sin2βin the BaBar Experiment - Vanderbilt University...BABAR Collaboration 9 Countries 72...

3/15/01 Colorado State University 1

sin2β in the BaBar ExperimentWalter Toki

Colorado State UniversityRepresenting the BaBar Collaboration

FRONTIERS IN CONTEMPORARY PHYSICS - II Vanderbilt University

March 5-10, 2001

• CKM physics• Unitarity Triangle, Mixing, CP eigenstates

• PEPII & BaBar detector

• sin2β analysis• reconstruction, vertexing, tagging, fitting

• Summary

OUTLINE

In the Standard Model for weak interactions the charged hadroniccurrent is

The weak eigenstate quarks are related to the mass eigenstate quarksby unitary transformations,

This can be combined into another unitary matrix V called the Cabbibo-Kobayashi-Masakawa (CKM) Matrix.

This 3× 3 unitary matrix can be parametrized by 3 real parametersand 1 complex phase, which introduces CP violation.

��

tbtstd

cbcscd

ubusud

VVVVVVVVV

VUU †

LLcc duJ ′′= µµ γ

†uLL Uuu =′ LdL dUd =′

This is simplified by the Wolfenstein parametrization to order λ3,Where λ=sinθC.

( ) ��

��

−−−−−

−−≅

��

2/12/1

ληρλλλλ

ηρλλλ

VVVVVVVVV

tbtstd

cbcscd

ubusud

A unitarity constraint (columns 1 & 3) yields,

( ) ( ) 011

=−−++++−

ηρηρ iiVVVV

VVVVVV

tbtdcbcdubud

These complex numbers form a triangle in the ρ−η plane

(ρ, η)*

Unitary Triangle in the Complex ρ − η plane

��

�−= *

VVVVβ

β��

��

�−= *

VVVVγ

��

�−= *

VVVVα

We note that since is real, then *cbcdVV β2

tdtb eVVVV =

Notation: Belle uses φ1 for β

-1 -0.5 0 0.5 1

∆ms/∆md

|Vub/Vcb|

Constraints for the (ρ,η) triangle apex

Bd mixing � ∆mdb→ ulν, B →ρlν � Vub , D*lν � VcbBs mixing � ∆ms / ∆mdKaon mixing & BK decays � εK

Blue blobs, 95% CL estimates of a set oftheoretical models

Using K0 mixing formalism, the B wavefunction iswritten as, . The mass matrix is then,( ) ( ) 00 BtbBta +=ψ

( )( )

( )( )��

��

Γ−Γ−Γ−Γ−

=��

��

iMiMiMiM

2/2/2/*2/

( ) ( ) ( ) ( ) ( ) ( )

( ) [ ] *12

12122/2/

000000

Γ−Γ−=±=

∆−∆Γ−−Γ−±

+−−+

pqeeeetf

BtfBtfqptBBtf

pqBtftB

tdmitimtt

B meson time evolution,

BB Mixing

B0 B0 Mixing into self tagging final states f and f

bu,c,t u,c,tW WB0 B0

The dominant diagrams use the top quark and the calculation yields, 2*

12 62 tbtd

BBtFd VVBfMmGMm

π==∆

If the final states f and f are self tagging distinguishing B0

or B0 decays, then we have conventional mixing via box diag.

( ) ( )( ) ( )

( ) ( )( ) ( )��

��

� ∆−∝�→Γ

��

� ∆+∝�→Γ

2cos10

tmeftBB

dt Unmixed

( ) ( )( ) ( ) ( ) ( )

( ) ( )( ) ( ) ( ) ( )��

��

�∆+∆

−−

+∝→Γ

��

�∆−∆

+∝→Γ

mtmtetfB

sinImcos2

λλλ

( )( )cp

cpCP fA

fApqηλ ≡with and ( ) ( ) cpcpcpcp fHBfAfHBfA 00 , ==

Squaring the amplitudes leads to CP violation effects

B0 SCP KJf ψ/=B0

If decays occur to a common CP eigenstate fcp, accessibleto both B0 and B0, there is mixing and interference via twoamplitudes,

B0 B0 Mixing into CP eigenstates fcp

( )CPCP fCP=η

The best mode has the quark decay , with modes

( )( ) 1,

*≅==≡ − λ

ψψλ βi

tbtd eVV

VVKsJAKsJA

sccb →

,',','

,/,/,/

cpcLcSc

KJKJKJ

χχχ

ηηη

ψψψ

The golden mode, J/ψKs, has the largest measureable rate,λ directly measures the 2β phase, and has magnitude 1.

