Experimental Heavy Quark Physics

Experimental Heavy Quark Physics

Fabrizio Bianchi

University of Torino, Italy and INFN - Torino

F. Bianchi XXX Nathiagali Summer College

2

Outline

• Lecture 1:• Big Questions in Particle Physics• Goals of Heavy Quark Physics• Tools for Heavy Quark Physics

• Lecture 2:• CP Primer• Observation of Direct CP Violation• Measurement of sin2

• Lecture 3:• Measurement of and • Measurement of |Vcb| and |Vub|


3

(0,0) (0,1)

(,)

Vub Vud

Vcd Vcb

*

*

Vtd Vtb

Vcd Vcb

*

*

Measuring

B → B → B →

ubud

tbtdargVV

VV


4

The Route to sin(2)Access to from the interference of a b→u decay () with B0B0 mixing ()

d

d

0B

*tbV

tdV

b

b

0Bt

t

*tdV

tbV

** // tdtbtdtb VVVVpq

B0B0 mixing

du

dd0B

ubV

*udV

b u

Tree decay

ubudVVA *

)cos()sin()( tmCtmStA dd

sin

)2sin(1 2

C

CS eff

ii

iii

eePT

eePTe

2

du

dd

0B

gb

utcu ,,

Penguin decay

tbtdVVA *

Inc. penguin contribution

0

)2sin(

C

S

222 iii eeeA

A

p

q

How can we obtain α from αeff ?

Time-dep. asymmetry :

NB : T = "tree" amplitude P = "penguin" amplitude


5

Taming the Penguins: Isospin Analysis

)( 0 BAΑ

)( 00000 BAΑ

)( 00 BAΑ2|

eff|

)(~ 0 BAΑ

)(~ 00000 BAΑ

Gronau and London, Phys. Rev. Lett. 65, 3381 (1990)

The decays B are related by SU(2) Isospin relations between amplitudes A+-, A+0, A00

Central observation is that states can have I = 2 or 0, but penguins only contribute to I = 0 (I = ½ rule) is pure I = 2, so only tree amplitude |A+0| = |A-0|


6

CP Asymmetries in B0 →

0 30 0.17 0 030 09 0.15 0.04

S . .C .

hep-ex/0501071

33467n

K crossfeed

(submitted to PRL)

Ignoring penguins:

deg 99 5 2

BB million 227

B0

B0


7

Now we need B→

Analysis method reconstructs and fits B→and B→Ktogether

60 10)4.06.08.5()( BB

B→B→

B→KB→K

02.010.001.0)( 0 BACP

60 10)6.07.00.12()( KBB

Inserts show background components

B→hB→h


8

…and B→

6000 10)10.032.017.1()( BB

06.056.012.000 C

B±→±0

3 B.F.sB0BB0

2 asymmetriesC

C

Using isospinrelations and

Isospin analysis not currently viable in the B→ system

|eff |< 35°

61±17 events in signal peak (227MBB)

Signal significance = 5.0

13167


9

Comparison between BaBar and Belle

S = - 0.67 ± 0.16(stat) ± 0.06(syst)

C = - 0.56 ± 0.12(stat) ± 0.06(syst).

Belle: hep-ex/0502035

S = - 0.30 ± 0.17(stat) ± 0.03(syst)

C = - 0.09 ± 0.15(stat) ± 0.04(syst).

BaBar: hep-ex/0501071


10

from B →

021.0029.0014.0978.0

Lf

P → VV decay, three possible ang mom states:•S wave (L=0, CP even)

•P wave (L=1, CP odd)

•D wave (L=2, CP even)

Blessing #1: helicity angle~100% longitudinally

polarized!

Angular analysis needed

~pure CP-even final state

22

12

41

22

12

21

2

sinsin)1(coscoscoscos

LL ff

dd

Nd

Preliminary


11

from B0 →

fit in events 68703 ,M232 BB

52617)( BN

08.014.024.033.0

S

09.018.003.0 C

tags0B

tags0B

)ps(t

Preliminary

Preliminary

04.003.003.099.0

long

Lf60 10)5430()( BB

BaBar: hep-ex/0503049


12

Search for B0 → : Blessing #2

Didn’t find it? Excellent!

