aa r X i v : . [ h e p - e x ] J a n December 21, 2018
Measurements of Inclusive B → X u ℓν Decays
Concezio Bozzi
Istituto Nazionale di Fisica NucleareSezione di Ferrara, I-44122 Ferrara, ITALYon behalf of the Babar and Belle Collaborations
Recent results on inclusive charmless semileptonic decays of B mesonsare reviewed. Emphasis is given to measurements on the recoil of fullyreconstructed B mesons, which allow to exploit several regions of phasespace. Preliminary averages of the CKM matrix element | V ub | from theHeavy Flavour Working Group are shown, using four different theoreticalcalculations. PROCEEDINGS OF CKM2010 the 6th International Workshop on the CKM UnitarityTriangle, University of Warwick, UK, 6-10 September 2010 Introduction
Measurements of inclusive charmless semileptonic decays of B mesons, B → X u ℓν ,are directly related to the CKM matrix element | V ub | . The theoretical description [1]of the hadronic current involved in these decays, relying on the Operator Product Ex-pansion (OPE) technique, allows the determination of | V ub | from the total decay ratewith a small uncertainty. However, in order to suppress background from semilep-tonic decays with charm, B → X c ℓν , measurements of partial branching fraction areperformed in restricted kinematic regions. Unfortunately, OPE breaks down in someof these regions, and the theoretical uncertainty increases significantly. Contributionsdue to weak annihilation also play a role in part of the kinematic regions, and needto be carefully assessed. In short, theory and backgound subtraction give conflictingrequirements, and a trade-off must be found. Due to the improved knowledge of B → X c ℓν transitions and to the abundant data samples collected at the B factories,recent results based on phase space regions which are increasingly larger allow for animproved precision in the | V ub | determinations.Experimental measurements of charmless semileptonic decays are reviewed in Sec-tion 2, with emphasis on new preliminary results from Babar. Preliminary | V ub | averages from the Heavy Flavour Averaging Group by using the available theorycalculations are presented in Section 3. Conclusions are given in Section 4. Measurements in the endpoint region of the lepton momentum spectrum are concep-tually simple, being based on the identification of an high momentum lepton only.However, the kinematic region selected by the high lepton momentum requirementto suppress charmed background suffers from sizeable theoretical uncertainties. Allexperimental efforts [2] have been devoted to reducing the lepton momentum cut aslow as allowed by background knowledge. Signal-to-background ratios (S/B) of theorder of 1/10 have been achieved, with signal efficiencies at the 30% level or less.An improved analysis [3], based on the measurement of missing energy to estimatethe maximum kinematically allowed hadronic mass squared, s maxh , resulted in S/B ofabout 1/2. A summary of the available endpoint measurements is given in Table 1.The recoil technique aims at fully reconstructing one of the two B mesons ( B reco )from the Υ (4 S ) decay in a fully hadronic decay, which allows to determine completelythe decay kinematics of the other B ( B recoil ). It is therefore possible to access relevantkinematic variables, such as the invariant mass of the hadronic system, m X , the light-cone momentum component P + = E X − | ~p X | , and the squared invariant mass ofthe lepton pair, q . Semileptonic events are identified by an high-momentum lepton( p ∗ ℓ > L ( f b − ) E ℓ (GeV) ∆ B (10 − )E1 Babar 81.4 2.0–2.6 5 . ± . ± . . ± . ± . . ± . ± . s maxh < ) 81.4 2.0–2.6 4 . ± . ± . B ( B → X u ℓν ) (10 − )Babar R1 M X < .
55 GeV /c ±
73 1 . ± . ± . M X < .
70 GeV /c ±
82 1 . ± . ± . P + < .
66 GeV 902 ±
80 0 . ± . ± . q > /c ±
53 0 . ± . ± . p ∗ ℓ > /c, ( M X , q ) fit 1441 ±
102 1 . ± . ± . p ∗ ℓ > . /c ±
55 0 . ± . ± . p ∗ ℓ > /c, ( M X , q ) fit 1032 ±
91 1 . ± . ± . p ∗ ℓ > /c . The uncertainty onthe yields is statistical only.are subtracted by studying the distribution of the beam-energy substituted mass m ES for the B reco candidates. About 1000 hadronic modes are reconstructed, withefficiencies at the 0.3% (0.5%) level for neutral (charged) B decays.Background from B → X c ℓν is reduced mainly by vetoing charged kaons and K S ,whose production is highly suppressed in signal, and charged and neutral soft pionskinematically compatible with B → D ∗ ℓν decays.Both B Factory experiments published results using the recoil technique [4]. Babarrecently released [5] a preliminary update based on the full dataset (426 f b − ), whichis detailed in the following. The integrated luminosity analysed by Belle is 626 f b − .Partial rates for charmless semileptonic decays have been measured in severalphase space regions, defined in Table 2, as well as for charged and neutral B decaysseparately. The latter is achieved by explicitly requiring the (absolute) B reco chargeto be one or zero, respectively, after subtacting with Monte Carlo a small fractionof events where the B reco charge was not correctly reconstructed. In addition to the m X , P + and ( m X , q ) distributions, the lepton momentum p ∗ ℓ was also studied. Abackground-enriched control sample, obtained by reversing the vetoes on kaons andsoft pions mentioned above, was used to determine the relative contribution due