Measurement of the D*(2010)+ meson width and the D*(2010)+ - D0 mass difference

We measure the mass difference, \Delta m_0, between the D*(2010)+ and the D0 and the natural line width, \Gamma, of the transition D*(2010)+ ->D0 pi+. The data were recorded with the BABAR detector at center-of-mass energies at and near the Upsilon(4S) resonance, and correspond to an integrated luminosity of approximately 477 1/fb. The D0 is reconstructed in the decay modes D0 ->K- pi+ and D0 ->K- pi+ pi- pi+. For the decay mode D0 ->K- pi+ we obtain Gamma = (83.4 +- 1.7 +- 1.5) keV and \Delta m_0 = (145 425.6 +- 0.6 +- 1.8) keV, where the quoted errors are statistical and systematic, respectively. For the D0 ->K- pi+ pi- pi+ mode we obtain \Gamma = (83.2 +- 1.5 +- 2.6) keV and \Delta m_0 = (145 426.6 +- 0.5 +- 2.0) keV. The combined measurements yield \Gamma = (83.3 +- 1.2 +- 1.4) keV and \Delta m_0 = (145 425.9 +- 0.4 +- 1.7) keV; the width is a factor of approximately 12 times more precise than the previous value, while the mass difference is a factor of approximately 6 times more precise.

allowing the calculation of g B Ã B , which is needed for a model-independent extraction of jV ub j [5,6] and which forms one of the larger theoretical uncertainties for the determination of jV ub j [7]. We study the D Ãþ ! D 0 þ transition, using the D 0 ! K À þ and D 0 ! K À þ À þ decay modes, to extract values of the D Ãþ width À and the difference between the D Ãþ and D 0 masses Ám 0 . Values are reported in natural units and the use of charge conjugate reactions is implied throughout this Letter. The only prior measurement of the width is À ¼ ð96 AE 4 AE 22Þ keV by the CLEO Collaboration, where the uncertainties are statistical and systematic, respectively [8]. In the present analysis, we use a data sample that is approximately 50 times larger. This allows us to apply restrictive selection criteria to reduce background and to investigate sources of systematic uncertainty with high precision.
To extract À, we fit the distribution of the mass difference between the reconstructed D Ãþ and the D 0 masses, Ám. The signal component is described with a P-wave relativistic Breit-Wigner (RBW) function convolved with a resolution function based on a GEANT4 Monte Carlo (MC) simulation of the detector response [9].
The FWHM of the RBW line shape (%100 keV) is much less than the FWHM of the almost Gaussian resolution function which describes more than 99% of the signal (% 300 keV). Therefore, near the peak, the observed FWHM is dominated by the resolution function shape. However, the shapes of the resolution function and the RBW differ far away from the pole position. Starting ð1:5-2:0Þ MeV from the pole position, and continuing to ð5-10Þ MeV away (depending on the D 0 decay channel), the RBW tails are much larger. The observed event rates in this region are strongly dominated by the intrinsic linewidth of the signal, not the signal resolution function or the background rate. We use the very different resolution and RBW shapes, combined with the good signal-to-background rate far from the peak, to measure À precisely [10].
This analysis is based on a data set corresponding to an integrated luminosity of approximately 477 fb À1 recorded at, and 40 MeV below, the Çð4SÞ resonance [11]. The data were collected with the BABAR detector at the PEP-II asymmetric energy e þ e À collider, located at the SLAC National Accelerator Laboratory. The BABAR detector is described in detail elsewhere [12,13]; we summarize the relevant features below. The momenta of charged particles are measured with a combination of a cylindrical drift chamber and a five-layer silicon vertex tracker (SVT), both operating within the 1.5 T magnetic field of a superconducting solenoid. Information from a ring-imaging Cherenkov detector is combined with specific ionization (dE=dx) measurements from the SVT and the cylindrical drift chamber to identify charged kaon and pion candidates. Electrons are identified, and photons measured, with a CsI(Tl) electromagnetic calorimeter. The return yoke of the superconducting coil is instrumented with tracking chambers for the identification of muons.
