of 28
arXiv:1306.2895v2 [hep-ex] 4 Oct 2013
arXiv:1306.2895[hep-ex]
SLAC-PUB-15524
B
A
B
AR
-PUB-13/003
Production of charged pions, kaons and protons in
e
+
e
annihilations into hadrons at
s
= 10
.
54 GeV
J. P. Lees, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules
(LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vie
ux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament
ECM, E-08028 Barcelona, Spain
A. Palano
ab
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
G. Eigen and B. Stugu
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, M. Lee, and G. Lynch
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, California 94720, USA
H. Koch and T. Schroeder
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. So
University of British Columbia, Vancouver, British Columb
ia, Canada V6T 1Z1
A. Khan
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kin
gdom
V. E. Blinov, A. R. Buzykaev, V. P. Druzhinin, V. B. Golubev, E. A. Kr
avchenko, A. P. Onuchin,
S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, K. Yu. Todysh
ev, and A. N. Yushkov
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630
090, Russia
D. Kirkby, A. J. Lankford, and M. Mandelkern
University of California at Irvine, Irvine, California 926
97, USA
C. Buchanan and B. Hartfiel
University of California at Los Angeles, Los Angeles, Calif
ornia 90024, USA
B. Dey, J. W. Gary, O. Long, and G. M. Vitug
University of California at Riverside, Riverside, Califor
nia 92521, USA
C. Campagnari, M. Franco Sevilla, T. M. Hong, D. Kovalskyi, J. D. Rich
man, and C. A. West
University of California at Santa Barbara, Santa Barbara, C
alifornia 93106, USA
A. M. Eisner, W. S. Lockman, A. J. Martinez, B. A. Schumm, and A. S
eiden
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin, P. On
gmongkolkul, and F. C. Porter
California Institute of Technology, Pasadena, California
91125, USA
R. Andreassen, Z. Huard, B. T. Meadows, M. D. Sokoloff, and L. Su
n
University of Cincinnati, Cincinnati, Ohio 45221, USA
2
P. C. Bloom, W. T. Ford, A. Gaz, U. Nauenberg, J. G. Smith, and S. R
. Wagner
University of Colorado, Boulder, Colorado 80309, USA
R. Ayad
and W. H. Toki
Colorado State University, Fort Collins, Colorado 80523, U
SA
B. Spaan
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44
221 Dortmund, Germany
K. R. Schubert and R. Schwierz
Technische Universit ̈at Dresden, Institut f ̈ur Kern- und T
eilchenphysik, D-01062 Dresden, Germany
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
S. Playfer
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
,
I. Garzia
ab
, E. Luppi
ab
, L. Piemontese
a
, and V. Santoro
a
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a
di Ferrara
b
, I-44122 Ferrara, Italy
R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,
S. Martellotti, P. Patteri, I. M. Peruzzi,
M. Piccolo, M. Rama, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
R. Contri
ab
, E. Guido
ab
, M. Lo Vetere
ab
, M. R. Monge
ab
, S. Passaggio
a
, C. Patrignani
ab
, and E. Robutti
a
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
B. Bhuyan and V. Prasad
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
M. Morii
Harvard University, Cambridge, Massachusetts 02138, USA
A. Adametz and U. Uwer
Universit ̈at Heidelberg, Physikalisches Institut, Philo
sophenweg 12, D-69120 Heidelberg, Germany
H. M. Lacker
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, Ne
wtonstr. 15, D-12489 Berlin, Germany
P. D. Dauncey
Imperial College London, London, SW7 2AZ, United Kingdom
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, W. T. Meyer, S. Prell, and A. E. Rubin
Iowa State University, Ames, Iowa 50011-3160, USA
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder,
A. M. Lutz, B. Malaescu, P. Roudeau, A. Stocchi, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, F
rance
3
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. P
ayne, and C. Touramanis
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, F. Di Lodovico, and R. Sacco
