Lecture Plan

1
Lecture Plan

• Lecture 1 Introduction The Standard Model B
  Decays
• Lecture 2 Higher Order Processes Loop Box
  Diagrams CP Violation
• Beyond the Standard Model Experimental
  Techniques

2
Lecture 1 Survey of B Physics

• Weak Decays
• The CKM matrix
• Semileptonic Decays
• Inclusive
• Exclusive
• Lifetimes
• CKM matrix elements Vcb Vub
• Hadronic decays

3
Lecture 1 Introduction The Standard Model B
Decays

• Theoretical Background
• Physical States in the Standard Model
• The gauge bosons W, g Zo and the Higgs Ho
• Lagrangian for charged current weak decays
• Where

VMNS
New
4
The CKM Matrix

• Unitary with 92 numbers ? 4 independent
  parameters
• Many ways to write down matrix in terms of these
  parameters

5
Parameterization of the CKM Matrix

• Wolfenstein parameterization good to l3 in real
  part l5 in imaginary part
• l, A, r h are fundamental constants of nature!

d s
b
u
c
t
6
Weak Charged Current Decays

• It all starts with muon decay
• Since Gm?tmh, measuring the muon lifetime gives
  GF

A tree level diagram
7
Vud
8
More on Vud II
9
More on Vud III

• Vud 0.973770.000110.000150.00019

10
Semileptonic K- Decay

• s quark charged current
• decay
• If we didnt have to worry about the fact that
  the s quark is paired with a u quark to form a K-
  a uu then forms a po, we could measure the
  decay rate for K-?poe-n by measuring the K-
  lifetime the branching ratio then find Vus
• Taking into account the hadronic physics we find
  Vusl0.22050.0018 (2004) Now 0.22570.0021

g
11
Semileptonic B Decays

• Two CKM elements can
• be measured, Vcb Vub
• Necessary ingredients
• B lifetimes
• Branching fractions
• Theory or Model to take care of hadronic physics
• Now let us investigate how the lifetime
  measurements are done

12
B Production Using ee-

• Ways of producing b-quarks
• ee-??(4S)?BB- or BoBo (CESR, DORIS, PEP II,
  KEK) s1 nb
• ee-?b b X (PEP, PETRA, LEP, SLC)

13
B Production Using Hadrons
Q b or c

• pp ?b b X
• (TEVATRON)
• Measured sbb normalizes to 100 mb at 1.8 TeV near
  90o D0 measures 2.3 x in forward region
• 3rd order diagrams very important
• Calculations low by factor of 2!
• All b species produced

14
B Lifetime Measurements

• First at 30 GeV ee- machines (PEP PETRA)
• Measured b quark lifetime
• Used impact parameter method
• Impact parameter minimum distance
• of approach of a track from a vertex
• Like to measure decay distance Lgbct, where t is
  the decay time of the individual particle
• Events will be distributed exponentially, the
  1/slope of the exponent is the lifetime e-t/t
• Uncertainty results from errors on L and momentum
  and contributions of backgrounds

b
15
Precision Lifetime Measurements

• LEP exp- individual lifetimes measured
• Used semileptonic decays
• Some fully reconstructed hadronic decays
• CDF uses fully reconstructed hadronic decays

16
B Lifetime Results
1.6380.011

• Note ratio tB/tBo
• 1.0710.009, a
• clear difference
• Also tL ? tBo
• According to
• proponents of the
• Heavy Quark Expansion theory, there should be
  at most a 10 difference between Lb Bo
• General reasons for a lifetime difference

1.5300.009
1.4660.059
1.2300.074
b
17
B Decay Diagrams

• Each diagram contributes to the decay width
• a) is dominant
• No direct evidence for c) or d)
• More diagrams for baryons

• What about charm?

18
B Lifetime Differences

• Bo and B- If gt1 diagram leads to the same final
  state interference occurs
• Interference between b) a) occurs only for B-
  for Bo there are different final states
• ex B-?Dop- a) b), but for Bo?Dp- only a)

u
19
Problem with tB/tBo

• Relative width measurements
• This shows that the interference is positive,
  i.e. rate for (a)(b) gt (a) (reverse of charm)
• But this should ? tB lt tBo contrary to what is
  observed
• This is an outstanding problem!

