of 12
arXiv:1506.05864v1 [hep-ex] 19 Jun 2015
SLAC-PUB-16311
B
A
B
AR
-PUB-15/001
Collins asymmetries in inclusive charged
KK
and
pairs produced
in
e
+
e
annihilation
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano
ab
,
3
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
M. J. 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
abc
,
9
A. R. Buzykaev
a
,
9
V. P. Druzhinin
ab
,
9
V. B. Golubev
ab
,
9
E. A. Kravchenko
ab
,
9
A. P. Onuchin
abc
,
9
S. I. Serednyakov
ab
,
9
Yu. I. Skovpen
ab
,
9
E. P. Solodov
ab
,
9
K. Yu. Todyshev
ab
,
9
A. J. Lankford,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
M. Franco Sevilla,
12
T. M. Hong,
12
D. Kovalskyi,
12
J. D. Richman,
12
C. A. West,
12
A. M. Eisner,
13
W. S. Lockman,
13
W. Panduro Vazquez,
13
B. A. Schumm,
13
A. Seiden,
13
D. S. Chao,
14
C. H. Cheng,
14
B. Echenard,
14
K. T. Flood,
14
D. G. Hitlin,
14
T. S. Miyashita,
14
P. Ongmongkolkul,
14
F. C. Porter,
14
M. R ̈ohrken,
14
R. Andreassen,
15
Z. Huard,
15
B. T. Meadows,
15
B. G. Pushpawela,
15
M. D. Sokoloff,
15
L. Sun,
15
P. C. Bloom,
16
W. T. Ford,
16
A. Gaz,
16
J. G. Smith,
16
S. R. Wagner,
16
R. Ayad,
17,
W. H. Toki,
17
B. Spaan,
18
D. Bernard,
19
M. Verderi,
19
S. Playfer,
20
D. Bettoni
a
,
21
C. Bozzi
a
,
21
R. Calabrese
ab
,
21
G. Cibinetto
ab
,
21
E. Fioravanti
ab
,
21
I. Garzia
ab
,
21
E. Luppi
ab
,
21
L. Piemontese
a
,
21
V. Santoro
a
,
21
A. Calcaterra,
22
R. de Sangro,
22
G. Finocchiaro,
22
S. Martellotti,
22
P. Patteri,
22
I. M. Peruzzi,
22,
M. Piccolo,
22
A. Zallo,
22
R. Contri
ab
,
23
M. R. Monge
ab
,
23
S. Passaggio
a
,
23
C. Patrignani
ab
,
23
B. Bhuyan,
24
V. Prasad,
24
A. Adametz,
25
U. Uwer,
25
H. M. Lacker,
26
U. Mallik,
27
C. Chen,
28
J. Cochran,
28
S. Prell,
28
H. Ahmed,
29
A. V. Gritsan,
30
N. Arnaud,
31
M. Davier,
31
D. Derkach,
31
G. Grosdidier,
31
F. Le Diberder,
31
A. M. Lutz,
31
B. Malaescu,
31,
P. Roudeau,
31
A. Stocchi,
31
G. Wormser,
31
D. J. Lange,
32
D. M. Wright,
32
J. P. Coleman,
33
J. R. Fry,
33
E. Gabathuler,
33
D. E. Hutchcroft,
33
D. J. Payne,
33
C. Touramanis,
33
A. J. Bevan,
34
F. Di Lodovico,
34
R. Sacco,
34
G. Cowan,
35
D. N. Brown,
36
C. L. Davis,
36
A. G. Denig,
37
M. Fritsch,
37
W. Gradl,
37
K. Griessinger,
37
A. Hafner,
37
K. R. Schubert,
37
R. J. Barlow,
38,
§
G. D. Lafferty,
38
R. Cenci,
39
B. Hamilton,
39
A. Jawahery,
39
D. A. Roberts,
39
R. Cowan,
40
R. Cheaib,
41
P. M. Patel,
41,
S. H. Robertson,
41
N. Neri
a
,
42
F. Palombo
ab
,
42
L. Cremaldi,
43
R. Godang,
43,
∗∗
D. J. Summers,
43
M. Simard,
44
P. Taras,
44
G. De Nardo
ab
,
45
G. Onorato
ab
,
45
C. Sciacca
ab
,
45
G. Raven,
46
C. P. Jessop,
47
J. M. LoSecco,
47
K. Honscheid,
48
R. Kass,
48
M. Margoni
ab
,
49
M. Morandin
a
,
49
M. Posocco
a
,
49
M. Rotondo
a
,
49
G. Simi
ab
,
49
F. Simonetto
ab
,
49
R. Stroili
ab
,
49
S. Akar,
50
E. Ben-Haim,
50
M. Bomben,
50
G. R. Bonneaud,
50
H. Briand,
50
G. Calderini,
50
J. Chauveau,
50
Ph. Leruste,
50
G. Marchiori,
50
J. Ocariz,
50
M. Biasini
ab
,
51
E. Manoni
a
,
51
A. Rossi
a
,
51
C. Angelini
ab
,
52
G. Batignani
ab
,
52
S. Bettarini
ab
,
52
M. Carpinelli
ab
,
52,
††
G. Casarosa
ab
,
52
M. Chrzaszcz
a
,
52
F. Forti
ab
,
52
M. A. Giorgi
ab
,
52
A. Lusiani
ac
,
52
B. Oberhof
ab
,
52
E. Paoloni
ab
,
52
M. Rama
a
,
52
G. Rizzo
ab
,
52
J. J. Walsh
a
,
52
D. Lopes Pegna,
53
J. Olsen,
53
A. J. S. Smith,
53
F. Anulli
a
,
54
R. Faccini
ab
,
54
F. Ferrarotto
a
,
54
F. Ferroni
ab
,
54
M. Gaspero
ab
,
54
A. Pilloni
ab
,
54
G. Piredda
a
,
54
C. B ̈unger,
55
