Measurement of the decay $B^0\toπ^-\ell^+ν$ and determination of $|V_{ub}|$

0.2 MB·English

by  H. Ha

Belle Preprint 2010-22
KEK Preprint 2010-37
Measurement of the decay B0 → π−ℓ+ν and determination of |Vub|
H. Ha,20 E. Won,20 I. Adachi,8 H. Aihara,48 T. Aziz,43 A. M. Bakich,42 V. Balagura,15 E. Barberio,26 A. Bay,22
K. Belous,14 V. Bhardwaj,38 B. Bhuyan,11 M. Bischofberger,28 A. Bondar,1,36 A. Bozek,32 M. Braˇcko,24,16
T. E. Browder,7 Y. Chao,31 A. Chen,29 P. Chen,31 B. G. Cheon,6 C.-C. Chiang,31 I.-S. Cho,53 K. Cho,19
K.-S. Choi,53 Y. Choi,41 J. Dalseno,25,44 M. Danilov,15 Z. Doleˇzal,2 A. Drutskoy,3 W. Dungel,13 S. Eidelman,1,36
N. Gabyshev,1,36 B. Golob,23,16 J. Haba,8 K. Hayasaka,27 H. Hayashii,28 Y. Horii,47 Y. Hoshi,46 W.-S. Hou,31
Y. B. Hsiung,31 H. J. Hyun,21 T. Iijima,27 K. Inami,27 R. Itoh,8 M. Iwabuchi,53 Y. Iwasaki,8 N. J. Joshi,43
1 T. Julius,26 J. H. Kang,53 T. Kawasaki,34 C. Kiesling,25 H. J. Kim,21 H. O. Kim,21 M. J. Kim,21 S. K. Kim,40
1 Y. J. Kim,5 K. Kinoshita,3 B. R. Ko,20 S. Korpar,24,16 P. Kriˇzan,23,16 T. Kuhr,18 T. Kumita,49 A. Kuzmin,1,36
0
Y.-J. Kwon,53 S.-H. Kyeong,53 J. S. Lange,4 M. J. Lee,40 S.-H. Lee,20 Y. Li,51 A. Limosani,26 C. Liu,39 Y. Liu,31
2
D. Liventsev,15 R. Louvot,22 S. McOnie,42 K. Miyabayashi,28 H. Miyata,34 Y. Miyazaki,27 G. B. Mohanty,43
n
T. Mori,27 Y. Nagasaka,9 E. Nakano,37 M. Nakao,8 H. Nakazawa,29 Z. Natkaniec,32 S. Neubauer,18 S. Nishida,8
a
J K. Nishimura,7 O. Nitoh,50 T. Nozaki,8 S. Ogawa,45 T. Ohshima,27 S. Okuno,17 S. L. Olsen,40,7 P. Pakhlov,15

8 G. Pakhlova,15 C. W. Park,41 H. Park,21 H. K. Park,21 R. Pestotnik,16 M. Petriˇc,16 L. E. Piilonen,51 M. Ro¨hrken,18
2 S. Ryu,40 H. Sahoo,7 Y. Sakai,8 O. Schneider,22 C. Schwanda,13 A. J. Schwartz,3 K. Senyo,27 M. E. Sevior,26

M. Shapkin,14 C. P. Shen,7 J.-G. Shiu,31 F. Simon,25,44 P. Smerkol,16 Y.-S. Sohn,53 A. Sokolov,14 S. Staniˇc,35
]
x M. Stariˇc,16 T. Sumiyoshi,49 Y. Teramoto,37 K. Trabelsi,8 S. Uehara,8 T. Uglov,15 Y. Unno,6 S. Uno,8
e
S. E. Vahsen,7 G. Varner,7 K. E. Varvell,42 A. Vossen,10 C. H. Wang,30 M.-Z. Wang,31 P. Wang,12 M. Watanabe,34
-
p Y. Watanabe,17 Y. Yamashita,33 Z. P. Zhang,39 P. Zhou,52 V. Zhulanov,1,36 T. Zivko,16 and A. Zupanc18
e
h (The Belle Collaboration)
[ 1Budker Institute of Nuclear Physics, Novosibirsk
4 2Faculty of Mathematics and Physics, Charles University, Prague
v 3University of Cincinnati, Cincinnati, Ohio 45221
0 4Justus-Liebig-Universit¨at Gießen, Gießen
9 5The Graduate University for Advanced Studies, Hayama
0 6Hanyang University, Seoul
0 7University of Hawaii, Honolulu, Hawaii 96822
2. 8High Energy Accelerator Research Organization (KEK), Tsukuba
1 9Hiroshima Institute of Technology, Hiroshima
0 10University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
1 11Indian Institute of Technology Guwahati, Guwahati
: 12Institute of High Energy Physics, Chinese Academy of Sciences, Beijing
v
13Institute of High Energy Physics, Vienna
i
X 14Institute of High Energy Physics, Protvino
15Institute for Theoretical and Experimental Physics, Moscow
r
a 16J. Stefan Institute, Ljubljana
17Kanagawa University, Yokohama
18Institut fu¨r Experimentelle Kernphysik, Karlsruher Institut fu¨r Technologie, Karlsruhe
19Korea Institute of Science and Technology Information, Daejeon
20Korea University, Seoul
21Kyungpook National University, Taegu
22E´cole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne
23Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana
24University of Maribor, Maribor
25Max-Planck-Institut fu¨r Physik, Mu¨nchen
26University of Melbourne, School of Physics, Victoria 3010
27Nagoya University, Nagoya
28Nara Women’s University, Nara