Queen Mary, University of London, London, E1 4NS, United Kin
gdom
G. Cowan
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
J. Bougher, D. N. Brown, and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, and E.
Prencipe
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Ker
nphysik, D-55099 Mainz, Germany
R. J. Barlow
and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingd
om
E. Behn, R. Cenci, B. Hamilton, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan, D. Dujmic, and G. Sciolla
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib, P. M. Patel,
§
and S. H. Robertson
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
P. Biassoni
ab
, N. Neri
a
, and F. Palombo
ab
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
L. Cremaldi, R. Godang,
P. Sonnek, and D. J. Summers
University of Mississippi, University, Mississippi 38677
, USA
X. Nguyen, M. Simard, and P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo
ab
, D. Monorchio
ab
, G. Onorato
ab
, and C. Sciacca
ab
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
M. Martinelli and G. Raven
NIKHEF, National Institute for Nuclear Physics and High Ene
rgy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
J. Brau, R. Frey, N. B. Sinev, D. Strom, and E. Torrence
University of Oregon, Eugene, Oregon 97403, USA
E. Feltresi
ab
, M. Margoni
ab
, M. Morandin
a
, M. Posocco
a
, M. Rotondo
a
, G. Simi
a
, F. Simonetto
ab
, and R. Stroili
ab
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
4
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand,
G. Calderini, J. Chauveau, Ph. Leruste, G. Marchiori, J. Ocariz, an
d S. Sitt
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
M. Biasini
ab
, E. Manoni
a
, S. Pacetti
ab
, and A. Rossi
ab
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06100 Perugia, Italy
C. Angelini
ab
, G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
∗∗
G. Casarosa
ab
, A. Cervelli
ab
, F. Forti
ab
,
M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, A. Perez
a
, G. Rizzo
ab
, and J. J. Walsh
a
INFN Sezione di Pisa
a
; Dipartimento di Fisica, Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
D. Lopes Pegna, J. Olsen, and A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, M. Gaspero
ab
, L. Li Gioi
a
, and G. Piredda
a
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
C. B ̈unger, S. Christ, O. Gr ̈unberg, T. Hartmann, T. Leddig, H.
Schr ̈oder,
§
C. Voß, and R. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
S. Emery, G. Hamel de Monchenault, G. Vasseur, and Ch. Y`eche
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
F. Anulli
a
, D. Aston, D. J. Bard, J. F. Benitez, C. Cartaro, M. R. Convery,
J. Dorfan, G. P. Dubois-Felsmann,
W. Dunwoodie, M. Ebert, R. C. Field, B. G. Fulsom, A. M. Gabareen, M
. T. Graham, T. Haas, T. Hadig, C. Hast,
W. R. Innes, P. Kim, M. L. Kocian, D. W. G. S. Leith, P. Lewis, D. Linde
mann, B. Lindquist, S. Luitz,
V. Luth, H. L. Lynch, D. B. MacFarlane, D. R. Muller, H. Neal, S. Nels
on, M. Perl, T. Pulliam, B. N. Ratcliff,
A. Roodman, A. A. Salnikov, R. H. Schindler, J. Schwiening, A. Snyde
r, D. Su, M. K. Sullivan, J. Va’vra,
A. P. Wagner, W. F. Wang, W. J. Wisniewski, M. Wittgen, D. H. Wright,
H. W. Wulsin, and V. Ziegler
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
W. Park, M. V. Purohit, R. M. White,
††
and J. R. Wilson
University of South Carolina, Columbia, South Carolina 292
08, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, T. S. Miyashita, and E. M. T. Puccio
Stanford University, Stanford, California 94305-4060, US
A
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Av
iv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie, A. M. Ruland, R. F. Schwitters, and B. C. Wray
University of Texas at Austin, Austin, Texas 78712, USA
5
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi
ab
, F. De Mori
ab
, A. Filippi
a
, D. Gamba
ab
, and S. Zambito
ab
INFN Sezione di Torino
a
; Dipartimento di Fisica Sperimentale, Universit`a di Tori
no
b
, I-10125 Torino, Italy
L. Lanceri
ab
and L. Vitale
ab
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
F. Martinez-Vidal, A. Oyanguren, and P. Villanueva-Perez
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
H. Ahmed, J. Albert, Sw. Banerjee, F. U. Bernlochner, H. H. F. Ch
oi, G. J. King, R. Kowalewski,
M. J. Lewczuk, T. Lueck, I. M. Nugent, J. M. Roney, R. J. Sobie, a
nd N. Tasneem
University of Victoria, Victoria, British Columbia, Canad
a V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4
7AL, United Kingdom
H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
(Dated: 11 June, 2013)
Inclusive production cross sections of
π
±
,
K
±
and
p/
p
per hadronic
e
+
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
B
A
B
AR
experiment at the PEP-II
B
-factory at the SLAC National Accelerator
Laboratory. The drift chamber and Cherenkov detector provi
de clean samples of identified
π
±
,
K
±
,
and
p/
p
over a wide range of momenta. Since the center-of-mass energ
y is below the threshold to
produce a
B
B
pair, with
B
a bottom-quark meson, these data represent a pure
e
+
e
q
q
sample
with four quark flavors, and are used to test QCD predictions a
nd 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.
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 qual-
itative models, but there are few quantitative theoreti-
cal predictions. Detailed experimental information about
hadron production allows the confining property of the
strong interaction to be probed. An empirical under-
standing of confinement is important to the interpreta-
tion of much current and future high-energy data, in
which the observable products of interactions and de-
cays of heavy particles, known and yet to be discov-
Now at the University of Tabuk, Tabuk 71491, Saudi Arabia
Also with Universit`a di Perugia, Dipartimento di Fisica, P
erugia,
Italy
Now at the University of Huddersfield, Huddersfield HD1 3DH,
UK
§
Deceased
Now at University of South Alabama, Mobile, Alabama 36688,
USA
∗∗
Also with Universit`a di Sassari, Sassari, Italy
††
Now at Universidad T ́ecnica Federico Santa Maria, Valparai
so,
Chile 2390123
ered, appear as jets of hadrons. Measurements involv-
ing identified hadrons probe the influence on this pro-
cess of hadron masses and quantum numbers such as
strangeness, baryon number, and spin.
The process
e
+
e
q
q
hadrons
is understood to
proceed through three stages. First, 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 per-
turbative quantum chromodynamics (QCD), and there
are calculations for up to four final-state partons, corre-
sponding to second order in the strong coupling
α
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
α
S
in the modified leading logarithm approximation
(MLLA) [3]. There are also “parton shower” Monte
Carlo simulations [4] that include an arbitrary number
of
q
qg
,
g
gg
and
g
q
q
branchings, with probabili-
ties determined up to next-to-leading logarithm level.
