LHCb sensitivity to with B h + h - and U-spin Symmetry

Laura Fabbri 1

LHCb sensitivity to with Bh+h- and U-spin Symmetry

Physics at LHCPhysics at LHCVienna, 13 -17 July 2004 Vienna, 13 -17 July 2004

Laura Fabbrion behalf of the LHCb collaboration

Vienna, 13–17 July 2004 Physics at LHC Laura Fabbri 2

Outline

Physics motivation Extraction of the weak phase from the

Bd+- and BsK+K- decays

Bd(s)h+h- event selection Strategy, event yields and background-to-

signal ratios CP sensitivity

Bayesian determination of Conclusions


CKM (new?) physics

When LHCb starts taking data in 2007, sin2 will be already known with very good accuracy

To isolate signals of new physics, it is crucial to measure the other two angles of the Unitarity Triangle, as ( -arg Vub)

In case of new physics, more complementary measurements of will help to understand where the new contributions come from Bh+ h- have sizeable

contribution from penguin graphs which may evidence new physics in loops

from LHCb?

Indirect CKM fits

expect 65o

Tree Diagram

Penguin Diagram


()(,,)()(,,,)()(,,)()(,,,)dirCPdmixCPdddirsCPmixssCPABfdABfdABKKfdABKKfdϑϑφϑϑφ+−+−+−+−→=→=′′→=′′→=01020304

Extracting from Bd+- and BsK+K-

4 equations and 5 unknowns: d, ϑ, d’, ϑ’ (hadronic parameters) and

One needs other inputs to solve for

()()()()()(())(())cossin(())(())coshsinhdirmixssCPCPCPssCPBtfBtfAmtAmtAtBtfBtftAtΔΓΓ→−Γ→Δ⋅+Δ⋅==ΔΓΔΓΓ→+Γ→⋅−⋅000022

s =-22 Bs-Bs mixing phase(can be probed with BsJ/)

d =2 Bd-Bd mixing phase(measured with BdJ/Ks)

[R.Fleischer, Phys. Lett. B459 (1999)]

ctiPPuutTPPbAAdeRAAAϑ⎛⎞−=⎜⎟+−⎝⎠1

ubbcbVRV⎛⎞≡−⎜⎟⎝⎠2112

PT


⎩⎨⎧

′=

′=⇒

ϑϑdd

U-spin symmetry6 eqs. and 5 unknowns

the system can be solved unambiguously

Unique solution for

oo

os

od dd

65,160

,3.0,0,55

==′=

=′===

ϑϑ

φφ

−+→ 0from),( BAA mixCP

dirCP

−+→ KKBAA smixCP

dirCP

0from),(

−+

−+

→

→

KKBAA

BA

smixCP

dirCP

dirCP

0

0

from),(

andfrom ππ

Using U-spin Symmetry

Bd+- U-spin (d,s quark exchange) BsK+K-

In this example


Bd(s)h+h- event selection

Selection cuts are simultaneously optimized in order to maximize

Two major sources of backgrounds taken into account Combinatorial background from bb inclusive events

Due to the huge minimum bias MC statistics required for a detailed study of combinatorial background, we make the plausible assumption that most of the combinatorial background will come from beauty events (presence of high pT and large IP tracks from B)

Specific background from B decays with same two-track topology e.g. BdK+-, BsK+K-, Bs+K- as backgrounds for Bd+-

After event selection, tagging and trigger algorithms are tuned on selected events

/SSB+

LHCb Public Note 2003-123


Selection cuts

B0(s)

, K

, KIP

IPIPB L

Beam axis (z)

Selection cuts on the candidate B pT

IP/IP

L/L

Invariant mass

Reconstruction and Particle ID Each charged track identified as

a Pion or Kaon using the Particle ID detectors (RICHs in particular)

Selection cuts on identified tracks p Max[pT(h+), pT(h-)] Min[pT(h+), pT(h-)] Max[IP/IP(h+), IP/IP(h-)] Min[IP/IP(h+), IP/IP(h-)] 2 of common vertex


Mass spectrasignals + specific backgrounds

only

Bd+- BdK+-

BsK+K- Bs+K-

Two-body background only

Mostly BdK+-

(same signature)

if not using RICH…

17 MeV/c2


Proper time acceptance and resolution

Resolution on proper time fitted with double

Gaussian(single Gaussian 40 fs)

1=341 fs2=673 fs (15%)

Acceptance suppression at low proper time due to cuts on IPs and distance

of flight


Signal yields and

background-to-signal ratios

Event type AssumedBR (x10-6)

Bbb/S Untaggedannual yield

D2

Bd +- 4.8 0.42 26000 4%

Bd K+- 18.5 0.16 135000 4%

Bs K+K- 18.5 0.31 37000 6%

Bs +K- 4.8 0.67 5300 6%

Annual yields after L0+L1 triggers and offline selection (assumed bb = 0.5 mb and L = 2 fb-1/yr)


CP sensitivity studies

Fast Monte Carlo Simulation In order to study the sensitivity on the angle we

generated many data samples, each corresponding to different settings of the relevant unknown parameters: Ms,, s, d, ϑ, etc.

The Fast Monte Carlo produces proper time and invariant mass distributions {(t, m)k; k=1, N} of tagged B decays (combinatorial background included).

The {(t, m)k; k=1, N} distributions are parameterized according to the proper time acceptance, resolution and invariant mass distributions obtained from the full GEANT simulation, which takes into account realistic pattern recognition, trigger and offline selection.


Likelihood Fit

In order to extract CP asymmetries and mistag fraction simultaneously from data we perform a combined extended unbinned maximum likelihood fit of Bd+ - and BdK+ - (BsK+K- and Bs+K-) event samples (plus background) BdK+ - (Bs+ K-) is a flavour specific decay and is used as

control channel Bd+ - (BsK+ K- ) and BdK+ - (Bs+ K-) have the same two-

track topology (same tagging power) extract the wrong tag probability from data itself The fit is performed against 17 parameters describing the

shape of the decay rate and invariant mass distributions In particular we obtain the joint p.d.f. for the CP

asymmetry coefficients Adir and Amix

Bivariate gaussians G(Adir, Amix) for the Bd+ - andGKK(Adir, Amix) for the BsK+ K-

LHCb Public Note 2003-124


Bayesian approach to determine the p.d.f.

()()()()()()()()(),,,,, ,, , ,,,,,, dirmixddirmixsKKKdssddKsKKGAdAdGAFddAgdgddππππππϑγϑγφϑγϑγϑγφφφφφ=×××××∫∫00

Exp. joint p.d.f. (bivariate gaussian)

for (, ) & (, )dirmix∂∂∂∂dirmixKKKKAAAAGaussian priors for the weak mixing

phases(from LHCb BdJ/KS and BsJ/)

To propagate the experimental joint p.d.f. for Adir,

Amix, the weak mixing phases d and s to a joint p.d.f. for d, and the Bayesian approach is used:


)(df

Sensitivity on from Bd+- and BsK+K- (1

year) d d()(,,)fFddϑϑ=∫∫

95% confidence region from BsK+K-

only

95% confidence region from Bd+- only

()oóã≈5Perfect U-spin

O(20%) U-spin breaking would induce only a few

degrees shift on YellowYellow and WhiteWhite contours: 68% and 95% confidence regions using all the

information

Fake solution(disappears with more

statistics)

)(fCorrect

Solution 65o

d- plane


Sensitivity scan

() vs ms

() vs d=0.3, = 160°, =65°, s=-0.04°,

s/s=0.1

d=0.3, = 160°, s=-0.04°, s/s=0.1, ms=20 ps-1


Conclusions

The LHCb experiment will select and tag very large samples of Bd (Bs) charmless two-body decays

By combining the measurements of the Bd+- and BsK+K- asymmetry coefficients LHCb can measure

with a 5° statistical uncertainty, in one year, assuming U-spin symmetry and Standard Model

This strategy could disclose new physics effects in penguin diagrams providing a different measurement of with respect to e.g. and see LHCb talks by Eduardo Rodrigues and Sandra Amato

ssBDK±→ 0m * BDK→ 00


Backup slides


Charmless two-body decays of B mesons:

diagrams

W

g

oZã,

W

W

W

WoZã, W W

W g

TTree

C colour-suppressed

Tree

Pgluonic Penguin

PAPenguin Annihilation

PEW

electroweak Penguin

PCEW

colour-suppressed electroweak Penguin

E Exchange

A Annihilation

Gronau, Hernandez, London and Rosner, Phys. Rev. D50 (1994) 4529


Bd+- and BsK+K-

decay amplitudes ()****uuctTPPPdubudubudcbcdtbtdABVVAVVAVVAVVApp+−→=+++0

()()iidABCedeγϑππ+−→=−0 ()uutTPPbCARAAAλ≡+−3

ctiPPuutTPPbAAdeRAAAϑ⎛⎞−≡⎜⎟+−⎝⎠1

()****uuctsusTuscstsPPPububcbtbABKKVVAVVAVVAVVA+−′′′′→=+++0

()/ iisABKKCedeγϑλλλλ′+−⎛⎞−′′→=+⎜⎟−⎝⎠2022112

(), uutTPPbctiPPuutTPPbCARAAAAAdeRAAAϑλ′′′′′≡+−′′⎛⎞−′≡⎜⎟′′′+−⎝⎠31

Bd+-

BsK+K-

ubbcbVRV⎛⎞≡−⎜⎟⎝⎠2112


Distributions of selection variables for BsK+K- and

combinatorial bb background

bb background

——— signal

cut value andaccepted

region

2 of common vertex

Max[pT(K+), pT(K-)]

Min[pT(K+), pT(K-)]

Max[IP/IP(K+), IP/IP(K-)]

Min[IP/IP(K+), IP/IP(K-)]

Bs Mass

Bs pT

Bs IP/IP

Bs L/L


Selection cuts

Channel: Bd+ - BdK+ - BsK+ K-

Bs+ K-

Pmin (GeV/c) 2.50 2.75 2.75 2.75

Pmax (GeV/c) 100 200 125 100

(PT)each(GeV/c)

1.2 1.2 0.8 1.4

(PT)one (GeV/c) 3.2 3.0 2.6 3.4

(IP/IP)each 6 6 5 7

(IP/IP)one 12 11 9 14

2max 4 5 5 4

(PT)min (GeV/c) 1.6 1.4 1.0 1.6

(IP/IP)max 2.25 2.50 2.75 2.25

(L/L)min 19 17 14 20

m (MeV/c2) 50 50 50 40

can

did

ate

B

Iden

tifi

ed

tr

acks


Fast MC input values

Nominal parameters: Bd +-, Bd K+- Bs K+K-, Bs +K-

tagging efficiency 42% 50% wrong tagging fraction 35% 33% M 0.5 ps-1 20 ps-1

1/1.54 ps-1 1/1.46 ps-1

/ 0 0.1 d 0.3 0.3 ϑ 160o 160o

65o 65o

weak mixing phase 0.82 -0.04

Sensitivity scan: parameters are varied one at a time d: 0.1 0.2 (0.3) 0.4 ϑ: 120o 140o (160o) 180o 200o

: 55o (65o) 75o 85o 95o 105o

s: 0 (-0.04) -0.1 -0.2

Ms (ps-1) 15 (20) 25 30

s/ s: 0 (0.1) 0.2


0.1 0.2 (0.3) 0.4

1.8° 2.7° 4.9° 9.0°

120° 140° (160°) 180° 200°

3.8° 3.8° 4.9° 6.7° 5.2°

55° (65°) 75° 85° 95° 105°

5.8° 4.9° 4.3° 4.7° 4.7° 4.7°

0 (-0.04) -0.1 -0.2

4.9° 4.9° 4.9° 5.4°

0 (0.1) 0.2

5.2° 4.9° 4.5°

15 ps-1 (20 ps-1) 25 ps-

1

30 ps-

1

4.0° 4.9° 5.9° 8.5°

d( )

( )

( )

( )

( )

( )

ϑ

sφ

ss /

sM

Resolution computed as half the 68% confidence

interval

Sensitivity on


U-spin Symmetry

How much rely on it? U-spin symmetry in the relations d=d’ and ϑ=ϑ’ is not

broken within naïve factorization approximation (Fleischer, Phys. Lett. B459, 1999)

Fleischer and Matias (hep-ph/0204101) allow for a SU(3) violation of 20%: d’/d 0.8÷1.2

Matias (hep-ph/0311042) claims that a SU(3) breaking of 20% would induce only a 5o shift on ; a phase difference ϑ=ϑ’-ϑ as large as 40o induces only a shift on of 1o

Beneke (hep-ph/0308040) estimates through QCD factorization a possible SU(3) violation at 30% level:d’/d 0.85÷1.3, ϑ ±15o

A better understanding of SU(3) breaking would be desirable, but a O(20%) breaking does not spoil the measurement


BsK+K-

Mass spectrasignals + combinatorial beauty

background only

Bs+K-BsK+

K-

BdK+-

Bd+-

Documents

LHCb sensitivity to with B h + h - and U-spin Symmetry