29National Central University, Chung-li
30National United University, Miao Li
31Department of Physics, National Taiwan University, Taipei
32H. Niewodniczanski Institute of Nuclear Physics, Krakow
33Nippon Dental University, Niigata
2
34Niigata University, Niigata
35University of Nova Gorica, Nova Gorica
36Novosibirsk State University, Novosibirsk
37Osaka City University, Osaka
38Panjab University, Chandigarh
39University of Science and Technology of China, Hefei
40Seoul National University, Seoul
41Sungkyunkwan University, Suwon
42School of Physics, University of Sydney, NSW 2006
43Tata Institute of Fundamental Research, Mumbai
44Excellence Cluster Universe, Technische Universita¨t Mu¨nchen, Garching
45Toho University, Funabashi
46Tohoku Gakuin University, Tagajo
47Tohoku University, Sendai
48Department of Physics, University of Tokyo, Tokyo
49Tokyo Metropolitan University, Tokyo
50Tokyo University of Agriculture and Technology, Tokyo
51CNP, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
52Wayne State University, Detroit, Michigan 48202
53Yonsei University, Seoul
WepresentameasurementofthecharmlesssemileptonicdecayB0 →π−ℓ+ν usingadatasample
containing 657×106 BB¯ events collected with the Belle detector at the KEKB asymmetric-energy
e+e− collider operating near the Υ(4S) resonance. We determine the total branching fraction of
thedecay,B(B0 →π−ℓ+ν)=(1.49±0.04(stat)±0.07(syst))×10−4. Wealso report anew precise
measurement of the differential decay rate, and extract the Cabibbo-Kobayashi-Maskawa matrix
element |Vub| using model-independent and model-dependent approaches. From a simultaneous fit
tothemeasureddifferentialdecayrateandlatticeQCDresults,weobtain|Vub|=(3.43±0.33)×10−3,
where theerror includes both experimental and theoretical uncertainties.
PACSnumbers: 12.15.Hh,13.20.He,12.38.Qk
Weak transitions among quark flavors in the standard range [8, 9], resulting in |Vub| = (3.38 ± 0.36)× 10−3
model (SM) are described by the Cabibbo-Kobayashi- using the experimental data in Ref. [10] for the decay
Maskawa (CKM) matrix [1], in which |Vub| is one of the B0 → π−ℓ+ν where the error includes both theoretical
least known elements. Precise measurements of the val- and experimental uncertainties. The experimental un-
ues of the CKM matrix elements are necessary to probe certainty is a 6% while the theoretical contribution is
thequarkmixingmechanismoftheSMandtosearchfor estimated to be an 8.5% [9]. In addition, Ref. [11] re-
possible physics beyond the SM. The magnitude of the ports |Vub| = (2.95±0.31)× 10−3 by combining mea-
CKMelementVub canbe determinedfromexclusiveb→ surements of B0 → π−ℓ+ν and B+ → π0ℓ+ν; here the
uℓν semileptonicdecays,ofwhichB0 →π−ℓ+ν [2]yields errorcontainsa3%contributionfromthebranchingfrac-
the most precise value for |Vub|. The differential rate of tion measurement, a 5% from the shape of the q2 spec-
thisdecaycanbeexpressedintermsof|Vub|andtheform trum measured in data, and an 8.5% from the theoreti-
factor f (q2), where q2 is the square of the momentum calnormalization. Herewedescribe astudy ofthe decay
+
transferred from the B meson to the outgoing leptons, B0 →π−ℓ+ν andmeasurethebranchingfractionandthe
q2 = (pℓ+pν)2 [3]. The present theoretical understand- q2 spectrum. We thencomparewithotherrecentstudies
ing of f (q2) is limited, which is a significant source for of this decay [10–15]. The differential branching frac-
+
systematicuncertaintyintheextractionof|Vub|fromthis tionis measuredin13binsofq2,and|Vub| isdetermined
decay. Predictionshavebeenobtainedinunquenchedlat- usingboth model-independent andmodel-dependent ap-
ticeQCD [4,5],inlightconesumrule(LCSR)theory[6] proaches.