In the second stage, these partons “hadronize”, or
transform into “primary” hadrons, a step that is not
understood quantitatively. The ansatz of local parton-
hadron duality (LPHD) [3], that inclusive distributions of
6
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
ξ
=
ln
x
p
for
different hadrons. Here,
x
p
=2
p
/E
CM
is the scaled mo-
mentum, and
p
and
E
CM
are the hadron momentum
and the
e
+
e
energy, respectively, in the
e
+
e
center-of-
mass (CM) frame. Predictions include the shape of the
ξ
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 el-
ements. Although proper lifetimes and decay branching
fractions have been measured for many hadron species,
these decays complicate fundamental measurements be-
cause many of the stable particles are decay products
rather than primary hadrons. Previous measurements at
e
+
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 ob-
served and contribute additional secondary hadrons. Ide-
ally one would measure every hadron species and distin-
guish primary hadrons from decay products on a statis-
tical 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 ma-
trix elements and parton-shower simulations. For the
hadronization stage, the HERWIG model splits the glu-
ons 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 represents the color field between
the partons by a “string”, and breaks the string ac-
cording to an iterative algorithm into several pieces,
each corresponding to a primary hadron. The UCLA
model generates whole events according to weights de-
rived from phase space and Clebsch-Gordan coefficients.
Each model contains free parameters controlling various
aspects of the hadronization process, whose values have
been tuned to reproduce data from
e
+
e
annihilations.
With a large number of parameters, JETSET has the po-
tential 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
ex-
cept for the effects of hadron masses/phase space and the
running of
α
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
α
S
under a number of assump-
tions about the dependence on event flavor and particle
type [10]. Improved precision at 10.54 GeV would pro-
vide stringent tests of such assumptions and more robust
measurements of
α
S
.
The production of the charged hadrons
π
±
,
K
±
, and
p/
p
has been studied in
e
+
e
annihilations at
E
CM
val-
ues 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 mea-
sured
π
±
and
K
±
production at 10.52 GeV [20]. Results
for 91 GeV, near the
Z
0
pole, include precise measure-
ments in inclusive hadronic events, as well as measure-
ments 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 vio-
lations in detail and provide sensitive new tests of QCD
calculations and hadronization models.
In this article, we present measurements of the inclu-
sive normalized production cross sections of charged pi-
ons, kaons, and protons per
e
+
e
q
q
event. We use
0.91 fb
1
of data recorded by the
B
A
B
AR
detector at the
PEP-II storage ring at SLAC in March, 2002, at a CM en-
ergy of 10.54 GeV. This is a small fraction of the
B
A
B
AR
“off-resonance” data, recorded during a period dedicated
to the delivery of stable beams and constant luminos-
ity. The detector experienced relatively low backgrounds
and ran in its most efficient configuration, which was not
changed in this period. In parallel, we analyze 3.6 fb
1
of
data recorded at the
Υ
(4
S
) resonance (10.58 GeV) dur-
ing the remainder of this period, February–April, 2002.
This “on-resonance” sample provides independent, strin-
gent systematic checks, and the combined samples pro-
vide data-derived calibrations of the tracking and parti-
cle identification performance. The uncertainties on the
results are dominated by systematic contributions.
The detector and event selection are described in sec-
tions II–III. The selection of high quality charged tracks
and their identification as pions, kaons or protons is
discussed in section IV. The measurement of the cross
sections, including corrections for the effects of back-
grounds, detector efficiency and resolution, and the boost
of the
e
+
e
system in the
B
A
B
AR
laboratory frame, are
described in section V. The results are compared with
previous results and with the predictions of QCD and
hadronization models in section VI, and are summarized
in section VII.
7
II. THE
B
A
B
AR
DETECTOR
The
e
+
e
system is boosted in the
B
A
B
AR
laboratory
frame by
βγ
= 0
.
56 along the
e
beam direction. We
call this direction “forward”, +
z
, and denote quantities
in the
e
+
e
CM frame with an asterisk, and those in the
laboratory frame with a subscript ‘lab’. For example,
p
denotes the magnitude of a particle’s momentum in
the CM frame and
θ
its angle with respect to the
e
beam direction, and
p
lab
and
θ
lab
denote the correspond-
ing quantities in the laboratory frame. For
e
+
e
q
q
events at
E
CM
= 10
.
54 GeV, the maximum
p
value
is
E
CM
/
2 = 5
.
27 GeV
/c
, but the maximum
p
lab
value
depends on polar angle, with values of 3.8 GeV
/c
at
cos
θ
lab
=
0
.
8 and 7 GeV
/c
at cos
θ
lab
= +0.9. Thus,
particles with a given
p
value have different
p
lab
val-
ues in different regions of the detector, and are measured
with different efficiencies and systematic uncertainties.
The
B
A
B
AR
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 calorime-
ter (EMC) to identify electron tracks and construct quan-
tities used in the event selection. These subdetectors op-
erate 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 (
φ
) the beam axis. The DCH
includes 40 layers of axial and stereo wires. Their com-
bined resolution is
σ
p
t
/p
t
= 0
.
45%
(0
.
13%
·
p
t
[ GeV
/c
]),
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 photomul-
tiplier tubes. It covers the polar angle range
0
.
8
<
cos
θ
lab
<
0
.
9. The refractive index of 1.473 corresponds
to Cherenkov thresholds of 0.13, 0.48 and 0.87 GeV
/c
for
π
±
,
K
±
and
p/
p
, respectively. The Cherenkov angles of
detected photons are measured with an average resolu-
tion of 10.2 mrad. Tracks with very high
p
lab
yield an
average of 20 detected photons at cos
θ
lab
= 0, rising to
65 photons at the most forward and backward angles.
The EMC comprises 5,760 CsI(Tl) crystals in a pro-
jective geometry that measure clusters of energy with
a resolution of
σ
E
/E
= 1
.
