Search for $B^0 \to K^{*0} \overline{K}{}^{*0}$, $B^0 \to K^{*0} K^{*0}$ and $B^0 \to K^+π^- K^{\mp}π^{\pm}$ Decays

0.22 MB·English

by  C. -C. Chiang

Search for B0 → K∗0K∗0, B0 → K∗0K∗0 and B0 → K+π−K∓π± Decays
C.-C. Chiang,25 H. Aihara,42 K. Arinstein,1,30 V. Aulchenko,1,30 T. Aushev,17,11 A. M. Bakich,36 V. Balagura,11
0 E. Barberio,20 K. Belous,9 V. Bhardwaj,32 M. Bischofberger,22 A. Bondar,1,30 A. Bozek,26 M. Braˇcko,18,12
1 T.E.Browder,6 P.Chang,25 Y.Chao,25 A.Chen,23 P.Chen,25 B.G.Cheon,5 I.-S.Cho,45 Y.Choi,35 J.Dalseno,19,38
0
A. Das,37 Z. Doleˇzal,2 A. Drutskoy,3 S. Eidelman,1,30 M. Feindt,14 N. Gabyshev,1,30 P. Goldenzweig,3 H. Ha,15
2
T. Hara,7 K. Hayasaka,21 H. Hayashii,22 Y. Horii,41 Y. Hoshi,40 Y. B. Hsiung,25 T. Iijima,21 K. Inami,21
n
R. Itoh,7 M. Iwasaki,42 N. J. Joshi,37 J. H. Kang,45 P. Kapusta,26 T. Kawasaki,28 C. Kiesling,19 H. J. Kim,16
a
J H. O. Kim,16 K. Kinoshita,3 B. R. Ko,15 S. Korpar,18,12 M. Kreps,14 P. Kriˇzan,46,12 P. Krokovny,7 Y.-J. Kwon,45

6 S.-H. Kyeong,45 J. S. Lange,4 M. J. Lee,34 S.-H. Lee,15 J. Li,6 A. Limosani,20 C. Liu,33 Y. Liu,25 D. Liventsev,11
2 R. Louvot,17 A. Matyja,26 S. McOnie,36 K. Miyabayashi,22 H. Miyata,28 Y. Miyazaki,21 E. Nakano,31 M. Nakao,7

Z. Natkaniec,26 S. Neubauer,14 S. Nishida,7 K. Nishimura,6 O. Nitoh,43 S. Ogawa,39 S. Okuno,13 S. L. Olsen,34,6
]
x W. Ostrowicz,26 G. Pakhlova,11 C. W. Park,35 H. Park,16 H. K. Park,16 K. S. Park,35 R. Pestotnik,12 M. Petriˇc,12
e
L. E. Piilonen,44 M. Ro¨hrken,14 S. Ryu,34 H. Sahoo,6 Y. Sakai,7 O. Schneider,17 C. Schwanda,8 A. J. Schwartz,3
-
p K. Senyo,21 M. E. Sevior,20 J.-G. Shiu,25 R. Sinha,10 P. Smerkol,12 A. Sokolov,9 S. Staniˇc,29 M. Stariˇc,12
e
h J. Stypula,26 K. Sumisawa,7 M. Tanaka,7 Y. Teramoto,31 K. Trabelsi,7 Y. Unno,5 P. Urquijo,20 Y. Usov,1,30
[ G. Varner,6 K. E. Varvell,36 K. Vervink,17 C. H. Wang,24 M.-Z. Wang,25 M. Watanabe,28 Y. Watanabe,13

E. Won,15 B. D. Yabsley,36 Y. Yamashita,27 Z. P. Zhang,33 T. Zivko,12 A. Zupanc,14 and O. Zyukova1,30
1
v (The Belle Collaboration)
5
1Budker Institute of Nuclear Physics, Novosibirsk
9
2Faculty of Mathematics and Physics, Charles University, Prague
5
3University of Cincinnati, Cincinnati, Ohio 45221
4
4Justus-Liebig-Universit¨at Gießen, Gießen
.