and in relativistic quark models [7]. However, these pre-
dictions typically assume a specific shape for f (q2) and The Belle detector [16, 17] is a large-solid-angle mag-
+
provide reliable predictions only in a limited q2 range neticspectrometerthatconsistsofasiliconvertexdetec-
(lattice QCD is valid near q2 maximum, while LCSR tor (SVD), a 50-layer central drift chamber (CDC), an
is reliable near the minimum value of q2). Recently, it array of aerogel threshold Cherenkov counters (ACC),
has been shown that a determination of |Vub| indepen- a barrel-like arrangement of time-of-flight scintillation
dent of a form factor shape calculation can be achieved counters (TOF), and an electromagnetic calorimeter
by simultaneously fitting the measured q2 spectrum and composed of CsI(Tl) crystals (ECL) located inside a su-
lattice QCD results computed near the zero recoil of q2 perconducting solenoid coil that provides a 1.5 T mag-
neticfield. Anironflux-returnlocatedoutsideofthecoil
3
is instrumented with resistive plate chambers to detect that of the missing energy. To select events compati-
K0 mesons and to identify muons (KLM). ble with the signal decay mode, we require |Q | ≤
L total
Thedatasamplecorrespondstoanintegratedluminos- 3, where Qtotal is the net charge of the event, and
ity of 605 fb−1 taken at a center-of-mass (c.m.) energy E > 0 GeV. We denote the combined system of
miss
neartheΥ(4S)resonance,containing657×106BB¯ pairs. the signal pion and lepton as Y. The kinematics of
For the first sample of 152×106 BB¯ events, an inner de- the decay constrain the cosine of the angle between
tector configuration with a 2.0 cm beampipe and a 3- the B and Y directions in the c.m. frame, defined by
layer SVD was used, while a 1.5 cm beampipe, a 4-layer cosθBY = (2EbeamEY −m2B −MY2)/(2|p~B||p~Y|), where
SVD and a small-cell inner drift chamber were used to mB and|pB|=pEb2eam−m2B refertothemassandmo-
record the remaining 505×106 BB¯ pairs [18]. Another mentum of the B meson, and EY, MY, and pY refer to
68 fb−1 data sample taken at a c.m. energy 60 MeV be- the energy, mass, and momentum of the reconstructed
low the resonance is used to study the continuum back- Y. Background, on the other hand, is not similarly con-
ground, e+e− → qq¯, where q = u,d,s,c. Monte Carlo strained. In what follows we require |cosθBY| ≤ 1.
(MC) [19, 20] simulated events equivalent to at least ten Signal candidates are classified by their beam-energy-
times the integratedluminosity weregeneratedto model constrainedmass,Mbc =pEb2eam−|p~π +~pℓ+~pν|2,and
thesignal. Samplesequivalenttotentimesandsixtimes energy difference, ∆E =Ebeam−(Eπ +Eℓ+Eν). Can-
the integratedluminosity weregeneratedtosimulate the didates outside of the signal region, defined by the re-
two largest background components, b → c decays and quirements M > 5.19 GeV/c2 and |∆E| < 1 GeV,
bc
continuum, respectively. To simulate rare b→u decays, are rejected. To suppress background from the contin-
samples equivalent to twenty times the integrated lumi- uum, the ratio of second to zeroth Fox-Wolfram mo-
nosity were generated. Final state radiation (FSR) from ments [25] is required to be less than 0.35. Background
charged particles in the final state is modeled using the from J/ψ → µ+µ− decays with one muon misidentified
PHOTOS package [21]. as a pion is rejected by vetoing events with a Y mass
The decay B0 → π−ℓ+ν is reconstructed from pairs between 3.07 GeV/c2 and 3.13 GeV/c2. The sample of
of oppositely chargedleptons and pions. Electroncandi- signal candidates is divided into 13 bins of q2 from 0 to
