Production of charged pions, kaons, and protons in
e
þ
e
annihilations
into hadrons at
ffiffiffi
s
p
¼
10
:
54 GeV
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
M. Lee,
5
G. Lynch,
5
H. Koch,
6
T. Schroeder,
6
C. Hearty,
7
T. S. Mattison,
7
J. A. McKenna,
7
R. Y. So,
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
D. Kirkby,
10
A. J. Lankford,
10
M. Mandelkern,
10
C. Buchanan,
11
B. Hartfiel,
11
B. Dey,
12
J. W. Gary,
12
O. Long,
12
G. M. Vitug,
12
C. Campagnari,
13
M. Franco Sevilla,
13
T. M. Hong,
13
D. Kovalskyi,
13
J. D. Richman,
13
C. A. West,
13
A. M. Eisner,
14
W. S. Lockman,
14
A. J. Martinez,
14
B. A. Schumm,
14
A. Seiden,
14
D. S. Chao,
15
C. H. Cheng,
15
B. Echenard,
15
K. T. Flood,
15
D. G. Hitlin,
15
P. Ongmongkolkul,
15
F. C. Porter,
15
R. Andreassen,
16
Z. Huard,
16
B. T. Meadows,
16
M. D. Sokoloff,
16
L. Sun,
16
P. C. Bloom,
17
W. T. Ford,
17
A. Gaz,
17
U. Nauenberg,
17
J. G. Smith,
17
S. R. Wagner,
17
R. Ayad,
18,
†
W. H. Toki,
18
B. Spaan,
19
K. R. Schubert,
20
R. Schwierz,
20
D. Bernard,
21
M. Verderi,
21
S. Playfer,
22
D. Bettoni,
23a
C. Bozzi,
23a
R. Calabrese,
23a,23b
G. Cibinetto,
23a,23b
E. Fioravanti,
23a,23b
I. Garzia,
23a,23b
E. Luppi,
23a,23b
L. Piemontese,
23a
V. Santoro,
23a
R. Baldini-Ferroli,
24
A. Calcaterra,
24
R. de Sangro,
24
G. Finocchiaro,
24
S. Martellotti,
24
P. Patteri,
24
I. M. Peruzzi,
24,
‡
M. Piccolo,
24
M. Rama,
24
A. Zallo,
24
R. Contri,
25a,25b
E. Guido,
25a,25b
M. Lo Vetere,
25a,25b
M. R. Monge,
25a,25b
S. Passaggio,
25a
C. Patrignani,
25a,25b
E. Robutti,
25a
B. Bhuyan,
26
V. Prasad,
26
M. Morii,
27
A. Adametz,
28
U. Uwer,
28
H. M. Lacker,
29
P. D. Dauncey,
30
U. Mallik,
31
C. Chen,
32
J. Cochran,
32
W. T. Meyer,
32
S. Prell,
32
A. E. Rubin,
32
A. V. Gritsan,
33
N. Arnaud,
34
M. Davier,
34
D. Derkach,
34
G. Grosdidier,
34
F. Le Diberder,
34
A. M. Lutz,
34
B. Malaescu,
34
P. Roudeau,
34
A. Stocchi,
34
G. Wormser,
34
D. J. Lange,
35
D. M. Wright,
35
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
G. Cowan,
38
J. Bougher,
39
D. N. Brown,
39
C. L. Davis,
39
A. G. Denig,
40
M. Fritsch,
40
W. Gradl,
40
K. Griessinger,
40
A. Hafner,
40
E. Prencipe,
40
R. J. Barlow,
41,
§
G. D. Lafferty,
41
E. Behn,
42
R. Cenci,
42
B. Hamilton,
42
A. Jawahery,
42
D. A. Roberts,
42
R. Cowan,
43
D. Dujmic,
43
G. Sciolla,
43
R. Cheaib,
44
P. M. Patel,
44,
*
S. H. Robertson,
44
P. Biassoni,
45a,45b
N. Neri,
45a
F. Palombo,
45a,45b
L. Cremaldi,
46
R. Godang,
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
M. Martinelli,
49
G. Raven,
49
C. P. Jessop,
50
J. M. LoSecco,
50
K. Honscheid,
51
R. Kass,
51
J. Brau,
52
R. Frey,
52
N. B. Sinev,
52
D. Strom,
52
E. Torrence,
52
E. Feltresi,
53a,53b
M. Margoni,
53a,53b
M. Morandin,
53a
M. Posocco,
53a
M. Rotondo,
53a
G. Simi,
53a
F. Simonetto,
53a,53b
R. Stroili,
53a,53b
S. Akar,
54
E. Ben-Haim,
54
M. Bomben,
54
G. R. Bonneaud,
54
H. Briand,
54
G. Calderini,
54
J. Chauveau,
54
Ph. Leruste,
54
G. Marchiori,
54
J. Ocariz,
54
S. Sitt,
54
M. Biasini,
55a,55b
E. Manoni,
55a
S. Pacetti,
55a,55b
A. Rossi,
55a,55b
C. Angelini,
56a,56b
G. Batignani,
56a,56b
S. Bettarini,
56a,56b
M. Carpinelli,
56a,56b,
¶
G. Casarosa,
56a,56b
A. Cervelli,
56a,56b
F. Forti,
56a,56b
M. A. Giorgi,
56a,56b
A. Lusiani,
56a,56c
B. Oberhof,
56a,56b
E. Paoloni,
56a,56b
A. Perez,
56a
G. Rizzo,
56a,56b
J. J. Walsh,
56a
D. Lopes Pegna,
57
J. Olsen,
57
A. J. S. Smith,
57
R. Faccini,
58a,58b
F. Ferrarotto,
58a
F. Ferroni,
58a,58b
M. Gaspero,
58a,58b
L. Li Gioi,
58a
G. Piredda,
58a
C. Bu
̈
nger,
59
S. Christ,
59
O. Gru
̈
nberg,
59
T. Hartmann,
59
T. Leddig,
59
H. Schro
̈
der,
59,
*
C. Voß,
59
R. Waldi,
59
T. Adye,
60
E. O. Olaiya,
60
F. F. Wilson,
60
S. Emery,
61
G. Hamel de Monchenault,
61
G. Vasseur,
61
Ch. Ye
`
che,
61
F. Anulli,
62
D. Aston,
62
D. J. Bard,
62
J. F. Benitez,
62
C. Cartaro,
62
M. R. Convery,
62
J. Dorfan,
62
G. P. Dubois-Felsmann,
62
W. Dunwoodie,
62
M. Ebert,
62
R. C. Field,
62
B. G. Fulsom,
62
A. M. Gabareen,
62
M. T. Graham,
62
T. Haas,
62
T. Hadig,
62
C. Hast,
62
W. R. Innes,
62
P. Kim,
62
M. L. Kocian,
62
D. W. G. S. Leith,
62
P. Lewis,
62
D. Lindemann,
62
B. Lindquist,
62
S. Luitz,
62
V. Luth,
62
H. L. Lynch,
62
D. B. MacFarlane,
62
D. R. Muller,
62
H. Neal,
62
S. Nelson,
62
M. Perl,
62
T. Pulliam,
62
B. N. Ratcliff,
62
A. Roodman,
62
A. A. Salnikov,
62
R. H. Schindler,
62
J. Schwiening,
62
A. Snyder,
62
D. Su,
62
M. K. Sullivan,
62
J. Va’vra,
62
A. P. Wagner,
62
W. F. Wang,
62
