1. B Physics Beyond CP Violation — Semileptonic B Decays —
Masahiro Morii
Harvard University
Columbia University Nuclear/Particle & Astroparticle Physics Seminar
29 March 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
29 March 2006
M. Morii, Harvard

3. Mass and the Generations
Particle mass (eV/c2)
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 =  /3 1/3
29 March 2006
M. Morii, Harvard

4. M and N are arbitrary 33 unitary matrices
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
That’s a poor choice of basis vectors
M and N are arbitrary 33 unitary matrices
Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V
29 March 2006
M. Morii, Harvard

5. Cabibbo-Kobayashi-Maskawa matrix
Turn the masses back on
Masses uniquely define the u, c, t, and d, s, b states
We don’t know what creates masses  We don’t 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
Cabibbo-Kobayashi-Maskawa matrix
or CKM for short
29 March 2006
M. Morii, Harvard

6. Structure of the CKM matrix
The CKM matrix looks like this 
It’s not completely diagonal
Off-diagonal components are small
Transition across generations is allowed but suppressed
The “hierarchy” can be best expressed in the Wolfenstein parameterization:
One irreducible complex phase  CP violation
The only source of CP violation in the minimal Standard Model
“this smallest one is Vub” Expand V in 3x3?
Vub
29 March 2006
M. Morii, Harvard

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 < 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
29 March 2006
M. Morii, Harvard

8. 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
29 March 2006
M. Morii, Harvard

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 true as of summer 2004
Still large enough for New Physics to hide
Precision of sin2b outstripped the other measurements
Must improve the others to make more stringent test
29 March 2006
M. Morii, Harvard

10. Next Step: |Vub| Goal: Accurate determination of both |Vub| and sin2b
Zoom in to see the overlap of “the other” contours
It’s obvious: we must make the green ring thinner
Left side of the Triangle is
Uncertainty dominated by 15% on |Vub|
Measurement of |Vub| is complementary to sin2b
Measurement of |Vub| is “complementary” to sin2beta, in the sense that measuring both of them precisely will teach us something each individual measurement will never do.
Goal: Accurate determination of both |Vub| and sin2b
29 March 2006
M. Morii, Harvard

11. decoupled from hadronic effects
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
29 March 2006
M. Morii, Harvard

12. Form Factor (3 FFs for vector mesons)
Detecting b → un
Inclusive: Use mu << mc  difference in kinematics
Maximum lepton energy 2.64 vs 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?
2.31
2.64
point the endpoint for 2.31 and 2.64.
Form Factor (3 FFs for vector mesons)
29 March 2006
M. Morii, Harvard

13. u quark turns into 1 or more hardons
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!
29 March 2006
M. Morii, Harvard

14. Lepton Endpoint Select electrons in 2.0 < E < 2.6 GeV
BABAR PRD 73: Belle PLB 621:28 CLEO 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 background is crucial!
Measure the partial BF
BABAR
Data
MC bkgd. b  cv
Data – bkgd.
E (GeV)
DB (10-4)
BABAR 80fb-1
2.0–2.6
5.72 ± 0.41stat ± 0.65sys
Belle 27fb-1
1.9–2.6
8.47 ± 0.37stat ± 1.53sys
CLEO 9fb-1
2.2–2.6
2.30 ± 0.15stat ± 0.35sys
MC signal b  uv
cf. Total BF is ~2103
29 March 2006
M. Morii, Harvard

15. E vs. q2 Use pv = pmiss in addition to pe  Calculate q2
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)
BABAR
DB (10-4)
BABAR 80fb-1
3.54 ± 0.33stat ± 0.34sys
Small systematic errors
29 March 2006
M. Morii, Harvard

16. Fully reconstructed B  hadrons
BABAR hep-ex/ Belle PRL 95:241801
Measuring mX and q2
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 reconstructed B  hadrons v
lepton X
29 March 2006
M. Morii, Harvard

17. For example: mX < 1.7 GeV and q2 > 8 GeV2
BABAR hep-ex/ Belle PRL 95:241801
Measuring Partial BF
Measure the partial BF in regions of (mX, q2)
For example: mX < 1.7 GeV and q2 > 8 GeV2
Phase Space
DB (10-4)
BABAR 211fb-1
mX < 1.7, q2 > 8
8.7 ± 0.9stat ± 0.9sys
Belle 253fb-1
mX < 1.7
12.4 ± 1.1stat ± 1.0sys
8.4 ± 0.8stat ± 1.0sys
P+ < 0.66
11.0 ± 1.0stat ± 1.6sys
Large DB thanks to the high efficiency of the mX cut
29 March 2006
M. Morii, Harvard

