Analysis of the
D
þ
!
K
þ
e
þ
e
decay channel
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,
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
A. Randle-Conde,
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. Adametz,
27
J. Marks,
27
U. Uwer,
27
F. U. Bernlochner,
28
M. Ebert,
28
H. M. Lacker,
28
T. Lueck,
28
A. Volk,
28
P. D. Dauncey,
29
M. Tibbetts,
29
P. K. Behera,
30
U. Mallik,
30
C. Chen,
31
J. Cochran,
31
H. B. Crawley,
31
L. Dong,
31
W. T. Meyer,
31
S. Prell,
31
E. I. Rosenberg,
31
A. E. Rubin,
31
A. V. Gritsan,
32
Z. J. Guo,
32
N. Arnaud,
33
M. Davier,
33
D. Derkach,
33
J. Firmino da Costa,
33
G. Grosdidier,
33
F. Le Diberder,
33
A. M. Lutz,
33
B. Malaescu,
33
A. Perez,
33
P. Roudeau,
33
M. H. Schune,
33
J. Serrano,
33
V. Sordini,
33,
‡
A. Stocchi,
33
L. Wang,
33
G. Wormser,
33
D. J. Lange,
34
D. M. Wright,
34
I. Bingham,
35
C. A. Chavez,
35
J. P. Coleman,
35
J. R. Fry,
35
E. Gabathuler,
35
R. Gamet,
35
D. E. Hutchcroft,
35
D. J. Payne,
35
C. Touramanis,
35
A. J. Bevan,
36
F. Di Lodovico,
36
R. Sacco,
36
M. Sigamani,
36
G. Cowan,
37
S. Paramesvaran,
37
A. C. Wren,
37
D. N. Brown,
38
C. L. Davis,
38
A. G. Denig,
39
M. Fritsch,
39
W. Gradl,
39
A. Hafner,
39
K. E. Alwyn,
40
D. Bailey,
40
R. J. Barlow,
40
G. Jackson,
40
G. D. Lafferty,
40
J. Anderson,
41
R. Cenci,
41
A. Jawahery,
41
D. A. Roberts,
41
G. Simi,
41
J. M. Tuggle,
41
C. Dallapiccola,
42
E. Salvati,
42
R. Cowan,
43
D. Dujmic,
43
G. Sciolla,
43
M. Zhao,
43
D. Lindemann,
44
P. M. Patel,
44
S. H. Robertson,
44
M. Schram,
44
P. Biassoni,
45a,45b
A. Lazzaro,
45a,45b
V. Lombardo,
45a
F. Palombo,
45a,45b
S. Stracka,
45a,45b
L. Cremaldi,
46
R. Godang,
46,
x
R. Kroeger,
46
P. Sonnek,
46
D. J. Summers,
46
X. Nguyen,
47
M. Simard,
47
P. Taras,
47
G. De Nardo,
48a,48b
D. Monorchio,
48a,48b
G. Onorato,
48a,48b
C. Sciacca,
48a,48b
G. Raven,
49
H. L. Snoek,
49
C. P. Jessop,
50
K. J. Knoepfel,
50
J. M. LoSecco,
50
W. F. Wang,
50
L. A. Corwin,
51
K. Honscheid,
51
R. Kass,
51
J. P. Morris,
51
N. L. Blount,
52
J. Brau,
52
R. Frey,
52
O. Igonkina,
52
J. A. Kolb,
52
R. Rahmat,
52
N. B. Sinev,
52
D. Strom,
52
J. Strube,
52
E. Torrence,
52
G. Castelli,
53a,53b
E. Feltresi,
53a,53b
N. Gagliardi,
53a,53b
M. Margoni,
53a,53b
M. Morandin,
53a
M. Posocco,
53a
M. Rotondo,
53a
F. Simonetto,
53a,53b
R. Stroili,
53a,53b
E. Ben-Haim,
54
G. R. Bonneaud,
54
H. Briand,
54
G. Calderini,
54
J. Chauveau,
54
O. Hamon,
54
Ph. Leruste,
54
G. Marchiori,
54
J. Ocariz,
54
J. Prendki,
54
S. Sitt,
54
M. Biasini,
55a,55b
E. Manoni,
55a,55b
A. Rossi,
55a,55b
C. Angelini,
56a,56b
G. Batignani,
56a,56b
S. Bettarini,
56a,56b
M. Carpinelli,
56a,56b,
k
G. Casarosa,
56a,56b
A. Cervelli,
56a,56b
F. Forti,
56a,56b
M. A. Giorgi,
56a,56b
A. Lusiani,
56a,56c
N. Neri,
56a,56b
E. Paoloni,
56a,56b
G. Rizzo,
56a,56b
J. J. Walsh,
56a
D. Lopes Pegna,
57
C. Lu,
57
J. Olsen,
57
A. J. S. Smith,
57
A. V. Telnov,
57
F. Anulli,
58a
E. Baracchini,
58a,58b
G. Cavoto,
58a
R. Faccini,
58a,58b
F. Ferrarotto,
58a
F. Ferroni,
58a,58b
M. Gaspero,
58a,58b
L. Li Gioi,
58a
M. A. Mazzoni,
58a
G. Piredda,
58a
F. Renga,
58a,58b
T. Hartmann,
59
T. Leddig,
59
H. Schro
̈
der,
59
R. Waldi,
59
T. Adye,
60
B. Franek,
60
E. O. Olaiya,
60
F. F. Wilson,
60
S. Emery,
61
G. Hamel de Monchenault,
61
G. Vasseur,
61
Ch. Ye
`
che,
61
M. Zito,
61
M. T. Allen,
62
D. Aston,
62
D. J. Bard,
62
R. Bartoldus,
62
J. F. Benitez,
62
C. Cartaro,
62
M. R. Convery,
62
J. Dorfan,
62
G. P. Dubois-Felsmann,
62
W. Dunwoodie,
62
R. C. Field,
62
M. Franco Sevilla,
62
B. G. Fulsom,
62
A. M. Gabareen,
62
M. T. Graham,
62
P. Grenier,
62
C. Hast,
62
W. R. Innes,
62
M. H. Kelsey,
62
H. Kim,
62
P. Kim,
62
M. L. Kocian,
62
D. W. G. S. Leith,
62
S. Li,
62
B. Lindquist,
62
S. Luitz,
62
V. Luth,
62
H. L. Lynch,
62
D. B. MacFarlane,
62
H. Marsiske,
62
D. R. Muller,