1 5Hanyang University, Seoul
0 6University of Hawaii, Honolulu, Hawaii 96822
0 7High Energy Accelerator Research Organization (KEK), Tsukuba
1 8Institute of High Energy Physics, Vienna
v: 9Institute of High Energy Physics, Protvino
i 10Institute of Mathematical Sciences, Chennai
X 11Institute for Theoretical and Experimental Physics, Moscow
r 12J. Stefan Institute, Ljubljana
a 13Kanagawa University, Yokohama
14Institut fu¨r Experimentelle Kernphysik, Karlsruhe Institut fu¨r Technologie, Karlsruhe
15Korea University, Seoul
16Kyungpook National University, Taegu
17E´cole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne
18University of Maribor, Maribor
19Max-Planck-Institut fu¨r Physik, Mu¨nchen
20University of Melbourne, School of Physics, Victoria 3010
21Nagoya University, Nagoya
22Nara Women’s University, Nara
23National Central University, Chung-li
24National United University, Miao Li
25Department of Physics, National Taiwan University, Taipei
26H. Niewodniczanski Institute of Nuclear Physics, Krakow
27Nippon Dental University, Niigata
28Niigata University, Niigata
29University of Nova Gorica, Nova Gorica
30Novosibirsk State University, Novosibirsk
31Osaka City University, Osaka
32Panjab University, Chandigarh
33University of Science and Technology of China, Hefei
34Seoul National University, Seoul
35Sungkyunkwan University, Suwon
36School of Physics, University of Sydney, NSW 2006
2
37Tata Institute of Fundamental Research, Mumbai
38Excellence Cluster Universe, Technische Universita¨t Mu¨nchen, Garching
39Toho University, Funabashi
40Tohoku Gakuin University, Tagajo
41Tohoku University, Sendai
42Department of Physics, University of Tokyo, Tokyo
43Tokyo University of Agriculture and Technology, Tokyo
44IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
45Yonsei University, Seoul
46Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana
We report a search for the decays B0 → K∗0K∗0 and B0 → K∗0K∗0. We also measure other
charmless decay modes with K+π−K−π+ and K+π−K+π− final states. The results are obtained
from a data sample containing 657×106 BB pairs collected with the Belle detector at the KEKB
asymmetric-energye+e− collider. WesetupperlimitsonthebranchingfractionsforB0 →K∗0K∗0
and B0 →K∗0K∗0 of 0.81×10−6 and 0.20×10−6, respectively,at the 90% confidencelevel.
PACSnumbers: 11.30.Er,12.15.Hh,13.25.Hw,14.40.Nd
The charmless decay B0 → K∗0K∗0 [1] proceeds a K+π−K−π+ or K+π−K+π− final state using a data
through electroweak and gluonic b → d “penguin” loop sample 1.7 times larger than that of BaBar. The data
diagrams. It provides an opportunity to probe the dy- sample used in the analysis contains 657 × 106 BB
namics of both weak and strong interactions,which play pairs collected with the Belle detector [12, 13] at the
an important role in CP violation phenomena. For a B KEKB asymmetric-energy e+e− (3.5 GeV and 8 GeV)
meson decaying to two vector particles, B → VV, the- collider[14]operatingattheΥ(4S)resonance. TheBelle
oretical models based on the frameworks of either QCD detectorincludesasiliconvertexdetector,a50-layercen-
factorization or perturbative QCD predict the fraction tral drift chamber (CDC), an array of aerogel threshold
of longitudinal polarization (f ) to be ∼ 0.9 for tree- Cherenkov counters (ACC), and a barrel-like arrange-
L
dominateddecaysand∼0.75forpenguin-dominatedde- ment of time-of-flight scintillation counters (TOF). Sig-
cays [2, 3]. However, the measured polarization fraction nal Monte Carlo (MC) events are generated with EVT-
in the pure penguin decay B → φK∗ has a somewhat GEN [15], and final-state radiationis taken into account
lower value of f ∼ 0.5 [4]. This unexpected result has with the PHOTOS package [16]. Generated events are
L
motivated further studies [5]. processed through a full detector simulation program
OneresolutiontothispuzzleisasmallerB →K∗ form based on GEANT3 [17].
factor that could reduce f significantly [6]. If this ex- We reconstruct signal decays from neutral combina-
L
planationiscorrect,thepenguin-dominateddecayB0 → tions of four charged tracks fitted to a common vertex.
