B Physics Beyond CP Violation

Transcription

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

2 Outline n Introduction: Why semileptonic B decays? n CKM matrix Unitarity Triangle CP violation n V ub vs. sin2b n V ub from inclusive b ulv decays n Measurements: lepton energy, hadron mass, lepton-neutrino mass n Theoretical challenge: Shape Function n Latest from BABAR Avoiding the Shape Function n V ub from exclusive b ulv decays n Measurements: G(B plv) n Theoretical challenge: Form Factors n Summary 3 April 2006 M. Morii, Harvard 2

3 Mass and the Generations Particle mass (ev/c 2 ) e 3 10 Q = /3-1/3 t c u b s d n Fermions come in three generations n They differ only by the masses n The Standard Model has no explanation for the mass spectrum n The masses come from the interaction with the Higgs field n... whose nature is unknown n 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 3 April 2006 M. Morii, Harvard 3

4 If there were no masses n Nothing would distinguish u from c from t n We could make a mixture of the wavefunctions and pretend it represents a physical particle u c t = M u c t n Suppose W ± connects u d, c s, t b n That s a poor choice of basis vectors d s b = N u u d d d c = M c M s = M N s = V s t t b b b 3 April 2006 M. Morii, Harvard 4 d s b M and N are arbitrary 3 3 unitary matrices Weak interactions between u, c, t, and d, s, b are mixed by matrix V

5 Turn the masses back on n Masses uniquely define the u, c, t, and d, s, b states n We don t know what creates masses è We don t know how the eigenstates are chosen è M and N are arbitrary n V is an arbitrary 3 3 unitary matrix u d Vud Vus Vub d c W ± V s = V V V s n The Standard Model does not predict V cd cs cb t b V V V b Cabibbo-Kobayashi-Maskawa matrix td ts tb or CKM for short n... for the same reason it does not predict the particle masses 3 April 2006 M. Morii, Harvard 5

6 Structure of the CKM matrix n The CKM matrix looks like this è n It s not completely diagonal n Off-diagonal components are small n Transition across generations is allowed but suppressed V = n The hierarchy can be best expressed in the Wolfenstein parameterization: V n One irreducible complex phase è CP violation 3 ( i ) = + A (1 i ) A A O ( ) 2 A n The only source of CP violation in the minimal Standard Model 3 April 2006 M. Morii, Harvard 6 1 V ub

7 CP violation and New Physics Are there additional (non-ckm) sources of CP violation? n The CKM mechanism fails to explain the amount of matterantimatter imbalance in the Universe n... by several orders of magnitude n New Physics beyond the SM is expected at 1-10 TeV scale n e.g. to keep the Higgs mass < 1 TeV/c 2 n Almost all theories of New Physics introduce new sources of CP violation (e.g. 43 of them in supersymmetry) New sources of CP violation almost certainly exist n Precision studies of the CKM matrix may uncover them 3 April 2006 M. Morii, Harvard 7

8 The Unitarity Triangle n V V = 1 gives us V V + V V + V V = * * * ud us cd cs td ts V V + V V + V V = * * * ud ub cd cb td tb VV + VV + VV = * * * us ub cs cb ts tb This one has the 3 terms in the same order of magnitude A triangle on the complex plane V V ud ub VcdVcb * VudV 0 ub VV VV n Measurements of angles and sides constrain the apex (r, h) td cd * tb V V * cb td V V cd tb cb 1 = arg = arg = arg VV td V V ud VcdV VV td VudV V V cd * tb * ub * cb * tb * ub * cb 3 April 2006 M. Morii, Harvard 8

9 Consistency Test n Compare the measurements (contours) on the (r, h) plane n If the SM is the whole story, they must all overlap n The tells us this is true as of summer 2004 n Still large enough for New Physics to hide n Precision of sin2b outstripped the other measurements n Must improve the others to make more stringent test 3 April 2006 M. Morii, Harvard 9

10 Next Step: V ub n Zoom in to see the overlap of the other contours n It s obvious: we must make the green ring thinner n Left side of the Triangle is VV VV ud ub cd cb n Uncertainty dominated by ±15% on V ub Measurement of V ub is complementary to sin2b Goal: Accurate determination of both V ub and sin2b 3 April 2006 M. Morii, Harvard 10

11 Measuring V ub n Best probe: semileptonic b u decay l decoupled from hadronic effects b V ub Tree level u n The problem: b clv decay ( b u l ) = G F 2 V ub 2 m 5 b ( b ul ) V 1 ub ( b 2 cl ) Vcb 50 2 n How can we suppress 50 larger background? 3 April 2006 M. Morii, Harvard 11

