Measurement of the mass and width of the
D
s
1
ð
2536
Þ
þ
meson
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
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. A. West,
12
A. M. Eisner,
13
J. Kroseberg,
13
W. S. Lockman,
13
A. J. Martinez,
13
T. Schalk,
13
B. A. Schumm,
13
A. Seiden,
13
C. H. Cheng,
14
D. A. Doll,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
A. Y. Rakitin,
14
R. Andreassen,
15
M. S. Dubrovin,
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
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
D. Bettoni,
22a
C. Bozzi,
22a
R. Calabrese,
22a,22b
G. Cibinetto,
22a,22b
E. Fioravanti,
22a,22b
I. Garzia,
22a,22b
E. Luppi,
22a,22b
M. Munerato,
22a,22b
M. Negrini,
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
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
P. D. Dauncey,
30
M. Tibbetts,
30
P. K. Behera,
31
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
H. B. Crawley,
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
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
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
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
G. Simi,
42
C. Dallapiccola,
43
E. Salvati,
43
R. Cowan,
44
D. Dujmic,
44
G. Sciolla,
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,
‡
R. Kroeger,
47
P. Sonnek,
47
D. J. Summers,
47
X. Nguyen,
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
N. L. Blount,
53
J. Brau,
53
R. Frey,
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
M. Bomben,
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
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,
x
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
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
C. Buenger,
60
T. Hartmann,
60
T. Leddig,
60
H. Schro
̈
der,
60
R. Waldi,
60
T. Adye,
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. 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
P. Lewis,
63
S. Li,
63
B. Lindquist,
63
S. Luitz,
63
V. Luth,
63
H. L. Lynch,
63
D. B. MacFarlane,
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
S. H. Robertson,
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
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
M. S. Alam,
67
J. A. Ernst,
67
N. Guttman,
68
A. Soffer,
68
PHYSICAL REVIEW D
83,
072003 (2011)
1550-7998
=
2011
=
83(7)
=
072003(14)
072003-1
Ó
2011 American Physical Society
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
L. Lanceri,
73a,73b
L. Vitale,
73a,73b
N. Lopez-March,
74
F. Martinez-Vidal,
74
A. Oyanguren,
74
H. Ahmed,
75
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
E. M. T. Puccio,
76
H. R. Band,
77
S. Dasu,
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
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
J. P. LEES
et al.
PHYSICAL REVIEW D
83,
072003 (2011)
072003-2
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 14 March 2011; published 19 April 2011)
The decay width and mass of the
D
s
1
ð
2536
Þ
þ
meson are measured via the decay channel
D
þ
s
1
!
D
þ
K
0
S
using
385 fb
1
of data recorded with the
BABAR
detector in the vicinity of the
ð
4
S
Þ
resonance
at the PEP-II asymmetric-energy electron-positron collider. The result for the decay width is
ð
D
þ
s
1
Þ¼
0
:
92
0
:
03
ð
stat
:
Þ
0
:
04
ð
syst
:
Þ
MeV
. For the mass, a value of
m
ð
D
þ
s
1
Þ¼
2535
:
08
0
:
01
ð
stat
:
Þ
0
:
15
ð
syst
:
Þ
MeV
=c
2
is obtained. The mass difference between the
D
þ
s
1
and the
D
þ
is
measured to be
m
ð
D
þ
s
1
Þ
m
ð
D
þ
Þ¼
524
:
83
0
:
01
ð
stat
:
Þ
0
:
04
ð
syst
:
Þ
MeV
=c
2
, representing a signifi-
cant improvement compared to the current world average. The unnatural spin-parity assignment for the
D
þ
s
1
meson is confirmed.
DOI:
10.1103/PhysRevD.83.072003
PACS numbers: 14.40.Lb, 13.25.Ft, 13.66.Bc
*
Now at Temple University, Philadelphia, PA 19122, USA
†
Also with Universita
`
di Perugia, Dipartimento di Fisica, Perugia, Italy
‡
Now at University of South AL, Mobile, AL 36688, USA
x
Also with Universita
`
di Sassari, Sassari, Italy
MEASUREMENT OF THE MASS AND WIDTH OF THE
...