18. Theoretical Issues Tree level rate must be corrected for QCD
Operator Product Expansion gives us 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
Tree-level rate was calculated at the quark level, but what we observe is the hardrons.
known to O(as2)
Suppressed by 1/mb2
29 March 2006
M. Morii, Harvard

19. We must determine the Shape Function from experimental data
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
Cannot be calculated by theory
Leading term is O(1/mb) instead of O(1/mb2)
We must determine the Shape Function from experimental data
29 March 2006
M. Morii, Harvard

20. BABAR PRD 72:052004, hep-ex/0507001 Belle hep-ex/0407052 CLEO hep-ex/0402009
b → sg Decays
Measure: Same SF affects (to the first order) b → sg decays
Measure Eg spectrum in b → sg
Predict partial BFs in b → uv
Extract f(k+) K*
Inclusive
Sum of exclusive
BABAR
Partial BF/bin (10-3)
Inclusive g measurement. Photon energy in the Y(4S) rest frame
Exclusive Xs + g measurement. Photon energy determined from the Xs mass
29 March 2006
M. Morii, Harvard

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v spectrum calculations
Bosch, Lange, Neubert, Paz, NPB 699:335
Lange, Neubert, Paz, PRD 72:073006
Ready to extract |Vub|
Buchmüller & Flächer hep-ph/
Lepton-energy spectrum by BLNP
29 March 2006
M. Morii, Harvard

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/
Last Belle result(*) used a simulated annealing technique
Phase Space
|Vub| (10-3)
Reference
BABAR 80fb-1
E > 2.0
4.41 ± 0.29exp ± 0.31SF,theo
PRD 73:012006
Belle 27fb-1
E > 1.9
4.82 ± 0.45exp ± 0.30SF,theo
PLB 621:28
CLEO 9fb-1
E > 2.2
4.09 ± 0.48exp ± 0.36SF,theo
PRL 88:231803
E > 2.0, shmax < 3.5
4.10 ± 0.27exp ± 0.36SF,theo
PRL 95:111801
BABAR 211fb-1
mX < 1.7, q2 > 8
4.75 ± 0.35exp ± 0.32SF,theo
hep-ex/
Belle 253fb-1
mX < 1.7
4.06 ± 0.27exp ± 0.24SF,theo
PRL 95:241801
Belle 87fb-1*
4.37 ± 0.46exp ± 0.29SF,theo
PRL 92:101801
29 March 2006
M. Morii, Harvard

23. |Vub| world average, Winter 2006
Inclusive |Vub| as of 2005
|Vub| world average, Winter 2006
|Vub| determined to 7.4%
The SF parameters can be improved with b → sg, b  cv measurements
What’s the theory error?
Statistical
2.2%
Expt. syst.
2.7%
b  cv model
1.9%
b  uv model
2.1%
SF params.
4.1%
Theory
4.2%
29 March 2006
M. Morii, Harvard

24. Theory Errors Subleading Shape Function  3.8% 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) or G(D0  Xv)/G(Ds  Xv) to improve the constraint
Also: study q2 spectrum near endpoint (CLEO hep-ex/ )
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%
29 March 2006
M. Morii, Harvard

25. Avoiding the Shape Function
Possible to combine b  uv and b → sg so that the SF cancels
Leibovich, Low, Rothstein, PLB 486:86
Lange, Neubert, Paz, JHEP 0510:084, Lange, JHEP 0601:104
No need to assume functional forms for the Shape Function
Need b → sg spectrum in the B rest frame
Only one measurement (BABAR PRD 72:052004) available
Cannot take advantage of precise b  cv data
How well does this work? Only one way to find out…
Weight function
29 March 2006
M. Morii, Harvard

26. SF-Free |Vub| Measurement
BABAR hep-ex/
SF-Free |Vub| Measurement
BABAR applied LLR (PLB 486:86) to 80 fb-1 data
G(B  Xuv) with varying mX cut
dG(B  Xsg)/dEg from PRD 72:052004
With mX < 1.67 GeV
SF error  Statistical error
Also measured mX < 2.5 GeV
Almost (96%) fully inclusive  No SF necessary
Attractive new approaches with increasing statistics
mX cut (GeV)
1.67
Theory error
Expt. error
stat.
syst.
theory
Theory error ±2.6%
29 March 2006
M. Morii, Harvard

