B Physics Beyond CP Violation — Semileptonic B Decays — Masahiro Morii Harvard University University of Illinois Urbana-Champaign HETEP Seminar 3 April 2006

M. Morii, Harvard2 Outline Introduction: Why semileptonic B decays? CKM matrix — Unitarity Triangle — CP violation |V ub | vs. sin2  |V ub | from inclusive b → u v decays Measurements: lepton energy, hadron mass, lepton-neutrino mass Theoretical challenge: Shape Function Latest from B A B AR – Avoiding the Shape Function |V ub | from exclusive b → u v decays Measurements:  (B →  v) Theoretical challenge: Form Factors Summary

3 April 2006M. Morii, Harvard3 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 Particle mass (eV/c 2 ) Q =  /3  1/3 The origin of mass is one of the most urgent questions in particle physics today

3 April 2006M. Morii, Harvard4 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

3 April 2006M. Morii, Harvard5 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

3 April 2006M. Morii, Harvard6 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 V ub

3 April 2006M. Morii, Harvard7 CP violation and New Physics 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/c 2 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 Are there additional (non-CKM) sources of CP violation?

3 April 2006M. Morii, Harvard8 The Unitarity Triangle V † V = 1 gives us Measurements of angles and sides constrain the apex ( ,  ) This one has the 3 terms in the same order of magnitude A triangle on the complex plane

3 April 2006M. Morii, Harvard9 Consistency Test Compare the measurements (contours) on the ( ,  ) 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 sin2  outstripped the other measurements Must improve the others to make more stringent test

3 April 2006M. Morii, Harvard10 Next Step: |V ub | 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 |V ub | Measurement of |V ub | is complementary to sin2  Goal: Accurate determination of both |V ub | and sin2 

3 April 2006M. Morii, Harvard11 Measuring |V ub | Best probe: semileptonic b  u decay The problem: b  c v decay How can we suppress 50× larger background? Tree level decoupled from hadronic effects

3 April 2006M. Morii, Harvard12 Detecting b → u Inclusive: Use m u << m c  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   v, B   v, B   v, B   v, … Example: the rate for B   v is How accurately do we know the FFs? Form Factor (3 FFs for vector mesons)

3 April 2006M. Morii, Harvard13 There are 3 independent variables in B → X v Signal events have smaller m X  Larger E and q 2 Inclusive b → u u quark turns into 1 or more hardons q 2 = lepton-neutrino mass squared m X = hadron system mass E = lepton energy Not to scale!

3 April 2006M. Morii, Harvard14 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 E (GeV)   (10 -4 ) B A B AR 80fb – ± 0.41 stat ± 0.65 sys Belle 27fb – ± 0.37 stat ± 1.53 sys CLEO 9fb – ± 0.15 stat ± 0.35 sys BABAR PRD 73: Belle PLB 621:28 CLEO PRL 88: B A B AR MC bkgd. b  c v Data Data – bkgd. MC signal b  u v cf. Total BF is ~2  10  3

3 April 2006M. Morii, Harvard15 E vs. q 2 Use p v = p miss in addition to p e  Calculate q 2 Define s h max = the maximum m X squared Cutting at s h max < m D 2 removes b  c v while keeping most of the signal S/B = 1/2 achieved for E > 2.0 GeV and s h max < 3.5 GeV 2 cf. ~1/15 for the endpoint E > 2.0 GeV Measured partial BF BABAR PRL 95: B A B AR   (10 -4 ) B A B AR 80fb ± 0.33 stat ± 0.34 sys b  c v E (GeV) q 2 (GeV 2 ) b  u v Small systematic errors

3 April 2006M. Morii, Harvard16 Measuring m X and q 2 Must reconstruct all decay products to measure m X or q 2 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 m miss ~ 0 All left-over particles belong to X We can now calculate m X and q 2 Suppress b → c v by vetoing against D (*) decays Reject events with K Reject events with B 0 → D *+ (→ D 0  + ) − v BABAR hep-ex/ Belle PRL 95: Fully reconstructed B  hadrons lepton v X