We remove a large amount of combinatorial and B meson decay background by requiring D Ãþ mesons produced in e þ e À ! c " c reactions to exhibit an e þ e À centerof-mass-frame momentum greater than 3.6 GeV. The entire decay chain is fit using a kinematic fitter with geometric constraints at the production and decay vertex of the D 0 and the additional constraint that the D Ãþ laboratory momentum points back to the luminous region of the event. The pion from D Ãþ decay is referred to as the ''slow pion'' (denoted þ s ) because of the limited phase space available in the D Ãþ decay. The selection criteria are chosen to provide a large signal-to-background ratio (S=B), in order to increase the sensitivity to the long signal (RBW) tails in the Ám distribution; they are not optimized for statistical significance. The criteria are briefly mentioned here and presented in detail in the archival reference for this analysis [10]. The resolution in Ám is dominated by the resolution of the þ s momentum, especially the uncertainty of its direction due to Coulomb multiple scattering. We implement criteria to select well-measured pions. We define our acceptance angle to exclude the very-forward region of the detector, where track momenta are not accurately reconstructed, as determined using an independent sample of reconstructed K 0 S ! À þ decays. The K 0 S reconstructed mass is observed to vary as a function of the polar angle of the K 0 S momentum measured in the laboratory frame with respect to the electron beam axis. To remove contributions from the very-forward region of the detector we reject events with any D Ãþ daughter track for which cos > 0:89; this criterion reduces the final samples by approximately 10%.
Our fitting procedure involves two steps. In the first step we model the finite detector resolution associated with track reconstruction by fitting the Ám distribution for correctly reconstructed MC events using a sum of three Gaussians and a function to describe the non-Gaussian component [10]. These simulated D Ãþ decays are generated with À ¼ 0:1 keV, so that the observed spread of the MC distribution can be attributed to event reconstruction. The non-Gaussian function describes þ s decays in flight to a , for which coordinates from both the and segments are used in track reconstruction.
The second step uses the resolution shape parameters from the first step and convolves the Gaussian components with a RBW function to fit the measured Ám distribution in data. The RBW function is defined by where À D Ã D is the partial width to D 0 þ s , m is the D 0 þ s invariant mass, m 0 is the invariant mass at the pole, À total ðmÞ is the total D Ãþ decay width, and À is the natural linewidth we wish to measure. The partial width is defined by Here, is a Blatt-Weisskopf form factor for a vector particle with radius parameter r and daughter momentum p, and the subscript zero denotes a quantity measured at the mass pole m 0 [14,15]. We use the value r ¼ 1:6GeV À1 from Ref. [16]. For the purpose of fitting the Ám distribution, we obtain dÀðÁmÞ=dÁm from Eqs. (1) and (2) through the substitution m ¼ mðD 0 Þ þ Ám, where mðD 0 Þ is the nominal D 0 mass [17].
As in the CLEO analysis [8], we approximate the total D Ãþ decay width À total ðmÞ % À D Ã D ðmÞ, ignoring the electromagnetic contribution from D Ãþ ! D þ . This approximation has a negligible effect on the extracted values, as it appears only in the denominator of the RBW function.
To allow for differences between MC simulation and data, the root-mean-square deviation of each Gaussian component of the resolution function is allowed to scale in the fit process by the common factor (1 þ ). Events that contribute to the non-Gaussian component have a wellunderstood origin ( s decay in flight), which is accurately reproduced by MC simulation. In the fit to data, the non-Gaussian function has a fixed shape and relative fraction, and is not convolved with the RBW. The relative contribution of the non-Gaussian function is small (& 0:5% of the signal), and the results from fits to validation signal-MC samples are unbiased without convolving this term. The background is described by a phase-space model of continuum background near the kinematic threshold [10]. We fit the Ám distribution from the kinematic threshold to Ám ¼ 0:1665 GeV using a binned maximum likelihood fit and an interval width of 50 keV.
In the initial fits to data, we observed a strong dependence of Ám 0 on the slow pion momentum. This dependence, which originates in the modeling of the magnetic field map and the material in the beam pipe and SVT, is not replicated in the simulation. Previous BABAR analyses have observed similar effects, for example, the measurement of the Ã þ c mass [18]. In that analysis the material model of the SVT was altered in an attempt to correct for the energy loss and the underrepresented small-angle multiple scattering (due to nuclear Coulomb scattering). However, the momentum dependence of the reconstructed Ã þ c mass could be removed only by adding an unphysical amount of material to the SVT. In this analysis we use a different approach to correct the observed momentum dependence and adjust track momenta after reconstruction.