W. J. Wisniewski,
62
M. Wittgen,
62
D. H. Wright,
62
H. W. Wulsin,
62
V. Ziegler,
62
W. Park,
63
M. V. Purohit,
63
R. M. White,
63,
**
J. R. Wilson,
63
A. Randle-Conde,
64
S. J. Sekula,
64
M. Bellis,
65
P. R. Burchat,
65
T. S. Miyashita,
65
E. M. T. Puccio,
65
M. S. Alam,
66
J. A. Ernst,
66
R. Gorodeisky,
67
N. Guttman,
67
D. R. Peimer,
67
A. Soffer,
67
S. M. Spanier,
68
J. L. Ritchie,
69
A. M. Ruland,
69
R. F. Schwitters,
69
B. C. Wray,
69
J. M. Izen,
70
X. C. Lou,
70
F. Bianchi,
71a,71b
F. De Mori,
71a,71b
A. Filippi,
71a
D. Gamba,
71a,71b
S. Zambito,
71a,71b
L. Lanceri,
72a,72b
L. Vitale,
72a,72b
F. Martinez-Vidal,
73
A. Oyanguren,
73
P. Villanueva-Perez,
73
H. Ahmed,
74
J. Albert,
74
Sw. Banerjee,
74
F. U. Bernlochner,
74
H. H. F. Choi,
74
G. J. King,
74
R. Kowalewski,
74
M. J. Lewczuk,
74
T. Lueck,
74
I. M. Nugent,
74
J. M. Roney,
74
R. J. Sobie,
74
N. Tasneem,
74
T. J. Gershon,
75
P. F. Harrison,
75
T. E. Latham,
75
H. R. Band,
76
S. Dasu,
76
Y. Pan,
76
R. Prepost,
76
and S. L. Wu
76
PHYSICAL REVIEW D
88,
032011 (2013)
1550-7998
=
2013
=
88(3)
=
032011(26)
032011-1
Ó
2013 American Physical Society
(
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
Departament ECM, Facultat de Fisica, Universitat de Barcelona, 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, V6T 1Z1 Canada
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Los Angeles, Los Angeles, California 90024, USA
12
University of California at Riverside, Riverside, California 92521, USA
13
University of California at Santa Barbara, Santa Barbara, California 93106, USA
14
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
15
California Institute of Technology, Pasadena, California 91125, USA
16
University of Cincinnati, Cincinnati, Ohio 45221, USA
17
University of Colorado, Boulder, Colorado 80309, USA
18
Colorado State University, Fort Collins, Colorado 80523, USA
19
Fakulta
̈
t Physik, Technische Universita
̈
t Dortmund, D-44221 Dortmund, Germany
20
Technische Universita
̈
t Dresden, Institut fu
̈
r Kern- und Teilchenphysik, D-01062 Dresden, Germany
21
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France
22
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
23a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
23b
Dipartimento di Fisica e Scienze della Terra, Universita
`
di Ferrara, I-44122 Ferrara, Italy
24
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
25a
INFN Sezione di Genova, I-16146 Genova, Italy
25b
Dipartimento di Fisica, Universita
`
di Genova, I-16146 Genova, Italy
26
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India
27
Harvard University, Cambridge, Massachusetts 02138, USA
28
Universita
̈
t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany
29
Humboldt-Universita
̈
t zu Berlin, Institut fu
̈
r Physik, Newtonstrasse 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
Royal Holloway and Bedford New College, University of London, 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
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
44
McGill University, Montre
́
al, Que
́
bec H3A 2T8, Canada
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 H3C 3J7, Canada
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
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032011 (2013)
032011-2
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, IN2P3/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 V8W 3P6, Canada
75
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
76
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 12 June 2013; published 26 August 2013)
Inclusive production cross sections of
,
K
and
p=
p
per hadronic
e
þ
e
annihilation event are
measured at a center-of-mass energy of 10.54 GeV, using a relatively small sample of very high quality
data from the
BABAR
experiment at the PEP-II
B
-factory at the SLAC National Accelerator Laboratory.
The drift chamber and Cherenkov detector provide clean samples of identified
,
K
, and
p=
p
over a
wide range of momenta. Since the center-of-mass energy is below the threshold to produce a
B
B
pair, with
B
a bottom-quark meson, these data represent a pure
e
þ
e
!
q
q
sample with four quark flavors, and are
used to test QCD predictions and hadronization models. Combined with measurements at other energies,
in particular at the
Z
0
resonance, they also provide precise constraints on the scaling properties of the
hadronization process over a wide energy range.
