b physics beyond cp violation — semileptonic b decays — masahiro morii harvard university...

B Physics Beyond CP Violation

— Semileptonic B Decays —

Masahiro Morii

Harvard University

University of Illinois Urbana-Champaign HETEP Seminar

3 April 2006

3 April 2006 M. Morii, Harvard 2

Outline Introduction: Why semileptonic B decays?

CKM matrix — Unitarity Triangle — CP violation |Vub| vs. sin2

|Vub| from inclusive b → uv decays Measurements: lepton energy, hadron mass, lepton-neutrino mass Theoretical challenge: Shape Function Latest from BABAR – Avoiding the Shape Function

|Vub| from exclusive b → uv decays Measurements: (B → v) Theoretical challenge: Form Factors

Summary


Mass and the Generations Fermions come in three generations

They differ only by the masses The Standard Model has no explanation

for the mass spectrum The masses come from the interaction

with the Higgs field ... whose nature is unknown We are looking for the Higgs particle at

the Tevatron, and at the LHC in the future

310

410

510

610

710

810

910

1010

1110

Part

icle

mas

s (e

V/c

2 )

1210

e

u

c

t

d

s

b

Q = 1 0 +2/3 1/3

The origin of mass is one of the most urgent questions in particle physics today


If there were no masses Nothing would distinguish u from c from t

We could make a mixture of the wavefunctions and pretend it represents a physical particle

Suppose W connects u ↔ d, c ↔ s, t ↔ b

That’s a poor choice of basis vectors

u u

c c

t t

M

d d

s s

b b

N M and N are arbitrary33 unitary matrices

1 1 1

u u d d d

c c s s s

t t b b b

M M M N V

Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V


Turn the masses back on Masses uniquely define the u, c, t, and d, s, b states

We don’t know what creates masses We don’t know how the eigenstates are chosen M and N are arbitrary

V is an arbitrary 33 unitary matrix

The Standard Model does not predict V ... for the same reason it does not predict the particle masses

ud us ub

cd cs cb

td ts tb

Wu d V V V d

c s V V V s

t b V V V b

V

Cabibbo-Kobayashi-Maskawa matrix or CKM for short


Structure of the CKM matrix The CKM matrix looks like this

It’s not completely diagonal Off-diagonal components are small

Transition across generations isallowed but suppressed

The “hierarchy” can be best expressed in theWolfenstein parameterization:

One irreducible complex phase CP violation The only source of CP violation in the minimal Standard Model

0.974 0.226 0.004

0.226 0.973 0.042

0.008 0.042 0.999

V

0.974 0.226 0.004

0.226 0.973 0.042

0.008 0.042 0.999

V

3212

2 2 41

32

2

1

1 ( )

1

( )

(1 )

A i

i AA

A

V O

Vub


CP violation and New Physics

The CKM mechanism fails to explain the amount of matter-antimatter imbalance in the Universe ... by several orders of magnitude

New Physics beyond the SM is expected at 1-10 TeV scale e.g. to keep the Higgs mass < 1 TeV/c2

Almost all theories of New Physics introduce new sources of CP violation (e.g. 43 of them in supersymmetry)

Precision studies of the CKM matrix may uncover them

New sources of CP violation almost certainly existNew sources of CP violation almost certainly exist

Are there additional (non-CKM) sources of CP violation?


The Unitarity Triangle V†V = 1 gives us

Measurements of angles and sides constrain the apex (, )

* * *

* * *

* * *

0

0

0

ud us cd cs td ts

ud ub cd cb td tb

us ub cs cb ts tb

V V V V V V

V V V V V V

V V V V V V

This one has the 3 terms in the same

order of magnitude

A triangle on the complex plane

1

td tb

cd cb

V V

V V

ud ub

cd cb

V V

V V

0

*ud ubV V

*td tbV V

*cd cbV V

*

*

*

*

*

*

arg

arg

arg

td tb

ud ub

cd cb

td tb

ud ub

cd cb

V V

V V

V V

V V

V V

V V


Consistency Test Compare the measurements (contours) on the (, ) plane

If the SM is the whole story,they must all overlap

The tells us this is trueas of summer 2004 Still large enough for New

Physics to hide Precision of sin2 outstripped

the other measurements Must improve the others to

make more stringent test


Next Step: |Vub|

Zoom in to see the overlap of “the other” contours It’s obvious: we must make

the green ring thinner Left side of the Triangle is

Uncertainty dominated by15% on |Vub|

ud ub cd cbV V V V

Measurement of |Vub| is complementary to sin2

Goal: Accurate determination of both |Vub| and sin2


Measuring |Vub|

Best probe: semileptonic b u decay

The problem: b cv decay

How can we suppress 50× larger background?

