Determination of |V_ub| from Measurements of the Inclusive Charmless Semileptonic Partial Rates of B Mesons using Full Reconstruction Tags

0.18 MB·English

by  Belle Collaboration

Determination of V from Measurements of the Inclusive Charmless Semileptonic
ub
Partia|l R|ates of B Mesons using Full Reconstruction Tags
I. Bizjak,12 K. Abe,7 K. Abe,41 H. Aihara,43 Y. Asano,47 S. Bahinipati,4 A. M. Bakich,38 Y. Ban,32
E. Barberio,19 M. Barbero,6 A. Bay,16 U. Bitenc,12 S. Blyth,24 A. Bondar,1 A. Bozek,25 M. Braˇcko,7,18,12
J. Brodzicka,25 T. E. Browder,6 Y. Chao,24 A. Chen,22 W. T. Chen,22 B. G. Cheon,3 R. Chistov,11 S.-K. Choi,5
Y. Choi,37 Y. K. Choi,37 A. Chuvikov,33 S. Cole,38 J. Dalseno,19 M. Danilov,11 M. Dash,48 L. Y. Dong,9
A. Drutskoy,4 S. Eidelman,1 Y. Enari,20 F. Fang,6 S. Fratina,12 N. Gabyshev,1 A. Garmash,33 T. Gershon,7
G. Gokhroo,39 B. Golob,17,12 A. Goriˇsek,12 J. Haba,7 T. Hara,30 H. Hayashii,21 M. Hazumi,7 L. Hinz,16
T. Hokuue,20 Y. Hoshi,41 S. Hou,22 W.-S. Hou,24 T. Iijima,20 A. Imoto,21 K. Inami,20 A. Ishikawa,7 R. Itoh,7
M. Iwasaki,43 Y. Iwasaki,7 J. H. Kang,49 J. S. Kang,14 P. Kapusta,25 N. Katayama,7 H. Kawai,2 T. Kawasaki,27
H. R. Khan,44 H. Kichimi,7 H. J. Kim,15 S. M. Kim,37 K. Kinoshita,4 S. Korpar,18,12 P. Kriˇzan,17,12
6 P. Krokovny,1 R. Kulasiri,4 S. Kumar,31 C. C. Kuo,22 A. Kuzmin,1 Y.-J. Kwon,49 G. Leder,10 S. E. Lee,36
0 T. Lesiak,25 J. Li,35 A. Limosani,7 S.-W. Lin,24 D. Liventsev,11 J. MacNaughton,10 G. Majumder,39
0
F. Mandl,10 T. Matsumoto,45 A. Matyja,25 Y. Mikami,42 W. Mitaroff,10 K. Miyabayashi,21 H. Miyake,30
2
H. Miyata,27 R. Mizuk,11 T. Nagamine,42 Y. Nagasaka,8 I. Nakamura,7 E. Nakano,29 M. Nakao,7
n
Z. Natkaniec,25 S. Nishida,7 O. Nitoh,46 T. Nozaki,7 S. Ogawa,40 T. Ohshima,20 T. Okabe,20 S. Okuno,13
a
J S. L. Olsen,6 Y. Onuki,27 W. Ostrowicz,25 P. Pakhlov,11 H. Park,15 N. Parslow,38 L. S. Peak,38 R. Pestotnik,12

2 L. E. Piilonen,48 M. Rozanska,25 H. Sagawa,7 Y. Sakai,7 N. Sato,20 T. Schietinger,16 O. Schneider,16
2 P. Scho¨nmeier,42 C. Schwanda,10 K. Senyo,20 M. E. Sevior,19 H. Shibuya,40 B. Shwartz,1 V. Sidorov,1 A. Somov,4

N. Soni,31 R. Stamen,7 S. Staniˇc,28 M. Stariˇc,12 T. Sumiyoshi,45 S. Suzuki,34 S. Y. Suzuki,7 O. Tajima,7
2
v F. Takasaki,7 K. Tamai,7 N. Tamura,27 M. Tanaka,7 Y. Teramoto,29 X. C. Tian,32 T. Tsuboyama,7
8 T. Tsukamoto,7 S. Uehara,7 T. Uglov,11 K. Ueno,24 S. Uno,7 P. Urquijo,19 G. Varner,6 K. E. Varvell,38
8
S. Villa,16 C. C. Wang,24 C. H. Wang,23 Y. Watanabe,44 Q. L. Xie,9 B. D. Yabsley,48 A. Yamaguchi,42
0
5 Y. Yamashita,26 M. Yamauchi,7 Heyoung Yang,36 L. M. Zhang,35 Z. P. Zhang,35 V. Zhilich,1 and D. Zˇontar17,12
0 (The Belle Collaboration)
5
0 1Budker Institute of Nuclear Physics, Novosibirsk
/ 2Chiba University, Chiba
x 3Chonnam National University, Kwangju
e 4University of Cincinnati, Cincinnati, Ohio 45221