27. One FF for B → pv with massless lepton
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
One FF for B → pv with massless lepton
explain what is FF.
29 March 2006
M. Morii, Harvard

28. Form Factor Calculations
Unquenched LQCD calculations started to appear in 2004
Fermilab (hep-lat/ ) and HPQCD (hep-lat/ )
Uncertainties are ~11%
f+(q2) and f0(q2)
LCSR* Fermilab HPQCD ISGW2
q2 (GeV2)
Measure dG(B → pv)/dq2 as a function of q2
Compare with different calculations
*Ball-Zwicky PRD71:014015
29 March 2006
M. Morii, Harvard

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 
Tagged by B  D(*)v
Tagged by B  hadrons
B(B0 → p+v) [10-4]
29 March 2006
M. Morii, Harvard

30. Untagged B → pn Missing 4-momentum = neutrino
BABAR PRD 72: CLEO PRD 68:072003
Untagged B → pn
Missing 4-momentum = neutrino
Reconstruct B → pv and calculate mB and DE = EB – Ebeam/2
BABAR
data
MC signal
signal with wrong p
b  uv
BABAR
b  cv
other bkg.
29 March 2006
M. Morii, Harvard

31. BABAR hep-ex/0506064, 0506065 Belle hep-ex/0508018
D(*)n-tagged B → pn
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 are efficient but less pure
Two neutrinos in the event
Event kinematics determined assuming known mB and mv  v p D
soft p
cos2fB 1 for signal
data
MC signal
MC background
29 March 2006
M. Morii, Harvard

32. Hadronic-tagged B → pn
BABAR hep-ex/
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 to extract the signal yield
soft p p D 
p or K v
data
MC signal
b  uv
b  cv
other bkg.
29 March 2006
M. Morii, Harvard

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]
< 16 GeV2
0.89 ± 0.06 ± 0.06
> 16 GeV2
0.40 ± 0.04 ± 0.04
Errors on |Vub| dominated by the FF normalization
29 March 2006
M. Morii, Harvard

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 71:034506
Arnesen, Grinstein, Rothstein, Stewart PRL 95:071802
Ball, Zwicky, PLB 625:225
Becher, Hill, PLB 633:61-69
29 March 2006
M. Morii, Harvard

35. How Things Mesh Together
b → sg
Shape Function Eg mb
Inclusive b → cv mX E
HQE Fit
SSFs
Inclusive b → uv E
Exclusive b → uv
|Vub| q2
B → pv FF
LCSR
LQCD mX
wv, hv ?
duality WA
unquenching
29 March 2006
M. Morii, Harvard

36. The UT 2004  2005 Dramatic improvement in |Vub|!
sin2b went down slightly  Overlap with |Vub/Vcb| smaller
29 March 2006
M. Morii, Harvard

37. Summary
Precise determination of |Vub| complements sin2b to test the (in)completeness of the Standard Model
7.4% 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
|Vub|
29 March 2006
M. Morii, Harvard

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 612:13)
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%
We’ve got the Shape Function
Buchmüller & Flächer hep-ph/
29 March 2006
M. Morii, Harvard

39. Predicting b → un Spectra
Soft Collinear Effective Theory is used to predict the triple-differential rate:
Developed since 2001 by Bauer, Fleming, Luke, Pirjol, Stewart
A triple-diff. rate calculation available since Spring 2005
Bosch, Lange, Neubert, Paz, NPB 699:335
Lange, Neubert, Paz, hep-ph/
We use BLNP to extract |Vub|
New calculations are appearing
Aglietti, Ricciardi, Ferrera, hep-ph/ , ,
Andersen, Gardi, hep-ph/
Numerical comparison with BLNP will be done soon
Lepton-energy spectrum by BLNP
29 March 2006
M. Morii, Harvard

40. |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)
Careful evaluation of theory errors
Consistency between different calculations
Exclusive
Inclusive
what to say about new calculations.
29 March 2006
M. Morii, Harvard

41. SF-free |Vub| errors
29 March 2006
M. Morii, Harvard