CP= −1CP= +1

Measured by BaBar

Choice of fCP eigenstates

BB mixingB0→J/ψΚ0

Κ0 →ΚS

gluonB0

Amplitude ~ VcbVcs*~Aλ2

Amplitude ~ VubVus*~Aλ4 (ρ-iη)Penguin contamination

Leading amplitude forB0→J/ψΚS

These “golden modes” are clean. The leading term is VcbVcs*whereas the Penguin term is VubVus*.

other VtbVts* term has same phase

gluonB0

Amplitude ~ VcbVcd*~Aλ3

Amplitude ~ VtbVtd*~Aλ3 (1-ρ-iη)Penguin contamination

Leading amplitude forB0→D+D−,J/ψπ0

Other possible quark decays include, b→ ccd, These include CP modes, B0→D+D−, J/ψπ0, However leading term, VcbVcd* , in this mode is not much larger than, VtbVtd* , so these modes are less desirable.

B0SCP KJf ψ/=,, πν DeD −+ ( ) 040 BsB �ϒ⇐

( ) ( )( )fBftBt

fB ttmettP −∆−=−Γ− sin2sin1, β

Since the velocity in the CMS is very small, measuringposition in the CMS is hopeless.

( ) ( )( )fBftBt

fB ttmettP −∆+=−Γ− sin2sin1, β

B’s are coherently pair produced, , in the reaction, . In the center mass system, ( ) 004 BBsee →ϒ→−+

Experimental Considerations( ) ( ) ( ) ( )1221 0000 BBBB −

Tagging B

A special trick is used to measure the time difference usinga moving CMS in the lab frame. The Lorentz transform yields,

( ) ( )( )**

ffBBfB

ctzctzzz

−≅

−−−=−

βγβγ

The time difference ∆t is translated into a ∆z difference.Hence we measure the difference in z ( boost direction ) Between the fCP and the recoiling/tagging B, ∆z ~ few 100 µm

Other experimental challenges• reconstructing the fCP CP eigenstates, • reconstructing vertices • flavor of the Recoiling B.

Moving CMS � Asymmetric Collider

( )( )

( )( )tme

∆∆−

=→Γ

∆∆+

=→Γ

∆−

( )( )( )

( )( )( )tme

∆∆−

=→Γ

∆∆+

=→Γ

∆−

0perfect ∆z resolution smeared ∆z resolution

Expected ∆z distributions for Mixing into states f, f ,fCP

PEPII e+e- Collider

• Beam energies, e−/e+ , 9/3.1 GeV provide γβ=.56 • e+/e− currents of 2.14/.92 amperes• Peak Luminosity ~3.1 x 1033 cm-2s-1

• SLAC Linac highly efficient injector for PEPII• BaBar detector data logging efficiency +95%• Max. integrated luminosity in one day is 170 pb-1

• overall performance has been astonishingly good

02000400060008000

100001200014000160001800020000220002400026000

6/1/997/1/998/1/999/1/9910/1/9911/1/9912/1/991/1/002/1/003/1/004/1/005/1/006/1/007/1/008/1/009/1/0010/1/0011/1/00

