B physics beyond cp violation semileptonic b decays
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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 —

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

  • 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

  • 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 by15% 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  cv decay

    • How can we suppress 50× larger background?

decoupled from hadronic effects

Tree level

M. Morii, Harvard

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

  • 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

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

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

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

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

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

  • 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


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

  • 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

  • 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 |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 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 |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

  • 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

  • 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

  • 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

  • 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→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.

M. Morii, Harvard

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

M. Morii, Harvard



  • 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

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

  • 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 → cv










How Things Mesh Together


Inclusiveb → uv


Exclusive b → uv




wv, hv?




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



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

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