62
H. Neal,
62
S. Nelson,
62
C. P. O’Grady,
62
I. Ofte,
62
M. Perl,
62
T. Pulliam,
62
B. N. Ratcliff,
62
A. Roodman,
62
A. A. Salnikov,
62
V. Santoro,
62
R. H. Schindler,
62
J. Schwiening,
62
A. Snyder,
62
D. Su,
62
M. K. Sullivan,
62
S. Sun,
62
K. Suzuki,
62
J. M. Thompson,
62
J. Va’vra,
62
A. P. Wagner,
62
M. Weaver,
62
PHYSICAL REVIEW D
83,
072001 (2011)
1550-7998
=
2011
=
83(7)
=
072001(35)
072001-1
Ó
2011 American Physical Society
W. J. Wisniewski,
62
M. Wittgen,
62
D. H. Wright,
62
H. W. Wulsin,
62
A. K. Yarritu,
62
C. C. Young,
62
V. Ziegler,
62
X. R. Chen,
63
W. Park,
63
M. V. Purohit,
63
R. M. White,
63
J. R. Wilson,
63
S. J. Sekula,
64
M. Bellis,
65
P. R. Burchat,
65
A. J. Edwards,
65
T. S. Miyashita,
65
S. Ahmed,
66
M. S. Alam,
66
J. A. Ernst,
66
B. Pan,
66
M. A. Saeed,
66
S. B. Zain,
66
N. Guttman,
67
A. Soffer,
67
P. Lund,
68
S. M. Spanier,
68
R. Eckmann,
69
J. L. Ritchie,
69
A. M. Ruland,
69
C. J. Schilling,
69
R. F. Schwitters,
69
B. C. Wray,
69
J. M. Izen,
70
X. C. Lou,
70
F. Bianchi,
71a,71b
D. Gamba,
71a,71b
M. Pelliccioni,
71a,71b
M. Bomben,
72a,72b
L. Lanceri,
72a,72b
L. Vitale,
72a,72b
N. Lopez-March,
73
F. Martinez-Vidal,
73
A. Oyanguren,
73
J. Albert,
74
Sw. Banerjee,
74
H. H. F. Choi,
74
K. Hamano,
74
G. J. King,
74
R. Kowalewski,
74
M. J. Lewczuk,
74
C. Lindsay,
74
I. M. Nugent,
74
J. M. Roney,
74
R. J. Sobie,
74
T. J. Gershon,
75
P. F. Harrison,
75
T. E. Latham,
75
E. M. T. Puccio,
75
H. R. Band,
65
S. Dasu,
65
K. T. Flood,
65
Y. Pan,
65
R. Prepost,
65
C. O. Vuosalo,
65
and S. L. Wu
65
(
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/IN
2
P
3
, 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
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
28
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstrasse 15, D-12489 Berlin, Germany
29
Imperial College London, London, SW7 2AZ, United Kingdom
30
University of Iowa, Iowa City, Iowa 52242, USA
31
Iowa State University, Ames, Iowa 50011-3160, USA
32
Johns Hopkins University, Baltimore, Maryland 21218, USA
33
Laboratoire de l’Acce
́
le
́
rateur Line
́
aire, IN
2
P
3
/CNRS et Universite
́
Paris-Sud 11,
Centre Scientifique d’Orsay, B.P. 34, F-91898 Orsay Cedex, France
34
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
35
University of Liverpool, Liverpool L69 7ZE, United Kingdom
36
Queen Mary, University of London, London, E1 4NS, United Kingdom
37
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
38
University of Louisville, Louisville, Kentucky 40292, USA
39
Johannes Gutenberg-Universita
̈
t Mainz, Institut fu
̈
r Kernphysik, D-55099 Mainz, Germany
40
University of Manchester, Manchester M13 9PL, United Kingdom
41
University of Maryland, College Park, Maryland 20742, USA
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
072001 (2011)
072001-2
42
University of Massachusetts, Amherst, Massachusetts 01003, USA
43
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
44
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
45a
INFN Sezione di Milano, I-20133 Milano, Italy;
45b
Dipartimento di Fisica, Universita
`
di Milano, I-20133 Milano, Italy
46
University of Mississippi, University, Mississippi 38677, USA
47
Universite
́
de Montre
́
al, Physique des Particules, Montre
́
al, Que
́
bec, Canada H3C 3J7
48a
INFN Sezione di Napoli, I-80126 Napoli, Italy;
48b
Dipartimento di Scienze Fisiche, Universita
`
di Napoli Federico II, I-80126 Napoli, Italy
49
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
50
University of Notre Dame, Notre Dame, Indiana 46556, USA
51
Ohio State University, Columbus, Ohio 43210, USA
52
University of Oregon, Eugene, Oregon 97403, USA
53a
INFN Sezione di Padova, I-35131 Padova, Italy;
53b
Dipartimento di Fisica, Universita
`
di Padova, I-35131 Padova, Italy
54
Laboratoire de Physique Nucle
́