85%
(2
.
32%
/
4
E
[ GeV]),
An algorithm identifies electrons using track momen-
tum 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
+
e
q
q
event multi-
plicity distribution, while minimizing backgrounds from
other physics processes and beam-wall and beam-gas in-
teractions. 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
χ
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
|
cos
θ
thrust
|
<
0
.
8;
6. the track with the highest
p
lab
not to be identi-
fied 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
+
e
e
+
e
,
μ
+
μ
, and
τ
+
τ
. Criteria 4 and 5 ensure that the
event is well contained within the sensitive volume of
the 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
Υ
(4
S
) decays.
We evaluate the performance of the event selection us-
ing the data and a number of simulations, each consist-
ing of a generator for a certain type of event combined
with a detailed simulation of the
B
A
B
AR
detector using
the GEANT4 [27] package. For signal
e
+
e
q
q
events,
we use the JETSET [8] event generator and obtain simu-
lated 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 JET-
SET, 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
θ
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 consistency between data
and simulation in a number of distributions of event and
track quantities; the largest discrepancy we observe is a
8
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
μ
- and
τ
-pair events. The former provide a negligible contribu-
tion, but the latter are the largest source of background,
estimated to be 4.5% of the selected events and to con-
tribute up to 25% of the charged tracks at the highest mo-
menta. However, the relevant properties of
τ
-pair events
are well measured [29], and their contributions can be
simulated and subtracted reliably.
Radiative Bhabha events (
e
+
e
e
+
e
γ
) are an
especially problematic background, as their cross sec-
tion in the very forward and backward regions is larger
than the
q
q
cross section and varies rapidly with cos
θ
.
Bremsstrahlung, photon conversions, and other interac-
tions 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. Simu-
lations 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 comparison of
e
+
and
e
angular distribu-
tions in the selected data indicates a larger contribution.
Therefore, we impose the tighter
e
±
vetoes given in cri-
terion 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 mo-
menta and
|
cos
θ
lab
|
values.
Initial-state radiation (ISR),
e
+
e
γe
+
e
γq
q
,
produces hadronic events with a lower effective CM en-
ergy. 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
Υ
(1
S
),
Υ
(2
S
) and
Υ
(3
S
) resonances (whose decays
have very different inclusive properties from
e
+
e
q
q
events) and events with a very energetic ISR photon re-
coiling 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
θ
thrust
reduces the energetic-ISR background to negligible levels,
and the
Υ
(
nS
) background to one event in 10
5
.
We use the GAMGAM [32] generator to study
backgrounds from 2-photon (
γγ
) processes,
e
+
e
e
+
e
γγ
e
+
e
+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
distri-
bution 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
τ
-pair simulations, but can be described qualitatively by
the addition of
γγ
events. Since the mixture of final
states is unknown, we consider
γγ
π
+
π
π
+
π
, 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
γγ → 4π
0
4
8
12
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
0
100
200
300
400
500
Events / 0.25 GeV
Data
x10
3
Simulation
sim.
FIG. 1: 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
τ
-pair simulations is normalized to the data in the region
above 5 GeV, and the
γγ
simulation is normalized arbitrarily.
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 dis-
tribution similar to that in
τ
-pair events. We take this as
an upper limit on our
γγ
background and vary its con-
tribution over a wide range in evaluating the systematic
uncertainty, as discussed in Sec. V B.
Backgrounds from beam-gas and beam-wall interac-
tions 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 cri-
teria 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
+
e
q
q
events, with the background dominated by
τ
-pairs and
the uncertainty by
γγ
events. The on-resonance calibra-
tion sample contains the same mixture of
e
+
e
q
q
and
background events, plus a 27% contribution from
Υ
(4
S
)
decays.
9
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
measured coordinates in the DCH; ii) at least 5 coordi-
nates 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
θ
lab
satisfying
0
.
78
<
cos
θ
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 combina-
tion 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
Λ
hadrons, which are included
in many previous measurements. Here, we report cross
sections for two classes of tracks, denoted “prompt” and
“conventional”. We first measure prompt hadrons, de-
fined 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 decay-
ing strange particles, but not those of weakly decaying
strange particles. We then obtain the conventional quan-
tities 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 mea-
surements of
K
0
S
and strange baryon production [33, 34].
Either or both cross sections can be compared with other
measurements, and used to test QCD and model predic-
tions.
In selected simulated events, these criteria accept 82%
of the prompt charged particles generated within the tar-
get
θ
lab
range and with
p
t
>
0
.
2 GeV
/c
. This efficiency
rises slowly from 80% at
p
lab
=0
.
2 GeV
/c
to 86% at the
highest momentum, and is almost independent of parti-
cle type, polar angle, event flavor, and track multiplicity.
Corrections to the simulation are discussed in Sec. V C.
Since the
e
+
e
system is boosted in the labora-
tory frame, we divide the selected tracks into six re-
gions of cos
θ
lab
: [
0.78,
0.33], [
0.33,0.05], [0.05,0.36],
[0.36,0.6], [0.6,0.77] and [0.77,0.88], denoted
θ
1 to
θ
6, and
analyze each region separately. These correspond to re-
gions of roughly equal width in cos
θ
between
0.92 and
+0.69. The tracks in each region arise from the same
underlying
p
distribution, but are boosted into differ-
ent ranges of
p
lab
. Also, heavier particles are boosted to
higher cos
θ
lab
, with low-
p
protons and kaons populat-
ing the forward cos
θ
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 differ-
ent region of the detector. Their comparison provides a
powerful set of cross checks on detector performance and
material interactions, backgrounds, the true
θ
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
π
±
(
p/
p
and
K
±
) below about 0.5 (0.8) GeV
/c
.