datesareidentifiedusingtheratiooftheenergydetected
in the ECL to the track momentum, the ECL shower
shape, position matching between the track and ECL 0 < q2 < 16 GeV2/c2 q2 > 16 GeV2/c2
cluster, the energy loss in the CDC, and the response MeVMeV44000000 (a) B0 fi p l n (b)
oftheACCcounters[22]. Bremsstrahlungphotonsemit- 5 5 B fi Xu l n 22000000
121233000000 B fi Xc l n
tuesdedcltoosecotroretchtetehleecetlreocntrdoinremctoiomnenatruemrec[2o3n]s.trMucutoendsaanrde vents / vents / 22000000 ConDtaintauum 11550000
identifiedbasedontheirpenetrationrangeandtransverse EE 11000000
scattering in the KLM detector [24]. In the momentum
11000000
550000
regionrelevanttothisanalysis,chargedleptonsareiden-
tifiedwithanefficiencyofabout90%whilethe probabil-
00--11 --00..55 00 00..55 11 00--11 --00..55 00 00..55 11
ity to misidentify a pion as an electron (muon) is 0.25% DD EE ((GGeeVV)) DD EE ((GGeeVV))
(1.4%). Pion candidates are selected with an efficiency
obfas8e5d%onantdhearkesapoonnmseissiodfenthtiefiCcaDtiCon, ApCroCbaabnidlitTyOoFf 1s9u%b-, 22MeV/cMeV/c44000000 (c) 22000000 (d)
detectors. All chargedparticles are requiredto originate 25 25 33000000
6.6. 11550000
from the interaction point (IP) and to have associated s / s /
hits in the SVD. The pion and lepton candidates are fit- entent22000000 11000000
vv
tedtoacommonvertexandtheconfidencelevelofthefit EE
11000000 550000
isrequiredtobegreaterthan1.0%. Theelectron(muon)
isrequiredtohavealaboratoryframemomentumgreater
00 55..22 55..2222 55..2244 55..2266 55..2288 00 55..22 55..2222 55..2244 55..2266 55..2288
than 0.8 GeV/c (1.1 GeV/c). MM ((GGeeVV//cc22)) MM ((GGeeVV//cc22))
bbcc bbcc
The missing energy and momentum in the c.m. frame
are defined as Emiss ≡ 2Ebeam − PiEi and p~miss ≡ FIG.1: Fitprojections(a,b)in∆EwithMbc>5.27GeV/c2,
−Pi~pi,respectively,whereEbeam isthebeamenergyin atinodns(c(,a,cd)) ainndM(bbc,dw)itshhow|∆Eth|e<reg0i.o1n2s5qG2eV<. 1T6heGepVro2j/ecc2-
the c.m. frame, and the sums include all charged and and q2 > 16 GeV2/c2, respectively. The points with er-
neutral particle candidates in the event. A threshold ror bars are Υ(4S) data, the histograms are (from top to
energy of 50 (100) MeV is required for photon candi- bottom) B0 → π−ℓ+ν signal (open), B → Xuℓν (cross-
dates in the central (side) region of the ECL. The neu- hatched), B → Xcℓν (hatched) and continuum background
trino 4-momentum is taken to be pν = (|p~miss|, p~miss), (black-filled). Thesmallererrorbarsarestatisticalonlywhile
since the determination of ~p is more accurate than thelarger ones include systematic uncertainties.
miss
4
26.4 GeV2/c2 (the bin width is 2 GeV2/c2, except for The partial branching fractions ∆B are calculated us-
the last bin). The value of q2 is calculated as the square ing the signal efficiencies obtained from MC simulation.
ofthe difference between the 4-momentaof the B meson The total branching fraction B is the sum of partial
andthatofthepion. AstheB directionisonlykinemati- branchingfractionstakingintoaccountcorrelationswhen
callyconstrainedtolieonaconearoundtheY direction, calculating the errors. We find B(B0 → π−ℓ+ν) =
we take a weighted average over four different possible (1.49±0.04(stat)±0.07(syst))×10−4,wherethe firster-
configurationsoftheB direction[26]. Backgroundisfur- roris statisticaland the seconderroris systematic. This
ther suppressed by applying selection criteria as a func- resultissignificantlymoreprecisethanourpreviousmea-
tion of q2 to the following quantities: the angle between surement[13]withB →D(∗)ℓ+ν tagsona253fb−1 data
the thrust axis of the Y system and the thrust axis of sample.