-
p 5Gyeongsang National University, Chinju
e 6University of Hawaii, Honolulu, Hawaii 96822
h 7High Energy Accelerator Research Organization (KEK), Tsukuba
: 8Hiroshima Institute of Technology, Hiroshima
v
i 9Institute of High Energy Physics, Chinese Academy of Sciences, Beijing
X 10Institute of High Energy Physics, Vienna
r 11Institute for Theoretical and Experimental Physics, Moscow
a 12J. Stefan Institute, Ljubljana
13Kanagawa University, Yokohama
14Korea University, Seoul
15Kyungpook National University, Taegu
16Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne
17University of Ljubljana, Ljubljana
18University of Maribor, Maribor
19University of Melbourne, Victoria
20Nagoya University, Nagoya
21Nara Women’s University, Nara
22National Central University, Chung-li
23National United University, Miao Li
24Department of Physics, National Taiwan University, Taipei
25H. Niewodniczanski Institute of Nuclear Physics, Krakow
26Nippon Dental University, Niigata
27Niigata University, Niigata
28Nova Gorica Polytechnic, Nova Gorica
29Osaka City University, Osaka
30Osaka University, Osaka
31Panjab University, Chandigarh
2
32Peking University, Beijing
33Princeton University, Princeton, New Jersey 08544
34Saga University, Saga
35University of Science and Technology of China, Hefei
36Seoul National University, Seoul
37Sungkyunkwan University, Suwon
38University of Sydney, Sydney NSW
39Tata Institute of Fundamental Research, Bombay
40Toho University, Funabashi
41Tohoku Gakuin University, Tagajo
42Tohoku University, Sendai
43Department of Physics, University of Tokyo, Tokyo
44Tokyo Institute of Technology, Tokyo
45Tokyo Metropolitan University, Tokyo
46Tokyo University of Agriculture and Technology, Tokyo
47University of Tsukuba, Tsukuba
48Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
49Yonsei University, Seoul
We present a measurement of the Cabibbo-Kobayashi-Maskawa matrix element |Vub|, based on
253 fb−1 of data collected by the Belle detector at the KEKB e+e− asymmetric collider. Events
are tagged by fully reconstructing one of the B mesons, produced in pairs from Υ(4S). The signal
for b → u semileptonic decay is distinguished from the b → c background using the hadronic
mass MX, the leptonic invariant mass squared q2 and the variable P+ ≡ EX −|p~X|. The results
∗
are obtained for events with the prompt-lepton momentum, pℓ ≥ 1GeV/c, in three kinematic
regions (1) MX < 1.7 GeV/c2, (2) MX < 1.7 GeV/c2 combined with q2 > 8 GeV2/c2, and by
(3) P+ < 0.66 GeV/c, allowing for a comparison of the three methods. The matrix element |Vub|
is found to be (4.09±0.19±0.20+0.14 ±0.18)×10−3, where the errors are statistical, systematic
−0.15
including Monte Carlo modeling, theoretical and from shape function parameter determination,
respectively.
