Dalitz plot analysis of
D
þ
s
!
K
þ
K
þ
P. del Amo Sanchez,
1
J. P. Lees,
1
V. Poireau,
1
E. Prencipe,
1
V. Tisserand,
1
J. Garra Tico,
2
E. Grauges,
2
M. Martinelli,
3a,3b
D. A. Milanes,
3a,3b
A. Palano,
3a,3b
M. Pappagallo,
3a,3b
G. Eigen,
4
B. Stugu,
4
L. Sun,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
G. Lynch,
5
I. L. Osipenkov,
5
H. Koch,
6
T. Schroeder,
6
D. J. Asgeirsson,
7
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
A. Khan,
8
V. E. Blinov,
9
A. R. Buzykaev,
9
V. P. Druzhinin,
9
V. B. Golubev,
9
E. A. Kravchenko,
9
A. P. Onuchin,
9
S. I. Serednyakov,
9
Yu. I. Skovpen,
9
E. P. Solodov,
9
K. Yu. Todyshev,
9
A. N. Yushkov,
9
M. Bondioli,
10
S. Curry,
10
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
E. C. Martin,
10
D. P. Stoker,
10
H. Atmacan,
11
J. W. Gary,
11
F. Liu,
11
O. Long,
11
G. M. Vitug,
11
C. Campagnari,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. West,
12
A. M. Eisner,
13
C. A. Heusch,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
T. Schalk,
13
B. A. Schumm,
13
A. Seiden,
13
L. O. Winstrom,
13
C. H. Cheng,
14
D. A. Doll,
14
B. Echenard,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
M. S. Dubrovin,
15
G. Mancinelli,
15
B. T. Meadows,
15
M. D. Sokoloff,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
M. Nagel,
16
U. Nauenberg,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
*
W. H. Toki,
17
H. Jasper,
18
T. M. Karbach,
18
A. Petzold,
18
B. Spaan,
18
M. J. Kobel,
19
K. R. Schubert,
19
R. Schwierz,
19
D. Bernard,
20
M. Verderi,
20
P. J. Clark,
21
S. Playfer,
21
J. E. Watson,
21
M. Andreotti,
22a,22b
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
A. Cecchi,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
P. Franchini,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
22a,22b
M. Munerato,
22a,22b
M. Negrini,
22a,22b
A. Petrella,
22a,22b
L. Piemontese,
22a
R. Baldini-Ferroli,
23
A. Calcaterra,
23
R. de Sangro,
23
G. Finocchiaro,
23
M. Nicolaci,
23
S. Pacetti,
23
P. Patteri,
23
I. M. Peruzzi,
23,
†
M. Piccolo,
23
M. Rama,
23
A. Zallo,
23
R. Contri,
24a,24b
E. Guido,
24a,24b
M. Lo Vetere,
24a,24b
M. R. Monge,
24a,24b
S. Passaggio,
24a
C. Patrignani,
24a,24b
E. Robutti,
24a
S. Tosi,
24a,24b
B. Bhuyan,
25
V. Prasad,
25
C. L. Lee,
26
M. Morii,
26
A. J. Edwards,
27
A. Adametz,
28
J. Marks,
28
U. Uwer,
28
F. U. Bernlochner,
29
M. Ebert,
29
H. M. Lacker,
29
T. Lueck,
29
A. Volk,
29
P. D. Dauncey,
30
M. Tibbetts,
30
P. K. Behera,
31
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
H. B. Crawley,
32
L. Dong,
32
W. T. Meyer,
32
S. Prell,
32
E. I. Rosenberg,
32
A. E. Rubin,
32
A. V. Gritsan,
33
Z. J. Guo,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
34
J. Firmino da Costa,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
A. Perez,
34
P. Roudeau,
34
M. H. Schune,
34
J. Serrano,
34
V. Sordini,
34,
‡
A. Stocchi,
34
L. Wang,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
I. Bingham,
36
C. A. Chavez,
36
J. P. Coleman,
36
J. R. Fry,
36
E. Gabathuler,
36
R. Gamet,
36
D. E. Hutchcroft,
36
D. J. Payne,
36
C. Touramanis,
36
A. J. Bevan,
37
F. Di Lodovico,
37
R. Sacco,
37
M. Sigamani,
37
G. Cowan,
38
S. Paramesvaran,
38
A. C. Wren,
38
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
A. Hafner,
40
K. E. Alwyn,
41
D. Bailey,
41
R. J. Barlow,
41
G. Jackson,
41
G. D. Lafferty,
41
J. Anderson,
42
R. Cenci,
42
A. Jawahery,
42
D. A. Roberts,
42
G. Simi,
42
J. M. Tuggle,
42
C. Dallapiccola,
43
E. Salvati,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
44
M. Zhao,
44
D. Lindemann,
45
P. M. Patel,
45
S. H. Robertson,
45
M. Schram,
45
P. Biassoni,
46a,46b
A. Lazzaro,
46a,46b
V. Lombardo,
46a
F. Palombo,
46a,46b
S. Stracka,