therestoftheevent;theangleofthemissingmomentum
To estimate the systematic uncertainties on ∆B, we
with respect to the beam axis; the helicity angle of the
include the following contributions: the uncertainties in
ℓνsystem[27];andthemissingmasssquaredoftheevent,
lepton and pion identification, the charged particle re-
M2 =E2 −p~ 2 . Thehelicityangleistheanglebe-
miss miss miss construction,the photondetection efficiency,andthe re-
tween the lepton direction and the direction opposite to quirement on the χ2 probability of the vertex fit, which
the B meson in the ℓν rest frame. These selections are
is estimated by comparing results with and without this
optimizedseparatelyineachbinofq2 bymaximizingthe
requirement. The results are summarized as detector ef-
figure-of-meritS/p(S+B),whereS (B)istheexpected fects in Table I. They depend weakly on q2 and amount
number of signal (background) events. to 3.4% for the entire q2 range. We vary the branching
The fraction of events that have multiple candidates fractions of the decays contributing to the b → uℓν and
is 66%. To remove multiple signal candidates in a single b → cℓν backgrounds within ±1 standard deviation of
event,thecandidatewiththesmallestℓν helicityangleis theirworld-averagevalues [31]andassignanuncertainty
selected. After imposing all selections described above, of 0.6% to the total yield. We further consider form fac-
the reconstruction efficiency for signal ranges from 7.7% tor uncertainties in the decays B0 →π−ℓ+ν [14], B0 →
to 15.0% over the entire q2 range. The fraction of the ρ−ℓ+ν [6, 32], B0 → D−ℓ+ν and B0 → D∗−ℓ+ν [33],
self-cross-feed component, in which one or more of the and uncertainties in the shape function parameters of
signal tracks are not correctly reconstructed, is 3.5%. the inclusive b → uℓν model [34]. These uncertainties
The signal yield is determined by performing a two-
dimensional, binned maximum likelihood fit to the
(M ,∆E) plane in 13 bins of q2 [28]. Background con-
bc
tributions from b → uℓν, b → cℓν and non-BB¯ con-
· 10-6
tinuum are considered in the fit. Probability density
2
c20
functions (PDFs) corresponding to these fit components 2/
V
are obtained from MC simulations. To reduce the num- e18
G
ber of free parameters, the q2 bins of the background 2
components are grouped into coarser bins: four bins for ) / 16
2q
b → uℓν, and three bins for b → cℓν. The choice of the B(14
binning was chosenfrom the total statisticalerror,num-
D 12
ber of parameters to fit, and the complexity of the fits.
Theq2 distributionofthe continuumMC[29]simulation 10
is reweighted to match the corresponding distribution in
8
ISGW2
off-resonancedata. For this procedure,a continuumMC
sample about 60 times the integrated luminosity of the 6 HPQCD
off-resonance data is used. The continuum normaliza- FNAL
4
tionisfixedtothescalednumberofoff-resonanceevents, LCSR
52928events. Includingsignalyieldsineachq2 bin,there 2 Data
are 20 free parameters in the fit. 0
0 5 10 15 20 25
We obtain 21486 ± 548 signal events, 52543 ± 1148
Unfolded q2 (GeV2/c2)
b → uℓν events, and 161829±976 b → cℓν background
events. These yields agree well with the expectations
FIG. 2: Distribution of the partial branching fraction as
from MC simulation studies. The χ2/n.d.f. of the fit is a function of q2 after unfolding (closed circles). The er-
2962/3308. The projections of the fit result in ∆E and ror bars show the statistical and the total uncertainty on
Mbc areshowninFig.1forthe regionsq2 <16GeV2/c2 the data. The curve is the result of a fit of the BK form
and q2 > 16 GeV2/c2. Bin-to-bin migrations due to factor parameterization [35] to our data. The four his-
q2 resolutionarecorrectedbyapplyingtheinversedetec- tograms (dashed:ISGW2; plain:HPQCD; dotted:FNAL; dot-
dashed:LCSR) show various form factor predictions.
tor response matrix [30] to the measured partial yields.
5
TABLEI:Valuesof∆B(q2)andrelativeuncertainties(%). TheuncertaintiesinMCinputparametersaregivenseparatelyfor
branchingfractions (BF) and form factors (FF).
q2(GeV2/c2) 0 - 6 6 - 12 12 - 18 18 - 26.4 0 - 16 16 - 26.4 Total
∆B (× 107) 391.19 434.25 389.47 279.18 1096.34 397.75 1494.09
Detectoreffects 3.4 3.5 3.5 3.5 3.4 3.5 3.4
Physics parameters (BF) 0.8 0.7 0.6 0.7 0.6 0.6 0.6
Physics parameters (FF) 1.9 1.7 1.9 1.8 1.3 1.8 1.1
Continuum correction 4.4 2.3 3.4 2.3 2.1 2.6 1.8
Othersources 2.1 2.5 2.4 2.4 2.1 2.3 2.0
Total statistical error 5.3 3.9 4.8 6.1 3.0 5.3 2.6
Total error 8.2 6.5 7.5 8.1 5.7 7.5 5.2
correspond to a 1.1% error on B(B0 → π−ℓ+ν). The product of the form factor f (q2) and the functions P
+ +
∞ i
uncertainty in the correction of the continuum MC is andφ+ hasthesimpleform,Pi=0aiz . Wefitthelattice
estimated by varying its weights by their statistical un- QCD results and experimental data with a third-order
certainties. The other sources of systematic uncertainty polynomial where the free parameters of the fit are the
in Table I include the uncertainty in the Υ(4S)→B0B¯0 coefficientsaiandtherelativenormalizationbetweenlat-
branching fraction [31], limited MC statistics, the effect ticeQCDresultsandexperimentalresults,whichis|Vub|.
