Evidence for $CP$ violation in $B^{+} \to K^{*}(892)^{+} \pi^{0}$ from a Dalitz plot analysis of $B^{+} \to K^{0}_{\rm S} \pi^{+} \pi^{0}$ decays

0.5 MB·English

by  J. P. Lees

BABAR-PUB-14/011
SLAC-PUB-16186
Evidence for CP violation in B+ K∗(892)+π0 from a Dalitz plot analysis of
B+ →K0π+π0 decays
→ S
J. P. Lees, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
Universit´e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
5 E. Grauges
1 Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
0
2 A. Palanoab
n INFN Sezione di Baria; Dipartimento di Fisica, Universita` di Barib, I-70126 Bari, Italy
a
J G. Eigen and B. Stugu

4 University of Bergen, Institute of Physics, N-5007 Bergen, Norway

]
x D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, M. J. Lee, and G. Lynch
e Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
-
p
H. Koch and T. Schroeder
e
h Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany
[

C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. So
1
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
v
5
0 A. Khan
7 Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
0
0 V. E. Blinovabc, A. R. Buzykaeva, V. P. Druzhininab, V. B. Golubevab, E. A. Kravchenkoab,
.
1 A. P. Onuchinabc, S. I. Serednyakovab, Yu. I. Skovpenab, E. P. Solodovab, and K. Yu. Todyshevab
0 Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090a,
5 Novosibirsk State University, Novosibirsk 630090b,
1 Novosibirsk State Technical University, Novosibirsk 630092c, Russia
:
v
i A. J. Lankford
X
University of California at Irvine, Irvine, California 92697, USA
r
a
B. Dey, J. W. Gary, and O. Long
University of California at Riverside, Riverside, California 92521, USA
M. Franco Sevilla, T. M. Hong, D. Kovalskyi, J. D. Richman, and C. A. West
University of California at Santa Barbara, Santa Barbara, California 93106, USA
A. M. Eisner, W. S. Lockman, W. Panduro Vazquez, B. A. Schumm, and A. Seiden
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin,
T. S. Miyashita, P. Ongmongkolkul, F. C. Porter, and M. Ro¨hrken
California Institute of Technology, Pasadena, California 91125, USA
R. Andreassen, Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D. Sokoloff, and L. Sun
University of Cincinnati, Cincinnati, Ohio 45221, USA
2
P. C. Bloom, W. T. Ford, A. Gaz, J. G. Smith, and S. R. Wagner
University of Colorado, Boulder, Colorado 80309, USA
R. Ayad∗ and W. H. Toki
Colorado State University, Fort Collins, Colorado 80523, USA
B. Spaan
Technische Universita¨t Dortmund, Fakult¨at Physik, D-44221 Dortmund, Germany
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
S. Playfer
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
D. Bettonia, C. Bozzia, R. Calabreseab, G. Cibinettoab, E. Fioravantiab,
I. Garziaab, E. Luppiab, L. Piemontesea, and V. Santoroa
INFN Sezione di Ferraraa; Dipartimento di Fisica e Scienze della Terra, Universita` di Ferrarab, I-44122 Ferrara, Italy
A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Martellotti,
P. Patteri, I. M. Peruzzi,† M. Piccolo, M. Rama, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
R. Contriab, M. R. Mongeab, S. Passaggioa, and C. Patrignaniab
INFN Sezione di Genovaa; Dipartimento di Fisica, Universita` di Genovab, I-16146 Genova, Italy
B. Bhuyan and V. Prasad
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
A. Adametz and U. Uwer
Universita¨t Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
H. M. Lacker
Humboldt-Universita¨t zu Berlin, Institut fu¨r Physik, D-12489 Berlin, Germany
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, and S. Prell
Iowa State University, Ames, Iowa 50011-3160, USA
H. Ahmed
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudia Arabia
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder,
A. M. Lutz, B. Malaescu,‡ P. Roudeau, A. Stocchi, and G. Wormser
Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3/CNRS et Universit´e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. Payne, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
3
A. J. Bevan, F. Di Lodovico, and R. Sacco
Queen Mary, University of London, London, E1 4NS, United Kingdom
G. Cowan
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
D. N. Brown and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, and K. R. Schubert
Johannes Gutenberg-Universit¨at Mainz, Institut fu¨r Kernphysik, D-55099 Mainz, Germany
R. J. Barlow§ and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingdom
R. Cenci, B. Hamilton, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib, P. M. Patel,¶ and S. H. Robertson
McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8
N. Neria and F. Palomboab
INFN Sezione di Milanoa; Dipartimento di Fisica, Universita` di Milanob, I-20133 Milano, Italy
L. Cremaldi, R. Godang,∗∗ and D. J. Summers
University of Mississippi, University, Mississippi 38677, USA
M. Simard and P. Taras
Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7
G. De Nardoab, G. Onoratoab, and C. Sciaccaab
INFN Sezione di Napolia; Dipartimento di Scienze Fisiche,
Universita` di Napoli Federico IIb, I-80126 Napoli, Italy
G. Raven
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
M. Margoniab, M. Morandina, M. Posoccoa, M. Rotondoa, G. Simiab, F. Simonettoab, and R. Stroiliab
INFN Sezione di Padovaa; Dipartimento di Fisica, Universita` di Padovab, I-35131 Padova, Italy
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand,
G. Calderini, J. Chauveau, Ph. Leruste, G. Marchiori, and J. Ocariz
Laboratoire de Physique Nucl´eaire et de Hautes Energies,
IN2P3/CNRS, Universit´e Pierre et Marie Curie-Paris6,
Universit´e Denis Diderot-Paris7, F-75252 Paris, France
M. Biasiniab, E. Manonia, and A. Rossia
INFN Sezione di Perugiaa; Dipartimento di Fisica, Universita` di Perugiab, I-06123 Perugia, Italy
4
C. Angeliniab, G. Batignaniab, S. Bettariniab, M. Carpinelliab,†† G. Casarosaab, M. Chrzaszcza,
F. Fortiab, M. A. Giorgiab, A. Lusianiac, B. Oberhofab, E. Paoloniab, G. Rizzoab, and J. J. Walsha
INFN Sezione di Pisaa; Dipartimento di Fisica, Universita` di Pisab; Scuola Normale Superiore di Pisac, I-56127 Pisa, Italy
D. Lopes Pegna, J. Olsen, and A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
F. Anullia, R. Facciniab, F. Ferrarottoa, F. Ferroniab, M. Gasperoab, A. Pilloniab, and G. Pireddaa
INFN Sezione di Romaa; Dipartimento di Fisica,
Universita` di Roma La Sapienzab, I-00185 Roma, Italy
C. Bu¨nger, S. Dittrich, O. Gru¨nberg, M. Hess, T. Leddig, C. Voß, and R. Waldi
Universita¨t Rostock, D-18051 Rostock, Germany
T. Adye, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
S. Emery and G. Vasseur
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
D. Aston, D. J. Bard, C. Cartaro, M. R. Convery, J. Dorfan, G. P. Dubois-Felsmann, W. Dunwoodie, M. Ebert,
R. C. Field, B. G. Fulsom, M. T. Graham, C. Hast, W. R. Innes, P. Kim, D. W. G. S. Leith, D. Lindemann,
S. Luitz, V. Luth, H. L. Lynch, D. B. MacFarlane, D. R. Muller, H. Neal, M. Perl,¶ T. Pulliam, B. N. Ratcliff,
A. Roodman, R. H. Schindler, A. Snyder, D. Su, M. K. Sullivan, J. Va’vra, W. J. Wisniewski, and H. W. Wulsin
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
M. V. Purohit and J. R. Wilson
University of South Carolina, Columbia, South Carolina 29208, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, and E. M. T. Puccio
Stanford University, Stanford, California 94305-4060, USA
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie and R. F. Schwitters
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchiab, F. De Moriab, A. Filippia, and D. Gambaab
INFN Sezione di Torinoa; Dipartimento di Fisica, Universita` di Torinob, I-10125 Torino, Italy
L. Lanceriab and L. Vitaleab
INFN Sezione di Triestea; Dipartimento di Fisica, Universita` di Triesteb, I-34127 Trieste, Italy
F. Martinez-Vidal, A. Oyanguren, and P. Villanueva-Perez
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
5
J. Albert, Sw. Banerjee, A. Beaulieu, F. U. Bernlochner, H. H. F. Choi, G. J. King, R. Kowalewski,
M. J. Lewczuk, T. Lueck, I. M. Nugent, J. M. Roney, R. J. Sobie, and N. Tasneem
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
WereportaDalitzplotanalysisofcharmlesshadronicdecaysofchargedBmesonstothefinalstate
K0π+π0 usingthefullBABAR datasetof470.9±2.8 million BB eventscollectedattheΥ(4S)reso-
S
nance. We measure the overall branching fraction and CP asymmetry to be B B+ →K0π+π0 =
45.9±2.6±3.0+8.6 ×10−6 and A B+ →K0π+π0 = 0.07±0.05±0.03+0.02, where the un-
−0.0 CP −(cid:0)0.03 (cid:1)
certainties are statistical, systematic, and due to the signal model, respectively. This is the first
(cid:0)measurement of the(cid:1)branching fraction(cid:0)for B+ →K0π+(cid:1)π0. We find first evidence of a CP asym-
metry in B+ →K∗(892)+π0 decays: A B+→K∗(892)+π0 = −0.52±0.14±0.04+0.04. The
CP −0.02
significance of this asymmetry, including systematic and model uncertainties, is 3.4 standard devi-
(cid:0) (cid:1)
ations. We also measure the branching fractions and CP asymmetries for three other intermediate
decay modes.