aire et de Hautes Energies, IN
2
P
3
/CNRS, Universite
́
Pierre et Marie Curie-Paris6,
Universite
́
Denis Diderot-Paris7, F-75252 Paris, France
55a
INFN Sezione di Perugia, I-06100 Perugia, Italy;
55b
Dipartimento di Fisica, Universita
`
di Perugia, I-06100 Perugia, Italy
56a
INFN Sezione di Pisa, I-56127 Pisa, Italy;
56b
Dipartimento di Fisica, Universita
`
di Pisa, I-56127 Pisa, Italy;
56c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
57
Princeton University, Princeton, New Jersey 08544, USA
58a
INFN Sezione di Roma, I-00185 Roma, Italy;
58b
Dipartimento di Fisica, Universita
`
di Roma La Sapienza, I-00185 Roma, Italy
59
Universita
̈
t Rostock, D-18051 Rostock, Germany
60
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
61
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
62
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
63
University of South Carolina, Columbia, South Carolina 29208, USA
64
Southern Methodist University, Dallas, Texas 75275, USA
65
Stanford University, Stanford, California 94305-4060, USA
66
State University of New York, Albany, New York 12222, USA
67
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel
68
University of Tennessee, Knoxville, Tennessee 37996, USA
69
University of Texas at Austin, Austin, Texas 78712, USA
70
University of Texas at Dallas, Richardson, Texas 75083, USA
71a
INFN Sezione di Torino, I-10125 Torino, Italy;
71b
Dipartimento di Fisica Sperimentale, Universita
`
di Torino, I-10125 Torino, Italy
72a
INFN Sezione di Trieste, I-34127 Trieste, Italy;
72b
Dipartimento di Fisica, Universita
`
di Trieste, I-34127 Trieste, Italy
73
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
74
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
75
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
76
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 13 December 2010; published 1 April 2011)
Using
347
:
5fb
1
of data recorded by the
BABAR
detector at the PEP-II electron-positron collider,
244
10
3
signal events for the
D
þ
!
K
þ
e
þ
e
decay channel are analyzed. This decay mode is
dominated by the
K
ð
892
Þ
0
contribution. We determine the
K
ð
892
Þ
0
parameters:
m
K
ð
892
Þ
0
¼ð
895
:
4
0
:
2
0
:
2
Þ
MeV
=c
2
,
0
K
ð
892
Þ
0
¼ð
46
:
5
0
:
3
0
:
2
Þ
MeV
=c
2
, and the Blatt-Weisskopf parameter
r
BW
¼
2
:
1
0
:
5
0
:
5
ð
GeV
=c
Þ
1
, where the first uncertainty comes from statistics and the second from
systematic uncertainties. We also measure the parameters defining the corresponding hadronic form
factors at
q
2
¼
0
(
r
V
¼
V
ð
0
Þ
A
1
ð
0
Þ
¼
1
:
463
0
:
017
0
:
031
,
r
2
¼
A
2
ð
0
Þ
A
1
ð
0
Þ
¼
0
:
801
0
:
020
0
:
020
) and the
*
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 Alabama, Mobile, AL 36688, USA.
k
Also with Universita
`
di Sassari, Sassari, Italy.
ANALYSIS OF THE
D
þ
!
K
þ
e
þ
e
DECAY CHANNEL
PHYSICAL REVIEW D
83,
072001 (2011)
072001-3
value of the axial-vector pole mass parametrizing the
q
2
variation of
A
1
and
A
2
:
m
A
¼ð
2
:
63
0
:
10
0
:
13
Þ
GeV
=c
2
. The
S
-wave fraction is equal to
ð
5
:
79
0
:
16
0
:
15
Þ
%
. Other signal components
correspond to fractions below 1%. Using the
D
þ
!
K
þ
þ
channel as a normalization, we measure
the
D
þ
semileptonic branching fraction:
B
ð
D
þ
!
K
þ
e
þ
e
Þ¼ð
4
:
00
0
:
03
0
:
04
0
:
09
Þ
10
2
,
where the third uncertainty comes from external inputs. We then obtain the value of the hadronic form
factor
A
1
at
q
2
¼
0
:
A
1
ð
0
Þ¼
0
:
6200
0
:
0056
0
:
0065
0
:
0071
. Fixing the
P
-wave parameters, we
measure the phase of the
S
wave for several values of the
K
mass. These results confirm those obtained
with
K
production at small momentum transfer in fixed target experiments.
DOI:
10.1103/PhysRevD.83.072001
PACS numbers: 13.20.Fc, 11.15.Ha, 11.30.Er, 12.38.Gc
I. INTRODUCTION
A detailed study of the
D
þ
!
