Matter-Antimatter asymmetry in the B-meson system

Fred BlancUniversity of Colorado

EPFL, Lausanne, April 11th, 2005

Outline

• Introduction on CP violation

• The angles of the Unitarity Triangle

• α (B→ππ, ρπ, ρρ)

• γ (B→DK, Bs)• β (B→J/ΨKS, φKS , η’KS etc...)

• An interesting case study: B0→ η’KS and related decays in BABAR

b→sg

The CP (a)symmetry

• The CP operation is the combination of

• charge conjugation C operator (inversion of charge)

• parity P operator Ψ(x) → Ψ(-x)

• CP is conserved if P (A→B+C) = P (CP[A→B+C])

Example: CP violation in K0 decay

• Neutral kaon system:produced K0 and K0 have different lifetimes

• P(K0 → π+π-,t) ≠ P(K0 → π+π-,t)

• CPLEAR measured these rates (Phys. Lett. B458 (1999) 545)

Thomas Schietinger 3 December 2003Role of the b quark in particle physics 17

PS 1

95

Since then measured with high precision: (for instance CPLEAR) Angelopoulos et al.,

Phys. Lett. B 458, 545 (1999)

K0 !"#$#%

K0 !"#$#%

decays

decay time [&S]

Nb decays

Decay time [τs]

How to generate CP violation

• CP violation is seen when

• a process occurs through 2 (or more) “paths”

• 2 amplitudes have different weak AND strong phases

• A = A1eiγ + A2eiδ A = A1e-iγ + A2eiδ

(γ≠0 and δ≠0 ) ⇒ |A|2 ≠ |A|2

weak phase strong phasedifference γ difference δ

Direct CP violation

11/14/03 Owen Long, UCSB 6

+!

+!

-!

-!" "

B!f

B!f

B!f

B!f

A

A

A A

Weak phase difference: !

Strong phase difference: "No strong phase difference

Non-zero strong phase difference

|A|=|A|

|A|#|A|!

Interfering amplitudes

11/14/03 Owen Long, UCSB 6

+!

+!

-!

-!" "

B!f

B!f

B!f

B!f

A

A

A A

Weak phase difference: !

Strong phase difference: "No strong phase difference

Non-zero strong phase difference

|A|=|A|

|A|#|A|!

Interfering amplitudes

11/14/03 Owen Long, UCSB 6

+!

+!

-!

-!" "

B!f

B!f

B!f

B!f

A

A

A A

Weak phase difference: !

Strong phase difference: "No strong phase difference

Non-zero strong phase difference

|A|=|A|

|A|#|A|!

Interfering amplitudes

δ=0

|A| = |A|

δ≠0

|A| ≠|A|

Direct CP in B0→K+π-

• 1999: Direct CP violation first observed in K0 decays=> very small effect (~10-6)

• 2004: Direct CP violation seen in B0 → K+π-

ACP = -0.109 ± 0.019 (5.7σ)

!"#$%&'(')&*$+,''--'./(0$1*

B0 → K +π-

! Observation of direct CP in B0→K±! " decays

NBB

NK!

ACP

signif.

BABAR 227M 1606±51 -0.133±0.030±0.009 4.2"Belle 275M 2140±53 -0.101±0.025±0.005 3.9"

B0→K+! -B0→K-! +

B0→K+! -

B0→K-!+

Significantasymmetry insignal region

!"#$%&'(')&*$+,''--'./(0$1*

B0 → K +π-

! Observation of direct CP in B0→K±! " decays

NBB

NK!

ACP

signif.

BABAR 227M 1606±51 -0.133±0.030±0.009 4.2"Belle 275M 2140±53 -0.101±0.025±0.005 3.9"

B0→K+! -B0→K-! +

B0→K+! -

B0→K-!+

Significantasymmetry insignal region

Phases in the standard model

• Strong phase δ

• from final state interactions (FSI)

• doesn’t change sign under CP

• Weak phase

• from weak processes in quark sector qu → W+ qd (+c.c)

• charged currents between all up-type and down-type quarks(not only within each family)

• 3 x 3 = 9 possible currents(u→d, u→s, u→b, c→d, c→s, c→b, t→d, t→s,t→b)

u c t

d s b

The CKM matrix

• Amplitude of current qi → qj : Vij

• (Vij) => Cabibbo-Kobayashi-Maskawa (CKM) matrix

• Constraints (unitarity, unphysical phases) => 4 parameters

• 3 angles + 1 irreducible complex phase

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

( )Sole source of CP violation

in the standard model

Wolfenstein parametrisation

• λ = 0.22 (=> λ2 ≈ 0.05, λ3 ≈ 0.01)

• A, ρ and η ≈ 1

• Unitarity => ∑ VijV*kj = 0 and ∑ VijV*ik = 0=> 6 triangles in the complex plane!