We use a sample of K 0 S ! þ À events from D Ãþ ! D 0 þ s decays, where D 0 ! K 0 S þ À , and require that the K 0 S daughter pions satisfy the same tracking criteria as the þ s candidates for the D 0 !K À þ and D 0 !K À þ À þ signal modes. The K 0 S decay vertex is required to lie inside the beam pipe and to be well separated from the D 0 vertex. These selection criteria yield an extremely clean K 0 S sample (over 99.5% pure), which is used to determine three fractional corrections to the overall magnetic field and to the energy losses in the beam pipe and, separately, in the SVT. We determine the best set of correction parameters by minimizing the difference between the þ À invariant  1 (color online). Fits to data for the D 0 ! K À þ and D 0 ! K À þ À þ decay modes. The total probability density function (PDF) is shown as the solid curve, the convolved RBW-Gaussian signal as the dashed curve, and the background as the dotted curve. The total PDF and signal component are indistinguishable in the peak region. Normalized residuals are defined as ðN observed À N predicted Þ= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi N predicted p .  [17] in 20 intervals of laboratory momentum in the range 0.0 to 2.0 GeV. The best-fit parameters increase the magnitude of the magnetic field by 4.5 G and increase the energy loss in the beam pipe and SVT by 1.8% and 5.9%, respectively [10]. The momentum dependence of Ám 0 in the preliminary results was mostly due to the slow pion. However, the correction is applied to all D Ãþ daughter tracks. All fits to data described in this analysis are performed using masses and Ám values calculated using corrected momenta. Simulated events do not require correction because the same field and material models used to propagate tracks are used for their reconstruction. Figure 1 presents the results of the fits to data for both the D 0 ! K À þ and D 0 ! K À þ À þ decay modes. The normalized residuals show good agreement between the data and our fits. Table I summarizes the results of the fits to data for both D 0 decay modes. Table I also shows the S=B at the peak and in the high Ám tail of each distribution.
We estimate systematic uncertainties related to a variety of sources. The data are divided into disjoint subsets corresponding to intervals of D Ãþ laboratory momentum, D Ãþ laboratory azimuthal angle , and reconstructed D 0 mass, in order to search for variations larger than those expected from statistical fluctuations. These are evaluated using a method similar to the Particle Data Group scale factor [10,17]. The corrections to the overall momentum scale and dE=dx loss in detector material are varied to account for the uncertainty on the K 0 S mass. To estimate the uncertainty in the Blatt-Weisskopf radius we model the D Ãþ as a pointlike particle. We vary the parameters of the resolution function according to the covariance matrix reported by the fit to estimate systematic uncertainty of the resolution shape. We vary the end point used in the fit, which affects whether events are assigned to the signal or to the background component. This variation allows us to evaluate a systematic uncertainty associated with the background parametrization; within this systematic uncertainty, the residual plots shown in Fig. 1 are consistent with being entirely flat. Additionally, we vary the description of the background distribution near threshold. We fit MC validation samples to estimate systematic uncertainties associated with possible biases. Finally, we use additional MC validation studies to estimate possible systematic uncertainties due to radiative effects. All these uncertainties are estimated independently for the D 0 ! K À þ and D 0 ! K À þ À þ modes, as discussed in detail in Ref. [10] and summarized in Table II. The largest systematic uncertainty arises from an observed sinusoidal dependence for Ám 0 on . Variations with the same signs and phases are seen for the reconstructed D 0 mass in both D 0 ! K À þ , D 0 ! K À þ À þ , and for the K 0 S mass. An extended investigation revealed TABLE I. Summary of the results from the fits to data for the D 0 !K À þ and D 0 !K À þ À þ channels (statistical uncertainties only). S=B is the ratio of the convolved signal PDF to the background PDF at the given Ám and is the number of degrees of freedom. TABLE II. Summary of systematic uncertainties with correlation between the D 0 ! K À þ and D 0 ! K À þ À þ modes. The K À þ and K À þ À þ invariant masses are denoted by mðD 0 reco Þ.