of final state radiation,which is estimated by investigat- Theresultingexperimentaldata(whicharescaledbythe
ing MC samples with and without bremsstrahlung cor- fitted |Vub| value) andthe lattice QCDresults areshown
rections calculated using the PHOTOSpackage,and the in Fig. 3. We obtain |Vub| = (3.43±0.33)×10−3, a0 =
uncertainty in the number of BB¯ pairs in the data sam- 0.022±0.002, a =−0.032±0.004, a =−0.080±0.020
1 2
ple. For values of∆B in individual q2 bins, a breakdown and a = 0.081±0.066, where the χ2/n.d.f. of the fit is
3
of the systematic uncertainties is presented in Table V approximately12/20. Statistically,wefindnosignificant
andthestatisticalandsystematiccorrelationsisgivenin difference in the fitted value of |Vub| using second- and
Table III and Table IV. fourth-orderpolynomialfits. Note that the errorin|Vub|
We fit the ∆B distribution using the two-parameter includesbothexperimentalandtheoreticaluncertainties.
BK parameterization [35] of f (q2), taking into account We find that the error includes a 3% contribution from
+
statistical and systematic correlations. The result is thebranchingfractionmeasurement,a4%fromq2 shape
shown in Fig. 2. Although this parameterization has
beencriticized[36],wepresentthefitresultinordertodi-
rectlycomparewithotherexistingresults[10]. Weobtain
|Vub|f+(0)=(9.24±0.18(stat)±0.21(syst))×10−4 and 0.04
+
α = 0.60±0.03(stat)±0.02(syst), where α is a positive f
+ MILC lattice points
coofntshteanfitttihsa6t2%sc.alWesewailtshomcaBlcu[3la5t].e tThheeχχ22prporboabbaibliitliiteys f P+0.035 Belle data scaled by |Vub| from fit
Simultaneous fit
of different theoretical form factor predictions with our 0.03
binned data. We obtain probabilities of 42% and 43%
for the HPQCD [4] and the FNAL [5] lattice QCD cal- 0.025
culations,respectively,and49%fortheLCSRtheory[6].
TheISGW2quarkmodel[7],forwhichthe probabilityis 0.02
2.3×10−6, is incompatible with the experimental data.
0.015
AsdescribedinRef.[9],theCKMmatrixelement|Vub|
canbeextractedfromasimultaneousfittoexperimental
0.01
andlatticeQCDresults(fromtheFNAL/MILCCollabo- -0.3 -0.2 -0.1 0 0.1 0.2
z
ration[9]),takingintoaccountstatisticalandsystematic
correlations. To this end, the q2 variable is transformed
FIG. 3: |Vub| extraction from a simultaneous fit of exper-
toadimensionlessvariablez [8,36]. Inaddition,thetwo imental (closed circles) and FNAL/MILC lattice QCD re-
functions, P+ andφ+ aretakenfromRef.[37],whereP+ sults (open circles) [9]. The error for each experimental data
is a function that accounts for the pole at q2 =m2 and pointisthetotalexperimentaluncertainty. Thesmallererror
B∗
φ is an analyticfunction that controlsthe values ofthe bars of the lattice QCD results are statistical only while the
+
ai series coefficients. In terms of the new variable z, the larger ones also includesystematic uncertainties.
6
TABLEII:Valuesextractedfor|Vub|usingdifferentformfac-
tor predictions. The first error on |Vub| is the experimental
error including statistical, systematic uncertainties and the [1] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49,
uncertainty in the B0 lifetime [31], the last asymmetric er- 652(1973);N.Cabibbo,Phys.Rev.Lett.10,531(1963).
rors arise from theuncertainty in ∆ζ. [2] Throughout this paper, the inclusion of the charge-
conjugatedecaymodeisimpliedunlessotherwisestated.
f+(q2) q2 (GeV2/c2) ∆ζ (ps−1) |Vub| (10−3) [3] M. Neubert,Phys.Rept. 245, 259 (1994).
HPQCD [4] >16 2.07±0.57 3.55±0.13+−00..6421 [4] E. Dalgic, A. Gray, M. Wingate, C. T. H. Davies,
FNAL [5] >16 1.83±0.50 3.78±0.14+0.65 G.P.LepageandJ.Shigemitsu,Phys.Rev.D73,074502
−0.43 (2006). [Erratum-ibid. D 75, 119906 (2007)].
LCSR [6] <16 5.44±1.43 3.64±0.11+−00..6400 [5] M. Okamoto et al., Nucl. Phys. Proc. Suppl. 140, 461
(2005).
[6] P. Ball and R.Zwicky,Phys. Rev.D 71, 014015 (2005).