PACSnumbers: 13.25.Hw,12.15.Hh,11.30.Er
I. INTRODUCTION QCDpenguin contributionscanbe eliminated by con-
structing a linear combination of the weak decay am-
plitudes for B+ K∗π to form a pure isospin I = 3
The Cabibbo-Kobayashi-Maskawa (CKM) mecha- state [3]: → 2
nism [1, 2] for quark mixing describes all weak charged
currenttransitionsbetweenquarksintermsofaunitarity A =A K∗0π+ +√2A K∗+π0 . (1)
3
matrix with four parameters: three rotation angles and 2
an irreducible phase. The unitarity of the CKM matrix Sincealltransitions(cid:0)fromI(cid:1)= 1 toI(cid:0)= 3 sta(cid:1)tesoccurvia
2 2
is usually expressed as triangle relationships among its only ∆I = 1 operators, A3 is free from QCD contribu-
2
elements. The interference between tree-level and loop tions. The weak phase of A is often denoted as
3
(“penguin”) amplitudes can give rise to direct CP vio- 2
lation, which is sensitive to the angles of the Unitarity Φ = 1Arg A¯ /A , (2)
3 3 3
Triangle, denoted α, β, and γ. Measurements of the pa- 2 −2 2 2
rameters of the CKM matrix provide an important test whereA¯ istheCP conjugate(cid:16)oftheam(cid:17)plitudeinEq.(1).
3
of the Standard Model (SM) since any deviation from 2
The phase Φ in Eq. (2) is the CKM angle γ in the
unitarity or discrepancies between measurements of the 3
2
same parameter in different decay processes would im- absence of EWP contributions [4].
ply a possible signature of new physics. Tree ampli- Measurements of the rates and CP asymmetries in
tudes in B K∗π decays are sensitive to γ, which can B Kπ have generated considerable interest because
be extracted→from interferences between the intermedi- of p→ossible hints of new-physics contributions [5, 6]. Of
ate states that populate the Kππ Dalitz plane. How- particular interest is the difference, ∆ACP, between the
ever, these amplitudes are Cabibbo-suppressed relative CP asymmetry in B+ K+π0 and the CP asymme-
→
to contributions carrying a different phase and involv- try in B0 K+π−, which in the SM is expected to be
→
ingradiationofeitheragluon(QCDpenguin)orphoton consistent with zero within the theoretical uncertainties
(electroweak penguin or EWP) from a loop. assuming U-spin symmetry and in the absence of color-
suppressedtreeandelectroweakamplitudes [7,8]. Using
theaveragevaluesofA ofK+π0 andK+π− decays[9],
CP
∆A (Kπ) is
CP
∗Nowat: UniversityofTabuk,Tabuk71491,Saudi Arabia
∆A (Kπ) = A K+π0 A K+π−
†Also at: Universit`a di Perugia, Dipartimento di Fisica, I-06123 CP CP − CP
Perugia,Italy = 0.122 0.022, (3)
‡Nowat: LaboratoiredePhysiqueNucl´eaireetdeHautesEnergies, (cid:0)± (cid:1) (cid:0) (cid:1)
IN2P3/CNRS,F-75252Paris,France which differs from zero by 5.5 standard deviations. Un-
§Nowat: UniversityofHuddersfield,HuddersfieldHD13DH,UK fortunately, hadronic uncertainties prevent a clear inter-
¶Deceased
pretation of these results in terms of the new-physics
∗∗Nowat: UniversityofSouth Alabama, Mobile,Alabama36688,
implications [3, 10]. Additional information can be ob-
USA
††Alsoat: Universit`adiSassari,I-07100Sassari,Italy tainedthroughstudiesoftherelatedvector-pseudoscalar
6
decaysB K∗π andB Kρ[11–13],forwhichthe ra- II. AMPLITUDE ANALYSIS FORMALISM
→ →
tiosoftree-to-penguinamplitudesareexpectedtobetwo
to three times larger than for B Kπ decays. Hence, A number of intermediate states contribute to the
B K∗π and B Kρ decays co→uld have considerably decay B+ K0π+π0. Their individual contributions
lar→ger CP asymme→tries. are measur→ed bSy performing a maximum likelihood fit
to the distribution of events in the Dalitz plot formed
In this article, we present the results from an ampli-
ctuhdaregaencaolnyjsuisgoafteBp+ro→cesKseS0sπi+sπim0pdleiecdaytsh.roTuhgehionuctlutshiiosnaor-f fLraoumrat+h+e[t2w4o] svoafrtiwaabrleest,omp2KerS0fπo+rmantdhims fi2πt+.π0. We use the
ticle, except when referring to CP asymmetries. This is The total signal amplitudes for the B+ and the B−
the first Dalitz plot analysis of this decay by BABAR; the decays are given in the isobar formalism by [25, 26]
onlypreviousBABARanalysisofthisdecaywasrestricted
A m2 ,m2 = c F m2 ,m2 , (4)
to measuring the branching fraction and CP asymmetry KS0π+ π+π0 j j KS0π+ π+π0
of B+ K0ρ+ [14]. An upper limit on the branching (cid:16) (cid:17) Xj (cid:16) (cid:17)
flarabcotriaotn→iofno:r B(+B+→KK0π0+ππ+0π0w)a<s s6e6t by10t−h6e[C15L]E. O Col- A¯(cid:16)m2KS0π−,m2π−π0(cid:17)=Xj c¯jF¯j(cid:16)m2KS0π−,m2π−π0(cid:17), (5)
B → ×
where c is the complex coefficient for a given resonant
Two contributions to the K0π+π0 final state arise j
S decay mode j contributing to the Dalitz plot. This com-
from the resonant decays B+ K∗(892)0π+ and
B+ K∗(892)+π0. Although bo→th the rate and CP plex coefficient contains the weak-interaction phase de-
asym→metriesforB+ K∗(892)0π+ havebeenwellmea- pendence that is measured relative to one of the con-
sured, with K∗0 K→+π−, by both the BABAR [16] and tributing resonant channels. In this article we report
→ results for the relative phases between each pair of am-
Belle [17] Collaborations, the measurements of the rate
plitudes.