1233)( 2220

000 BN

C.L.%90101.1

10)19.054.0()(6

636.032.0

000

BB

)M227( BB000 B

B (B→= 30 x 106

c.f. B→

B.F.= 4.7 x 106

and B→

B.F.= 1.2 x 106

BaBar: Phys.Rev.Lett.94:131801,2005


13

Taking the world average

and thanks to

we apply the isospin analysis to B→ The small rate of means

|eff | is small[er] P/T is small in the B→ system

(…Relative to B→ system)

Isospin analysis using B→

61.64.6

0 10)4.26()(

BB

1 longLf

000 B

|eff |< 11°

)(11.)(4.)(1096 penguinsyststat


14

Combined Measurements of

Isospin analyses in and , time-dep Dalitz analysis in

From combined results

from B0 → (

6113 2717

α = (106 ± 8)o U (170 ± 9)o


15

(0,0) (0,1)

(,)

Vub Vud

Vcd Vcb

*

*

Vtd Vtb

Vcd Vcb

*

*

Measuring

cbcd

ubudargVV

VV

B± → D(*)K(*)

GLW, ADS and D0-Dalitz methods


16

Measuring in B → DK

BB

CP

r

DKBDKB

DKBDKBA

sinsin

)()(

)()(

cbV

*usVIn general: need ≥ 2 amplitudes with

different weak and strong phases leading to the same final state

ubV

*csV

fDD 00 , where decays Choose

Relative amplitude rB, weak phase and strong phase B

Use additional dof in D decay to determine simultaneously

rB, , B

•Three methods on the market:

GLW, ADS, D0 Dalitz

Critical parameter:)(

)(

cbA

ubArB


17

The GLW Method: choose D → fCP

( ) ( ) 2 sin sin

( ) ( )CP CP

CP CPCP

CP

B BB D K B D K

B D K B D K

rAR

02( ) ( )

1 2 cos cos( )

CB B B

P PCP

CB D K B D K

B D Kr rR

,0 KKDCP

000 SCP KD

KDB CP0

0CPDB

214 M BB

95 15CPN 76 13CPN

•Theoretically clean

•B → D background

•Limited statistics

4 observables (ACP+-,RCP+-)

to determine rB, , B

07.017.021.0

08.015.040.0

08.014.080.0

06.014.087.0

CP

CP

A

A

R

R

KDCP0

)()10.015.0(

07.034.033.0

06.020.009.0

06.029.076.0

12.037.077.1

CPCP

CP

CP

AA

A

A

R

R

KDCP0

03.004.0

*

*

23.010.0

007.0021.0086.0

CP

CP

A

R

KDCP0

BBM123BBM227BBM214

No useful constraints yet. Need more data!


18

The ADS method: choose D → K

KDB 0

0

0

| ( ) |0.060 0.003

| ( ) |D

A D K

A Dr

K

2 2([ ] ) ([ ] )2 cos( )cos

([ ] ) ([ ] ) D B DD D BA S BR r r rBr K K Br K K

Br K K Br K Kr

([ ] ) ([ ] )

2 sin( )sin /([ ] ) ([ ] ) BADS ADSD D B

Br K K Br K K

Br Kr

K Br Kr

KA R

Phys.Rev.Lett.91:171801,2003

K

KDB 0

favored

suppressed

K

KDB 0favored

suppressed

Interference

Strong phase D

unknown

→ scan all values


19

The ADS Method: results = no signal!

0B D K

0 0*[ ]DB D K

0*[ ]DB D K

0.0110.009

4.03.2

0.01

4 7

3

.

ADSR

N

1.3

0.0100.006

0.80.2

0.001ADSR

N

0.0190.013

2.11.4

0.01

1 2

1

.

