Bottom Quark: Discovered in 1977

Home , Bottomness

B CP Violation in the System An Experimental View

Kevin Pitts University of Illinois February 17, 2000 B CP Violation in the System

Outline

1. Introduction:

Charged Current Decays

the CKM Matrix

B=B Mixing

2. CP violation

Introduction

0 J= K

the Mode

2 3. the Measurement of sin

the Fermilab Tevatron

the CDF Detector

0 J= K

the Sample S

Flavor Tagging

Results

4. Outlook: Other CP Modes

5. Summary

Kevin T. Pitts 1 February 17, 2000 B CP Violation in the System

Cheat Sheet Fermions (spin 1/2) generation I II III charge

Leptons:

e -1

e 0 free particles

Quarks:

c t

u +2/3

s b

d -1/3

q qqq bound states: q ,

Mesons:

B = jbd > B = jbd >

B = jbu > B = jbu >

B = jbs > = jbs > B

s s

0 +

K = (jds > +jsd >) = jud >

= K (jds > jsd >) = jud >

J= = jcc > = (juu > +jdd >) 2

Kevin T. Pitts 2 February 17, 2000 B CP Violation in the System

Weak Decays Interactions: The only decay mechanism that changes ﬂavor is the weak interaction.

Strong Interaction:

! K K jss >! jsu > +jsu > ! ( )

! conserves ﬂavor

Electromagnetic interaction:

! juu >! ! ( )

! conserves ﬂavor

Weak neutral current:

! Z ! bb

! conserves ﬂavor

Charged neutral current:

B ! D ` b ! c ! ( )

! does not conserve ﬂavor

Kevin T. Pitts 3 February 17, 2000 B CP Violation in the System

Why are B ’s so Interesting? Bottom quark: discovered in 1977. Several thousand papers since then (theory+experiment: production, decay, couplings, mixing, etc.) Two new accelerators + several new experiments

have been built to study B hadrons.

Why is this B east so interesting?

m ' 5m

it’s heavy:

b p

it couples most strongly to the ultramassive top

' 175m

quark (m )

t p

! but it can’t decay to top!

= 1:5 psec

it has a long lifetime

= 450 m

(c )

B =B it has a long mixing frequency

! fully mixes in about 4.4 lifetimes CP

expected to show LARGE violating effects

' 10 30%

! LARGE

0:1% CP ! violation in the kaon system:

Kevin T. Pitts 4 February 17, 2000 B CP Violation in the System

The Cabibbo-Kobayashi-Maskawa Matrix

Weak charged-current decay (W exchange):

e- e- Vus - - W – W – - ν ν µ e s e K- – u u ν µ – 0

u π

J W + h:c:; L =

cc 2

where

J = ( ; ; ) u ; c ; t ) V +(

e L L L CKM

and !

V V V

ud us ub

V = V V V

cd cs cb

V V V

td ts tb

is the Cabibbo-Kobayashi-Maskawa (CKM) Mixing Matrix which rotates quark mass eigenstates into weak eigenstates.

Kevin T. Pitts 5 February 17, 2000 B CP Violation in the System

The Cabibbo-Kobayashi-Maskawa Matrix

The Wolfenstein parameterization:

0 1

2 3

1 =2 A ( i )

2 2

@ A

V '

1 =2 A

3 2

A (1 i ) A 1

= sin = 0:22

, sine of the Cabibbo angle,

2 2

(K ! ) jV j sin =

Ð '

us C

V V = 1

unitarity )

) V V + V V + V V = 0

td cd ud

tb cb ub

The unitarity triangle

Kevin T. Pitts 6 February 17, 2000 B CP Violation in the System

The Unitary Triangle

Goal of current and future experiments is to measure both sides and three angles in as many ways possible: overconstrain the triangle to look for new physics.

Examples:

B B ) jV =V j

and mixing are

d td ts

) jV j b ! u

decays

CP )

violation in J= K

0 +

CP ! )

violation in B

CP ! D K )

violation in B

s s

Kevin T. Pitts 7 February 17, 2000 B CP Violation in the System

Unitarity Relations Unitary Cabibbo-Kobayashi-Maskawa (CKM) Mixing

Matrix:

V V V

ud us ub

V = V V V

cd cs cb

V V V

td ts tb

y y

V V = V V = 1

Unitarity )

! ! !