K
þ
e
þ
e
decay chan-
nel is of interest for three main reasons:
(i) It allows measurements of the different
K
resonant
and nonresonant amplitudes that contribute to this
decay. In this respect, we have measured the
S
-wave
contribution and searched for radially excited
P
-wave and
D
-wave components. Accurate mea-
surements of the various contributions can serve as
useful guidelines to
B
-meson semileptonic decays,
where exclusive final states with mass higher than
the
D
mass are still missing.
(ii) High statistics in this decay allows accurate mea-
surements of the properties of the
K
ð
892
Þ
0
meson,
the main contribution to the decay. Both resonance
parameters and hadronic transition form factors can
be precisely measured. The latter can be compared
with hadronic model expectations and lattice QCD
computations.
(iii) Variation of the
K S
-wave phase versus the
K
mass can be determined, and compared with other
experimental determinations.
Meson-meson interactions are basic processes in QCD
that deserve accurate measurements. Unfortunately, meson
targets do not exist in nature and studies of these interac-
tions usually require extrapolations to the physical region.
In the
K
system,
S
-wave interactions proceeding
through isospin equal to
1
=
2
states are of particular interest
because, contrary to exotic
I
¼
3
=
2
final states, they de-
pend on the presence of scalar resonances. Studies of the
candidate scalar meson
K
0
ð
800
Þ
can thus benefit from
more accurate measurements of the
I
¼
1
=
2
S
-wave phase
below
m
K
¼
1 GeV
=c
2
[
1
]. The phase variation of this
amplitude with the
K
mass also enters in integrals which
allow the determination of the strange quark mass in the
QCD sum rule approach [
2
,
3
].
Information on the
K S
-wave phase in the isospin
states
I
¼
1
=
2
and
I
¼
3
=
2
originates from various experi-
mental situations, such as kaon scattering,
D
!
K
Dalitz plot analyses, and semileptonic decays of charm
mesons and
leptons. In kaon scattering fixed target ex-
periments [
4
,
5
], measurements from the Large Aperture
Solenoid Spectrometer (LASS) [
5
] start at
m
K
¼
0
:
825 GeV
=c
2
, a value which is
0
:
192 GeV
=c
2
above
threshold. Results from Ref. [
4
] start at
0
:
7 GeV
=c
2
but
are less accurate. More recently, several high statistics
three-body Dalitz plot analyses of charm meson hadronic
decays have become available [
6
–
9
]. They provide values
starting at threshold and can complement results from
K
scattering, but in the overlap region, they obtain somewhat
different results. It is tempting to attribute these differences
to the presence of an additional hadron in the final state.
The first indication in this direction was obtained from the
measurement of the phase difference between
S
and
P
waves versus
m
K
in
B
0
!
J=
c
K
þ
[
10
], which agrees
with LASS results apart from a relative sign between the
two amplitudes. In this channel, the
J=
c
meson in the final
state is not expected to interact with the
K
system.
In
decays into
K
, there is no additional hadron in
the final state and only the
I
¼
1
=
2
amplitude contributes.
A study of the different partial waves requires separation of
the
polarization components using, for instance, infor-
mation from the decay of the other
lepton. No result is
available yet on the phase of the
K S
wave [
11
] from
these analyses. In
D
þ
!
K
þ
e
þ
e
there is also no addi-
tional hadron in the final state. All the information needed
to separate the different hadronic angular momentum com-
ponents can be obtained through correlations between the
leptonic and hadronic systems. This requires measurement
of the complete dependence of the differential decay rate
on the five-dimensional phase space. Because of limited
statistics, previous experiments [
12
–
14
] have measured an
S
-wave component but were unable to study its properties
as a function of the
K
mass. We present the first semi-
leptonic charm decay analysis which measures the phase of
the
I
¼
1
=
2
K S
wave as a function of
m
K
from thresh-
old up to
1
:
5 GeV
=c
2
.
Table
I
lists strange particle resonances that can appear
in Cabibbo-favored
D
þ
semileptonic decays.
J
P
¼
1
þ
states do not decay into
K
and cannot be observed in
the present analysis. The
K
ð
1410
Þ
is a
1
radial excitation
and has a small branching fraction into
K
. The
K
ð
1680
Þ
has a mass close to the kinematic limit and its production is
disfavored by the available phase space. Above the
K
ð
892
Þ
, one is thus left with possible contributions from
the
K
0
ð
1430
Þ
,
K
ð
1410
Þ
, and
K
2
ð
1430
Þ
which decay into
K
through
S
,
P
, and
D
waves, respectively. At low
K
mass values, one also expects an
S
-wave contribution
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
072001 (2011)
072001-4
which can be resonant (
) or not. A question mark is placed
after the
K
0
ð
800
Þ
, as this state is not well established.
This paper is organized in the following way. In Sec.
II
general aspects of the
K
system in the elastic regime,
which are relevant to present measurements, are explained.
In particular, the Watson theorem, which allows us to relate
the values of the hadronic phase measured in various
processes, is introduced. In Sec.
III
, previous measure-
ments of the
S
-wave
K
system are explained and com-
pared. The differential decay distribution used to analyze
the data is detailed in Sec.
IV
. In Sec.
V
a short description
of the detector components which are important in this
measurement is given. The selection of signal events, the
background rejection, the tuning of the simulation, and the
fitting procedure are then considered in Sec.
VI
. Results of
a fit that includes the
S
-wave and
K
ð
892
Þ
0
signal compo-
nents are given in Sec.