25

2

2( )

192 ubF

b

Gb mVu

b

u

ubV

2

2

( ) 1

( ) 50ub

cb

Vb u

b c V

Tree level

decoupled from hadronic effects


Detecting b → u Inclusive: 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?

Exclusive: Reconstruct final-state hadrons B v, B v, B v, B v, … Example: the rate for B v is

How accurately do we know the FFs?

E

b c

b u

222 3 2

2 3

( )( )

24F

ub

Gd BV p f q

dq

Form Factor(3 FFs for vector mesons)

2.64

2.31


There are 3 independent variables in B → Xv

Signal events have smaller mX Larger E and q2

Inclusive b → u

2q

b c

b u

uX

B

u quark turns into 1 or more hardons

q2 = lepton-neutrino mass squaredq2 = lepton-neutrino mass squared

mX = hadron system massmX = hadron system mass

E = lepton energyE = lepton energy

E

b c

b u

Xm

b cb u

Not to scale!Not to scale!


Lepton Endpoint Select electrons in 2.0 < E < 2.6 GeV

Push below the charm threshold Larger signal acceptance Smaller theoretical error

Accurate subtraction of backgroundis crucial!

Measure the partial BF

E (GeV) (10-4)

BABAR 80fb-1 2.0–2.6 5.72 ± 0.41stat ± 0.65sys

Belle 27fb-1 1.9–2.6 8.47 ± 0.37stat ± 1.53sys

CLEO 9fb-1 2.2–2.6 2.30 ± 0.15stat ± 0.35sys

BABAR PRD 73:012006Belle PLB 621:28

CLEO PRL 88:231803

BABAR

MC bkgd.b cv

Data

Data – bkgd.

MC signalb uv

cf. Total BF is ~2103


E vs. q2

Use pv = pmiss in addition to pe Calculate q2

Define shmax = the maximum mX squared

Cutting at shmax < mD

2 removes b cv while keeping most of the signal

S/B = 1/2 achieved for E > 2.0 GeV and sh

max < 3.5 GeV2

cf. ~1/15 for the endpoint E > 2.0 GeV

Measured partial BF

BABAR PRL 95:111801

BABAR (10-4)

BABAR 80fb-1 3.54 ± 0.33stat ± 0.34sys

0.5 1 1.5 2 2.5

5

10

15

20

25

b cv

E (GeV)

q2 (G

eV2 )

b uv

Small systematic errors


Measuring mX and q2

Must reconstruct all decay products to measure mX or q2

Select events with a fully-reconstructed B meson Rest of the event contains one “recoil” B

Flavor and momentum known

Find a lepton in the recoil B Neutrino = missing momentum

Make sure mmiss ~ 0

All left-over particles belong to X We can now calculate mX and q2

Suppress b → cv by vetoing against D(*) decays Reject events with K Reject events with B0 → D*+(→ D0+)−v

BABAR hep-ex/0507017Belle PRL 95:241801

Fully reconstructedB hadrons

lepton

v

X


Measuring Partial BF Measure the partial BF in regions of (mX, q2)

BABAR hep-ex/0507017Belle PRL 95:241801

Phase Space (10-4)

BABAR 211fb-1 mX < 1.7, q2 > 8 8.7 ± 0.9stat ± 0.9sys

Belle 253fb-1

mX < 1.7 12.4 ± 1.1stat ± 1.0sys

mX < 1.7, q2 > 8 8.4 ± 0.8stat ± 1.0sys

P+ < 0.66 11.0 ± 1.0stat ± 1.6sys

Large thanks tothe high efficiency of the mX cut

For example:mX < 1.7 GeV and

q2 > 8 GeV2


B

uX

b

u

ubVB

uX

Theoretical Issues Tree level rate must be corrected for QCD Operator Product Expansion gives

us the inclusive rate Expansion in s(mb) (perturbative)

and 1/mb (non-perturbative)

Main uncertainty (5%) from mb5 2.5% on |Vub|

But we need the accessible fraction (e.g., Eℓ > 2 GeV) of the rate

2

15

22

2

3( )

