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### B Physics Beyond CP Violation— Semileptonic B Decays —

Masahiro Morii

Harvard University

KEK Theory Group Seminar

15 November 2005

Outline

- Introduction: Why semileptonic B decays?
- CKM matrix — Unitarity Triangle — CP violation
- |Vub| vs. sin2b

- |Vub| from inclusiveb→ uv decays
- Measurements: lepton energy, hadron mass, lepton-neutrino mass
- Theoretical challenge: Shape Function

- |Vub| from exclusiveb→ uv decays
- Measurements: G(B→ pv)
- Theoretical challenge: Form Factors

- Summary

M. Morii, Harvard

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

- We don’t know the origin of the EW symmetry breaking Fermion masses and the CKM matrix are inputs to the SM

M. Morii, Harvard

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

M. Morii, Harvard

CP violation and New Physics

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

- 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 exist

M. Morii, Harvard

The Unitarity Triangle

- V†V = 1 gives us
- Measurements of angles and sides constrain the apex (r, h)

This one has the 3 terms in the same order of magnitude

A triangle on the complex plane

M. Morii, Harvard

Consistency Test

- Compare the measurements (contours) on the (r, h) 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 NewPhysics to hide

- Precision of sin2b outstrippedthe other measurements
- Must improve the others tomake more stringent test

M. Morii, Harvard

Next Step: |Vub|

- Zoom in to see the overlap of “the other” contours
- It’s obvious: we must makethe green ring thinner

- Left side of the Triangle is
- Uncertainty dominated by15% on |Vub|

Measurement of |Vub| is complementary to sin2b

Goal: Accurate determination of both |Vub| and sin2b

M. Morii, Harvard

Measuring |Vub|

- Best probe: semileptonic b u decay
- The problem: b cv decay
- How can we suppress 50× larger background?

decoupled from hadronic effects

Tree level

M. Morii, Harvard

Detecting b → un

- 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
- Bpv, Brv, Bwv, Bhv, …
- Example: the rate for Bpv is
- How accurately do we know the FFs?

Form Factor(3 FFs for vector mesons)

M. Morii, Harvard

Inclusive b → un

- There are 3 independent variables in B→Xv
- Signal events have smaller mX Larger E and q2

E = lepton energy

q2 = lepton-neutrino mass squared

u quark turns into 1 or more hardons

mX = hadron system mass

Not to scale!

M. Morii, Harvard

BABARhep-ex/0509040Belle PLB 621:28CLEO PRL 88:231803

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

BABAR

Data

MC bkgd.b cv

Data – bkgd.

MC signalb uv

cf. Total BF is ~2103

M. Morii, Harvard

BABAR PRL 95:111801

BABAR

E vs. q2- Use pv = pmiss in addition to pe Calculate q2
- Define shmax = the maximum mX squared
- Cutting at shmax < mD2 removes b cv while keeping most of the signal

- S/B = 1/2 achieved for E> 2.0 GeV and shmax < 3.5 GeV2
- cf. ~1/15 for the endpoint E> 2.0 GeV

- Define shmax = the maximum mX squared
- Measured partial BF

q2 (GeV2)

b uv

b cv

E (GeV)

Small systematic errors

M. Morii, Harvard

BABARhep-ex/0507017Belle hep-ex/0505088

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 s(mX) = 350 MeV
- 4-momentum conservation; equal mB on both sides; mmiss = 0

- Use a kinematic fit s(mX) = 350 MeV

Fully reconstructedB hadrons

v

lepton

X

M. Morii, Harvard

BABARhep-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*+(→ D0p+)−v

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

M. Morii, Harvard

BABARhep-ex/0507017Belle hep-ex/0505088

Partial BF Results- P+ = EX |PX| is a theoretically clean variable
- Bosch, Lange, Neubert, PazPRL 93:221802
- Efficiency high
- Signal vs. backgroundseparation is limited

Large DB thanks tothe high efficiency of the mX cut

Belle

M. Morii, Harvard

Theoretical Issues

- Tree level rate must be corrected for QCD
- Operator Product Expansion givesus the inclusive rate
- Expansion in as(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

known to O(as2)

Suppressed by 1/mb2

M. Morii, Harvard

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 O(1/mb) instead of O(1/mb2)

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

Details, especially the tail, are unknown

M. Morii, Harvard

BABARhep-ex/0507001, 0508004Belle hep-ex/0407052CLEO hep-ex/0402009

BABAR

Sum of exclusive

Partial BF/bin (10-3)

Inclusive

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

Measure Egspectrum inb → sg

Predictpartial BFs inb → uv

Extract f(k+)

K*

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

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

M. Morii, Harvard

Extracting the Shape Function

- We can fit the b→ sg spectrum with theory prediction
- Must assume a functional form of f(k+)
- Example:

- Must assume a functional form of f(k+)
- New calculation connect the SF moments with the b-quark mass mb and kinetic energy mp2(Neubert, PLB 612:13)
- Determined precisely from b→ sgand b cv decays
- from b→ sg, and from b cv