S. Dittrich,
55
O. Gr ̈unberg,
55
M. Hess,
55
T. Leddig,
55
C. Voß,
55
R. Waldi,
55
T. Adye,
56
E. O. Olaiya,
56
F. F. Wilson,
56
S. Emery,
57
G. Vasseur,
57
D. Aston,
58
D. J. Bard,
58
C. Cartaro,
58
M. R. Convery,
58
J. Dorfan,
58
G. P. Dubois-Felsmann,
58
W. Dunwoodie,
58
M. Ebert,
58
R. C. Field,
58
B. G. Fulsom,
58
M. T. Graham,
58
C. Hast,
58
W. R. Innes,
58
P. Kim,
58
D. W. G. S. Leith,
58
S. Luitz,
58
V. Luth,
58
D. B. MacFarlane,
58
D. R. Muller,
58
H. Neal,
58
T. Pulliam,
58
B. N. Ratcliff,
58
A. Roodman,
58
R. H. Schindler,
58
A. Snyder,
58
D. Su,
58
M. K. Sullivan,
58
J. Va’vra,
58
W. J. Wisniewski,
58
H. W. Wulsin,
58
M. V. Purohit,
59
J. R. Wilson,
59
A. Randle-Conde,
60
S. J. Sekula,
60
M. Bellis,
61
P. R. Burchat,
61
E. M. T. Puccio,
61
M. S. Alam,
62
J. A. Ernst,
62
R. Gorodeisky,
63
N. Guttman,
63
D. R. Peimer,
63
A. Soffer,
63
S. M. Spanier,
64
J. L. Ritchie,
65
R. F. Schwitters,
65
J. M. Izen,
66
X. C. Lou,
66
F. Bianchi
ab
,
67
F. De Mori
ab
,
67
A. Filippi
a
,
67
D. Gamba
ab
,
67
L. Lanceri
ab
,
68
L. Vitale
ab
,
68
F. Martinez-Vidal,
69
A. Oyanguren,
69
J. Albert,
70
Sw. Banerjee,
70
A. Beaulieu,
70
F. U. Bernlochner,
70
H. H. F. Choi,
70
G. J. King,
70
R. Kowalewski,
70
M. J. Lewczuk,
70
T. Lueck,
70
I. M. Nugent,
70
J. M. Roney,
70
R. J. Sobie,
70
N. Tasneem,
70
T. J. Gershon,
71
P. F. Harrison,
71
T. E. Latham,
71
H. R. Band,
72
S. Dasu,
72
Y. Pan,
72
R. Prepost,
72
and S. L. Wu
72
(The
B
A
B
AR
Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules
(LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vie
ux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament
ECM, E-08028 Barcelona, Spain
2
3
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
5
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, California 94720, USA
6
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columb
ia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kin
gdom
9
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630
090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 6300
92
c
, Russia
10
University of California at Irvine, Irvine, California 926
97, USA
11
University of California at Riverside, Riverside, Califor
nia 92521, USA
12
University of California at Santa Barbara, Santa Barbara, C
alifornia 93106, USA
13
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California
91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, U
SA
18
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44
221 Dortmund, Germany
19
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
20
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
21
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a
di Ferrara
b
, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
23
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
25
Universit ̈at Heidelberg, Physikalisches Institut, D-691
20 Heidelberg, Germany
26
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-
12489 Berlin, Germany
27
University of Iowa, Iowa City, Iowa 52242, USA
28
Iowa State University, Ames, Iowa 50011-3160, USA
29
Physics Department, Jazan University, Jazan 22822, Kingdo
m of Saudi Arabia
30
Johns Hopkins University, Baltimore, Maryland 21218, USA
31
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
32
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
33
University of Liverpool, Liverpool L69 7ZE, United Kingdom
34
Queen Mary, University of London, London, E1 4NS, United Kin
gdom
35
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