K∗0K∗0 shouldexhibitasimilarpolarizationfraction. A Neutral K∗ mesons are reconstructed via K∗0 →K+π−
time-dependent angular analysis of B0 →K∗0K∗0 could and K∗0 → K−π+. Charged track candidates are re-
distinguish between penguin annihilation and rescatter- quired to have a distance of closest approach to the in-
ing as mechanisms for the f observed in B → φK∗ de- teractionpoint of less than 2.0 cm in the directionalong
L
cays [7]. The B0 → K∗0K∗0 mode can also be used the positron beam (z axis), and less than 0.1 cm in the
to extract the branching fraction corresponding to the transverse plane. Tracks are also required to have a lab-
longitudinal helicity final state, determine hadronic pa- oratorymomentumintherange[0.5,4.0]GeV/c,apolar
rameters for the b → s decay B → K∗0K∗0, and help angleintherange[32.2,127.2]◦,andatransversemomen-
s
constrain the angles φ (α) and φ (γ) of the Cabibbo- tum p >0.1GeV/c. Chargedpions are identified using
2 3 T
Kobayashi-Maskawaunitarity triangle [8]. The topologi- informationfromthe CDC (dE/dx), ACC,andTOFde-
cally similar decay B0 →K∗0K∗0 is strongly suppressed tectors [18]. We distinguish charged kaons from pions
in the Standard Model (SM); its observationwouldindi- using a likelihood ratio R = L /(L + L ), where
K K K π
cate new physics. L (L ) is the likelihood value for the pion (kaon) hy-
π K
Theoretical calculations predict the branching frac- pothesis. We require RK < 0.4 (RK > 0.6) for the two
tionsforB0 →K∗0K∗0 andB0 →K∗0K∗0 tobe(0.17− chargedpions (kaons). The kaon(pion) identificationef-
0.92)×10−6 [9]and(2.9±0.2)×10−15[10],respectively. ficiency is 83% (90%), and 6% (12%) of pions (kaons)
The BaBar collaboration [11] has reported a branching are misidentified as kaons (pions). We also use the lep-
fraction B(B0 → K∗0K∗0) = (1.28+−00..3350±0.11)×10−6 ton identification likelihood Rx (x denotes either µ or
and has set an upper limit B(B0 → K∗0K∗0) < 0.41× e) described in Ref. [18]: charged particles identified as
10−6 at the 90% confidence level (C.L.). In this pa- electrons (Re >0.9) or muons (Rµ >0.9) are removed.