DOI:
10.1103/PhysRevD.88.032011
PACS numbers: 13.66.Bc, 13.87.Fh, 12.38.Qk
I. INTRODUCTION
The production of hadrons from energetic quarks and
gluons in high-energy collisions is well described by quali-
tative models, but there are few quantitative theoretical
predictions. Detailed experimental information about had-
ron production allows the confining property of the strong
interaction to be probed. An empirical understanding of
confinement is important to the interpretation of much
current and future high-energy data, in which the observ-
able products of interactions and decays of heavy particles,
*
Deceased.
†
Present address: University of Tabuk, Tabuk 71491, Saudi
Arabia.
‡
Also at Dipartimento di Fisica, Universita
`
di Perugia,
Perugia, Italy.
§
Present address: University of Huddersfield, Huddersfield
HD1 3DH, United Kingdom.
∥
Present address: University of South Alabama, Mobile,
Alabama 36688, USA.
¶
Also at Universita
`
di Sassari, Sassari, Italy.
**
Present address: Universidad Te
́
cnica Federico Santa Maria,
2390123 Valparaiso, Chile.
PRODUCTION OF CHARGED PIONS, KAONS, AND
...
PHYSICAL REVIEW D
88,
032011 (2013)
032011-3
known and yet to be discovered, appear as jets of hadrons.
Measurements involving identified hadrons probe the
influence on this process of hadron masses and quantum
numbers such as strangeness, baryon number, and spin.
The process
e
þ
e
!
q
q
!
hadrons is understood to
proceed through three stages. In the first stage, the quark
(
q
) and antiquark (
q
) ‘‘fragment’’ via the radiation of
gluons (
g
), each of which can radiate further gluons or
split into a
q
q
pair. This process is, in principle, calculable
in perturbative quantum chromodynamics (QCD), and
there are calculations for up to four final-state partons,
corresponding to second order in the strong coupling
S
[
1
], where by ‘‘parton’’ we mean either a quark or a gluon.
In addition, leading-order calculations exist for as many as
six partons [
2
], as well as calculations to all orders in
S
in
the modified leading logarithm approximation (MLLA)
[
3
]. There are also ‘‘parton shower’’ Monte Carlo simula-
tions [
4
] that include an arbitrary number of
q
!
qg
,
g
!
gg
and
g
!
q
q
branchings, with probabilities deter-
mined up to next-to-leading logarithm level.
In the second stage, these partons ‘‘hadronize,’’ or trans-
form into ‘‘primary’’ hadrons, a step that is not understood
quantitatively. The ansatz of local parton-hadron duality
(LPHD) [
3
], that inclusive distributions of primary hadrons
are the same up to a scale factor as those for partons, allows
MLLA QCD to predict properties of distributions of the
dimensionless variable
¼
ln
x
p
for different hadrons.
Here,
x
p
¼
2
p
=E
CM
is the scaled momentum, and
p
and
E
CM
are the hadron momentum and the
e
þ
e
energy,
respectively, in the
e
þ
e
center-of-mass (CM) frame.
Predictions include the shape of the
distribution and its
dependence on hadron mass and
E
CM
. At sufficiently high
x
p
, perturbative QCD has also been used to calculate the
E
CM
dependence of the
x
p
distributions [
5
].
In the third stage, unstable primary hadrons decay into
more stable particles, which can reach detector elements.
Although proper lifetimes and decay branching fractions
have been measured for many hadron species, these decays
complicate fundamental measurements because many of
the stable particles are decay products rather than primary
hadrons. Previous measurements at
e
þ
e
colliders [
6
]
indicate that decays of vector mesons, strange baryons,
and decuplet baryons produce roughly two thirds of the
stable particles; scalar and tensor mesons and radially
excited baryons have also been observed and contribute
additional secondary hadrons. Ideally one would measure
every hadron species and distinguish primary hadrons from
decay products on a statistical basis. A body of knowledge
could be assembled by reconstructing increasingly heavy
states and subtracting their known decay products from the
measured rates of lighter hadrons. The measurement of the
stable charged hadrons constitutes a first step in such a
program.
There are several phenomenological models of hadronic
jet production. To model the parton production stage, the
HERWIG 5.8
[
7
],
JETSET 7.4
[
8
] and
UCLA 4.1
[
9
] event
generators rely on combinations of first-order matrix
elements and parton-shower simulations. For the hadroni-
zation stage, the
HERWIG
model splits the gluons produced
in the first stage into
q
q
pairs, combines these quarks and
antiquarks locally to form colorless ‘‘clusters,’’ and decays
the clusters into primary hadrons. The
JETSET
model rep-
resents the color field between the partons by a ‘‘string,’’
and breaks the string according to an iterative algorithm
into several pieces, each corresponding to a primary had-
ron. The
UCLA
model generates whole events according to
weights derived from phase space and Clebsch-Gordan
coefficients. Each model contains free parameters control-
ling various aspects of the hadronization process, whose
values have been tuned to reproduce data from
e
þ
e
annihilations. With a large number of parameters,
JETSET
has the potential to model many hadron species in detail,
whereas
UCLA
and
HERWIG
seek a more global description
with fewer parameters, including only one or two that
control the relative rates of different species.
The scaling properties, or
E
CM
dependences, of hadron
production are of particular interest. Since the process is
governed by QCD, it is expected to be scale invariant, i.e.
distributions of
x
p
should be independent of
E
CM
except
for the effects of hadron masses/phase space and the run-
ning of
S
. The quark flavor composition varies with
E
CM
,
and may also have substantial effects. Mass effects are
observed to be large unless
x
p
m
h
=E
CM
, where
m
h
is
the mass of the hadron in question, although current
experimental precision is limited at lower energies. At
high
x
p
, the expected scaling violations have been calcu-
lated [
5
] and found to be consistent with available data,
but experimental precision is limited for specific hadron
species. The scaling violation for inclusive charged tracks
has been used to extract
S
under a number of assumptions
about the dependence on event flavor and particle type
[
10
]. Improved precision at 10.54 GeV would provide
stringent tests of such assumptions and more robust mea-
surements of
S
.