PACSnumbers: 12.15.Hh,11.30.Er,13.25.Hw
An accurate knowledge of the Cabibbo-Kobayashi- bytheoreticalstudies[1,2],basedonthethreekinematic
Maskawamatrixelement Vub iscrucialtotestStandard variables, and are directly compared by this analysis.
| |
Model predictions for CP violation. Currently, the best The value of Vub is extracted using recent theoretical
| |
precisionmaybeachievedbymeasuringtheinclusiverate calculations [2, 3] that include all the currently known
∆Γuℓν(∆Φ)ofB Xuℓν decaysinarestrictedregionof contributions. MX and q2 selections were already used
→
the phase space (∆Φ) where the dominant charm back- to to extract Vub [4, 5]. The presentanalysisis the first
| |
ground is suppressed and theoretical uncertainties are onetouseP andtodirectlycomparethethreemethods.
+
minimized. ThetheoreticalfactorR(∆Φ)directlyrelates
The data were collected with the Belle detector [6] at
the inclusive rate to Vub , with no extrapolation to the
| | the asymmetric-energy KEKB storage ring [7]. The re-
full phase space: |Vub|2 = ∆Γuℓν(∆Φ)/R(∆Φ). Here we sults presented in this paper are based on a 253 fb−1
reportmeasurementsof∆Γuℓν(∆Φ)forseveralchoicesof
sample recorded at the Υ(4S) resonance, which con-
∆Φ and derive the corresponding values of |Vub|. tains 275 106 BB pairs. An additional 28 fb−1 sam-
×
ple taken at a center-of-mass energy 60MeV below the
The measurements are made with a sample of events
Υ(4S)resonanceisusedtosubtractthebackgroundfrom
wherethehadronicdecaymodeofthetaggingsideB me-
e+e− qq¯(q =u, d, s, c).
son, Btag, is fully reconstructed, while the semileptonic →
decayofthesignalsideBmeson,B ,isidentifiedbythe Monte Carlo (MC) simulated events were used to de-
sig
presence of a high momentum electron or muon. B de- termine efficiencies as well as signal and background
notes both charged and neutral B mesons. This method distributions. The detector simulation was based on
allows the construction of the invariant masses of the GEANT [8]. To model B Xuℓν we use the Evt-
→
hadronic(MX)andleptonic(pq2)systeminthesemilep- Gen generator [9] with various models, where Xu is π
tonic decay, and the variable P+ EX p~X , where or ρ [10], an excited Xu state [11], or a non-resonant
≡ − | |
EX is the energy and p~X the magnitude of the three- multiparticle final state [12]. The B Xcℓν transitions
| | →
momentumofthehadronicsystem. Theseinclusivekine- are simulated according to the QQ generator [13]. For
matic variables can be used to separate the B Xuℓν the two dominant contributions, D∗ℓν and Dℓν, we use
→
decaysfromthemuchmoreabundantB Xcℓν decays. anHQET-basedparametrizationofformfactors[14]and
Three competing kinematic regions (∆Φ)→were proposed ISGW2 model [11], respectively. For the D∗∗ we use
3
qdIBSuu→GacDtrWBik1o→ℓn2iνnD+osm∗Bif∗d→oℓaeνdDets2∗hlhℓeaνapnBe=dmffu0oen.rs3cot5sniuo±bins-c0i[m1o.22mp3,lp.e1om5nT]eethnnhettaesdtmDdwo1etisitocahnrnitdbhoeefDsittn2∗hhtesreeobbt- 2nts / 1 MeV/c 2205000000 (a) Events / bin 450000 bb→→uc (MMbCC)
e data
quark momentum distribution inside the B meson. Ev 15000 300
The Btag candidates are reconstructed in the modes 10000 200
BK+π→+π−Dπ(−∗),πK/ρ0/πa01,/KDs(0∗π),+πD−0, K→0π+Kπ−+ππ0−a,ndKK+π+−Kπ−0,, 5000 100
S S S
DKK−S0+πK−−→ππ−+π.+KD+a∗nπd−mπeK−so,+nKsK−a+rπeπ−−r,eπca−onnπds0t,rDus+cKteS0d→π−by,KcS0KoKmS0+bπi−naiπnn0dg, 05.22 5.24 5.26Mbc(Ge5.V28/c2) 00 0.5 1 1.5 2 M2x .5(GeV3/c2)
a D candidate and a soft pion or photon. (Inclusion of FIG. 1: (a) Distribution in Mbc (data) of Btag candidates
charge conjugate decays is implied throughout this pa- in events satisfying Bsig selection. (b) MX distribution for
per.) The selection of B candidates is based on the events with q2 > 8 GeV2/c2, with fitted contributions of
tag
abneadmt-hceonesntrearginyeddiffmearessn,ceM, b∆cE==pEE∗b∗2eamE/c∗4−.p∗B2H/ecr2e, B→Xcℓν and B→Xuℓν.