V V V

V V V 1 0 0

ud us ub ud cd td

V V V =

V V V 0 1 0

cd cs cb

us cs ts

V V V 0 0 1

V V V

td ts tb

ub cb tb

V + V V + V V = 0 ) V

td cd ud

tb cb ub

This relation is quite useful because each term is of 3

order .

Kevin T. Pitts February 17, 2000 B

CP Violation in the System

B Mixing

0 B

For initial state = :

e P (B (t)) = (1 + cos(m t))

P ( B (t)) = e (1 cos(m t))

start with a B0 beam Prob(B0(t)) 0.5 – 0 Prob(B (t)) – 1/N dN/dt Prob(B0(t)+B0(t)) 0.25

0 0246810 time (nsec) 1 – – A = (N(B0)-N(B0))/(N(B0)+N(B0))

0 Asymmetry at ∆mt=π, no B0

-1 0246810

time (nsec)

weak eigenstates strong eigenstates

: mass difference between the heavy and

m = 0 )

light weak eigenstates ( no mixing) d

Kevin T. Pitts 8 February 17, 2000 B

CP Violation in the System

=B B Mixing

Vtd – – b W d – – – – B0 u,c,t u,c,t B0 W d b Vtd

Vtd – – – – – b u,c,t d – B0 W W B0 u,c,t d b

Vtd

B ; B : Flavor Eigenstates

0 0

B ; B : Mass Eigenstates

H L

m = m m

d H L

(' 0) =

H L

0 B

For initial state = :

1 1

0 t

P (B (t)) = e (cosh( t) + cos(m t))

2 2

t 0

e ( 1 + cos(m t)) (t)) ' P (B

B mt = ' 4:4 fully mixes to B after lifetimes

Kevin T. Pitts 9 February 17, 2000 B CP Violation in the System

Example Mixing Measurement Ph.D. thesis of P. Maksimovic«

PRL 80, 2057 (1998).

+ + 0

B ! ` D

3000 ev

0 +

B ! ` D

2000 ev

0 +

B ! ` D

4300 ev

B top plot: charged do not mix!

middle/bottom plots:

N N

unmixed mixed =

* A

N +N

unmixed mixed

A = 1 )

all unmixed

A = 1 )

all mixed

jAj < 1

due to experimental effects max

Kevin T. Pitts 10 February 17, 2000 B CP Violation in the System

Symmetries

1. parity inversion: P look in the mirror

P (~r ) ! (~r ) )

left-handed right-handed

P je >! je >

L R !

2. charge conjugation: C particle antiparticle !

particle antiparticle

C jp >! jp >

3. time reversal: T run the ﬁlm backwards

T (t) ! (t)

Symmeties are “preserved” if the operator commutes with the Hamiltonian. e.g. the electromagnetic interaction conserves all

three of the above symmetries:

[H ; P ] = [H ; C ] = [H ; T ] = 0

em em em

Kevin T. Pitts 11 February 17, 2000 B CP Violation in the System

CP Violation

If CP is a valid symmetry, then an interaction for a left-handed particle must be the same as an interaction for a

right-handed antiparticle

" "

P C

If CP is violated, then some force of nature must be able to tell the difference between a left-handed quark and right-handed antiquark

Note: CP violation is one of the conditions necessary for the universal matter asymmetry... some process must create (and destroy) quarks and antiquarks at unequal rates!!!

Kevin T. Pitts 12 February 17, 2000 B CP Violation in the System

CP Violation

Since 1964, CP violation has still only been seen in the neutral kaon system. The standard model predicts that we should see it in

the neutral B system as well:

B = jbd >

Now, we will discuss a search for CP violation in CP the neutral B system. The type of violation we

are looking for is of the form:

dN dN

0 0 0

) 6= ) (B ! J= K (B ! J= K

S S

dt dt

where

J= = jcc > J= !

0 + 0

(jds > +jsd >) K ! K =

S S

2 0

and J= K is a CP eigenstate:

0 0

> >= jJ= K CP jJ= K

S S

Kevin T. Pitts 13 February 17, 2000 B CP Violation in the System

“Mixing Induced” CP Violation

Two paths to the same ﬁnal state:

0 0

B ! J= K

direct decay ( )

0 0

B ! B ! J= K

mixed decay ( ) S

The mixed decay accumulates a phase relative to the direct decay.