ADSR

N

227 M BB

hep-ex/0408028 It’s a hard road ahead…

7348

20 D

1Dr

)CL %90( 23.0Br


20

0D

2m202 )(

SKmm202 )(

SKmm

KDCS

0D

2m

Interference

Use the phase information across the

Dalitz plane to determine rB, , B

from B → D(*)0K, D0 → KS

0D

2m

2m


21

The D0→KS Dalitz model

Determine on clean, high statistics sample of 81500 D*→D0 events ASSUME no D-mixing or CP violation in D decays Build model from 15 known resonances (+2 unidentified scalar resonances)

d.o.f. = 3824/(3054-32) = 1.27

2m

2m 2

m

K

KDCS


22

D0 Dalitz method : B→D(*)0K (227 MBB)

KDB 0

KDB D0

282 ± 20

44 ± 8

KDB 0

B+

B+

B+

B

B2m

2m

2m

202 )( SKmm

2m

B2m

K

DCS

KDB D

00

89 ± 11

Maximum likelihood fit extracts rB(*),,

(*) from a fit to mES, E, Fisher and the D0→KS Dalitz model.


23

D0 Dalitz method : B→D(*)0K : result

DK : rB < 0.19

D*K : rB = 0.155

(90% C.L.)

+0.0700.077 ± 0.040 ± 0.020

B = 114°±41°±8°±10° (+n)

B = 303°±34°±14°±10° (+n)

BaBar: hep-ex/0408088 γ = (70 ± 26 ± 10 ± 10)o

Belle: hep-ex/0504013B+→D0K*+

γ = (112 ± 35 ± 9 ± 11 ± 8)o

Belle: hep-ex/0411049

γ = (68 ± 15 ± 13 ± 11)o


24

Combined measurement of

3rd error is due attributed to the Dalitz model

Measurement of : twofold ambiguity in extraction

γ = 64.0 ± 18.2 ([30.1,99.8] @ 95% CL)

γ = -116.0 ± 18.2 ([-149.7,-80.4] @ 95% CL)

Belle B+→D0K*+

γ = (112 ± 35 ± 9 ± 11)not used


25

Putting the Angles Together…


26

Measuring the sides of the UT Sides of Unitarity Triangle related to CKM matrix elements.

|Vub| and |Vcb| constrain the distance of the apex of the triangle from the origin.

Vub| and |Vcb| measurement complementary to sin2

|Vub| and |Vcb| measured in semileptonic B decays


27

Semileptonic B decays Inclusive: B → Xcℓv or Xuℓv

Tree-level rates are

QCD corrections must be calculated Operator Product Expansion (OPE)

How do we separate Xu from Xc? c = 50 × u Much harder problem for |Vub|

Exclusive: B → D*ℓv, Dℓv, ℓv, ℓv, etc. Need form factors to relate the rate to |Vcb|, |Vub|

B

X

22 5

2( )

192F

u ub b

Gb u V m

22 2 3

2( ) ( )

192F

c cb b b c

Gb c V m m m

|Vcb| , |Vub|

plep

q

Mx


28

Understanding inclusive SL decays

The Operator Product Expansion provides a systematic method of separating perturbative from non-perturbative scales

OPE + Heavy Quark symmetry HQE Heavy Quark Expansion now calculated to αs

2, mB-3

Essentially all we need to know for bcℓν Coefficients of operators calculated perturbatively (EW and

QCD); non-perturbative physics enters through matrix elements of operators


29

Inclusive bcℓν Measure electron momentum spectrum and mass of hadronic

system in SL decay Determine moments to allow comparison with parton-level

calculations (duality assumed) Calculations exist for the following:

Strategy: measure spectrum + as many moments as possible Fit for HQE parameters and |Vcb|

),,,,,,( 33220

00LSDGcbnE

nlBEE

nl mmEfdEE

l

),,,,,,( 33220

00LSDGcb

xnE

nXBEE

nx mmEfdMM

l

Mass of hadronic system

Lepton energy spectrum


30

Observables Define 8 moments from inclusive Eℓ and mX spectra

Integrations are done for Eℓ > Ecut, with Ecut varied in 0.6–1.5 GeV

0B

dM

1

E dM

d

1( 2,3)

i

i

E M dM i

d

( 1,2,3,4)iXX

i

m dM i

d

Partial branching fraction

Lepton energymoments

Hadron massmoments


31

Electron Energy Spectrum BABAR data, 47.4 fb-1 at (4S) + 9.1 fb-1 off-peak Select events with an electron

having p*>1.4 GeV; study spectrum of 2nd electron for p* > 0.5 GeV as f n of charge Unlike-sign events dominated by

