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Jan 28, 2014 - distance between two constituents of a Feshbach resonance state as well as a ... of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. ... of the resonance state is evaluated as a complex number, whose ...
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Workshop on the CKM Unitarity Triangle, IPPP Durham, April 2003
CKM03 A Preliminary Measurement of Hadronic Mass Moments in Semileptonic B Meson Decays Vera G. L¨ utha
representing the BABAR Collaboration
arXiv:hep-ex/0307073v1 27 Jul 2003
Stanford Linear Accelerator Center PO Box 20450, Stanford, CA 94309, USA A preliminary measurement of the second moments of the hadron mass in B → Xℓν decays by the BABAR Collaborations is reported. These measurements are performed as a function of the lepton momentum above a given threshold.
For many years semileptonic decays have been the topic of a large variety of studies because they are theoretically simple at the parton level, sensitive to the coupling of quarks to the weak charged current, and allow us to probe the impact of strong interactions on the bound quark. Experimentally they are readily accessible, because of the large branching fraction and clear signature in form of a high momentum lepton. The principal goal for studies of semileptonic B meson decays is the determination of the CKM matrix elements |Vcb | and |Vub |. The decay width for inclusive semileptonic B decays to the charm states Xc can be written as ΓcSL ≡ B(B → Xc ℓ− ν)/τB = γc |Vcb |2 ,
i.e., |Vcb | can be determined from the branching fraction and the average B lifetime, provided the factor γc is known. The theoretical QCD parameter γc requires both perturbative and non-perturbative input. In the framework of Heavy Quark Effective Theory the uncertainties in the estimate of γc can be reduced by using information from other inclusive measurements, for instance, the moments of the mass distribution of the hadrons Xc . Like the total decay rate, this inclusive observable can be calculated using expansions in powers of the strong coupling constant αs (mb ) and in inverse powers of the B meson mass, mB , that include non-perturbative parameters. At order 1/m2B , there ¯ λ1 , and λ2 . From the B ∗ − B are three parameters, Λ, mass splitting, we have λ2 = 0.128 ± 0.010 GeV2 . In the following, we report a preliminary measurement performed with the BABAR detector [ 1] operating at the Υ (4S) resonance at the PEP-II energy asymmetric e+ e− storage ring [ 2] at SLAC. This measurement of the second moment of the hadron mass distribution as a function of the minimum lepton momentum was ∗ Work
supported by the US Department of Energy
first reported last summer [ 3]. An update of this measurement is expected for this summer’s conferences. We measure the second moment of the invariant mass MX distribution of the hadronic system X in 2 B → Xℓν decays, hMX − m2D i, where mD = (mD + 3mD∗ )/4 = 1.975 GeV/c2 is the spin-averaged D meson mass. This measurement is similar to one performed by CLEO [ 5]. The analysis is based on a sample of 55 million BB events, from which we select a subsample of 5,800 events (above a background of 3,600 events that are statistically subtracted using the energy constrained B mass distribution). In these events one B meson is fully reconstructed in a hadronic decay mode and the semileptonic decay of the second B is identified by a high momentum electron or muon. The system X in the decay B → Xℓν is made up of hadrons and photons that are not associated with the Breco candidate. We exploit the available kinematic information of the full BB event by performing a 2C kinematic fit that imposes four-momentum conservation, the equality of the masses of the two B mesons, and 2 forces Mmiss = Mν2 = 0. The fit takes into account event-by-event the measurement errors of all individual particles and the measured missing mass. This leads not only to a significant improvement of the r.m.s. of the mass resolution of the X system but also provides an almost unbiased estimator of the mean MX and a resolution that is largely independent of 2 Mmiss . Figure 1 shows the resultant MX distribution of the se∗ lected events, for a minimum lepton momenta Pmin = 0.9 GeV/c. Different B → Xc lν decays contribute to this distribution. The dominant decays are B → D∗ lν and B → Dlν, but we also expect contributions from decays to higher mass charm states, D∗∗ resoreso nances with a mass distribution XH peaked near 2.4 2 GeV/c , and potentially non-resonant D∗ π final states
nreso for which we assume a broad mass distribution XH extending to the kinematic limit. The background is dominated by secondary semileptonic charm decays, contributions from lepton (primarily muon) misidentification are much smaller. The backgrounds decrease ∗ significantly for higher Pmin .