PHYSICAL REVIEW D
83,
072003 (2011)
072003-3
I. INTRODUCTION
The theoretical description of
D
þ
s
mesons is problematic
because, unlike
D
mesons, the masses and widths of the
D
s
0
ð
2317
Þ
þ
and
D
s
1
ð
2460
Þ
þ
states [
1
–
6
] are not in agree-
ment with potential model calculations based on HQET
[
7
]. Theoretical explanations for the discrepancy invoke
D
ðÞ
K
molecules [
8
], chiral partners [
9
,
10
], unitarized
chiral models [
11
,
12
], tetraquarks [
13
,
14
], and lattice cal-
culations [
15
,
16
], but a satisfactory description is still
lacking (see [
17
,
18
] for more details). Improved measure-
ments of the
D
þ
s
1
meson parameters can lead to a better
understanding of these states.
In this analysis a precise measurement of the
D
s
1
ð
2536
Þ
þ
mass and decay width is performed based on
a high statistics data sample [
19
]. The
D
s
1
ð
2536
Þ
þ
meson,
referred to as the
D
þ
s
1
below, was first seen in
c
c
-continuum
reactions [
20
], and more recently in
B
decays. The current
world average mass value published by the Particle Data
Group is based on measurements with large statistical and
systematic uncertainties:
2535
:
29
0
:
20 MeV
=c
2
[
21
];
the mass difference between the
D
þ
s
1
and the
D
þ
meson
has been measured to be
525
:
04
0
:
22 MeV
=c
2
[
21
]. An
upper limit on the decay width (
<
2
:
3 MeV
at 90%
confidence level), and a measurement of the spin-parity
of the
D
þ
s
1
meson (
J
P
¼
1
þ
), have been obtained, but based
on low-statistics data samples only [
21
–
23
]. The mixing
between the
D
þ
s
1
meson and the other
J
P
¼
1
þ
state
D
s
1
ð
2460
Þ
þ
was investigated in Ref. [
24
].
This analysis is based on a data sample corresponding to
an integrated luminosity of
349 fb
1
recorded at the
ð
4
S
Þ
resonance and
36 fb
1
recorded 40 MeV below that reso-
nance with the
BABAR
detector at the asymmetric-energy
e
þ
e
collider PEP-II at the SLAC National Accelerator
Laboratory. In this analysis,
D
þ
s
1
mesons are reconstructed
from
c
c
continuum events in the
D
þ
K
0
S
channel; those
originating from
B
decays are rejected.
The
BABAR
detector is described briefly in Sec.
II
.
The principal criteria used in the reconstruction of
the
D
þ
K
0
S
mass spectrum and the selection of
D
þ
s
1
-candidates are discussed in Sec.
III
. The relevant
Monte Carlo (MC) simulations are described in Sec.
IV
,
while the detector resolution parametrization is considered
in Sec.
V
. Measurements of the mass and total width for
the
D
þ
s
1
state are obtained from a fit to the
D
þ
K
0
S
invariant mass distribution as discussed in Sec.
VI
. Decay
angle distributions are studied in Sec.
VII
, where the
implications for the spin-parity of the
D
þ
s
1
state are also
discussed. Sources of systematic uncertainty are described
in Sec.
VIII
, and the results of the analysis are summarized
in Sec.
IX
and
X
.
II. THE
BABAR
DETECTOR
The
BABAR
detector is described in detail elsewhere
[
25
]. Charged particles are detected, and their momenta
measured, with a combination of five layers of double-
sided silicon microstrip detectors (SVT) and a 40-layer
cylindrical drift chamber (DCH), both coaxial with the
cryostat of a superconducting solenoidal magnet that
produces a magnetic field of 1.5 T. Charged particle
identification is achieved by measurements of the
energy-loss
dE=dx
in the tracking devices and with an
internally reflecting, ring-imaging Cherenkov detector.
The energy of photons and electrons is measured with a
CsI(Tl) electromagnetic calorimeter, covering 90% of
the
4
solid angle in the
ð
4
S
Þ
rest frame. The instru-
mented flux return of the magnetic field is used to identify
muons and
K
0
L
’s.