E∗ = √s/2 5.290GeV is the beBam− enbeeragmy in the
e+beea−mcenter-of-m≃ass system (cms), and p∗ and E∗ are moving poorly measured soft charged tracks and impos-
B B ing several additional requirements to reject poorly re-
the cms momentum and energy of the reconstructed B
constructed events and suppress the B Xcℓν back-
meson. (Throughout this paper the variables calculated →
ground. We require that the event contain exactly one
in the cms are denoted with an asterisk.)
lepton and have zero net charge and that the invariant
The combinatorial background from jet-like e+e− mass squared of the missing four-momentum m2
qqqu¯irpermoecnestsbesaseisdsounptphreesnsoedrmbaylizeadnseevcoenntd Ftoopxo-Wlogoylfrar→me- (pΥ(4S) − pBtag − pX − pℓ)2 (pΥ(4S), pBtag and pmXissar≡e
four-momenta of the Υ(4S), B , and hadronic system
tag
moment R2 < 0.5 [16], and for some modes also by (X), respectively) be within 1 m2 0.5GeV2/c4.
cosθ∗ <0.8, where θ∗ is the angle between the − ≤ miss ≤
| thrust| thrust To suppress the B Xcℓν background, events with
thrust axis of the Btag candidate and that of the rest a K± or KS0 candida→te on the signal side are rejected
of the event. To minimize the fraction of events with (kaon veto). To reject events containing a K0, we re-
L
incorrect separation of tag and signal sides while main-
quire that the angle between the missing momentum
taining high signal efficiency, a loose selection require- and the direction of any K0 candidate, reconstructed
mentofMbc ≥5.22GeV/c2 and−0.2<∆E <0.05GeV in the KL0 detector, be greaLter than 37 degrees. We
is made. If an event has multiple Btag candidates, we also reject B0 D∗+ℓ−ν¯ events by detecting the slow
Dchocoasnedtihdeatoenemhaasvs,inagntdhethsemDall∗est χD2 mbaassesddoinffe∆reEn,cethief mpioomne(nπtsu)mfrothme→Dm∗o+me→ntuDm0πosf+thanedDd∗e+d.ucTinhgefrmomissiintgs
−
applicable. mass squared m2miss(D∗) = (pB − pD∗ − pℓ)2 is calcu-
For events tagged by fully reconstructed Btag candi- lated from the reconstructed quantities, and events with
dates,wesearchforelectronsormuonsfromsemileptonic m2 > 3GeV2/c4 are rejected.