per, we report a search for the decays B0 → K∗0K∗0, We veto B → D(∗)±X, B → D±X, B → D0X, and
s
B0 → K∗0K∗0, and other charmless decay modes with B0 → φX decays that result in the K+π−K−π+ final
3
state, and we veto B → D(∗)±X and B → D0X de- events that is obtained from the signal MC simulation
cays that result in the K+π−K+π− final state. For the (events in the sideband regionM <5.26 GeV/c2). For
bc
B → D(∗)±X and B → D±X vetos, we remove can- additionalsuppression,wealsouseaflavortaggingqual-
s
didates that satisfy either |M(K±K∓π∓) − m | < ityvariablerprovidedbytheBelletaggingalgorithm[20]
D∓
13 MeV/c2, |M(K±π∓π∓) − m | < 13 Me(Vs)/c2, that identifies the flavor of the accompanying B0 meson
D(∓s) intheΥ(4S)→B0B0 decay. The variabler rangesfrom
|M(K±h∓π∓)−m |<13MeV/c2,or|M(K±h∓π∓)−
K D∓ π r =0fornoflavordiscriminationtor =1forunambigu-
m | < 13 MeV/c2, where m are the masses of the
D∓ D∓ ous flavor assignment, and it is used to divide the data
(s)
D∓ mesons, and h∓ (h∓) is the kaon (pion) mass as- sample into six r bins. As the discrimination between
(s) K π
signal and continuum events depends on the r-bin, we
signed to a pion (kaon) candidate track [i.e., a kaon
impose different requirements on R for each bin. The
(pion) was misidentified as a pion (kaon)]. For the
B → D0X veto, we remove candidates satisfying ei- requirements are determined by maximizing a figure-of-
ther |M(K±K∓)−m |<13 MeV/c2 or |M(K±h∓)− merit Ns/ Ns+Nqq, where Ns (Nqq) is the expected
D0 K
m | < 13 MeV/c2, where m is the mass of the D0 number ofpsignal(continuum) events in the signalregion
D0 D0
∆E ∈[−0.045, 0.045] GeV, M ∈[5.27, 5.29] GeV/c2,
meson. For the B → φX veto, we remove candidates bc
satisfying |M(K±h∓K)−mφ|<20 MeV/c2, where mφ is anIdnMa1b,2o(uKtπ1)7∈%[0o.f82e6v,en0.t9s66th]eGreeVa/rce2.multiple B0 →
the mass of the φ meson. These vetos together remove
9.7% (3.6%) of longitudinally polarized B0 → K∗0K∗0 K∗0K∗0 or B0 → K∗0K∗0 candidates. For these events
(B0 →K∗0K∗0) signal, according to MC simulation. we select the candidate with the smallest χ2 value for
the B0 decay vertex reconstruction. This selects the
Signal event candidates are characterized by two
correct combination 87% (97%) of the time for longi-
kinematic variables: the beam-energy-constrained mass, tudinally (transversely) polarized B0 → K∗0K∗0 and
Mbc = Eb2eam−PB∗2, and the energy difference, ∆E = B0 → K∗0K∗0 decays. The overall reconstruction ef-
EB∗ −Ebpeam,whereEbeam istherun-dependentbeamen- ficiency for B0 → K∗0K∗0 as obtained from MC sim-
ergy, and P∗ and E∗ are the momentum and energy of
B B ulation is 4.43% (5.23%) for longitudinal (transverse)
theBcandidateintheΥ(4S)center-of-mass(CM)frame.
polarization. The overall reconstruction efficiency for
We distinguish nonresonant B0 → KKππ decays from B0 → K∗0K∗0 is 5.74% (5.92%) for longitudinal (trans-
our signal modes by fitting the two-dimensional mass
verse)polarization. Theefficiencyforlongitudinalpolar-
distributions M(K+π−) vs. M(K−π+) or M(K+π−) izationislower,asinthiscasetheK∗0daughtersproduce
vs. M(K+π−). There are two possible combina-
lower momentum kaons and pions.
tions in B0 → K∗0K∗0 reconstruction for M(K+π−) The signal yields for B0 → K∗0K∗0 and other B0 →
vs. M(K+π−): (K1+π1−)(K2+π2−) and (K1+π2−)(K2+π1−), K+π−K−π+ decays are extracted by performing an ex-
where the subscripts label the momentum ordering, i.e.,
tended unbinned maximum likelihood (ML) fit to the
sKid1+e(rπb1−o)thha(Ks h1+iπgh1−e)r(Km2+omπ2−en)taunmd(tKha1+nπK2−)2+(K(π2+2−π).1−W)ceomcobni-- vaanrdiaMble2sM≡bMc,∆(KE−,πM+1),.anTdhMis2,fowuhr-edreimMen1s≡ionMal(Kfit+πd−is)-
nations and select candidate events if either one of the criminatesamongK∗0K∗0, K∗0Kπ, K∗(1430)K∗(1430),
0 0
combined masses lies within the signal window of [0.7, K∗(1430)K∗0, K∗(1430)Kπ,andnonresonantKKππ fi-
1.7] GeV/c2. If both combinations fall within the signal 0 0
nal states. Since there are large overlaps between these
window,weselectthe(K+π−)(K+π−)combination. Ac-
1 2 2 1 states, we distinguish them by fitting a large (M1,M2)
cording to MC simulation, this choice selects the correct region: M ∈ [0.7, 1.7] GeV/c2. We use a likelihood
1,2
combination for signal decays 99% of the time. For fit-
function
ting,wesymmetrizetheM2(K+π−)vs.M2(K+π−)plot
by plotting M2(K+π−) [M2(K+π−)] on the horizontal Ncand
1 2 L=exp − n n Pi , (1)
axis for events with an even [odd] event number. This (cid:18) j(cid:19) (cid:18) j j(cid:19)
number denotes the location of the event in the data set Xj iY=1 Xj
(i.e., n =1,2,3...N ).
