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B Physics Beyond CP Violation

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B Physics Beyond CP Violation Semileptonic B Decays Masahiro Morii Harvard University Yale University Experimental Particle Physics Seminar – PowerPoint PPT presentation

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Title: B Physics Beyond CP Violation


1
B Physics Beyond CP Violation Semileptonic B
Decays
  • Masahiro Morii
  • Harvard University
  • Yale University Experimental Particle Physics
    Seminar
  • 28 February 2006

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
  • Latest from BABAR Avoiding the 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 PRD 73012006Belle 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 PRL 95241801
  • Must reconstruct all decay products to measure mX
    or q2
  • Select events with a fully-reconstructed B meson
  • Rest of the event contains one recoil B
  • Flavor and momentum known
  • Find a lepton in the recoil B
  • Neutrino missing momentum
  • Make sure mmiss 0
  • All left-over particles belong to X
  • We can now calculate mX and q2
  • Suppress b ? c?v by vetoing against D() decays
  • Reject events with K
  • Reject events with B0 ? D(? D0p)?-v

Fully reconstructedB ? hadrons
v
lepton
X
17
Measuring Partial BF
BABAR hep-ex/0507017Belle PRL 95241801
  • Measure the partial BF in regions of (mX, q2)

For examplemX lt 1.7 GeV and q2 gt 8 GeV2
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
18
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
19
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 parallelto the u quark
    velocity
  • Cannot be calculated by theory
  • Leading term is O(1/mb) insteadof O(1/mb2)

We must determine the Shape Function from
experimental data
20
b ? sg Decays
BABAR PRD 72052004, hep-ex/0507001Belle
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
21
Predicting b ? u?n Spectra
  • Fit the b ? sg spectrum to extract the SF
  • Must assume functional forms, e.g.
  • Additional information from b ? c?v decays
  • E? and mX moments ? b-quark mass and kinetic
    energy
  • NB mb is determined to better than 1
  • ? First two moments of the SF
  • Plug in the SF into the b ? u?vspectrum
    calculations
  • Bosch, Lange, Neubert, Paz, NPB 699335
  • Lange, Neubert, Paz, PRD 72073006
  • Ready to extract Vub

Buchmüller Flächerhep-ph/0507253
Lepton-energyspectrum byBLNP
22
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 PRD 73012006
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 PRL 95241801
Belle 87fb-1 mX lt 1.7, q2 gt 8 4.38 0.46exp 0.30SF,theo PRL 92101801
23
Inclusive Vub as of 2005
Vub world average, 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
24
Theory Errors
  • Subleading Shape Function ? ?3.5 error
  • Higher order non-perturbative corrections
  • Cannot be constrained with b ? sg
  • Weak annihilation ? ?1.9 error
  • Measure G(B0 ? Xu?v)/G(B ? Xu?v) orG(D0 ?
    X?v)/G(Ds ? X?v) to improve the constraint
  • Also study q2 spectrum near endpoint (CLEO
    hep-ex/0601027)
  • Reduce the effect by rejecting the high-q2 region
  • Quark-hadron duality is believed to be negligible
  • b ? c?v and b ? sg data fit well with the HQE
    predictions
  • Ultimate error on inclusive Vub may be 5

25
Avoiding the Shape Function
  • Possible to combine b ? u?v and b ? sg so that
    the SF cancels
  • Leibovich, Low, Rothstein, PLB 48686
  • Lange, Neubert, Paz, JHEP 0510084, Lange, JHEP
    0601104
  • No need to assume functional forms for the Shape
    Function
  • Need b ? sg spectrum in the B rest frame
  • Only one measurement (BABAR PRD 72052004)
    available
  • Cannot take advantage of precise b ? c?v data
  • How well does this work? Only one way to find out

Weight function
26
SF-Free Vub Measurement
BABAR hep-ex/0601046
  • BABAR applied LLR (PLB 48686) to 80 fb-1 data
  • G(B ? Xu?v) with varying mX cut
  • dG(B ? Xsg)/dEg from PRD 72052004
  • With mX lt 1.67 GeV
  • SF error ? Statistical error
  • Also measured mX lt 2.5 GeV
  • Almost (96) fully inclusive ? No SF necessary
  • Attractive new approaches with increasing
    statistics

Theory error
Expt. error
stat.
syst.
theory
Theory error 2.6
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
  • Fermilab (hep-lat/0409116) andHPQCD
    (hep-lat/0601021)
  • Uncertainties are 11

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 PRD 72051102CLEO 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, PLB 63361-69

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
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 ? p?n form factor is needed

38
Extracting the Shape Function
  • Data are not (yet) precise enough to extract the
    SF from scratch
  • We must assume a few plausible functional forms
  • Example
  • First two moments of the SF are connected with
    the b-quark mass mb and kinetic energy mp2
    (Neubert, PLB 61213)
  • Can be determined from b ? sg and/or 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
  • Weve got the Shape Function

Buchmüller Flächerhep-ph/0507253
39
Predicting b ? u?n Spectra
  • Soft Collinear Effective Theory isused to
    predict the triple-differential rate
  • Developed since 2001 by Bauer,Fleming, Luke,
    Pirjol, Stewart
  • A triple-diff. rate calculationavailable since
    Spring 2005
  • Bosch, Lange, Neubert, Paz, NPB 699335
  • Lange, Neubert, Paz, hep-ph/0504071
  • We use BLNP to extract Vub
  • New calculations are appearing
  • Aglietti, Ricciardi, Ferrera, hep-ph/0507285,
    0509095, 0509271
  • Andersen, Gardi, hep-ph/0509360
  • Numerical comparison with BLNP will be done soon

Lepton-energyspectrum byBLNP
40
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
41
SF-free Vub errors
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