There is also modest separation, of 1–3 standard devi-
ations (
σ
), in the relativistic rise region above about
2 GeV
/c
, and the separation varies rapidly at interme-
diate
p
lab
. For each accepted track, we calculate a set of
five likelihoods
L
DCH
i
,
i
=
e, μ, π, 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
provides very good separation between particles with
p
lab
between the Cherenkov threshold and the resolution limit
of about 4 GeV
/c
for
π
±
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 hypoth-
esis that only background is present. To make full use of
this information, we maximize a global likelihood for the
set of reconstructed tracks in each event, which considers
backgrounds, 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
=
e, μ, π, K, p
, assuming the best hypothesis for
all other tracks. These provide
K
±
-
π
±
(
p/
p
-
K
±
) separa-
tion that rises rapidly with
p
lab
from zero at the
π
±
(
K
±
)
Cherenkov threshold of 0.13 (0.48) GeV
/c
, to a roughly
constant value, from which it falls off above about 2.5
(4.5) GeV
/c
.
To make use of both DCH and DIRC information, we
consider the log-likelihood differences
l
det
ij
= ln(
L
det
i
)
ln(
L
det
j
), where det = DCH, DIRC, and we identify
tracks by their positions in the
l
DCH
ij
vs.
l
DIRC
ij
planes.
The procedure is illustrated in Fig. 2 for simulated
π
±
(lower left) and
K
±
(upper right) with 0
.
6
< p
lab
<
0
.
625 GeV
/c
and cos
θ
lab
>
0
.
05. Here the DIRC pro-
vides 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
dis-
tributions for both
π
±
and
K
±
. The DCH separation
is smaller, but the tails are shorter. To be identified as
a
π
±
, a track must lie below a line in the
l
DCH
l
DIRC
plane (see Fig. 2) and below another line in the
l
DCH
l
DIRC
plane. Similarly, an identified
K
±
lies above a line
10
-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
-
π
log-likelihood dif-
ference
l
from the DCH vs. that from the DIRC for
π
±
and
K
±
in hadronic events generated with 0
.
6
< p
lab
<
0
.
625 GeV
/c
and cos
θ
lab
>
0
.
05. The
π
±
and
K
±
are con-
centrated in the lower left and upper right regions, respec-
tively. The edge bins include overflows. The solid (dashed)
line represents an upper (lower) bound on identified
π
±
(
K
±
).
(dashed in Fig. 2) in the
l
DCH
l
DIRC
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
l
DIRC
and
l
DCH
pK
l
DIRC
pK
planes.
The parameters describing the lines vary smoothly
with
p
lab
and
θ
lab
, and are optimized [35] to keep
the misidentification rates as low as reasonably possi-
ble, while maintaining high identification efficiencies that
vary slowly with both
p
lab
and cos
θ
lab
. The slopes are
zero (i.e. only d
E/
d
x
information is used) for
p
lab
be-
low 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 out-
lying 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. V E). They can be suppressed at
this point using calorimeter and muon system informa-
tion, 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 mini-
mized by including
e
±
and
μ
±
in the pion category at
this stage, and subtracting them later. We therefore de-
fine a (
eμπ
)
±
sample. High-momentum
e
±
and almost all
μ
±
are indistinguishable from
π
±
in the DCH or DIRC,
so are included by the criteria noted so far. The DIRC
does separate
μ
±
from
π
±
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
l
DIRC
and
l
DCH
eK
l
DIRC
eK
planes.
We quantify the performance of our hadron identi-
fication 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
=
(
eμπ
)
, K, p
. The matrix predicted by the detector simu-
lation for our most forward polar angle region,
θ
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
sep-
aration is good, then transition smoothly to a plateau
where the Cherenkov angle provides good separation,
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 par-
ticle type at low
p
lab
, 1–3% are classified as ambiguous
in the plateau regions, and larger fractions are so classi-
fied as the efficiency falls off, since we choose to maintain
constant or falling misidentification rates.
Similar performance is predicted in the other cos
θ
lab
regions. In
θ
1 and
θ
2, the two most backward regions,
p
lab
does not exceed 3.5–4 GeV
/c
, so no fall off is visible
in
E
pp
at high
p
lab
, and
E
ππ
and
E
KK
drop only to 30–
70% of their plateau values. Thus we are able to measure
the high
p
range well in multiple cos
θ
lab
regions. In the
next few subsections, however, we focus on
θ
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 simi-
lar as possible to our selected tracks. For example, we
construct
K
0
S
π
+
π
candidates from tracks satisfying
criteria (i) and (iv)–(vi) presented at the beginning of
Sec. IV, with a less restrictive requirement of three coor-
dinates 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 ver-
tex, 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
π
±
that are produced in hadronic events and cross most
11
0.2
0.4
0.6
0.8
1.0
Simulated
Corrected
0.2
0.4
0.6
0.8
1.0
Identification Efficiency
0
2
4
6
0.0
0.2
0.4
0.6
0.8
1.0
0
2
4
6
Laboratory Momentum, p (GeV/c)
lab
0
2
4
6
True
π
True K
True p
0.77<cos
θ
<0.88
π→π
K
→π
p
→π
(x10)
π→
K (x10)
K
K
p
K (x10)
π→
p (x10)
K
p (x10)
p
p
Identified
π
Identified K
Identified p
(x10)
FIG. 3: The simulated (dashed lines) and corrected (gray/gr
een bands) efficiency matrix for the most forward polar angle
region,
θ
6, where 0
.
