Mixing at the B-Factories

Daniel MarlowPrinceton University

Beauty 2003 10/16/03 the “Iron City”

Neutral B Oscillations

00 )()()( BtbBtat

Flavor decomposition:

Time propagation:

Effective Hamiltonian matrix:

Standard Assumptions

Eigenvalues: )2/()2/( 1212, iMp

qiMLH

If CPT is a good symmetry:

22112211 and MMM

122MMMm LH

121212 Re2 MMLH

Expected to be small in the SM and often taken to be ~0

. . . Neutral B Oscillations

00

00

BqBpB

BqBpB

L

H

12212

*122

*12

i

i

M

M

p

q

Eigenvectors:

12

12

2

Im1Mp

q

1 then )BBP()BP(B If2

0000 p

qIndirect CP violation:

Dilepton MixingAt the B-Factories the B0’s are produced in pairs such that

The study of like- and opposite-sign dileptons provides a conceptually and experimentally simple way to observe the mixing, which is sensitive to Δm

)cos(1),( tmetP dt Same flavor:

)cos(1),( tmetP dt Opposite flavor:

0000

2

1)0( BBBBt

. . . Dilepton MixingThe relative populations of the same-flavor and opposite-flavor samples as well as the time dependence are important. The measurement is characterized by high statistics.

Belle: 29.4 fb-1 PRD 67 052004

In addition to Δmd, the measurement yields information on charged to neutral B production.

09.003.001.1

ps 010.0008.0503.0

0

-1

ff

md

,,,0 XXKXf

B

Other Measurements of Δmd

A variety of other techniques can be used to extract Δmd.

“Tag”

(exclusively reconstructed)

Sc

zt

4)(

1z 2 z

m 20012

zzz

*0 DB

Other Measurements of Δmd

MixedUnmixed

BaBar: 23M B-pairs hep-ex/0212017 submitted to PRD

Other Measurements

of Δmd

-1ps 007.0507.0 dm

Belle & BaBar Combined

Other Measurements of

Δmd

All experiments combined.

-1ps 006.0502.0 dm

Δmd is now very well measured!

More DileptonsOne can also search for CP violation in the mixing by looking for an asymmetry in the number of like-sign dileptons:

12

12

2

Im1Mp

q 32

2

1212

12 10Im

b

c

m

m

M

In SM effects are expected to be small.

CP & T Violation in Dileptons

background

signal Like-sign dilepton Δz distribution.

23M B-pairs

CP & T Violation in Dileptons

23M B-pairs

PRL 88 231801 (2002)

Thinking the unthinkable: CPT ViolationThe mixing analysis can be extended to incorporate possible CPT violating effects via the inclusion of the parameter θ. If CPT is a good symmetry θ=π/2.

cos and 2

1sin 2

for that Note2

Thinking the unthinkable: CPT ViolationBelle did a second fit to their dilepton data, allowing for the possibility of CPT violation.

Belle: 29.4 fb-1 N.Hastings et al.PRD 67 052004

unmP

Coherent Time Evolution at the Y(4S)

B-Flavor Tagging

Exclusive B Meson

Reconstruction

Vertexing &Time DifferenceDetermination

PEP-II (SLAC)

BaBar W.Verkerke EPS2003

BaBar W.Verkerke EPS2003

hep-ex/0303043

Time dependent B decay rates allowing 0, CP/T/CPT violation

BaBar has introduced a new parameterization wherein a fit is done to samples of the form

tag

tagflavor00

,

,)4(

ff

ffBBSee

CPFit to

)Im,ReRe

,,)sgn(Re ;( zzp

qtp

CP

CPCP

LH p

q

A

A

CP

CPCP where and

cot

4 2

221122211

i

i

m

MMz CPT 0z

BaBar 82 fb-1

hep-ex/0303043

Time dependent B decay rates allowing 0, CP/T/CPT violation: fit results

025.0029.0038.0Im

034.0035.0014.0ReRe

011.0013.0029.1

018.0037.0008.0)sgn(Re

z

z

p

q

CP

CP

CP

The Future: Δmd006.0502.0 :(HFAG) average rldCurrent wo dm

Single Measurement Errors

Method(s) Statistical Systematic*

Now

(30 fb-1)

Dilepton ±0.008 ±0.010

“Hadronic” ±0.016 ±0.010

Future

(300 fb-1)

Dilepton ±0.003 ±0.004 ~ ±0.007

“Hadronic” ±0.005 ±0.005 ~ ±0.007

We are nearing the end of the road, but a ~twofold improvement may still be in the cards.

*Systematic error projections from C.Bozzi CKM Workshop CERN 2002

The Future: CPT Parameters

BaBar (82 fb-1)

Im(z) = 0.038 ± 0.029 ± 0.025

Re(z) = 0.014 ± 0.035 ± 0.034

Belle (29 fb-1)

Im(cosθ) = 0.03 ± 0.01 ± 0.03

Re(cosθ) = 0.00 ± 0.12 ± 0.02

Once again, there is room for some improvement, but we are bumping up against systematic errors.

We shouldn’t forget the possibility of new ideas!