VII
. Since the fit model with only
S
- and
P
-wave components does not seem to be adequate at
large
K
mass, fit results for signal models which com-
prise
S
þ
K
ð
892
Þ
0
þ
K
ð
1410
Þ
0
and
S
þ
K
ð
892
Þ
0
þ
K
ð
1410
Þ
0
þ
D
components are given in Sec.
VIII
. In the
same section, fixing the parameters of the
K
ð
892
Þ
0
com-
ponent, measurements of the phase difference between
S
and
P
waves are obtained, for several values of the
K
mass. In Sec.
IX
, measurements of the studied semilep-
tonic decay channel branching fraction, relative to the
D
þ
!
K
þ
þ
channel, and of its different components
are obtained. This allows one to extract an absolute nor-
malization for the hadronic form factors. Finally, in Sec.
X
results obtained in this analysis are summarized.
II. THE
K
SYSTEM IN THE ELASTIC
REGIME REGION
The
K
scattering amplitude (
T
K
) has two isospin
components denoted
T
1
=
2
and
T
3
=
2
. Depending on the
channel studied, measurements are sensitive to different
linear combinations of these components. In
D
þ
!
K
þ
e
þ
e
,
!
K
0
S
, and
B
0
!
J=
c
K
þ
de-
cays, only the
I
¼
1
=
2
component contributes. The
I
¼
3
=
2
component was measured in
K
þ
p
!
K
þ
þ
n
reactions [
4
], whereas
K
p
!
K
þ
n
depends on the
two isospin amplitudes:
T
K
þ
¼
1
3
ð
2
T
1
=
2
þ
T
3
=
2
Þ
.In
Dalitz plot analyses of three-body charm meson decays,
the relative importance of the two components has to be
determined from data.
Agiven
K
scattering isospin amplitude can be ex-
panded into partial waves:
T
I
ð
s; t; u
Þ¼
16
X
1
‘
¼
0
ð
2
‘
þ
1
Þ
P
‘
ð
cos
Þ
t
I
‘
ð
s
Þ
;
(1)
where the normalization is such that the differential
K
scattering cross section is equal to
d
I
d
¼
4
s
j
T
I
ð
s; t; u
Þj
2
ð
16
Þ
2
;
(2)
where
s
,
t
, and
u
are the Mandelstam variables,
is the
scattering angle, and
P
‘
ð
cos
Þ
is the Legendre polynomial
of order
‘
.
Close to threshold, the amplitudes
t
I
‘
ð
s
Þ
can be expressed
as Taylor series:
Re
t
I
‘
ð
s
Þ¼
1
2
ffiffiffi
s
p
ð
p
Þ
2
‘
ð
a
I
‘
þ
b
I
‘
ð
p
Þ
2
þ
O
ð
p
Þ
4
Þ
;
(3)
where
a
I
‘
and
b
I
‘
are, respectively, the scattering length and
the effective range parameters, and
p
is the
K
or
momentum in the
K
center-of-mass (CM) frame. This
expansion is valid close to threshold for
p
<m
. Values
of
a
I
‘
and
b
I
‘
are obtained from chiral perturbation theory
[
16
,
17
]. In Table
II
these predictions are compared with a
determination [
18
] of these quantities obtained from an
analysis of experimental data on
K
scattering and
!
K
K
. Constraints from analyticity and unitarity of
the amplitude are used to obtain its behavior close to
threshold. The similarity between predicted and fitted
values of
a
1
=
2
0
and
b
1
=
2
0
is a nontrivial test of chiral pertur-
bation theory [
17
].
The complex amplitude
t
I
‘
ð
s
Þ
can also be expressed in
terms of its magnitude and phase. If the process remains
elastic, this gives
t
I
‘
ð
s
Þ¼
ffiffiffi
s
p
2
p
1
2
i
ð
e
2
i
I
‘
ð
s
Þ
1
Þ¼
ffiffiffi
s
p
2
p
sin
I
‘
ð
s
Þ
e
i
I
‘
ð
s
Þ
:
(4)
Using the expansion given in Eq. (
3
), close to the threshold
the phase
I
‘
ð
s
Þ
is expected to satisfy the following
expression:
I
‘
ð
s
Þ¼ð
p
Þ
2
l
þ
1
ð
þ
ð
p
Þ
2
Þ
:
(5)
TABLE II. Predicted values for scattering length and effective
range parameters.
Parameter
[
17
][
18
]
a
1
=
2
0
ð
GeV
1
Þ
1.52
1
:
60
0
:
16
b
1
=
2
0
ð
GeV
3
Þ
47.0
31
:
2
1
:
5
a
1
=
2
1
ð
GeV
3
Þ
5.59
7
:
0
0
:
4
TABLE I. Possible resonances contributing to Cabibbo-
favored
D
þ
semileptonic decays [
15
].
Resonance
XJ
P
B
ð
X
!
K
Þ
Mass
MeV
=c
2
Width
MeV
=c
2
K
0
ð
800
Þ
(?)
0
þ
100(?)