∗ miss(D∗) −
decays of Bsig. We require a lepton with momentum pℓ Finally,thekinematicvariablesMX andP+ arecalcu-
exceeding1GeV/cinthelaboratorypolarangularregion lated from the measured momenta of all charged tracks
of26◦ θ 140◦. LeptonsfromJ/ψ decay,photoncon- and energy deposits of all neutral clusters in the elec-
≤ ≤
versionin the material of the detector, and π0 decay are tromagnetic calorimeter that are not used in the B
tag
rejected based on the invariant mass they form in com- reconstruction or for the lepton candidate. The four-
bination with an oppositely charged lepton and for elec- momentum of the leptonic system is calculated as q =
ttrhoenBctaagndciadnadtiedsaatelsoiswchitahrgaend,awdediatlisoonarelqpuhiroetotnh.e lWephtoenn apnΥd(4SP)+−aprBetaogb−taipnXed. TbyhefitdtiisntgribthuetioMnsbcodfiesvtreinbtustiinonM, aXs
charge to be consistent with that from prompt semilep- described above, in bins of MX and P+. Figures 1(b),
tonic decay. The signal yield is obtained by fitting the 2(a) and 3(a) show the resulting MX and P+ distribu-
Mbc distributiontothesumofanempiricalparametriza- tions. We define three kinematic signalregions (∆Φ) for
tion of the combinatorial background shape [17] plus a eventswherethepromptleptonhasp∗ 1GeV/c: P <
ℓ +
signal shape [18] that peaks at the B mass and taking 0.66 GeV/c,MX <1.7 GeV/c2,andM≥X <1.7 GeV/c2
the part of the signal that lies in the “signal region,” combined with q2 > 8 GeV2/c2. These three regions
Mbc ≥ 5.27GeV/c2, as shown in Fig. 1(a). The cut- are denoted as P+, MX and MX/q2, respectively. To
off for Mbc reduces the uncertainty from the incorrect minimizethesystematiceffectsofuncertaintiesinlepton
assignment of tag and signal sides in signal events. selection and full reconstruction, we normalize the par-
The B Xuℓν signal events are selected by re- tialrateforeachsignalregionwiththetotalsemileptonic
→
4
TsiAgnBaLlEregI:ioNnsbr.→awu, εsbe→lu, F and rbsl→u for the three kinematic nts / bin23500000 (a) 10 MeV110200 rseiggnioanl← (b)
∆MΦX/q2 26N8br±→aw2u7 2ε6sb.e→5l%u 1.F03 0.687rbs±l→0u.014 Eve12500000 dbba→→tauc MMCC Events / 1468000
MX 404±37 28.7% 1.07 0.700±0.011
20
P+ 340±32 25.5% 1.01 0.700±0.012 1000
0
500
-20
0
0 1 2 3 4 5 0 0.5 1 1.5 2
rate: P+ (GeV) P+ (GeV)
W = ∆Γuℓν(∆Φ) = Nbr→awu F εsfrlec εsℓl . (1) FIG. 2: (a) The P+ distribution for theselected events,with
Γ(Xℓν) Nsl ×εsbe→lu ×εfbr→ecu×εbℓ→u fitted contributions from B → Xcℓν and B → Xuℓν, (b)
P+ distribution (symbols with error bars) after subtracting
To extract the raw number of signal events, Nbr→awu, we B→Xcℓν,with fitted B→Xuℓν contribution (histogram).
fit the MX and P+ distributions with MC-determined
shapes for B Xuℓν and B Xcℓν and subtract the
B Xcℓν con→tribution. The r→esults for the MX/q2 and TABLEII:Partialratestothethreekinematicsignalregions
→ with relative errors (in %).
P regionsareshowninFigs.1(b)and2(a),respectively.
+
MC simulation is used to estimate the conversion factor ∆Φ ∆Γuℓν(∆Φ) stat syst b→u b→c
F of the observed number of events Nbr→awu to the num- MX/q2 5.24×10−4 ps−1 10.0 8.9 6.2 5.3
ber of signal events produced in the region in question MX 7.71×10−4 ps−1 9.1 7.1 6.1 2.2
and observed anywhere, and to estimate the efficiency P+ 6.89×10−4 ps−1 9.4 9.3 6.4 8.7
for these events, εb→u.