PEPII Delivered Luminosity

Total Recorded Luminosity

Off-peak Recorded Luminosity

Integrated Luminosity October 1999 to November 2000

RunI ~23fb-1, 23M BB produced in October 99 -November 00

New Run started, expects to log >32 fb-1 by August 31

1 2 3 4 5 6 7

30 Series2Series3Series1

1999 2000 2001 2003 2003 2004 2005

)Projected annual PEPII Luminosity

ity (1

0+33 )

peak L integrated L/year total integrated L

=> Terrific motivation for grads. & postdocs to join BaBar

BABARBABAR CollaborationCollaboration9 Countries72 Institutions554 Physicists

USA [35/276]California Institute of TechnologyUC, IrvineUC, Los AngelesUC, San DiegoUC, Santa BarbaraUC, Santa CruzU of CincinnatiU of ColoradoColorado StateFlorida A&MU of IowaIowa State ULBNLLLNLU of LouisvilleU of MarylandU of Massachusetts, AmherstMITU of MississippiMount Holyoke CollegeNorthern Kentucky UU of Notre DameORNL/Y-12U of OregonU of PennsylvaniaPrairie View A&MPrincetonSLACU of South CarolinaStanford UU of TennesseeU of Texas at DallasVanderbiltU of WisconsinYale

Italy [12/89]INFN, U of BariINFN, U of FerraraLab. Nazionali di Frascati dell' INFNINFN, U of GenovaINFN, U of MilanoINFN, U of NapoliINFN, U of PadovaINFN, U of PaviaINFN, U of PisaINFN, U of Roma and U "La Sapienza"INFN, U of TorinoINFN, U of Trieste

Norway [1/3]U of Bergen

Russia [1/13]Budker Institute, Novosibirsk

United Kingdom [10/80]U of BirminghamU of BristolBrunel UniversityU of EdinburghU of LiverpoolImperial CollegeQueen Mary & Westfield CollegeRoyal Holloway, University of LondonU of ManchesterRutherford Appleton Laboratory

Canada [4/16]U of British ColumbiaMcGill UU de MontréalU of Victoria

China [1/6]Inst. of High Energy Physics, Beijing

France [5/50]LAPP, AnnecyLAL OrsayLPNHE des Universités Paris 6/7Ecole PolytechniqueCEA, DAPNIA, CE-Saclay

Germany [3/21]U RostockRuhr U BochumTechnische U Dresden

DIRC (PID)144 quartz bars

11000 PMs

1.5T solenoid

EMC6580 CsI(Tl) crystals

Drift Chamber40 stereo layers

Instrumented Flux Returniron / RPCs (muon / neutral hadrons)

Silicon Vertex Tracker5 layers, double sided strips

e+ (3.1GeV)

e- (9GeV)

BaBar Detector

• SVT: B vertex z resolution ~70 microns• Tracking : σ(pT)/pT = 0.13% × pT ⊕ 0.45%• DIRC : K-πseparation >3.4σ for P<3.5GeV/c• EMC : σE/E = 2.3%⋅E-1/4 ⊕ 1.8%See Stefano Bettarini’s talk, Monday parallel

BaBar DetectorPhoto

BaBarControl RoomPhoto

Red line is PEPII luminosity. nearly continuous

Green Bar; BaBar logging data

Black Bar; BaBar not loggingdata while PEP beams available

High efficiency data loggingand high peak L leads tovery high integrated L

PEPII refill time is afew minutes!!

Daily Operations PEPII Performance Plot

• Reconstruction of exclusive fCP or BCP eigenstates

• Reconstruction of the vertices• reconstruction of CP state• reconstruction of recoiling/tagging B

• B flavor tagging mistag rates• reconstruction of self tagging Bflav modes to measuremistag rates and dilutions of tagging categories

• Fitting and extracting sin2β• fit sin2β and dilutions using both BCP and Bflav modes

Analysis Steps

Reconstruction of CP states( ) ( )

( ) ( )( ) L

−+−+

−+−+−+−+

−+−+−+

µµψ

ππψππµµψ

ππππµµψ

,,,/ 00

• R2 Shape, cosθthrust cuts to reject continuum • BB events are spherical

•Particle ID on Leptons• EMC and IFR cuts

• Helicity angle cut on Lepton (λψ= ±1)• signal ~ sin2θH , bkgd cosθH~ ±1

• J/ψ, ψ′, π0, KS mass cuts• KS vertices detached• ∆E ( = EB −Ebeam) and MES (= sqrt(Ebeam

2−PB2 ) ) cuts

• variables are uncorrelated, bkgd is usually flat

J/ψ sin2θH

sin2θB

• ∆Ε versus MES

• MES

• ∆Ε

Reaction is very clean and backgrounds are uniformlydistributed

J/ψ(µ+µ−) Ks (π+π−)

Identified K−

Indicates a recoiling B0.

