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

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

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 = 1 0 +2/3 1/3 29 March 2006 M. Morii, Harvard

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

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

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

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

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

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

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

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

Form Factor (3 FFs for vector mesons) 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? 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

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

Lepton Endpoint Select electrons in 2.0 < E < 2.6 GeV BABAR PRD 73:012006 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

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

Fully reconstructed B  hadrons BABAR hep-ex/0507017 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

For example: mX < 1.7 GeV and q2 > 8 GeV2 BABAR hep-ex/0507017 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

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

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

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

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/0507253 Lepton-energy spectrum by BLNP 29 March 2006 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 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/0507017 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

|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

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/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% 29 March 2006 M. Morii, Harvard

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

SF-Free |Vub| Measurement BABAR hep-ex/0601046 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

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

Form Factor Calculations Unquenched LQCD calculations started to appear in 2004 Fermilab (hep-lat/0409116) and HPQCD (hep-lat/0601021) 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

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

Untagged B → pn Missing 4-momentum = neutrino BABAR PRD 72:051102 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

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

Hadronic-tagged B → pn BABAR hep-ex/0507085 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

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

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

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

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

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

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/0507253 29 March 2006 M. Morii, Harvard

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/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-energy spectrum by BLNP 29 March 2006 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) Careful evaluation of theory errors Consistency between different calculations Exclusive Inclusive what to say about new calculations. 29 March 2006 M. Morii, Harvard

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