The production of the charged hadrons
,
K
, and
p=
p
has been studied in
e
þ
e
annihilations at
E
CM
values
of 10 GeV [
11
], 29 GeV [
12
], 34 and 44 GeV [
13
], 58 GeV
[
14
], 91 GeV [
15
–
18
], and at several points in the range
130–200 GeV [
19
]. Recently, Belle has measured
and
K
production at 10.52 GeV [
20
]. Results for 91 GeV, near
the
Z
0
pole, include precise measurements in inclusive
hadronic events, as well as measurements for separated
quark flavors, quark and gluon jets, and leading particles
[
21
,
22
]. The higher- and lower-energy measurements are,
however, limited in precision and
x
p
coverage. Improved
precision over the full
x
p
range at 10.54 GeV would probe
the large scaling violations in detail and provide sensitive
new tests of QCD calculations and hadronization models.
In this article, we present measurements of the inclusive
normalized production cross sections of charged pions,
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032011 (2013)
032011-4
kaons, and protons per
e
þ
e
!
q
q
event. We use
0
:
91 fb
1
of data recorded by the
BABAR
detector at the
PEP-II storage ring at SLAC in March, 2002, at a CM
energy of 10.54 GeV. This is a small fraction of the
BABAR
‘‘off-resonance’’ data, recorded during a period dedicated
to the delivery of stable beams and constant luminosity.
The detector experienced relatively low backgrounds and
ran in its most efficient configuration, which was not
changed in this period. In parallel, we analyze
3
:
6fb
1
of data recorded at the
ð
4
S
Þ
resonance (10.58 GeV)
during the remainder of this period, February–April,
2002. This ‘‘on-resonance’’ sample provides independent,
stringent systematic checks, and the combined samples
provide data-derived calibrations of the tracking and par-
ticle identification performance. The uncertainties on the
results are dominated by systematic contributions.
The detector and event selection are described in Secs.
II
and
III
. The selection of high quality charged tracks and
their identification as pions, kaons or protons is discussed
in Sec.
IV
. The measurement of the cross sections, includ-
ing corrections for the effects of backgrounds, detector
efficiency and resolution, and the boost of the
e
þ
e
system
in the
BABAR
laboratory frame, are described in Sec.
V
.
The results are compared with previous results and with the
predictions of QCD and hadronization models in Sec.
VI
,
and are summarized in Sec.
VII
.
II. THE
BABAR
DETECTOR
The
e
þ
e
system is boosted in the
BABAR
laboratory
frame by
¼
0
:
56
along the
e
beam direction. We call
this direction ‘‘forward,’’
þ
z
, and denote quantities in the
e
þ
e
CM frame with an asterisk, and those in the labora-
tory frame with a subscript ‘‘lab.’’ For example,
p
denotes
the magnitude of a particle’s momentum in the CM frame
and
its angle with respect to the
e
beam direction, and
p
lab
and
lab
denote the corresponding quantities in the
laboratory frame. For
e
þ
e
!
q
q
events at
E
CM
¼
10
:
54 GeV
, the maximum
p
value is
E
CM
=
2
¼
5
:
27 GeV
=c
, but the maximum
p
lab
value depends on polar
angle, with values of
3
:
8 GeV
=c
at
cos
lab
¼
0
:
8
and
7 GeV
=c
at
cos
lab
¼þ
0
:
9
. Thus, particles with a given
p
value have different
p
lab
values in different regions of
the detector, and are measured with different efficiencies
and systematic uncertainties.
The
BABAR
detector is described in detail in Ref. [
23
].
In this analysis, we use charged tracks measured in the
silicon vertex tracker (SVT) and the drift chamber (DCH),
and identified in the DCH and the detector of internally
reflected Cherenkov light (DIRC). We also use energy
deposits measured in the CsI(Tl) crystal calorimeter
(EMC) to identify electron tracks and construct quantities
used in the event selection. These subdetectors operate in a
1.5 T solenoidal magnetic field.
The SVT comprises five double-sided layers of strip
detectors, each of which measures a coordinate along (
z
)
and azimuthally around (
) the beam axis. The DCH
includes 40 layers of axial and stereo wires. Their com-
bined resolution is
p
t
=p
t
¼
0
:
45%
ð
0
:
13%
p
t
½
GeV
=c
Þ
,
where
p
t
is the momentum transverse to the beam axis. The
DCH measures ionization energy loss (
d
E=
d
x
) with a
resolution of 8%.
The DIRC [
24
] consists of 144 fused silica radiator bars
that guide Cherenkov photons to an expansion volume
filled with water and equipped with 10,752 photomultiplier
tubes. It covers the polar angle range
0
:
8
<
cos
lab
<
0
:
9
.
The refractive index of 1.473 corresponds to Cherenkov
thresholds of 0.13, 0.48 and
0
:
87 GeV
=c
for
,
K
and
p=
p
, respectively. The Cherenkov angles of detected pho-
tons are measured with an average resolution of 10.2 mrad.
Tracks with very high
p
lab
yield an average of 20 detected
photons at
cos
lab
¼
0
, rising to 65 photons at the most
forward and backward angles.
The EMC comprises 5,760 CsI(Tl) crystals in a projec-
tive geometry that measure clusters of energy with a
resolution of
E
=E
¼
1
:
85%
ð
2
:
32%
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E
½
GeV
4
p
Þ
,An
algorithm identifies electrons using track momentum
combined with EMC measurements of energy and shower
shape. It has better than 95% efficiency for
p
lab
>
0
:
2 GeV
=c
, and hadron misidentification rates of up to
1% for
p
lab
<
0
:
5 GeV
=c
and at most 0.1% for higher
momenta.