20
Exclusive Semileptonic B Decays (formalism)

• Amplitude for decay into a pseudoscalar m
• where , and
• P is 4-vector of B
• p is 4-vector of m
• q2 is 4-momentum transfer between B m

21
Exclusive Semileptonics continued

• Note that maximum q2 corresponds to pm pB,
  minimum q2 where pm is largest
• Term ? f-(q2)ml2, 0 for le, m in b decay
• where
• is the momentum of m in the B rest
  frame

22
Exclusive semileptonicsformalism summary

• For pseudoscalar to pseudoscalar transitions, to
  find Vij we need to
• measure lifetime of B and shape of form-factor
• get f(0) from theoretical models
• where g(q2) is the measured shape function
• For 0- ? 1 transitions, in general, there are 3
  form-factors

23
Homework

• Evaluate Vcs from Charm Decays

24
HQET

• Heavy Quark Effective THEORY (HQET) (N. Isgur
  M. Wise)
• QCD is flavor independent, so in the limit of
  heavy quarks infinitely qa?qb occurs with unit
  form-factor when the quarks are moving with the
  same invariant 4-velocity, w1.
• Corrections to the M? quark limit are in
  principle calculable along with QCD corrections

25
Vcb Determinations

• HQET is applicable to B?D?n
• Use B?Dl n because the decay rate is largest
• In general 3 form-factors but they are related in
  HQET.
• We are left with only one form-factor whose shape
  is NOT predicted
• To find Vcb measure value at w1, here D is at
  rest in B rest frame
• F(1)1 in lowest order

26
Vcb Using B?D?n

• To be precise

27
Heavy Quark Effective Theory

• HQET tells us that in first order when a b quark
  transforms to a c quark with the c going at the
  same velocity as the b, the form factor is 1 in
  first order AND the corrections to 1 can be
  calculated
• The form-factor therefore known to be
  1-correction, at maximum q2, called w1, where

28
CLEO Measurement
29
CLEO Results for F(1)Vcb

• Fit to function shape given by Caprini et al.
• Yields value of F(1)Vcb shape, parameterized
  by r2.
• F(1)Vcb
• (42.2?1.3?1.8)?10-3
• r21.610.09

30
LEP Results

• CLEO result gt LEP results
• Correlation between Vcb r

31
Belle Results

• F(1)Vcb(36.2?1.5?1.8)?10-3

32
Theoretical calculations of F(1)

• F(1)hQEDhQCD(1d1/m2)
• Lukes theorem no d1/m corrections (would be in
  Dln)
• d1/m2 involves 1/mb2, 1/mc2, 1/mcmb. 0.550.035
• hQED1.007, hQCD0.9600.007 at two loops
• F(1)0.9130.042 (BABAR book)
• Bigi, F(1)0.88 0.05
• PDG (Artuso Barberio) F(1)0.910.05
• First Lattice Gauge calculations
  (quenched-no light quark loops)
  ultimate solution

33
What is Vcb from B?D?n ?

• Should use the same value for F(1)
• Using PDG value of F(1)0.910.05
• CLEO Vcb(46.42.32.5)x10-3
• LEP Vcb(39.11.92.1)x10-3
• Belle Vcb(39.82.62.1)x10-3
• Note, CLEO fits lower value of DX?n, then LEP
  uses from Model of Leibovich, et al. PRD 57, 308
  (1997)
• Average Vcb(42.11.1exp1.9thy)x10-3

34
Vcb From Inclusive b?cl?

• Vcb 2 h(?, mb) ? ?(b?cl?)
• h(?, mb) ? B(b?cl?)/?b
• h(?, mb) from Heavy Quark Expansion
• Perturbative non-perturbative pieces
• Quark-hadron duality assumed integrated over
  enough exclusive charm bound states enough
  phase space, the inclusive hadronic result will
  match quark-level
• But what is the uncertainty associated with the
  duality assumption?