III. SELECTION AND RECONSTRUCTION
OF EVENTS
The
D
þ
s
1
is reconstructed via its decay mode
D
þ
K
0
S
, with
K
0
S
!
þ
and
D
þ
!
D
0
þ
. The
D
0
is
reconstructed through two decay modes,
K
þ
and
K
þ
þ
, which will be labeled
K
4
and
K
6
, respectively, in the following. To improve the mass
resolution, the mass difference
m
ð
D
þ
s
1
Þ¼
m
ð
D
þ
s
1
Þ
m
ð
D
þ
Þ
m
ð
K
0
S
Þ
is examined.
Events are selected by requiring at least five charged
tracks, at least one of which is identified as a charged kaon.
Also, at least one neutral kaon candidate is required.
Each track must approach the nominal
e
þ
e
interaction
point to within 1.5 cm in the transverse direction, and to
within 10 cm in the longitudinal (beam) direction. Kaon
candidates are identified using the normalized kaon,
pion and proton likelihood values (
L
K
,
L
and
L
p
)
obtained from the particle identification system, by requir-
ing
L
K
=
ð
L
K
þ
L
Þ
>
0
:
50
and
L
K
=
ð
L
K
þ
L
p
Þ
>
0
:
018
.
Furthermore, the track must be inconsistent with the elec-
tron hypothesis or have a momentum less than
0
:
4 GeV
=c
.
Tracks that fulfill
L
K
=
ð
L
K
þ
L
Þ
<
0
:
98
and
L
p
=
ð
L
p
þ
L
Þ
<
0
:
98
are selected as pions.
Candidates for the
D
0
decay are formed by selecting all
K
þ
pairs (
K
þ
þ
combinations in the second
mode) that have an invariant mass within
100 MeV
=c
2
of the nominal mass [
21
]. Candidates for the
D
þ
decay
are formed by adding a
þ
to the
D
0
, such that the mass
difference between
D
þ
and
D
0
is less than
170 MeV
=c
2
.
A
K
0
S
candidate consists of a
þ
pair with invariant
mass within
25 MeV
=c
2
of the nominal mass [
21
]. A
kinematic fit is applied to the complete decay chain, con-
straining the
D
þ
s
1
candidate vertex to be consistent with the
e
þ
e
interaction region. Mass constraints are not applied
to intermediate states. Those
D
þ
s
1
candidates with a
2
fit
probability greater than 0.1% are retained. To suppress
combinatorial background and events from
B
decays,
we require the momentum
p
ð
D
þ
s
1
Þ
of the
D
þ
s
1
in the
ð
4
S
Þ
center-of-mass (CM) frame to exceed
2
:
7 GeV
=c
.
J. P. LEES
et al.
PHYSICAL REVIEW D
83,
072003 (2011)
072003-4
The
K
and
K
mass spectra for accepted
D
0
can-
didates, shown in Figs.
1(a)
and
1(d)
, are fitted with a signal
function consisting of a sum of two Gaussians with a
common mean value, and a linear background function.
The width of the signal regions for
D
0
,
D
þ
and
K
0
S
candidates is defined as twice the full width at half maxi-
mum (FWHM) of the signal line shapes. A signal window
of
18
ð
14
Þ
MeV
=c
2
for the
K
4
(
K
6
) mode around
the mean mass of
1863
:
5
ð
1863
:
5
Þ
MeV
=c
2
obtained from
the fit is used to select
D
0
candidates. For these candidates,
the
D
0
þ
D
0
mass difference distributions are shown in
Figs.
1(b)
and
1(e)
. These are fitted with the sum of a
relativistic Breit-Wigner signal function and a background
function consisting of a polynomial times an exponential
function. A
D
þ
signal region of
1MeV
=c
2
around the
fitted mean value of
145
:
4MeV
=c
2
is chosen for both
decay modes. To further reduce the background, the
angle between the flight direction of the
K
0
S
candidate
and the line connecting the
e
þ
e
interaction point
and the
K
0
S
decay vertex is required to be less than 0.15
radians. For candidates passing these selection criteria,
the
K
0
S
candidate invariant mass distributions (Figs.