III. HADRONIC EVENT SELECTION
The event selection is optimized for low bias across the
hadron momentum spectra and
e
þ
e
!
q
q
event multi-
plicity distribution, while minimizing backgrounds from
other physics processes and beam-wall and beam-gas
interactions. After fitting each combination of three or
more reconstructed charged tracks to a common vertex,
we require
(1) at least three charged tracks and one good vertex,
where a good vertex has a
2
confidence level above
0.01;
(2) the good vertex with the highest track multiplicity
to lie within 5 mm of the beam axis, and within 5 cm
of the center of the collision region in
z
;
(3) the second Fox-Wolfram moment [
25
] to be less
than 0.9;
(4) the sum of the energies of the charged tracks and
unassociated neutral clusters
E
tot
to be in the range
5–14 GeV;
(5) the polar angle of the event thrust [
26
] axis in the
CM frame to satisfy
j
cos
thrust
j
<
0
:
8
;
(6) the track with the highest
p
lab
not to be identified as
an electron in events with fewer than six tracks, and
neither of the two highest-
p
lab
tracks to be identified
as an electron in events with only three tracks.
Criteria 3 and 6 reject leptonic events,
e
þ
e
!
e
þ
e
,
þ
, and
þ
. Criteria 4 and 5 ensure that the
event is well contained within the sensitive volume of the
PRODUCTION OF CHARGED PIONS, KAONS, AND
...
PHYSICAL REVIEW D
88,
032011 (2013)
032011-5
detector, resulting in smaller corrections and lower biases.
These criteria select 2.2 million events in our off-resonance
signal sample and 11.8 million events in our on-resonance
calibration sample. About 27% of the events in the latter
sample are
ð
4
S
Þ
decays.
We evaluate the performance of the event selection using
the data and a number of simulations, each consisting of a
generator for a certain type of event combined with a
detailed simulation of the
BABAR
detector using the
GEANT4
[
27
] package. For signal
e
þ
e
!
q
q
events, we
use the
JETSET
[
8
] event generator and obtain simulated
selection efficiencies of 0.68 for
u
u
,
d
d
and
s
s
events, and
0.73 for
c
c
events. As cross-checks, we also use the
UCLA
model combined with
GEANT4
, and the
JETSET
,
UCLA
and
HERWIG
models with a fast detector simulation and several
different parameter sets. These give efficiency variations of
at most 0.5%. In all cases, the largest signal loss is due to
the requirement on
thrust
, which ensures that the event is
well contained within the sensitive volume of the detector,
resulting in low
p
and multiplicity biases. We find con-
sistency between data and simulation in a number of
distributions of event and track quantities; the largest
discrepancy we observe is a possible shift in the
E
tot
distribution (see Fig.
1
), which could indicate an efficiency
difference of at most 0.5%.
We use the
KORALB
[
28
] generator to simulate
-
and
-pair events. The former provide a negligible
contribution, but the latter are the largest source of back-
ground, estimated to be 4.5% of the selected events and to
contribute up to 25% of the charged tracks at the highest
momenta. However, the relevant properties of
-pair events
are well measured [
29
], and their contributions can be
simulated and subtracted reliably.
Radiative Bhabha events (
e
þ
e
!
e
þ
e
) are an
especially problematic background, as their cross section
in the very forward and backward regions is larger than
the
q
q
cross section and varies rapidly with
cos
.
Bremsstrahlung, photon conversions, and other inter-
actions in the detector material are difficult to simulate in
these regions, and can result in events with 3–6 tracks,
most of which are from electrons or positrons. Simulations
using the
BHWIDE
[
30
] generator predict that these events
are reduced to a negligible level by criteria 1–5 plus a
requirement that the highest-
p
lab
track in the 3- and 4-track
events not be identified as an electron. However, a com-
parison of
e
þ
and
e
angular distributions in the selected
data indicates a larger contribution. Therefore, we impose
the tighter
e
vetoes given in criterion 6, and estimate from
the data a residual radiative Bhabha event contribution of
0.1% of the selected events and up to 8% of the charged
tracks at our highest momenta and
j
cos
lab
j
values.
Initial-state radiation (ISR),
e
þ
e
!
e
þ
e
!
q
q
,
produces hadronic events with a lower effective CM
energy. Low-energy ISR photons are present in all events
and are simulated adequately in the
JETSET
model. The
event selection is designed to suppress events with higher-
energy ISR photons, including radiative return to the
ð
1
S
Þ
,
ð
2
S
Þ
and
ð
3
S
Þ
resonances (whose decays have
very different inclusive properties from
e
þ
e
!
q
q
events) and events with a very energetic ISR photon recoil-
ing against a hadronic system, which can mimic 2-jet
events. Using the
AFKQED
generator [
31
], we find that the
combination of the requirements on
E
tot
and
thrust
reduces
the energetic-ISR background to negligible levels, and the
ð
nS
Þ
background to one event in
10
5
.
We use the
GAMGAM
[
32
] generator to study back-
grounds from two-photon (
) processes,
e
þ
e
!
e
þ
e
!
e
þ
e
þ
hadrons. Neither the total cross sec-
tion nor those for any specific final states are known, but
such events have relatively low track multiplicity and
E
tot
since the final-state
e
and some of the hadrons generally
go undetected along the beam direction. The
E
tot
distribu-
tion for events in the data satisfying all other selection
criteria is shown in Fig.
1
. It features a structure in the
1–5 GeV range that is not described by the signal plus
-pair simulations, but can be described qualitatively by
the addition of
events. Since the mixture of final states
is unknown, we consider
!
þ
þ
, which has
the largest fraction of events with
E
tot
>
5 GeV
of any
final state with at least three tracks. The simulated
E
tot
distribution is shown as the shaded histogram in Fig.