672
40
550
34
K
ð
892
Þ
1
100
895
:
94
0
:
22 48
:
7
0
:
8
K
1
ð
1270
Þ
1
þ
0
1272
790
20
K
1
ð
1400
Þ
1
þ
0
1403
7
174
13
K
ð
1410
Þ
1
6
:
6
1
:
3 1414
15
232
21
K
0
ð
1430
Þ
0
þ
93
10 1425
50
270
80
K
2
ð
1430
Þ
2
þ
49
:
9
1
:
2 1432
:
4
1
:
3
109
5
K
ð
1680
Þ
1
38
:
7
2
:
5 1717
27
322
110
ANALYSIS OF THE
D
þ
!
K
þ
e
þ
e
DECAY CHANNEL
PHYSICAL REVIEW D
83,
072001 (2011)
072001-5
Using Eqs. (
3
)–(
5
) one can relate
and
to
a
I
‘
and
b
I
‘
:
¼
a
I
‘
and
¼
b
I
‘
þ
2
3
ð
a
I
‘
Þ
3
l
0
:
(6)
In Eq. (
6
), the symbol
l
0
is the Kronecker
function:
00
¼
1
,
l
0
¼
0
for
l
0
.
The Watson theorem [
19
] implies that, in this elastic
regime, phases measured in
K
elastic scattering and in a
decay channel in which the
K
system has no strong
interaction with other hadrons are equal modulo
radians
[
20
] for the same values of isospin and angular momentum.
In this analysis, this ambiguity is solved by determining the
sign of the
S
-wave amplitude from data. This theorem does
not provide any constraint on the corresponding amplitude
moduli. In particular, it is not legitimate (though it is
nonetheless frequently done) to assume that the
S
-wave
amplitude in a decay is proportional to the elastic ampli-
tude
t
I
‘
ð
s
Þ
. The
K
scattering
S
wave,
I
¼
1
=
2
, remains
elastic up to the
K
threshold, but since the coupling to this
channel is weak [
21
], it is considered, in practice, to be
elastic up to the
K
0
threshold.
Even if the
K
system is studied without any accom-
panying hadron, the
S
-or
P
-wave amplitudes cannot be
measured in an absolute way. Phase measurements are
obtained through interference between different waves.
As a result, values quoted by an experiment for the phase
of the
S
wave depend on the parameters used to determine
the
P
wave. For the
P
wave, the validity domain of the
Watson theorem is
a priori
more restricted because the
coupling to
K
is no longer suppressed. However, the
p
3
dependence of the decay width implies that this contri-
bution is an order of magnitude smaller than
K
for
m
K
<
1
:
2 GeV
=c
2
.
For pseudoscalar-meson elastic scattering at threshold,
all phases are expected to be equal to zero [see Eq. (
5
)].
This is another important difference as compared with
Dalitz plot analyses where arbitrary phases exist between
the different contributing waves due to interaction with the
spectator hadron. It is thus important to verify if, apart from
a global constant,
S
-wave phases measured versus
m
K
,in
three-body
D
!
K
Dalitz plot analyses, depend on the
presence of the third hadron. Comparison between present
measurements and those obtained in three-body Dalitz plot
analyses are given in Sec.
VIII B
.
III. PREVIOUS MEASUREMENTS
In the following sections, we describe previous mea-
surements of the phase and magnitude of the
K S
-wave
amplitude obtained in
K
p
scattering at small transfer, in
semileptonic decays,
D
-meson three-body decays, and in
charm semileptonic decays.
A.
K
production at small momentum transfer
A
K
partial wave analysis of high statistics data for the
reactions
K
p
!
K
þ
n
and
K
p
!
K
þþ
at
13 GeV, on events selected at small momentum transfer
[
4
], provided information on
K
scattering for
m
K
in the
range
½
0
:
7
;
1
:
9
GeV
=c
2
. The
I
¼
3
=
2
K
scattering was
studied directly from the analyses of
K
þ
p
!
K
þ
þ
n
and
K
p
!
K
þþ
reactions. The phase of the elastic
amplitude
ð
3
=
2
S
Þ
was measured and was used to extract
the phase of the
I
¼
1
=
2
amplitude from measurements of
K
þ
scattering. Values obtained for
1
=
2
S
are displayed in
Fig.
1
for
m
K
<
1
:
3 GeV
=c
2
, a mass range in which the
interaction is expected to remain elastic. Above
1
:
46 GeV
=c
2
there were several solutions for the
amplitude.
A few years later, the LASS experiment analyzed data
from
11 GeV
=c
kaon scattering on hydrogen:
K
p
!
K
þ
n
[
5
]. It performed a partial wave analysis of
1
:
5
10
5
events which satisfied cuts to ensure
K
pro-
duction dominated by pion exchange and no excitation of
the target into baryon resonances.
The
K
,
I
¼
1
=
2
,
S
wave was parametrized as the sum
of a background term (BG) and the
K
0
ð
1430
Þ
, which were
combined such that the resulting amplitude satisfied
unitarity:
A
1
=
2
S
¼
sin
1
=
2
BG
e
i
1
=
2
BG
þ
e
2
i
1
=
2
BG
sin
K
0
ð
1430
Þ
e
i
K
0
ð
1430
Þ
¼
sin
ð
1
=
2
BG
þ
K
0
ð
1430
Þ
Þ
e
i
ð
1
=
2
BG
þ
K
0
ð
1430
Þ
Þ
;
(7)
where
1
=
2
BG
and
K
0
ð
1430
Þ
depended on the
K
mass.