- Fit data from BABAR, Belle, CLEO, DELPHI, CDF
- NB: mb is determined to better than 1%
Determine the SF

- NB: mb is determined to better than 1%

- Determined precisely from b→ sgand b cv decays

Buchmüller & Flächerhep-ph/0507253

M. Morii, Harvard

Predicting b → un Spectra

- OPE + SF can predict triple-differential rate
- Unreliable where OPE converges poorly
- ... that is where the signal is

- Unreliable where OPE converges poorly
- 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

Lepton-energyspectrum byBLNP

M. Morii, Harvard

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→ sg 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

Weight function

M. Morii, Harvard

Turning DB into |Vub|

- Using BLNP + the SF parameters from b→ sg, b cv
- Adjusted to mb = (4.60 0.04) GeV, mp2 = (0.20 0.04) GeV2
- Theory errors from Lange, Neubert, Paz, hep-ph/0504071
- Last Belle result(*) used a simulated annealing technique

M. Morii, Harvard

Status of Inclusive |Vub|

|Vub| world average as of Summer 2005

- |Vub| determined to 7.6%
- The SF parameters can be improved with b→ sg,b cv measurements
- What’s the theory error?

M. Morii, Harvard

Theory Errors

- Quark-hadron duality is not considered
- b cv and b→ sg data fit well with the HQE predictions

- Weak annihilation 1.9% error
- Expected to be <2% of the total rate
- Measure G(B0 Xuv)/G(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→ sg

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

M. Morii, Harvard

Exclusive B → pn

- Measure specific final states, e.g., B→pv
- Can achieve good signal-to-background ratio
- Branching fractions in O(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

- Lattice QCD(q2 > 15 GeV2)

M. Morii, Harvard

Form Factor Calculations

- Unquenched LQCD calculations started to appear in 2004
- Preliminary B→ pv FF fromFermilab (hep-lat/0409116) andHPQCD (hep-lat/0408019)
- Uncertainties are ~11%

- Validity of the techniqueremains controversial
- Important to measure dG(B→ pv)/dq2 as afunction of q2 Compare with differentcalculations

f+(q2) and f0(q2)

LCSR*FermilabHPQCDISGW2

q2 (GeV2)

- Measure dG(B→ pv)/dq2 as a function of q2
- Compare with differentcalculations

*Ball-Zwicky PRD71:014015

M. Morii, Harvard

Measuring B→ pn

- Measurements differ in what you do with the “other”B
- Total BF is
- 8.4% precision

B(B0 → p+v) [10-4]

M. Morii, Harvard

BABARhep-ex/0507003CLEO PRD 68:072003

Untagged B→pn- Missing 4-momentum = neutrino
- Reconstruct B→pv and calculate mB and DE = EB–Ebeam/2

BABAR

data

MC signal

signal withwrong p

b uv

b cv

BABAR

other bkg.

M. Morii, Harvard

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

soft p

p

D

v

v

D(*)n-taggedB→pn- Reconstruct one B and look for Bpv in the recoil
- Tag with either B D(*)v or B hadrons

- Semileptonic (B D(*)v) tags areefficient but less pure
- Two neutrinos in the event

- Event kinematics determined assumingknown mB and mv

cos2fB 1 for signal

data

MC signal

MC background

M. Morii, Harvard

BABARhep-ex/0507085

Hadronic-taggedB→pn- Hadronic tags have high purity, but low efficiency
- Event kinematics is known by a 2-C fit
- Use mB and mmiss distributions toextract the signal yield

soft p

p

D

p or K

v

data

MC signal

b uv

b cv

other bkg.

M. Morii, Harvard

dB(B → pn)/dq2

- Measurements start to constrain the q2 dependence
- ISGW2 rejected

- Partial BF measured to be

Errors on |Vub| dominated by the FF normalization

M. Morii, Harvard

Future of B → pn

- 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, StewartPRL 95:071802
- Ball, Zwicky, PLB 625:225
- Becher, Hill, hep-ph/0509090

M. Morii, Harvard

b → sg

Inclusive b → cv

Eg

E

mX

ShapeFunction

HQE Fit

mb

FF

LQCD

LCSR

How Things Mesh TogetherSSFs

Inclusiveb → uv

E

Exclusive b → uv

|Vub|

mX

B→pv

wv, hv?

mX-q2

duality

WA

M. Morii, Harvard

The UT 2004 2005

- Dramatic improvement in |Vub|!
- sin2b went down slightly Overlap with |Vub/Vcb| smaller

M. Morii, Harvard

|Vub| vs. the Unitarity Triangle

- Fitting everything except for|Vub|, CKMfitter Group finds
- Inclusive average is
- 2.0s off
- UTfit Group finds 2.8s

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

Exclusive

Inclusive

M. Morii, Harvard

|Vub|

Summary- Precise determination of |Vub| complements sin2b 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→pn form factor is needed

M. Morii, Harvard