andCP asymmetryfor B+ K∗(892)+π0 [18] havesig-
nificant statistical uncertain→ties and could benefit from The function Fj describes the dynamics of the decay
amplitudes and is the product of a resonant lineshape
the additional information provided by a full amplitude
(R ), two Blatt-Weisskopf barrier factors [27] (X ), and
analysis. InTableIwereviewtheexistingmeasurements j L
an angular-dependent term (T ) [28]:
of the rates and CP asymmetries in the B K∗(892)π j,L
→
system. F =R X (~p , p~ ) X (~q , ~q ) T (~p,~q), (6)
j j L 0 L 0 j,L
× | | | | × | | | | ×
whereListheorbitalangularmomentumbetweenthein-
termediateresonanceandthebachelorparticle(thebach-
TABLE I: Average values of the branching fractions B and elorparticleisthedaughteroftheB decaythatdoesnot
CP asymmetries A for B → K∗(892)π decays as deter- arise from the resonance), ~q is the momentum of one of
CP
mined by theHeavy Flavor Averaging Group [9]. the daughters of the resonance in the rest frame of the
Mode B(10−6) A References resonance,p~is themomentumofthebachelorparticlein
CP
the rest frame of the resonance, and p~ and ~q are the
K∗+π− 8.5±0.7 −0.23±0.06 [19–22] 0 0
values of p~ and ~q, respectively, at the nominal mass of
K∗+π0 8.2±1.8 −0.06±0.24 [18]
the resonance. The Blatt-Weisskopf barrier factors are
K∗0π+ 9.9+0.8 −0.038±0.042 [16, 17]
−0.9 given by
K∗0π0 2.5±0.6 −0.15±0.13 [19, 23]
X (~u , ~u ) = 1, (7)
L=0 0
| | | |
1+z
0
This article is organised as follows. The isobar model XL=1(~u , ~u0 ) = , (8)
| | | | 1+z
used to parameterize the complex amplitudes describing r
the intermediateresonancescontributingto the K0π+π0 (z 3)2+9z
S X (~u , ~u ) = 0− 0, (9)
final state is presented in Section II. A brief descrip- L=2 | | | 0| s (z 3)2+9z
tion of the BABAR detector and the dataset is given in −
Section III. The event reconstruction and selection are wherez =(~u rBW)2,z0 =(~u0 rBW)2,~uiseither~q orp~,
| | | |
discussed in detail in Section IV, the background study andr =4.0(GeV/c)−1isthemesonradiusparameter.
BW
in Section V, and a description of the extended maxi- The uncertainty in r , used for systematic variations,
BW
mumlikelihoodfitinSectionVI.Theresultsaregivenin is 2 (GeV/c)−1 fortheK∗ resonances,andrangesfrom
±
Section VII, and a study of the systematic uncertainties 1.0 to +2.0 (GeV/c)−1 for the ρ(770)+ [28]. The an-
is presented in Section VIII. In Section IX, we provide −gular term depends on the spin of the resonance and is
a summary and conclusion, discussing the results and given by [29, 30]
combining the branching fractions and CP asymmetries
for the decays B+ K∗(892)0π+, B+ K∗(1430)0π+, Tj,L=0 = 1, (10)
and B+ K∗(892→)+π0 with previou→s BA0BAR results T = 2p~.~q, (11)
j,L=1
obtained→from the final states B+ K+π−π+ and −4
B+ K+π0π0. → Tj,L=2 = 3(p~.~q)2 (p~ ~q )2 . (12)
→ 3 − | || |
h i
7
decaying to spin-0 particles, Γ(m) can be expressed as
(K π+)π0 (K π0)π+ (π+π0)K
S S S
π+(q) KS(q) π+(q) Γ(m)=Γ |~q| 2L+1 m0 X (~q , ~q )2, (14)
0 L 0
~q m | | | |
(cid:18)| 0|(cid:19) (cid:16) (cid:17)
where m and Γ are the nominalmass andwidth of the
π0(p) π+(p) K (p) 0 0
S
resonance.