36
University of Louisville, Louisville, Kentucky 40292, USA
37
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Ker
nphysik, D-55099 Mainz, Germany
38
University of Manchester, Manchester M13 9PL, United Kingd
om
39
University of Maryland, College Park, Maryland 20742, USA
40
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
41
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
42
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
43
University of Mississippi, University, Mississippi 38677
, USA
44
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
45
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
46
NIKHEF, National Institute for Nuclear Physics and High Ene
rgy Physics, NL-1009 DB Amsterdam, The Netherlands
47
University of Notre Dame, Notre Dame, Indiana 46556, USA
48
Ohio State University, Columbus, Ohio 43210, USA
49
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
50
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
51
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
52
INFN Sezione di Pisa
a
; Dipartimento di Fisica,
Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
53
Princeton University, Princeton, New Jersey 08544, USA
54
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
55
Universit ̈at Rostock, D-18051 Rostock, Germany
56
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
57
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
58
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
3
59
University of South Carolina, Columbia, South Carolina 292
08, USA
60
Southern Methodist University, Dallas, Texas 75275, USA
61
Stanford University, Stanford, California 94305-4060, US
A
62
State University of New York, Albany, New York 12222, USA
63
Tel Aviv University, School of Physics and Astronomy, Tel Av
iv, 69978, Israel
64
University of Tennessee, Knoxville, Tennessee 37996, USA
65
University of Texas at Austin, Austin, Texas 78712, USA
66
University of Texas at Dallas, Richardson, Texas 75083, USA
67
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
68
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
69
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
70
University of Victoria, Victoria, British Columbia, Canad
a V8W 3P6
71
Department of Physics, University of Warwick, Coventry CV4
7AL, United Kingdom
72
University of Wisconsin, Madison, Wisconsin 53706, USA
We present measurements of Collins asymmetries in the inclu
sive process
e
+
e
h
1
h
2
X
,
h
1
h
2
=
KK, Kπ, ππ
, at the center-of-mass energy of 10.6 GeV, using a data sampl
e of 468 fb
1
collected by
the
B
A
B
AR
experiment at the PEP-II
B
factory at SLAC National Accelerator Center. Considering
hadrons in opposite thrust hemispheres of hadronic events,
we observe clear azimuthal asymmetries
in the ratio of unlike- to like-sign, and unlike- to all charg
ed
h
1
h
2
pairs, which increase with hadron
energies. The
asymmetries are similar to those measured for the
ππ
pairs, whereas those
measured for high-energy
KK
pairs are, in general, larger.
PACS numbers: 13.66.Bc, 13.87.Fh, 13.88.+e, 14.65.-q
The Collins effect [1] relates the transverse spin com-
ponent of a fragmenting quark to the azimuthal distri-
bution of final state hadrons about its flight direction.
The chiral-odd, transverse momentum-dependent Collins
fragmentation function (FF) provides a unique probe of
quantum chromodynamics (QCD), such as factorization
and evolution with the energy scale
Q
2
[2–5].
