Jochen Dingfelder, SLAC Semileptonic Decay Studies with B A B AR Annual DOE HEP Program Review, June 5-8, 2006, SLAC B D   X c,X u

2 We study semileptonic decays B  X c,u ℓ Leptonic and hadronic currents factorize! Experimental approaches: inclusive or exclusive (B →  ℓ  ) Semileptonic B-Meson Decays Exclusive Decays  Lower signal rate, better bkg reduction  Need Form Factors to describe hadronization process  Measurement as function of q 2, angles Inclusive Decays  Large signal rate, high bkg  Total rate calculated with HQE  Need Shape Function (b-quark motion in B meson)  smears kin. spectra. SF param. from b  s  or b  cl. E ℓ q 2 = p ℓ 2 +p 2 M X D, electroweak interaction  coupling |V cb |, |V ub | strong interaction  meson structure

3 HQE fit theo. error band |V cb | from E e and M X Moments 1 st to 4 th M X moments, 0 th to 3 rd E e moments (as function of min. cut on E e ) Enough d.o.f. to fit 8 parameters: Global fit to E e, M X, E  (b  s  ) moments: |V cb | = ( ) x m b (kin) = ± GeV   2 (kin) = ± GeV Shape function par. needed for |V ub | Measure moments of lepton momentum and hadronic mass spectra in B  X c ℓ  (|V cb |) = 1.7%  (m b ) = 1%  (m c ) = 5% high mass charm states M x 2 [GeV 2 /c 4 ]

4 The decay rate is: f (w=1) = 1 in heavy quark limit; lattice QCD says: f (1) = Shape of f (w) expressed in terms of  2 (slope at w=1) and form-factor ratios R1, R2. Measure decay angles  ℓ,  V, . Fit  3D  distribution in bins of w  to extact  2, R1, R2. |V cb | from B  D* ℓ Phase space Form factor Here we use w = D * boost in B rest frame Hashimoto et al, PRD 66 (2002) Caprini, Lellouch, Neubert Nucl. Phys. B 530, 153 (1998) –0.035

5 B  D* ℓ  Form Factors & |V cb | stat. MC stat. syst. Factor 5 improvement on FF uncertainty from previous CLEO measurement (1996!) 1D projections of fit result : 88M BB w  cos  V cos  l Total systematic error on |V cb | : 4.5%  3.5% B A B AR

6 Inclusive |V ub | from Lepton Endpoint Study inclusive decays B  X u ℓ  Large charm bkg from B  X c ℓ  need accurate bkg subtraction  Restrict phase space (problematic for HQE !)  shape function becomes important Select events with high-E lepton: 2.0 < E ℓ < 2.6 GeV  Lower E ℓ cut below charm threshold  Larger acceptance, smaller theoretical error |V ub |=(4.44±0.25 exp ±0.22 theo )  – 0.38 SF fully corrected spectrum B A B AR MC bkg b  cl Data Data – bkg MC signal b  ul 88M BB

7 M X <1.67 GeV: |V ub | = (4.43 ± 0.45 exp ± 0.29 theo )  Hadronic B tag: Fully reconstruct one B tag in hadronic decay mode  known momentum, flavor, charge of other B signal M X 7 GeV 2 New “ shape function-independent ” approach:  Combine b  ul rate with b  s  spectrum  Or measure full M X spectrum Inclusive |V ub | with Hadronic B tag |V ub |=(4.65±0.34 exp ±0.23 theo )  – 0.38 SF B tag B signal XuXuXuXu l e-e-e-e- D*D*D*D*  e+e+e+e+ Leibovich, Low, Rothstein hep-ph/ , theory uncertainties signal M X max 88M BB

8 |V ub | from B   ℓ  Experimentally:  Good S/B ratio, untagged & tagged analyses  Measure q 2 dependence of form factor Theoretically:  Complementary to inclusive approach  Form-factor norm. dominates error on |V ub | Untagged analysis: Reconstruct neutrino from missing 4-momentum of event 83 x 10 6 BB disfavors ISGW II quark model |V ub | = (3.82 ± 0.26 exp )  – 0.53 FF Form Factor LQCD2  Data Signal MC Comb. Sig. Crossfeed b  cl qq m ES (GeV) 82M BB

9 Form factor f (q 2 = M 2 D s )  decay constant f Ds Leptonic decay proceeding through weak annihilation of quarks D S +     and Decay Constant f Ds D s →  signal N  = 489±55 Preliminary 248M BB stat syst D s →  Aubin et al. PRL (2005) LQCD: Validates LQCD predictions at 10% level c s + + = +++ |f Ds | 2 |V cs | 2  + D s ( * ) mesons from e + e -  cc Tag one D ( * ), reconstruct signal side via D* S  D S    Normalize to D s   :

10 Conclusions  B A B AR has broad program of semileptonic/leptonic B decays. SLAC plays a leading role here.  Much progress in the last 1-2 years: |V cb |  2%, |V ub |  7-8%, form factors, …  BABAR is now also exploiting their large D-meson samples. Charm semileptonic decays provide high-quality “lattice calibration”. Techniques validated by charm decays can be applied to beauty decays !  These measurements have reached precision to allow critical comparisons with theory calculations: Form Factors & HQE Parameters f Ds results: CKM constraints (“tree” quantities) 2004  2006 status 2004

11 SLAC’s Contribution B  X c l  incl.  Mass spectra, moments, |V cb | Buchmüller, Lüth B  D*l : Form factors, |V cb | Snyder B  X s  : Branching Fraction, moments Ozcan, Libby, Jessop B  X u l incl. : Momentum endpoint spectrum, |V ub | Lüth B  X u l incl. : Shape function independent, |V ub | Langenegger B   l &  l : Branching fraction, form factor, |V ub | Weinstein, Dingfelder, Kelsey, Lüth D s   : Branching fraction, decay constant Stelzer, Schindler

12 Backup Slides

13 Testing Theory with D  K/  l |V cs | from unitarity  determine |f + (q 2 )| |f + (q 2 )| from LQCD  determine |V cs | Goal: measure ratio B(D   l ) / B(D  Kl )  compare with lattice |f +  (q 2 )| / |f + K (q 2 )| m pole = ± ±  pole = 0.43 ± 0.03 ± 0.04 D Study D-meson decays from e + e -  cc with high statistics Tag one c quark via full reconstruction of D ( * ) meson Dramatically reduces bkg from u, d, s and B mesons Charm SL decays provide high-quality lattice calibration. Techniques validated by charm decays can be applied to beauty decays!