Vincenzo Vagnoni INFN Bologna LHCb light meeting 2 September, 2003

1. Vincenzo Vagnoni INFN Bologna LHCb light meeting 2 September, 2003

2. Overview • Selection efficiency summary • New parametrization of signal acceptance • bb background mass and proper time spectra • Proper time resolution studies • Changes to fast MC and fitter • Sensitivity on CP asymmetry terms • Sensitivity on the gamma angle

3. Annual yields and B/S ratios • Annual yields after L0xL1 triggers and offline selection as quoted in the TDR draft • B/S before trigger (only combinatorial bb background) • Agreed to use central values for B/S instead of upper limits

4. Parametrization of signal acceptance vs proper time • New parametrization of signal acceptance used • Depending on only one free parameter • No discontinuity of first derivative for t[0, ) • Better physical behavior and good fits with one less parameter New parametrization Old parametrization

5. Acceptance fits with new parametrization

6. bb background mass spectra • bb mass spectra after trigger and with slightly reduced offline-selection cuts (exponential fit) Bd2PiPi Slope=-1.7 Bs2KK Slope=-1.2 Bd2KPi Slope=-0.54 Bs2PiK Slope=-0.44

7. bb background proper time spectra (I) • Functional form for bb bacground proper time spectra guessed from untagged signal ones and fitted to bb data after trigger with slightly reduced offline selection cuts Bd2PiPi “lifetime” = (0.98±0.11) ps Bs2KK “lifetime” = (1.13±0.17) ps

8. bb background proper time spectra (II) Bd2KPi “lifetime” = (0.87±0.11) ps Bs2PiK “lifetime” = (1.15±0.16) ps

9. Proper time resolution (I) • Proper time resolution fitted with double gaussians Bd2PiPi Bs2KK Bs2PiK Bd2KPi

10. Proper time resolution (II) • Proper time resolution vs true proper time (triggered and offline selected events)

11. Proper time resolution (III) • Proper time resolution vs true proper time (triggered and offline selected events)

12. Changes to fast MC • As before only bb combinatorial background considered • Specific backgrounds that may exhibit their own CP violation not included in the model for the moment • Background mass generated in wide mass window with exponential shape according to fits to bb data • It is assumed that HLT will select mass in the range (4.9, 5.7) GeV/c2 • Background rate generated according to results of fits to bb data • Bd2PiPi and Bs2KK generated as before, simulating tagging and CP violation • Bd2KPi and Bs2PiK generated simulating tagging and direct CP violation (charge asymmetry) • Charge_asymmetry(Bd2KPi)  Adir(Bs2KK) and Charge_asymmetry(Bs2PiK)  Adir(Bd2PiPi)since they differ in the spectator quark only • New parametrization of signal acceptance taken into account

13. Fast MC: input values Nominal parameters: Bd2PiPi,Bd2Kpi Bs2KK,Bs2PiK tagging efficiency 41.8% 49.8% wrong tagging fraction 35% 33% M 0.5 ps-1 20 ps-1  1/1.54 ps-1 1/1.46 ps-1 / 0 0.1 d 0.3 0.3 theta 160 degrees 160 degrees gamma angle 65 degrees 65 degrees phi_s ---------------- -0.04 phi_d 0.818 ---------------- Sensitivity scan: parameters are varied one at a time d: 0.1, 0.2, (0.3), 0.4 theta: 120, 140, (160), 180, 200 degrees gamma angle: 55, (65), 75, 85, 95, 105 degrees phi_s: 0, (-0.04), -0.1, -0.2 M: 15, (20), 25, 30 ps-1 / : 0, (0.1), 0.2

14. Changes to the fitter (I) • Combined extended maximum likelihood fit of Bd2PiPi and Bd2KPi (Bs2KK and Bs2PiK) in order to extract mistag fraction from data • Proper time resolution (double gaussian) and proper time acceptance with new parametrization from full GEANT simulation are used • The likelihood is multiplied by gaussian priors in order to use the measurements from • LHCb J/PsiPhi ( and  for the Bs) • LHCb DsPi (M for the Bs) • PDG 2003 values ( and M for the Bd) • Results from LHCb JPsi/Ks on  and M not available • Power series expansion in ,  and M inside the likelihood function very useful to reduce fit computing time • Details in forthcoming LHCb note