77
<
cos
θ
lab
<
0
.
88. The widths of the bands indicate the uncertainties deriv
ed from the control samples
discussed in the text. The off-diagonal elements have been sc
aled up by a factor of ten for clarity.
12
of the tracking system. In simulated events, this sample
has
E
πj
values within 0.5% of those of the prompt
π
±
in
the same events. We calculate efficiencies from this
K
0
S
sample in both data and simulation, and use their differ-
ences to correct the prompt
π
±
simulation. This sample
covers
p
lab
up to about 1.5 GeV
/c
with high precision.
A similar selection of
Λ
and
Λ
+
candi-
dates provides a sample of 0.4–3.5 GeV
/c p/
p
(and an-
other sample of soft pions) in hadronic events. We also
reconstruct two samples of
φ
K
+
K
decays in which
either the
K
+
or
K
is identified, providing 0.2–2 GeV
/c
K
and
K
+
samples that are subsamples of our main
sample. These samples contain substantial backgrounds,
and we extract
E
pj
,
E
pj
,
E
K
+
j
and
E
K
j
from sets of
simultaneous fits to the four
p/
or
K
+
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 π
±
and
K
±
by
reconstructing candidate
D
+
D
0
π
+
K
π
+
π
+
(and charge conjugate) decays and selecting those with
a
K
π
+
π
+
K
π
+
mass difference in the range 143–
148 MeV
/c
2
. The
K
π
+
invariant distribution shows
a
D
0
signal with a peak signal-to-background of eleven.
These tracks are predominantly from
Υ
(4
S
) decays and
c
c
events, but have simulated
E
Kj
and
E
πj
values within
1% and 0.5%, respectively, of those from all prompt
K
±
and
π
±
in hadronic events. Requiring the
π
(
K
+
) can-
didate track to be so identified and the
K
(
π
+
) track
to satisfy our selection criteria, we evaluate
E
K
j
(
E
π
+
j
)
as the fraction of the sideband-subtracted entries in the
D
0
peak in which the
K
(
π
+
) is identified as type
j
.
We select
e
+
e
τ
+
τ
events in which one of the
τ
decays contains a single charged track (1-prong) and
the other contains one or three (3-prong) charged tracks.
These tracks constitute (
eμπ
)
±
samples that are not from
a hadronic jet environment and have different
e
±
:
μ
±
:
π
±
content, as well as a small but well known
K
±
compo-
nent. However, these samples have simulated identifi-
cation efficiencies within a few percent of those for
π
±
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
independent electron and muon selectors to the 1-prong
sample, in order to check that the small differences in
performance between
e
±
,
μ
±
and
π
±
are simulated cor-
rectly.
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 pro-
vided by these samples, we derive corrections to the sim-
ulated
E
ij
elements that vary smoothly with
p
lab
and
cos
θ
lab
. The correction to each
E
ij
in each cos
θ
lab
region
is a continuous, piecewise-linear function of
p
lab
, with an
uncertainty given by the statistically most precise cali-
bration sample at each point. The resulting calibrated
efficiencies in the
θ
6 region are shown as the gray/green
bands in Fig. 3; their centers represent the calibrated
efficiencies, and their half widths the uncertainties.
The pion efficiencies
E
πj
(left column of Fig. 3) are
measured well over the full
p
lab
range, with corrections
and uncertainties near or below the percent level for
p
lab
<
2
.
5 GeV
/c
. There are substantial corrections to
E
ππ
and
E
πK
in the 3–5 GeV
/c
range, which is sensitive
to the details of the DIRC geometry and backgrounds.
The kaon efficiencies
E
Kj
(middle column of Fig. 3)
are measured for
p
lab
>
0
.
4 GeV
/c
with somewhat larger
uncertainties than for
E
πj
. The corrections to
E
KK
and
E
are similar at most
p
lab
to those on
E
ππ
and
E
πK
,
respectively, as expected from the near symmetry in the
d
E/
d
x
and Cherenkov angle measurements. They have
opposite sign, as expected, in the region just above kaon
threshold, 0.5–1 GeV
/c
. The large correction to
E
Kp
near 6 GeV
/c
is consistent with the corrections to
E
πK
and
E
with
p
lab
scaled by a factor of roughly 1.9, the
ratio of the proton and kaon masses, as expected.
Below 0.4 GeV
/c
, the kaon calibration samples have
high backgrounds and do not yield useful results. How-
ever, the identification efficiencies are very high, we ex-
pect strong correlations between hadron types up to
0.6 GeV
/c
, and the calibration data are consistent with
full correlation between 0.4 and 0.6 GeV
/c
. Therefore, we
apply the same small corrections to
E
KK
as for
E
ππ
, and
to
E
and
E
Kp
as for
E
πK
at 0.2 GeV
/c
, with the uncer-
tainty doubled arbitrarily to account for any incomplete
correlation. We apply the corrections and uncertainties
from the kaon calibration samples to
E
KK
and
E
at
0.6 GeV
/c
, and vary the corrections and uncertainties
linearly between 0.2 and 0.6 GeV
/c
. Due to the higher
proton mass, the corresponding region in
E
Kp
extends to
1.0 GeV
/c
, so we match the corrections at that value.