sel
N =(9.14 0.05) 104isthenumberofeventshaving
sl
atleastonelep±tonwit×hp∗ 1GeV/c,determinedfroma
ℓ
≥
fittothecorrespondingM distribution(Fig.1(a)),and choice of specific theoretical models and values of the
bc
correctedfor the expected fraction of backgroundevents parameters used in our MC predictions. For signal
from non-semileptonic decays (14.0%), as estimated by B Xuℓν MC, the shape function parameters ΛSF =
MC simulation. The factor εsfrlec/εfbr→ecu accounts for a (0.6→6±0.15)GeV/c2 and λS1F =−(0.40±0.20)GeV2/c2
possible difference in the B reconstruction efficiency were varied within the stated limits, taking into account
tag
in the presence of a semileptonic or B Xuℓν decay; the negative correlationbetween them [20]. To take into
εsl/εb→u is the ratio of both lepton ide→ntification effi- accountthe uncertaintyofthe predictioninRef. [12], we
ℓ ℓ
ciencies and fractions of semileptonic decay leptons with use a factor of two larger error for ΛSF than was deter-
p∗ 1GeV/c, in the whole kinematic phase space for mined in Ref. [20]. For B Xcℓν MC, the uncertainty
ℓ ≥ →
semileptonic decays, and within the kinematic signal re- due to our limited knowledge of branching fractions is
∗
gion for signal events. The product of efficiency ratios studied by varying the contributions of Dℓν and D ℓν
rubsll→atuio≡n.εTsfrlaecb/leεbfrI→ecsuu×mmεsℓal/rεizℓbe→suthiseorbestualitnsedforfrNomrawM,Cεbs→imu-, aconndtrthibeurteelatotivDe∗f∗rℓaνcttioonesotfimnaartreotwhestmatoedseDlin1gaenrdroDr2∗ofththaet
b→u sel
F and rsl for all three signal regions, where the error
b→u
in Nraw is statistical only. Inserting these values in Eq.
1, web→oubtain the three values of W. As both numerator 2eV/c800 rseiggnioanl← (a) 2eV/c112550 rseiggnioanl← (b)
anddenominatorofW havebeenobtainedfromthesame M700 M
thaagssnaomdpelep,etnhdeenBc0e/oBn+liwfeetiigmhetisn.gMs aurletitphlyeinsagmWe, abnydtWhe nts / 120 560000 dbba→→tauc MMCC nts / 120 17050
average measured semileptonic rate Γ(Xℓν) = (B Eve400 Eve50
B →
Xℓν)/τB, obtainedfrom (B Xℓν)=0.1073 0.0028 300 25
B → ±
and τB = (1.604 0.016) ps [19], gives the average 200 0
±
∆Γuℓν(∆Φ). The results with relative errors are given 100 -25
in Table II. 0
0 1 2 3 4 5 0 1 2 3 4 5
We divide the experimental error into four categories: M (GeV/c2) M (GeV/c2)
x x
statistical, systematic, b c and b u MC mod-
→ →
eling errors, and summarize them in Table II for the FIG.3: MX distribution(noq2 requirement)withfittedcon-
three ∆Γuℓν(∆Φ) measurements. The two modeling er- tributions from Xcℓν and Xuℓν: (a) before and (b) after
rors include the uncertainty in signal event extraction, subtractingtheXcℓν contribution (symbolswith error bars),
efficiency and unfolding factor determination due to the shown with theprediction for Xuℓν (MC, histogram).
5
D∗∗ region. The uncertainty from form factor modeling
in Dℓν andD∗ℓν wasstudied by varyingthe parameters TABLEIII:Valuesfor|Vub|withrelativeerrors(in%)forthe
three kinematic signal regions. Shape function parameters
ρ2D = 1.15±0.16 and ρ2A = 1.56±0.13 within their er- used in the calculation are mb(SF) = (4.60±0.04) GeV/c2
rors [19]. The validity of the B → Xcℓν simulation was and µ2π(SF)=(0.20±0.04) GeV2/c2.
tested on a B Xcℓν enhanced control sample, where
→
all selection requirements are applied but with the kaon ∆Φ |Vub|×103 stat syst b→u b→c SF th.
veto reversed. The kinematic distributions of this con- MX/q2 4.70 5.0 4.4 3.1 2.7 4.2 +−45..82
trol sample are accurately described by the simulation. MX 4.09 4.6 3.5 3.1 1.1 4.5 +−33..58
Othersourcesofuncertainties,namelylimitedMCstatis- P+ 4.19 4.7 4.6 3.2 4.4 5.8 +−33..45
tics, extraction of rsl , fitting procedure and imperfect
b→u
detectorsimulationarecombinedinthesystematicerror.
