Vincenzo Vagnoni INFN Bologna LHCb light meeting 2 September, 2003

Studies ySensitivit CP hh B -sd,

Vincenzo VagnoniVincenzo Vagnoni

INFN BolognaINFN Bologna

LHCb light meetingLHCb light meeting

2 September, 20032 September, 2003

Vincenzo Vagnoni LHCb light meeting, 2 September 2003 2

OverviewOverview

Selection efficiency summarySelection efficiency summary New parametrization of signal acceptanceNew parametrization of signal acceptance bb background mass and proper time spectrabb background mass and proper time spectra Proper time resolution studiesProper time resolution studies Changes to fast MC and fitterChanges to fast MC and fitter Sensitivity on CP asymmetry termsSensitivity on CP asymmetry terms Sensitivity on the gamma angleSensitivity on the gamma angle


Annual yields and B/S ratiosAnnual yields and B/S ratios

Event typeEvent typeB/S

(central values)

Untagged annual yield

BBdd + + -- 0.42 26000

BBdd K+ K+ -- 0.16 135000

BBs s K+ K- K+ K- 0.31 37000

BBs s + K-+ K- 0.67 5300

Annual yields Annual yields after L0xL1 triggers and offline selection as quoted in the TDR draftafter L0xL1 triggers and offline selection as quoted in the TDR draft B/S before trigger B/S before trigger (only (only combinatorial bb backgrouncombinatorial bb background)d)

Agreed to use central values for B/S instead of upper limits


Parametrization of signal Parametrization of signal acceptance vs proper timeacceptance vs proper time

New parametrization of signal acceptance usedNew 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

b

at

atNt

3

3

1)(

)exp(1)(

at

Nt

Old parametrization New parametrization


Acceptance fits with new Acceptance fits with new parametrizationparametrization


bb background mass spectrabb background mass spectra bb mass spectra after trigger and with slightly reduced bb mass spectra after trigger and with slightly reduced

offline-selection cuts (exponential fit)offline-selection cuts (exponential fit)

Bd2PiPi

Slope=-1.7

Bs2KK

Slope=-1.2

Bd2KPi

Slope=-0.54

Bs2PiK

Slope=-0.44


bb background proper time bb background proper time spectra (I)spectra (I)

Functional form for bb bacground proper time spectra Functional form for bb bacground proper time spectra guessed from untagged signal ones and fitted to bb data guessed from untagged signal ones and fitted to bb data after trigger with slightly reduced offline selection cutsafter trigger with slightly reduced offline selection cuts

)exp()exp(1

)( bxt

NtR

a

Bd2PiPi

“lifetime” = (0.98±0.11) ps

Bs2KK

“lifetime” = (1.13±0.17) ps


bb background proper time bb background proper time spectra (II)spectra (II)

Bd2KPi

“lifetime” = (0.87±0.11) ps

Bs2PiK

“lifetime” = (1.15±0.16) ps


Proper time resolution (I)Proper time resolution (I) Proper time resolution fitted with double gaussiansProper time resolution fitted with double gaussians

Bd2PiPi Bs2KK

Bd2KPi Bs2PiK


Proper time resolution (II)Proper time resolution (II) Proper time resolution vs true proper time (triggered and Proper time resolution vs true proper time (triggered and

offline selected events)offline selected events)


Proper time resolution (III)Proper time resolution (III) Proper time resolution vs true proper time (triggered and Proper time resolution vs true proper time (triggered and

offline selected events)offline selected events)


Changes to fast MCChanges to fast MC As before only bb combinatorial background consideredAs 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 Background mass generated in wide mass window with exponential shape according to fits to bb dataexponential 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 Background rate generated according to results of fits to

bb databb data Bd2PiPi and Bs2KK generated as before, simulating Bd2PiPi and Bs2KK generated as before, simulating

tagging and CP violationtagging and CP violation Bd2KPi and Bs2PiK generated simulating tagging and Bd2KPi and Bs2PiK generated simulating tagging and

direct CP violation (charge asymmetry)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 New parametrization of signal acceptance taken into accountaccount


