Measurement of the Branching Fraction for B->eta' K and Search for B->eta'pi+

We report measurements for two-body charmless B decays with an eta' meson in the final state. Using 11.1X10^6 BBbar pairs collected with the Belle detector, we find BF(B^+ ->eta'K^+)=(79^+12_-11 +-9)x10^-6 and BF(B^0 ->eta'K^0)=(55^+19_-16 +-8)x10^-6, where the first and second errors are statistical and systematic, respectively. No signal is observed in the mode B^+ ->eta' pi^+, and we set a 90% confidence level upper limit of BF(B^+->eta'pi^+)<7x10^-6. The CP asymmetry in B^+- ->eta'K^+- decays is investigated and a limit at 90% confidence level of -0.20

We report measurements for two-body charmless hadronic B decays with an η ′ meson in the final state. Using 11.1×10 6 BB pairs collected with the Belle detector, we find BF (B + → η ′ K + ) = (79 +12 −11 ±9)×10 −6 and BF (B 0 → η ′ K 0 ) = (55 +19 −16 ±8)× 10 −6 , where the first and second errors are statistical and systematic, respectively. No signal is observed in the mode B + → η ′ π + , and we set a 90% confidence level upper limit of BF (B + → η ′ π + ) < 7 × 10 −6 . The CP asymmetry in B ± → η ′ K ± decays is investigated and a limit at 90% confidence level of −0.20 < A CP < 0.32 is obtained. PACS: 13.25.Hw, 14.40.Nd Charmless hadronic B decays provide a rich ground for studying the mechanisms of B meson decay and the phenomenon of CP violation. The decay B → η ′ K is an example of such a charmless decay with an unexpectedly large branching fraction [1]. Within the framework of the Standard Model, the B → η ′ K decay proceeds primarily through b → s penguin diagrams with a contribution from the b → u tree diagram. Recent theory calculations [2,3] underestimate the measured decay rate [4] published by the CLEO collaboration. If the large branching fraction persists after more precise measurements, we will likely need an additional SU(3)-singlet contribution [5] or new physics beyond the Standard Model to explain it. Moreover, if the unitarity triangle angle φ 3 (or γ), defined by arg( , is greater than 90 degrees, as suggested from interpretations of B → Kπ, ππ results [6,7] under the factorization assumption, B + → η ′ K + will be enhanced relative to B 0 → η ′ K 0 [2,8]. Although expected to be small [9], it is also of interest to examine the direct CP asymmetry in B ± → η ′ K ± decays since new physics may contribute. In this paper we report on measurements of the branching fractions of B mesons decaying to η ′ K + , η ′ π + , and η ′ K 0 final states, where only the K 0 S → π + π − transition is considered for K 0 . Inclusion of charge conjugate modes is implied unless explicitly stated otherwise. The results are obtained from data collected by the Belle detector [10] at the KEKB asymmetric e + e − storage ring [11]. The data sample corresponds to an integrated luminosity of 10.4 fb −1 and consists of 11.1 million BB pairs at the Υ(4S) resonance. The branching fractions are calculated assuming that B + B − and B 0B0 are produced equally.
A detailed description of the Belle detector can be found in Ref. [10]; here we only describe briefly the parts used in this analysis. Charged tracks are reconstructed inside a 1.5 T solenoidal magnet with a three layer doublesided silicon vertex detector (SVD) and a central drift chamber (CDC) that consists of 50 layers segmented into 6 axial and 5 stereo superlayers. The CDC covers the polar angle range between 17 • and 150 • in the laboratory frame and, together with the SVD, gives a transverse momentum resolution of (σ pt /p t ) 2 = (0.0019 p t ) 2 +(0.0030) 2 , where p t and σ pt are in GeV/c. Charged kaon and pion identification is performed using a combination of three devices: an array of 1188 aerogelČerenkov counters (ACC) covering the momentum range 1-4 GeV/c, a time-of-flight scintillation counter system (TOF) for track momenta below 1.5 GeV/c, and dE/dx information from the CDC for particles with very low or high momenta. Situated between these devices and the solenoid coil is an electromagnetic calorimeter (ECL) consisting of 8736 CsI(Tℓ) crystals with typical cross-section of 5.5 × 5.5 cm 2 at the front surface and a depth of 16.2 X 0 . The ECL provides a photon energy resolution of (σ E /E) 2 = 0.013 2 + (0.0007/E) 2 + (0.008/E 1/4 ) 2 , where E and σ E are in GeV.