• 4 triangles are squashed (different powers of λ)

• 2 triangles have all sides of similar size (λ3)

1.4 Violation in the Standard Model 21

!

" #

$

A%

(b) 7204A57–92

1

VtdVtb&

|VcdVcb|&

VudVub&

|VcdVcb|&

VudVub&

VtdVtb&

VcdVcb&

$

#

"

0

0

(a)

Figure 1-2. The rescaled Unitarity Triangle, all sides divided by .

The rescaled Unitarity Triangle (Fig. 1-2) is derived from (1.82) by (a) choosing a phase convention

such that is real, and (b) dividing the lengths of all sides by ; (a) aligns one side

of the triangle with the real axis, and (b) makes the length of this side 1. The form of the triangle

is unchanged. Two vertices of the rescaled Unitarity Triangle are thus fixed at (0,0) and (1,0). The

coordinates of the remaining vertex are denoted by . It is customary these days to express the

CKM-matrix in terms of four Wolfenstein parameters with playing

the role of an expansion parameter and representing the -violating phase [27]:

(1.83)

is small, and for each element in , the expansion parameter is actually . Hence it is sufficient

to keep only the first few terms in this expansion. The relation between the parameters of (1.78)

and (1.83) is given by

(1.84)

This specifies the higher order terms in (1.83).

REPORT OF THE BABAR PHYSICS WORKSHOP

Vtd ≠ V*td

Vub ≠ V*ub

“The” Unitarity Triangle (UT)

• 1st and 3rd columns => V*ubVud+ V*cbVcd+ V*tbVtd=0

• 3 sides of order λ3 => large angles

• phases from V*ub (γ) and Vtd (β)

1.4 Violation in the Standard Model 21

!

" #

$

A%

(b) 7204A57–92

1

VtdVtb&

|VcdVcb|&

VudVub&

|VcdVcb|&

VudVub&

VtdVtb&

VcdVcb&

$

#

"

0

0

(a)

Figure 1-2. The rescaled Unitarity Triangle, all sides divided by .

The rescaled Unitarity Triangle (Fig. 1-2) is derived from (1.82) by (a) choosing a phase convention

such that is real, and (b) dividing the lengths of all sides by ; (a) aligns one side

of the triangle with the real axis, and (b) makes the length of this side 1. The form of the triangle

is unchanged. Two vertices of the rescaled Unitarity Triangle are thus fixed at (0,0) and (1,0). The

coordinates of the remaining vertex are denoted by . It is customary these days to express the

CKM-matrix in terms of four Wolfenstein parameters with playing

the role of an expansion parameter and representing the -violating phase [27]:

(1.83)

is small, and for each element in , the expansion parameter is actually . Hence it is sufficient

to keep only the first few terms in this expansion. The relation between the parameters of (1.78)

and (1.83) is given by

(1.84)

This specifies the higher order terms in (1.83).

REPORT OF THE BABAR PHYSICS WORKSHOP

B physics: strategy

• Measure the UT sides and angles with as many independent measurements as possible=> constrain the UT... and hopefully see inconsistency

• Review here current status of the measurements of the angles α, β and γ

Measuring the UT angles in B decays

• Phases in B (Bd, Bu) physics

• b→u (CKM suppressed) => phase γ

• mixing => phase β

• no phase from dominant b→c transitions

• Methods for measuring the angles

• B0 mixing + b→c => β

• B0 mixing + b→u => π - β - γ = α

• B decays with b→u transition => γ

Current Experimental Status

• Review measurements of the UT angles(in an unusual order...)