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7
TABLE III:Correlation coefficients of the∆B(B0 →π−ℓ+ν) statistical errors.
q2(GeV2/c2) 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26.4
0-2 1.000 -0.275 0.109 0.036 0.021 0.020 0.031 -0.005 -0.001 -0.002 -0.003 -0.004 -0.007
2-4 -0.275 1.000 -0.292 0.168 -0.008 0.026 0.029 -0.005 -0.001 -0.002 -0.004 -0.003 -0.004
4-6 0.109 -0.292 1.000 -0.229 0.156 0.049 0.101 -0.014 -0.003 -0.005 -0.004 -0.004 -0.002
6-8 0.036 0.168 -0.229 1.000 -0.255 0.123 0.064 -0.009 -0.003 -0.004 -0.003 -0.002 -0.003
8-10 0.021 -0.008 0.156 -0.255 1.000 -0.156 0.225 -0.032 -0.001 -0.004 -0.004 -0.004 -0.006
10-12 0.020 0.026 0.049 0.123 -0.156 1.000 -0.054 0.023 -0.007 -0.002 -0.006 -0.007 -0.009
12-14 0.031 0.029 0.101 0.064 0.225 -0.054 1.000 -0.239 0.007 -0.028 -0.007 -0.011 -0.013
14-16 -0.005 -0.005 -0.014 -0.009 -0.032 0.023 -0.239 1.000 -0.013 0.144 -0.030 -0.006 -0.010
16-18 -0.001 -0.001 -0.003 -0.003 -0.001 -0.007 0.007 -0.013 1.000 0.101 -0.028 -0.002 -0.004
18-20 -0.002 -0.002 -0.005 -0.004 -0.004 -0.002 -0.028 0.144 0.101 1.000 -0.167 -0.025 -0.040
20-22 -0.003 -0.004 -0.004 -0.003 -0.004 -0.006 -0.007 -0.030 -0.028 -0.167 1.000 -0.036 0.006
22-24 -0.004 -0.003 -0.004 -0.002 -0.004 -0.007 -0.011 -0.006 -0.002 -0.025 -0.036 1.000 -0.111
24-26.4 -0.007 -0.004 -0.002 -0.003 -0.006 -0.009 -0.013 -0.010 -0.004 -0.040 0.006 -0.111 1.000
TABLE IV:Correlation coefficients of the ∆B(B0 →π−ℓ+ν) systematic errors.
q2(GeV2/c2) 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26.4
0-2 1.000 -0.256 0.187 -0.162 0.297 0.181 0.224 0.114 0.104 0.112 0.084 0.020 0.069
2-4 -0.256 1.000 0.142 0.570 0.075 0.163 0.162 0.193 0.202 0.210 0.244 0.303 0.282
4-6 0.187 0.142 1.000 0.202 0.459 0.451 0.469 0.212 0.368 0.329 0.332 0.322 0.336
6-8 -0.162 0.570 0.202 1.000 -0.017 0.240 0.202 0.280 0.256 0.284 0.312 0.333 0.272
8-10 0.297 0.075 0.459 -0.017 1.000 0.375 0.633 0.156 0.321 0.290 0.258 0.244 0.231
10-12 0.181 0.163 0.451 0.240 0.375 1.000 0.433 0.214 0.328 0.332 0.252 0.284 0.230
12-14 0.224 0.162 0.469 0.202 0.633 0.433 1.000 -0.013 0.337 0.278 0.291 0.245 0.246
14-16 0.114 0.193 0.212 0.280 0.156 0.214 -0.013 1.000 0.334 0.500 0.287 0.337 0.322
16-18 0.104 0.202 0.368 0.256 0.321 0.328 0.337 0.334 1.000 0.452 0.334 0.356 0.344
18-20 0.112 0.210 0.329 0.284 0.290 0.332 0.278 0.500 0.452 1.000 0.208 0.430 0.333
20-22 0.084 0.244 0.332 0.312 0.258 0.252 0.291 0.287 0.334 0.208 1.000 0.222 0.402
22-24 0.020 0.303 0.322 0.333 0.244 0.284 0.245 0.337 0.356 0.430 0.222 1.000 0.220
24-26.4 0.069 0.282 0.336 0.272 0.231 0.230 0.246 0.322 0.344 0.333 0.402 0.220 1.000
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TABLE V:The raw, unfolded yields, signal efficiencies and thepartial branchingfractions and theirrelative errors (%) from various sources in 13 binsof q2.