Charged tracks are required to come from the collision point and have transverse momenta p t above 100 MeV/c. These charged tracks are then refitted with their vertex position constrained to the run-averaged profile of B meson decay vertices in the transverse plane. For η ′ → ρ 0 γ decays, in order to reduce backgrounds, the minimum p t requirement is increased to 200 MeV/c. Charged K and π mesons coming directly from two-body B decays are identified by combining K/π probabilities from the CDC (dE/dx) and the ACC to form a K(π) likelihood L K (L π ). As these mesons have momenta above 1.5 GeV/c in the laboratory frame, TOF information does not provide any discrimination. Discrimination between kaons and pions is then achieved through the likelihood ratio, L K /(L π + L K ). The performance of hadron identification is studied using a high momentum D * + data sample, where D * + → D 0 π + , D 0 → K − π + . Selected K and π tracks are required to be in the same kinematic region as those from two-body B decays. We measure the pion and kaon identification efficiencies to be (92.4 ± 2.4)% and (84.9 ± 2.1)%, respectively. The rate for true pions to be misidentified as kaons is (4.3 ± 0.4)% while the rate for true kaons to be misidentified as pions is (10.4 ± 0.6)%. For charged pions from η ′ decays, tracks identified to be highly kaon-like (including TOF information) are rejected. This loose kaon rejection requirement is studied using K 0 S → π + π − events. The typical efficiency for charged pions is (98.2 ± 1.0)%. K 0 S candidates are reconstructed by constraining a pair of oppositely charged tracks with a common vertex. This vertex is required to be distinct from the collision point and consistent with the K 0 S flight direction. The invariant mass is required to be within ±30 MeV/c 2 of the nominal K 0 S mass.
Candidate B mesons are identified using the beam constrained mass M bc = E 2 beam − P 2 B and the energy difference ∆E = E B −E beam , where E beam = 5.29 GeV, and P B and E B are the momentum and energy of a B candidate in the Υ(4S) rest frame. In the B + → η ′ h + (h = K, π) study, E B is computed with a kaon mass hypothesis for h + , which results in a shift of +44 MeV in ∆E for η ′ π + events. This shift in ∆E provides additional discrimination between the η ′ K + and η ′ π + final states. The parameterizations of the signal in M bc and ∆E are determined by a GEANT [12] based Monte Carlo (MC) simulation and verified using a sample of B + →D 0 π + ,D 0 → K + π − π 0 events. The Gaussian width of the signal in M bc is about 2.9 MeV/c 2 , and mainly comes from the beam energy spread. The ∆E distribution is found to be slightly asymmetric with a small tail on the lower side due to γ interactions with material in front of the calorimeter and shower leakage out of the back side of the crystals. This ∆E distribution is modeled by a sum of two Gaussians, one of which is asymmetric. The signal region is defined as M bc > 5.27 GeV/c 2 and −0.10 GeV < ∆E < 0.08 GeV. Events located in the region M bc < 5.265 GeV/c 2 are defined as sideband events and are used for background studies. Events with M bc > 5.2 GeV/c 2 and |∆E| < 250 MeV are selected for the final analysis.
