TRES +0.00019 (MC corr =0) TEFF-RAWM +0.00026 take +0.00013 +0.00013 use 97-8 estimate IP Smear Systematic ------------------- All 96 MC samples ran with IP smeared by 100 microns for all events. Compare raw MC (RAWM) and the smeared IP MC (SMIP): Hemisphere Double Correlation Correlation Sample tag eff(%) tag evt lambda (%) (Cx-1) uds RAWM 0.0651+-0.0062 0 uds SMIP 0.2680+-0.0125 1 c RAWM 1.0458+-0.0220 9 -0.245+-0.268 -0.23196+-0.25244 c SMIP 6.3583+-0.0527 740 4.810+-0.377 0.70839+-0.05465 b RAWM 57.0611+-0.0842 56661 0.985+-0.192 0.00741+-0.00145 b SMIP 58.2672+-0.0839 58922 0.654+-0.193 0.00469+-0.00139 Making event weighting: 0.995*RAWM + 0.005*SMIP -> dRb(IP smear - no IP tail) = -0.00017 Effect of hard Gluon Radiation ------------------------------ Hard gluon radiation resulting 2 b's in the same hemisphere is happening at a rate of 1.62% in the bb MC passing Rb analysis event selection. Using both all flavor and bb MC from 97-98 with no detector corrections: Hard gluon statistics: All notag tag-glu tag-bb tag both Two b in same hemisphere 16844 5866 83 10726 169 Two b in opposite hemisp. 1025468 137754 475283 412431 tag eff Opposite b hemisphere 0.6339 2b in same hemisphere 0.6468 +- 0.0037 hard glu hemisphere 0.0150 +- 0.0009 The effect of with-without hard gluon events on b correlation: Delta(Cb-1) = -0.00037 Delta(Lambda) = -0.00063 -> dRb = -0.00008 for 100% of the hard gluon population. Tom Wright's thesis shows that we in observe the 2b in same hemisphere rate in data at 2.45+-0.74% (different event selection). LEPEWWG recommends varying MC by +-30%. This will leads to an estimate of dRb=0.00003, slightly smaller than before. Rb Result Combination --------------------- Combine 93-95 96 97-8 Measurement values 0.21603 0.21460 0.21441 0.21633 Statistical correlation Matrix 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 Data Statistics 0.00094 0.00337 0.00289 0.00104 MC statistics 0.00013 0.00064 0.00039 0.00014 Event selection bias 0.00019 0.00028 0.00018 0.00018 Running b mass 0.00026 0.00026 0.00026 0.00026 Tracking resolution 0.00032 0.00096 0.00055 0.00024 Tracking efficiency 0.00015 0.00040 0.00018 0.00013 tail 0.00002 0.00010 0.00017 0.00000 Lambda_b production 0.00005 0.00008 0.00011 0.00004 b hadron lifetime 0.00000 -0.00004 0.00000 0.00000 B decay multiplicity -0.00019 -0.00003 -0.00037 -0.00018 bbg hard gluon 0.00003 0.00008 0.00003 0.00003 QCD hemisph. correlation 0.00005 0.00029 0.00003 0.00003 b-corr costh effect 0.00008 0.00001 0.00009 0.00009 xEb 0.00005 0.00019 0.00002 0.00004 xEc -0.00017 -0.00006 -0.00016 -0.00018 cc->D+ production -0.00010 -0.00011 -0.00007 -0.00010 cc->Ds production -0.00011 -0.00004 -0.00011 -0.00011 cc->Lambda_c production -0.00011 -0.00011 -0.00013 -0.00011 Dzero lifetime -0.00003 -0.00003 -0.00003 -0.00003 Dplus lifetime -0.00002 -0.00001 -0.00003 -0.00002 Ds lifetime -0.00003 -0.00002 -0.00002 -0.00003 Lc lifetime -0.00001 -0.00001 0.00000 -0.00001 D decay multiplicity -0.00026 -0.00012 -0.00016 -0.00028 D->K0 production 0.00019 0.00025 0.00019 0.00019 D->no pi0 -0.00009 -0.00009 -0.00010 -0.00009 glu->bb -0.00024 -0.00015 -0.00026 -0.00024 glu->cc -0.00021 -0.00003 -0.00019 -0.00023 long lived light hadron -0.00001 -0.00003 -0.00001 -0.00001 Rc 0.171+-0.006 -0.00020 -0.00021 -0.00020 -0.00020 ** Total error 0.00122 0.00365 0.00307 0.00129 ** Summed error check 0.00122 0.00140 0.00103 0.00076 Weight fraction 1.00000 0.06500 0.09577 0.83924 Combined result = 0.21603+- 0.00094+- 0.00078 (compare summer-01 0.21641+- 0.00092+- 0.00080 )