• α (φ2)

• γ (φ3)

• β (φ1)

14

CKM angle α

• α is measured by modes that involve mixing (=> B0) and b→u (“tree”) transition

• B → ππ

• B → ρπ

• B → ρρ

B0 → π+π-

• B0 → π+π-

• B0 mixing => Vtd => phase β decay tree => Vub => phase γ => γ+β = π-α => measure of α ☺

• Unfortunately, π+π- can also occur through a loop transition=> no phase => measured asymmetry αeff ≠ α (“penguin pollution”)

• Solution: Determine penguin contribution with an isospin analysis (B0,+ → π+π- , π+π0 , π0π0 and c.c.)FNAL - March 11, 2005 J. Olsen 17

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ACP = sin2α sin(ΔmΔt)

B → ππ Isospin analysis

• Gronau-London (PRL 65 (1990), 3391)

• ππ decays relatedby SU(2) symmetry:

• I=0 and I=2 ππ states

• penguins → I=0 only

• π+π0 is a pure I=2 state => no penguin => |A+0| = |A-0|

• Measure all three decay modes (+c.c) => α

• If too small => Grossman-Quinn limit

• But π0π0 is large (larger than expected)=> poor limit

• ...but hopes for using GL method!

6.1 Theoretical Background: The Role of Penguins and -Extraction 333

6.1.2.1

In the absence of penguin contributions, the asymmetry in measures . However,

penguins can contribute to this decay. Indeed, as was argued above, it appears that such penguin

contributions are sizeable. Since the weak phase of the penguin diagram is different from that

of the tree diagram, penguin pollution can affect the clean extraction of from this process. An

isospin analysis can be used to eliminate the penguin pollution in this case [4].

The isospin decomposition of the amplitudes ,

and is shown in Table 6-1. Note that because of Bose statistics the

two-pion state produced in decay has no contribution. Thus the three two-pion decay

amplitudes depend only on two isospin amplitudes, hence there is one relationship,

(6.19)

between them. Thus they form a triangle, as drawn in Fig. 6-1.

The amplitudes for the -conjugate processes , and are

obtained from the amplitudes by simply changing the sign of the CKM phases; the strong phases

remain the same. These amplitudes also form a triangle:

(6.20)

The measurements of the total rates for and yield and ,

respectively. The measurement of the time-dependent decay rates for and

!""

6–98

8418A3

A(B° "°"°)~

A(B° "°"°)A(B° "+"

–)

~

A(B "–"°) = A(B

+ "

+"°)

~

1

2

A(B° "+"

–)

1

2

Figure 6-1. Isospin analysis of decays.

REPORT OF THE BABAR PHYSICS WORKSHOP

κ = 2(αeff-α)

α from B → ππ

• Large π0π0 => | αeff - α | < 35o => 67o < α < 113o

• Poor limit fromππ modes alone

HFAG plotsMoriond 2005

http://www.slac.stanford.edu/xorg/hfag/

Comparison BABAR / Belle

• Until 2004, BABAR and Belle numbers diagreed

• Since 2005, the agreement seems acceptable (2.2σ)

-1

-0.5

0

-1 -0.5 0

88122

227

85

152 275

Belle

BABAR

S!!

C !!

-1

-0.5

0

-1 -0.5 0

Belle

2.2!

BABAR

S""

C ""

B → ρπ & B → ρρ

• B → ρπ

• time-dependent Dalitz analysis

• α = ( 113 +27-17 6 )o => better than ππ

• B → ρρ

• Vector-Vector decay=> longitudinal (CP even) & transverse (mixed CP) polarizations

• Analysis shows ~100% longitudinally polarized => CP even

• B → ρ0ρ0 very small => good limit on | αeff - α | < 11o => even better than ρπ

α: summary

• HFAG (CKM Fit): α = ( 101 +16-9 )o

CKM angle γ

• Phase of Vub

• Measuring it at the Bd factories:

• B → DK: difficult... but Dalitz analysis => γ=(70±10±10)o (average of Belle+BABAR)

• B → K+π - : ACP≠0 is direct evidence for γ≠0 !...but large uncertainty on the strong phase :-(

• Domain of BS decays => LHCb

CKM angle β from charmonium

• Charmonium modes B→(cc)KS (e.g. J/Ψ KS)

• decay dominated by one b→c amplitude (no phase)=> only phase from mixing (2β)

• theoretically clean(negligible uncertainty)

• experimentally accessible

=> sin2β = 0.726±0.037 (HFAG)