The dominant background for two-body B decay events comes from the e + e − → qq continuum. In order to reduce this background, several shape variables are chosen to distinguish spherical BB events from jet-like continuum events. The variable θ T is defined as the angle between the candidate η ′ direction and the thrust axis formed by the momenta of particles not from the B candidate. The continuum background, which accumulates mainly very near | cos θ T | = 1.0, is first reduced by requiring | cos θ T | < 0.9. Two other variables used are θ B , the angle between the B flight direction and the beam axis, and S ⊥ [13], the scalar sum of the transverse momenta of all particles outside a 45 • cone around the candidate η ′ direction divided by the scalar sum of their momenta. Furthermore, we introduce a set of variables inspired from the Fox-Wolfram moments [14], defined as: where p indicates particle momentum, P l is the Legendre polynomial of lth order, k is either η ′ or h from the B candidate, and i, j enumerate all remaining photons and charged particles in the event. Since R so 1 , R so 3 , and R oo 1 are found to be correlated with M bc , we do not use them. We combine the other five variables (l ≤ 4) together with cos θ T and S ⊥ to form a Fisher discriminant F , where α l , β l , c 1 and c 2 are determined by optimizing the separation between BB events and continuum events. For the channel with ργ in the final state, additional discrimination is gained by using the helicity variable H, which is the cosine of the angle between the π + momentum direction in the ρ rest frame and the ρ momentum direction in the η ′ rest frame. Although there is a small non-resonant contribution in the η ′ → π + π − γ process, experimental data [15] indicate that the helicity distribution can still be described by 1 − H 2 .
The variables cos θ B , F and H (for the ργ channel) are found to be independent. The probability density functions (PDF) for these variables are obtained using MC simulations for signal, and sideband events for qq background (see Fig. 2). These variables are then combined to form a likelihood ratio LR = L s /(L s + L qq ), where L s(qq) is the product of signal (qq) probability densities. Since each channel has a different background, we optimize the LR requirement mode by mode by studying the signal significance (N S / √ N S + N B ) using both MC and data samples, where N S and N B are signal yields and background yields, respectively. For instance, a loose LR requirement (LR > 0.4) for the ηπ + π − mode keeps 83% of the η ′ K + signal and reduces 74% of the background, while for the ργ mode a tighter requirement (LR > 0.6) is used with a signal efficiency of 70% and a background rejection of 88%. The effect of these requirements is studied by comparing B + →D 0 π + in data and MC with different values of LR. The background from b → c transitions is negligible as determined by MC study. Fig. 3 shows the M bc and ∆E distributions for the combined ηππ and ργ samples (and ηππ separately) in the η ′ K + , η ′ π + and η ′ K 0 S decay modes. Events in the M bc (∆E) plots are required to be in the ∆E (M bc ) signal region after all selection criteria are applied. Clear signal peaks appear in both the η ′ K + and η ′ K 0 S channels. The M bc and ∆E distributions in each sample are fitted simultaneously with signal and background functions using an extended unbinned maximum likelihood fit. For N input candidates, the likelihood is defined as where P S i and P B i are the probability densities for event i to be signal and background for variables M bc and ∆E, respectively. In the extended maximum likelihood (ML) fit, the extracted yields for signal (N S ) and for background (N B ) are considered separately to follow the Poisson statistics. In this definition, the sum of N S and N B equals the number of input candidates N when the likelihood is maximized. The M bc background shape is modeled with a smooth function [16] with parameters determined using events outside of the ∆E signal region. The ∆E background shape is modeled by a linear function with the slope determined from the sideband data and cross-checked using MC events. Since significant signal peaks are observed in the η ′ K + channel, we can expect contamination in the η ′ π + signal region from η ′ K + . Therefore, an η ′ K + signal shape is added in the ∆E PDF for η ′ π + . The final signal yields are then obtained by this two dimensional (2-D) fit with the statistical significance (Σ) defined as −2 ln(L 0 /L max ), where L 0 and L max denote the likelihood values at zero signal events and the best fit numbers, respectively. The second and third columns of Table 1 list the fit yields and their significances.
The systematic error for the signal yield is estimated by varying each parameter of the fit functions by ±1σ from the measured values. The shifts in signal yield are then added in quadrature. In order to study intrusions into the signal regions from other rare B decays, a large MC sample of all known rare B decay processes has been generated. No significant contributions are found.