Additional interest has been sparked by the obser-
vation of azimuthal asymmetries for pions and kaons
in semi-inclusive deep inelastic scattering experiments
(SIDIS) [6–9]. These are sensitive to the product of a
Collins FF and a chiral-odd transversity parton distribu-
tion function (PDF), one of the three fundamental PDFs
needed to describe the spin content of the nucleon. Al-
though these observations require nonzero Collins FFs,
independent direct measurements of one of these chiral-
odd functions are needed to determine each of them.
In
e
+
e
annihilation, one can measure the product of
two Collins FFs, and detailed measurements have been
made for pairs of charged pions [10–12]. No measure-
ments are available for
and
KK
pairs, which are
sensitive to different quark-flavor combinations, in par-
ticular the contribution of the strange quark. Such mea-
surements could be combined with SIDIS data to simulta-
neously determine the Collins FFs and transversity PDF
for up, down, and strange quarks [13–18].
In this Letter, we report the measurement of the
Collins effect (or Collins asymmetry) for inclusive pro-
duction of hadron pairs in the process
e
+
e
q
q
h
1
h
2
X
, where
h
1
,
2
=
K
±
or
π
±
,
q
stands for light quarks
u
or
d
or
s
, and
X
for any combination of additional
hadrons.
The probability that a transversely polarized quark
(
q
) with momentum direction
ˆ
k
and spin
S
q
fragments
into a spinless hadron
h
with momentum
P
h
, is defined in
terms of unpolarized
D
q
1
and Collins
H
q
1
fragmentation
functions [19]:
D
q
h
(
z,
P
hT
) =
D
q
1
(
z, P
2
hT
)+
H
q
1
(
z, P
2
hT
)
(
ˆ
k
×
P
hT
)
·
S
q
zM
h
,
(1)
where
M
h
,
P
hT
, and
z
= 2
E
h
/
s
are the hadron mass,
momentum transverse to
ˆ
k
, and fractional energy, re-
spectively, with
E
h
its total energy and
s
the
e
+
e
center-of-mass (c.m.) energy. The term including
H
1
in-
troduces an azimuthal modulation around the direction
of the fragmenting quark, called Collins asymmetry.
Experimentally, we do not know
ˆ
k
or
S
q
for a given
e
+
e
q
q
event, but the quark and anti-quark must
be produced back-to-back in the
e
+
e
c.m. frame, with
their spins aligned with each other and polarized along
the
e
+
or
e
direction. The event thrust axis ˆ
n
[20, 21]
approximates the
q
q
axis, so an azimuthal correlation be-
tween two hadrons in opposite thrust hemispheres reflects
the product of the two Collins functions.
Figure 1 shows the thrust reference frame (RF12) [10].
If not otherwise specified, all kinematic variables are de-
fined in the
e
+
e
c.m. frame. The Collins effect results in
a cosine modulation of the azimuthal angle
φ
12
=
φ
1
+
φ
2
of the di-hadron yields. Expressing the yield as a function
of
φ
12
[10] (after the integration over
P
hT
), and divid-
ing by the average bin content, we obtain the normalized
rate
R
12
(
φ
12
) = 1+
sin
2
θ
th
1 + cos
2
θ
th
cos
φ
12
·
H
1
(
z
1
)
H
1
(
z
2
)
D
1
(
z
1
)
D
1
(
z
2
)
,
(2)
where
θ
th
is defined in Fig. 1,
z
1(2)
is the fractional energy
4
FIG. 1. (color online). Thrust reference frame (RF12). The
azimuthal angles
φ
1
and
φ
2
are the angles between the scatter-
ing plane and the transverse hadron momenta
p
t
1(
t
2)
around
the thrust axis
ˆn
. The polar angle
θ
th
is the angle between
ˆn
and the beam axis. Note that the difference between
p
t
1(
t
2)
and
P
hT
is that the latter is calculated with respect to the
q
q
axis.
of the first (second) hadron, and the bar denotes the FF
for the
q
.