V – V cb c cb c – J/ψ –J/ψ b W c b W c 0 – 0 B V – B V cs s 0 cs s 0 KS – –KS d d d d

– V V td d 0 td d 0 – – – KS t –KS b t d V s – b d V s 0 W – 0 cs 0 W 0 cs B W – B W B c – B c t W ψ t W – ψ J/ – – J/ V V c V V c

d td b cb d td b cb

" "

t = 0 B t = 0 produce B at produce at

Kevin T. Pitts 14 February 17, 2000 B CP Violation in the System

“Mixing Induced” CP Violation The “direct” decay interferes with the mixed decay.

0 ψ 0 – 0 ψ 0 B J/ KS B J/ KS

– B0 B0 β β

e2i e-2i

! J= K 2

For B the phase arises from the S

interference.

t = 0

produce B at :

0 t=

( B ! J= K ) / e (1 + sin 2 sin mt)

t = 0

produce B at :

0 0 t=

(B ! J= K ) / e (1 sin 2 sin mt)

s dt

Kevin T. Pitts 15 February 17, 2000 B CP Violation in the System

CP Violation

6= e The interference causes dN =dt

1 – 0 0 B → J/ψKs

-2 0 0

1/N dN/dt → ψ 10 B J/ Ks

-4 10

-6 10

-8 10

0 102030

lifetime (psec)

t = 0

produce B at :

0 t=

( B ! J= K ) / e (1 + sin 2 sin mt)

t = 0

produce B at :

0 0 t=

(B ! J= K ) / e (1 sin 2 sin mt)

0 0 0

dN dN

(B ! J= K ) (B ! J= K )

S S

dt dt

A (t) =

dN dN

0 0

(B ! J= K (B ! J= K ) + )

S S

dt dt

Kevin T. Pitts 16 February 17, 2000 B CP Violation in the System

CP Violation

0 0 0

dN dN

(B ! J= K ) (B ! J= K )

S S

dt dt

A (t) =

dN dN

0 0

B ! J= K ) + ( (B ! J= K )

S S

dt dt

A (t) = sin 2 sin(m t)

CP d

" "

amplitude mixing

Goal: to measure sin . m

(Note: well-measured.)

2 ' 0:75

(Standard Model expectation: sin .)

2 = 0 CP If sin ,no violation, the Standard Model

is wrong!

2 6= 0 CP B If sin , observe violation in the system for the ﬁrst time.

Kevin T. Pitts 17 February 17, 2000 B

CP Violation in the System

Time Integrated sin

0 0 0

dN dN

(B ! K ) (B ! K )

S S

dt dt

A =

dN dN

0 0

(B ! K (B ! K ) + )

S S

dt dt

A (t) = sin 2 sin(mt) CP

time integrated:

R R

0 0 0

dN dN

( (B ! K )dt B ! K )dt

S S

dt dt

A =

R R

dN dN

0 0

)dt + )dt (B ! K (B ! K

S S

dt dt

0 0 0

) N (B ) B ! K ! K N (

S S

A =

0 0

N (B ! K ) + N (B ! K )

S S

d B

A = sin 2

1 + (m )

d B

A ' 0:47 sin 2

CP b Note: only valid for incoherent b production (true at hadron colliders.)

Kevin T. Pitts 18 February 17, 2000 B CP Violation in the System

Assumptions

0 0 0

dN dN

B ! J= K ) ( (B ! J= K )

S S

dt dt

A (t) =

dN dN

0 0

B ! J= K ( (B ! J= K ) + )

S S

dt dt

A (t) = sin 2 sin(mt) CP

We assume the following things to be true in this

analsysis: (all assumptions are quite good)

= ' 0

H L

0 0

B ! J= K

via penguin is small

g ! cc

! is mass-suppressed

A (t)

! if present, complicates with

mt)

cos( term

K 100% CP

is even

N (B ) = N (B ) t = 0

! p p ! bbX

! strong interaction preserves bottomness

Kevin T. Pitts 19 February 17, 2000 B CP Violation in the System

Outline

1. Introduction:

Charged Current Decays

the CKM Matrix

B=B Mixing

2. CP violation

Introduction

0 J= K

the Mode

2 3. the Measurement of sin

the Fermilab Tevatron

the CDF Detector

0 J= K

the Sample S

Flavor Tagging

Results

4. Outlook: Other CP Modes

5. Summary

Kevin T. Pitts 20 February 17, 2000 B CP Violation in the System

Analysis Overview

Steps to measure sin :

B ! J= K

sample of decays S

! lifetime information helps, but not required

= B B need to determine the ﬂavor of the at the time of production

! this is the limiting factor, so we need to use as many handles as possible

need to handle potential charge biases in the detector

use a maximum likelihood ﬁt to weight events:

! combines many handles to differentiate signal from background

! accounts for our multiple methods to

0 B discriminate B from

Kevin T. Pitts 21 February 17, 2000 B CP Violation in the System

The Fermilab Tevatron

collisions

1:8 TeV ! center of mass energy =

! the highest energy collider in the world

data shown here is from the 1992-1996 period

The high energy of the Tevatron allows us to study

the most massive particles known:

Z t W boson, boson, quark but it also yields (incredibly) copious production of

“lighter” particles, like b quarks, which ONLY weigh

5 times more than a proton!

bb The Tevatron produces 10 pairs in a year.