Fast MC: input valuesFast MC: input valuesNominal parameters:Nominal parameters: Bd2PiPi,Bd2KpiBd2PiPi,Bd2Kpi Bs2KK,Bs2PiKBs2KK,Bs2PiK tagging efficiency tagging efficiency 41.8%41.8% 49.8%49.8% wrong tagging fraction wrong tagging fraction 35%35% 33%33% M M 0.5 ps0.5 ps-1-1 20 ps20 ps-1-1

1/1.54 ps1/1.54 ps-1-1 1/1.46 ps1/1.46 ps-1-1

// 0 0 0.10.1 dd 0.30.3 0.30.3 thetatheta 160 degrees160 degrees 160 degrees160 degrees gamma anglegamma angle 65 degrees65 degrees 65 degrees65 degrees phi_sphi_s -------------------------------- -0.04-0.04 phi_dphi_d 0.8180.818 --------------------------------Sensitivity scan: parameters are varied one at a timeSensitivity scan: parameters are varied one at a time d: 0.1, 0.2, (0.3), 0.4d: 0.1, 0.2, (0.3), 0.4 theta: 120, 140, (160), 180, 200 degreestheta: 120, 140, (160), 180, 200 degrees gamma angle: 55, (65), 75, 85, 95, 105 degreesgamma angle: 55, (65), 75, 85, 95, 105 degrees phi_s: 0, (-0.04), -0.1, -0.2phi_s: 0, (-0.04), -0.1, -0.2 M: 15, (20), 25, 30 psM: 15, (20), 25, 30 ps-1-1

/ / : 0, (0.1), 0.2: 0, (0.1), 0.2


Changes to the fitter (I)Changes to the fitter (I)

CombinedCombined extended maximum likelihood fit of extended maximum likelihood fit of Bd2PiPi and Bd2PiPi and Bd2KPiBd2KPi ( (Bs2KK and Bs2PiKBs2KK and Bs2PiK) in order to ) in order to extract mistag extract mistag fraction from datafraction from data

Proper time resolution (double gaussian) and proper time Proper time resolution (double gaussian) and proper time acceptance with new parametrization from full GEANT acceptance with new parametrization from full GEANT simulation are usedsimulation are used

The likelihood is multiplied by gaussian priors in order to The likelihood is multiplied by gaussian priors in order to use the measurements fromuse 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 Power series expansion in , , and and M inside the M inside the

likelihood function very useful to reduce fit computing timelikelihood function very useful to reduce fit computing time Details in forthcoming LHCb note


Changes to the fitter (II)Changes to the fitter (II)

The likelihood fit is performed against 17 The likelihood fit is performed against 17 parameters: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)


Changes to the fitter (III)Changes to the fitter (III) Once the fit has converged Once the fit has converged Re(Re() ) andand Im( Im() ) are transformed are transformed

to to AdirAdir and and AmixAmix 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 techniquePropagation 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)


Bd2PiPi Bs2KK

Bd2KPi Bs2PiK

Fast MC mass spectra with Fast MC mass spectra with projection of likelihood fit projection of likelihood fit

superimposed (1 year)superimposed (1 year)


Results and discussionResults and discussion Resolution on wrong tagging fraction after one yearResolution 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 In the previous analysis an error of 1% was assumed both for Bd2PiPi and Bs2KKBs2KK

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 The larger error on wrong tag fraction for Bs2KK,Bs2PiK is due to the smaller event yield of Bs2PiKsmaller event yield of Bs2PiK

This larger error has the effect of introducing a dependence of the CP 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 sensitivity of Bs2KK on the true values of Adir and Amix, and also a non negligible correlation between the two termsnegligible 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 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 moderatethe dependence on the true values of Adir and Amix remains moderate