The proton efficiencies
E
pj
(right column of Fig. 3) are
measured well in the range 0.8–3.5 GeV
/c
, and the cor-
rections show the expected correlations with the other
elements. Again, we expect complete correlations at low
p
lab
, and we apply the same corrections to
E
,
E
pK
,
and
E
pp
as for
E
πp
,
E
Kp
, and
E
KK
, respectively, at
0.2 GeV
/c
, with doubled uncertainties. We then match
them to their respective proton calibration values at
1 GeV
/c
. Above 3.5 GeV
/c
, the statistical precision of
the proton calibration sample is limited, and we exploit
the correlation expected between
E
pp
in the 2–6.5 GeV
/c
range, and
E
ππ
and
E
KK
in the corresponding 1.1–
3.4 GeV
/c
range. The three corrections are consistent
in the lower part of this range, and in the upper part we
average the corrections to
E
ππ
and
E
KK
, scale them up
in
p
lab
, and apply them to
E
pp
with an uncertainty twice
that on the
E
KK
correction. We match to the proton
calibration sample at 3.1 GeV
/c
, where the uncertainties
from the two approaches are comparable.
Due to the low value of the proton fraction, the criteria
for proton identification are more stringent than for pion
or kaon identification at high
p
lab
, so that
E
and
E
pK
are smaller than the other misidentification rates, as are
the corrections.
Corrections to the efficiencies in the other cos
θ
lab
re-
13
gions are similar in form and generally smaller than those
shown in Fig. 3. Even though the uncertainties of some
misidentification rates are relatively large, they result
in small systematic uncertainties of the result, since the
rates themselves are sufficiently low. The uncertainties
of the correct identification efficiencies are important, es-
pecially at high
p
lab
. However, high-
p
particles are mea-
sured well in the more backward cos
θ
lab
regions, and the
final result is an average over the six regions.
V. MEASUREMENT OF THE DIFFERENTIAL
CROSS SECTIONS
The objects of this measurement are the production
cross sections per unit
p
, (1
had
tot
) (
i
/dp
),
i
=
π, K, p
,
normalized to the total hadronic event cross section
σ
had
tot
= 3
.
39 nb at our CM energy of 10.54 GeV. We
present these in the equivalent and conventional form
(1
/N
evt
) (
dn
i
/dp
), where
N
evt
and
n
i
are the numbers
of hadronic events and
i
-particles, respectively.
From our samples of identified
π
±
,
K
±
and
p/
p
, we use
the corrected identification efficiency matrices described
in the preceding section to construct the raw production
rates (1
/N
sel
evt
) (
dn
i
/dp
lab
),
i
= (
eμπ
)
, K, p
, defined as the
numbers of reconstructed particles per selected event per
unit momentum in the laboratory frame. We subtract
backgrounds and apply corrections to account for the ef-
fects of detector efficiency and resolution, and the event
selection procedure. We do this separately in each of the
six cos
θ
lab
regions, and also in the on-resonance sample
for control purposes.
We transform each corrected rate into a cross section in
the
e
+
e
CM frame, where we compare and combine the
results from the six cos
θ
lab
regions. Subtracting the ex-
pected contributions from leptons, we obtain our prompt
results, (1
/N
evt
)(
dn
prompt
i
/dp
). We add the expected
contributions from decays of
K
0
S
and weakly decaying
strange baryons to obtain conventional cross sections,
and we calculate ratios of cross sections and charged
hadron fractions. Each of these steps is described in
detail in the following subsections, and each involves a
number of systematic checks and uncertainties. The sys-
tematic uncertainties are summarized in the final subsec-
tion.
A. Cross Sections in the Laboratory Frame
In each
p
lab
bin, we count
n
j
, the number of tracks
identified as type
j
= (
eμπ
)
, K, p
. These can be related
to the true fractions
f
i
of tracks that are of type
i
by
n
j
=
i
E
ij
f
i
, where
n
is the total number of selected
tracks and the efficiency matrix
E
is described in Sec. IV.
We first solve this set of equations in each bin for the
three
f
i
values, and check that their sum is consistent
with unity. This check is sensitive to many systematic
effects on
E
, and if we apply no corrections to the sim-
π
±
K
±
p/
p
0
1
2
3
4
5
6
p (GeV/c)
lab
0
0.2
0.4
0.6
0.8
1.0
Fraction
π
±
K
±
p/
p
Sum
0.98
0.99
1.00
1.01
1.02
Sum
0.77<cos
θ
<0.88
Free
Constrained
FIG. 4: Raw
π
±
(circles),
K
±
(squares) and
p/
p
(diamonds)
fractions measured in
θ
6, the most forward cos
θ
lab
region.
The solid (open) symbols represent the results with (with-
out) the constraint that they sum to unity in each
p
lab
bin.
They are indistinguishable in most cases. The sums of un-
constrained fractions are shown as the triangles, and in an
expanded view in the upper plot. The error bars include
statistics and the systematic uncertainties arising from t
he
calibration of the particle identification efficiencies.
ulated
E
, we find significant differences from unity in
several places, most notably in the DCH-DIRC crossover
region near 0.7 GeV
/c
and at the highest momenta in
the forward polar angle regions. The on-resonance con-
trol sample shows the same differences. After the correc-
tions, the sum is consistent with unity in all bins within
the systematic uncertainties obtained by propagating the
uncertainties on the nine
E
ij
. The fractions and their
sum in the most forward cos
θ
lab
region,
θ
6, are shown
in Fig. 4. Neighboring points are correlated due to the
efficiency correction procedure.