Kevin T. Pitts 22 February 17, 2000 B CP Violation in the System

B Physics at the Tevatron

Strong interaction produces b quarks:

pp ! bb + X

e.g.

b q b

– – –

b q b q “gluon fusion”“q annihilation”

Quarks fragment into hadrons:

0 0

= b = bd B s B = bu = bdu

B , , ,

b s

and then decay via weak interaction:

+ +

! D b ! c

B ( )

0 0

! J= K b ! ccs

B ( )

S ) CP violation arises via the weak interaction decay mechanism

Kevin T. Pitts 23 February 17, 2000 Important aspects:

Ð Silicon vertex detector (SVX)

typical 2D vertex error: 60

= 450 m

(c ) B

Ð Central tracking chamber (CTC) 0

typical J= K mass resolution:

10 MeV =c Ð Muon systems, calorimeter crucial for triggering and lepton identiﬁcation

Kevin T. Pitts 24 February 17, 2000 B CP Violation in the System

Triggering

p 286 kHz ) 3:5 s p crossing rate crossing every

(2 interactions/crossing on average) Hz We can write events to tape at a rate of 5 Triggering is CRUCIAL to this experiment. 3 level trigger:

Level 1

! look for calorimeter energy and muon stubs

! operates on every crossing

286 kHz 2 kHz ! in; out

Level 2

! calorimeter clustering, tracking available

! ﬁnd jets, match tracks to muons, match

tracks to clusters (e),

! 10 15 s

decision in -

! 2 kHz Hz in; 20 out

Level 3 ) ! full event read out processor farm

! run a fast version of ofﬂine reconstruction

20 Hz 3 Hz ! in; out to mass storage Kevin T. Pitts 25 February 17, 2000 B CP Violation in the System

Data Sample

The data shown today were accumulated in the

1992-1996 run of the Tevatron.

6 10 pp

Roughly interactions.

100 million About events written to tape.

(roughly 20 Terabytes of data)

In the period 2001-2003, we anticipate accumulating about 50 times as much data.

about 1 Petabyte of data

Kevin T. Pitts 26 February 17, 2000 B

CP Violation in the System

! J= K

B Event Selection

J= !

look for

! = central track + muon chamber track

0 +

K !

look for S

! take advantage of long lifetime to reject

L = 5

background: require >

xy L

B ! J= K

perform 4-track ﬁt assuming : S

µ+ µ-

+ 0

Ð constrained to PDG mass

B J=

Ð K “points” to ( ) vertex S

π+

J= Ð constrained to PDG mass

Ð B candidate “points” back to primary vertex B decay π-

primary

“quality” of ﬁt is used to reject background

Kevin T. Pitts 27 February 17, 2000 B

CP Violation in the System

! J= K B Candidate Event

Run 61377 Event61197 EVT.RAW 12AUG94 17:31:56 25-JAN-98 Et(METS)=/ 8.5 GeV Phi = 118.0 Deg Sum Et = 65.5 GeV

Emax = 8.5 GeV

PHI: 129. CMX east <-- 2.20 Cm --> CMX west ETA: -0.32

Run 61377 Event61197 EVT.RAW 12AUG94 17:31:56 25-JAN-98 Pt Phi Eta Et(METS)=/ 8.5 GeV 5.1 129 -0.32 Phi = 118.0 Deg 4.2 268 0.71 Sum Et = 65.5 GeV -3.9 164 -0.67 2.5 283 -0.22 2.2 243 -0.47 2.2 56 -0.42 -1.7 109 -0.41 -1.7 66 -1.62 -1.4 59 -0.20 -1.3 256 -0.13 1.2 44 -0.61 1.1 93 -0.68 -1.0 159 -0.86 -0.9 266 -0.05 0.9 25 1.21 0.9 140 -0.39 0.8 113 -0.05 0.8 39 -0.51 0.8 49 -0.49 0.8 258 1.01 -0.7 281 -0.28 0.7 290 -0.35 0.7 315 0.59 0.7 317 0.15 0.7 224 0.21 -0.7 230 0.46 0.6 74 -0.23 -0.6 270 -0.49 0.6 27 0.23 -0.6 274 0.00 -0.5 228 0.60 -0.5 47 0.36 0.5 187 1.43 -0.5 280 0.07 6 more trks... hit & to display PHI: 129. ETA: -0.32

