Experimental methods for precise determination of CKM matrix sides

ITEP Meeting on the future of heavy flavour physics 1

Experimental methods for precise determination of CKM matrix sides

Marie-Hélène Schune

Member of the BaBar and LHCb collaborations

LAL-Orsay

•Introduction

•Present status • Vtd, Vts :

• B mixing • Rare B decays

•Vcb, Vub : • Semileptonic decays• B

•Charm physics

•Overall status and future• B factories : • LHCb :

• Radiative B decays • Bs mixing


Introduction


Mass eigenstates weak interaction eigenstates mixing matrix : the Cabbibo-Kobayashi-Maskawa matrix

Weak interaction eigenstates

Mass eigenstatesCKM matrix

Transition amplitude between the quarks i and j : Vij

b u

W

Vub

Vij complex CP violation

Framework : the CKM matrix

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

d’

s’

b’

=

d

s

b

1-2 A 3(-i)

- 1- 2/2 A 2

A3(1- -i) -A 2 1

+ O(4)

Wolfenstein parametrisation


3 families + CKM matrix unitarity 4 parameters

Relations between the CKM matrix elements

The unitarity triangle

/2

/1 /3

(,)

(0,0)

(1,0)

*ub

cb

V

V*td

cb

V

V

* * *ub ud tb td cb cdV V V V V V 0

1-2 A 3(-i)

- 1- 2/2 A 2

A3(1- -i) -A 2 1

4 parameters known with different precisions :

=sin(c) ~0.4 %

A ~ 1.7 %

~ 15 %

~ 5 %

CKM : present status


Some of the experiments

BELLE

CDF D0

BABAR

e+e- (4s)

pp

s=1.96 TeV

LHCb pit june 2006

pp s=14 TeV


Present status


Vtd and Vts

top quark couplings

loop or box diagrams

Search for New Physics

Vtb

Vts

b

ds

b

ds

W

W

Vtd

t t

Vtb

Vtd

Vts

Bd,s0Bd,s

0

b

ds

ds

b

W W

Vtb

Vtd

Vts

tVtb

Vtd

Vts

Bd,s0Bd,s

0

B B mixing :

t

Top quark contribution dominates

b

d W , ,t c u0B

d

ds

K*

Radiative B decays

Top quark contribution dominates


B0-B0 oscillations

( )0 /1( ) 1 cos( )

2 t

q qP t e mB t

Time-dependent probability for a produced at t=0 to be observed as a

or at time t

0qB

0qB

0qB

Can be predicted in the SM framework

0 00 0

2222 2 2

2 26 qq qqB BtF

q tb W Btq BW

fMG

m V V M M B SM

Non-perturbative QCD

perturbative QCD

Reconstruct the decay time (t)

Tag the B production state :

Other B information (B factories and pp colliders)

Same side tagging (for pp colliders only/ Bs)


B0-B0 Oscillations: md

SU(3) flavour breaking

smaller theoretical uncertainties

HFAG

=1

00

0

0

0

0

0 0

2 2

22d

s

d

ss

d d

s

B B BBtd

B B

d

s Bts B

f B

f

MV

m B

m

MV

md : a high precision measurement (~0.8%) dominated by B factories results

md = 0.5070.004 ps-1

Asy

mm

etr

y

co

s(

mdt)

|t| (ps)

Weak constraint on the UT triangle due to the knowledge of

BELLE 152 106 BB . Full B reconstruction

0 02

d dB Bf B

useDue to the size of the CKM elements ms >> md


Several analysis from LEP, SLD, Tevatron

Combine different limits : the amplitude method

measurement of A at each ms

At a given ms :• A=0 : no oscillation• A=1 : oscillation

ms excluded at 95% CL : A+1.645A<1

Sensitivity : same relation with A=0

00 1

A( ) 1 cos2

tss sP B B e m t

( )( )

First limit was set in 1993 at ms>1.8 ps-1 at 95%CL !

Bs-Bs oscillations: ms

HFAG

LEP/SLD 1999LEP/SLD 2002

ms : already a high precision measurement (~2.3%)

0.42 -10.2117.33 0.07 pssm

CDF 2006


Implications of md/ ms measurements on the CKM parameters determinations

Two very precise measurements : (~0.8 % and 2%)

5.9 -14.221.7 pssmIndirect measurement of ms (prediction) :

But it does not translate into a precise determination of the SM parameters …

2

22

s

d

B tss

d B td

m Vmm m V

known to 5-8%


Radiative B decays

BR(b d ) |Vtd|2

BR(b s ) |Vts|2

b

,u d W , ,t c u

ds

,u d

Semi-inclusive analysis (~55% of the modes reconstructed)

K* peak visible due to the good resolution

New Physics

BF of bs and bd

Standard Model

E spectrum in b s|Vcb| and |Vub|

BF(bs)/BF(bd) |Vtd|2/|Vtd|2

Inclusive photon energy spectrum sensitive to b-quark motion inside B meson

reduces the systematic uncertainty in the Vcb and Vub extractions

bs


B/

First observation: 5.5

signal

qq

K*other B

2BR( / )

BR( )td

ts

B

B

V

VK

SU(3) breaking correction

weak annihilation diagram for BR(B )

Experiment BF(B )

BaBar (211 x 106 BB)

Belle (386 x 106 BB)

68%CL

95%CL

Full UT fit

0.34 0.10 60.31 0.091.32 10

With the present statistics : use of all the modes, in future only ?