46a,46b
L. Cremaldi,
47
R. Godang,
47,
x
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
48
M. Simard,
48
P. Taras,
48
G. De Nardo,
49a,49b
D. Monorchio,
49a,49b
G. Onorato,
49a,49b
C. Sciacca,
49a,49b
G. Raven,
50
H. L. Snoek,
50
C. P. Jessop,
51
K. J. Knoepfel,
51
J. M. LoSecco,
51
W. F. Wang,
51
L. A. Corwin,
52
K. Honscheid,
52
R. Kass,
52
J. P. Morris,
52
N. L. Blount,
53
J. Brau,
53
R. Frey,
53
O. Igonkina,
53
J. A. Kolb,
53
R. Rahmat,
53
N. B. Sinev,
53
D. Strom,
53
J. Strube,
53
E. Torrence,
53
G. Castelli,
54a,54b
E. Feltresi,
54a,54b
N. Gagliardi,
54a,54b
M. Margoni,
54a,54b
M. Morandin,
54a
M. Posocco,
54a
M. Rotondo,
54a
F. Simonetto,
54a,54b
R. Stroili,
54a,54b
E. Ben-Haim,
55
G. R. Bonneaud,
55
H. Briand,
55
G. Calderini,
55
J. Chauveau,
55
O. Hamon,
55
Ph. Leruste,
55
G. Marchiori,
55
J. Ocariz,
55
J. Prendki,
55
S. Sitt,
55
M. Biasini,
56a,56b
E. Manoni,
56a,56b
A. Rossi,
56a,56b
C. Angelini,
57a,57b
G. Batignani,
57a,57b
S. Bettarini,
57a,57b
M. Carpinelli,
57a,57b,
k
G. Casarosa,
57a,57b
A. Cervelli,
57a,57b
F. Forti,
57a,57b
M. A. Giorgi,
57a,57b
A. Lusiani,
57a,57c
N. Neri,
57a,57b
E. Paoloni,
57a,57b
G. Rizzo,
57a,57b
J. J. Walsh,
57a
D. Lopes Pegna,
58
C. Lu,
58
J. Olsen,
58
A. J. S. Smith,
58
A. V. Telnov,
58
F. Anulli,
59a
E. Baracchini,
59a,59b
G. Cavoto,
59a
R. Faccini,
59a,59b
F. Ferrarotto,
59a
F. Ferroni,
59a,59b
M. Gaspero,
59a,59b
L. Li Gioi,
59a
M. A. Mazzoni,
59a
G. Piredda,
59a
F. Renga,
59a,59b
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60
R. Waldi,
60
T. Adye,
61
B. Franek,
61
E. O. Olaiya,
61
F. F. Wilson,
61
S. Emery,
62
G. Hamel de Monchenault,
62
G. Vasseur,
62
Ch. Ye
`
che,
62
M. Zito,
62
M. T. Allen,
63
D. Aston,
63
D. J. Bard,
63
R. Bartoldus,
63
J. F. Benitez,
63
C. Cartaro,
63
M. R. Convery,
63
J. Dorfan,
63
G. P. Dubois-Felsmann,
63
W. Dunwoodie,
63
R. C. Field,
63
M. Franco Sevilla,
63
B. G. Fulsom,
63
A. M. Gabareen,
63
M. T. Graham,
63
P. Grenier,
63
C. Hast,
63
W. R. Innes,
63
M. H. Kelsey,
63
H. Kim,
63
P. Kim,
63
M. L. Kocian,
63
D. W. G. S. Leith,
63
S. Li,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
63
H. Marsiske,
63
D. R. Muller,
63
H. Neal,
63
S. Nelson,
63
C. P. O’Grady,
63
I. Ofte,
63
M. Perl,
63
T. Pulliam,
63
B. N. Ratcliff,
63
A. Roodman,
63
A. A. Salnikov,
63
V. Santoro,
63
R. H. Schindler,
63
J. Schwiening,
63
A. Snyder,
63
D. Su,
63
M. K. Sullivan,
63
S. Sun,
63
K. Suzuki,
63
J. M. Thompson,
63
J. Va’vra,
63
PHYSICAL REVIEW D
83,
052001 (2011)
1550-7998
=
2011
=
83(5)
=
052001(20)
052001-1
Ó
2011 American Physical Society
A. P. Wagner,
63
M. Weaver,
63
W. J. Wisniewski,
63
M. Wittgen,
63
D. H. Wright,
63
H. W. Wulsin,
63
A. K. Yarritu,
63
C. C. Young,
63
V. Ziegler,
63
X. R. Chen,
64
W. Park,
64
M. V. Purohit,
64
R. M. White,
64
J. R. Wilson,
64
A. Randle-Conde,
65
S. J. Sekula,
65
M. Bellis,
66
P. R. Burchat,
66
T. S. Miyashita,
66
S. Ahmed,
67
M. S. Alam,
67
J. A. Ernst,
67
B. Pan,
67
M. A. Saeed,
67
S. B. Zain,
67
N. Guttman,
68
A. Soffer,
68
P. Lund,
69
S. M. Spanier,
69
R. Eckmann,
70
J. L. Ritchie,
70
A. M. Ruland,
70
C. J. Schilling,
70
R. F. Schwitters,
70
B. C. Wray,
70
J. M. Izen,
71
X. C. Lou,
71
F. Bianchi,
72a,72b
D. Gamba,
72a,72b
M. Pelliccioni,
72a,72b
M. Bomben,
73a,73b
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
N. Lopez-March,
74
F. Martinez-Vidal,
74
A. Oyanguren,
74
J. Albert,
75
Sw. Banerjee,
75
H. H. F. Choi,
75
K. Hamano,
75
G. J. King,
75
R. Kowalewski,
75
M. J. Lewczuk,
75
C. Lindsay,
75
I. M. Nugent,
75
J. M. Roney,
75
R. J. Sobie,
75
T. J. Gershon,
76
P. F. Harrison,
76
T. E. Latham,
76
M. R. Pennington,
76,
{
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
77
K. T. Flood,
77
Y. Pan,
