CP Violation in B0s mesons

Results from a flavor tagged analysis of B0s J/ y f

Joe Boudreau

University of Pittsburgh

Experimental results from CDF (and other experiment)

A very brief abstract of this talk first. The following topics will be developed:

CDF and D0 use B0s J/ y f

to measure CKM phases. Wedetermine from this decay thequantity bs.

This is in exact analogy to B factory measurement of the b, an angle of the unitarity triangle.

The standard model makes very precise predictions for both angles.

But other new particles & processes,lurking potentially in quantum mechanicalloops such as box diagrams and penguin diagrams can change the prediction.

Vub*Vud Vtb

*Vtd

Vcb*Vcd

b

Vub*Vus

Vtb*Vts

Vcb*Vcs

bs

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

The interaction of quarks with the charged weak current is governed byone Universal coupling constant modulated by a matrix, the CKM matrix:

W+

u

d

W+

u

s

W+

u

b

W+

c

d

W+

c

s

W+

c

b

W+

t

d

W+

t

s

W+

t

b

Vub*Vud + Vtb

*Vtd + Vcb*Vcd=0

Vub*Vud Vtb

*Vtd

Vcb*Vcd

b

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

Unitarity triangles, a graphical representation of the unitarity of the CKM matrix

Vub*Vus + Vtb

*Vts + Vcb*Vcs=0

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

There are six unitarity triangles. The one we shall talk about today is the (bs)unitarity triangle, and, especially, its angle bs , which is predicted precisely, nowmeasured, too:

Vub*Vus

Vtb*Vts

Vcb*Vcs

bs

CP Violation

≠

• The operator that transforms matter into antimatter in quantum mechanics is the CP operator.

•CP = composition between two transformations:

P (parity): spatial inversion. Left-handed particle->Right handed particle.

C (charge conjugation): Inverts every internal quantum number, like electric charge, isospin… => turns a particle into its antiparticle.

CP turns a left-handed particle into a right-handed antiparticle.

CP symmetry says [H,CP]=0:

* eigenstates of the Hamiltonian are eigenstates of CP* transitions from CP even states to CP odd states do not occur.* amplitudes for particular processes are equal to those of the CP-conjugate process.

CP Symmetry

http://ckmfitter.in2p3.fr/

The verification of the model was carried out by validating its chief prediction,the Unitarity of the CKM matrix elements.

CP Violation: discovered in 1964…(Cronin, Fitch)

attributed in 1973 to the Higgs, Yukawa sector…(Kobayashi, Maskawa)

experimentally validatedin this decade by Belle, BabarCDF

There are 12 observed instances of CP violation.

1. Indirect CP violation in the kaon system (eK)2. Direct CP violation in the kaon system e’/e3. CP Violation in the interference of mixing and decay in B0 → J/y K0.4. CP Violation in the interference of mixing and decay in B0->h’K0

5. CP Violation in the interference of mixing and decay in B0->K+K-Ks

6. CP Violation in the interference of mixing and decay in B0->p+p-

7. CP Violation in the interference of mixing and decay in B0->D*+D-

8. CP Violation in the interference of mixing and decay in B0->f0K0s

9. CP Violation in the interference of mixing and decay in B0->yp0

10. Direct CP Violation in the decay B0 K-p+

11. Direct CP Violation in the decay B rp12. Direct CP Violation in the decay B p+p-

Also:

Direct CP Violation in the decay B- K-p0

B Mixing

There are two states in the B0s system,

the so-called “Flavor eigenstates”

They evolve according to the Schrödinger eqn

0

0

s

s

B bs

B bs

a adi H

b bdt

2

iH M and M, G Hermitian Matrices

M: Dispersive diagrams G: Absorptive diagrams

u, c

u, c

The mixing of eigenstates gives rise to oscillations of frequency Dm,determined by the magnitude of the box diagram

The phase of the diagram gives the complex number q/p, with magnitude of very nearly 1 (in the standard model).

0 / 2 0 0

0 / 2 0 0

( ) cos sin2 2

( ) cos cos2 2

ts s s

ts s s

mt q mtB t e B B

p

mt p mtB t e B B

q

0 0 0,

0 0 0,

S L S S

S H S S

B p B q B

B p B q B

0 0 0

2 2 2 22*

12 02 212

s s sF W B B B B tts tb

W

G M M B f MM S V V

M

22

122

mM

*

*Mi tb ts

tb ts

q V Ve

p V V

Mixing phenomenology:

Mixing probability /1( ) (1 cos( ))

2tP t e mt

Mixing occurs when a B0s decays as a B0

s.

Decay to a flavor specific final state eg (Ds+p-) tags the flavor

at decay.

One of three tagging algorithms tags the flavor at production.

Good triggering, full reconstruction of hadronic decays,excellent vertex resolution, and high dilution taggingare all essential for this measurement, which made news in 2006.

•There is a similarity here to Faraday rotation, in optics: rotation of the polarization of light:

•Start with polarized light.•Decompose it into two states of circular polarization.•In a sugar solution these states propagate with different speeds.•So one helicity arrives early, or, there is a phase difference.•When the two beams recohere, the polarization has rotated.

In B mesons ….:

b

s b

s

W W

t

t

Bs0 Bs

0

B0

B0

I needed two polarizing filters for the demonstration.CDF needs initial state flavor tagging, and looks at decays to flavor-specific final states.

Δms = 17.77 ± 0.10(sta) ± 0.07(sys) ps-1

|Vtd/Vts| = 0.2060 ± 0.0007 (exp) + 0.0081 – 0.0060 (theor)

(PRL 97, 242003 2006)

Δms = 18.56 ± 0.87(stat) ps-1

(D0 CONF Note 5474)

Many of the “new” CP observables are “CP violation in the interference of mixing and decay”:

|B 0 >

|B 0 >

| J/y K0s >

Vub*Vud Vtb

*Vtd

Vcb*Vcd

b

BABAR, BELLE have used this decayto measure precisely the value of sin(2b) an angle of the bd unitaritytriangle

B0

B0

CP violation in the interference of mixing and decay:

Imagine we filter for circularly polarized light, here at the end:

Sin(2b) = 0.728 ± 0.056(stat) ±0.023(syst)

K. Abe et al., Phys. Rev. D71, 072003 (2005).

Interference of mixing and decay:

Uses decay to CP eigenstates to analyze the mixing.

Measures q/p relative to A/A (ratio of decay amplitudes)

Physical observable

q A

p A

There was a fourfold ambiguity in the Belle, Babar measurementof b.

Two are irreducible: all observablesupon either sin(2b) or cos(2b)

The B factory experiments resolvedthis with a complicated decays

B J/y K0*

A decay to two vector mesons, a final state which is neither CP evennor odd, but CP-mixed.

B0s→J/y f.

B->V V decay to actually three distinct final states (S-wave, P-wave, and D-wave).

S,D Wave: CP even, short-lived, light.P Wave: CP odd, long-lived, heavy.

These “final” states are actually intermediate states (final state is m+m-K+K-) so there is interference.

* Pure S, P,or D wave states would have distinct angular distributions.

* With a mix of orbital angular momentum final states one can separate the decays on a statistical basis (angular analysis)

A. S. Dighe, I. Dunietz, H. J. Lipkin, and J. L. Rosner, Phys. Lett. B 369, 144 (1996), 184

hep-ph/9511363.

•Spin correlation of the vector mesons resembles that of the two photons two photons in positronium decay.

•Polarization of vector mesons can be perpendicular (CP odd), or parallel (CP even)

•And also longitudinal (CP even)

•Distributions in the angles q, f, and y sensitive to polarization.

ˆ (sin cos ,sin sin ,cos )n

||0

( )sin ( )( ( )cos , , )

2 2

A t A tA A t i

29ˆ( , , , ) | ( ) |

16P t A t n

{ A, A||, A0 }: transition amplitude <Bs0|P>to each final states { P, P||, P0 }

{ Ā, Ā||, Ā0 }: transition amplitude <Bs0|P> “ “ “ “ “ “ “ “ “ “

I n the phys ica l B 0s , p h y s meson the f l avor con ten t changes (B 0

s -B 0s

osc i l l a t i ons ) w i th fas t f requency o f 17 .77 ± 0 .12 ps - 1

The ampl i tude <Bs,phys0(t)|P> = A(t) (amplitude for a particle born

as a B 0s to decay in to the s tate |P> af ter a t ime t ) decays and

osci l la tes.

Time dependence of the angular distributions:

ˆ (sin cos ,sin sin ,cos )n

||0

( )sin ( )( ( )cos , , )

2 2

A t A tA A t i

29ˆ( , , , ) | ( ) |

16P t A t n

This innocent expression hides a lot of richness:

* CP Asymmetries through flavor tagging.* sensitivity to CP without flavor tagging.* sensitivity to both sin(2bs) and cos(2bs) simultaneously.* Width difference* Mixing Asymmetries

… formula suggests an analysis of an oscillating polarization.

CP Violation in the interference of mixing and decay for the B 0s system

Take: q/p from the mixing of B 0s - B 0

s

Take: Ā/A from the decay into { P, P||, P0 }

Form: the (phase) convention-independent and observablequantity:

q A

p A

This number is real and unimodular if [H,CP]=0

|B 0 >

|B 0 >

| P0 >

| P >

| P|| >

|m+m-K0sp0>

Babar, Belle an ambiguity in b by analyzing the decay

B0 J/y K0* which is BV V and measures sin(2b) and cos(2b)

This involves angular analysis as described previously

J/y K0*

| B 0 >

|B s0 >

|B s0 >

| P0 >

| P >

| P|| >

|m+m-K+K->

J/ y f

Today I will tell you about an analysis of an almost exact analogy,|B s

0 > J/ y f (but I think that in the B0s system the phenomenology

is even richer! Because of the width difference! )

| B s0 >

This is a complicated business but there is a nice analogy one can do to understandwhat happens to B0

s and in the decay to J/ y f:

Birefringent zone/weak interaction, boxdiagrams, / 10%.DG G

PolarizingFilter initial stateflavor tagging.

Filtered slits CP even andodd final states

Interference on the far screenangular analysis

CP violation ~ a preferred direction in the space B0s/B0

s in mixing or in the decay.

b ds

cc

W WW

dB0 →J/y K0*

b ss

cc

W WW

sB0 →J/y f

Vub*Vud Vtb

*Vtd

Vcb*Vcd

b Vub*Vus

Vtb*Vts

Vcb*Vcs

The decay B0sJ/y f obtains from the decay B0J/y K0* by the

replacement of a d antiquark by an s antiquark

bs

We are measuring then not the bd unitarity triangle but the bs unitarity triangle:

Vub*Vud = O(l3) Vtb

*Vtd= O(l3)

Vcb*Vcd = O(l3)

b

Vub*Vus= O(l4)

Vtb*Vts= O(l2)

Vcb*Vcs= O(l2)

b’

=

With l = 0.2272± 0.0010 A = 0.818 (+0.007 -0.017) r = 0.221 (+0.064-0.028) h = 0.340 (+0.017-0.045)

One easily obtains a predictionfor bs :

2bs = 0.037±0.002

bs, the phase of Vts is expected to be close to zero in the standard model.and should not lead to detectable CP violation.

~

~~

~

However there maybe other contributionsto CP violation from other sources;

This is what makes thisan important measurement.

Small phase, small CP violation

Flavor structure of BSM physics unknown

“Hidden richness”

where i = 0, para, perp and

B

B

An analysis of the decay canbe done with either a mix ofB and B mesons (untagged) or with a partially separated sample (flavor tagged). Latter is moredifficult and more powerful.

ˆ (sin cos ,sin sin ,cos )n ||

0

( )sin ( )( ) ( ( )cos , , )

2 2

A t A tA t A t i

29ˆ( , , , ) | ( ) |

16P t A t n

/ 22( ) ( ) ( )

cos2 ( )

imt tii

i

H L s L H

a e eA t E t e E t

/ 22( ) ( ) ( )

cos2 ( )s

imt tii

i

H L s L H

a e eA t E t e E t

( ) ( )

4 2 4 21

( )2

m mi t i t

E t e e

These expressions are:

* used directly to generate simulated events.

* expanded, smeared, and used in a Likelihood function.

* summed over B and ̅B (untagged analysis only)

reference material

obtain the overall time and angular dependence:

For reference: expanded, smeared , normalized rates:reference material

Explicit time dependence is here:

… then, replace exp, sin*exp, cos*exp with smeared functions.

reference material

The analysis of B0s→J/ y f can extract these physics parameters:

bs CP phase

=DG GH-GL Width difference

=2/(t GH+GL) Average lifetime

A (phase d) Decay Amplitude t=0

A॥ (phase d॥ ) Decay Amplitude t=0

A0 (phase 0) Decay Amplitude t=0

The exact symmetry..

… is an experimentalheadache.

Curiosity #1: cos(2bs) is easier to measure than sin(2bs). It can be donein the untagged analysis for which the PDF contains time dependent terms:

Physically this is accessible because one particular lifetime state (long or short)decays to the “wrong” angular distributions. Needs DG≠0; no equivalent in B0 J/y K0*.

Some fine print: in the interference term, in an untagged analysis, there is a term including sin(2bs); however this term does notdetermine the sign of sin(2bs) so it does not solve any ambiguity.

Curiosity #2:

Sensitivity to Dms (tagged analysis only; even in the absence of CP)

How much sensitivity? Well, we did not exploit it yet butit could be important news at the LHC!

| P0 >

| P >

| P|| >

|m+m-K+K->

J/ y f

| B s0 >

Where does the sensitivity to Dms come from ?

|B s0 >

|B s0 >

|B s , L >

|B s , H >

| P0 >

| P >

| P|| >

|m+m-K+K->

J/ y f

| B s0 >

Where does the sensitivity to Dms come from ?

Interference terms tag the flavor at decay.

Big simplification…:

Time dependence of interference term is contained in the factor:

CDF Detector showing as seen by the B physicsgroup.

Muon chambersfor triggering on the J/y→m+m- and mIdentification.

Strip chambers,calorimeter for electron ID

Central outer trackerdE/dX and TOF system for particle ID r < 132 cm B = 1.4 T for momentum resolution.

L00: 1.6 cm from the beam. 50 mm strip pitch Low mass, low M-S.

Excellent vertex resolution from three silicon subsystems:

SVX II ISL

CDF, 2506 ± 51 events .. And in D0, 1967 ± 65total.. … but 2019 ± 73 tagged events, all tagged.

Next, we’ll run through the CDF analysis, show what you get from flavor tagging, then show the D0 results.

The Analysis needs the proper decay time, decay angles and flavor-at-production of a B0

s or B0s decaying to J/y f.

S

Proper decay time estimation

Selection

Flavor Tagging

Modeling of detector sculpting

SLikelihood fit

Extraction of confidence region

Artificial Neural Network selection trained on data + MC Uses:

• transverse momentum PT and vertex probability prob(c2) of B, J/ y mass and vertex probability of f

• pT and Particle ID (TOF, dE/dx) of K+, K-

Candidate events should have NN > 0.6

We reconstruct

B0s J/y f 2.5K 1.7 fb-1 for untagged tagged analysis

B0s J/y f 2.0K 1.35 fb-1 for flavor-tagged analysis

B0 J/y K0* 7.8K 1.35 fb-1 B V V decay for crosscheck of angular analysis

B± J/y K± 19K 1.35 fb-1 Measure dilution of opposite side tagging.

Results from 1.7 fb-1 of untagged decays.

s fixed to its Standard Model value

Results untagged analysis

StandardModel Fit(no CP violation)

HQET: ct(B0s)= (1.00±0.01) ct(B0) PDG: ct(B0) = 459 ±0.027 mm

arXiv:0710.1789 [hep-ex]

More results, untagged analysis

Applying the HQET lifetime constraint:

An angular analysis can also be applied to the decay B0-> J/ y K*

to extract amplitudes ~ CP even / Odd fractions in the final state:

Angular fit projections B0 J/y K0*

Angular fit projections B0 J/ y f

CDF B0 Angular Analysis

53%

23%

24%

Longitudinal

Transverse Parallel

Transverse Perpendicular

A consistent picture of the CP Odd/Even fraction in B0→J/y K*,B0

s→J/ y f in CDF, Babar, and Belle experiments:

B0s

CDF B0s Angular Analysis

57%

21%

22%

Longitudinal

Transverse Parallel

Transverse Perpendicular

Belle B0 Angular Analysis

57%23%

20%

Transverse Longitudinal

Transverse Parallel

Transverse Perpendicular

Babar B0

56%

21%

23%

Longitudinal

Transverse Parallel

Transverse Perpendicular

B0

B0 B0

R. Itoh et al. Phys Rev. Lett. 98, 121801, 2007 (Belle) B. Aubert et al. PRD 76 (2007) 031102 (Babar)

This plot is Feldman-Cousins confidence region in the space of the parameters2bs and DG

The symmetry you see occurs because the untagged analysis depends almostonly on cos(2bs) and almost not at all on sin(2bs). Clearly the tagged analysis willremove this ambiguity. As you are about to see.

Results from 1.35 fb-1 of tagged decays.

s floating

Tagged analysis: likelihood contour in the space of the parameters bs and DG

One ambiguity is gone, now this one remains

Constrain strong phases d|| and d to BaBar Values (for B0J/y K* !!)

Constrain ts to PDG Value for B0 Apply both constraints.

B. Aubert et al. (BABAR Collaboration), Phys. Rev. D 71, 032005 (2005).

using values reported in:

The standard model predictions of 2bs and DG data consistent with theCDF data at the 15% confidence level, corresponding to 1.5 Gaussian standard deviations.

One dimensional Feldman-Cousins confidence intervals on 2bs ( DG treated as a nuisance parameter):

2bs [0.32, 2.82] at the 68% CL.

Assuming |G12| = 0.048 ± 0.018 and the relation DG = 2|G12|cos(2bs):

2bs [0.24,1.36] U [1.78, 2.90] at the 68% CL.

If we additionally constrain the strong phases d|| and d to the results from B0 J/y K*0 decays and the Bs mean width to the world average Bd width, we find

2bs [0.40, 1.20] at 68% CL

A Feldman-Cousins confidence region in the bs-DG plane is the main result.This interval is based on p-values obtained from Toy Monte Carlo and represents regions that contain the true value of the parameters 68% (95%)of the time.

The standard model agrees with the data at the 15% CL

arXiv:0712.2397v1

D0 Result: arXiv:0802.2255v1

Strong phases varying around the world average values ( for B0J/y K* !!)

Uncertainty taken to be ± p/5

Likelihood contours for just DGand for just fs=-2bs

Outlook

Note fs = -2bs

• Fluctuation or something more, it does go in the same direction.• CDF estimates confidence level at 15% using p-values to obtain Ln(L/L0) • D0 estimates confidence level a 6.6% using the probability to extract a lower value than seen in the data, from toy.

UTFit group has made an “external” combination.

CDF and D0 plan to make an “internal combination” for the near future.

• “re-introduces” the ambiguity into the D0 result.• does so by symmetrizing.• cannot fully undo the strong phase constraint.

• I am showing you this conclusion, but not endorsing it very enthusiastically.

Elsewhere there is another anomaly that may also have to do with bs

* Direct CP in B+K+ p0 and B0 K+p- are generated by theb s transition. These should have the same magnitude.

* But Belle measures (4.4 s)

* Including BaBar measurements: > 5s

•The electroweak penguin can break the isospin symmetry•But then extra sources of CP violating phase would be required in the penguin

Lin, S.-W. et al. (The Belle collaboration) Nature 452,332–335 (2008).

Conclusion

• Towards the end of a 20-year program in proton-antiproton physics: some terribly interesting times for the physics of the b-quark.

• An anomaly from the B factories• Are quantum loop corrections to the bs transitions are to blame?

• If so, precision measurements of the CP asymmetries in the B0s system are

a clean way to sort it out.

• D0 and CDF have just demonstrated the feasibility of doing those measurements.

• Higher precision, higher statistics measurements could give us a even stronger hint before the LHC turns on.

Baseline expectation w/ 6/fb

σ ~ 4.5o

FIN

Free Bonus Slides

Phenomenology of the B0s system

B0

s a two-state system like the B0, K0, and D0 systems.

All of these neutral mesons have (to varying extent):

* particle antiparticle oscillations, can be analyzed in flavor specific final states, governed by the parameter Dm

* width differences governed by the parameter /DG G

* CP violation in the mixing… |q/p| ≠ 1

* CP violation in the decay |Ā/A| ≠ 1

* CP violation in interference of mixing and decay qĀ/pA ≠ 1

bs

The extent to which these features show up depends upon numerical values ofthe constants governing mixing, decay, direct CP violation and CP asymmetries:

The B0s system is characterized by the following standard model expectations:

• Very fast oscillation frequency.• Small but observable (~10%) lifetime difference.• Very small CP violation in the standard model.

Species x=Dm/G y= /DG G Striking feature

K0 0.474 0.997 Width difference

B0 0.77 <0.01 CP violation

B0s 27 0.15 Fast Oscillation

D0 0.01 0.01 None

Contrast this phenomenology with that of B0 mesons.

dbB

dbB

0

0 Slow oscillation Dmd = 0.507 ±0.005 ps-1

Oscillation length cT = 3.7 mmLarge Standard Model CP violation

sbB

sbB

s

s

0

0 Fast oscillation Dms ~ 18 ps-1

Oscillation length cT = 110 mmZero Standard Model CP violation (almost)

*

*

sin(2 ) 0.668 0.028

cd cb

td tb

V VArg

V V

*

*

sin(2 ) 0.037 0.002

ts tbs

cs cb

s

V VArg

V V

http://utfit.roma1.infn.it/

L

dR

L

uR

d

d

d

Mddd

u

u

u

Muuu

3

2

1

321

3

2

1

321

),,(

),,(

ijdij

ijuij

GM

GM

2

v

~

2

v

b

s

d

DUtcu

d

d

d

uuu LLLL *

3

2

1

321 ),,(),,(

Higgs Field vevQuark mass matrix:

The charged weak currents:… involves a matrix,the CKM matrix (unitary!)