< 1.2 10-6 at 90% CL

Expect new BaBar results at ICHEP


32

02( , , ) 1

n

QCDl X n

nl X b

f E q m CE q m m

+

Vcb or Vub

Exclusive and inclusive semileptonic approaches : different theoretical uncertainties

Weak decay of a free quark :

2

3

] 5[2

[ ]192

c

b

u bFGb c u m

V

free quark decay Perturbative +non-perturbative corrections

At the hadron level :

Exclusive decays : depend on QCD form factors from eg LQCD, quark models...Inclusive decays : use Heavy Quark symmetry+ OPE

measure OPE parameters from data (spectra and moments of bs and b cℓ distributions)

Complication for charmless decays:

need to apply kinematic cuts to suppress b cℓ background measurements of partial branching fractions in restricted phase space regions

theoretical uncertainties more difficult to evaluate

501

V

V

)clb()ulb(

2cb

2ub

Semileptonic decays: Vub and Vcb


Vcb inclusive (Buchmüller/Flächer):

Vcb from semileptonic decays

Good agreement

|Vcb|F(1)= (37.60.8)10-3

Vcb exclusive ~5% precision

|Vcb|= (41.960.23exp 0.35HQE0.59SL)10-3

~2% precision

|Vcb|= (41.32.0)10-32

with F(1) = 0.91 0.04theo

Does not contain the latest result from BaBar : |Vcb|=

1.5 3stat exp 1.3theo37.6 0.3 1.3 10


Vub in inclusive B decaysIn these regions the theory (OPE) breaks down, acceptance sensitive to Fermi motion of b quark inside the B meson

Several approaches :

Method S/B Pros & Cons

UntaggedElectron spectrum endpoint

0.050.2 High statisticsBkg subtraction

UntaggedEe vs q2 neutrino reconstruction

~0.5 High statisticsLower syst. on shape functionsBkg subtraction

Breco TagsmX vs q2 analysis

~2 Low backgroundVery small syst. on SF paramSmall statistics

signal


B 0 ℓB + ℓ

Vub exclusive : Bℓ Bℓ = missing of the event ; ,E p

[[[[[[[[[[[[[[can add Breco tag to improve S/B

Missing mass2

ℓ

ℓ ℓ

ℓ

Measure the form factor q2 dependance.Compare with theoretical calculations

BF(B ℓ ) precision~8%

Various experimental results in good agreement

signal

Yields :36 -ℓ, 34 0ℓ


Vub from semileptonic decays summary

Vub inclusive (HFAG) Vub determination from exclusive decays

BF precision~8% but |Vub| precision ~20%

theory dominated

~8% precision

|Vub|~ (4.40.2 0.3 )10-3 inclusive|Vub|~ (3.70.2 0.7 )10-3 exclusive

Understanding of the difference ?


B

22222 2 4

B2 ubBR( ) 1 f 10 in the SMV8

F B B

B

mG mB m

m In the SM it measures fB |Vub|

Direct measurement of fB when using |Vub| from SL decays (to be compared to LQCD predictions)

Test of NP (e.g.: charged Higgs could enhance BF)

Experimental technique

One B fully reconstructed (hadronic or semileptonic)

Search for in the rest of the event (2)

BR(B) . 104

BABAR 232 106 BB < 2.6 at 90% CL

BELLE 447 106 BB 0.34 0.18

0.28 0.161.06 4.2

Electromagnetic energy not associated with the Btag nor the 0 from the decay (GeV)

b

u

B

WVub

~216 signal events

Using |Vub| from HFAG : 28 20

23 19176 MeVBf


Charm physics

Measurements of fD+ and fDs

improved prediction of fB/fBs

precise measurements of md and ms

precise determination of Vtd/Vts parameters

+

D BF measurements

Vcd

Extraction of D form factors

Validation of LQCD (DK ℓ )

B form factors (D /ℓ)

precise determination of Vub/Vcb parameters


Recent lattice result (hep-lat/0506030)

Measuring fD and fDs

Pseudo scalar decay :