77
R. Prepost,
77
C. O. Vuosalo,
77
and S. L. Wu
77
(
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universite
́
de Savoie, CNRS/IN2P3,
F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy;
3b
Dipartimento di Fisica, Universita
`
di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universita
̈
t Bochum, Institut fu
̈
r Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universita
̈
t Dortmund, Fakulta
̈
t Physik, D-44221 Dortmund, Germany
19
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
20
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France
21
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
22a
INFN Sezione di Ferrara, I-44100 Ferrara, Italy;
22b
Dipartimento di Fisica, Universita
`
di Ferrara, I-44100 Ferrara, Italy
23
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
24a
INFN Sezione di Genova, I-16146 Genova, Italy;
24b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
25
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
26
Harvard University, Cambridge, Massachusetts 02138, USA
27
Harvey Mudd College, Claremont, California 91711
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstr. 15, D-12489 Berlin, Germany
30
Imperial College London, London, SW7 2AZ, United Kingdom
31
University of Iowa, Iowa City, Iowa 52242, USA
32
Iowa State University, Ames, Iowa 50011-3160, USA
33
Johns Hopkins University, Baltimore, Maryland 21218, USA
34
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN2P3/CNRS et Universite
́
Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France
35
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
36
University of Liverpool, Liverpool L69 7ZE, United Kingdom
37
Queen Mary, University of London, London, E1 4NS, United Kingdom
38
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
39
University of Louisville, Louisville, Kentucky 40292, USA
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
052001 (2011)
052001-2
40
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
41
University of Manchester, Manchester M13 9PL, United Kingdom
42
University of Maryland, College Park, Maryland 20742, USA
43
University of Massachusetts, Amherst, Massachusetts 01003, USA
44
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
45
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
46a
INFN Sezione di Milano, I-20133 Milano, Italy;
46b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
47
University of Mississippi, University, Mississippi 38677, USA
48
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
49a
INFN Sezione di Napoli, I-80126 Napoli, Italy;
49b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
50
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
51
University of Notre Dame, Notre Dame, Indiana 46556, USA
52
Ohio State University, Columbus, Ohio 43210, USA
53
University of Oregon, Eugene, Oregon 97403, USA
54a
INFN Sezione di Padova, I-35131 Padova, Italy;
54b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
55
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN2P3/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
56a
INFN Sezione di Perugia, I-06100 Perugia, Italy;
56b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
57a
INFN Sezione di Pisa, I-56127 Pisa, Italy;
57b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy;
57c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
58
Princeton University, Princeton, New Jersey 08544, USA
59a
INFN Sezione di Roma, I-00185 Roma, Italy;
59b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
60
Universita
̈
t Rostock, D-18051 Rostock, Germany
61
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
62
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
63