Candidate Event

Final sample of KS modes for CP fitting

387 events in the KS mode, ~96% purity MES>5.27 GeV, ∆E<3σ

J/ψKL Analysis• KL will produce hadronic showers in the EMC and IFR

• Require EMC shower (>200 MeV) and the IFR hits (2 layers) not associated with a charged track

• Combine KL direction and reconstructed J/ψ momentum to kinematically predict KL energy.

• Increased efficiency at the cost of larger backgrounds

• CP Opposite to golden KS modes

∆E=E(J/ψ)-E(KL )- Ebeam, Signal peaks at zero

386 Events total in the KL mode, ~39% purity

J/ψKL Analysis

EMC IFR

Vertexing BCP and Btag

P(e-)= 9 GeV

P(e+)= 3.1GeV

• ∆z = γβc∆t= .56 c ∆t• B lifetime, ∆z = ~250 microns• z vertex resolution of J/ψ of BCP ~70 µm (core ~45 µm)• z vertex resolution of BTAG is ~170 microns

• charm decays removed by refitting w/o high χ2 tracks• identified KS and Λ tracks directions used in fit

• B direction is used to correct ∆z event by event• final ∆z resolution is ~190 microns

B flavor Tagging

• B0 tagging in separate mutually exclusive categories• fast lepton, pe >1 GeV, pµ >1.1 GeV • sum of charged Kaons ≠ 0, • neural net 1, mostly isolated unidentified leptons• neural net 2, mostly slow pions from c → D*→ π+D

• Each category has different• efficiencies ε, mistag rates w and dilutions, D=1-2w • effective tagging efficiencies, Q= ε(1-2w)2 , σ(sin2β) ∝ 1/sqrt(Q)

• Each category is measured with data and cross checked with MC• Fit dilution & sin2β in both BCP and Bflav modes simultaneously.

µ−,e−

s K−

B0W−tag

Bflav modes (f and f ) separated by tag category

Self tagging Bflavmodes includeD∗+ π−, D∗+ ρ−,D∗+ a1

−, D+π−,D+ρ−, D+a1

−,J/ψΚ∗0 (Κ+π−)

Results of fitting for mistag rates

• efficiency ε• average mistag rate [w(B0)+w(B0)] /2 • difference in mistag rate between w(B0)- w(B0) • effective tagging efficiency Q• values reproduced using separate D*lν sample

∆t distributions for self tagged Bflav modes by B0/B0 tag

Preliminary mixing results∆md=0.519 ± 0.020± 0.016 ps-1

Cross checks with other physics, fit for ∆md

Asymmetry

∆z distributions ( ) ( )( ) ( )

( )tmtNtNtNtNA

unmixmix

∆∆∝∆+∆∆−∆=

Mixing ∆md

Comparisons

See BaBar talk fromGregory Dubois,Wednesday parallel

separated KS & KL Modes whichhave opposite CP => opposite shifts in ∆t.

∆t distributions for BCP Modes by B0/B0 tag

• Simultaneously fit CP events (BCP) and Mixing (Bflav) events to extractsin2β (1 parameter ) and the dilutions for each tag category anddilution differences between B0 and B0 (2 x 4 parameters )• This uses all measured information and properly correlates errors• other parameters

• ∆z resolution (9 parameters )• background dilutions ( 8 parameters )• background resolutions ( 3 parameters )• backgrounds ∆t distribution ( 6 parameters )

• TOTAL 35 parameters• Fix ∆md =0.472 ps-1 and τB =1.548 ps to PDG values

Likelihood

Other remarks• J/ψKL bkgd fit has non-symmetric CP for J/ψKLπ0 bkgd(-.68=sin2β)• Dilutions allowed D(B0) and D(B0) allowed to differ• A(cp) value was hidden to avoid people bias until 2wks before conf.Checks