12 Detecting b uln n Inclusive: Use m u << m c à difference in kinematics n Maximum lepton energy 2.64 vs GeV n First observations (CLEO, ARGUS, 1990) used this technique n Only 6% of signal accessible n How accurately do we know this fraction? n Exclusive: Reconstruct final-state hadrons n B plv, B rlv, B wlv, B hlv, n Example: the rate for B plv is d ( B l ) dq G 24 2 F = ub + V p f ( q ) n How accurately do we know the FFs? 2 b b c u Form Factor (3 FFs for vector mesons) E l 3 April 2006 M. Morii, Harvard 12

13 Inclusive b uln n There are 3 independent variables in B Xlv B l E l = lepton energy q 2 = lepton-neutrino mass squared u quark turns into 1 or more hardons X u m X = hadron system mass n Signal events have smaller m X à Larger E l and q 2 Not to scale! b c b c b c b u b u b u 2 E l q m X 3 April 2006 M. Morii, Harvard 13

14 Lepton Endpoint BABAR PRD 73: Belle PLB 621:28 CLEO PRL 88: n Select electrons in 2.0 < E l < 2.6 GeV n Push below the charm threshold è Larger signal acceptance è Smaller theoretical error n Accurate subtraction of background is crucial! n Measure the partial BF E l (GeV) DB (10-4 ) BABAR 80fb ± 0.41 stat ± 0.65 sys Belle 27fb ± 0.37 stat ± cf. Total BF is ~ sys CLEO 9fb ± 0.15 stat ± MC bkgd. b clv BABAR Data Data bkgd. MC signal b ulv 3 April 2006 M. Morii, Harvard 14

15 BABAR PRL 95: E l vs. q 2 n Use p v = p miss in addition to p e è Calculate q 2 q 2 (GeV 2 ) b clv b ulv E l (GeV) n Define s h max = the maximum m X squared n Cutting at s h max < m D2 removes b clv while keeping most of the signal n S/B = 1/2 achieved for E l > 2.0 GeV and s h max < 3.5 GeV 2 n cf. ~1/15 for the endpoint E l > 2.0 GeV n Measured partial BF DB (10-4 ) BABAR 80fb ± 0.33 stat ± Small 0.34systematic errors BABAR 3 April 2006 M. Morii, Harvard 15

16 Measuring m X and q 2 BABAR hep-ex/ Belle PRL 95: n Must reconstruct all decay products to measure m X or q 2 n Select events with a fully-reconstructed B meson n Rest of the event contains one recoil B n Flavor and momentum known n Find a lepton in the recoil B n Neutrino = missing momentum n Make sure m miss ~ 0 n All left-over particles belong to X n We can now calculate m X and q 2 n Suppress b clv by vetoing against D (*) decays n Reject events with K n Reject events with B 0 D *+ ( D 0 p + )l v Fully reconstructed B hadrons v lepton X 3 April 2006 M. Morii, Harvard 16

17 Measuring Partial BF BABAR hep-ex/ Belle PRL 95: n Measure the partial BF in regions of (m X, q 2 ) For example: m X < 1.7 GeV and q 2 > 8 GeV 2 BABAR 211fb -1 m X < 1.7, q 2 > 8 Belle 253fb -1 Phase Space DB (10-4 ) 8.7 ± 0.9 stat ± 0.9 sys m X < ± 1.1 stat ± 1.0 sys m X < 1.7, q 2 > ± 0.8 stat ± 1.0 sys Large DB thanks to the high efficiency of the m X cut 3 April 2006 M. Morii, Harvard 17

18 Theoretical Issues n Tree level rate must be corrected for QCD n Operator Product Expansion gives us the inclusive rate n Expansion in a s (m b ) (perturbative) and 1/m b (non-perturbative) b B GF Vu b mb s B X ul = 1 O mb ( ) L V ub u l X u known to O(a s2 ) Suppressed by 1/m b 2 n Main uncertainty (±5%) from m b 5 à ±2.5% on V ub n But we need the accessible fraction (e.g., E l > 2 GeV) of the rate 3 April 2006 M. Morii, Harvard 18

19 Shape Function n OPE doesn t work everywhere in the phase space n OK once integrated n Doesn t converge, e.g., near the E l end point n Resumming turns non-perturb. terms into a Shape Function n» b quark Fermi motion parallel to the u quark velocity f( k + ) n Cannot be calculated by theory n Leading term is O(1/m b ) instead of O(1/m 2 b ) k + We must determine the Shape Function from experimental data 0 = M m B b 3 April 2006 M. Morii, Harvard 19