Wouter Verkerke, NIKHEF

Combined golden modes result for sin2b

sin2ß = 0.722 ± 0.040 (stat) ± 0.023 (sys)No evidence for additional CPV in decay |?|=0.950±0.031(stat.)±0.013

J/? KL (CP even) mode(cc) KS (CP odd) modes

(2002 measurement: sin(2ß) = 0.741±0.067±0.034)

he p- e x/ 0408127

hep-ex/0408127

CKM angle β from b→s gluon

• b→sg modes

• penguin loop:

• Vtb & Vts => no phase

• ...but Vub from b→u treemay be non-negligible

• φKS: no u-quark in final state => clean (±0.05th)

• η’KS, π0KS, ωKS, KSKSKS, etc...

• may get contribution from tree diagram => sin2βeff

• theoretical estimates for σth for each mode (difficult)

a

g b

Fred Blanc 4DPF'04

SM expectations for h'KS and p0K

S

! DS = sin2bcharmonium

– sin2beff

= 0

! B0 ! h'K

S

" DS bound from SU(3) analysis:

using B0 decays to pairs of light

pseudoscalar mesons

⇒ |DS| < ~0.1 [Grosman et al., PRD68, 015004 (2003)]

[Chiang et al., PRD68, 074012 (2003)]

" Specific model calculations: DS ~0.01[Beneke et al., NuclPhys B675, 333 (2003)]

! B0 ! p0

KS (b ! sdd is dominant)

" SU(3): DS ~0.2 [Gronau et al., PLB579, 331 (2004)]

" model-dependent QCD: DS ~0.1[Buras et al., Ciuchini et al, Charles et al.]

?

mixing

penguin (dominant)

Physics beyond the SM

may enter the loop

(sensitivity to high virtual mass)

tree (CKM + color-supressed)

phase g

β from b→s gluon: results

Estimated theoretical uncertainty for each mode

3.7σ apart!(naive average of b→sg modes)

BABAR+Belleaverages

β: summary

• Accurate measurement of sin2β from (cc)KS modes => sin2β = 0.726±0.037 (5% uncertainty)

• sin2β from b→sg systematically low

• Question 1: is this effect significant? => need more measurements and better theoretical understanding

• Question 2: what is the cause of this shift? => standard model? e.g. if tree contamination is poorly understood => new physics? e.g. heavy non-SM particle entering the penguin loop! ATTRACTIVE ALTERNATIVE!!!

• => Need more measurements...

• SM describes wellmost measurements

• amazing consistency betweenindependent measurements

• ...but hints of disagreement!

=> need to understand better the SM predictions for b→sg asymmetries=> need more accurate measurements

• study case: B→η’KS (BABAR analysis)

CKM: Summaryη

ρ

B →η’K decays

• η’K first seen by CLEO

• BF ≈ 70x10-6

• Expect sin2β if purepenguin decay

• tree polution => sin2βeff

• need to estimate tree contribution

• use BF of related B → η(’)X decays

a

g b

Fred Blanc 4DPF'04

SM expectations for h'KS and p0K

S

! DS = sin2bcharmonium

– sin2beff

= 0

! B0 ! h'K

S

" DS bound from SU(3) analysis:

using B0 decays to pairs of light

pseudoscalar mesons

⇒ |DS| < ~0.1 [Grosman et al., PRD68, 015004 (2003)]

[Chiang et al., PRD68, 074012 (2003)]

" Specific model calculations: DS ~0.01[Beneke et al., NuclPhys B675, 333 (2003)]

! B0 ! p0

KS (b ! sdd is dominant)

" SU(3): DS ~0.2 [Gronau et al., PLB579, 331 (2004)]

" model-dependent QCD: DS ~0.1[Buras et al., Ciuchini et al, Charles et al.]