1(c)
and
1(f)
) are fitted with the sum of a signal function,
consisting of the sum of two Gaussians, and a linear back-
ground function. A signal window of
6MeV
=c
2
around
the fitted mean mass of
497
:
2MeV
=c
2
is selected for both
decay modes.
In the case of an event with multiple candidates, the
candidate with the best fit probability is chosen. The
m
ð
D
þ
s
1
Þ
candidate spectra after all selection criteria are
shown in Figs.
2(a)
and
2(b)
. The fits to these spectra
use a Double-Gaussian signal function and a linear back-
ground function. Note that for this preliminary fit the
intrinsic width and the resolution are not taken into ac-
count. The FWHM values obtained are
ð
2
:
2
0
:
1
Þ
MeV
and
ð
2
:
0
0
:
1
Þ
MeV
, respectively, with corresponding
signal yields of about 3500 and 4000 entries.
IV. MONTE CARLO SIMULATION
AND COMPARISON WITH DATA
Monte Carlo events are generated for
D
þ
s
1
!
D
þ
K
0
S
,
D
þ
!
D
0
þ
, with
D
0
!
K
þ
and
D
0
!
K
þ
þ
,by
EVTGEN
[
26
]. The detector response is
simulated using the
GEANT4
[
27
] package. For each
D
0
decay mode, and for each of the corresponding
D
s
1
decays,
776000 events are generated. The
D
þ
s
1
line shape is gen-
erated using a nonrelativistic Breit-Wigner function
having central value
m
ð
D
þ
s
1
Þ
gen
¼
2535
:
35 MeV
=c
2
and
intrinsic width
ð
D
þ
s
1
Þ
gen
¼
1 MeV
(this sample is labeled
1
in the following). The range of generated
D
þ
s
1
masses is
restricted to values between
m
ð
D
þ
s
1
Þ
gen
10 MeV
=c
2
and
m
ð
D
þ
s
1
Þ
gen
þ
15 MeV
=c
2
. The masses of the daughter par-
ticles are taken from Ref. [
21
].
]
2
) [GeV/c
π
m(K
1.8
1.85
1.9
1.95
2
Entries / 1.7 MeV/c
0
2
4
6
8
10
12
14
16
18
20
22
3
10
×
]
2
) [GeV/c
0
) - m(D
*+
m(D
0.14
0.145
0.15
0.155
2
Entries / 0.2 MeV/c
0
10
20
30
40
50
3
10
×
]
2
) [GeV/c
-
π
+
π
m(
0.48
0.49
0.5
0.51
0.52
2
Entries / 0.45 MeV/c
0
1
2
3
4
5
6
3
10
×
]
2
) [GeV/c
π
π
π
m(K
1.8
1.85
1.9
1.95
2
Entries / 1.7 MeV/c
0
10
20
30
40
50
3
10
×
]
2
) [GeV/c
0
) - m(D
*+
m(D
0.14
0.145
0.15
0.155
2
Entries / 0.2 MeV/c
0
10
20
30
40
50
60
70
3
10
×
]
2
) [GeV/c
-
π
+
π
m(
0.48
0.49
0.5
0.51
0.52
2
Entries / 0.45 MeV/c
0
1
2
3
4
5
6
7
8
3
10
×
(a)
(d)
(b)
(e)
(c)
(f)
FIG. 1 (color online). (a, d)
D
0
candidate invariant mass distributions; (b, e) Difference between the
D
þ
and
D
0
candidate invariant
masses. (c, f)
K
0
S
candidate invariant mass distributions; (a–c)
K
4
mode; (d–f)
K
6
mode. Signal regions are indicated by the
vertical lines. The signal and background line shapes fitted to the mass distributions are described in the text.
MEASUREMENT OF THE MASS AND WIDTH OF THE
...
PHYSICAL REVIEW D
83,
072003 (2011)
072003-5
In order to test the mass resolution model, a second set of
MC samples with 381000 events for each
D
0
decay mode
is generated using a Breit-Wigner width of
ð
D
þ
s
1
Þ
gen
¼
2 MeV
(
2
sample). In addition to these signal MC
samples, separate
D
0
and
K
0
S
samples are created from
data and generic
c
c
MC simulations without requiring a
D
þ
or
D
þ
s
1
. They are used mainly for resolution studies.