tosemileptonic decays into P-wave D mesons directly on data; Monte-Carlo simulation2 (GeV/c X M E n t r i e s / b i n -1000100200300 ) (GeV/c X M E n t r i e s / b i n -1000100200300 E n t r i e s / b i n E n t r i e s / b i n (a) (GeV/c) + P E n t r i e s / b i n (GeV/c) + P E n t r i e s / b i n E n t r i e s / b i n E n t r i e s / b i n (b) ) /c (GeV q E n t r i e s / b i n < 1.7 GeV/c X M ) /c (GeV q E n t r i e s / b i n E n t r i e s / b i n E n t r i e s / b i n < 1.7 GeV/c X M (c) (GeV/c) l p* E n t r i e s / b i n (GeV/c) l p* E n t r i e s / b i n E n t r i e s / b i n E n t r i e s / b i n (d) Figure 1: Upper row: M X (a), P + (b), q with M X < . /c (c) and p ∗ ℓ (d)spectra (data points), measured in Babar data. The result of the fit to the sum ofthree MC contributions is shown in the histograms: B → X u ℓν decays generatedinside (no shading) and outside (dark shading) the selected kinematic region, and B → X c ℓν and other background (light shading). Lower row: corresponding spectrafor B → X u ℓν (not corrected for efficiency) after background subtraction.was then reweighted accordingly. Although the impact on signal yields was almostnegligible, the fit chisquares improved significantly.The event yields and partial branching fractions are given in Table 2. The distribu-tions of the kinematic variables under study, before and after background subtraction,are shown in Figure 1. Statistical uncertainties range from 7% to 9%.A summary of the systematic uncertainties is given in Table 3, which also showsthe corresponding uncertainties from the Belle recoil analysis. The statistical andexperimental systematic uncertainties are of the same order. Detector-related uncer-tainties are dominated by undetected or mismeasured particles ( e.g. K L and addi-tional neutrinos) from background. Progress on the knowledge of exclusive B → X c ℓν decays reflects in a relatively small uncertainty due to background composition. In themost inclusive phase space region (R5), the dominant uncertainty is due to the signalmodel, in particular to the knowledge of heavy quark parameters and the branchingfraction of exclusive B → X u ℓν decays, which are used in the simulation to determinesignal efficiency. Total uncertainties range between 9% and 13%.Measurements of partial rates for charged and neutral B mesons allow to determinethe relative contribution of weak annihilation to the total rate, γ W A / Γ. The resulting90% confidence level regions are reported in Table 4; they are in agreement withprevious determinations [6]. 3abar BelleSource R1 R2 R3 R4 R5 R6 R5Statistical error 7.1 8.9 8.9 8.0 7.1 8.9 8.8MC statistics 1.3 1.3 1.3 1.6 1.1 1.2Detector-related: 2.8 3.7 5.5 4.1 3.2 2.7 3.3Fit-related: 2.7 4.9 3.2 3.2 2.1 2.5 3.6Signal model: 2.7 3.0 3.5 1.9 6.6 7.9 6.3Background model: 2.0 2.6 3.4 2.8 2.8 2.2 1.7Total systematics: . − . . − . . − . . − . . − . . − . ± . . − . . − . . − . . − . . − . . − . ± . | V ub | determinations The value of | V ub | is related to the measured partial branching fractions by | V ub | = vuut ∆ B ( B → X u ℓν ) τ B · ∆Γ theory , (1)where the B → X u ℓν width according to the applied cuts, ∆Γ theory , and its un-certainty are determined by four theoretical calculations [8, 9, 10, 11]. Theoreticaluncertainties can be divided in parametric terms, due to uncertainties on heavy quarkparameters and α s , and non-parametric contributions due, for instance, to higher or-der terms in the heavy quark expansion, weak annihilation, leading and subleadingshape functions, renormalization scale.The procedure for performing the averages is documented in [7]. The average Blifetime used is 1.578 ps. The input values for the heavy quark parameters have beendetermined by a global fit in the kinetic scheme, translated to the scheme needed byPhase Space Region ( R + / −
1) 90% C.L. on γ W A / ΓR1 -0.020 ± ± − . , . ± ± − . , . ± ± − . , . ± ± − . , . R + / −
1) and limits on γ W A / Γ for the various kinematic regionsunder study by Babar. 4 in. Expt. BLNP DGE GGOU ADFRregion [8] [9] [10] [11]Endpoint analysesE1 Babar 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . E2 Belle 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . E3 CLEO 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . E4 Babar 4 . ± . +0 . − . . ± . +0 . − . n.a. 3 . ± . +0 . − . Sim.ann. Belle 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . Recoil AnalysesR1 Babar 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . R2 Babar 3 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . R3 Babar 3 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . R4 Babar 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . R5 Babar 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . R6 Babar 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . R5 Belle 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . Average 4 . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . . ± . +0 . − . χ /d.o.f. (CL) 12.2/11 (0.36) 7.52/11 (0.76) 12.2/10 (0.27) 28.2/11 (0.003) Table 5: Results for | V ub | obtained with four theoretical calculations. The uncer-tainties are experimental ( i.e. sum of statistical and experimental systematical) andtheoretical, respectively. The phase space regions are defined in Tables 1 and 2.each model, where both b → cℓν and b → sγ moments are used, giving m b ( kin ) =4 . ± .
031 GeV, µ π ( kin ) = 0 . ± .