Kevin T. Pitts 28 February 17, 2000 B CP Violation in the System

Event Yield

= 110 pb CDF Run I, L :

CDF preliminary 225 0 0 events B → J/ψKs 200 395 ± 31 events

175 S/N = 0.7

150

125

100

0 -20 -15 -10 -5 0 5 10 15 20 0 σ

(Mµµππ-MB )/ M

395 31

events

m m

m =

“normalized” mass is:

nor m

m is the mass from the four track ﬁt

the experimental error on that ﬁtted mass.

m 5:2792 GeV =c

= (world average) B

Kevin T. Pitts 29 February 17, 2000 B CP Violation in the System

Where Did All of the Events Go?

During our data taking, the Tevatron produced

bb about 10 pairs. We were able to reconstruct about 400 events in this decay mode. Why?

probability that:

0 B

b becomes 35%

0 0

! J= K

B 0.04%

J= !

0 +

! 67% S

tracks are in the detector acceptance 0.4%

10 total “efﬁciency” 2

Yield = events “efﬁciency”

10 8

10 quarks) (2 10 ) = 400 Yield = (2 events

Good news: copious production of b quarks. Bad news: environment is dense, signatures are difﬁcult to reconstruct.

Kevin T. Pitts 30 February 17, 2000 B CP Violation in the System

Flavor Tagging

0 B Determining the “ﬂavor” (B versus ) at the time of production

same side π µ+ µ-

π+ primary

π- Lxy 2nd B

jet charge

lepton (e or µ)

same-side tagging

opposite-side jet charge tagging

e opposite-side and tagging Kevin T. Pitts 31 February 17, 2000 B CP Violation in the System

Flavor Tagging Classify a ﬂavor tagging algorithm by two

quantities:

= N =N

tagging efﬁciency:

tag tot

D = (N N )=(N + N )

tagging dilution:

R W R W

! N

(N ) number of right(wrong) sign tags.

R W

! N + N = N

R W tag

The statistical error on a measured asymmetry:

A /

D N

tot

2 D

is the “effective tagging efﬁciency”

D 1% typical

Kevin T. Pitts 32 February 17, 2000 B CP Violation in the System

Flavor Tagging Example

We have a sample of 200 events. 100

events are tagged

) = N =N = 100=200 = 50%

efﬁciency

tag tot

Of those 100 tagged events: 60

are right-sign 40

are wrong-sign.

) D = (60 40)=(60 + 40) = 20% dilution

Effective tagging efﬁciency:

2 2

D = (0:50) (0:20) = 2%

The statistical power of our sample:

ND = 4 “perfectly tagged” events

The ﬂavor tagging penalty is severe.

Kevin T. Pitts 33 February 17, 2000 B CP Violation in the System

Opposite Side Tagging b Initial state: produce b

For this slide, assume:

b ! B ! J= K

0 + 0

B = B ; B ; B ; b ! B

( etc.)

2 2 s

We try to use the other B to identify the initial 2 ﬂavor.

Soft Lepton Tagging (SLT)

B ! ` + X

! looking for

2 ` ! = electrons and muons

! very high dilution, very low efﬁciency

Jet Charge Tagging (JetQ)

B ! X

! looking for 2

! ﬁnd a “jet” of charge tracks )

! momentum weighted charge sum

B correlated with B or

! higher efﬁciency, but lower dilution

Kevin T. Pitts 34 February 17, 2000 B CP Violation in the System

Calibration of Taggers

! J= K We use the B sample to calibrate the ﬂavor tagging algorithms:

CDF preliminary 2 225 ± ± B → J/ψK 200 998 ± 51 events

175

150 events/0.005 GeV/c

125

100

0 5.15 5.175 5.2 5.225 5.25 5.275 5.3 5.325± 5.35 5.375 5.4

µµK mass (GeV/c2) B since we are fully reconstructing a charged

decay, we already know the answer

B B (charge of the K tells us or )

the decay mode and trigger are virtually

! J= K

identical to B S Kevin T. Pitts 35 February 17, 2000 B CP Violation in the System

