B Physics Beyond CP Violation

1
B Physics Beyond CP Violation Semileptonic B
Decays

• Masahiro Morii
• Harvard University
• University of Tokyo ICEPP Seminar
• 14 November 2005

2
Outline

• Introduction Why semileptonic B decays?
• CKM matrix Unitarity Triangle CP violation
• Vub vs. sin2b
• Vub from inclusive b ? u?v decays
• Measurements lepton energy, hadron mass,
  lepton-neutrino mass
• Theoretical challenge Shape Function
• Vub from exclusive b ? u?v decays
• Measurements G(B ? p?v)
• Theoretical challenge Form Factors
• Summary

3
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

The origin of mass is one of the most urgent
questions in particle physics today
Q ?1 0 2/3 ?1/3
4
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?
• Thats a poor choice of basis vectors

M and N are arbitrary3?3 unitary matrices
Weak interactions between u, c, t, and d, s, b
are mixed by matrix V
5
Turn the masses back on

• Masses uniquely define the u, c, t, and d, s, b
  states
• We dont know what creates masses? We dont know
  how the eigenstates are chosen? M and N are
  arbitrary
• V is an arbitrary 3?3 unitary matrix
• The Standard Model does not predict V
• ... for the same reason it does not predict the
  particle masses

or CKM for short
Cabibbo-Kobayashi-Maskawa matrix
6
Structure of the CKM matrix

• The CKM matrix looks like this ?
• Its 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

Vub
7
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 lt 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
8
The Unitarity Triangle

• VV 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
9
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

10
Next Step Vub

• Zoom in to see the overlap of the other
  contours
• Its 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
11
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
12
Detecting b ? u?n

• Inclusive Use mu ltlt 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?

2.64
2.31
Form Factor(3 FFs for vector mesons)
13
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!
14
Lepton Endpoint
BABAR hep-ex/0509040Belle PLB 62128CLEO PRL
88231803

• Select electrons in 2.0 lt E? lt 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 ? c?v
Data bkgd.
E? (GeV) DB (10-4)
BABAR 80fb-1 2.02.6 5.72 0.41stat 0.65sys
Belle 27fb-1 1.92.6 8.47 0.37stat 1.53sys
CLEO 9fb-1 2.22.6 2.30 0.15stat 0.35sys
MC signalb ? u?v
cf. Total BF is 2?10?3
15
E? vs. q2
BABAR PRL 95111801

• Use pv pmiss in addition to pe ? Calculate q2
• Define shmax the maximum mX squared
• Cutting at shmax lt mD2 removes b ? c?v while
  keeping most of the signal
• S/B 1/2 achieved for E? gt 2.0 GeV and shmax lt
  3.5 GeV2
• cf. 1/15 for the endpoint E? gt 2.0 GeV
• Measured partial BF

q2 (GeV2)
b ? u?v
b ? c?v
E? (GeV)
DB (10-4)
BABAR 80fb-1 3.54 0.33stat 0.34sys
Small systematic errors
16
Measuring mX and q2
BABAR hep-ex/0507017Belle hep-ex/0505088

• 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
v
lepton
X
17
Measuring Partial BF
BABAR hep-ex/0507017Belle hep-ex/0505088

• 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 lt 1.7 GeV and q2 gt 8 GeV2

18
Partial BF Results
BABAR hep-ex/0507017Belle hep-ex/0505088
Phase Space DB (10-4)
BABAR 211fb-1 mX lt 1.7, q2 gt 8 8.7 0.9stat 0.9sys
Belle 253fb-1 mX lt 1.7 12.4 1.1stat 1.0sys
Belle 253fb-1 mX lt 1.7, q2 gt 8 8.4 0.8stat 1.0sys
Belle 253fb-1 P lt 0.66 11.0 1.0stat 1.6sys
Large DB thanks tothe high efficiency of the mX
cut

• P EX ? PX is a theoretically clean variable
• Bosch, Lange, Neubert, PazPRL 93221802
• Efficiency high
• Signal vs. backgroundseparation is limited

Belle
19
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 gt 2
  GeV) of the rate

known to O(as2)
Suppressed by 1/mb2
20
Shape Function

• OPE doesnt work everywhere in the phase space
• OK once integrated
• Doesnt 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
21
b ? sg Decays
BABAR hep-ex/0507001, 0508004Belle
hep-ex/0407052CLEO hep-ex/0402009