The MC and data are in good agreement for the trans-
verse momentum distributions of pions, kaons,
D
and
D
mesons, and for the number of SVT coordinates of pions
and kaons. The agreement is worse for the number of DCH
coordinates, where the data show systematically fewer
coordinates than the MC, giving rise to a resolution that
is about 10% smaller in the MC than in data. This is
illustrated in Fig.
3
, which shows the
p
ð
K
0
S
Þ
and
p
ð
D
0
Þ
dependence of the ratio between the FWHM of the reso-
lution functions in
c
c
MC and data, where
p
is the
momentum in the CM frame. This effect will be discussed
further in Sec.
VIII
. There is also disagreement between
the number of
D
þ
s
1
signal entries in MC and data as a
function of
p
ð
D
þ
s
1
Þ
(Fig.
4
). This effect will be addressed
in Sec.
V
and
VIII
.
V. RESOLUTION MODEL
The resolution model is derived from the
D
þ
s
1
signal MC
by studying the difference
m
res
between the reconstructed
and generated
D
þ
s
1
mass values. The Multi-Gaussian
ansatz
G
ð
m
res
Þ¼
Z
r
0
0
1
r
2
e
ððð
m
res
m
res0
Þ
2
Þ
=
ð
2
2
ÞÞ
d
(1)
is found to accurately model the mass resolution spectra.
This represents a superposition of Gaussian distributions
with the same mean value
m
res0
but variable width
,
starting from minimum width
0
and increasing to
maximum width
r
0
. The FWHM of the distribution is
numerically calculable once
0
and
r
are known. The mass
resolution for the different particles depends on the
CM momentum
p
ð
D
þ
s
1
Þ
. Therefore, the parameter
0
of
Eq. (
1
) is obtained as a function of
p
ð
D
þ
s
1
Þ
.
Figs.
5(a)
and
5(b)
show
m
res
distributions for the full
p
ð
D
þ
s
1
Þ
range. From these plots the value of the parameter
r
is determined to be
4
:
78
0
:
04
and
5
:
20
0
:
05
for the
K
4
and
K
6
modes, respectively. Events are divided
into 30
p
ð
D
þ
s
1
Þ
intervals from
2
:
7 GeV
=c
to
4
:
7 GeV
=c
and the fit repeated for each interval, resulting in
p
ð
D
þ
s
1
Þ
-dependent
0
values (Figs.
6(a)
and
6(b)
). The
corresponding
p
ð
D
þ
s
1
Þ
-dependent FWHM of the resolu-
tion functions is shown in Figs.
7(a)
and
7(b)
.
In order to validate this resolution model, the
p
ð
D
þ
s
1
Þ
-dependent resolution function with the cor-
responding parameters
0
and
r
is convolved with a
) [GeV/c]
0
S
(K
*
p
123
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
) [GeV/c]
0
(D
*
p
2
2.5
3
3.5
0.7
0.8
0.9
1
1.1
1.2
1.3
(a)
(b)
FWHM(MC)
FWHM(Data)
FWHM(MC)
FWHM(Data)
FIG. 3 (color online).
p
-dependence of the ratio between the
FWHM of the resolution functions from
c
c
-MC and data.
(a)
K
0
S
!
þ
. (b)
D
0
!
K
þ
þ
. The solid line shows
the fitted mean ratio with a value of 0.9.
]
2
) [GeV/c
+
s1
m(D
∆
0.01
0.02
0.03
0.04
0.05
2
Entries / 0.4 MeV/c
0
100
200
300
400
500
]
2
) [GeV/c
+
s1
m(D
∆
0.01
0.02
0.03
0.04
0.05
2
Entries / 0.4 MeV/c
0
100
200
300
400
500
600
700
(a)
(b)
FIG. 2 (color online).
m
ð
D
þ
s
1
Þ¼
m
ð
D
þ
s
1
Þ
m
ð
D
þ
Þ
m
ð
K
0
S
Þ
invariant mass distributions in data after applying all
selection criteria for the (a)
K
4
and (b)
K
6
mode. A
Double-Gaussian signal function and a linear background func-
tion are used to describe the data in a preliminary fit.