20 b sg Decays BABAR PRD 72:052004, hep-ex/ Belle hep-ex/ CLEO hep-ex/ n Measure: Same SF affects (to the first order) b sg decays Measure E g spectrum in b sg Extract f(k + ) Predict partial BFs in b ulv K * Inclusive Partial BF/bin (10-3 ) Sum of exclusive BABAR Inclusive g measurement. Photon energy in the Y(4S) rest frame Exclusive X s + g measurement. Photon energy determined from the X s mass 3 April 2006 M. Morii, Harvard 20

21 Predicting b uln Spectra n Fit the b sg spectrum to extract the SF n Must assume functional forms, e.g. n Additional information from b clv decays n E l and m X moments è b-quark mass and kinetic energy 2 2 m = (4.60 ± 0.04) GeV, = (0.20 ± 0.04) GeV b n NB: m b is determined to better than 1% è First two moments of the SF n Plug in the SF into the b ulv spectrum calculations n Bosch, Lange, Neubert, Paz, NPB 699:335 n Lange, Neubert, Paz, PRD 72: n Ready to extract V ub (1 ) ( ) (1 ) a a x f k N x e + + = ; x= k+ Buchmüller & Flächer hep-ph/ Lepton-energy spectrum by BLNP 3 April 2006 M. Morii, Harvard 21

22 Turning DB into V ub n Using BLNP + the SF parameters from b sg, b clv Phase Space V ub (10-3 ) Reference BABAR 80fb -1 E l > ± 0.29 exp ± 0.31 SF,theo PRD 73: Belle 27fb -1 E l > ± 0.45 exp ± 0.30 SF,theo PLB 621:28 CLEO 9fb -1 E l > ± 0.48 exp ± 0.36 SF,theo PRL 88: BABAR 80fb -1 E l > 2.0, s h max < ± 0.27 exp ± 0.36 SF,theo PRL 95: BABAR n Adjusted 211fb -1 to m b = (4.60 ± 0.04) GeV, µ p2 = (0.20 ± 0.04) GeV 2 X < 1.7, q 2 > ± 0.35 exp ± hep-ex/ n Theory errors from Lange, Neubert, Paz, hep-ph/ SF,theo n Last Belle result m ( * ) used a simulated annealing technique Belle 253fb -1 X < ± 0.27 exp ± PRL 95: SF,theo 3 April 2006 M. Morii, Harvard 22-1 m X < 1.7, q 2 > ± 0.46 exp ± PRL 92:101801

23 Inclusive V ub as of 2005 V ub world average, Winter 2006 n V ub determined to ±7.4% Statistical ±2.2% Expt. syst. ±2.7% b clv model ±1.9% b ulv model ±2.1% SF params. ±4.1% Theory ±4.2% n The SF parameters can be improved with b sg, b clv measurements n What s the theory error? 3 April 2006 M. Morii, Harvard 23

24 Theory Errors n Subleading Shape Function è ±3.8% error n Higher order non-perturbative corrections b n Cannot be constrained with b sg B n Weak annihilation è ±1.9% error n Measure G(B 0 X u lv)/g(b + u X u lv) or G(D 0 Xlv)/G(D s Xlv) to improve the constraint n Also: study q 2 spectrum near endpoint (CLEO hep-ex/ ) n Reduce the effect by rejecting the high-q 2 region n Quark-hadron duality is believed to be negligible n b clv and b sg data fit well with the HQE predictions n Ultimate error on inclusive V ub may be ~5% g l 3 April 2006 M. Morii, Harvard 24

25 Avoiding the Shape Function n Possible to combine b ulv and b sg so that the SF cancels n Leibovich, Low, Rothstein, PLB 486:86 n Lange, Neubert, Paz, JHEP 0510:084, Lange, JHEP 0601:104 n No need to assume functional forms for the Shape Function n Need b sg spectrum in the B rest frame 2 Vub d ( B Xs ) ( B X ul ) = W( E ) de 2 V de ts n Only one measurement (BABAR PRD 72:052004) available n Cannot take advantage of precise b clv data Weight function n How well does this work? Only one way to find out 3 April 2006 M. Morii, Harvard 25

26 BABAR hep-ex/ SF-Free V ub Measurement n BABAR applied LLR (PLB 486:86) to 80 fb -1 data n G(B X u lv) with varying m X cut n dg(b X s g)/de g from PRD 72: n With m X < 1.67 GeV V = (4.43 ± 0.38 ± 0.25 ± 0.29) 10 ub stat. syst. theory n SF error è Statistical error n Also measured m X < 2.5 GeV n Almost (96%) fully inclusive è No SF necessary V ub = (3.84 ± 0.70 ± 0.30 ± 0.10) 10 Theory error ±2.6% n Attractive new approaches with increasing statistics 3 Theory error Expt. error m X cut (GeV) 3 April 2006 M. Morii, Harvard 26