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

Measure Egspectrum inb ? sg
Predictpartial BFs inb ? u?v
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
22
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 61213)
• Determined precisely from b ? sg and 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
23
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 699335
• Lange, Neubert, Paz, hep-ph/0504071
• BABAR and Belle use BLNP toextract Vub in the
  latest results

Lepton-energyspectrum byBLNP
24
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

Phase Space Vub (10-3) Reference
BABAR 80fb-1 E? gt 2.0 4.39 0.25exp 0.32SF,theo hep-ex/0509040
Belle 27fb-1 E? gt 1.9 4.82 0.45exp 0.31SF,theo PLB 62128
CLEO 9fb-1 E? gt 2.2 4.02 0.47exp 0.35SF,theo PRL 88231803
BABAR 80fb-1 E? gt 2.0, shmax lt 3.5 4.06 0.27exp 0.36SF,theo PRL 95111801
BABAR 211fb-1 mX lt 1.7, q2 gt 8 4.76 0.34exp 0.32SF,theo hep-ex/0507017
Belle 253fb-1 mX lt 1.7 4.08 0.27exp 0.25SF,theo hep-ex/0505088
Belle 87fb-1 mX lt 1.7, q2 gt 8 4.38 0.46exp 0.30SF,theo PRL 92101801
25
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
• Whats the theory error?

Statistical ?2.2
Expt. syst. ?2.5
b ? c?v model ?1.9
b ? u?v model ?2.2
SF params. ?4.7
Theory ?4.0
26
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 lt2 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

27
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 gt 15 GeV2)
• Existing calculations are quenched ? 15
  uncertainty
• Light Cone Sum Rules (q2 lt 14 GeV2)
• Assumes local quark-hadron duality ? 10
  uncertainty
• ... and other approaches

One FF for B ? p?vwith massless lepton
28
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)
LCSRFermilabHPQCDISGW2
q2 (GeV2)

• Measure dG(B ? p?v)/dq2 as a function of q2
• Compare with differentcalculations

Ball-Zwicky PRD71014015
29
Measuring B ? p?n

• Measurements differ in what you do with the
  other B
• Total BF is
• ?8.4 precision

Technique Efficiency Purity
Untagged High ? Low Low ? High
Tagged by B ? D()?v High ? Low Low ? High
Tagged by B ? hadrons High ? Low Low ? High
B(B0 ? p??v) 10-4
30
Untagged B ? p?n
BABAR hep-ex/0507003CLEO PRD 68072003

• Missing 4-momentum neutrino
• Reconstruct B ? p?v and calculate mB and DE EB
  Ebeam/2

BABAR
data
MC signal
signal withwrong p
b ? u?v
b ? c?v
BABAR
other bkg.
31
D()?n-tagged B ? p?n
BABAR hep-ex/0506064, 0506065Belle hep-ex/0508018

• 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
data
MC signal
MC background
32
Hadronic-tagged B ? p?n
BABAR hep-ex/0507085

• 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 ? u?v
b ? c?v
other bkg.
33
dB(B ? p?n)/dq2

• Measurements start to constrain the q2 dependence
• ISGW2 rejected
• Partial BF measured to be

q2 range DB 10-4
lt 16 GeV2 0.89 0.06 0.06
gt 16 GeV2 0.40 0.04 0.04
Errors on Vub dominated by the FF normalization
34
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 71034506
• Arnesen, Grinstein, Rothstein, StewartPRL
  95071802
• Ball, Zwicky, PLB 625225
• Becher, Hill, hep-ph/0509090

35
How Things Mesh Together
SSFs
Inclusiveb ? u?v
Exclusive b ? u?v
E?
Vub
B ? p?v
q2
w?v, h?v ?
mX
duality
WA
unquenching
36
The UT 2004 ? 2005

• Dramatic improvement in Vub!
• sin2b went down slightly ? Overlap with Vub/Vcb
  smaller

37
Vub vs. the Unitarity Triangle

• Fitting everything except forVub, CKMfitter
  Group finds
• Inclusive average is
• 2.0s off
• UTfit Group finds 2.8s
• Not a serious conflict (yet)
• Careful evaluation of theory errors
• Consistency between different calculations

Exclusive
Inclusive
38
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
• BABAR and Belle will pursue increasingly precise
  measurements over the next few years
• Will the SM hold up?

B physics continues to offer exciting potential
for discovering (or constraining) New Physics
beyond the Standard Model