15. Changes to the fitter (II) • The likelihood fit is performed against 17 parameters: • Re(), Im() for Bd2PiPi (Bs2KK) • Charge asymmetry for Bd2KPi (Bs2PiK) • Mean Bd (Bs) mass and mass resolution (2 parameters) • One parameter for mass distribution of background for Bd2PiPi (Bs2KK) • One parameter for mass distribution background for Bd2KPi (Bs2PiK) • 2 parameters for proper time distribution of background for Bd2PiPi (Bs2KK) • 2 parameters for proper time distribution of background for Bd2KPi (Bs2PiK) • M for the Bd (Bs) •  for the Bd (Bs) •  for the Bd (Bs) • Wrong tagging fraction for Bd2PiPi and Bd2KPi (Bs2KK and Bs2PiK) • Tagged event yield for Bd2PiPi (Bs2KK) • Tagged event yield for Bd2KPi (Bs2PiK)

16. Changes to the fitter (III) • Once the fit has converged Re() and Im() are transformed to Adir and Amix • Fit not performed directly on Adir and Amix since Re() has an ambiguous sign if expressed in terms of Adir and Amix • Error and correlation propagation from Re() and Im() to Adir and Amix if performed analytically is far from being trivial: one has to calculate a new full 17x17 covariance matrix (due to correlations) • Propagation is quite easy if performed with a MC technique • Generate multivariate 17-dimensional gaussian distribution according to covariance matrix returned by the likelihood fit • For each extraction of the 17-tuple of random numbers take Re() and Im() and calculate Adir and Amix • Estimate errors and correlation for Adir and Amix on a large sample of random generations (done with 1000000 of random samples per fit) • Library function to perform the generation available from CERNLIB (CORSET, CORGEN)

17. Fast MC mass spectra with projection of likelihood fit superimposed (1 year) Bd2PiPi Bs2KK Bs2PiK Bd2KPi

18. Results and discussion • Resolution on wrong tagging fraction after one year • 1.0% for Bd2PiPi and Bd2KPi • 6.1%, 6.7%, 7.9%, 9.1% for Bs2KK and Bs2PiK (depending on M=15, 20, 25, 30 ps-1) • In the previous analysis an error of 1% was assumed both for Bd2PiPi and Bs2KK • It was right for Bd2PiPi but underestimated for Bs2KK • Thus, the importance of making a combined fit • The larger error on wrong tag fraction for Bs2KK,Bs2PiK is due to the smaller event yield of Bs2PiK • This larger error has the effect of introducing a dependence of the CP sensitivity of Bs2KK on the true values of Adir and Amix, and also a non negligible correlation between the two terms • It is possible to demonstrate that this fact is expected • It’s then necessary to make a scan also on the true values of Adir and Amix to study the sensitivity • The same thing does not apply to the Bd2PiPi, where the error is 1% and the dependence on the true values of Adir and Amix remains moderate

19. and CP sensitivity for

20. and CP sensitivity for

21. Sensitivity

22. (d, gamma) plane plot Corresponding to default input parameters

23. Conclusions • Physics model rather advanced • But in the future need to include specific two body backgrounds that may exhibit their own CP violation • Systematics still to be studied and understood • Sensitivity results for TDR frozen now • A bit of delay, but it was important to make a combined fit to extract mistag fraction from data, rather hard to make a realistic estimate of the resolution on omega otherwise • Dependence of sensitivity on true values of Adir and Amix for the Bs2KK channel introduced by larger error on omega. Scan required and done! • Update TDR B2hh CP sensitivity section • Within one day from now will send around a modified version accounting for the new approach and results • Finalize and release notes on selection and sensitivity studies • Note on selection quite advanced • Note on sensitivity quite advanced in the description of the formalism. Need to include all the results • Drafts of both can be released in 2-3 days from now