27 Exclusive B pln n Measure specific final states, e.g., B plv n Can achieve good signal-to-background ratio n Branching fractions in O(10-4 ) à Statistics limited n Need Form Factors to extract V ub d ( B l ) dq G 24 2 F = 2 3 n f + (q 2 ) has been calculated using n Lattice QCD (q 2 > 15 GeV 2 ) V ub p f+ ( q ) n Existing calculations are quenched è ~15% uncertainty n Light Cone Sum Rules (q 2 < 14 GeV 2 ) n Assumes local quark-hadron duality è ~10% uncertainty n... and other approaches One FF for B plv with massless lepton 3 April 2006 M. Morii, Harvard 27

28 Form Factor Calculations n Unquenched LQCD calculations started to appear in 2004 n Fermilab (hep-lat/ ) and HPQCD (hep-lat/ ) n Uncertainties are ~11% LCSR* Fermilab HPQCD ISGW2 f + (q 2 ) and f 0 (q 2 ) q 2 (GeV 2 ) *Ball-Zwicky PRD71: n Measure dg(b plv)/dq 2 as a function of q 2 n Compare with different calculations 3 April 2006 M. Morii, Harvard 28

29 Measuring B pln n Measurements differ in what you do with the other B Technique Untagged Tagged by B D (*) lv Tagged by B hadrons Efficiency Purity High Low Û Ü Low High n Total BF is (1.35 ± 0.08 ± 0.08 ) 10 stat n ±8.4% precision syst 4 B(B 0 p - l + v) [10-4 ] 3 April 2006 M. Morii, Harvard 29

30 Untagged B pln BABAR PRD 72: CLEO PRD 68: n Missing 4-momentum = neutrino n Reconstruct B plv and calculate m B and DE = E B E beam /2 BABAR data MC signal signal with wrong p b ulv BABAR b clv other bkg. 3 April 2006 M. Morii, Harvard 30

31 D (*) ln-tagged B pln BABAR hep-ex/ , Belle hep-ex/ n Reconstruct one B and look for B plv in the recoil n Tag with either B D (*) lv or B hadrons n Semileptonic (B D (*) lv) tags are efficient but less pure n Two neutrinos in the event n Event kinematics determined assuming known m B and m v p l v soft p v l D cos 2 f B 1 for signal data MC signal MC background 3 April 2006 M. Morii, Harvard 31

32 BABAR hep-ex/ Hadronic-tagged B pln n Hadronic tags have high purity, but low efficiency n Event kinematics is known by a 2-C fit n Use m B and m miss distributions to extract the signal yield 0 B + l B 0 l p l v soft p D p or K data MC signal b ulv b clv other bkg. 3 April 2006 M. Morii, Harvard 32

33 db(b pln)/dq 2 Errors on V ub dominated by the FF normalization V ub n Measurements start to constrain the q 2 dependence n ISGW2 rejected n Partial BF measured to be q 2 range DB [10 4 ] < 16 GeV ± 0.06 ± 0.06 > 16 GeV ± 0.04 ± 0.04 HFAG 2006 Winter 3 2 (3.36 ± 0.15 expt FF) 10 Ball-Zwicky q < 16 = ± > 3 2 ( expt FF) 10 HPQCD q (3.75 ± 0.26 expt FF) 10 Fermilab q > 16 3 April 2006 M. Morii, Harvard 33

34 Future of B pln n Form factor normalization dominates the error on V ub n Experimental error will soon reach ±5% n Significant efforts in both LQCD and LCSR needed n Spread among the calculations still large n Reducing errors below ±10% will be a challenge n Combination of LQCD/LCSR with the measured q 2 spectrum and dispersive bounds may improve the precision n Fukunaga, Onogi, PRD 71: n Arnesen, Grinstein, Rothstein, Stewart PRL 95: n Ball, Zwicky, PLB 625:225 n Becher, Hill, PLB 633: April 2006 M. Morii, Harvard 34

35 How Things Mesh Together b sg E g Inclusive b clv SSFs E l m X Shape Function HQE Fit Inclusive b ulv E l q 2 m X duality m b V ub FF Exclusive b ulv B plv wlv, hlv? WA LCSR LQCD unquenching 3 April 2006 M. Morii, Harvard 35

36 The UT 2004 à 2005 n Dramatic improvement in V ub! n sin2b went down slightly è Overlap with V ub /V cb smaller 3 April 2006 M. Morii, Harvard 36

37 Summary n Precise determination of V ub complements sin2b to test the (in)completeness of the Standard Model n ±7.4% accuracy achieved so far è 5% possible? n Close collaboration between theory and experiment is crucial n Rapid progress in inclusive V ub in the last 2 years n Improvement in B pln form factor is needed 3 April 2006 M. Morii, Harvard 37