The Gounaris-Sakurai (GS) parametrization [34] is
usedtodescribethelineshapeoftheρresonancedecaying
K (-q) π0(-q) π0(-q) into two pions. The parametrization takes the form
S
1+Γ d/m
RGS = 0· 0 , (15)
j m2 m2+f(m) im Γ(m)
0− − 0
FIG.1: Schematicrepresentationofthedefinitionsof~qandp~
used in this analysis for the(left) KS0π+, (center) KS0π0, and where Γ(m) is given by Eq. (14). Expressions for f(m),
(right) π+π0 resonances. in terms of Γ and m, and the constant d can be found
0
in Ref. [34]. The parameters specifying the ρ lineshape
are taken from Refs. [31, 32], which provides lineshape
TABLE II: Parameters of the Dalitz plot model for informationderivedfromfits to e+e− annihilationandτ
B+ →K0π+π0 usedin thenominal fit. Themass andwidth
S lepton decay data.
oftheρ(770)+andtheiruncertaintiesaretakenfromtheanal-
For the JP = 0+ component of the Kπ spectrum, de-
yses by the ALEPH [31] and CMD2 [32] Collaborations. All
other parameters are taken from Ref. [28]. The resonance noted (Kπ)∗0/+, we make use of the LASS parametriza-
0
shapes are a Gounaris-Sakurai (GS) function, a relativistic tion [33], which consists of a K∗ resonant term together
0
Breit-Wigner(RBW)function,orbasedonmeasurementsby with an effective-range, nonresonant component to de-
theLASSCollaboration[33],withathescatteringlengthand scribe the slowly increasing phase as a function of the
r the effectiverange of theLASS parametrization. Kπ mass:
Resonance Lineshape Parameters
m
Resonance mass Width RLASS = +
MeV/c2 (MeV) j ~q cotδB i ~q
| | − | |
ρ(770)+ GS 7(cid:0)75.5±0.(cid:1)6 148.2±0.8 e2iδB m0Γ0|mq~00| , (16)
K∗(892)+ RBW 891.7±0.3 50.8±0.9 (m2 m2) im Γ |q~|m0
K∗(892)0 RBW 896.1±0.2 50.7±0.6 0− − 0 0m|q~0|
(Kπ)∗0/+ LASS 1412±50 294±80
0 mcutoff =1800MeV/c2 [16] where cotδB = a|1q~| + 12r|~q|. The values used for the
a=2.1±0.1 (GeV/c)−1 [16] scattering length a and the effective range r are given
r=3.3±0.3 (GeV/c)−1 [16] in Table II. The effective-range component has a cutoff
imposed at 1800MeV/c2 [16]. Integrating separately the
resonant term, the effective-range term, and the coher-
The choice of which resonance daughter is defined to entsum, wefind thatthe K0∗(1430)0 andthe K0∗(1430)+
carry the momentum ~q is a matter of convention. How- resonances account for 88% of the sum, and the effec-
ever, its definition is important when comparing mea- tive range component 49%; the 37% excess is due to de-
surements from different experiments. In Fig. 1, we il- structive interference between the two terms. The LASS
lustrate the momentum definitions used for the K0π+, parametrization is the least-well-determined component
S
K0π0, and π+π0 resonance combinations. of the signal model; we discuss the impact of these un-
S
certainties in Section VIII.
Table II lists the resonances used to model the signal.
We determine a nominal model from data by studying The complex coefficients cj and c¯j in Eqs. (4,5)
changes in the log likelihood values for the best fit when can be parametrized in different ways; we follow the
omitting or adding a resonance to the fit model, as de- parametrization used in Ref. [16] as it avoids a bias in
scribed in Section VI. themeasurementofamplitudesandphaseswhentheres-
For the K∗(892)0 and K∗(892)+ resonances, we use a onant components have small magnitudes:
relativistic Breit-Wigner (RBW) lineshape [28]:
c = (x +∆x )+i(y +∆y ), (17)
j j j j j
1 c¯ = (x ∆x )+i(y ∆y ),
RjRBW(m)= m2 m2 im Γ(m), (13) j j − j j − j
0− − 0
where x ∆x and y ∆y are the real and imagi-
j j j j
± ±
where m is the two-body invariant mass and Γ(m) is nary parts of the amplitudes. The quantities ∆x and
j
the mass-dependent width. In general, for a resonance ∆y parametrize the CP violation in the decay. The CP
j
8
asymmetry for a given intermediate state is given by experimental conditions [38, 39]. The EvtGen [40] and
Jetset7.4[41]softwarepackagesareusedtogeneratesig-
c¯j 2 cj 2 nalandbackgroundMonte-Carlo(MC) eventsamples in
A = | | −| | (18)
CP,j c¯ 2+ c 2 order to determine efficiencies and evaluate background
j j
| | | | contributions for different selection criteria.
2(x ∆x +y ∆y )
j j j j
= . (19)
−x2+∆x2+y2+∆y2
j j j j
IV. EVENT SELECTION
The results quoted for the resonances in the follow-
ing analysis use fit fractions (FF ) as phase-convention-
j
independentquantitiesrepresentingthefractionalrateof WereconstructB+ K0π+π0candidatesfromoneπ0
→ S
each contribution in the Dalitz plot. The FF for mode j candidate,oneK0candidatereconstructedfromapairof
S
is defined as oppositely charged pions, and a charged pion candidate.