B Xcev Like-sign events from D Xev,

B0 mixing As done by ARGUS, CLEO…

BABAR PR D69:111104

Unlike-sign

Like-sign

BABAR


32

Electron Energy Spectrum

Determine Ee spectrum

Subtract B Xueυ Correct for efficiency Correct for the detector

material (Bremsstrahlung) Move from (4S) to B rest frame Correct for the final state radiation using PHOTOS

Calculate 0th-3rd Ee moments for Ecut = 0.6 … 1.5 GeV

BABAR

BABAR PR D69:111104

All but ~few % can be measured

Ee (GeV)


33

Hadron Mass Moments BABAR data, 81 fb-1 on U(4S) resonance Select events with a fully-reconstructed B meson

Use ~1000 hadronic decay chains Rest of the event contains one “recoil” B

Flavor and momentum known Find a lepton with E > Ecut in the recoil-B

Lepton charge consistent with the B flavor mmiss consistent with a neutrino

All left-over particles belong to Xc Improve mX with a kinematic fit = 350 MeV

4-momentum conservation; equal mB on both sides; mmiss = 0

BABAR PR D69:111103

Fully reconstructedB hadrons

lepton

v

Xc


34

Hadron Mass Moments Unmeasured particles

measured mX < true mX

Calibrate using simulation Depends (weakly) on decay

multiplicity and mmiss

Validate in MC after applyingcorrection

Validate on data using partiallyreconstructed D*± D0 ±, tagged by the soft ± and lepton

Calculate 1st-4th mass moments with Ecut = 0.9 … 1.6 GeV

BABAR

BABAR PR D69:111103

Validation:


35

Inputs to OPE Fit

mX moments

Eℓ moments

BABAR

BABAR PRL 93:011803

Error bars are stat. & syst.with comparable sizes


36

OPE Fit Parameters Calculation by Gambino & Uraltsev (hep-ph/0401063,0403166)

Kinetic mass scheme to Eℓ moments

mX moments 8 parameters to determine

8 moments available with several E0

Sufficient degrees of freedom to determineall parameters without external inputs

Fit quality tells us how well OPE works

cbV bm cm 2

2G

3D

3LS( )cB X B

kinetic

chromomagnetic

Darwin

spin-orbit

2(1/ )bmO

3(1/ )bmO

3(1/ )bmO2( )sO

( )sO

BABAR PRL 93:011803


37

Fit Results

mX moments

Eℓ moments

● = used, ○ = unusedin the nominal fit

Red line: OPE fitYellow band: theory errors

BABAR

2/ndf = 20/15

BABAR PRL 93:011803


38

Fit Results

Impressive agreement between data and theory ≈ identical results obtained in another renorm. scheme: Bauer,

Ligeti, Luke, Manohar, Trott in hep-ph/0408002

s

s

s

3exp HQE th

exp HQE

exp HQE

exp HQE

2 2exp HQE

2exp HQE

(41.4 0.4 0.4 0.6 ) 10

(10.61 0.16 0.06 )%

(4.61 0.05 0.04 0.02 )GeV

(1.18 0.07 0.06 0.02 )GeV

(0.45 0.04 0.04 0.01 )GeV

(0.27 0.06 0.03 0.0

cb

c

b

c

G

V

m

m

B

s

s

s

2

3 3exp HQE

3 3exp HQE

2 )GeV

(0.20 0.02 0.02 0.00 )GeV

( 0.09 0.04 0.07 0.01 )GeV

D

LS

kinetic mass scheme with μ=1 GeV

Fitted values consistent with

external knowledge

2/ndf = 20/15

Uncalculatedcorrections to

BABAR PRL 93:011803

precision on mb = 1.5%

precision on |Vcb| = 2%


39

Inclusive |Vcb| in Perspective


40

Inclusive |Vub|

|Vub| can be measured from

The problem: b → cℓv decay

Use mu << mc difference in kinematics Maximum lepton energy 2.64 vs. 2.31 GeV First observations (CLEO, ARGUS, 1990)

used this technique Only 6% of signal accessible

How accurately do we know this fraction?