1
.If
normalized to account for the entire excess in the data, such
events would make up less than 1% of the selected sample
(
5
<E
tot
<
14 GeV
), with a track momentum distribution
similar to that in
-pair events. We take this as an upper
γγ → 4π
04812
E
tot
(GeV)
0
100
200
300
400
500
Events / 0.25 GeV
u
u,d
d,s
s
c
c
B
B
τ
+
τ
−
sum
Data
x10
3
Simulation
sim.
FIG. 1 (color online). Distributions of the total visible energy
per event, after all other selection criteria have been applied, in
the on-resonance data and simulation. The sum of the hadronic
and
-pair simulations is normalized to the data in the region
above 5 GeV, and the
simulation is normalized arbitrarily.
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032011 (2013)
032011-6
limit on our
background and vary its contribution over
a wide range in evaluating the systematic uncertainty, as
discussed in Sec.
VB
.
Backgrounds from beam-gas and beam-wall interactions
can be studied using distributions of event vertex position
in the data. From the distribution in distance from the beam
axis for events satisfying all selection criteria except those
on the vertex position, we conclude that the beam-wall
background is negligible. From the distribution in
z
after
including the requirement that the vertex be within 5 mm of
the beam axis, we estimate that four beam-gas events are
selected per
10
5
signal events. We neglect both of these
backgrounds.
We consider a number of other possible backgrounds,
including two-photon events with one or both
e
detected
and other higher-order quantum electrodynamics (QED)
processes producing four charged leptons or two leptons
and a
q
q
pair; all are found to be negligible. We estimate
that the selected sample is
95
:
4
1
:
1%
pure in
e
þ
e
!
q
q
events, with the background dominated by
-pairs and
the uncertainty by
events. The on-resonance calibration
sample contains the same mixture of
e
þ
e
!
q
q
and
background events, plus a 27% contribution from
ð
4
S
Þ
decays.
IV. CHARGED TRACK SELECTION AND
IDENTIFICATION
The identification of charged tracks as pions, kaons or
protons is performed using an algorithm that combines the
momentum and ionization energy loss measured in the
DCH and the velocity measured via the Cherenkov angle
in the DIRC. To ensure reliable measurements of these
quantities, we require tracks to have (i) at least 20 mea-
sured coordinates in the DCH; (ii) at least 5 coordinates in
the SVT, including at least 3 in
z
; (iii) a distance of closest
approach to the beam axis of less than 1 mm; (iv) a
transverse momentum
p
t
>
0
:
2 GeV
=c
; (v) a polar angle
lab
satisfying
0
:
78
<
cos
lab
<
0
:
88
; and (vi) an
extrapolated trajectory that intersects a DIRC bar. The first
criterion ensures good
d
E=
d
x
resolution, the first three
criteria select tracks from particles that originate from
the primary interaction and do not decay in flight or
interact before reaching the DIRC, and the combination
of all six criteria yields tracks well within the DIRC
fiducial volume, with good momentum and polar angle
resolution.
These criteria suppress tracks from decays of long-lived
particles such as
K
0
S
and
hadrons, which are included in
many previous measurements. Here, we report cross sec-
tions for two classes of tracks, denoted ‘‘prompt’’ and
‘‘conventional.’’ We first measure prompt hadrons, defined
as primary hadrons or products of a decay chain in which
all particles have lifetimes shorter than
10
11
s
. This
includes products of all charmed hadron decays, as well
as those of strongly or electromagnetically decaying
strange particles, but not those of weakly decaying strange
particles. We then obtain the conventional quantities by
adding the decay daughters of particles with lifetimes in
the range
1
–
3
10
11
s
, i.e.,
K
0
S
and weakly decaying
strange baryons. For this we use existing measurements
of
K
0
S
and strange baryon production [
33
]. Either or both
cross sections can be compared with other measurements,
and used to test QCD and model predictions.
In selected simulated events, these criteria accept 82%
of the prompt charged particles generated within the target
lab
range and with
p
t
>
0
:
2 GeV
=c
. This efficiency rises
slowly from 80% at
p
lab
¼
0
:
2 GeV
=c
to 86% at the
highest momentum, and is almost independent of particle
type, polar angle, event flavor, and track multiplicity.
Corrections to the simulation are discussed in Sec.
VC
.
Since the
e
þ
e
system is boosted in the laboratory
frame, we divide the selected tracks into six regions of
cos
lab
:
½
0
:
78
;
0
:
33
,
½
0
:
33
;
0
:
05
, [0.05, 0.36], [0.36,
0.6], [0.6, 0.77] and [0.77, 0.88], denoted
1
to
6
, and
analyze each region separately. These correspond to
regions of roughly equal width in
cos
between
0
:
92
and
þ
0
:
69
. The tracks in each region arise from the same
underlying
p
distribution, but are boosted into different
ranges of
p
lab
. Also, heavier particles are boosted to higher
cos
lab
, with low-
p
protons and kaons populating the
forward
cos
lab
regions preferentially. Thus we perform
multiple (up to six) measurements for each
p
value, each
from a different
p
lab
range and in a different region of the
detector. Their comparison provides a powerful set of
cross-checks on detector performance and material inter-
actions, backgrounds, the true
and
p
distributions, and
the boost value itself.
A. Charged hadron identification
The
d
E=
d
x
measurement from the DCH provides very
good separation between low-
p
lab
particles, i.e., between
K
and
(
p=
p
and
K
) below about
0
:
5
ð
0
:
8
Þ
GeV
=c
.
There is also modest separation, of 1–3 standard deviations
(
), in the relativistic rise region above about
2 GeV
=c
,
and the separation varies rapidly at intermediate
p
lab
.For
each accepted track, we calculate a set of five likelihoods
L
DCH
i
,
i
¼
e
,
,
,
K
,
p
, each reflecting the degree of
consistency of its measured
d
E=
d
x
value with hypothesis
i
.