0.1 0.2 (0.3) 0.4

0.063 0.064 0.064 0.064

0.052 0.054 0.055 0.056

-0.43 -0.43 -0.43 -0.43

0.0034 0.0035 0.0035 0.0035

120° 140° (160°) 180° 200°

0.065 0.064 0.064 0.064 0.063

0.055 0.055 0.055 0.055 0.054

-0.45 -0.44 -0.43 -0.41 -0.41

0.0035 0.0035 0.0035 0.0035 0.0035

55° (65°) 75° 85° 95° 105°

0.064 0.064 0.064 0.064 0.064 0.064

0.057 0.055 0.053 0.053 0.053 0.055

-0.41 -0.43 -0.44 -0.43 -0.40 -0.37

0.0035 0.0035 0.0035 0.0035 0.0035 0.0035

d

dCPA

KA

mCP

dCP AACorr ,

mCPA

dCPA

KA

mCP

dCP AACorr ,

mCPA

dCPA

KA

mCP

dCP AACorr ,

mCPA

CP sensitivity for -

d B K Bd and

0.1 0.2 (0.3) 0.4

0.060 0.055 0.050 0.051

0.064 0.076 0.067 0.062

-0.17 -0.33 -0.22 -0.14

0.023 0.023 0.024 0.024

120° 140° (160°) 180° 200°

0.061 0.059 0.050 0.049 0.050

0.053 0.064 0.067 0.071 0.067

-0.28 -0.32 -0.22 -0.02 0.20

0.023 0.023 0.024 0.024 0.024

55° (65°) 75° 85° 95° 105°

0.051 0.050 0.048 0.049 0.051 0.049

0.066 0.067 0.064 0.065 0.068 0.066

-0.20 -0.22 -0.20 -0.21 -0.20 -0.18

0.024 0.024 0.024 0.023 0.023 0.023

d

0 (-0.04) -0.1 -0.2

0.052 0.050 0.050 0.052

0.067 0.067 0.070 0.079

-0.22 -0.22 -0.22 -0.23

0.023 0.024 0.024 0.024

0 (0.1) 0.2

0.055 0.050 0.046

0.072 0.067 0.060

-0.20 -0.22 -0.21

0.023 0.024 0.024

15 ps-1 (20 ps-1)) 25 ps-1 30 ps-1

0.042 0.050 0.059 0.076

0.057 0.067 0.076 0.096

-0.22 -0.22 -0.19 -0.18

0.023 0.024 0.024 0.024

s

/

M

KA

dCPA

mCPA

mCP

dCP AACorr ,

CP sensitivity for -

s B KK K Bs and

KA

dCPA

mCPA

mCP

dCP AACorr ,

KA

dCPA

mCPA

mCP

dCP AACorr ,

KA

dCPA

mCPA

mCP

dCP AACorr ,

KA

dCPA

mCPA

mCP

dCP AACorr ,

KA

dCPA

mCPA

mCP

dCP AACorr ,

0.1 0.2 (0.3) 0.4

1.8° 2.7° 4.9° 9.0°

120° 140° (160°) 180° 200°

3.8° 3.8° 4.9° 6.7° 5.2°

55° (65°) 75° 85° 95° 105°

5.8° 4.9° 4.3° 4.7° 4.7° 4.7°

0 (-0.04) -0.1 -0.2

4.9° 4.9° 4.9° 5.4°

0 (0.1) 0.2

5.2° 4.9° 4.5°

15 ps-1 (20 ps-1) 25 ps-1 30 ps-1

4.0° 4.9° 5.9° 8.5°

d

s

/

M

Sensitivity


(d, gamma) plane plot(d, gamma) plane plot

Corresponding to default input

parameters


ConclusionsConclusions Physics model rather advancedPhysics 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 understoodSystematics still to be studied and understood Sensitivity results for TDR frozen nowSensitivity 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 sectionUpdate 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 studiesFinalize 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

Documents

Vincenzo Vagnoni INFN Bologna LHCb light meeting 2 September, 2003