B0, B0 and the measurement of at LHCb

Patrick Robbe, LAL Orsay, 26 September 2006, for the LHCb Collaboration

2

Introduction

1. How to measure

2. Measurements in LHCb:

1. Performances and sensitivity with B0 +-0

2. Performances and sensitivity with B0

3. Combination and LHCb sensitivity to

3

The angle of the Unitarity Triangle

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CKM Matrix

B0 decays to charmless CP final states are sensitive to + = -, the relative weak phase between tree and penguin contributions.

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4

Current status of measurements

• Direct measurements at B factories:

• B

• B

• B

• Combined (with from BABAR only):

• Indirect (without direct measurements):

)5.92( 9.12

5.10

)8.205.96(

) 5.176() 5.83( :

) 5.91(:0.121.46

5.138.22

9.602.18

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BABAR

) 5.92( 8.10

3.9

) 1.98( 1.5

4.19

5

measurements in LHCb

• In LHCb, measurement is performed with:

• Time dependant Dalitz analysis of B0 +-0

• SU(2) analysis of B0 +-, B0 00 and B+ +0.

• Typical event in LHCb:

• Challenge to reconstruct multi-track final states and final states with .

6

• 4 devices: Scintillator Pad Detector (SPD), Preshower (PRS), Electromagnetic Calorimeter (ECAL) and Hadronic Calorimeter (HCAL).

• Provides with acceptance 30 mrad to 300 (250) mrad:

• Level-0 trigger information (high transverse momentum hadrons, electrons, photons and 0, and multiplicity)

• Kinematic measurements for and 0 with E/E =

• Particle ID information for e, , and 0.

LHCb Calorimeter

E 1%

10%

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0 reconstruction at LHCb

• Resolved 0: reconstructed from 2 isolated photons

• m = 10 MeV/c2

• Merged 0: pair of photons from high energy pion which forms a single ECAL cluster, where the 2 showers are merged.

The pair is reconstructed with a specific algorithm based on the expected shower shape.

• m = 15 MeV/c2

• Reconstruction efficiency: 0 = 53 % for B0+-0

Resolved π0

Merged π0

π0 mass (Mev/c²)

MergedResolved

Transverse energy (GeV)

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with B (1)• Assuming that the decay B0+-0 proceeds through the resonance, 6 interfering decay modes contribute to the +-0 Dalitz plot:

• B0+-, B0-+, and B000

• B0-+, B0+-, and B000

• Tree or Penguin transitions contribute to each decay mode. The time dependant analysis of the tagged Dalitz plot gives enough information to determine at the same time and the relative amplitudes and strong phases between all processes. [Snyder, Quinn, 1993]

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B0

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9

with B (2)Maximize a Likelihood with 9 parameters ( + background fractions r )

Experimental acceptances

Experimental resolutions

Experimental(mis)taggingtag = +1/0/-1

Backgroundcontamination

Experimental ingredients

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Theoretical ingredients Phenomenological ingredients

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= ( , T-+ , -+ , T00 , 00 , P-+ , -+ , P+- , +- )

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B Selection• Multivariate Selection based on:

• Particle Identification: Charged pion ID, neutral 0 clusters, …

• Kinematical criteria: transverse momenta, …

• Vertexing criteria: impact parameters, vertex isolation

• Combined PDF:

Signal Inclusive bb

XPDF

signal

signal

inclusive bb

Θ(PV-SV,PB)

Momenta sum

vertices-B-momentum.

alignment

ΣPt(π±o)/B (GeV)

inclusive bb

π+π- vertex isolation

signal

inclusive bb

dmin (mm)

π±

e,μ,K,p

π± identification

ΔLL(π)