222

22 21

18 F D cd

DD

mD G m M V

Mf

Vcd

wave function overlap

CLEO-c 281 pb-1

50 events NBkgd=2.920.50

79223 16 MeV

Df

201 3 17 MeV

D*S DS and normalize to Ds

Ds → signal

N = 489±55Preliminary

stat syst Ds→

LQCD Aubin et al. PRL 95 122002 (2005)

/ 1.25 0.14

as expected from LQCDs

BaBar CLEOD Dff


Semi-leptonic D decays

DK ℓ form factor : comparison of recent experimental results with LQCD calculation

e

K e

0

0

0

0

(3770)

,

D

D

D

D K eK

0Example: D e

CLEO BF relative to PDG

(~117 events)

Events

/ 1

0 M

eV

U ( = Emiss – |Pmiss| )

CLEO-c


Overall status and future


Phases and sides measurements in good agreement

The CKM mechanism works well… NP should appear as correction to this framework

Preferred region using only the sides measurements


Future from the sides point of view : the B factories

The existing B factories will collect about 1 ab-1 (X2 present samples) per experiment

B measurement will improve confrontation with LQCD predictionsB/ determination will improve Vub analyses will be able to discriminate between theoretical models improved Vub extraction

B factories : charm factories !

Super B factory ? Japanese project, based on KEK2 experience : 40 ab-1 before 2020More futuristic : Italian project (linked to ILC development) : 50 ab-1 before 2015Improvement of all the above points :

• eg : expect few thousands BR(B) signal events !


Future from the sides point of view : LHCb

Use of radiative B decays :

N/year B/S at 90% CL

BdK* ~0.41% 35k <0.7

Bs ~0.64% 9.3k <2.4

Bd(0) ~0.03% 40 <3.5Analysis complicated by the presence of a 0

Bd0 should be easierBELLE has ~6 signal events in this mode

LHCb 2005-01

But the extraction of |Vtd/Vts| is not completely clean from a theoretical point of view (SU(3) breaking, presence of a weak annihilation diagram in (and not in K*)

Full simulation of bb inclusive events


Very precise measurement of ms using Bs Ds(KK ) events :

One year of data taking (2fb-1) : 80k fully reconstructed events with B/S~0.3 and (t) ~40 fs

ms (ps-1) 20

stat(ms) (ps-1) 0.011

(ms) will be dominated by the systematics (eg knowledge of the time scale)

LHCb 2003-127

The tagging performances will be checked on data (similar self tagging decay modes, double tagging technique Ksame)

Tag eff (%)

Opposite Side 3.90.3 (1.50.1 CDF)

Same Side 2.10.3(3.40.5 CDF)

Recent NN approaches lead to ~9% for Bs

Expected unmixed Bs Ds sample

in one year of LHCb data taking


And then …

Preferred region determined by sides measurements

2010 : B factories 2 x 1 ab-1

LHCb : 4 fb-1

Vub ~ 5%Vcb ~ 1%(ms) = 0.3 ps-1

fBBB ~ 5% ~ 3%BK ~ 5%

Lattice QCD < 1° ~ 7 ° ~ 5°(half B-factories/half LHCb)

Experimental inputs

Theoretical inputs

Sides and angles determination of () : similar precision

Hopefully this picture will not be the one we will see in 2010 and sides and angles measurements will be incompatible !


SummaryB factories : Vcb and Vub determinations

More and more inputs from data to constraint the theory improved Vub and Vcb measurements.

fB extraction from B measurement

Increasing role of charm physics which provide high-quality “lattice calibration” improvement on the precision of the CKM parameters

Hadronic colliders : Very precise measurement of the Bs–Bs mixing frequency

Measurements of BK*, Bs and B/

All modes with neutrinos are difficult in hadronic environment

Many new results expected for ICHEP !


Backup slides


bcℓ and buℓ Bd and Bs mixingK : CPV in K decaysBccs : 1 /B// : 2/BDK : 3/

2 sides ; 3 angles aim : to overconstrain this unitarity triangle

precision test of the Standard Model

Constraints in the (,) plane


The “B” experiments : main characteristics

Experiment Integrated luminosity

Boost Main points

CDF/D0 1.6 fb-12 large bb/had small trigger

bb large

Incoherent production ( extra tagging dilution) All B speciesMany particles not associated with the 2 b hadrons

LHCb 2 fb-1 (/year)

BaBar/BELLE 380+630 fb-1 small bb/had ~ 0.2

Coherent BB production Only B and Bd

BB pair alone


Experimental techniques at B factories B-Flavour tagging

t=1.6 ps z 200, 250 m

Exclusive B meson reconstruction

/rec tagt t t z c

coherent BB production

Beam Energy-substituted mass Energy difference Event shape*2 *2

ES beam Bm E p * *B beamE E E

(mES) 3 MeV (E) : mode dependent

qq events(q=u,d,s,c)

BB events

Exploit kinematic constraints from beam energies

(4S) rest frame

Documents

Experimental methods for precise determination of CKM matrix sides