3 April 2006M. Morii, Harvard17 Measuring Partial BF Measure the partial BF in regions of (m X, q 2 ) BABAR hep-ex/ Belle PRL 95: Phase Space   (10 -4 ) B A B AR 211fb -1 m X ± 0.9 stat ± 0.9 sys Belle 253fb -1 m X < ± 1.1 stat ± 1.0 sys m X ± 0.8 stat ± 1.0 sys P + < ± 1.0 stat ± 1.6 sys Large   thanks to the high efficiency of the m X cut For example: m X 8 GeV 2

3 April 2006M. Morii, Harvard18 Theoretical Issues Tree level rate must be corrected for QCD Operator Product Expansion gives us the inclusive rate Expansion in  s (m b ) (perturbative) and 1/m b (non-perturbative) Main uncertainty (  5%) from m b 5   2.5% on |V ub | But we need the accessible fraction (e.g., E ℓ > 2 GeV) of the rate known to  (  s 2 ) Suppressed by 1/m b 2

3 April 2006M. Morii, Harvard19 Shape Function 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  (1/m b ) instead of  (1/m b 2 ) We must determine the Shape Function from experimental data

3 April 2006M. Morii, Harvard20 b → s  Decays Measure: Same SF affects (to the first order) b → s  decays Measure E  spectrum in b → s  Extract f(k + ) Predict partial BFs in b → u v BABAR PRD 72:052004, hep-ex/ Belle hep-ex/ CLEO hep-ex/ Inclusive Sum of exclusive B A B AR Partial BF/bin (10 -3 ) Inclusive  measurement. Photon energy in the Y(4S) rest frame Exclusive X s +  measurement. Photon energy determined from the X s mass K*K*

3 April 2006M. Morii, Harvard21 Predicting b → u Spectra Fit the b → s  spectrum to extract the SF Must assume functional forms, e.g. Additional information from b  c v decays E and m X moments  b-quark mass and kinetic energy NB: m b 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: Ready to extract |V ub | Buchmüller & Flächer hep-ph/ Lepton-energy spectrum by BLNP

3 April 2006M. Morii, Harvard22 Turning   into |V ub | Using BLNP + the SF parameters from b → s  b  c v Adjusted to m b = (4.60  0.04) GeV,   2 = (0.20  0.04) GeV 2 Theory errors from Lange, Neubert, Paz, hep-ph/ Last Belle result ( * ) used a simulated annealing technique Phase Space|V ub | (10 -3 )Reference B A B AR 80fb -1 E > ± 0.29 exp ± 0.31 SF,theo PRD 73: Belle 27fb -1 E > ± 0.45 exp ± 0.30 SF,theo PLB 621:28 CLEO 9fb -1 E > ± 0.48 exp ± 0.36 SF,theo PRL 88: B A B AR 80fb -1 E > 2.0, s h max < ± 0.27 exp ± 0.36 SF,theo PRL 95: B A B AR 211fb -1 m X ± 0.35 exp ± 0.32 SF,theo hep-ex/ Belle 253fb -1 m X < ± 0.27 exp ± 0.24 SF,theo PRL 95: Belle 87fb -1 * m X ± 0.46 exp ± 0.29 SF,theo PRL 92:101801

3 April 2006M. Morii, Harvard23 Inclusive |V ub | as of 2005 |V ub | determined to  7.4% The SF parameters can be improved with b → s  b  c v measurements What’s the theory error? |V ub | world average, Winter 2006 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%

3 April 2006M. Morii, Harvard24 Theory Errors Subleading Shape Function   3.8% error Higher order non-perturbative corrections Cannot be constrained with b → s  Weak annihilation   1.9% error Measure  (B 0  X u v)/  (B +  X u v) or  (D 0  X v)/  (D s  X v) to improve the constraint Also: study q 2 spectrum near endpoint (CLEO hep-ex/ ) Reduce the effect by rejecting the high-q 2 region Quark-hadron duality is believed to be negligible b  c v and b → s  data fit well with the HQE predictions Ultimate error on inclusive |V ub | may be ~5%

3 April 2006M. Morii, Harvard25 Avoiding the Shape Function Possible to combine b  u v and b → s  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 → s  spectrum in the B rest frame Only one measurement (B A B AR 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