Calibration of Jet Charge Tag

CDF preliminary JETQ tagging 70 ± ± B → J/ψK mistag fraction: (39.2 ± 3.3)% 60 dilution: (21.5 ± 6.6)% events N = 272.7 ± 21.8 events 50 R

40 ± NW = 175.4 19.7 events 30 20 10 0 5.15 5.175 5.2 5.225 5.25 5.275 5.3 5.325 5.35 5.375 5.4 µµK mass (GeV/c2) 140 ± ± → ψ ± B J/ K N0 = 549.6 32.0 events 120 ε ± % untagged events =Ntag/(Ntag+N0) = (44.9 2.2) 100events 80 60 40 20 0 5.15 5.175 5.2 5.225 5.25 5.275 5.3 5.325 5.35 5.375 5.4

µµK mass (GeV/c2)

From a sample of 998 J= K events:

273 right-sign events

175 wrong-sign events

= N =N = (44:9 2:2)%

Tagging efﬁciency:

tag tot

N N

R W

= = (21:5 6:6)%

Tagging dilution: D

N +N

R W

= (39:2 3:3)% mistag fraction: w

Kevin T. Pitts 36 February 17, 2000 B CP Violation in the System

“Same-side” Tagging

Problems with opposite-side tagging: b opposite -hadron is central (within detector

acceptance) only 50% of the time

b B B

if opposite -hadron is or , mixing s degrades ability to tag

Same Side Tagging (SST): B use charged particles around meson to get

the b ﬂavor

Ð correlation could be through fragmentation

Ð or through excited states (B )

π+

u u – + – π d d **+ d B 0 0 B d B – – b b

fragmentation via B**

70%

high tagging efﬁciency ( ) B no requirement on second

Kevin T. Pitts 37 February 17, 2000 B CP Violation in the System

Summary of Flavor Tagging Algorithms

(D )

type tagger class efﬁciency() dilution

35:5 3:7 16:6 2:2

same-side same-side SVX

38:1 3:9 17:4 3:6

same-side non-SVX

:6 1:8 62:5 14:6

opposite side soft lepton all events 5

:2 3:9 23:5 6:9 jet charge all events 40

y an SLT tag overrides jet-charge

The tagging algorithms all have similar power:

2 D

tagger

:1 0:5

same-side 2

:2 1:3

jet charge 2

:2 1:0 soft lepton 2 When we combine these ﬂavor tagging algorithms (accounting for correlations and double tags) we

measure:

D = (6:3 1:1)%

Which means that, after tagging, a sample of 400

events has the statistical power of about 25 ‘perfectly tagged’ events.

Kevin T. Pitts 38 February 17, 2000 B CP Violation in the System

Combining Flavor Tags

= 16:6%

Example: same-side tag (D ) and

= 21:5% jet charge tag (D )

if the tags agree:

D = (D + D )=(1 + D D )

ef f 1 2 1 2

D = (0:215+0:166)=(1+(0:166)(0:215)) = 36:8% ef f

if they disagree:

D = (D D )=(1 D D )

ef f 1 2 1 2

D = (0:2150:166)=(1(0:166)(0:215)) = 5:1% ef f

and the sign of the tag would come from the jet charge tag. Each event is weighted by its dilution in the ﬁt.

Kevin T. Pitts 39 February 17, 2000 B CP Violation in the System

Tagging Asymmetries We explicitly account for the tagging algorithms which are not completely charge symmetric. An asymmetric tagging algorithm could arise from:

a charge bias in tracking efﬁciency

K N K N versus cross section differences

charge asymmetric background (beampipe spallation)

When allowing for this asymmetry, we end up with

four tagging parameters for each tagging method: D

: the dilution for (+) tags

+ D

: the dilution for (-) tags

: the tagging efﬁciency for (+) tags

: the tagging efﬁciency for (-) tags

Kevin T. Pitts 40 February 17, 2000 B CP Violation in the System

Outline

1. Introduction:

Charged Current Decays

the CKM Matrix

B=B Mixing

2. CP violation

Introduction

0 J= K

the Mode

2 3. the Measurement of sin

the Fermilab Tevatron

the CDF Detector

0 J= K

the Sample S

Flavor Tagging

Results

4. Outlook: Other CP Modes

5. Summary

Kevin T. Pitts 41 February 17, 2000 B CP Violation in the System

Results

We measure:

+0:41

sin 2 = 0:79 (stat: + syst:)

0:44

CDF preliminary 4 asymmetry versus lifetime low ct precision lifetime sample resolution 202±18 events 193±26 events sin2 3 β true asymmetry

2 2

1 1

0 0

-1 solid: full likelihood fit -1 ∆ md fixed dashed: full likelihood fit ∆ md floating -2 0 0.05 0.1 0.15 0.2 0.25

ct (cm)

A = sin 2 sin(m ) d

Kevin T. Pitts 42 February 17, 2000 B CP Violation in the System

Systematic Uncertainties Speciﬁcally splitting off the systematic error, we

ﬁnd:

sin 2 = 0:79 0:39(stat) 0:16(syst)

Summary of systematic error evaluation:

sin 2 parameter evaluated tagging dilution in ﬁt 0.16

tagging efﬁciency in ﬁt m

in ﬁt 0.01

d 0

in ﬁt 0.01 B

m reﬁt 0.01 B

trigger bias external negligible 0

K regeneration external negligible

L D “Systematic” error dominated by , which is statistics limited.

Kevin T. Pitts 43 February 17, 2000 B

CP Violation in the System m

Float

d m

When we let ﬂoat in the ﬁt, we measure:

+0:44

sin 2 = 0:88

0:41

and

m = 0:68 0:17 ps

d The 1 contour: CDF preliminary

) 0.9 -1 contours are 1σ (39%) (ps d

m 0.8 ∆

0.7

∆ md floating 0.6

0.5

∆ md fixed to world average 0.4

0.3 0 0.2 0.4 0.6 0.8 1 1.2

sin2β

m = 0:464 0:018 ps

the PDG value is . d

Kevin T. Pitts 44 February 17, 2000 B CP Violation in the System

Toy Monte Carlo

+0:41

sin 2 =

The error on our result is . We use

0:44 a “toy MC” to generate the relevant observables for many “experiments” to see if this error is reasonable:

The top plot shows that average error from the toy is 0.44, consistent with our measurement. The bottom plot shows from the “pull” distribution that the error returned from the ﬁt correctly estimates the uncertainty in the result.

Kevin T. Pitts 45 February 17, 2000 B CP Violation in the System

Limits

We measure:

+0:41

sin 2 = 0:79 (stat: + syst:)

0:44 m

(Note: this result is with constrained to the world average.) d

A scan of the likelihood function:

Feldman-Cousins frequentist:

0 < sin 2 < 1 93% CL

Bayesian (assuming ﬂat prior in sin )

0 < sin 2 < 1 95% CL

2 = 0

Assume sin

:79 ! 1

integrate Gaussian from 0 :

sin 2 > 0:79 3:6% Prob( )=

Kevin T. Pitts 46 February 17, 2000 B CP Violation in the System

Direct Measurements

OPAL (January ’98)

D. Ackerstaff et al., Euro.Phys.Jour. C5, 379 (1998).

+1:8

! sin 2 = 3:2 (stat:) 0:5 (syst:)

2:0

14 B ! J= K

! from decays S

CDF (February ’99)

T.Affolder et al., Phys.Rev.D (2000). hep-ex/9909003

+0:41

! sin 2 = 0:79 (stat: + syst:)

0:44

400 B ! J= K

! from decays S

ALEPH (November ’99)

R.Forty et al., ALEPH 99-099.

+0:64 +0:36

! sin 2 = 0:93 (stat:) (syst:)

0:88 0:24

16 B ! J= K

! from decays S

LEP measurements have much fewer events, but are able to do much better ﬂavor tagging.

B factories will do even better at ﬂavor tagging.

Kevin T. Pitts 47 February 17, 2000 B CP Violation in the System

“Combined Result” Combining: CDF + ALEPH + OPAL results (R. Forty, ALEPH)

L 4 (a) Preliminary ln − 3

2 ALEPH CDF 1 OPAL

Log-likelihood Log-likelihood Combined 0 (b) 1.0 L

0.5 Likelihood Likelihood

0 -2-1.5 -1 -0.5 0 0.5 1 1.5 2

sin 2β

sin 2 = 0:91 0:35

CDF result dominates the combined result.

Kevin T. Pitts 48 February 17, 2000 B

CP Violation in the System

2 Future Measurements of sin

The CDF analysis sees an “indication” that there is B indeed CP violation in the system, but we have not made a deﬁnitive observation.