22

91

19F u

b

b b su

G

m

V mB X

O

known to (s2) Suppressed by 1/mb

2


Shape Function OPE doesn’t work everywhere in the phase space

OK once integrated Doesn’t converge, e.g., near the E end point

Resumming turns non-perturb. terms into a Shape Function b quark Fermi motion parallel

to the u quark velocity Cannot be calculated by theory Leading term is (1/mb) instead

of (1/mb2) k

( )f k

B bM m 0We must determine the Shape Function

from experimental data


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

Measure E

spectrum inb → s

Extract f(k+) Predict

partial BFs inb → uv

BABAR PRD 72:052004, hep-ex/0507001Belle hep-ex/0407052

CLEO hep-ex/0402009

Inclusive

Sum of exclusive BABAR

Part

ial B

F/bi

n (1

0-3)

Inclusive measurement. Photon energy in the Y(4S) rest frame

Exclusive Xs + measurement. Photon energy determined from the Xs mass

K*


Predicting b → u Spectra Fit the b → s spectrum to extract the SF

Must assume functional forms, e.g. Additional information from b cv decays

E and mX moments b-quark mass and kinetic energy

NB: mb is determined to better than 1%

First two moments of the SF Plug in the SF into the b uv

spectrum calculations Bosch, Lange, Neubert, Paz, NPB 699:335 Lange, Neubert, Paz, PRD 72:073006

Ready to extract |Vub|

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

2 2(4.60 0.04)GeV, (0.20 0.04)GeVbm Buchmüller & Flächerhep-ph/0507253

Lepton-energyspectrum by

BLNP


Turning into |Vub|

Using BLNP + the SF parameters from b → sb cv

Adjusted to mb = (4.60 0.04) GeV, 2 = (0.20 0.04) GeV2

Theory errors from Lange, Neubert, Paz, hep-ph/0504071 Last Belle result(*) used a simulated annealing technique

Phase Space |Vub| (10-3) Reference

BABAR 80fb-1 E > 2.0 4.41 ± 0.29exp ± 0.31SF,theoPRD 73:012006

Belle 27fb-1 E > 1.9 4.82 ± 0.45exp ± 0.30SF,theoPLB 621:28

CLEO 9fb-1 E > 2.2 4.09 ± 0.48exp ± 0.36SF,theoPRL 88:231803

BABAR 80fb-1 E > 2.0, shmax < 3.5 4.10 ± 0.27exp ± 0.36SF,theo

PRL 95:111801

BABAR 211fb-1 mX < 1.7, q2 > 8 4.75 ± 0.35exp ± 0.32SF,theohep-ex/0507017

Belle 253fb-1 mX < 1.7 4.06 ± 0.27exp ± 0.24SF,theoPRL 95:241801

Belle 87fb-1* mX < 1.7, q2 > 8 4.37 ± 0.46exp ± 0.29SF,theoPRL 92:101801


Inclusive |Vub| as of 2005

|Vub| determined to 7.4%

The SF parameters can be improved with b → sb cv measurements

What’s the theory error?

|Vub| world average, Winter 2006

Statistical 2.2%

Expt. syst. 2.7%

b cv model 1.9%

b uv model 2.1%

SF params. 4.1%

Theory4.2

%


Theory Errors Subleading Shape Function 3.8% error

Higher order non-perturbative corrections Cannot be constrained with b → s

Weak annihilation 1.9% error Measure (B0 Xuv)/(B+ Xuv) or(D0 Xv)/(Ds Xv) to improve the constraint Also: study q2 spectrum near endpoint (CLEO hep-ex/0601027)

Reduce the effect by rejecting the high-q2 region Quark-hadron duality is believed to be negligible

b cv and b → sdata fit well with the HQE predictions

Ultimate error on inclusive |Vub| may be ~5%

b

u

B

g


Avoiding the Shape Function Possible to combine b uv and b → s so that the SF cancels

Leibovich, Low, Rothstein, PLB 486:86 Lange, Neubert, Paz, JHEP 0510:084, Lange, JHEP 0601:104

No need to assume functional forms for the Shape Function Need b → s spectrum in the B rest frame

Only one measurement (BABAR PRD 72:052004) available Cannot take advantage of precise b cv data

How well does this work? Only one way to find out…

2

2 ( )( )

( ) ub su

ts

W EV d B X

B X dEdEV

Weight function


SF-Free |Vub| Measurement

BABAR applied LLR (PLB 486:86) to 80 fb-1 data (B Xuv) with varying mX cut

d(B Xs)/dE from PRD 72:052004

With mX < 1.67 GeV

SF error Statistical error

Also measured mX < 2.5 GeV Almost (96%) fully inclusive No SF necessary

Attractive new approaches with increasing statistics

mX cut (GeV)1.67

3(4.43 0.38 0.25 0.29) 10ubV

stat. syst. theory

3(3.84 0.70 0.30 0.10) 10ubV Theory error ±2.6%

BABAR hep-ex/0601046

Theory error

Expt. error


Exclusive B → Measure specific final states, e.g., B → v

Can achieve good signal-to-background ratio Branching fractions in (10-4) Statistics limited