• lifetime consistent PDG (1.55), τ(B0) =1.51± .05± .03ps • mixing consistent with PDG, • toy MC checks on fitting, fitting MC samples, • fitting non-CP data, split data sets, • independent fitting and tagging programs

CP Vertex Parametrization• event by event ∆z errors used in fit• 3 gaussians, core (88%)+tail(11%)+outlier(1%)• fit variables

• scale factors of core and tail (2) • fractions of tail and outlier (2)• ∆z bias for 4 tagging categories and tail (5)

Likelihood Function for CP and mixing events( )�

��

� ∆∆+

��

� ∆+Γ=

∆Γ−0,

1sinIm

tagBCPN

tRtMDDe λ

( )��

��

⊗��

��

� ∆∆−�

��

∆−Γ�

∆Γ−

=RtMDDe tBtagCPN

isinIm

( )��

��

� ∆∆−

��

� ∆+Γ=

∆Γ−0,

tagBmixN

tRtMDDe

( )��

��

� ∆∆+

��

� ∆+Γ=

∆Γ−0,

tagBunmixN

tRtMDDe

( )��

��

� ∆∆+

��

� ∆−Γ=

∆Γ−0,

BtagunmixN

tRtMDDe

( )��

��

� ∆∆−

��

� ∆−Γ=

∆Γ−0,

BtagmixN

tRtMDDe

200 BB DD

= 00 BB DDD −=∆

• uncorrected forDilution and backgrounds

KL modeηcpsin2β = 0.87± .51 (stat)

KS modeηcpsin2β = 0.25± .22 (stat)

( ) ( ) ( )( ) ( )tNtN

tNtNCPA

tagBCP

∆+∆

∆−∆= 00

Raw Asymmetry

( )CPCP fCP=η

KL modeKS modes Combined fit

± 1σ

Loglikelihood of sin2β measurements

sin2β=0.34 ±0.20(stat) ±0.05(sys)

CP fitting selected samples

Cross ChecksSeparate by mode and tagging categories, results randomlyscattered about median value

Ks mode only

Systematic sin2β Error Estimates

• largest ∆t error due to Dch-SVT alignment• some KS and KL errors anti-correlate and tend to cancel infull sample fits

sin2β values

Other experiments

World Average

sin2β measurement and Unitarity Triangle

Parameter Value � Error(s)

jVudj 0:97394� 0:00089

jVusj 0:2200� 0:0025

jVubj (3:49� 0:27� 0:55)� 10�3

jVcdj 0:224� 0:014

Parameters

jVcsj 0:969� 0:058

jVcbj (40:75� 0:40� 2:0)� 10�3

j�Kj (2:271� 0:017)� 10�3

CP violating

�md (0:487� 0:014) ps�1

�ms WA (Beauty2000) amplitude spectrum

Mixing Observables

sin2�BaBar 0:34� 0:21

sin2�WA 0:49� 0:16

mt (166� 5) GeV

mK (493:677� 0:016) MeV

�mK (3:4885� 0:0008)� 10�15 GeV

(5:2794� 0:0005) GeV

Experimental

(5:3696� 0:0024) GeV

Parameters

mW (80:419� 0:056) GeV

GF (1:16639� 0:00001)� 10�5 GeV�2

fK (159:8� 1:5) MeV

mc (1:3� 0:1) GeV

BK 0:87� 0:06� 0:13

�cc 1:38� 0:53

�ct 0:47� 0:04

Theoretical

�tt 0:574� 0:004

Parameters

�B(MS) 0:55� 0:01

fBdpBd (230� 28� 28) MeV

� 1:16� 0:03� 0:05

Parametersof theUnitarityTriangle

Summary• Worlds most precise sin2β measurement

• Other cross checking CP modes to be added, J/ψK*0, χKS

• Many other BaBar analyses presented and underway• see BaBar talks by Dubois, Vasseur, Colberg, Soffer

• New run started, data should be >doubled by August 2001

• By 2005 BaBar should log ~500 fb-1

sin2β=0.34 ±0.20(stat) ±0.05(sys)

sin2βin the BaBar Experiment - Vanderbilt University...BABAR Collaboration 9 Countries 72...

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