Other reference frames [10, 11] have been proposed to
overcome the finite resolution in the determination of the
thrust axis. The RF0 frame [22] uses the momentum
of one hadron as a reference axis, and defines a single
angle
φ
0
between the plane containing the two hadron
momenta and the plane defined by the beam and the
reference axis. The corresponding normalized yield in
the
e
+
e
c.m. system is
R
0
(2
φ
0
) = 1 +
sin
2
θ
2
1 + cos
2
θ
2
cos 2
φ
0
·
F
[
H
1
(
z
1
)
H
1
(
z
2
)]
F
[
D
1
(
z
1
)
D
1
(
z
2
)]
,
(3)
where
θ
2
is the angle between the hadron used as ref-
erence and the beam axis, and
F
is used to denote the
convolution integral
F
[
D
D
]
q
e
2
q
d
2
k
T
d
2
p
T
δ
2
(
p
T
+
k
T
q
T
)
D
q
(
z
1
, z
2
1
k
2
T
)
D
q
(
z
2
, z
2
2
p
2
T
)
,
(4)
with
k
T
,
p
T
, and
q
T
the transverse momentum of the
fragmenting quark, antiquark, and virtual photon from
e
+
e
annihilation, respectively, in the frame where the
two hadrons are collinear.
For this analysis we use a data sample of 468 fb
1
[23] collected at the c.m. energy
s
10
.
6 GeV with
the
B
A
B
AR
detector [24, 25] at the SLAC National Ac-
celerator Laboratory. We use tracks reconstructed in the
silicon vertex detector and in the drift chamber (DCH)
and identified as pions or kaons in the DCH and in
the Cherenkov ring imaging detector (DIRC). Detailed
Monte Carlo (MC) simulation is used to study detector
effects and to estimate contribution from various back-
ground sources. Hadronic events are generated using the
Jetset
[26] package and undergo a full detector simula-
tion based on
Geant4
[27].
We make a tight selection of hadronic events in or-
der to minimize biases due to detector acceptance and
hard initial-state photon radiation (ISR) or final-state
gluon (
q
qg
) radiation, since they can introduce fake az-
imuthal modulations. Requiring at least three charged
tracks consistent with the
e
+
e
primary vertex and a
total visible energy of the event in the laboratory frame
E
tot
>
11 GeV, we reject
e
+
e
τ
+
τ
and two-photon
backgrounds, as well as ISR (
q
qg
) events with the photon
(one jet) along the beam line. About 10% of ISR photons
are within our detector acceptance, and we reject events
with a photon candidate with energy above 2 GeV. We
require an event thrust value
T >
0
.
8 to suppress
q
qg
and
B
B
events, and
|
cos
θ
th
|
<
0
.
6 so that most tracks
are within the detector acceptance.
We assign randomly the positive direction of the thrust
axis, and divide each event into two hemispheres by
the plane perpendicular to it. To ensure tracks are as-
signed to the correct hemispheres, we require them to
be within a 45
angle of the thrust axis and to have
z >
0
.
15. A “tight” identification algorithm is used to
identify kaons (pions), which is about 80% (90%) efficient
and has misidentification rates below 10% (5%). We se-
lect those pions and kaons that lie within the DIRC ac-
ceptance region with a polar angle in laboratory frame
0
.
45 rad
< θ
lab
<
2
.
46 rad. To minimize backgrounds,
such as
e
+
e
μ
+
μ
γ
followed by photon conversion,
we require
z <
0
.
9.
We construct all the possible pairs of selected tracks
reconstructed in opposite thrust hemispheres, and we cal-
culate the corresponding azimuthal angles
φ
1
,
φ
2
, and
φ
0
in the respective reference frames. In this way, we iden-
tify three different samples of hadron pairs:
KK
,
,
and
ππ
. To reduce low-energy gluon radiation and the
contribution due to wrong hemispheres assignment, we
require
Q
t
<
3
.
5 GeV
/c
, where
Q
t
is the transverse mo-
mentum of the virtual photon from
e
+
e
annihilation in
the frame where the two hadrons are collinear [22].
The analysis is performed in intervals of hadron frac-
tional energies with the following boundaries: 0.15, 0.2,
0.3, 0.5, 0.9, for a total of 16 two-dimensional (
z
1
, z
2
)
intervals.
For each of the three samples, we evaluate the normal-
ized yield distributions
R
12
and
R
0
for unlike (
U
), like
(
L
), and any charge combination (
C
) of hadron pairs as
a function of
φ
1
+
φ
2
and 2
φ
0
, as shown in the left plot
of Fig. 2. These combinations of charged hadrons con-
tain different contribution of favored and disfavored FFs,
where a favored (disfavored) process refers to the pro-
5
duction of a hadron for which one (none) of the valence
quarks is of the same kind as the fragmenting quark. In
particular, by selecting
KK
pairs, we are able to study
the favored contribution
H
fav
s
of the strange quark, not
accessible when considering
ππ
pairs only.