?

mixing

penguin (dominant)

Physics beyond the SM

may enter the loop

(sensitivity to high virtual mass)

tree (CKM + color-supressed)

phase g

Measuring sin2β in B decays

• B0 and B0 produced coherently

• Proper time difference between Bη’Ks and other B (Btag) : Δt = tη’Ks - ttag

• Decay time distribution:

Standard model => S ≅ sin2β C ≅ 0

• Corrections:

• B mistag

• Δt resolution

3F. Blanc DPF/APS '03 Philadelphia, PA

CP-violation in B!h'K0

Only phase from interference between mixing and decay

If penguin amplitude dominates sin2b

If tree amplitude not negligible sin2beff

Proper time difference between Bh'K

and the other B (Btag

)

Dt = th'K

- ttag

Decay time distribution (F+ if BtagB

0, F- if BtagB0):

Standard model ! S sin2b & C 0

Correction for B0/B

0 mistag

Dt detector resolution (Dt) convolute F(Dt) with (Dt)

PEP-II Factory at SLAC

• PEP-II asymmetry e+e- B factory at SLAC

• 3.1 GeV e+ / 9.0 GeV e- => βγ = 0.56

• Peak luminosity: 9.2x1033 cm-2 s-1

• Lint = 244 fb-1

The BABAR detector

a

g b

Fred Blanc 5DPF'04

PEP-II and the BABAR detector

e- (9GeV)

e+ (3.1GeV)

Silicon Vertex Tracker5 double-sided layers

Instrumented Flux Return

1.5T Solenoid(superconducting)

Electro-Magnetic Calorimeter6580 CsI(Tl) crystals

DIRC (PID)

144 quartz bars

Drift Chamber40 layers

PEP-II

BABAR Lpeak

= 9.2 x 1033cm-2s-1

Lint

= 221fb-1 (on-peak)

(23fb-1 off-peak)

These results based on

Lint

= 205fb-1

=> 227x106 BB pairs

Analysis technique: overview

• Event selection:

• η’ → ηπ+π- (44%) η’ → ρ0γ (30%) with η → γγ (39%)

• reject continuum background

• loose cuts => keep sidebands for background fitting

• Extract S & C (and BF) from unbinned extended maximum likelihood fit

Discriminating variables

• Kinematic variables

• ΔE = EB - Ebeam

• mES = √(E2beam - p2B)

• resonance masses

• Event shape variables

• angle between B and “rest-of-event” thrust axes

• energy distribution about B thrust axis=> variables combined into Fisher discriminant (≈1σ separation)

• Time difference Δt

!"#$%&'&(%)#*+&&,,&-.'/#0)

mES

!E

mES

resolution

≈2-3MeV/c2

!E resolution ≈20-50MeV

Analysis techniques (I)! Experimental challenge: isolate tiny signal in very large

background (100s M events)

! Variables used to identify the signal:

" B kinematics (exploit the known total energy of the B candidate)

B mass: Energy:

mES

(BABAR) = mbc

(Belle)

" secondary resonance mass(es), etc...

!"#$%&'&(%)#*+&&,,&-.'/#0)

Analysis techniques (II)! Backgrounds:

" combinatoric e+e- → qq (q=u,d,s,c) (dominant background) # event shape variables

" other B decays

! Signal extracted with ML fit on discriminating variables

Δt and flavor tagginga

g b

Fred Blanc 8DPF'04

Dt variable and flavor tagging

Determine Dt from Dz:

Dz !"bgctB ! 260 mm

(sDz ! 180 mm)

Partially reconstructed B decay (Btag

)

# B flavor (lepton charge, kaon strangeness, etc...)

# decay vertex$ ~2/3 of the events are tagged$ Effective tagging efficiency Q ! 28.8%

Reconstructed exclusive

B decay (Brec

)

1.

2.3.

Btag

Brec

Dz

e-e+

%(4S)

Results: η’K Branching fractions

• ML fit => 804 ± 40 η’K0S events [hep-ex/0502017]

~2/3 are tagged => used in CP fit

• BF(B → η’K+) = (69 ± 2)x10-6 BF(B → η’K0) = (68 ± 3)x10-6

η’K+

η’K0S

5.25 5.26 5.27 5.28 5.29

Even

ts /

2 M

eV

0

100

200

300

400

5.25 5.26 5.27 5.28 5.29

Even

ts /

2 M

eV

0

100

200

300

400

-0.2 -0.1 0 0.1 0.2

Even

ts /

20 M

eV

0

200

400

-0.2 -0.1 0 0.1 0.2

Even

ts /

20 M

eV

0

200

400

(GeV) ESm5.25 5.26 5.27 5.28 5.290

50

100

150

(GeV) ESm5.25 5.26 5.27 5.28 5.290

50

100

150

E (GeV)!-0.2 -0.1 0 0.1 0.20

50

100

150

200

E (GeV)!-0.2 -0.1 0 0.1 0.20

50

100

150

200

(a) (b)