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
64
University of South Carolina, Columbia, South Carolina 29208, USA
65
Southern Methodist University, Dallas, Texas 75275, USA
66
Stanford University, Stanford, California 94305-4060, USA
67
State University of New York, Albany, New York 12222, USA
68
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
69
University of Tennessee, Knoxville, Tennessee 37996, USA
70
University of Texas at Austin, Austin, Texas 78712, USA
71
University of Texas at Dallas, Richardson, Texas 75083, USA
72a
INFN Sezione di Torino, I-10125 Torino, Italy;
72b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
73a
INFN Sezione di Trieste, I-34127 Trieste, Italy;
73b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
74
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
75
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
76
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
77
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 18 November 2010; published 3 March 2011)
We perform a Dalitz plot analysis of about 100 000
D
þ
s
decays to
K
þ
K
þ
and measure the complex
amplitudes of the intermediate resonances which contribute to this decay mode. We also measure
the relative branching fractions of
D
þ
s
!
K
þ
K
þ
and
D
þ
s
!
K
þ
K
þ
K
. For this analysis we use a
*
Now at Temple University, Philadelphia, PA 19122, USA
†
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy.
‡
Also with Universita
`
di Roma La Sapienza, I-00185 Roma, Italy.
x
Now at University of South AL, Mobile, AL 36688, USA.
k
Also with Universita
`
di Sassari, Sassari, Italy.
{
Also with Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UK.
DALITZ PLOT ANALYSIS OF
...
PHYSICAL REVIEW D
83,
052001 (2011)
052001-3
384
fb
1
data sample, recorded by the
BABAR
detector at the PEP-II asymmetric-energy
e
þ
e
collider
running at center-of-mass energies near 10.58
GeV
.
DOI:
10.1103/PhysRevD.83.052001
PACS numbers: 13.25.Ft, 11.80.Et, 14.40.Be, 14.40.Lb
I. INTRODUCTION
Scalar mesons are still a puzzle in light meson spectros-
copy. New claims for the existence of broad states close to
threshold such as
ð
800
Þ
[
1
] and
f
0
ð
600
Þ
[
2
], have reop-
ened discussion about the composition of the ground state
J
PC
¼
0
þþ
nonet, and about the possibility that states such
as the
a
0
ð
980
Þ
or
f
0
ð
980
Þ
may be 4-quark states, due to
their proximity to the
K
K
threshold [
3
]. This hypothesis
can be tested only through accurate measurements of the
branching fractions and the couplings to different final
states. It is therefore important to have precise information
on the structure of the
and
K
K
S
waves. In this context,
D
þ
s
mesons can shed light on the structure of the scalar
amplitude coupled to
s
s
. The
S
wave has been already
extracted from
BABAR
data in a Dalitz plot analysis of
D
þ
s
!
þ
þ
[
4
]. The understanding of the
K
K
S
wave is also of great importance for the precise mea-
surement of
CP
violation in
B
s
oscillations using
B
s
!
J=
c
[
5
,
6
].
This paper focuses on the study of
D
þ
s
meson decay to
K
þ
K
þ
[
7
]. Dalitz plot analyses of this decay mode have
been performed by the E687 and CLEO Collaborations
using 700 events [
8
], and 14 400 events [
9
] respectively.
The present analysis is performed using about 100 000
events.
The decay
D
þ
s
!
þ
is frequently used in particle
physics as the reference mode for
D
þ
s
decay. Previous
measurements of this decay mode did not, however,
account for the presence of the
K
K
S
wave underneath
the
peak. Therefore, as part of the present analysis, we
obtain a precise measurement of the branching fraction
B
ð
D
þ
s
!
þ
Þ
relative to
B
ð
D
þ
s
!
K
þ
K
þ
Þ
.