Future experiments at the Tevatron and elsewhere

will reduce the error on sin by a factor of 10:

e e B “ factories” at Cornell, SLAC(Stanford)

and KEK(Japan)

! e B ! B e at threshold

ﬁxed target at DESY (Germany)

! pN ! bbX

p p

at the Tevatron

! pp ! bbX

For example, each experiment expects

(sin 2 ) ' 0:08 )

world average uncertainty of

(sin 2 ) 0:03 , which is a precise test of the standard model.

Kevin T. Pitts 49 February 17, 2000 B CP Violation in the System

Comparison of B Factory Expectations

Summary of SOME CP Violation Measurements for the next generation of B experiments after 1 year of running (at design luminosity):

BELLE BaBar Hera-B D¯ CDF

dt (fb )

L 100 30 100 1 1

! K

N(B ) 2000 1100 1500 4k 5k

(sin 2 ) K

0.080 0.098 0.13 0.20 0.12 S

all modes 0.062 0.059 0.12 0.20 0.12

N(B ) 650 350 800 Ð 4.6k

+ 5

(B ! ) 10

BR ( ) 1.3 1.2 1.5 Ð 0.5

y +

(sin 2 ) 0.147 0.20 0.16 Ð 0.16 all modes 0.089 0.085 0.16 Ð 0.16

assumed branching ratio

+1:8

0 + 6

(B ! ) = (4:7 0:6) 10

CLEO measurement: BR

1:5

y assuming that penguin contamination can be unfolded An incomplete list for EVERY experiment.

CLEO-III should not be forgotten: CP

Measure (or limit) the asymmetry in

B ! D K =D K =D K sin2

CP ( )

0 0

BR(B ! K) BR(B ! )

measurements of & will help

0 +

! disentangle the penguin contribution to B

Kevin T. Pitts 50 February 17, 2000 B CP Violation in the System

Other Decay Modes

Another interesting CP violation mode is in the two

! body decay B : – u + u - –π π d d Vub Vub – – – B0 b uπ- B0 b uπ+ – – d d d d

– Vtd d Vtd d – 0 b – 0 + – 0 b 0 - π – π B B V B B V – d ub u d ub u V V td W – td W u - u + π –π d d

In this case, there is a phase coming from the 0

mixing (just like the J= K ﬁnal state.) S

But there is an additional phase coming from the

! u V

the b ( ) transition.

+ CP

Phase is then and asymmetry is

+ + =

proportional to: ( )

sin 2

However....

Kevin T. Pitts 51 February 17, 2000 B CP Violation in the System

Penguin Contamination

In fact, there is another set of diagrams which 0

contribute to this mode: (consider inital B here) u + –π V d – ub d - – – – π 0 - 0 u B b uπ B b – uπ+ d d d d

– V V td d td d - – – –π 0 b – 0 π+ 0 b – 0 u B B V B B u + d ub u d –π V V d td W – td W uπ- d

The penguin decay is now known to be signiﬁcant. There is in fact interference between the tree and penguin decays, as well as the unmixed and mixed diagrams.

This implies that there is a “direct” CP violation

! component in the B mode. It complicates the extraction of CKM information from this mode.

Kevin T. Pitts 52 February 17, 2000 B CP Violation in the System

Other Interesting/Important Measurements To over constrain the triangle and further test/understand the physics of the CKM matrix,

additional measurements will be important:

0 B

mixing

s V

improvement in

the angle (difﬁcult)

and in other modes B

rare decays:

+ + +

! B ! K

0 +

! B !

! b ! s

the B meson production and decay

B = judb >

baryon ( ) production and decay b

Kevin T. Pitts 53 February 17, 2000 B CP Violation in the System

Summary The ongoing program is to overconstrain the CKM matrix (and the unitarity triangle) to further understand and (hopefully) spot inconsistencies which point to physics beyond the standard model.

To fully understand the mechanism behind weak

decays, the CKM matrix and CP violation, we will need a number of measurements using a number of techniques.

This program will require important measurements

+ e at both e and hadron machines.

Kevin T. Pitts 54 February 17, 2000 B CP Violation in the System

Conclusion

Over 35 years since the observation of CP violation in the neutral kaon system.

We are now at the threshold of seeing and studying B CP violation in another system (neutral system).

Over the next several years, additional B measurements in the K and systems will help to shed light on the fundamental mechanisms behind

CP violation.

It’s starting to get interesting!

Stay tuned!

Kevin T. Pitts 55 February 17, 2000