Need Form Factors to extract |Vub|

f+(q2) has been calculated using Lattice QCD (q2 > 15 GeV2)

Existing calculations are “quenched” ~15% uncertainty Light Cone Sum Rules (q2 < 14 GeV2)

Assumes local quark-hadron duality ~10% uncertainty ... and other approaches

22 223

2 3

( )

24( )F

ub

Gd BV f

dqqp

One FF for B → vwith massless lepton


Form Factor Calculations Unquenched LQCD calculations started to appear in 2004

Fermilab (hep-lat/0409116) andHPQCD (hep-lat/0601021)

Uncertainties are ~11%

f +(q

2 ) a

nd f 0(

q2 )

q2 (GeV2)

Measure d(B → v)/dq2 as a function of q2

Compare with differentcalculations

LCSR*FermilabHPQCDISGW2

*Ball-Zwicky PRD71:014015


Measuring B → Measurements differ in

what you do with the “other” B

Total BF is

8.4% precision

(B0 → v) [10-4]

Technique Efficiency

Purity

Untagged High

Low

Low

High

Tagged by B D(*)v

Tagged by B hadrons

4stat syst(1.35 0.08 0.08 ) 10


Untagged B → Missing 4-momentum = neutrino Reconstruct B → v and calculate mB and E = EB – Ebeam/2

BABAR

BABAR

data

MC signalsignal withwrong

b uvb cvother bkg.

BABAR PRD 72:051102CLEO PRD 68:072003


D(*)-tagged B → Reconstruct one B and look for B v in the recoil

Tag with either B D(*)v or B hadrons Semileptonic (B D(*)v) tags are

efficient but less pure Two neutrinos in the event

Event kinematics determined assumingknown mB and mv

vv

D

soft

cos2B 1 for signaldata

MC signalMC background

BABAR hep-ex/0506064, 0506065Belle hep-ex/0508018


Hadronic-tagged B → Hadronic tags have high purity, but low efficiency

Event kinematics is known by a 2-C fit Use mB and mmiss distributions to

extract the signal yield

or Kv

D

soft

0B 0B

data

MC signal

b uvb cvother bkg.

BABAR hep-ex/0507085


d(B → )/dq2

Measurements start to constrain the q2 dependence ISGW2 rejected

Partial BF measured to be

q2 range [10−4]

< 16 GeV2 0.94 ± 0.06 ± 0.06

> 16 GeV2 0.39 ± 0.04 ± 0.04

3 2expt

3 2expt

3 2ex

FF

p

FF

FFt

0.550.370.630.430.650.43

(3.36 0.15 ) 10 Ball-Zwicky 16

(4.20 0.29 ) 10 HPQCD 16

(3.75 0.26 ) 10 Fermilab 16

ub

q

V q

q

Errors on |Vub| dominated by the FF normalization

HFAG 2006Winter


Future of B → Form factor normalization dominates the error on |Vub|

Experimental error will soon reach 5% Significant efforts in both LQCD and LCSR needed

Spread among the calculations still large Reducing errors below 10% will be a challenge

Combination of LQCD/LCSR with the measured q2 spectrum and dispersive bounds may improve the precision Fukunaga, Onogi, PRD 71:034506 Arnesen, Grinstein, Rothstein, Stewart

PRL 95:071802 Ball, Zwicky, PLB 625:225 Becher, Hill, PLB 633:61-69


Exclusive b → uv

How Things Mesh Together

B → vInclusiveb → uv q2

v, v ?

b → s

ShapeFunction

E

mb

Inclusive b → cv

mXE

HQE Fit

mX

E

WA

duality

|Vub|

SSFs

FF

LCSR LQCDunquenching


The UT 2004 2005

Dramatic improvement in |Vub|!

sin2 went down slightly Overlap with |Vub/Vcb| smaller


Summary Precise determination of |Vub| complements sin2 to test the

(in)completeness of the Standard Model 7.4% accuracy achieved so far 5% possible?

Close collaboration between theory and experiment is crucial Rapid progress in inclusive |Vub| in the last 2 years

Improvement in B → form factor is needed

|Vub |

b physics beyond cp violation — semileptonic b decays — masahiro morii harvard university...

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