J. P. LEES
et al.
PHYSICAL REVIEW D
83,
072003 (2011)
072003-6
nonrelativistic Breit-Wigner function and fitted to the
m
ð
D
þ
s
1
Þ
signal MC distribution (MC sample
1
). The
results are shown in Figs.
8(a)
and
8(b)
, and the recon-
structed values for mean
m
ð
D
þ
s
1
Þ
0
and width
ð
D
þ
s
1
Þ
are
listed in Table
I
. The corresponding generated values for
both decay modes are
m
ð
D
þ
s
1
Þ
gen
¼
27
:
744 MeV
=c
2
for
the mean and
ð
D
þ
s
1
Þ
gen
¼
1
:
000 MeV
for the width. The
small deviations between generated and reconstructed val-
ues are discussed in Sec.
VIII
.
VI. FIT TO THE
D
K
0
S
MASS SPECTRUM
For the final fit to the
D
K
0
S
mass spectra, as represented
by the
m
ð
D
þ
s
1
Þ
distributions of Figs.
2
and
9
, the signal
function consists of a relativistic Breit-Wigner line shape
numerically convolved with the
p
ð
D
þ
s
1
Þ
-dependent reso-
lution function (Eq. (
1
)). A linear function is used to
describe the background.
The relativistic Breit-Wigner function used takes the
form
p
1
;m
p
1
;m
0
2
L
þ
1
m
0
m
mF
L
ð
p
1
;m
Þ
2
ð
m
2
0
m
2
Þ
2
þ
2
m
m
2
0
;
(2)
where
m
0
is an abbreviation for
m
ð
D
þ
s
1
Þ
0
and
m
stands for
m
ð
D
þ
s
1
Þ
. The variable
p
1
;m
is the momentum of the
D
þ
in
the rest frame of the
D
þ
s
1
resonance candidate, which has
mass
m
, and
p
1
;m
0
is the value for
m
¼
m
0
. The respective
]
2
[GeV/c
res
m
∆
-0.005
0
0.005
2
Entries / 0.12 MeV/c
0
2
4
6
8
10
12
14
16
18
3
10
×
]
2
[GeV/c
res
m
∆
-0.005
0
0.005
2
Entries / 0.12 MeV/c
0
2
4
6
8
10
12
3
10
×
(a)
(b)
FIG. 5 (color online). Fit of the resolution function (Eq. (
1
)) to
m
res
with the
r
and
0
parameters free to vary for the (a)
K
4
and (b)
K
6
decay modes.
) [GeV/c]
+
s1
(D
*
p
3
3.5
4
4.5
5
yield / 60 MeV/c
+
s1
D
0
20
40
60
80
100
) [GeV/c]
+
s1
(D
*
p
3
3.5
4
4.5
5
yield / 60 MeV/c
+
s1
D
0
20
40
60
80
100
120
140
160
180
200
(a)
(b)
FIG. 4 (color online).
p
ð
D
þ
s
1
Þ
-dependence of the
D
þ
s
1
signal
yield for data (open squares) and reconstructed MC (solid points)
for the (a)
K
4
and (b)
K
6
decay modes.
) [GeV/c]
+
s1
(D
*
p
3
3.5
4
4.5
[MeV]
0
σ
0.26
0.265
0.27
0.275
0.28
0.285
0.29
0.295
0.3
) [GeV/c]
+
s1
(D
*
p
3
3.5
4
4.5
[MeV]
0
σ
0.24
0.245
0.25
0.255
0.26
0.265
0.27
0.275
0.28
0.285
(a)
(b)
FIG. 6.
p
ð
D
þ
s
1
Þ
dependence of the resolution function parame-
ter
0
, represented by a linear parametrization (
r
fixed) for the
(a)
K
4
and (b)
K
6
decay modes.
MEASUREMENT OF THE MASS AND WIDTH OF THE
...
PHYSICAL REVIEW D
83,
072003 (2011)
072003-7