2
φ
+
1
φ
-3
-2
-1
0
1
2
3
R
0.96
0.98
1
1.02
1.04
12
U
R
12
L
R
12
C
R
2
φ
+
1
φ
-3
-2
-1
0
1
2
3
12
UL
R
12
UC
R
FIG. 2. (color online). Distributions of normalized yields
(left plot) for unlike (
U
), like (
L
), and any charge combination
(
C
) of KK pairs, and their double ratios (right plot) in RF12.
The normalized distributions can be parametrized with
a cosine function:
R
i
α
=
b
α
+
a
i
α
cos
β
α
, where
α
= 0
,
12
indicates the reference frames,
i
=
U, L, C
the charge
combination of hadron pairs, and
β
12(0)
=
φ
12
(2
φ
0
).
The
R
i
α
distributions are strongly affected by instru-
mental effects. In order to reduce the impact of the de-
tector acceptance, we construct two double ratios (DR)
of normalized distributions,
R
U
α
/R
L
α
and
R
U
α
/R
C
α
. The
two ratios give access to the same physical quantities as
the independent
R
i
α
, that is the favored and disfavored
FFs, but in different combinations. We report the results
for both kind of DRs, which are strongly correlated since
they are obtained by using the same data set. These are
shown in the right plot of Fig. 2 for
KK
pairs in RF12.
For small asymmetry values, the double ratios are still
parametrized by a function that is linear in the cosine of
the corresponding combination of azimuthal angles:
R
ij
α
=
R
i
α
R
j
α
B
ij
α
+
A
ij
α
·
cos
β
α
,
(5)
with
B
and
A
free parameters, and
i, j
=
U, L, C
. The
constant term
B
must be consistent with unity, while
A
contains the information about the favored and disfa-
vored Collins FFs.
We fit the binned
R
ij
α
distributions independently for
KK
,
, and
ππ
hadron pairs. Using the MC sample,
we evaluate the
K/π
(mis)identification probabilities for
the 16 (
z
1
, z
2
) intervals in each of the three samples. For
example, the probability
f
KK
KK
that a true
KK
pair is re-
constructed as
KK
pair is about 90% on average, slightly
decreasing at higher momenta, while the probability
f
KK
that a true
pair is identified as
KK
is about 10%,
and
f
KK
ππ
is negligible.
The presence of background processes could introduce
azimuthal modulations not related to the Collins effect,
and modifies the measured asymmetry as follows:
A
meas
KK
=
F
KK
uds
·
(
nm
f
KK
nm
·
A
nm
)
+
i
F
KK
i
(
nm
f
(
KK
)
i
nm
·
A
i
nm
)
,
(6)
with
nm
=
KK, Kπ, ππ
, and
i
=
c
c, B
B, τ
+
τ
. In
Eq. 6,
A
nm
are the true Collins asymmetries produced
from the fragmentation of light quarks in the three sam-
ples,
A
i
nm
is the
i
-th background asymmetry contribu-
tion, and
F
KK
uds,i
are the fractions of kaon pairs coming
from
uds
and background events, calculated from the re-
spective MC samples. By construction,
i
F
i
+
F
uds
= 1.
A similar expression holds for
and
ππ
samples.
Previous studies [10] show that
e
+
e
B
B
and
τ
+
τ
events have negligible
A
i
nm
,
F
B
B
<
2%, and
F
τ
+
τ
sig-
nificantly different from zero only for the
ππ
sample
at high
z
values. Since
F
c
c
can be as large as 30%,
and
A
c
c
are unknown, we determine
A
c
c
nm
in Eq. (6)
from samples enhanced in
c
c
by requiring the recon-
struction of at least one
D
∗±
meson from the decay
D
∗±
D
0
π
±
, with the
D
0
candidate reconstructed in
the following four Cabibbo-favored decay modes:
K
π
+
,
K
π
+
π
π
+
,
K
0
s
π
+
π
, and
K
π
+
π
0
. We solve the sys-
tem of equations for
A
meas
KK
, A
meas
,
A
meas
ππ
, for the stan-
dard and charm-enhanced samples, and we extract si-
multaneously the Collins asymmetries
A
KK
, A
, and
A
ππ
, corrected for the contributions of the background
and
K/π
(mis)identification.
