b physics beyond cp violation — semileptonic b decays —

B Physics Beyond CP Violation

— Semileptonic B Decays —

Masahiro Morii

Harvard University

KEK Theory Group Seminar

15 November 2005

15 November 2005 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

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

Summary


CKM Matrix Cabibbo-Kobayashi-Maskawa matrix connects the weak and

mass bases of the quarks

We don’t know the origin of the EW symmetry breaking Fermion masses and the CKM matrix are inputs to the SM We are looking for the Higgs particle at the Tevatron, and at the

LHC in the future Unlike the fermion masses, the CKM matrix contains more

measurable quantities than the number of degrees of freedom

. .2

ud us ub

cd cs cb

td ts tb

L

L L L L

L

V V V

V V V

V V V

dg

u c t s W h c

b

L


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


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 TriangleV†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)


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 hep-ex/0509040Belle 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

E was much easier

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 in the recoil-B Lepton charge consistent with the B flavor mmiss consistent with a neutrino

All left-over particles belong to X Use a kinematic fit (mX) = 350 MeV

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

Fully reconstructedB hadrons

lepton

v

X

BABAR hep-ex/0507017Belle hep-ex/0505088


Measuring Partial BF Suppress b → cv by vetoing against D(*) decays

Reject events with K Reject events with B0 → D*+(→ D0+)−v

Measure the partial BF in regions of (mX, q2) For example: mX < 1.7 GeV and q2 > 8 GeV2



Partial BF Results

P+ = EX |PX| is a theoretically clean variable Bosch, Lange, Neubert, Paz

PRL 93:221802

Efficiency high Signal vs. background

separation is limited


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

Belle


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 leading term is (1/mb) instead of (1/mb

2)

k

( )f k

B bM m

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

Details, especially the tail, are unknown

0


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 hep-ex/0507001, 0508004Belle 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*


Extracting the Shape Function We can fit the b → s spectrum with theory prediction

Must assume a functional form of f(k+)

Example:

New calculation connect the SF moments with the b-quark mass mb and kinetic energy

2 (Neubert, PLB 612:13) Determined precisely from b → sand b cv decays

from b → sand from b cv

Fit data from BABAR, Belle, CLEO, DELPHI, CDF

NB: mb is determined to better than 1%

Determine the SF

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

nEnE

nXm

2 2(4.60 0.04)GeV, (0.20 0.04)GeVbm

Buchmüller & Flächerhep-ph/0507253


Predicting b → u Spectra OPE + SF can predict triple-differential rate

Unreliable where OPE converges poorly ... that is where the signal is

Soft Collinear Effective Theory offers the right tool Developed since 2001 by Bauer, Fleming, Luke, Pirjol, Stewart Applied to b → uv by several groups

A triple-diff. rate calculationavailable since Spring 2005 Bosch, Lange, Neubert, Paz, NPB 699:335 Lange, Neubert, Paz, hep-ph/0504071

BABAR and Belle use BLNP toextract |Vub| in the latest results

3

2

( )u

X

d B X

dE dm dq

Lepton-energyspectrum by

BLNP


Next in Theory of Inclusive |Vub|

New calculations of partial BFs are appearing Aglietti, Ricciardi, Ferrera, hep-ph/0507285, 0509095, 0509271 Andersen, Gardi, hep-ph/0509360 Numerical comparison with BLNP will be done soon

Combine b uv and b → s without going through the SF

Leibovich, Low, Rothstein, PLB 486:86 Lange, Neubert, Paz, hep-ph/0508178 Lange, hep-ph/0511098 No need to assume functional forms for the Shape Function

2

2 ( )( )

( ) ub su

ts

W EV d B X

B X dEdEV

Weight function


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 4.39 ± 0.25exp ± 0.32SF,theohep-ex/0509040

Belle 27fb-1 E > 1.9 4.82 ± 0.45exp ± 0.31SF,theoPLB 621:28

CLEO 9fb-1 E > 2.2 4.02 ± 0.47exp ± 0.35SF,theoPRL 88:231803

BABAR 80fb-1 E > 2.0, shmax < 3.5 4.06 ± 0.27exp ± 0.36SF,theo

PRL 95:111801

BABAR 211fb-1 mX < 1.7, q2 > 8 4.76 ± 0.34exp ± 0.32SF,theohep-ex/0507017

Belle 253fb-1 mX < 1.7 4.08 ± 0.27exp ± 0.25SF,theohep-ex/0505088

Belle 87fb-1* mX < 1.7, q2 > 8 4.38 ± 0.46exp ± 0.30SF,theoPRL 92:101801


Status of Inclusive |Vub|

|Vub| determined to 7.6%

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

What’s the theory error?

|Vub| world average as of Summer 2005

Statistical 2.2%

Expt. syst. 2.5%

b cv model 1.9%

b uv model 2.2%

SF params. 4.7%

Theory4.0

%


Theory Errors Quark-hadron duality is not considered

b cv and b → sdata fit well with the HQE predictions Weak annihilation 1.9% error

Expected to be <2% of the total rate Measure (B0 Xuv)/(B+ Xuv)

to improve the constraint Reduce the effect by rejecting the high-q2 region

Subleading Shape Function 3.5% error Higher order non-perturbative corrections Cannot be constrained with b → s

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

b

u

B

g


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


Form Factor Calculations Unquenched LQCD calculations started to appear in 2004

Preliminary B → v FF fromFermilab (hep-lat/0409116) andHPQCD (hep-lat/0408019)

Uncertainties are ~11% Validity of the technique

remains controversial Important to measure

d(B → v)/dq2 as afunction of q2 Compare with differentcalculations

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 hep-ex/0507003CLEO 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 0.89 ± 0.06 ± 0.06

> 16 GeV2 0.40 ± 0.04 ± 0.04

3 2expt FF

3 2expt FF

3 2expt FF

0.540.360.670.460.650.43

(3.27 0.16 ) 10 Ball-Zwicky 16

(4.47 0.30 ) 10 HPQCD 16

(3.78 0.25 ) 10 Fermilab 16

ub

q

V q

q

Errors on |Vub| dominated by the FF normalization


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, hep-ph/0509090


Exclusive b → uv

How Things Mesh Together

B → vInclusiveb → uv

mX-q2 v, v ?

b → s

ShapeFunction

E

mb

Inclusive b → cv

mXE

HQE Fit

mX

E

WA

duality

|Vub|

SSFs

FF

LCSRLQCD


The UT 2004 2005

Dramatic improvement in |Vub|!

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


|Vub| vs. the Unitarity Triangle

Fitting everything except for|Vub|, CKMfitter Group finds

Inclusive average is

2.0 off UTfit Group finds 2.8

Not a serious conflict (yet) We keep watch Careful evaluation of theory errors Consistency between different methods

3

CKM

0.250.22(3.56 ) 10ubV

3

incl.(4.38 0.33) 10ubV

Inclusive

Exclusive


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

(in)completeness of the Standard Model 7.6% 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 —

Documents

b physics

ckm matrixthe ckm matrix

source of cp violation

b xvsignal events

b cv decayhow

harvarddetecting b uninclusive

harvardcp violation

maskawa matrix