Singly Cabibbo-suppressed (SCS) and doubly Cabibbo-
suppressed (DCS) decays play an important role in studies
of charmed hadron dynamics. The naive expectations
for the rates of SCS and DCS decays are of the order of
tan
2
C
and
tan
4
C
, respectively, where
C
is the Cabibbo
mixing angle. These rates correspond to about 5.3% and
0.28% relative to their Cabibbo-favored (CF) counterpart.
Because of the limited statistics in past experiments,
branching fraction measurements of DCS decays have
been affected by large statistical uncertainties [
10
]. A
precise measurement of
B
ð
D
þ
s
!
K
þ
K
þ
Þ
B
ð
D
þ
s
!
K
þ
K
þ
Þ
has been recently
performed by the Belle experiment [
11
].
In this paper we study the
D
þ
s
decay
D
þ
s
!
K
þ
K
þ
(1)
and perform a detailed Dalitz plot analysis. We then mea-
sure the branching ratios of the SCS decay
D
þ
s
!
K
þ
K
K
þ
(2)
and the DCS decay
D
þ
s
!
K
þ
K
þ
(3)
relative to the CF channel (
1
). The paper is organized as
follows. Section
II
briefly describes the
BABAR
detector,
while Sec.
III
gives details of event reconstruction.
Section
IV
is devoted to the evaluation of the selection
efficiency. Section
V
describes a partial-wave analysis of
the
K
þ
K
system, the evaluation of the
D
þ
s
!
þ
branching fraction, and the
K
K
S
-wave parametrization.
Section
VI
deals with the description of the Dalitz plot
analysis method and background description. Results from
the Dalitz plot analysis of
D
þ
s
!
K
þ
K
þ
are given in
Sec.
VII
. The measurements of the
D
þ
s
SCS and DCS
branching fractions are described in Sec.
VIII
, while
Sec.
IX
summarizes the results.
II. THE
BABAR
DETECTOR AND DATASET
The data sample used in this analysis corresponds to
an integrated luminosity of
384 fb
1
recorded with the
BABAR
detector at the SLAC PEP-II collider, operated at
center-of-mass energies near the
ð
4
S
Þ
resonance. The
BABAR
detector is described in detail elsewhere [
12
].
The following is a brief summary of the components
important to this analysis. Charged particle tracks are
detected, and their momenta measured, by a combination
of a cylindrical drift chamber and a silicon vertex tracker,
both operating within a 1.5 T solenoidal magnetic field.
Photon energies are measured with a CsI(Tl) electro-
magnetic calorimeter. Information from a ring-imaging
Cherenkov detector, and specific energy-loss measure-
ments in the silicon vertex tracker and cylindrical drift
chamber are used to identify charged kaon and pion
candidates.
III. EVENT SELECTION AND
D
þ
s
!
K
þ
K
þ
RECONSTRUCTION
Events corresponding to the three-body
D
þ
s
!
K
þ
K
þ
decay are reconstructed from the data sample
having at least three reconstructed charged tracks with
net charge
1
. We require that the invariant mass of
the
K
þ
K
þ
system lie within the mass interval
½
1
:
9
–
2
:
05
GeV
=c
2
. Particle identification is applied to
the three tracks, and the presence of two kaons is required.
The efficiency that a kaon is identified is 90% while the
rate that a kaon is misidentified as a pion is 2%. The three
tracks are required to originate from a common vertex,
and the
2
fit probability (
P
1
) must be greater than 0.1%.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
052001 (2011)
052001-4
We also perform a separate kinematic fit in which the
D
þ
s
mass is constrained to its known value [
10
]. This latter fit
will be used only in the Dalitz plot analysis.
In order to help in the discrimination of signal from
background, an additional fit is performed, constraining
the three tracks to originate from the
e
þ
e
luminous region
(beam spot). The
2
probability of this fit, labeled as
P
2
,is
expected to be large for most of the background events,
when all tracks originate from the luminous region, and
small for the
D
þ
s
signal, due to the measurable flight
distance of the latter.
The decay
D
s
ð
2112
Þ
þ
!
D
þ
s
(4)
is used to select a subset of event candidates in order to
reduce combinatorial background. The photon is required
to have released an energy of at least 100 MeV into the
electromagnetic calorimeter. We define the variable
m
¼
m
ð
K
þ
K
þ
Þ
m
ð
K
þ
K
þ
Þ
(5)
and require it to be within
2
D
þ
s
with respect to
m
D
þ
s
where
m
D
þ
s
¼
144
:
94
0
:
03
stat
MeV
=c
2
and
D
þ
s
¼
5
:
53
0
:
04
stat
MeV
=c
2
are obtained from a
Gaussian fit of the
m
distribution.
