Inclusive semileptonic B decays: experimental Elisabetta Barberio University of Melbourne FPCP: Vancouver April 2006

April 2006 E. Barberio 2 Standard Model Consistency Tests V ub and V cb provide a test of CP violation in the Standard Model comparing the measurements on the ( ,  ) plane The width of the green ring need to be reduced to match sin2  and other measurements The error on the ring width is dominated by V ub Goal: Accurate determination of |V ub |

April 2006 E. Barberio 3 Semileptonic B decays tree level, short distance: decay properties depend directly on |V cb |, |V ub |,m b perturbative regime (  s n ) V cb, V ub u + long distance:,u But quarks are bound by soft gluons: non-perturbative (  QCD ) long distance interactions of b quark with light quark

April 2006 E. Barberio 4 Inclusive semileptonic decays Short distance is calculable Long distance leading order and short distance contribution are cleanly separated and probability to hadronnize is 1 To compare Operator Product Expansion predictions with experiments: integration over neutrino and lepton phase space provides smearing over the invariant hadronic mass of the final state Many theorists love inclusive semileptonic decays

April 2006 E. Barberio 5 Inclusive semileptonic decays V ub : 7.5% precision shared between experimental and theoretical errors small rate and large b  cl background space cuts to remove b  cl background which introduce O(1) dependence on non-preturbative b-quark distribution function V cb vs V ub V cb : most accurate determination from the inclusive decays 2% precision limited by theory error precise Heavy Quarks parameters, tests of OPE

April 2006 E. Barberio 6 V cb from inclusive semileptonic decays  sl described by Heavy Quark Expansion in (1/m b ) n and  s k The expansion depend on m b definition: non-perturbative terms are expansion dependent exp.  |V cb |<1% non perturbative parameters need to be measured Theory error was dominated by 1/m b 3 terms and above

April 2006 E. Barberio 7 X n are relate to non-perturbative parameters Bc moments in semileptonic decays higher moments are sensitive to 1/m b 3 terms  reduce theory error on V cb and HQ parameters moments evaluated on the full lepton spectrum or part of it: p > p min in the B rest frame

April 2006 E. Barberio 8 Difficulty to go from measured shape to true shape: e.g. QED corrections, accessible phase space, resolution, background rate shape |V cb | m c,  2 G, m b,  2  rate |V cb | shape Inclusive SL decays

April 2006 E. Barberio 9 Most recent measurements from Belle moments in semileptonic decays P l min =0.7 GeV P l min =0.4 GeV E : lepton energy spectrum in B  X c ( BaBar Belle CLEO Delphi ) M X 2 : hadronic mass spectrum in B  X c  ( BaBar CDF CLEO Delphi ) P * l (GeV) m x (GeV) P * l (GeV) from the moments of these distributions we get V cb and HQ parameters

April 2006 E. Barberio 10 Parameters Extraction BABAR: up to 1/m b 3 : fit ~90 measurement to extract HQ parameter and V cb at the same time M X moments o= used, = unused in the nominal fit B A B AR   2 /ndf =20/15 M1xM1x M2xM2x M3xM3x M4xM4x M0lM0l M1lM1l M2lM2l M3lM3l Red line: HQE fit Yellow band: theory errors P.Gambino, N.Uraltsev hep-ph/ hep-ph/

April 2006 E. Barberio 11 Vcb and HQ parameters Exp HQ  sl Global fit Kinetic scheme expansion (hep-ph/ )  V 2% m b < 1%, m 5%  (1S) expansion scheme has similar results used measurements:

April 2006 E. Barberio 12 V ub inclusive determination B  X u l rate tree level from OPE  corrected for perturbative  s and non-perturbative 1/m b terms BUT….. Br  B  X u l )/Br  B  X c l ) =1/50 In principle main uncertainty from m b 5

April 2006 E. Barberio 13 Shape Function Shape Function need to be determined from experimental data Limited phase space to reduce the B  X c l background: OPE doesn ’ t work everywhere in the phase space  non- perturbative Shape Function F(K + ) to extrapolate to the full phase space 0 F(K + )  = M B -m b K+K+ Detailed shape not constrained, in particular the low tail Mean and r.m.s. are known

April 2006 E. Barberio 14 Inclusive B  X u l B l XuXu Signal events have smaller M X and P +  Larger E l and q 2 m u << m c  exploits different kinematics q 2 = lepton-neutrino mass squared m X = hadron system mass E l = lepton energy P + = E X -|P X | bubu bcbc bubu bcbc bubu bcbc bubu bcbc Not to scale!