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B Results and Backgrounds

N3π = 14x103 events / 2 fb-1

Eq. LHCb time Nsel B/S

B0→ρ+ρ- 4 days 40 9%

B0→K*γ 1.3 days 10 6%

B0→Kππ0 12 days 90 5%

Other B0→ charmless 1.5h 5 29%

B+→ρ+ρ0 5 days 16 3%

Other B+→ charmless 1.5 h 3 17% Assume B/S = 1 in the following

Consistent with : B/S = 20% (B/S < 80% @ 90% CL)

• 33 millions of inclusive BB events➛ 15 min of LHCb at 2.1032 cm-2s-1

3 signal events selected and passing the trigger5 background events in side-bands (D(s)π,D(s)) and rejected by the trigger

• 1 million of fully simulated B events ➛ 10 days of LHCb at 2.1032 cm-2s-1

➛ 1300 events selected = BABAR ρπ statistics up to 2004, efficiency of 7x10-4

➛ 50% with merged π0s

• Few millions of specific charmless B decays

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B Fit: Signal acceptance• Acceptance in Dalitz plane:

selectedproduced

• Proper time acceptance:

s+

s-

s+

s-

t (ps)

ε (%

)

The lower corner of the Dalitz plot is highly depopulated due to the cut on the 0 energy.However, the upper region of the Dalitz figure contains enough information to allow the extraction.

Region of low lifetime depopulated due to thelarge impact parameters required in the selection

(%

)

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B Fit: Resolution and Tagging

• Flavour tagging:

→ Tagging efficiency ε = 40±2 % → Wrong tag fraction ω = 31±2 %

εeff = ε (1-2ω)²= 6±2 %

• NB : the untagged sample also enters in the global fit.

• Expected resolutions:

B mass (GeV/c²)Δt (ps)

σ = 60 MeV/c² σ = 50 fs

Resolutions are dominated by

calorimeter energy resolution

• Performance estimated from full MC simulation:

• The tagging performance actually depends on the position in Dalitz plane.• In the real experiment, the wrong tag fraction will be extracted from data (for example, using the self-tagged K+π-π0 decay)

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LHCb Sensitivity on with B Method

• Simulate the experimental effects (resolution, acceptance, wrong tag, ...)

• Maximize the likelihood with respect to: fit and the background ratios rfit (12-D fit)

• Assume a set of theoretical parameters gen

• Simulate a set of toy experiments accordingly

• Simulate backgrounds according to rgen ratios

α T-+ Φ-+ T00 Φ00 P+- δ+- P-+ δ-+

96.5° 0.47 0.00 0.14 0.00 -0.2 -0.5 0.15 2.0

Flat

+ +

ρ resonant B(Kρ,K*π)Kππ

50% 45% 5%

Background structure poorly known. Assume B/S = 1 and use a mixture made of:

Yield = 104 signal events = 2 fb-1

The same proper time distribution, resolutions and tagging dilution as signal are assumed.On real data, information on background will be extracted from the side-bands.

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LHCb Sensitivity on with B Results

<²> = 6.5

<²>=2

Average

85% converge to the correct solution

15% converge to a pseudo-mirror solution.Fraction decreases with increasing luminosity (<1% @ 10 fb-1)

αgen

gen

gen

70 toy experiments super-imposed ( L = 2 fb-1)

Distribution of fit error

90% of experiments with σ < 10°

The correct solutiongenerally corresponds

to a deep (if not deepest) minimum.

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LHCb Sensitivity on

)97( 9

4fit

ρ

η

A typical LHCb toy experiment (2fb-1):

Current BABAR measurement (Stat + Syst):

) 5.91( 9.60

2.18

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Measurement Systematics Estimates

Extracting via the 3π Dalitz analysis requires an accurate control of the inputs

The final analysis will be much more difficult than this prospective study

→ Not likely to be a ‘first year’ analysis for LHCb but very promising results

Non-uniform wrong-tag Δ = 1°

Proper time acceptance Δ = 0°

Dalitz acceptance Δ = 5°

ρ/ω mixing in signal Δ = 0°

ρ’ and ρ’’ contribution in signal Δ = 7°

Large ρ3 contribution (weight 20%) in signal Δ = 12°

What is the impact of imperfect knowledge of quantities included in the likelihood:

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with B

• Method: Recent measurements showed that the B0+- decay is predominantly longitudinally polarized, and then a pure CP eigenstate.