Signal efficiencies are first obtained using MC simulations and corrected by comparing data and MC predictions for other processes. The tracking efficiency is studied using high momentum D, η and K * (892) samples. The γγ reconstruction efficiency is verified by measuring the branching ratio of two D 0 decay channels, D 0 → K − π + π 0 to D 0 → K − π + , and four K * (892) decay channels, K + π − , K + π 0 , K 0 S π + , and K 0 S π 0 . The simulation of low momentum photons is further tested by comparing the decay angular distribution of η for data with MC predictions. The systematic errors on the charged track reconstruction efficiencies of η ′ → ηπ + π − and η ′ → ργ are estimated by comparing the ratio of η → π + π − π 0 to η → γγ in data with MC expectations. The reconstruction of high momentum K 0 S is studied using the ratio of D + → K 0 S π + to D + → K − π + π + . The final systematic errors, including contributions from reconstruction efficiency, hadron identification and 2-D fits, are estimated to be 12% for the η ′ K + and η ′ π + modes, and 15% for the η ′ K 0 S mode. Table 1 summarizes the fit results for each reconstructed decay channel. The systematic errors for the branching fractions combine the above systematic errors with that from the number of BB events. Results from the ηπ + π − and ργ channels are then combined by adding the −2 ln L(BF ) functions of branching fractions with appoximating N = N S +N B and extracting the values and 1σ deviations at maximum L(BF ). Since no significant signal is seen in the η ′ π + mode, a 90% confidence level (C.L.) upper limit is given by finding the branching fraction that corresponds to 90% of the integral of L(BF ). The final upper limit is then computed by adding one standard deviation of the systematic error. The final branching fractions, significance, upper limit, and theoretical predictions are listed in Table 2. With 11.1 million BB events, we measure the branching fractions to be (79 +12 −11 ± 9) × 10 −6 for B + → η ′ K + and (55 +19 −16 ± 8) × 10 −6 for B 0 → η ′ K 0 . The first errors are statistical and the second systematic. The 90% C.L. upper limit for B + → η ′ π + is 7 × 10 −6 . Our results are consistent with previous measurements given by CLEO [4], but larger than theoretical predictions [2]. The results are also compatible with the preliminary results from BABAR [17]. The upper limit on η ′ π + is currently the most restrictive experimental result.
To study charge asymmetry, the η ′ K ± sample is divided into two subsamples: η ′ K + and η ′ K − . The 2-D fit in the M bc vs. ∆E plane is performed for each subsample. The fitted number of signal events in the η ′ → ηππ, and η ′ → ργ modes are 18.  N(B + )). Since the systematic errors on η ′ reconstruction and the number of BB events cancel in the ratio, the systematic uncertainty of A CP comes mainly from the reconstruction efficiency of charged kaons and the 2-D fit. The asymmetry in the K ± efficiency is studied using inclusive charged kaons. The latter is measured by varying the parameters of the fit functions. We find the systematic errors for A CP are 0.01 for K ± reconstruction and 0.01 for the 2-D fit [18]. The A CP for the B ± → η ′ K ± decay is finally measured to be +0.06 ± 0.15 ± 0.01, which corresponds to −0.20 < A CP < 0.32 at the 90% confidence level.
In summary, we have searched for charmless hadronic B decays with η ′ mesons in the final state. Our results confirm that the branching fractions of B + → η ′ K + and B 0 → η ′ K 0 are large. The branching fraction of B + → η ′ π + is less than 7×10 −6 at the 90% C.L. With about 70 B ± → η ′ K ± events, no significant charge asymmetry is observed. Our value for B → η ′ K + is somewhat larger than that for B → η ′ K 0 , as predicted under the factorization assumption, but the difference is not statistically significant. If this difference is confirmed with better precision, it will, along with a measurement of time dependent CP asymmetry in B 0 → η ′ K 0 , provide information to understand the underlying dynamics of B → η ′ K decays. Table 1 Summary of results for each channel listed in the first column. The measured signal yield (N S ), statistical significance (Σ), reconstruction efficiency (ǫ), total efficiency including the secondary branching fraction (B s ), and the measured branching fractions are shown. The branching fractions are calculated by assuming that B + B − and B 0B0 are produced equally from Υ(4S) decays. Uncertainties shown in 2nd and 6th columns are statistical only.  Table 2 Combined branching fractions (BF ) or 90% C.L. limit, significance (Σ) of Belle, CLEO [4], BABAR [17] and theoretical expectations [2,3]. The branching fractions are in units of 10 −6 .