The π0 candidate is formed from a pair of neutral en-
c F 2+ c¯ F¯ 2 dm2 dm2 ergyclusters inthe EMC with laboratoryenergiesabove
| j j| j j Kπ ππ
FF = . (20) 0.05 GeVandlateralmoments[42]between0.01and0.6.
j R R (cid:16) |A|2+(cid:12)(cid:12)A¯ 2 (cid:12)(cid:12)d(cid:17)m2Kπdm2ππ We requirethe invariantmass ofthe reconstructedπ0 to
R R (cid:16) (cid:12) (cid:12) (cid:17) lieintherange0.11<mγγ <0.16 GeV/c2. TheKS0 can-
The sumof allthe fit fracti(cid:12)on(cid:12)sdoes notnecessarilyyield didate is required to have a π+π− invariant mass within
unityduetoconstructiveanddestructiveinterference,as 15 MeV/c2 ofthe K0 mass[28], andaproperdecaytime
S
quantified by the interference fit fractions given by [30] greaterthan0.5 10−11s. Toreducecombinatorialback-
ground, we also×require that the K0 candidates have a
S
FF = 2Re cic∗jFiFj∗ dm2Kπdm2ππ. (21) vertex probability greater than 10−6 and that the cosine
ij R R | (cid:2)kckFk|2d(cid:3)m2Kπdm2ππ tohfethKe0aflnigglhetbdeirtewceteionnt(haesKdeS0temrmoimneedntbuymthdeirienctteioranctainodn
S
The parametersRxR, ∆Px , y , and ∆y are determined point and the K0 vertex) be greater than 0.995. For the
j j j j S
in the fit, except for the reference amplitude. Fit frac- π+ candidate, we use information from the tracking sys-
tions, relative phases, and asymmetries are derived from tems, the EMC, and the DIRC to select a charged track
the fit parameters and their statistical uncertainties de- consistent with the pion hypothesis. We constrain the
terminedfrompseudoexperimentsgeneratedfromthefit π+ track and K0 candidate to originate from a common
S
results. vertex.
Signal events that are misreconstructed with the de-
cay products of one or more daughters completely or
III. THE BABAR DETECTOR AND MC partially exchanged with other particles in the rest of
SIMULATION the event have degraded kinematic resolution. We re-
fer to these as “self-cross-feed” (SCF) events. This mis-
The data used in the analysis were collected with reconstruction has a strong dependence on the energy
the BABAR detector at the PEP-II asymmetric-energy of the particles concerned and is more frequent for low-
e+e− collideratSLAC NationalAcceleratorLaboratory. energy particles, i.e., for decays in the corners of the
The sample consists of 429fb−1 of integrated luminosity Dalitz plot. Because of the presence of a π0 in the final
recorded at the Υ(4S) resonance mass (“on-peak”) and state,thereisasignificantprobabilityforsignaleventsto
45fb−1 collected40 MeVbelowtheresonancemass(“off- be misreconstructeddue to low-energyphotons from the
peak”) [35]. The on-peak sample corresponds to the full π0 decay. Using a classification based on MC informa-
BABAR Υ(4S) dataset and contains 470.9 2.8 million tion, we find that in simulated events the SCF fraction
BB events [30]. A detailed description of th±e BABAR de- dependsstronglyontheresonantsubstructureofthesig-
tector is given in Refs. [36, 37]. Charged-particle tracks nal and ranges from 34% for B+ K∗(892)+π0 to 50%
are measured by means of a five-layer double-sided sil- for B+ ρ(770)+K0. In events →simulated uniformly in
→ S
icon vertex tracker (SVT) and a 40-layer drift chamber phase space, hereafter referred to as nonresonant MC,
(DCH), both positioned within a solenoid that provides the SCF fraction varies from less than 10% in the center
a 1.5 T magnetic field. Charged-particle identification of the Dalitz plot to almost 70% in the two corners of
is achieved by combining the information from a ring- the Dalitz plot, where either the π0 or the π+ has low
imaging Cherenkov detector (DIRC) and specific ioniza- energy. We describe how the SCF events are handled in
tion energy loss (dE/dx) measurements from the DCH Section VI.
and SVT. Photons are detected and their energies mea- In order to suppress the dominant background,due to
sured in a CsI(Tl) electromagnetic calorimeter (EMC). continuum e+e− qq (q = u,d,s,c) events, we employ
→
Muon candidates are identified in the instrumented flux a boosted decision tree (BDT) algorithm that combines
return of the solenoid. four variables commonly used to discriminate jet-like qq
We use Geant4-based software to simulate the de- events from the more spherical BB events in the e+e−
tector response and account for the varying beam and center-of-mass(CM)frame. Thefirstoftheseistheratio
9
of the second-to-zeroth order momentum-weighted Leg- Each of the B candidates is refit to determine the
endre polynomial moments, Dalitz plot variables. In these fits the K0π+π0 invari-
S
antmassis constrainedto the worldaveragevalueofthe
L 12 3cos2θi−1 pi B mass [28] to improve position resolution within the
2 = i∈ROE , (22) Dalitz plot.