We then recalculate the fractions with the added con-
straint that their sum be unity. The recalculated frac-
tions are also shown in Fig. 4, and are almost indistin-
guishable from the unconstrained fractions. In the sys-
tematic error propagation, we account for the constraint
by varying the three efficiencies
E
jj
independently, and
in each case varying both corresponding misidentification
rates
E
jk
in the opposite direction. Both the statistical
and systematic uncertainties decrease slightly with the
addition of the constraint. It also introduces strong sta-
tistical correlations between the three particle types, but
since the results are dominated by systematic effects, we
neglect these.
Several additional systematic checks are performed, in-
14
cluding varying the misidentification rates by three times
their uncertainties, changing the
p
lab
ranges over which
we fit the corrections to
E
, using different event fla-
vor mixtures in the simulation, and using the efficiencies
measured in the control samples directly, rather than us-
ing them to correct the simulation. We find no change
in the results larger than the relevant systematic uncer-
tainty.
Each fraction is multiplied by the number of accepted
tracks in that bin and divided by the number of selected
hadronic events and by the bin width to obtain raw nor-
malized cross sections.
B. Background Subtraction
We subtract backgrounds due to other physics pro-
cesses, interactions in the detector material, and strange-
particle decay products. As discussed in Sec. III, there
are three physics processes with non-negligible back-
ground contributions to our event sample:
τ
-pair, two-
photon and radiative Bhabha events. Figure 5 shows the
simulated fractional contributions to the selected tracks
in region
θ
6 from these three sources.
The contribution from
τ
-pair events is small at low
p
lab
, but grows steadily to over 20% at higher momenta.
There are similar contributions in the other cos
θ
lab
re-
gions. The simulation of
τ
-pair production and decay
is reliable at the sub-percent level, and our detector
simulation is reliable (after the corrections described in
Sec. V C) to 1–2%. However, since we normalize per
selected event, we must consider the relative event selec-
tion efficiency. Here, our simulation is also quite reliable
for
τ
-pairs, but less so for hadronic events, discussed in
Sec. V F, and the uncertainty corresponds to a roughly
constant 10% relative uncertainty on the tracks from
τ
-
pair events. We therefore subtract the absolute predic-
tion of the simulation with a 10% relative uncertainty.
The contribution from two-photon events is not well
understood, but we can set an upper limit by scaling
our simulated
γγ
2
π
+
2
π
sample to account for the
structure observed at low
E
tot
, discussed in Sec. III and
shown in Fig. 1. The resulting contribution is shown
by the triangles in Fig. 5. Due to the kinematics of
γγ
events and the detector acceptance, this background is
highest in
θ
6, somewhat smaller in
θ
1, and about half
as large in the central regions. Most
γγ
events contain
more charged and neutral hadrons than the 2
π
+
2
π
final
state, some of which are outside the acceptance, yielding
smaller values of
E
tot
. Therefore, we expect to select far
fewer events than indicated by this sample, containing
mostly lower-
p
lab
tracks, and Fig. 5 shows a substantial
overestimate at high
p
lab
and an upper bound at lower
p
lab
. This limit is at most 4% and well below the
τ
-
pair contribution, so we make no correction, but assign a
systematic uncertainty corresponding to one half of the
limit in each bin.
As discussed in Sec. III, the simulation predicts a neg-
0
1
2
3
4
5
6
p (GeV/c)
lab
0
0.05
0.10
0.15
0.20
0.25
Fraction of Accepted Tracks
e
+
e
→ τ
+
τ
events
γγ → π
+
π
π
+
π
events (scaled)
e
+
e
→ γ
e
+
e
events
0.77<cos
θ
<0.88
FIG. 5: Fractional contributions to the selected track samp
le
from
τ
-pair (up triangles),
γγ
2
π
+
2
π
(down triangles)
and radiative Bhabha (line) events in
θ
6, as functions of the
measured
p
lab
. The
γγ
2
π
+
2
π
cross-section is scaled as
discussed in the text, and represents an upper bound.
ligible contribution from radiative Bhabha events, but
may be unreliable, especially in the forward and back-
ward directions. Due to the
t
-channel contribution to
their production process, such events would exhibit a
charge asymmetry with a characteristic dependence on
p
lab
and cos
θ
lab
. In our selected (
eμπ
)
±
sample, we ob-
serve significant differences between positively and neg-
atively charged tracks that reach 10% and
4% at the
highest
p
lab
in the most backward and forward cos
θ
lab
regions, respectively, and show an angular dependence
consistent with radiative Bhabha events. We make a
smooth parametrization of this difference, and subtract it
from our (
eμπ
) cross section. The effect is a few percent
at high momenta in the forward (see Fig. 5) and back-
ward cos
θ
lab
regions, but below 1% in the central regions.
This procedure also accounts for any residual events from
e
+
e
e
+
e
e
+
e
or other higher-order QED processes
with forward-peaking cross sections.
After subtracting these
τ
-pair and radiative Bhabha
backgrounds, we normalize by the estimated number
of hadronic events in the selected sample, to obtain
background-subtracted differential cross sections.
Interactions of particles with the detector material
can lead to tracking inefficiencies, which are discussed
in Sec. V C, and also to the production of extraneous
charged tracks that satisfy the signal-track criteria. Most
interaction products fail the selection criteria, but two
categories require care: a highly asymmetric photon con-
version can produce an electron or positron that points
back to the event vertex; and a pion interacting with a nu-
cleon through a ∆ resonance can produce a proton nearly
collinear with the pion. Figure 6 shows the simulated
fractional contributions from interaction products. Pho-
ton conversions account for the vast majority, as much