Each
D
þ
s
candidate is characterized by three variables:
the center-of-mass momentum
p
in the
e
þ
e
rest frame,
the difference in probability
P
1
P
2
, and the signed decay
distance
d
xy
¼
d
p
xy
j
p
xy
j
where
d
is the vector joining the beam
spot to the
D
þ
s
decay vertex and
p
xy
is the projection of the
D
þ
s
momentum on the
xy
plane. These three variables
are used to discriminate signal from background events:
in fact signal events are expected to be characterized by
larger values of
p
[
13
], due to the jetlike shape of the
e
þ
e
!
c
c
events, and larger values of
d
xy
and
P
1
P
2
,
due to the measurable flight distance of the
D
þ
s
meson.
The distributions of these three variables for signal
and background events are determined from data and are
shown in Fig.
1
. The background distributions are
estimated from events in the
D
þ
s
mass-sidebands, while
those for the signal region are estimated from the
D
þ
s
signal region with sideband subtraction. The normalized
probability distribution functions are then combined
in a likelihood-ratio test. A selection is performed on
this variable such that signal to background ratio is
maximized. Lower sideband, signal, and upper sideband
regions are defined between
½
1
:
911
–
1
:
934
GeV
=c
2
,
½
1
:
957
–
1
:
980
GeV
=c
2
, and
½
2
:
003
–
2
:
026
GeV
=c
2
, re-
spectively, corresponding to
ð
10
;
6
Þ
,
ð
2
;
2
Þ
,
and
ð
6
;
10
Þ
regions, where
is estimated from the fit
of a Gaussian function to the
D
þ
s
lines shape.
We have examined a number of possible background
sources. A small peak due to the decay
D
þ
!
þ
D
0
where
D
0
!
K
þ
K
is observed. A Gaussian fit to this
K
þ
K
spectrum gives
D
0
!
K
þ
K
¼
5
:
4 MeV
=c
2
.For
events within
3
:
5
D
0
!
K
þ
K
of the
D
0
mass, we plot the
mass difference
m
ð
K
þ
K
þ
Þ¼
m
ð
K
þ
K
þ
Þ
m
ð
K
þ
K
Þ
and observe a clean
D
þ
signal. We remove
events that satisfy
m
ð
K
þ
K
þ
Þ
<
0
:
15 GeV
=c
2
. The
surviving events still show a
D
0
!
K
þ
K
signal which
does not come from this
D
þ
decay. We remove events that
satisfy
m
ð
K
þ
K
Þ
>
1
:
85 GeV
=c
2
.
Particle misidentification, in which a pion
þ
mis
is
wrongly identified as a kaon, is tested by assigning the
pion mass to the
K
þ
. In this way we identify the back-
ground due to the decay
D
þ
!
K
þ
þ
which, for the
most part, populates the higher mass
D
þ
s
!
K
þ
K
þ
sideband. However, this cannot be removed without bias-
ing the
D
þ
s
Dalitz plot, and so this background is taken into
account in the Dalitz plot analysis.
We also observe a clean peak in the distribution of the
mass difference
m
ð
K
þ
mis
þ
Þ
m
ð
K
þ
mis
Þ
. Combining
m
ð
K
þ
mis
Þ
with each of the
0
meson candidates in
the event, we identify this contamination as due to
D
þ
!
þ
D
0
ð!
K
þ
0
Þ
with a missing
0
. We remove events
that satisfy
m
ð
K
þ
mis
þ
Þ
m
ð
K
þ
mis
Þ
<
0
:
15 GeV
=c
2
.
0
0.01
0.02
0.03
0.04
0.05
345
p* (GeV/c)
Probability
(a)
0
0.02
0.04
0.06
0.08
0.1
0.12
-0.1
0
0.1
0.2
0.3
d
xy
(cm)
(b)
0
0.02
0.04
0.06
0.08
00.51
P
1
- P
2
(c)
FIG. 1 (color online). Normalized probability distribution functions for signal (solid) and background events (hatched) used in a
likelihood-ratio test for the event selection of
D
þ
s
!
K
þ
K
þ
: (a) the center-of-mass momentum
p
, (b) the signed decay distance
d
xy
, and (c) the difference in probability
P
1
P
2
.
DALITZ PLOT ANALYSIS OF
...
PHYSICAL REVIEW D
83,
052001 (2011)
052001-5