L P (cid:0) p (cid:1)
0 i We find that 20% of the remaining events in nonreso-
i∈ROE
nant MC have two or more candidates. We choose the
P
where the summations are over all tracks and neutral bestcandidateinmultiple-candidateeventsbasedonthe
clusters in the event, excluding those that form the B highest B-vertex probability. This procedure is found to
candidate(the“restoftheevent”orROE);p isthepar- selectacorrectlyreconstructedcandidatemorethan60%
i
ticlemomentum,andθ istheanglebetweentheparticle of the time and does not bias the fit variables.
i
and the thrust axis of the B candidate, hereafter also The reconstruction efficiency over the Dalitz plot is
referred to as the B. The three other variables entering modeled using a two-dimensional (2D) binned distri-
the BDT are the absolute value of the cosine of the an- bution based on a generated sample of approximately
gle between the B direction and the collision axis, the 2 106 simulated B+ K0π+π0 MC events, where the
× → S
zeroth-order momentum-weighted Legendre polynomial events uniformly populate phase space. All selection cri-
moment,andthe absolutevalueoftheoutputofanother teria are appliedexcept for those correspondingto a Kπ
BDT used for “flavortagging”, i.e., for distinguishing B invariant-mass veto described below, which is taken into
from B decays using inclusive properties of the decay of account separately. The 2D histogram of reconstructed
the other B meson in the Υ(4S) BB event [43]. The MC events is then divided by the 2D histogram of the
momentum-weightedLegendrepo→lynomialmoments and generatedMCevents. Inordertoexpandregionsofphase
the cosine of the angle between the B direction and the spacewithlargeefficiencyvariations,theDalitzplotvari-
beam axis are calculated in the e+e− CM frame. The ablesaretransformedinto“squareDalitzplot”[44]coor-
BDT is trainedona sample of signalMC eventsand off- dinates. Weobtainanaverageefficiency,fornonresonant
peakdata. WeapplyaloosecriterionontheBDToutput MC events, of approximately 15%. In the likelihood fit
of BDT > 0.06, which retains approximately 70% of we use an event-by-event efficiency that depends on the
out
the signal while rejecting 92% of the qq background. Dalitz plot position.
InadditiontoBDT ,weusetwokinematic variables
out
to distinguish the signal from the background:
V. BB BACKGROUNDS
m = E2 p2 , (23)
ES X− B
In addition to continuum events, background arises
∆E = Eq⋆ √s/2, (24)
B− from non-signal BB events. A major source of BB
background arises from B+ D0 K0π0 π+ de-
where → → S
cays. To suppress this background, we veto events with
1.804<m <1.924GeV/c2. (cid:0) (cid:1)
EX =(s/2+pe+e− pB)/Ee+e−, (25) KS0π0
· TheremainingBB backgroundsarestudiedusingMC
and where √s is the total e+e− CM energy, with simulationsandclassifiedbasedontheshapeofthem ,
ES
(Ee+e−,pe+e−) and (EB,pB) the four-momenta of the ∆E, and Dalitz plot distributions. We identify nine cat-
initial e+e− system and the B candidate, respectively, egoriesofBB backgrounds: categories1,2and3include
both measured in the lab frame, while the star indicates different types of three- and four-body B decays involv-
thee+e− CMframe. Thesignalm distributionforcor- ing an intermediate D meson; categories4 and 5 include
ES
rectlyreconstructedeventsisapproximatelyindependent charmlessfour-bodyB decaystointermediateresonances
of their position in the K0π+π0 Dalitz plot and peaks where a π0 in the final state is not reconstructed; cate-
S
near the B mass with a resolution of about 3.4MeV/c2. gories 6 and 7 include two-body B decays with a radi-
We retain all candidates satisfying the following selec- ated photon misreconstructed as a π0 decay product or
tion criteria: 5.23 < m < 5.29GeV/c2 and 0.3 < where the π0 arises from the other B decay; category 8
ES
−
∆E < 0.3GeV. The signal region, where the final fit includescharmlessthree-bodyB decayswhereacharged
to data is performed, is defined by the tighter crite- pion is interchanged with a π0 meson from the other B;
ria 5.260 < m < 5.287GeV/c2 and 0.20 < ∆E < and finally category 9 includes all other simulated BB
ES
−
0.15GeV. We also use candidates in the sideband re- background contributions. Within each category, each
gion of m defined by 5.23 < m < 5.26GeV/c2 and of the m , ∆E, BDT , and Dalitz plot distributions
ES ES ES out
0.20 < ∆E < 0.15GeV and subtract from distribu- are formed by combining the contributions of all decay
−
tions for these events the BB background contributions modes in the category. The combinations are done by
predicted by MC simulations. We then add these dis- normalizingthe distributions foreachdecaymode to the
tributions to the off-peak data distributions to increase expected number of events in the recorded data sam-
the statistical precision of our model of the Dalitz plot ple, which is estimated using reconstruction efficiencies
distribution for continuum background. determined from MC, the number of BB pairs in the
10
recordeddata sample, and the branching fractions listed
i∆nER,efBs.D[9T,o2u8t,].aFnodrtehaechDcaaltietgzoprylo,tthvearhiiasbtolegsraamresuofsemdEaSs, 22)c 25
theprobabilitydensityfunctions(PDF)inthelikelihood V/
e
fit to data to model the BB background. G 20 A1
(
π0
2mπ+ 15
VI. THE MAXIMUM LIKELIHOOD FIT
10 D1
The extended likelihood function is given by
5
C3C4
C2 B3 B2
L=exp − Nk × (26) 0 C1 B1
! 0 5 10 15 20 25
Xk m2 (GeV/c2)2
Ne KSπ+
iY=1"Xk NkPki(cid:16)m2KS0π+,m2π+π0,mES,∆E,BDTout,qB(cid:17)# ,
FIG. 2: Diagram illustrating the division of the Dalitz plot
where N is the number of candidates in each signal or
k into different regions for the definition of the PDFs for self-
backgroundcategoryk, N is the total number of events
e crossfeed signal events. Each letterindicates whetherthede-
ienvetnhteid)aitsathsaempproled,uacntdofPtkihe(tPheDPFsDdFesfocrribcainteggtohreyDkaalintdz pendence is on m2π+π0 (A), m2KS0π+ (B), or m2KS0π0 (C). The
remaining region of the Dalitz plot (D1) is where we expect
plot, m , ∆E, and BDT distributions, with q the
ES out B to find fewer SCF events, and where the shapes for mES and
charge of the B candidate.