event total where i is the event identifier, j indicates one of the
The dominant source of background is continuum event type categories for signals and backgrounds, nj
e+e− → qq¯ (q = u,d,s and c) events. To distinguish denotes the yield of category j, and Pi is the prob-
j
signal from the jet-like continuum background, we use ability density function (PDF) of event i for cate-
modified Fox-Wolfram moments [19] that are combined gory j. The PDF is a product of two smoothed
into a Fisher discriminant. This discriminant is subse- two-dimensional functions: Pji = Pj(Mbic,∆Ei) ×
quently combined with the probabilities for the cosineof P (Mi,Mi) ≡ P (Mi ,∆Ei,Mi,Mi). The signal yields
j 1 2 j bc 1 2
the B flight direction in the CM frame and the distance for B0 →K∗0K∗0 and other B0 →K+π−K+π− decays
alongthe z axisbetweenthe twoB mesondecayvertices areextractedbyanotherfour-dimensionalfitinthesame
to form a likelihood ratio R = L /(L + L ). Here, way, except that for this fit M ≡M(K+π−).
s s qq 2
L (L ) is a likelihood function for signal (continuum) For the B signal components, the smoothed functions
s qq
4
P(M ,∆E)andP(M ,M )areobtainedfromMCsim- where x corresponds to the number of signal events. We
bc 1 2
ulation. For the M and ∆E PDFs, possible differences include the systematic uncertainty in the upper limit
bc
between data and the MC modeling are calibrated using (UL) by smearing the statistical likelihood function by
a large control sample of B0 → D−(K+π−π−)π+ de- a bifurcated Gaussian whose width is equal to the to-
cays. The signal mode PDF is divided into two parts: tal systematic error. We also smear L when calculating
oneiscorrectlyreconstructedevents(CR),andtheother the signalsignificance,except thatonly the additive sys-
is “self-cross-feed” events (SCF) in which at least one tematic errors related to signal yield are included in the
track from the signal decay is replaced by one from the convolved Gaussian width. Our upper limits correspond
accompanying B decay. We use different PDFs for CR to a longitudinal polarization fraction f = 1; as the ef-
L
and SCF events and fix the SCF fraction (f ) to that ficiency for f < 1 is higher than that for f = 1, our
SCF L L
obtained from MC simulation, i.e., limits are conservative.
To check our reconstruction efficiencies, we mea-
PSiignal = (1−fSCF)×PCR(Mbic,∆Ei,M1i,M2i) sure the yields of control samples B0 → D−π+ →
+ f ×P (Mi ,∆Ei,Mi,Mi). (2) (K+K−π−)π+ and B0 → D0K∗0 → (K+π−)(K+π−).