The mass dependence of
1
=
2
BG
was described by means of
an effective range parametrization:
0
50
100
150
200
1
1.5
2
m
K
π
(GeV/c
2
)
Phase (degrees)
LASS (I=1/2)
Estabrooks et al. (I=1/2)
LASS fit
FIG. 1 (color online). Comparison between the
I
¼
1
=
2
S
-wave phase measured in
K
production at small transfer for
several values of the
K
mass. Results from Ref. [
4
] are limited
to
m
K
<
1
:
3 GeV
=c
2
to remain in the elastic regime, where
there is a single solution for the amplitude. The curve corre-
sponds to the fit given in the second column of Table
III
.
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
072001 (2011)
072001-6
cot
ð
1
=
2
BG
Þ¼
1
a
1
=
2
S;
BG
p
þ
b
1
=
2
S;
BG
p
2
;
(8)
where
a
1
=
2
S;
BG
is the scattering length and
b
1
=
2
S;
BG
is the effec-
tive range. Note that these two parameters are different
from
a
I
‘
and
b
I
‘
introduced in Eq. (
3
), as the latter referred
to the total amplitude and also because Eq. (
8
) corresponds
to an expansion near threshold which differs from Eq. (
5
).
The mass dependence of
K
0
ð
1430
Þ
was obtained assuming
that the
K
0
ð
1430
Þ
decay amplitude obeys a Breit-Wigner
distribution:
cot
ð
K
0
ð
1430
Þ
Þ¼
m
2
K
0
ð
1430
Þ
m
2
K
m
K
0
ð
1430
Þ
K
0
ð
1430
Þ
ð
m
K
Þ
;
(9)
where
m
K
0
ð
1430
Þ
is the pole mass of the resonance and
K
0
ð
1430
Þ
ð
m
K
Þ
its mass-dependent total width.
The total
I
¼
1
=
2
S
-wave phase was then
1
=
2
LASS
¼
1
=
2
BG
þ
K
0
ð
1430
Þ
:
(10)
The LASS measurements were based on fits to moments
of angular distributions which depended on the interfer-
ence between
S
,
P
,
D
...
waves. To obtain the
I
¼
1
=
2
K
þ
S
wave amplitude, the measured
I
¼
3
=
2
compo-
nent [
4
] was subtracted from the LASS measurement of
T
K
þ
and the resulting values were fitted using Eq. (
10
).
The corresponding results [
22
] are given in Table
III
and
displayed in Fig.
1
.
B.
!
K
decays
The
BABAR
and Belle collaborations [
11
,
23
] measured
the
K
0
S
mass distribution in
!
K
0
S
. Results from
Belle were analyzed in Ref. [
24
] using, in addition to the
K
ð
892
Þ
, the following:
(i) a contribution from the
K
ð
1410
Þ
to the vector form
factor;
(ii) a scalar contribution, with a mass dependence com-
patible with LASS measurements but whose
branching fraction was not provided.
Another interpretation of these data was given in
Ref. [
25
]. Using the value of the rate determined from
Belle data, for the
K
ð
1410
Þ
, its relative contribution to
the
D
þ
!
K
þ
e
þ
e
channel was evaluated to be of the
order of 0.5%.
C. Hadronic
D
-meson decays
K
interactions were studied in several Dalitz plot
analyses of three-body
D
decays, and we consider only
D
þ
!
K
þ
þ
as measured by the E791 [
6
], FOCUS
[
7
,
8
], and CLEO-c [
9
] collaborations. This final state is
known to have a large
S
-wave component because there is
no resonant contribution to the
þ
þ
system. In practice,
each collaboration has developed various approaches and
results are difficult to compare.
The
S
-wave phase measured by these collaborations is
compared in Fig.
2(a)
with the phase of the (
I
¼
1
=
2
)
amplitude determined from LASS data. Measurements
from
D
þ
decays are shifted so that the phase is equal to
zero for
m
K
¼
0
:
67 GeV
=c
2
. The magnitude of the am-
plitude obtained in Dalitz plot analyses is compared in
Fig.
2(b)
with the ‘‘naive’’ estimate given in Eq. (
4
), which
is derived from the elastic (
I
¼
1
=
2
) amplitude fitted to
LASS data.
By comparing results obtained by the three experiments
analyzing
D
þ
!
K
þ
þ
, several remarks are formu-
lated.
(i) A
þ
þ
component is included only in the CLEO-c
measurement, and it corresponds to
ð
15
3
Þ
%
of the
decay rate.
(ii) The relative importance of
I
¼
1
=
2
and
I
¼
3
=
2
components can be different in
K
scattering and
in a three-body decay. This is because, even if
Watson’s theorem is expected to be valid, it applies
separately for the
I
¼
1
=
2
and
I
¼
3
=
2
components
and concerns only the corresponding phases of these
amplitudes. E791 and CLEO-c measured the total
K S
-wave amplitude and compared their results
with the
I
¼
1
=
2
component from LASS. FOCUS
[
7
], using the phase of the
I
¼
3
=
2
amplitude mea-
sured in scattering experiments, fitted separately the
two components and found large effects from the
I
¼
3
=
2
part. In Fig.
2(a)
the phase of the total
S
-wave amplitude which contains contributions
from the two isospin components, as measured by
FOCUS [
8
], is plotted.
(iii) Measured phases in Dalitz plot analyses have a
global shift, as compared to the scattering case (in
which phases are expected to be zero at threshold).
Having corrected for this effect (with some arbitra-
riness), the variation measured for the phase in
TABLE III. Fit results to LASS data [
22
] for two mass intervals.
