B Physics Beyond CP Violation — Semileptonic B Decays — Masahiro Morii Harvard University Osaka University High-Energy Physics Seminar 25 November 2005

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 |V ub | from exclusive b → u v decays Measurements:  (B →  v) Theoretical challenge: Form Factors Summary

25 November 2005M. 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

25 November 2005M. 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

25 November 2005M. 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

25 November 2005M. 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

25 November 2005M. 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?

25 November 2005M. 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

25 November 2005M. 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

25 November 2005M. 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 

25 November 2005M. 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

25 November 2005M. 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)

25 November 2005M. 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!

25 November 2005M. 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 hep-ex/ 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

25 November 2005M. 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

25 November 2005M. Morii, Harvard16 Measuring m X and q 2 Must reconstruct all decay products to measure m X or q 2 E was much easier Select events with a fully-reconstructed B meson Use ~1000 hadronic decay chains Rest of the event contains one “recoil” B Flavor and momentum known Find a lepton in the recoil-B Lepton charge consistent with the B flavor m miss consistent with a neutrino All left-over particles belong to X Use a kinematic fit   (m X ) = 350 MeV 4-momentum conservation; equal m B on both sides; m miss = 0 Fully reconstructed B  hadrons lepton v X BABAR hep-ex/ Belle hep-ex/

25 November 2005M. Morii, Harvard17 Measuring Partial BF Suppress b → c v by vetoing against D (*) decays Reject events with K Reject events with B 0 → D *+ (→ D 0  + ) − v Measure the partial BF in regions of (m X, q 2 ) For example: m X 8 GeV 2 BABAR hep-ex/ Belle hep-ex/

25 November 2005M. Morii, Harvard18 Partial BF Results P + = E X  |P X | is a theoretically clean variable Bosch, Lange, Neubert, Paz PRL 93: Efficiency high Signal vs. background separation is limited BABAR hep-ex/ Belle hep-ex/ 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 Belle

25 November 2005M. Morii, Harvard19 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

25 November 2005M. Morii, Harvard20 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 leading term is  (1/m b ) instead of  (1/m b 2 ) Rough features (mean, r.m.s.) are known Details, especially the tail, are unknown

25 November 2005M. Morii, Harvard21 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 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*

25 November 2005M. Morii, Harvard22 Extracting the Shape Function We can fit the b → s  spectrum with theory prediction Must assume a functional form of f(k + ) Example: New calculation connect the SF moments with the b-quark mass m b and kinetic energy   2 (Neubert, PLB 612:13) Determined precisely from b → s  and b  c v decays from b → s  and from b  c v Fit data from B A B AR, Belle, CLEO, DELPHI, CDF NB: m b is determined to better than 1%  Determine the SF Buchmüller & Flächer hep-ph/

25 November 2005M. Morii, Harvard23 Predicting b → u Spectra OPE + SF can predict triple-differential rate Unreliable where OPE converges poorly... that is where the signal is Soft Collinear Effective Theory offers the right tool Developed since 2001 by Bauer, Fleming, Luke, Pirjol, Stewart Applied to b → u v by several groups A triple-diff. rate calculation available since Spring 2005 Bosch, Lange, Neubert, Paz, NPB 699:335 Lange, Neubert, Paz, hep-ph/ B A B AR and Belle use BLNP to extract |V ub | in the latest results Lepton-energy spectrum by BLNP

25 November 2005M. Morii, Harvard24 Next in Theory of Inclusive |V ub | New calculations of partial BFs are appearing Aglietti, Ricciardi, Ferrera, hep-ph/ , , Andersen, Gardi, hep-ph/ Numerical comparison with BLNP will be done soon Combine b  u v and b → s  without going through the SF Leibovich, Low, Rothstein, PLB 486:86 Lange, Neubert, Paz, hep-ph/ Lange, hep-ph/ No need to assume functional forms for the Shape Function Weight function

25 November 2005M. Morii, Harvard25 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 > ± 0.25 exp ± 0.32 SF,theo hep-ex/ Belle 27fb -1 E > ± 0.45 exp ± 0.31 SF,theo PLB 621:28 CLEO 9fb -1 E > ± 0.47 exp ± 0.35 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 ± 0.34 exp ± 0.32 SF,theo hep-ex/ Belle 253fb -1 m X < ± 0.27 exp ± 0.25 SF,theo hep-ex/ Belle 87fb -1 * m X ± 0.46 exp ± 0.30 SF,theo PRL 92:101801

25 November 2005M. Morii, Harvard26 Status of Inclusive |V ub | |V ub | determined to  7.6% The SF parameters can be improved with b → s  b  c v measurements What’s the theory error? |V ub | world average as of Summer 2005 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%

25 November 2005M. Morii, Harvard27 Theory Errors Quark-hadron duality is not considered b  c v and b → s  data fit well with the HQE predictions Weak annihilation   1.9% error Expected to be <2% of the total rate Measure  (B 0  X u v)/  (B +  X u v) to improve the constraint Reduce the effect by rejecting the high-q 2 region Subleading Shape Function   3.5% error Higher order non-perturbative corrections Cannot be constrained with b → s  Ultimate error on inclusive |V ub | may be ~5%

25 November 2005M. Morii, Harvard28 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

25 November 2005M. Morii, Harvard29 Form Factor Calculations Unquenched LQCD calculations started to appear in 2004 Preliminary B →  v FF from Fermilab (hep-lat/ ) and HPQCD (hep-lat/ ) Uncertainties are ~11% Validity of the technique remains controversial Important to measure d  (B →  v)/dq 2 as a function of q 2  Compare with different calculations 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

25 November 2005M. Morii, Harvard30 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

25 November 2005M. Morii, Harvard31 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 hep-ex/ CLEO PRD 68:072003

25 November 2005M. Morii, Harvard32 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/

25 November 2005M. Morii, Harvard33 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/

25 November 2005M. Morii, Harvard34 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

25 November 2005M. Morii, Harvard35 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, hep-ph/

25 November 2005M. Morii, Harvard36 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

25 November 2005M. Morii, Harvard37 The UT 2004  2005 Dramatic improvement in |V ub |! sin2  went down slightly  Overlap with |V ub /V cb | smaller

25 November 2005M. Morii, Harvard38 |V ub | vs. the Unitarity Triangle Fitting everything except for |V ub |, CKMfitter Group finds Inclusive average is 2.0  off UTfit Group finds 2.8  Not a serious conflict (yet) Careful evaluation of theory errors Consistency between different calculations Inclusive Exclusive

25 November 2005M. Morii, Harvard39 Summary Precise determination of |V ub | complements sin2  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 |V ub | in the last 2 years Improvement in B →   form factor is needed |V ub |