SCF SCF bc 1 2
Thesemodeshaveasimilartopologytothesignalmodes
For the continuum and b → c decay backgrounds, we and are selected using the same selection criteria ex-
use the product of a linear function for ∆E, an ARGUS cept that, instead of D vetos, we require |M(KKπ)−
function [21] for Mbc, and a two-dimensional smoothed mD±|<13MeV/c2, |M(Kπ)−mD0|<13MeV/c2, and
function for M1-M2. The shape parameters of the linear 826 MeV/c2 < M(Kπ) < 966 MeV/c2. The efficiencies
and ARGUS functions for the continuum (b→c) events are 19% for B0 → D−π+ and 11% for B0 → D0K∗0.
arefloated(fixed)inthefit;theshapeoftheM -M func- Thedifferenceinsignalyieldsbetweenthemeasuredand
1 2
tions for the continuum and b → c events are obtained expected values are (5.8±5.8)% and (5.6±27.8)% for
from MC simulation and fixed in the fit. The yields of B0 → D−π+ and B0 → D0K∗0, respectively. These
the continuum and b→c decay backgrounds are floated differences are consistent with zero.
in the fit. For the charmless B decay backgrounds, we The systematic errors (in units of events) are sum-
use separate PDFs for B0 → K+K−K0, nonresonant marized in Tables II and III. For systematic uncer-
B0 →Kπππ,andothercharmlessBmodes;allthePDFs tainties due to fixed yields, e.g., that of charmless B
areobtainedfromMCsimulation. Note thatthe nonres- background, we vary the yields by their uncertainties
onant B0 → Kπππ decay will enter the sample if one (±1σ). For the systematic uncertainties due to B0 →
of the pions is misidentified as a kaon; in this case the K∗(1430)X decays, including B0 →K∗(1430)K∗(1430),
2 2 2
mean of the ∆E distribution shifts by about +75 MeV, B0 → K∗(1430)K∗(1430), B0 → K∗(1430)K∗0, and
2 0 2
since assigning a kaon mass instead of a pion mass in- B0 → K∗(1430)Kπ, we float their yields in the four-
2
creases the B candidate energy. In the fit, we fix the dimensionalML fit; the differencesbetween these results
yield of B0 → K+K−K0 to 32 events, corresponding to and the nominal fit values are taken as systematic er-
a branching fraction of 24.7×10−6 [22], and the yield of rors. Systematic uncertainties for the ∆E-M PDFs
bc
other known charmless B decays to that expected based are estimated by varying the signal peak positions and
on world average branching fractions [23]. We set the resolutions by ±1σ and repeating the fits. Systematic
branchingfractionforB0 →K∗(1430)X tozeroandonly uncertainties for the M -M PDFs are estimated in a
2 1 2
consider it in the systematics, as this mode has a large similar way; we vary the mean and width of K∗0 and
correlationwith B0 →K∗(1430)X. The yield of nonres- K∗(1430) mass shapes according to the uncertainties in
0 0
onant B0 →Kπππ is floated. For the fully nonresonant the worldaveragevalues [22]. A systematic error for the
modes,weassumethefinal-stateparticlesaredistributed longitudinal polarization fraction is obtained by chang-
uniformly in three- and four-body phase space. ing the fraction from the nominal value f = 1 to the
L
The fit results are listed in Table I, and projec- lowest possible value f =0 when evaluating the recon-
L
tions of the fit superimposed to the data are shown in struction efficiency. According to MC simulation, the
Figs. 1 and 2. The statistical significance is calculated signal SCF fractions are 13.4% for (longitudinally polar-
as −2ln(L0/Lmax), where L0 and Lmax are the val- ized) B0 → K∗0K∗0, 7.9% for B0 → K∗0Kπ, 6.7% for
uespof the likelihood function when the signal yield is B0 →K∗(1430)K∗(1430),6.7%forB0 →K∗(1430)K∗0,
0 0 0
fixed to zero andwhen it is allowedto vary,respectively. 7.6% for B0 → K∗(1430)Kπ, and 9.2% for nonresonant
0
We do not find significant signals for B0 → K∗0K∗0, B0 →KKππ. Weestimateasystematicuncertaintydue
B0 → K∗0K∗0, and other charmless decay modes with to these fractions by varying them by ±50%.