35
Formula
b0 is the one loop QCD function 25/3
36
Parameters of the HQE

• The heavy quark expansion of the B-meson (B?X l
  n) decay rate is described to the order
  (LQCD/mb)2 by three parameters
• l1 (1/2?MB) ltB(v) hv (iD)2 hv B(v)gt is the
  kinetic energy of the residual motion of the
  b-quark.
• l2 (-1/2?MB) ltB(v) hv (g/2)?smn Gmn hv B(v)gt
  the Chromo-magnetic coupling of the b-quark spin
  to the gluon field. Is determined from (MB-MB)
  mass splitting, namely it has been estimated to
  be 0.12 GeV2
• Decay rate also depends on quark-masses via,
• MBmbL-(l13?l2)/(2?mb) MBmbL-(l1-
  l2)/(2?mb)

37
Non-Perturbative parameters

• r1, r2, t1-t4 are small, L3 that enter in order
  1/MB3
• They are in general unknown, but there are
  constraints on them
• Can determine l1 and L, and thus Vcb by measuring
  moments in semileptonic decays
• Hadronic mass moments
• Semileptonic moments
• Can also use b?sg decays

38
B? Xc ln Hadronic Mass Moments

• Lepton (pgt1.5 GeV)
• ?-reconstruction p?
• Calculate recoil mass
• Fit spectrum w/B? Dln, B? Dln, B ? XHln
  (various models for XH)
• ?MX2 - MD2?, MD is spin-averaged D, D mass
• ?MX2-MD2? 0.287?0.065 GeV2
• 2nd moment 0.63 ?0.17 GeV4

CLEO
DATA Fit Dl? Dl? XHl?
?MX2 - MD2?
B(B? X ln)(10.49?0.17?0.43)
39
Lepton Moments

• Summary of results for different types of moments

40
Vub

• Three approaches
• Endpoint leptons Clear signal seen first this
  way new theory enables predictions
• Make mass cuts on the hadronic system, with a
  plethora of other cuts. Plot the lepton spectrum.
  Problems are the systematic error on the
  experiment and the theory.
• Exclusive B? pln or rln decays. Data are still
  poor as is theory.

41
Vub from lepton endpoint

• B value of Vub depends on model, since fraction
  of leptons in signal region depends on model! Use
  b ?sg spectrum to measure predict shape
• Vub(4.080.340.44
  0.16 0.24)x10-3
• theory errs Vub formula, using sg
• Luke additional error gt0.6x10-3 due to other
  uncertainties

? Y(4S) data b?cln continuum
CLEO
? b?uln
Shape from b ?sg
subleading twist, annihilation
42
Vub Using Inclusive Leptons

• ALEPH DELPHI, OPAL select samples of charm-poor
  semileptonic decays with a large number of
  selection criteria
• Mass lt MD ? b ? u
• Can they understand b ? cln feedthrough lt 1 ?
• Ligeti, Wise etc.. propose using q2 (Artuso 15
  years ago)
• Vub(4.09?0.37?0.44
  ?0.34)x10-3

43
Problem According to Luke
44
Optimized Cuts
(C. Bauer, Z. Ligeti and ML, hep-ph/0107074)
real gluon emission
NO rate at parton level (purely nonperturbative)
perturbative singularity (realvirtual gluons)
45
pln and rln Signals
CLEO

• pln p0ln
• rln r0ln woln

b?u backrounds cross-feeds
b?c backrounds
b?u backrounds cross-feeds
46
Form-factor Results

• In general 3 form-factors for 0- ? 1-
  transitions, but we do not have enough precision
  to disentangle them
• Data shows the need for more data
• CLEO plnrln
• Vub(3.25?0.14 ?0.55)x10-3
• BABAR rln
• Vub(3.69?0.23?0.24 )x10-3

0.21 -0.29
0.40 -0.59
47
Theoretical Status of Exclusive Vub

• Easiest to calculate is B?pln
• Non-perturbative need lattice unquenched
• Need to measure at high
• q2, low pion momenta