The uncertainties due to inaccurate simulation of track-
ing, particle identification, and cluster finding are esti- selection q2 > 8 GeV2/c2 to the MX analysis. Tak-
mated by varying for each source the efficiency within
ing correlations into account, we find that the difference
the expected error and taking the maximum change in between Vub values for MX/q2 and MX regions has a
∆Γuℓν(∆Φ) as the error. For each of these sources the significan|ce o|f 2.7σ. We conclude that the results are
effects on simulated b u and b c events are cor-
consistent within errors, but we do not rule out possible
→ →
related, and the associated shifts are summed linearly.
effects of duality violation or weak annihilation contri-
The net contributions from the three sources are then
bution. We chose the MX signal region result for our
summed in quadrature.
Vub determination, since it includes the largest portion
The CKM matrix element Vub is obtained directly |of ph|ase space and is least affected by the uncertainties:
| |
Rfro(∆mΦt)heispathrteiatlhreaotreetuicsianlgp|rVeudbi|c2ti=on∆oΓfu∆ℓνΓ(∆uℓΦν()∆/RΦ()∆, Φth)e. |tVhueb|er=ro(r4s.0a9re±st0a.t1i9st±ica0l,.2s0y−+st00e..11m54a±tic0.w1i8t)h×M1C0−m3o,dwelhinerge,
partialratewithapromptleptonwithp∗ 1GeV/c,di-
ℓ theoretical and from shape function parameter determi-
vtoidebdeb2y3.|7Vub|22..0T(hSeF)v+al2u.5e(sthof.)R, 4(i6n.1ps−14).≥2a(rSeFc)a+lc3u.5l(atthe.d) nation, respectively. The effectiveness of |Vub| measure-
and 39.4 ±±4.5(SF)+−22−..872(.t3h.) for the±MX/q2, M−3X.2 and manednt3s(ubs)i)n.gfullreconstructiontaggingisclear(Figs.2(b)
P signal regions, respectively. The R(∆Φ) values and
+ We thank the KEKB group for excellent accelerator
their errors(SF) are calculated using the shape function
operations, the KEK cryogenics group for efficient oper-
ascnhdemµe2([S1F5])p=ara(0m.2et0ers0m.0b4(S)FG)e=V(24/.c620±wi0th.04c)orGreelVat/iocn2 ation of the solenoid, and the KEK computer groupand
π ± NII for valuable computing and Super-SINET network
coefficient ρ = 0.26, obtained from the result of a
− support. WeacknowledgesupportfromMEXTandJSPS
global fit to moments of both b cℓν and b sγ
→ → (Japan); ARC and DEST (Australia); NSFC (contract
distributions [21]. While the dependence of R(∆Φ) on
No. 10175071, China); DST (India); the BK21 program
µ2(SF) is small, we can approximate the dependence on
π of MOEHRD and the CHEP SRC program of KOSEF
mmb0(=SF4).6a0s RG/eRV(/mc20b)a−nd1k=(∆kΦ(∆)Φis)f·o(umndb/tmo0bb−e 21.)0,9w,h2e.2r9e (Korea); KBN (contract No. 2P03B 01324, Poland);
b MIST (Russia); MHEST (Slovenia); SNSF (Switzer-
and 3.00 for the MX/q2, MX and P+ signal regions, re- land); NSC and MOE (Taiwan); and DOE (USA).