K+π−K∓π± finalstates,anddetermine90%C.L.upper A high-statistics MC study indicates that there are
limits for the yields (N). These limits are calculated via small fit biases; these are listed in Table I. We find that
fit biases occur due to the correlations between the two
N
L(x)dx sets of variables (∆E, M ) and (M , M ), which are
0 = 0.90, (3) bc 1 2
R∞L(x)dx not taken into account in our fit. We correct the fitted
0
R
5
TABLE I: Fit results for decay modes with final states K+π−K−π+ and K+π−K+π−. The fit bias (in units of events) is
obtainedfrom MCsimulation; theyield includesthebiascorrection; theefficiency εincludesthePIDefficiency correction and
branching fractions for K∗0 → K+π− and K∗(1430) → K+π− (66.5% and 66.7%, respectively); and the significance S is in
0
unitsof σ. The first (second) error listed is statistical (systematic).
Mode Fit bias Yield ε (%) S B×106 UL ×106
B0 →K∗0K∗0 1.5±0.7 7.7+9.7+2.8 4.43 (f =1.0) 0.9 0.26+0.33+0.10 <0.8
−8.5−2.2 L −0.29−0.08
B0 →K∗0K−π+ −5.4±2.9 18.2+48.4+41.7 1.31 0.3 2.11+5.63+4.85 <13.9
−45.3−40.9 −5.26−4.75
B0 →K∗(1430)K∗(1430) 2.1±5.1 78.5+70.6+56.4 3.72 0.8 3.21+2.89+2.31 <8.4
0 0 −69.6−56.8 −2.85−2.32
B0 →K∗(1430)K∗0 13.3±2.3 19.6+31.1+40.0 4.38 0.4 0.68±1.08+1.39 <3.3
0 −31.0−43.0 −1.49
B0 →K∗(1430)K−π+ 14.6±9.8 −222.8+171.5+159.8 1.34 — — <31.8
0 −170.8−168.6
Nonresonant B0 →K+π−K−π+ −10.8±7.3 158.4+120.6+104.1 0.82 1.0 29.41+22.39+19.32 <71.7
−117.8−105.0 −21.87−19.49
B0 →K∗0K∗0 1.0±0.5 −3.7±3.3+2.5 5.74 (f =1.0) — — <0.2
−2.7 L
B0 →K∗0K+π− −2.5±2.7 0.5±32.3+43.5 1.93 0.0 0.04±2.55+3.43 <7.6
−40.1 −3.16
B0 →K∗(1430)K∗(1430) 3.4±1.3 −28.4±16.1+87.7 4.28 — — <4.7
0 0 −21.1
B0 →K∗(1430)K∗0 8.2±1.6 8.0±18.7+23.9 5.14 0.3 0.24±0.55+0.71 <1.7
0 −30.3 −0.90
Nonresonant B0 →K+π−K+π− 7.7±2.2 10.8±28.3+31.4 1.98 0.3 0.83±2.17+2.42 <6.0
−101.5 −7.80
50 50
20 (a) 20 (b) 45 (c) 45 (d)
17.5 17.5 40 40
Events/ 10 MeV17211..50555 Events/ 2 MeV17211..50555 Events/ 50 MeV 112233050505 Events/ 50 MeV 112233050505
2.5 2.5 5 5
0 0 0 0
-0.1 -0.05 0 0.05 0.1 5.255.265.275.285.29 5.3 0.7 0.9 1.1 1.3 1.5 1.7 0.7 0.9 1.1 1.3 1.5 1.7
D E (GeV) M (GeV/c2) M(K+p -) (GeV) M(K-p +) (GeV)
bc 1 2
FIG. 1: Projections of the four-dimensional fit onto (a) ∆E, (b) M , (c) M(K+π−), and (d) M(K−π+) for candidates
bc
satisfying (except for the variable plotted) ∆E ∈ [−0.045, 0.045] GeV, Mbc ∈ [5.27, 5.29] GeV/c2, and M1,2(Kπ) ∈
[0.826, 0.966] GeV/c2. Thethick solid curveshows theoverall fitresult; thesolid shaded region represents theB0→K∗0K∗0
signal component; and the dotted, dot-dashed and dashed curves represent continuum background, b → c background, and
charmless B decay background,respectively.