2

2

( ) 1

( ) 50ub

cb

Vb u

b c V

E

b c

b u

22 5

2( )

192F

u ub b

Gb u V m

How can we suppress50× larger background?


41

b → uℓv Kinematics There are 3 independent variables in B → Xℓv

Take Eℓ, q2 (lepton-neutrino mass2), and mX (hadronic mass)

6%20%

70%

E

2q Xm

Technique Efficiency Theoretical Error

Eℓ Straightforward Low Large

q2 Complicated Moderate Moderate

mX Complicated High Large

Where does it come from?


42

Starting point: HQE Just like bcℓν…, and with similar accuracy

…until limited expt’l acceptance is considered Poor convergence of OPE in region where bcℓν decays

are kinematically forbidden Non-perturbative Shape Function must be used to calculate

partial rates

= scale which separates effects from long- and short-distance dynamics

AEW = EW corrections; Apert = pert. corrections (sj , s

k0)

32

2

52

22

32

3

52 12))(1(

21)(1||

1921)(

bb

Gpert

b

Gpertub

bFEWu m

Om

Am

AVmG

AXB


43

Shape Function – what is it? light-cone momentum distribution of b quark: F(k+) Property of a B meson; universal...but new “sub-leading”

SFs arise at each order in 1/mb

Consequences: changes effective mb, smears spectra

kB bM m

Rough features (mean Λ, r.m.s. λ1) are known

Detailed shape, and especially the low tail, are not constrained

0

kF


44

Shape Function – What to Do?

Measure: Same SF affects (to the first order) b → sg decays

Caveat: whole Eg spectrum is needed Only Eg > 1.8 GeV has been measured Background overwhelms lower energies

Compromise: assume functional forms of f(k+)

Example:

Fit b → sg spectrum to determine the parameters Try different functions to assess the systematics

Measure E

spectrum inb → s

Extract f(k+) Predict Eℓ

spectrum inb → uℓv

E1.8

(1 )( ) (1 ) ;a a x kf k N x e x

2 parameters( and a) to fit


45

SF from b → s CLEO and Belle has measured the b → sg spectrum

BABAR result on the way

CLEO hep-ex/0402009

Belle hep-ex/0407052

Belle

Fit

E

( )f k 3 models tried


46

Theory input for |Vub|

At present, all |Vub| measurements based on inclusive SL decays use fully differential SL rate calculated to O(αS, mb

-2) (DeFazio and Neubert, JHEP 06:017 (1999)) Input required includes values for the mean and r.m.s. of

the Shape Function. In what follows we use as input the parameters determined

by a fit (hep-ex/0407052) to the Belle bsγ spectrum:Λ = 0.66 GeV, λ1 = -0.40 GeV2 + associated covariance; δΛ ~ δmb ≈ 80 MeV


47

Measurements

BABAR has measured |Vub| using four different approaches

Statistical correlations are small Different systematics, different theoretical errors

Technique Reference

Eℓ > 2.0 GeV hep-ex/0408075

Eℓ vs. q2 hep-ex/0408045

mX < 1.55 GeVhep-ex/0408068

mX vs. q2

Inclusive B → Xev sample.High statistics, low purity.

Recoil of fully-reconstructed B.High purity, moderate statistics.


48

Lepton Endpoint BABAR data, 80 fb-1 on U(4S) resonance Select electrons in 2.0 < Eℓ < 2.6 GeV

Push below the charm threshold Larger signal acceptance Smaller theoretical error

Accurate subtraction of backgroundis crucial! Data taken below the 4S resonance

for light-flavor background Fit the Eℓ spectrum with b → uℓv,

B → Dℓv, B → D*ℓv, B → D**ℓv,etc. to measure

Data (eff. corrected)MC

Data (continuum sub)MC for BB background

BABAR hep-ex/0408075

4stat sys( , 2.0GeV) (4.85 0.29 0.53 ) 10u eB X e E B


49

Lepton Endpoint

Translate B into |Vub|

Compare results with different Eℓ cut

Theoretical error reduced with lower Eℓ cut

Eℓ (GeV)