The Cherenkov angle measurement from the DIRC pro-
vides very good separation between particles with
p
lab
between the Cherenkov threshold and the resolution limit
of about
4 GeV
=c
for
vs
K
and
6
:
5 GeV
=c
for
K
vs
p=
p
. The number of expected photons varies rapidly with
p
lab
just above threshold, and the number detected for
each track provides additional information. A track can
be classified as being below threshold by counting the
detected photons at the angles expected for each above-
threshold particle type and comparing with the hypothesis
that only background is present. To make full use of this
information, we maximize a global likelihood for the set of
PRODUCTION OF CHARGED PIONS, KAONS, AND
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PHYSICAL REVIEW D
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032011 (2013)
032011-7
reconstructed tracks in each event, which considers back-
grounds, photons that could have been emitted by more
than one track, and multiple angles from a given track. For
each track, we calculate a set of five likelihoods
L
DIRC
i
,
i
¼
e
,
,
,
K
,
p
, assuming the best hypothesis for all other
tracks. These provide
K
-
(
p=
p
-
K
) separation that
rises rapidly with
p
lab
from zero at the
(
K
) Cherenkov
threshold of
0
:
13
ð
0
:
48
Þ
GeV
=c
, to a roughly constant
value, from which it falls off above about
2
:
5
ð
4
:
5
Þ
GeV
=c
.
To make use of both DCH and DIRC information, we
consider the log-likelihood differences
l
det
ij
¼
ln
ð
L
det
i
Þ
ln
ð
L
det
j
Þ
, where
det
¼
DCH
, DIRC, and we identify tracks
by their positions in the
l
DCH
ij
vs
l
DIRC
ij
planes. The proce-
dure is illustrated in Fig.
2
for simulated
(lower left)
and
K
(upper right) with
0
:
6
<p
lab
<
0
:
625 GeV
=c
and
cos
lab
>
0
:
05
. Here the DIRC provides clear separation
for all but a few percent of the tracks (most of the entries at
the left and right edges are overflows), but long tails are
visible in the
l
DIRC
K
distributions for both
and
K
. The
DCH separation is smaller, but the tails are shorter. To be
identified as a
, a track must lie below a line in the
l
DCH
K
-
l
DIRC
K
plane (see Fig.
2
) and below another line in the
l
DCH
p
-
l
DIRC
p
plane. Similarly, an identified
K
lies above a
line (dashed in Fig.
2
) in the
l
DCH
K
-
l
DIRC
K
plane and below a
line in the
l
DCH
pK
-
l
DIRC
pK
plane, and an identified
p=
p
lies
above lines in the
l
DCH
p
-
l
DIRC
p
and
l
DCH
pK
-
l
DIRC
pK
planes.
The parameters describing the lines vary smoothly
with
p
lab
and
lab
, and are optimized [
34
] to keep the
misidentification rates as low as reasonably possible, while
maintaining high identification efficiencies that vary
slowly with both
p
lab
and
cos
lab
. The slopes are zero
(i.e. only
d
E=
d
x
information is used) for
p
lab
below the
lower of the two Cherenkov thresholds, begin to decrease
slowly at that threshold, and become large and negative
above about
2
:
5 GeV
=c
; although
d
E=
d
x
provides some
separation in this region, the systematic uncertainties are
minimized by using it only to reject outlying tracks. In
some cases the two lines in a given plane are the same; in
most cases they are nearly parallel and separated by a few
units, and tracks in between are not identified as any
hadron type. Fewer than 0.1% of the tracks are identified
as more than one type, and these are reclassified as
unidentified.
Electrons and muons represent only a small fraction of
the tracks in hadronic events at
E
CM
10 GeV
(at most
2%), and their production is understood at the level of 10%
or better (see Sec.
VE
). They can be suppressed at this
point using calorimeter and muon system information, and
we have done this as a cross-check, obtaining consistent
results. However, this also rejects some signal tracks, and
the total systematic uncertainties are minimized by includ-
ing
e
and
in the pion category at this stage, and
subtracting them later. We therefore define a
ð
e
Þ
sample. High-momentum
e
and almost all
are indis-
tinguishable from
in the DCH or DIRC, so are included
by the criteria noted so far. The DIRC does separate
from
in a narrow
p
lab
range near
0
:
2 GeV
=c
, but we
use only
d
E=
d
x
information in this range. To accommodate
low-momentum
e
, we include tracks with
p
lab
below
2 GeV
=c
that satisfy requirements in the
l
DCH
e
-
l
DIRC
e
and
l
DCH
eK
-
l
DIRC
eK
planes.
We quantify the performance of our hadron identifica-
tion procedure in terms of a momentum-dependent
identification efficiency matrix
E
, where each element
E
ij
represents the probability that a selected track from a
true
i
-hadron is identified as a
j
-hadron, with
i
,
j
¼ð
e
Þ
,
K
,
p
. The matrix predicted by the detector simulation for
our most forward polar angle region,
6
, which covers the
widest
p
lab
range, is shown as the dashed lines in Fig.
3
.
The efficiencies for correct identification are predicted to
be very high at low
p
lab
, where
d
E=
d
x
separation is good,
then transition smoothly to a plateau where the Cherenkov
angle provides good separation, and then fall off at higher
p
lab
where the Cherenkov angles for different particles
converge. The predicted probabilities for misidentifying a
particle as a different type are below 2.5%. Essentially
all tracks are identified as some particle type at low
p
lab
,
1%–3% are classified as ambiguous in the plateau regions,
and larger fractions are so classified as the efficiency falls
off, since we choose to maintain constant or falling
misidentification rates.