q2(GeV2/c2) 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26.4 0-16 16-26.4 Total
Raw yields 1225.80 1788.46 1756.48 2074.77 2100.64 2136.45 2139.00 1951.65 1537.95 1070.35 1422.80 1369.84 912.27 15173.25 6313.21 21486.46
Unfolded yields 1179.95 1873.57 1662.57 2141.65 2107.29 2192.33 2243.97 2066.70 1609.10 1011.85 1452.82 1323.35 621.30 15468.02 6018.44 21486.46
Efficiencies (%) 7.66 9.35 10.44 11.13 10.89 11.89 11.78 12.50 10.33 10.47 11.74 12.63 14.98
∆B (× 107) 117.33 152.58 121.28 146.54 147.32 140.39 145.00 125.90 118.57 73.59 94.21 79.80 31.59 1096.34 397.75 1494.09
Lepton ID 2.35 2.41 2.39 2.41 2.38 2.38 2.43 2.47 2.47 2.49 2.45 2.44 2.56 2.40 2.49 2.44
Pion ID 1.32 1.37 1.43 1.49 1.41 1.36 1.32 1.24 1.11 0.97 0.85 1.12 1.38 1.37 1.08 1.26
Tracking efficiency 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.01 2.45 2.00 2.09 2.04
γ efficiency 0.21 0.41 0.14 0.25 0.32 0.45 0.94 0.24 0.81 0.80 0.23 0.26 0.49 0.37 0.51 0.42
Vertexχ2 probability 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15
B→ρℓν BF 0.58 0.60 0.59 0.46 0.74 0.60 0.41 0.57 0.48 0.47 0.41 0.41 0.33 0.44 0.42 0.43
B→ωℓν BF 0.28 0.16 0.14 0.12 0.13 0.11 0.16 0.08 0.09 0.12 0.30 0.52 1.19 0.11 0.31 0.16
B→b1ℓν BF 0.30 0.16 0.14 0.12 0.13 0.12 0.13 0.09 0.11 0.12 0.11 0.14 0.59 0.14 0.14 0.14
Vub + otherXuℓν BF 4.43 1.55 0.96 0.87 0.45 0.35 0.45 0.61 0.13 0.13 0.12 0.17 0.77 0.19 0.15 0.15
∗
B→D ℓν BF 0.42 0.40 0.15 0.67 0.09 0.12 0.20 0.09 0.16 0.12 0.12 0.14 0.27 0.18 0.13 0.16
B→Dℓν BF 0.27 0.14 0.14 0.12 0.12 0.09 0.07 0.12 0.09 0.14 0.14 0.18 0.61 0.07 0.14 0.08
∗∗
B→D ℓν BF 0.20 0.16 0.16 0.14 0.14 0.12 0.11 0.11 0.42 0.15 0.14 0.20 0.11 0.11 0.22 0.13
OtherXcℓν BF 0.13 0.09 0.13 0.09 0.18 0.12 0.13 0.09 0.14 0.14 0.14 0.20 0.12 0.06 0.13 0.06
B0 →π−ℓ+ν FF 3.58 1.64 1.26 1.27 1.44 1.57 1.67 1.70 1.78 1.97 1.61 1.92 4.03 0.63 0.86 0.53
B0 →ρ−ℓ+ν FF 3.59 1.73 1.51 1.47 1.64 1.82 2.04 1.89 2.01 2.30 1.99 2.50 4.98 0.72 0.95 0.60
SFparameter 1.44 0.63 1.59 1.07 2.10 2.80 2.52 2.42 2.24 4.02 2.12 3.15 4.66 0.71 1.17 0.63
B0 →D∗−ℓ+ν FF 0.51 0.64 0.60 0.89 1.54 1.77 2.51 0.81 1.18 0.56 0.51 0.42 0.98 0.48 0.34 0.36
B0 →D−ℓ+ν FF 0.33 0.09 0.20 0.30 0.24 0.12 0.26 0.20 0.20 0.09 0.16 0.11 0.11 0.10 0.08 0.08
Υ(4S)→B0B¯0 BF 2.11 1.39 2.41 3.28 3.68 3.90 3.67 2.76 2.83 4.58 3.62 5.21 2.28 1.56 1.72 1.40
Signal MC stat. error 0.48 0.15 0.23 0.27 0.30 0.24 0.28 0.28 0.38 0.52 0.58 0.74 1.97 0.12 0.39 0.15
FSR 0.31 0.58 1.03 0.88 0.93 1.24 1.18 1.43 1.01 1.23 1.15 0.78 0.66 0.45 0.56 0.37
B counting 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36
Continuum q2 13.33 3.64 3.01 4.35 4.91 6.62 6.04 7.42 6.22 6.60 4.67 7.13 5.90 2.14 2.62 1.80
Total systematic error 15.63 6.23 6.14 7.19 8.04 9.56 9.27 9.60 8.71 10.30 7.80 10.63 11.23 4.78 5.26 4.54
Total statistical error 15.35 8.27 8.50 7.24 7.27 7.91 8.32 9.19 9.67 16.68 10.54 11.12 18.98 3.03 5.31 2.63
Total error 21.90 10.35 10.48 10.20 10.84 12.41 12.46 13.29 13.01 19.60 13.12 15.39 22.08 5.66 7.47 5.24
8