• The time dependant asymmetry gives access to eff = + , shift due to

penguin contributions:

• Constraints on can be obtained measuring B++0 and B000 branching fractions.

• Analysis similar to B0+- but with many advantages:

• B(B++0) and B(B0+-) 5 times larger,

• B(B000) is small: (1.20.40.3)x10-6

• Time dependant analysis of B000 could also provide additional information.

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A+-/√2

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A+-/√2

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LHCb performances for B0and B+

• Expected annual yields (2 fb-1):

• Selection for B0 ρ+ρ- and B+ ρ+ρ0 Multivariate selection as for B ρπ 2 and 1 neutral pion(s) in the final state, respectively Overall efficiency : 0.01 % and 0.045 % B mass resolution dominated by ECAL resolution : 80 MeV/c² and 52 MeV/c² Proper time resolution : 85 fs and 47 fs

B ρρ0 : 9000 B/S ~ 1 B0 ρ+ρ- : 2000 B/S < 5 @ 90%CL

One year of LHCb probably not competitive with current B factory performance.Will need several years to provide a sizeable contribution to C+-, S+- measurement.

The main contribution of LHCb to the B ρρ analysis could be the improvement of the measurement of the B0 ρ0ρ0 mode

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LHCb performances for B0

Selection: multivariate selection overall efficiency : 0.16%

Expected annual yield ( 2fb-1/year):

ICHEP06 : BR = (1.20.40.3)x10-

6 1000

Eq. LHCb time Nselected B

bb inclusive 15 min 0 < 4000

B0→ π+π-π+π- (Non Res.) 2.5 days 7 300

B0→ K+π-π+π- (Non Res.) 1 day 0 < 600

B mass

σ(mB) = 16 MeV/c²

Proper time

σ(t) = 32 fs

Background contamination:

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with BLHCb sensitivity(1)

• Measuring B00B00 = 1.2x10-6

σB00/B00 = 20%

• + Measuring C00 with time dependant analysis

C00 = 0.51 ; σC00= 0.4

• + Measuring S00 S00 = 0.30 ; σS00= 0.4

2.15

8.121.98

2006 WA : )8.205.96(

With 2 fb-1:

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with BLHCb sensitivity(2)

e.g. large S00: S00 = -0.61 ; σS00= 0.4

4.14

4.65.98

• resolution depends on the actual C00/S00 central value

The current indirect measurement is weakly constrained

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and : 2 fb-1 at LHCb• LHCb measurement with • LHCb 00 (C00/S00) + B factories +- and 0+ • LHCb (C+-/S+-) + B factories +0 and 00

WA 2006

LHCb 2 fb-1

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The time-dependent B0(ρπ)0 Dalitz plot analysis:

• No ambiguity on in [0,π] but pseudo-mirror solutions.• With 2 fb-1 LHCb may achieve σstat< 10° on • Require an accurate control of the ρ-lineshapes and the experimental efficiencies. • Ambitious but promising.• Probably several years to setup the analysis.

• 8-fold ambiguity on in [0,π].• Several years of LHCb needed to improve the current B0ρ+ρ- measurement.• With 2 fb-1 the main LHCb contribution could be the improved measurement of B0 ρ0ρ0.• Accessing the ρ0ρ0 time-dependent asymmetry will reduce the degeneracy of mirror-solutions and improve the current determination.• Performance strongly depends of the actual values of C00 and S00.

During LHCb era the stat. error on could reach the few degrees levelSU(2) breaking effects, electroweak penguin contributions could be an issue

Conclusions At LHCb, 2 complementary analyses developed to measure :

The time-dependent B0+- asymmetry and SU(2) analysis: