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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 | V ub | vs. sin2 b

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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


  • Introduction: Why semileptonic B decays?

    • CKM matrix — Unitarity Triangle — CP violation

    • |Vub| vs. sin2b

  • |Vub| from inclusiveb→ uv decays

    • Measurements: lepton energy, hadron mass, lepton-neutrino mass

    • Theoretical challenge: Shape Function

  • |Vub| from exclusiveb→ uv decays

    • Measurements: G(B→ pv)

    • Theoretical challenge: Form Factors

  • Summary

M. Morii, Harvard

Ckm matrix
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

M. Morii, Harvard

Structure of the ckm matrix
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
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
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
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 v ub
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 by15% on |Vub|

Measurement of |Vub| is complementary to sin2b

Goal: Accurate determination of both |Vub| and sin2b

M. Morii, Harvard

Measuring v ub
Measuring |Vub|

  • Best probe: semileptonic b  u decay

  • The problem: b  cv decay

    • How can we suppress 50× larger background?

decoupled from hadronic effects

Tree level

M. Morii, Harvard

Detecting b u n
Detecting b → un

  • 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pv, Brv, Bwv, Bhv, …

    • Example: the rate for Bpv is

      • How accurately do we know the FFs?

Form Factor(3 FFs for vector mesons)

M. Morii, Harvard

Inclusive b u n
Inclusive b → un

  • There are 3 independent variables in B→Xv

    • 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

Lepton endpoint

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



MC bkgd.b cv

Data – bkgd.

MC signalb uv

cf. Total BF is ~2103

M. Morii, Harvard

E vs q 2

BABAR PRL 95:111801


E vs. q2

  • Use pv = pmiss in addition to pe Calculate q2

    • Define shmax = the maximum mX squared

      • Cutting at shmax < mD2 removes b  cv 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

  • Measured partial BF

q2 (GeV2)

b uv

b cv

E (GeV)

Small systematic errors

M. Morii, Harvard

Measuring m x and q 2

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

Fully reconstructedB hadrons




M. Morii, Harvard

Measuring partial bf

BABARhep-ex/0507017Belle hep-ex/0505088

Measuring Partial BF

  • Suppress b → cv 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

Partial bf results

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


M. Morii, Harvard

Theoretical issues
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

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Shape function
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

B s g decays

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


Sum of exclusive

Partial BF/bin (10-3)


b→ sg Decays

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

Measure Egspectrum inb → sg

Predictpartial BFs inb → uv

Extract f(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
Extracting the Shape Function

  • We can fit the b→ sg 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 mp2(Neubert, PLB 612:13)

    • Determined precisely from b→ sgand b  cv decays

      • from b→ sg, and from b  cv

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

      • NB: mb is determined to better than 1%

         Determine the SF

Buchmüller & Flächerhep-ph/0507253

M. Morii, Harvard

Predicting b u n spectra
Predicting b → un 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→ uv 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 v ub
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  uv 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 d b into v ub
Turning DB into |Vub|

  • Using BLNP + the SF parameters from b→ sg, b  cv

    • 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 v ub
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  cv measurements

    • What’s the theory error?

M. Morii, Harvard

Theory errors
Theory Errors

  • Quark-hadron duality is not considered

    • b  cv 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  Xuv)/G(B+  Xuv)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 p n
Exclusive B → pn

  • Measure specific final states, e.g., B→pv

    • 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

M. Morii, Harvard

Form factor calculations
Form Factor Calculations

  • Unquenched LQCD calculations started to appear in 2004

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

    • Uncertainties are ~11%

  • Validity of the techniqueremains controversial

    • Important to measure dG(B→ pv)/dq2 as afunction of q2 Compare with differentcalculations

f+(q2) and f0(q2)


q2 (GeV2)

  • Measure dG(B→ pv)/dq2 as a function of q2

    • Compare with differentcalculations

*Ball-Zwicky PRD71:014015

M. Morii, Harvard

Measuring b p n
Measuring B→ pn

  • 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

Untagged b p n

BABARhep-ex/0507003CLEO PRD 68:072003

Untagged B→pn

  • Missing 4-momentum = neutrino

  • Reconstruct B→pv and calculate mB and DE = EB–Ebeam/2



MC signal

signal withwrong p

b uv

b cv


other bkg.

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D n tagged b p n

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

soft p






  • Reconstruct one B and look for Bpv 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


MC signal

MC background

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Hadronic tagged b p n



  • 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 or K



MC signal

b uv

b cv

other bkg.

M. Morii, Harvard

D b b p n dq 2
dB(B → pn)/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 p n
Future of B → pn

  • 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

How things mesh together

b → sg

Inclusive b → cv










How Things Mesh Together


Inclusiveb → uv


Exclusive b → uv




wv, hv?




M. Morii, Harvard

The ut 2004 2005
The UT 2004  2005

  • Dramatic improvement in |Vub|!

  • sin2b went down slightly  Overlap with |Vub/Vcb| smaller

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V ub vs the unitarity triangle
|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



M. Morii, Harvard




  • 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→pn form factor is needed

M. Morii, Harvard