spectively. The theoretical error of R (th.) is estimated
We are grateful to B. Lange, M. Neubert and G. Paz
byvaryingthesubleadingshapefunctions(fourmodels),
for providing us with their theoretical computations im-
the matchingscalesµh, µi, µ¯ andweakannihilation[15].
plemented in an inclusive generator. We would specially
Thevaluesof Vub witherrorsaregiveninTableIII.The
| | like to thank M. Neubert for valuable discussions and
totalerroron Vub is 10%, 9%and 11%for MX/q2, MX
| | suggestions.
and P regions, respectively. When the shape function
+
parameters and R are better determined, Vub can be
| |
recalculated from ∆Γuℓν(∆Φ) shown in Table II.
The precisionofthe Vub determinationis better than
| |
previous measurements [4, 5, 22], owing to the use of [1] C. W. Bauer, Z. Ligeti and M. Luke, Phys. Rev. D 64,
larger data sample, better shape function parameter de- 113004 (2001).
termination and improved theoretical predictions [2, 3]. [2] S. W. Bosch, B. O. Lange, M. Neubert and G. Paz,
We find that the usage of the variable P is more sensi- PhysRevLett.93,221801(2004); Nucl.Phys.B699,335
+
(2004).
tive to b c modeling and shape function parametriza-
→ [3] M. Neubert,Eur.Phys.J. C40, 165 (2005); Phys.Lett.
tion than the other two methods and will become com-
B612,13(2005);hep-ph/0411027;S.W.Bosch,M.Neu-
petitive in the future when the theoretical error of R bert and G. Paz, JHEP 0411, 073 (2004).
dominates. No significant experimental nor theoretical [4] B.Aubertetal.(BaBarCollaboration),Phys.Rev.Lett.
improvement was observed by applying the additional 92, 071802 (2004).
6
[5] H.Kakunoet al.(BelleCollaboration), Phys.Rev.Lett. (1978).
92, 101801 (2004). [17] H. Albrecht et al. (ARGUS Collaboration), Z. Phys. C
[6] A.Abashian et al. (Belle Collaboration), Nucl. Instrum. 48, 543 (1990).
and Meth. A 479, 117 (2002). [18] J. E. Gaiser et al., Phys.Rev.D 34, 711 (1986).
[7] S.KurokawaandE.Kikutani,Nucl.Instrum.andMeth. [19] S. Eidelman et al.,Phys.Lett. B 592, 1 (2004).
A 499, 1 (2003), and other papers in this Volume. [20] A. Limosani and T. Nozaki (Heavy Flavor Averaging
[8] R. Brun, F. Bruyant, M. Maire, A. C. McPherson and Group), hep-ex/0407052.
P.Zanarini, CERN Report No. DD/EE/84-1 (1984). [21] O. Buchmueller and H. Flaecher (Heavy Flavor Averag-
[9] D.J. Lange, Nucl. Instrum.Meth. A 462, 152(2001). ing Group), hep-ph/0507253.
[10] P.Ball, arXiv:hep-ph/0306251. [22] R. Barate et al. (ALEPH Collaboration), Eur. Phys. J.
[11] D.Scora and N.Isgur, Phys. Rev.D 52, 2783 (1995). C 6, 555 (1999); M. Acciarri et al. (L3 Collaboration),
[12] F. DeFazio and M. Neubert, JHEP 9906, 017 (1999). Phys. Lett. B 436 174 (1998); P. Abreu et al. (DELPHI
[13] QQeventgenerator, developedbyCLEO Collaboration, Collaboration),Phys.Lett.B47814(2000);G.Abbiendi
see http://www.lns.cornell.edu/public/CLEO/soft/QQ. et al. (OPAL Collaboration), Eur. Phys. J. C 21, 399
[14] M. Neubert,Phys. Rept.245, 259 (1994). (2001); A.Bornheimet al.(CLEOCollaboration), Phys.
[15] B. O. Lange, M. Neubert and G. Paz, hep-ph/0504071 Rev. Lett.88, 231803 (2002)
and privatecommunication with M. Neubert.
[16] G. C. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581