48
Why we care about Vcb Vub

• Since A (Vcb) l are known, parametrize
  knowledge in terms of
• h r
• Constraints from e, CP violation in KL decay,
  Vub/Vcb, B mixing
• e is a function of Vcb

1s errors shown

• Dominant errors in each case are theoretical,
  problem
• with theory describing quarks observations
  on hadrons

49
Vub Summary
50
Hadronic Decays

• M. Wise in advice to theorists If you drink the
  nonleptonic tonic your physics career will be
  ruined and you will end up face down and in the
  gutter.
• Why are hadronic decays so difficult to predict?
• Lots of gluons running around perturbation
  theory works where energies are large compared to
  LQCD 500 MeV
• Multibody decays impossible, stick with 2 body
  decays

51
Two-body B decays, old style treatment
hep-ph/970592

• Here we start dealing with two-body charm decays
  (Bauer, Stech Wirbel, Neubert Stech)
• Only one process for Bo but two for B-
• Call processes like Bo
• Class I and B- Class III

Called color suppressed, Amp1/3 of tree, why?
52
Effective Hamiltonian

• What are Class II?
• Process only reached by
• color suppressed diagram
• Effective Hamiltonian consist of local 4 quark
  operators renormalized at scale m and Wilson
  coefficients ci(m)

53
Evaluation of Wilson Coefficients

• Without QCD corrections c1(m)1, c2(m)0
• For NLO correction, using renormalization group
  equations c1(m)1.132, c2(m)-0.249

54
Factorization Amplitude

• For Bo?Dp- (Class I)
• fp
  given by G(p-?m-n)
• a1c1(mf)zc2(mf), z1/Nc, mfO(mb), gives
  factorization scale
• Then
• Fo form-factor can be calculated or measured, in
  principle

55
Class II III processes

• Class II Example B?J/y K
• a2c2(mf)zc1(mf)
• Class III Example B-?Dop-
• Here amplitudes involve a term a1xa2, where x
  1 from flavor symmetry, but we can allow a1, a2
  and x to be determined from the data

56
Determination of a1 a2

• Choose a1 from data, 1.080.04
• Evaluation of a2/a1
• Take a2 as 0.210.01
• Predicted decay rates (Neubert Stech)
• Class I
  Class II

57
First Measurements of Bo?Dopo

• CLEO Belle Results
• CLEO
• B(Bo?Dopo)(2.70.30.5)x10-4
• B(Bo?Dopo)(2.10.50.8)x10-4
• Belle

New BABAR B(Bo?Dopo)(2.90.30.4)x10-4
58
Class III Reactions

• x1 from Dop- data i.e. Class III reactions
  have larger branching ratios than the
  corresponding Class I reactions
• Just the opposite in D decays!
• Class III Class I

59
Isopin in B?Dp

• The 4-quark operator (du)(cb) is I1, I31
• Transforms Bo into final state with I1/2 or I
  3/2, final states (Dp-) and (Dopo)
• Transforms B- into final state with I3/2 only,
  final state (Dop-)
• The Isospin amplitudes should not be modified by
  final state interactions, so we can look for
  evidence of final state phase shifts by doing an
  isospin analysis

60
Isopin relations in B?Dp

• The decay amplitudes are related to the isospin
  amplitudes by
• Solving

Ao-
?2Aoo
A-
61
Results for Isospin Analysis

• 
  charged/neutral B ratio
• 2.3 s from 1.0 ? d is 30.3 degrees, an
  unexpectedly large phase shift, perhaps different
  from 0.
• Large phase shifts are good for measuring CP
  Violation via these modes. See Xing hep-ph/9507310

62
Factorization

• The amplitude of B (or D) hadronic decays can be
  expressed as the product of two independent
  hadronic currents

63
B? Dpp-p-po

• Understanding hadronic B decays is crucial to
  insuring that decay modes used for measurement of
  CP violation truly reflect the underlying quark
  decay mechanisms expected theoretically
• Yet only 12 of the B decay rate into hadrons
  has been measured. This includes J/y K(),
  D()Ds() and D()(np)-, 3? n ?1
• Here p-, r- and a1- dominate (quasi-two-body)
• Since the averaged charged multiplicity in
  hadronic B decays is 5.80.1, where 2.90.1 comes
  from the D(), we expect a large decay rate for 3
  charged and 1 neutral pion (4p)-