(c) (d)

Results: S & C

• S(η’K0S) = 0.30 ± 0.14 C(η’K0S) = -0.21 ± 0.10

• Systematics: ±0.02

• expected S ≈ 0.7!~3σ discrepancy

t (ps)!-10 -5 0 5 10

Asym

met

ry

-0.5

0

0.5(c)

t (ps)!-10 -5 0 5 10

Asym

met

ry

-0.5

0

0.5

0

50

100(b)

0

50

100

Even

ts /

( 1 p

s )

0

50

100(a)

Even

ts /

( 1 p

s )

0

50

100

a

g b

Fred Blanc 14DPF'04

B0 → h'K

S results: S & C

PRELIMINARY

B0 tag

B0 tag

Asymmetry

S(h'KS) = +0.27 ± 0.14

stat ± 0.03

syst

C(h'KS) = -0.21 ± 0.10

stat ± 0.03

syst

! Systematics dominated by MC statistics

and signal modeling ⇒ ±0.02! Single most accurate measurement from

non-charmonium mode!

sin2b value from BABAR charmonium decays

[BABAR-CONF-04/38]

3.0s

[hep-ex/0408090]

sin2β from charmonium

Interpretation

• Difference between η’K0S and charmoniumΔSexp = S - sin2β = -0.30±0.12

• Estimate of the tree contribution is necessary in the interpretation of the results

• Flavor SU(3) is used to set bounds on ΔS ΔSth < |ξ η’Ks |

• ξ η’Ks function of branching fractions of related modes

Setting bound on ΔS

• ξ η’Ks is function of flavor SU(3) related decay modes

• B → ηη, ηη’, η’η’, ηπ0, η’π0, π0π0

[Grossman et al. , PRD68 (2003) 015014][Gronau et al. PLB 596 (2004) 107]

• Need to measure BF for all these modes

• All modes with small BF (≈10-6 or smaller)

• Use ML fit technique to extract yields

bound most sensitive on these modes

Experimental issue: fit biases

• Sources of fit biases

• fitter bias [tested with “toy” MC samples generated from PDFs]

• BB bkg [tested with fit on “embedded” BB events passing the selection]

• correlations between fit variables [tested with samples containing fully simulated signal events]

• small sample biasML fit is unbiased for large samplesFor small (clean) samples, we observe a bias towards negative yieldsCorrection for this bias as determined from toy MC studies

• Limits on most modes(only B0→π0π0 has been observed)

• => ΔSth < ~0.1[compare to ΔSexp ≈ 0.3]

• ΔSexp>>0.1 => new physics!

• Need more accurate measurements...

Current bound on ΔS

!"#$%&'(')&*$+,''--'./(0$1*

B decays to pairs of light isoscalar mesons

! !Sth

= S("'KS) - sin2# < |$

"' Ks|

! $"'Ks

function of the BF for flavor SU(3)

related decay modes B0→" '" '," '" ,"" ," '%0," '%0,etc...[Grossman et.al., PRD68 (2003) 015014][Gronau et.al., PLB596 (2004) 107]

! Current limit: !Sth

<~0.1(compare to !S

exp ~ 0.3)

! If measure !Sexp

>> 0.1 => signature for new physics

! !Sth

will improve with better BF measurements

a

g b

Fred Blanc 15DPF'04

Comparison to SU(3) limits on DSh'Ks

! Correlated limits on S & C for B0 ! h'

KS

based on SU(3)

[Gronau et al., PLB 596, 107 (2004)]

! Uses experimental results

on B decays to pairs of

light mesons

⇒ limits on S & C

! See talk by A. Lazarro(session VII, Tuesday)

SM

SU(3) bounds

old h 'K

S result

(BABAR + Belle)

new h 'K

S

preliminary result

[Gronau et al., PLB 596, 107 (2004)]

η

ρ

Summary / Conclusion

• The B factories have obtainedan accurate measurement of sin2β

• sin2α also quite accurate (thanks to ρρ)

• Discrepancy between sin2β from charmonium and b→s penguin is probably the most intriguing result

Is it a sign for new physics?Need more measurements!

• Exciting time for all (and for LHCb in particular...)