Similar performance is predicted in the other
cos
lab
regions. In
1
and
2
, the two most backward regions,
p
lab
does not exceed
3
:
5
–
4 GeV
=c
, so no falloff is visible in
E
pp
at high
p
lab
, and
E
and
E
KK
drop only to 30%–70%
-40
-20
0
20
40
-40
-20
0
20
40
1
10
10
2
l
K
π
DIRC
l
K
π
DCH
FIG. 2. Simulated distribution of the
K
-
log-likelihood dif-
ference
l
K
from the DCH vs that from the DIRC for
and
K
in hadronic events generated with
0
:
6
<p
lab
<
0
:
625 GeV
=c
and
cos
lab
>
0
:
05
. The
and
K
are concentrated in the
lower left and upper right regions, respectively. The edge bins
include overflows. The solid (dashed) line represents an upper
(lower) bound on identified
(
K
).
J. P. LEES
et al.
PHYSICAL REVIEW D
88,
032011 (2013)
032011-8
of their plateau values. Thus we are able to measure the
high
p
range well in multiple
cos
lab
regions. In the next
few subsections, however, we focus on
6
, since it spans
the widest range in efficiencies and requires the largest
corrections to the simulation.
B. Calibration of the identification efficiencies
We calibrate the efficiency matrix from the combined
off- and on-resonance data set, using samples of tracks
with known hadron content and characteristics as similar as
possible to our selected tracks. For example, we construct
K
0
S
!
þ
candidates from tracks satisfying criteria (i)
and (iv)–(vi) presented at the beginning of Sec.
IV
, with a
less restrictive requirement of three coordinates in the SVT
and an additional requirement that there be a coordinate
from one of the two outer layers of the DCH. Pairs of
oppositely charged tracks must have a fitted vertex more
than 0.5 cm from the beam axis, a reconstructed total
momentum direction within 50 mrad of the line between
their fitted vertex and the event vertex, and an invariant
mass in the range
486
–
506 MeV
=c
2
. The percent-level
non-
K
0
S
contribution is predominantly from pions, so these
tracks constitute a clean sample of
that are produced
in hadronic events and cross most of the tracking system.
In simulated events, this sample has
E
j
values within
0.5% of those of the prompt
in the same events. We
calculate efficiencies from this
K
0
S
sample in both data and
simulation, and use their differences to correct the prompt
simulation. This sample covers
p
lab
up to about
1
:
5 GeV
=c
with high precision.
A similar selection of
!
p
and
!
p
þ
candi-
dates provides a sample of
0
:
4
–
3
:
5 GeV
=c p=
p
(and
another sample of soft pions) in hadronic events. We also
reconstruct two samples of
!
K
þ
K
decays in which
either the
K
þ
or
K
is identified, providing
0
:
2
–
2 GeV
=c
K
and
K
þ
samples that are subsamples of our main
sample. These samples contain substantial backgrounds,
and we extract
E
pj
,
E
pj
,
E
K
þ
j
and
E
K
j
from sets of
simultaneous fits to the four
p=
p
or
K
þ
K
invariant
mass distributions in which the
p=
p
or the other kaon is
identified as a pion, kaon, proton or no type.
We obtain samples of
0
:
6
–
5 GeV
=c
and
K
by reconstructing candidate
D
?
þ
!
D
0
þ
!
K
þ
þ
(and charge conjugate) decays and selecting those with a
K
þ
þ
K
þ
mass difference in the range
143
–
148 MeV
=c
2
. The
K
þ
invariant distribution shows
a
D
0
signal with a peak signal-to-background of 11. These
tracks are predominantly from
ð
4
S
Þ
decays and
c
c
events,
but have simulated
E
Kj
and
E
j
values within 1% and
0.5%, respectively, of those from all prompt
K
and
in hadronic events. Requiring the
(
K
þ
) candidate track
to be so identified and the
K
(
þ
) track to satisfy our
selection criteria, we evaluate
E
K
j
(
E
þ
j
) as the fraction
of the sideband-subtracted entries in the
D
0
peak in which
the
K
(
þ
) is identified as type
j
.
We select
e
þ
e
!
þ
events in which one of the
decays contains a single charged track (1-prong) and the
other contains one or three (3-prong) charged tracks. These
tracks constitute
ð
e
Þ
samples that are not from a
hadronic jet environment and have different
e
:
:
content, as well as a small but well known
K
component.
However, these samples have simulated identification effi-
ciencies within a few percent of those for
in hadronic
events, and they allow us to study high-
p
lab
tracks and
tracks that are isolated (1-prong) or relatively close
together (3-prong) in the detector. We also apply indepen-
dent electron and muon selectors to the 1-prong sample, in
order to check that the small differences in performance
between
e
,
and
are simulated correctly.
Results from the different calibration samples are con-
sistent where they overlap, as are those from positively and
negatively charged tracks and from on- and off-resonance
data. Considering the set of constraints provided by
these samples, we derive corrections to the simulated
E
ij
elements that vary smoothly with
p
lab
and
cos
lab
. The
correction to each
E
ij
in each
cos
lab
region is a continu-
ous, piecewise-linear function of
p
lab
, with an uncertainty
given by the statistically most precise calibration sample at
each point. The resulting calibrated efficiencies in the
6
0.2
0.4
0.6
0.8
1.0
Simulated
Corrected
0.2
0.4
0.6
0.8
1.0
Identification Efficiency
0246
0.0
0.2
0.4
0.6
0.8
1.0
0246
Laboratory Momentum, p (GeV/c)
lab
0246
True
π
True K
True p
0.77<cos
θ
<0.88
π→π
K
→π
p
→π
(x10)
π→
K (x10)
K
→
Kp
→
K (x10)
π→
p (x10)
K
→
p (x10)
p
→
p
Identified
π
Identified K
Identified p
(x10)
FIG. 3 (color online). The simulated (dashed lines) and cor-
rected (gray/green bands) efficiency matrix for the most forward
polar angle region,
6
, where
0
:
77
<
cos
lab
<
0
:
88
. The widths
of the bands indicate the uncertainties derived from the control
samples discussed in the text. The off-diagonal elements have
been scaled up by a factor of 10 for clarity.
PRODUCTION OF CHARGED PIONS, KAONS, AND
...
PHYSICAL REVIEW D
88,
032011 (2013)
032011-9