April 2006 E. Barberio 15 BaBar Lepton Endpoint  B (10 -4 ) BABAR 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 73:12006 Belle PLB 621:28 CLEO PRL 88: BaBar E l >2.0 GeV Belle E l > 1.9 GeV Crucial accurate subtraction of background is crucial! S/B ~1/10 eff~ 40% First measurement from CLEO E l >2.3 GeV

April 2006 E. Barberio 16 Measuring m X q 2 P + BABAR hep-ex/ Belle PRL 95: fully-reconstructed B meson flavor and momentum known lepton in the recoil-B m miss consistent with a neutrino lepton charge consistent with B flavor left-over particles belong to X equal m B on both sides; m miss = 0 Reconstruct all decay products to measure M X,q 2 or P + S/B ~ 2 Eff~ 0.1%

April 2006 E. Barberio 17 P + BLNP PRL93: Measuring Partial Branching Fraction  B (10 -4 ) BABAR 211fb -1 m X 88.7 ± 0.9 stat ± 0.9 sys Belle 253fb -1 first measurement of P + spectrum m X < ± 1.1 stat ± 1.0 sys m X 88.4 ± 0.8 stat ± 1.0 sys P + < ± 1.0 stat ± 1.6 sys

Turning  B into |V ub | HFAG main results: HQ parameters form b  X c l and b  X s  hep-ph/ Inclusive b → ulv q2q2 b → s  Shape Function EE mbmb Inclusive b → clv mXmX ElEl HQE Fit mXmX ElEl WA duality |V ub | SSFs

April 2006 E. Barberio 19 Belle E  >1.8 GeV Dealing with Shape Function Solution  use directly the  spectrum: easy to fit shape function Better resolution  K* peak (more difficult for SF) theory E*  (GeV) E  (GeV)

April 2006 E. Barberio 20 Inclusive |V ub |: BLNP framework Inputs: m b (SF) = 4.60  0.04 GeV   2 (SF) = 0.20  0.04 GeV 2 Statistical  2.2% Expt. syst.  2.7% B  X c l model  1.9% B  X u l model  2.1% Subleading SF  3.8% other theory error  4.5%  |V ub | =  7.3% |V ub | world average as of Winter 06 |V ub | BLNP =(4.45  0.20  0.26) 10 -3

April 2006 E. Barberio 21 Theory Errors Quark-hadron duality is not considered (cut dependent) b  cl and b  s  data fit well HQ predictions Weak annihilation   1.9% error l Expected to be <2% of the total rate l  w.a. /  (b  u) < 7.4 % from CLEO HQ parameters   4.1% mainly m b ; kinematics cuts depend on m b, ! Sub-leading shape function   3.8% dominated by the lepton endpoint measurements B u b l q q

April 2006 E. Barberio 22 Inclusive |V ub |: DGE framework DGE theory   2.9% matching scheme method and scale m b (MS)   1.3% on event fraction m b (MS)=4.20  0.04 GeV  s    1.0% on event fraction total  SL   3.0 % Dressed Gluon Exponentiation (DGE) on-shell b-quark calculation converted into hadronic variables used as approximation to the meson decay spectrum |V ub | DGE = (4.41  0.20  0.20) Still digesting the method

April 2006 E. Barberio 23 Weight function LLR m x <1.67 GeV OPE m x <2.50 GeV V ub without Shape Function Based on Leibovich, Low, Rothstein, PLB 486:86 First proposal by Neubert m x cut Babar

April 2006 E. Barberio 24 |V ub |: inclusive vs exclusive |V ub | inclusive W.A. Winter 06 |V ub | exclusive W.A. Winter 06

April 2006 E. Barberio 25 |V ub |: CKM consistency Most probable value of V ub from measurements of other CKM parameters Standard Model predictions with  ms measurement (thank to Pierini) V ub from exclusive measurements V ub from inclusive measurements

April 2006 E. Barberio 26 Conclusions b  cl V cb 2% error dominated by theory, m (kinetic and  (1S) schemes), m (kinetic scheme) but how well do we know the B  X c l spectrum? b  ul V ub ~7.4% error shared between theoretical and experimental inclusive vs exclusive less than 1.4  difference, depending on the inclusive extracting method We have now different methods to extract V ub |V ub 5% possible? Improve knowledge of B  X c l, B  X u l and more work on the theoretical error

April 2006 E. Barberio 27 Inclusive |V ub |: comparisons HQ parameters from cl and sg HQ parameters from sg only

April 2006 E. Barberio 28 M x unfolded spectrum for B  X c l D* D** D Belle

April 2006 E. Barberio 29 photon energy spectrum photon energy spectrum in B  X   not sensitive to new physics and give information on B structure E  >2 GeV Belle E  >1.8 GeV u, c, t CLEO E  : photon energy spectrum in B  s  ( BaBar Belle CLEO Delphi )