the measurement presented here. The data are also consistent with a measurement by the DELPHI Col∗ = 0GeV /c. laboration [ 6] that corresponds to Pmin
BABAR Preliminary CLEO
= 0.9 GeV/c
x2 = 25.4 0.6
D*+ / D*0 Events/ 83.3 MeV/c2
D+ / D0 XH
200 100 0 1.0
P*min [GeV/c] Figure 2. Measured mass moments as a function of the ∗ minimum lepton momentum, Pmin . The errors indicate the sum of the statistical and systematic uncertainties, they are highly correlated. The dashed curve shows the best description of the data by the OPE expansion [ 7] with λ1 and Λ¯ as free parameters. For comparison, the solid line shows variation of the moments for the parameters λ1 = −0.17 GeV2 and Λ¯ = 0.35 GeV [ 8]. 7-2002 8646A9
2.0 2.5 3.0 3.5 Mx [GeV/c2] ∗ Figure 1. The measured MX distribution for Pmin = 0.9 GeV/c. The hatched histograms show the fitted contributions from B → D∗ lν, B → Dlν and B → XH lν decays, as well as the background distribution. The white histogram represents the sum of all the individual distributions. 9-2002 8646A10
A binned χ2 -fit to the MX distribution is performed to determine the relative size of the three signal contributions, fD∗ , fD , and fXH , where fXH refers to the sum of the resonant and non-resonant high mass charm states. Taking into account the true particle masses (the D and D∗ masses are basically δ functions, and the mean of the XH contribution is taken from generated events) the second moments are calculated according to the following expression 2 hMX − m2D i
Figure 2 shows the second moment as a function of ∗ the lepton momentum above a minimum Pmin . The increase at lower momenta is attributed to contributions from the high mass states, i.e. the non-resonant nreso XH decays. The CLEO Collaboration has mea∗ sured the same moment for Pmin = 1.5 GeV/c, based on similar assumption about the high mass hadronic states. Their result [ 5] is in good agreement with
Extensive studies have been performed to assess the systematic uncertainties and potential biases in the moment measurement. These studies involve both changes in the event selection and variations of the corrections for efficiencies and resolution, and comparisons of data with Monte Carlo simulations. The leading systematic error is due to the uncertainty in the model for the higher mass states XH . Other errors are due to uncertainties in the Monte Carlo simulation of the detector resolution and efficiencies as well as in the background contributions. As one of the many cross checks we use the relative contributions fi to determine branching fractions by correcting for acceptance and setting the total semileptonic branching fraction to 10.87%. The resultant partial branching fractions are fully compatible ∗ with previous measurements and independent of Pmin . This is also the case when we split the XH contribution into a resonant and non-resonant part and allow both of them to vary independently. Heavy Quark Effective Theory (HQET) calculations 2 of the second mass moment hMX − m2D i have been carried out [ 7] using Operator Product Expansions (OPE) up to order α2s β0 and 1/m3B . These expansions
contain the non-perturbative parameters Λ¯ (O(mB )), λ1 and λ2 (O(m2B )). The observed dependence of the moments on the minimum lepton momentum can be reproduced, as long as we adjust the non-perturbative parameters. ∗ If we restrict the data to Pmin = 1.5 GeV/c and use a recent, independently measured value of Λ¯ = 0.35 ± 0.08 ± 0.10 GeV [ 8], we obtain λ1 = −0.17 ± 0.06 ± 0.07 GeV2 , a result that is in good agreement with the CLEO value of λ1 = −0.236 ± 0.071 ± 0.078 GeV2 . However, if we take this value of λ1 and Λ¯ = 0.35 GeV ∗ and calculate the moments as a function of Pmin , we find a much smaller momentum dependence than the data indicate (see Figure 2).
In summary, if the assumption is correct that there are significant contributions from charm states with masses extending well beyond the resonance D∗∗ , the second moment is expected to rise for lower lepton momenta, an effect that is not described by OPE using other independently measured values of the pa¯ On the other hand, we currently do not rameter Λ. have adequate knowledge of the branching ratios and mass distributions for higher resonant and mass resonant states in semileptonic B decays. And their contribution and mass distribution enter critically into the method that has been applied to extract the mass moments. It is expected that more direct methods to measure moments will reduce this dependency. Results are expected in the near future. Probably the best way to address this problem, is to perform more detailed measurements of various exclusive semileptonic branching fractions for decays to higher mass states. In addition, we expect to improve the method of determining moments, to measure higher mass moments, and to add moments of the lepton energy spectrum. Measurements of the inclusive photon spectrum in b → sγ will also add critical information on the nonperturbative effects that have impact on the translation of inclusive decays rates to |Vcb |, and |Vub |.
References 1. B. Aubert et al., BABAR Collaboration, Nucl. Instrum. Meth. A479 (2002) 1. 2. PEP-II , SLAC-418, LBL-5379 (1993). 3. B. Aubert et al., BABAR Collaboration, SLAC-PUB-9314, BABAR-CONF-02-029, Contribution to this Conference (ICHEP 2002), e-Print Archive: hep-ex/0207084. 4. Review of Particle Properties, Eur. Phys. J. C15 (2000) 1. 5. D. Cronin-Hennessy et al., CLEO-Collaboration, Phys. Rev. Lett. 87 (2001) 251808.
6. M. Calvi et al., DELPHI-Collaboration, hep-ex/0210046 (2002) 7. A.F. Falk and M.E. Luke, Phys. Rev. D57 (1998) 424., and also private communication. 8. S. Chen et al., CLEO Collaboration, Phys. Rev. Lett. 87 (2001) 251.