Parameter
m
K
2½
0
:
825
;
1
:
52
GeV
=c
2
m
K
2½
0
:
825
;
1
:
60
GeV
=c
2
m
K
0
ð
1430
Þ
ð
MeV
=c
2
Þ
1435
5
1415
3
K
0
ð
1430
Þ
ð
MeV
=c
2
Þ
279
6
300
6
a
1
=
2
S;
BG
ð
GeV
1
Þ
1
:
95
0
:
09
2
:
07
0
:
10
b
1
=
2
S;
BG
ð
GeV
1
Þ
1
:
76
0
:
36
3
:
32
0
:
34
ANALYSIS OF THE
D
þ
!
K
þ
e
þ
e
DECAY CHANNEL
PHYSICAL REVIEW D
83,
072001 (2011)
072001-7
three-body decays and in
K
scattering is roughly
similar, but a quantitative comparison is difficult.
Differences between the two approaches as a func-
tion of
m
K
are much larger than the quoted un-
certainties. They may arise from the comparison
itself, which considers the total
K S
wave in one
case and only the
I
¼
1
=
2
component for scatter-
ing. They could also be due to the interaction of the
bachelor pion which invalidates the application of
the Watson theorem.
It is thus difficult to draw quantitative conclusions
from results obtained with
D
þ
!
K
þ
þ
decays.
Qualitatively, one can say that the phase of the
S
-wave
component depends on
m
K
similarly to that measured by
LASS. Below the
K
0
ð
1430
Þ
, the
S
-wave amplitude magni-
tude has a smooth variation versus
m
K
. At the
K
0
ð
1430
Þ
average mass value and above, this magnitude has a sharp
decrease with the mass.
D.
D
‘
4
decays
The dominant hadronic contribution in the
D
‘
4
decay
channel comes from the (
J
P
¼
1
)
K
ð
892
Þ
resonant state.
E687 [
12
] gave the first suggestion for an additional com-
ponent. FOCUS [
13
], a few years later, measured the
S
-wave contribution from the asymmetry in the angular
distribution of the
K
in the
K
rest frame. They concluded
that the phase difference between
S
and
P
waves was
compatible with a constant equal to
=
4
, over the
K
ð
892
Þ
mass region.
In the second publication [
26
] they found that the asym-
metry could be explained if they used the variation of the
S
-wave component versus the
K
mass measured by the
LASS collaboration [
5
]. They did not fit to their data the
two parameters that governed this phase variation but took
LASS results:
cot
ð
BG
Þ¼
1
a
S;
BG
p
þ
b
S;
BG
p
2
;
a
S;
BG
¼ð
4
:
03
1
:
72
0
:
06
Þ
GeV
1
;
b
S;
BG
¼ð
1
:
29
0
:
63
0
:
67
Þ
GeV
1
:
(11)
These values corresponded to the total
S
-wave ampli-
tude measured by LASS which was the sum of
I
¼
1
=
2
and
I
¼
3
=
2
contributions, whereas only the former compo-
nent was present in charm semileptonic decays. For the
S
-wave amplitude they assumed that it was proportional to
the elastic amplitude [see Eq. (
4
)]. For the
P
wave, they
used a relativistic Breit-Wigner distribution with a mass-
dependent width [
27
]. They fitted the values of the pole
mass, the width, and the Blatt-Weisskopf damping parame-
ter for the
K
ð
892
Þ
. These values from FOCUS are given in
Table
IV
and compared with present world averages [
15
],
dominated by the
P
-wave measurements from LASS.
They also compared the measured angular asymmetry of
the
K
in the
K
rest frame versus the
K
mass with
0
100
200
11.52
m
K
π
(GeV/c
2
)
Phase (degrees)
CLEO
E791
FOCUS
LASS I=1/2
a)
0
1
2
3
1
1.5
2
m
K
π
(GeV/c
2
)
Amplitude
CLEO
E791
FOCUS
m/p
*
sin(
δ
LASS
1/2
)
b)
FIG. 2 (color online). (a) Comparison between the
S
-wave phase measured in various experiments analyzing the
D
þ
!
K
þ
þ
channel (E791 [
6
], FOCUS [
7
,
8
], and CLEO [
9
]) and a fit to LASS data (continuous line). The dashed line corresponds to the
extrapolation of the fitted curve. Phase measurements from
D
þ
decays are shifted to be equal to zero at
m
K
¼
0
:
67 GeV
=c
2
. (b) The
S
-wave amplitude magnitude measured in various experiments is compared with the elastic expression. Normalization is arbitrary
between the various distributions.
TABLE IV. Parameters of the
K
ð
892
Þ
0
measured by FOCUS
are compared with world average or previous values.
Parameter
FOCUS results [
26
]
Previous results
m
K
0
ð
MeV
=c
2
Þ
895
:
41
0
:
32
þ
0
:
35
0
:
43
895
:
94
0
:
22
[
15
]
0
K
0
ð
MeV
=c
2
Þ
47
:
79
0
:
86
þ
1
:
32
1
:
06
48
:
7
0
:
8
[
15
]
r
BW
ð
GeV
=c
Þ
1
3
:
96
0
:
54
þ
1
:
31
0
:
90
3
:
40
0
:
67
[
5
]
P. DEL AMO SANCHEZ
et al.
PHYSICAL REVIEW D
83,
072001 (2011)
072001-8