64
The Dpp-p-po Final State

• (a) DE sidebands
• 3.0 5.0 s
• (b) DE around 0 2.0s fit with sideband shape
  fixed norm allowed to float
• Also signals in Do?K-? ?o and Do?K-? ? ?- (not
  shown)
• Fit B yield in bins of M(4p)

Do?K-?
358?29
65
The pp- po Mass Distribution

• What are the decay mechanisms for the (4p)- final
  state?
• We examine the pp-po mass spectrum (2
  combinations/event). All 3 Do decay modes summed

Enlarged Dalitz plot exterior removed
66
The wp- Mass Distribution
Fit MB distribution in wp mass bins
only Do?K-?
All 3 Do decays used

• Possible resonance (A) at M1419?33 MeV,
  ?382?44 MeV

67
D(wp)- Angular Distributions

• For a spin-0 A the D w would be fully
  polarized
• Spin 0 ? c2/dof 3.5 (cosqD), 22 (cosqw) ?
  Ruled out
• Best fit ? GL/G 0.63?0.09 (D), 0.10?0.09
  (w)

Spin-0 expectation
68
The Dwp- Final State
only D?K?- ?-
only Do?K-?

• Signal DElt2s (18MeV) Sideband 3sltDElt7s
• No signal in w sidebands

69
The wp- Mass Distribution
Fit MB distribution in wp mass bins
Breit-Wigner Mass 1415?43 ?419?110 MeV

• Combined D?wp- and Dwp- modes (179 events)
• Consistent with Dwp result
• Select (1.1-1.7 GeV) for angular study (104
  events)

70
The Angular Distributions inB ? D A- A- ?
w p- , w ? p?p p-
? between normal of w decay plane w boost
? between A w decay planes
? between w in A frame A boost direction

• Small efficiency corrections applied
• For 1 and 2-, the longitudinal ratio (GL/G)
  floats

• 1- preferred, c2/dof (1-) 1.7, (2) 3.2

71
Identifying the A- with the r?

• Clegg Donnachie (t?(4p)n, ee-?pp-,
  ppp-p-) find two 1- states with (M, G)
  (1463?25, 311?62) MeV (1730?30, 400?100) MeV,
  mixed with non-qq states, only the lighter one
  decays to wp
• Godfrey Isgur Predict first radial excited
  r at 1450 MeV, G320 MeV, B (????wp?)39

Recall, we measure mass 1418?26?19 MeV,
(Preliminary) G 388?41?32 MeV
72
Evidence for r? from t Decay
t-?pop-n

• t-?wp-n

CLEO
CLEO
r
r
w signal
w sidebands
Difficult to ascertain the Mass and Width
73
Mass Width Values of r?
74
Summary Discussion of Rates

• r? dominates the wp? final state
• G(B??D?????) / G(B??D????) 1.04?0.21?0.06
• G(B??D?????) / G(B??D????)
  1.10?0.31?0.06
• G(B?D????) / G(B?D???)
  1.06?0.17?0.04
• Consistent with Heavy Quark Symmetry prediction (
  ratio 1 )
• With B (????wp?)39, G(B?D()???) G(B?D()??)

75
Factorization Tests Using Polarization

• GL/G (B?D?h?) GL/G (B?D?l?n )q2mh2
• Also use new Bo?D?Ds-, old D?r- CLEO data

?


(Determined using partial reconstruction)

76
More modern approaches to factorization

• For B?D()X. See Beneke et al. Nucl. Phys B591
  (2000) 313 Bauer et al., hep-ph/0107002
• More fundamental, also used for B?M1M2, where Mi
  are both light. See Beneke et al. hep-ph/0104110
  Keum et al., PRD 63 (2001) 074006 ibid PRD 63
  (2001) 054008
• Seems to be a problem in that (Wise)
• G(B-?Dop-)/G(Bo?Dp-)1O(LQCD/mb)