12 (a) 14 (b) 22.5 (c) 22.5 (d)
Events/ 10 MeV 14680 Events/ 2 MeV 1146802 Events/ 50 MeV11727112...5050555 Events/ 50 MeV11727112...5050555
2 2 2.5 2.5
0 0 0 0
-0.1 -0.05 0 0.05 0.1 5.255.265.275.285.29 5.3 0.7 0.9 1.1 1.3 1.5 1.7 0.7 0.9 1.1 1.3 1.5 1.7
D E (GeV) M (GeV/c2) M(K+p -) (GeV) M(K+p -) (GeV)
bc 1 2
FIG. 2: Same as for Fig. 1 but for the B0 →K∗0K∗0 →(K+π−)(K+π−) study: (a) ∆E, (b) M , (c) M (K+π−), and (d)
bc 1
M (K+π−).
2
6
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7
TABLEII: Summaryofsystematicerrors(inunitsofevents)fordecaymodeswithafinalstateK+π−K−π+. Theparameters
NB0→K∗(1430)X and Nb→u,d,s (the other known charmless B decays) correspond to branching fraction uncertainties for these
2
charmlessB decays. Valuesforf andf aretheuncertaintiesfor longitudinalpolarization andself-cross-feed, respectively.
L SCF
Source K∗0K∗0 K∗0K−π+ K∗(1430)K∗(1430) K∗(1430)K∗0 K∗(1430)K−π+ Nonresonant K+π−K−π+
0 0 0 0
Fitting PDF ±1.8 ±40.3 ±55.6 ±37.7 ±158.0 ±102.4
NB0→K∗(1430)X +1.1 +10.2 −7.1 −20.4 −52.8 −10.5
2
Nb→u,d,s ±0.0 ±0.1 ±0.2 ±0.1 ±0.7 ±1.0
f −0.1 — — — — —
L
f ±0.7 ±1.4 ±5.6 ±2.2 ±17.2 ±14.6
SCF
Fit Bias +1.5 +2.9 ±5.1 +13.3 +8.9 +7.3
−0.7 −5.4 −2.3 −14.7 −10.8
Tracking ±0.4 ±0.8 ±3.5 ±0.9 ±9.6 ±6.8
PID ±0.4 ±0.7 ±2.9 ±0.7 ±8.2 ±6.0
R requirement ±0.2 ±0.4 ±1.6 ±0.4 ±4.5 ±3.2
N ±0.1 ±0.3 ±1.1 ±0.3 ±3.1 ±2.2
BB
Sum +2.8 +41.7 +56.3 +40.0 +159.7 +104.1
−2.1 −40.7 −56.8 −43.0 −168.6 −104.9
TABLE III: Same as for Table II but for decay modes with a final state K+π−K+π−.
Source K∗0K∗0 K∗0K+π− K∗(1430)K∗(1430) K∗(1430)K∗0 Nonresonant K+π−K+π−
0 0 0
Fitting PDF ±2.4 ±40.0 ±20.7 ±22.5 ±30.5
NB0→K∗(1430)X,K∗(1430)Kπ −0.3 +16.8 +85.1 −20.2 −96.8
2 0
Nb→u,d,s ±0.0 ±0.4 ±0.1 ±0.3 ±0.3
f −0.7 — — — —
L
f ±0.1 ±0.2 ±0.8 ±0.5 ±0.2
SCF
Fit Bias +0.5 ±2.7 +1.3 +8.2 +7.7
−1.0 −3.4 −1.6 −2.2
Tracking ±0.2 ±0.0 ±1.2 ±0.4 ±0.5
PID ±0.2 ±0.0 ±1.0 ±0.3 ±0.4
Rrequirement ±0.1 ±0.0 ±0.6 ±0.2 ±0.2
N ±0.1 ±0.0 ±0.4 ±0.1 ±0.2
BB
Sum +2.5 +43.5 +87.7 +23.9 +31.4
−2.7 −40.1 −21.1 −30.3 −101.5