∆E are less dependent on their position in the Dalitz plot,
To avoid possible biases in the determination of the
furtherdescribed in Table III.
fit parameters [45], we use MC samples to study corre-
lations between the fit variables and the Dalitz plot pa-
rameters, m2 and m2 . We find that for correctly intheDalitzplotoftheSCFfractionandthemeandiffer-
reconstructeKdS0sπi+gnal canπd+idπa0tes, the ∆E distribution is ence between the true and reconstructed position in the
strongly dependent on m . This is mostly due to Dalitzplot;weincludemoreregionsinareasoftheDalitz
a dependence of the enerKgyS0πr+esolution of the B candi- plot where these quantities are largest. We use mES and
date on the π0 momentum. For SCF signal candidates, ∆E PDFs specific to each region, as listed in Table III.
both the m and ∆E distributions depend on all three Some of the PDFs used in the parametrization of the
ES
two-bodyinvariantmasses: m , m ,andm . SCF include Cruijff functions, Chebychev polynomials,
The m , ∆E, and BDT dKisSt0rπi+butioKnS0sπf0or continπu+uπm0 Gaussian functions, and two-piece Gaussian (BGauss)
ES out
and BB backgrounds have negligible correlations with functions. Atwo-pieceGaussianfunctionisanasymmet-
the Dalitz plot parameters. ric Gaussian described by the following functional form
Forcorrectlyreconstructedsignalcandidates,them (omitting normalization factor)
ES
and ∆E PDFs are parameterized by a Cruijff function,
which is given by (omitting normalization factor) (x m)2
f (x)=exp − − . (28)
BGauss 2σ2
(x m)2 " L,R #
f (x)=exp − − , (27)
Cruijff "2σL2,R+αL,R(x−m)2# funFcotriotnhe[46c]ontotinpuaurmambetaecrkizgerotuhnedm, we suhsaepea.nTAhReG∆UES
ES
wheremgivesthepeakofthedistributionandtheasym- distribution is described by a linear function, and the
metricwidthofthedistributionisgivenbyσ forx<m BDT distribution by an exponential function. The
L out
and σ for x > m. The asymmetric modulation is sim- m , ∆E, and BDT PDFs for BB backgrounds are
R ES out
ilarly given by α for x < m and α for x > m. The definedbythesumofthehistogramsfromtheMC simu-
L R
∆E PDFparametersarecalculatedonanevent-by-event lations for decay modes in each background category, as
basis in terms of the K0π+ invariant mass, as a linear described in Section V.
S
function for m2 < 20GeV2/c4 and as a quadratic ThecontinuumandBB backgroundDalitzplotdistri-
KS0π+
function for m2 > 20GeV2/c4. These functions are butionsareincludedinthelikelihoodastwo-dimensional
KS0π+ histograms. For BB backgrounds, we use MC samples.
determined by fitting the ∆E distribution in large non-
For continuum background, we combine events from the
resonant MC samples. For the SCF signal, in order to
off-peak data and the m sidebandin on-peak data, af-
followtherapidshapevariationsacrosstheDalitzplotof ES
tersubtractingcontributionsfromB decays,asdescribed
the m and∆E distributions, wedivide the Dalitz plot
ES in Section IV. For the 2D histograms, we use the square
intoseveralregionsasillustratedinFig.2. Eachletterin-
Dalitz plot coordinates. A linear interpolation between
dicates whether the dependence is onm2 , m2 , or
π+π0 KS0π+ bin centers is applied.
m2KS0π0. Theregionsarechosenbasedonthedistribution The free parametersin the fit arethe yields for signal,