1. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 1 Study of Spectral Moments in Semileptonic b Decays with the DELPHI Detector at LEP Marta Calvi Università di Milano Bicocca and I.N.F.N. On behalf of the DELPHI Collaboration Outline: Moments of hadronic mass spectrum Moments of lepton energy spectrum Interpretation

2. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 2 Improvement are possible with additional measurements of the characteristics of b–hadron semileptonic decays: · Moments of hadronic mass spectrum · Moments of lepton energy spectrum Comparison of results from different measurements provides a test of the consistency of O.P.E. predictions and of underlying assumptions Motivation (I) V cb, m b and m c are fundamental parameters of the Standard Model which have to be measured by experiments At present, the best accuracy is achievable in the determination of V cb from inclusive semileptonic b-hadron decays: 1 % accuracy Evaluated by theory based on O.P.E., few % accuracy

3. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 3 Motivation (II) b and b in separate hemispheres (  c  ~ 2 mm)  good secondary vertex reconstruction and signal/ background separation First measurement of spectral moments in semileptonic b decays at the Z 0 E B ~ 30 GeV  large boost Use full lepton energy spectrum in the B rest frame · Advantages of Z 0 kinematics: Get new insight:  Use of different theoretical formulations  Possible use of higher moments · Challenge: complete reconstruction of the B system

4. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 4 B d 0  D ** - exclusively reconstructed in the three channels: D **  D 0  +, D **  D +  -, D **  D *+  - with D 0, D + and D *+ fully reconstructed and p  >0.5 GeV/c Moments of hadronic mass distribution in b semileptonic decays (I) Signal/background separation with a discriminant variable based on: presence of additional charged particles at the charm vertex in addition to D (*), - and  impact parameter, secondary vertex quality etc.. theoretical expression for the moments with coefficients different wrt analyses with more stringent limits to the lepton phase space region Leptons with p(Lab)>2 GeV/c

5. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 5 Moments of hadronic mass distribution in b semileptonic decays (II) D  candidates separated in: “right-sign” ( D 0  +, D +  -, D *+  - ) “wrong-sign”  contributions only from D (*)  +  - D *+  - “right-sign” D *+  - “wrong-sign” Discriminant variable No evidence for signal in D  +  - states: BR(b  D 0  +  - - ) = BR(b  D +  +  - - ) < 0.18% at 90% C.L. BR(b  D *+  +  - - ) < 0.17% at 90%C.L. D** production rates Fit using background distributions from simulation and data

6. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 6 Moments of hadronic mass distribution in b semileptonic decays (III) · Fit to  m =m(D (*)  ) - m(D (*) ) distributions considering resonant D 0 *+,D 1 *+,D 1 +,D 2 + and non resonant D  states · Evaluate moments from the fitted D ** mass distribution: Study of the mass distribution of D** states 4 MeV resolution for completely reconstructed D  Plus 4/15 MeV smearing for missing  0/  D0+D0+ D+-D+- D *+  -

7. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 7 Moments of hadronic mass distribution in b semileptonic decays (IV) From the measured and using: = p D m n D +p D* m n D* +p D** p D** =1-p D -p D* derive moments of hadronic mass distribution: From the fit: BR(B 0  D ** - )=(2.6  0.5  0.4)% with broad D 1 * dominant contributing channel M 1 = = 0.534±0.041±0.074 GeV/c 2 M 2 = =1.51±0.20±0.23 (GeV/c 2 ) 2 M 2 ‘= ) 2 >=1.23±0.16±0.15 (GeV/c 2 ) 2 M 3 ‘= ) 3 >=2.97±0.67±0.48 (GeV/c 2 ) 3 DELPHI preliminary results

8. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 8  Reconstruct the B system: E (B) = E (vertex) + E ( ) + E (v ) Charm vertex from missing reconstruction with energy iterative procedure  E =3.2 GeV B direction from B reconstructed momentum and B decay flight direction  Boost lepton in B rest frame  E B /E B =12% (80% evts) t  Tag leptons muons (p> 2.5GeV/c) electrons (p> 3GeV/c) Inclusive semileptonic B decay reconstruction  E* lepton  250 MeV  Select Z 0  bb events with b-tag algorithm Moments of lepton spectrum in b s.l. decays (I)

9. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 9 Moments of lepton spectrum in b s.l. decays (II) Without introducing a bias to the lepton energy distribution Use combination of 2 sets of probabilistic variables based on: - Charge correlation - Event topology Background reduction Anti-tagged sampleTagged sample b  c  b  c  + b  c   c   misid. leptons decays

10. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 10 Moments of lepton spectrum in b s.l. decays (III) Unfold resolution effects to get original spectra Correct for: e.m. radiation b  u contribution B 0 s and  b contribution  1-3 MeV shifts Lepton energy spectrum measurement measured spectrum, background subtracted unfolded spectrum 18,300 electrons+ muons from 1994/95 data

11. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 11 Moments of lepton spectrum in b s.l. decays (IV)  E  = (1.383  0.012(stat.)  0.009 (syst.) ) GeV  (E   E  ) 2  =(0.192  0.005(stat.)  0.008(syst.) ) GeV 2  (E   E  ) 3  =(-0.029  0.005(stat.)  0.006(syst.) ) GeV 3 Preliminary DELPHI results: Preliminary systematic uncertainty from:  Monte Carlo modelling: B d,B s,  b fractions; D,D*,D** fractions, b fragmentation  Background subtraction (controlled with anti-tagged lepton sample)  Unfolding procedure and lepton energy resolution Stability of the result checked wrt e/  samples and different working points 

12. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 12 Interpretation of the measurements 2) Running quark masses (M.Voloshin and N.Uraltsev for  0  s 2 and 1/m b 3 corrections) Moments of hadronic mass spectrum and of lepton energy spectrum are sensitive to the nonperturbative parameters of the Heavy Quark Expansion. At order 1/m b 2  , 1, 2 ( 2  0.12 GeV 2 ). At order1/m b 3   1,  2,  1-4 Mass expansion: with: Two different approaches have been followed in this analysis: 1) Pole mass expansions (A.F.Falk, M.Luke and P.Gambino for lepton spectra)

13. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 13  1 =(0.-0.5 3 ) GeV 3  2 = T i =(-0.5 3,0.5 3 ) GeV 3 DELPHI preliminary results  = (0.44  0.07 (exp.)  0.07( 1 /m b 3,  s ) ) GeV 1 =(-0.23  0.07 (exp.)  0.08 ( 1 /m b 3,  s ) ) GeV 2 Constraints to 1 and  from first and second moment of hadronic mass spectrum and lepton energy spectrum Constraints to  and 1

14. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 14 Constraints to m c (1GeV) and   2 Use the correlation between m b and m c : Fix bottom mass from external measurements: m b = 4.60  0.05 GeV and extract m c : DELPHI preliminary results m c ( 1GeV ) = ( 1.19  0.07 ( exp. )  0.07 ( m b )  0.04 (  D 3 ) ) GeV

15. ICHEP 2002, Amsterdam Marta Calvi - Study of Spectral Moments… 15 CONCLUSIONS Measurement of the first three moments of hadronic mass distribution and lepton energy spectrum in semileptonic b decays at the Z 0 has been performed for the first time. Comparison with calculations for non-truncated spectra are satisfactory Constraints on non-perturbative parameters of Heavy Quark Expansion have been derived