VCKM = UL†DL

.].),(~

),([ * CHd

uuG

d

udG

Lj

jiRij

Lj

jiRij

Higgs Yukawa

couplings

CDF Timeline

Tevatron starts: 1985First physics: 1988 Run I start 1992 Top quark 1995Run II start 2001

Unique opportunity for B physics: The Tevatron produces all flavorsof B hadrons: B±, B0, B0

s, Lb, Bc, Sb, Xb, Wb, excited states…

Luminosity delivered and collected at CDF:

tagged analysisup to summer ’06(1.35 fb-1)

untagged analysis:a little more (1.7 fb-1)

Important detail:

* In the standard model bs0

* To estimate various standard model parameters with bs0

* The standard model bs constraint is applied in the fit.* Tagging information is not used.* The full data sample is used.

*Bounds on bs can be obtained without flavor tagging.

Data sample of 1.7 fb-1 without tagging has been used to perform both SM fits and to obtain bounds on bs.

The best bound on bs come from a flavor-tagged sample, but onlya subset of CDF’s data has calibrated flavor-tagging:

Flavor-tagged data sample of 1.3 fb-1 is used to obtain bounds onbs.

Proper decay time: distance between production & decay…..

Beam profile~ 30 microns.

Lxy

c = Lxy/sin /q bg

= LxyMB/PT

… transformed into the rest frame of the B meson:

Resolution is about 76 fs for the J/y f decay mode

Two techniques for initial state “flavor tagging”

•b, b quarks are always produced in pairs;

b quark always opposite bb antiquark always opposite b

Flavor-specific decay modes (eg semileptonic decays) of the opposite side b, or jet charge can be used to determine the sign of the b quark on the opposite side.

•The fragmentation chain produces weak correlations between b quark flavor and the sign of nearby pions and kaons in the fragmentation chain

Procedure to select leading p±, K± can be optimized to obtain the highest quality tag.

Each tagger returns:

•A decision (B or B)•An estimate of the quality of that decision (dilution D)

e = tag efficiencyD = 1-2ww = mistag rate

Performance of the flavor tag in CDF

Dilution: (27±4)%Efficiency: (50±1)%

Dilution: (11±2)%Efficiency: (96±1)%

Tagger performance in J/y f decays:

The quality of thePrediction of dilutionCan be checked againstthe data:

We reconstruct a sampleOf B± decays in which one knows the sign of the Bmeson.

We then “predict” the sign of the meson andplot the predicted dilutionvs the actual dilution.

Separately for B+

and B-

Scale (from lepton SVTthis sample; take thedifference B+/B- as anuncertainty).

Decay angles come from reconstructed track momentum of

K+, K-, m+ m- as determined by CDF’s tracking system. Detector efficiency modifies the differential rates:

F

cos (q)

Detector efficiency (MC)

Sources of inefficiency: detector acceptance limited to | h | < 1.0 neural network cuts on kinematic quantities such as pT

- Without detector efficiency, the time and angular PDF is analytically normalized:

- With detector efficiency: Likelihood function needs normalization:

- One technique:

This involves afew basis functions Ylm(cosq,f) x Pk (cos y)

Fit the efficiency functionin the same polynomials

… and N is analytic. This speeds up the numerical task greatly!

Other analysis sensitive to bs: Semileptonic asymmetry

•AsSL= 0.020 ± 0.028 (CDF)

Very weak dependence on fs=-2bs

DG/DMs =(49.7 ±9.4) ±10−4

(hep-ph/0612167)

Where:

http://www-cdf.fnal.gov/physics/new/bottom/070816.blessed-acp-bsemil/

•AsSL= 0.0001 ± 0.0090 (stat) (D0)

Phys. Rev. D 76, 057101 (2007)

Black: central value

Green: 68% allowed.

D0:Contours 39%CL