3 April 2006M. Morii, Harvard26 SF-Free |V ub | Measurement B A B AR applied LLR (PLB 486:86) to 80 fb -1 data  (B  X u v) with varying m X cut d  (B  X s  )/dE  from PRD 72: With m X < 1.67 GeV SF error  Statistical error Also measured m X < 2.5 GeV Almost (96%) fully inclusive  No SF necessary Attractive new approaches with increasing statistics m X cut (GeV) 1.67 stat.syst.theory Theory error ±2.6% BABAR hep-ex/ Theory error Expt. error

3 April 2006M. Morii, Harvard27 Exclusive B →  Measure specific final states, e.g., B →  v Can achieve good signal-to-background ratio Branching fractions in  (10 -4 )  Statistics limited Need Form Factors to extract |V ub | f + (q 2 ) has been calculated using Lattice QCD (q 2 > 15 GeV 2 ) Existing calculations are “quenched”  ~15% uncertainty Light Cone Sum Rules (q 2 < 14 GeV 2 ) Assumes local quark-hadron duality  ~10% uncertainty... and other approaches One FF for B →  v with massless lepton

3 April 2006M. Morii, Harvard28 Form Factor Calculations Unquenched LQCD calculations started to appear in 2004 Fermilab (hep-lat/ ) and HPQCD (hep-lat/ ) Uncertainties are ~11% f + (q 2 ) and f 0 (q 2 ) q 2 (GeV 2 ) Measure d  (B →  v)/dq 2 as a function of q 2 Compare with different calculations LCSR* Fermilab HPQCD ISGW2 *Ball-Zwicky PRD71:014015

3 April 2006M. Morii, Harvard29 Measuring B →  Measurements differ in what you do with the “ other ” B Total BF is  8.4% precision  (B 0 →    v) [10 -4 ] TechniqueEfficiencyPurity UntaggedHigh  Low  High Tagged by B  D (*) v Tagged by B  hadrons

3 April 2006M. Morii, Harvard30 Untagged B →  Missing 4-momentum = neutrino Reconstruct B →  v and calculate m B and  E = E B – E beam /2 BABAR data MC signal signal with wrong  b  u v b  c v other bkg. BABAR PRD 72: CLEO PRD 68:072003

3 April 2006M. Morii, Harvard31 D (*) -tagged B →  Reconstruct one B and look for B   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 m B and m v vv  D soft  cos 2  B  1 for signal data MC signal MC background BABAR hep-ex/ , Belle hep-ex/

3 April 2006M. Morii, Harvard32 Hadronic-tagged B →  Hadronic tags have high purity, but low efficiency Event kinematics is known by a 2-C fit Use m B and m miss distributions to extract the signal yield  or K v  D soft  data MC signal b  u v b  c v other bkg. BABAR hep-ex/

3 April 2006M. Morii, Harvard33 d  (B →  )/dq 2 Measurements start to constrain the q 2 dependence ISGW2 rejected Partial BF measured to be q 2 range   [10 −4 ] < 16 GeV ± 0.06 ± 0.06 > 16 GeV ± 0.04 ± 0.04 Errors on |V ub | dominated by the FF normalization HFAG 2006 Winter

3 April 2006M. Morii, Harvard34 Future of B →  Form factor normalization dominates the error on |V ub | 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 q 2 spectrum and dispersive bounds may improve the precision Fukunaga, Onogi, PRD 71: Arnesen, Grinstein, Rothstein, Stewart PRL 95: Ball, Zwicky, PLB 625:225 Becher, Hill, PLB 633:61-69

3 April 2006M. Morii, Harvard35 Exclusive b → u v How Things Mesh Together B →  v Inclusive b → u v q2q2  v,  v ? b → s  Shape Function EE mbmb Inclusive b → c v mXmX E HQE Fit mXmX E WA duality |V ub | SSFs FF LCSRLQCD unquenching

3 April 2006M. Morii, Harvard36 The UT 2004  2005 Dramatic improvement in |V ub |! sin2  went down slightly  Overlap with |V ub /V cb | smaller

3 April 2006M. Morii, Harvard37 Summary Precise determination of |V ub | complements sin2  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 |V ub | in the last 2 years Improvement in B →   form factor is needed |V ub |