(10-4) |Vub| (10-3)

BABAR 2.0–2.6 4.85 ± 0.29stat ± 0.53sys 4.40 ± 0.13stat ± 0.25sys ± 0.38theo

CLEO 2.2–2.6 2.30 ± 0.15exp ± 0.35sys 4.69 ± 0.15stat ± 0.40sys ± 0.52theo

Belle 2.3–2.6 1.19 ± 0.11exp ± 0.10sys 4.46 ± 0.20stat ± 0.22sys ± 0.59theo


CLEO PRL 88:231803

BELLE-CONF-0325


50

Inclusive |Vub| Results

Summary of BABAR |Vub| results

Statistical correlation between the mX andmX-q2 results is 72%. Others negligible

Theoretical error of the mX-q2 result is different from the rest Negligible SF dependence

Technique |Vub| × 103 D(SF) × 103

Eℓ > 2.0 GeV 4.40 ± 0.13stat ± 0.25sys ± 0.38theo 0.46

Eℓ vs. q2 4.99 ± 0.23stat ± 0.42sys ± 0.32theo 0.42

mX < 1.55 GeV 5.22 ± 0.30stat ± 0.31sys ± 0.43theo 0.45

mX vs. q2 4.98 ± 0.40stat ± 0.39sys ± 0.47theo 0.06

How much |Vub| moves if the SF is determined by the CLEO data





51

mX vs. q2

Inclusive |Vub| in Perspective

Eℓ endpoint

mX fit

Eℓ vs. q2

Results have been re-adjusted by the Heavy Flavor Averaging Group


52

Exclusive |Vub|

Measure specific final states, e.g., B → ℓv Good signal-to-background ratio Branching fraction in O(10-4) Statistics limited

So far B → ℓv and ℓv have been measured Also seen: B(B → ℓv) = (1.3±0.5)×10−4 [Belle hepex/0402023]

B(B → ℓv) = (0.84±0.36)×10−4 [CLEO PRD68:072003]

Need Form Factors to extract |Vub|

e.g.

How are they calculated?

22 223

2 3

( )

24( )F

ub

Gd BV f

dqqp


53

Form Factors Form Factors are calculated using:

Lattice QCD (q2 > 16 GeV2) Existing calculations are “quenched” ~15% uncertainty

Light Cone Sum Rules (q2 < 16 GeV2) Assumes local quark-hadron duality ~10% uncertainty

Unquenched LQCD starts to appear Preliminary B →ℓv FF from FNAL+MILC (hep-lat/0409116), HPQCD

(hep-lat/0408019) All of them have uncontrolled uncertainties

LQCD and LCSR valid in different q2 ranges No crosscheck Extrapolation to full q2 range introduces model dependent uncertainties Necessary measurement of partial rates in different q2 bins


54

B ℓ with Reconstruction

5 q2 bins

427 68 - ℓ147 23 0 ℓ

Data

Signal MC

Comb. Sig.

Crossfeed

bcl

qq

(B0 - ℓ ) = 2(B+ 0 ℓ )

82 fb-1


55

B ℓ ResultsBF(B0 - ℓ ) = (1.38 ± 0.10stat ± 0.16syst ± 0.08FF)10-4 (from BK)

BF(B0 - ℓ ) = (2.14 ± 0.21stat ± 0.48syst ± 0.28FF)10-4 (from LCSR)

|Vub| = (3.82 ± 0.14stat ± 0.22syst ± 0.11theo ± 0.72FF) 10-3 82 fb-1


56

|Vub| and |Vcb| Summary Inclusive |Vcb| measurement:

- error 2%, HQE validation

Inclusive |Vub| measurements:

- error 10%, different approaches, still room from improvements

New |Vub| result from B ℓ n untagged better FF knowledge necessary

|Vcb| = (41.4 ± 0.4exp ± 0.4HQE ± 0.6theo) 10-3

|Vub| = (4.70 ± 0.44exp+syst) 10-3

|Vub| = (3.82 ± 0.14stat ± 0.22syst ± 0.11theo ± 0.72FF) 10-3


57

Putting Everything Together…

Documents

Experimental Heavy Quark Physics