We test the DR method on the MC sample. Spin ef-
fects are not simulated in MC, and so the DR distribu-
tions should be uniform. However, when fitting the dis-
tributions for reconstructed
KK
pairs with Eq. (5), we
measure a cosine term in the full sample of 0
.
004
±
0
.
001
and 0
.
007
±
0
.
001 in the RF12 and RF0 frames, respec-
tively, indicating a bias. Smaller values are obtained for
and
ππ
pairs [28]. Studies performed on the MC
samples, both at generation level and after full simula-
tion, demonstrate that the main source of this bias is due
to the emission of ISR. We subtract the bias, which is ev-
erywhere smaller than the asymmetries measured in the
data sample in each bin, from the background-corrected
asymmetry.
Using the
uds
MC sample, or light quark
e
+
e
q
q
MC events, we study the difference between measured
and true azimuthal asymmetries. The asymmetry is in-
troduced into the simulation by reweighting the events
according to the distribution 1 +
a
·
cos
φ
gen
α
, where we
use different values of
a
ranging from 0 to 8% and
φ
gen
α
as azimuthal angles combinations calculated with respect
to the true
q
q
axis in RF12, or the generated hadron mo-
mentum in RF0. The reconstructed asymmetries in RF12
are systematically underestimated for the three samples
of hadron pairs, as expected since we use the thrust axis
6
instead of the
q
q
axis, while they are consistent with the
simulated ones in RF0, where only particle identification
and tracking reconstruction effects could introduce pos-
sible dilution. Since we measure the same dilution for
KK
,
, and
ππ
samples, the asymmetry is corrected
by rescaling
A
KK
,
A
, and
A
ππ
using the same correc-
tion factor, which ranges from 1.3 to 2.3 increasing with
z
. No corrections are needed for the asymmetries mea-
sured in RF0. The errors on the correction factors are
assigned as systematic errors.
All systematic effects, if not otherwise specified, are
evaluated for each bin of
z
. The main contribution comes
from the MC bias. We compare the bias results from
the nominal selection, with those obtained by requiring
different cuts on
E
tot
, and/or by changing the detector
acceptance region for the hadrons. The largest variation
of the bias is combined in quadrature with the MC sta-
tistical error and taken as systematic uncertainty. The
effects due to the particle identification are evaluated us-
ing tighter and looser selection criteria. The largest de-
viations with respect to the nominal selection are taken
as systematic uncertainties: the average relative uncer-
tainties are around 10%, 7%, and 5% for the
KK
,
,
and
ππ
pairs. Fitting the azimuthal distributions using
different bin sizes, we determine systematic uncertainties,
which are not larger than 5%, 1
.
9%, and 1% for the three
samples. The systematic uncertainty due to the
E
tot
cut
is obtained by comparing the measured asymmetries with
those obtained with the looser selection
E
tot
>
10 GeV.
The average systematic contribution is around 10% for
the three samples in both reference frames. We use dif-
ferent fitting functions with additional higher harmonic
terms. No significant changes in the value of the cosine
moments with respect to the standard fits are found. As
a cross-check of the double ratio method we fit the differ-
ence of
R
i
distributions, and we compare the two results.
The difference between the two procedures is negligible
for
and
ππ
pairs, while it reaches 1% and 3% for
kaon pairs in RF12 and RF0, respectively. All the other
systematic contributions are negligible [10].
The Collins asymmetries measured for the 16 two-
dimensional (
z
1
, z
2
) bins, for reconstructed
KK
,
, and
ππ
hadron pairs, are shown in Fig. 3 for RF12 and RF0,
and are summarized in tables reported in the Supple-
mental Material [28]. The asymmetries are corrected for
the background contributions and
K/π
contamination
following Eq. (6), the MC bias is subtracted, and the
corrections due to the dilution effects are applied. The
total systematic uncertainties are obtained by adding in
quadrature the individual contributions, and are repre-
sented by the bands around the data points.
An increasing asymmetry with increasing hadron ener-
gies is visible for the
U/L
double ratio in both reference
frames. The largest effects, but with less precision, are
observed for
KK
pairs, for which
A
UL
12
is consistent with
zero at low
z
, and reaches 22% in the last
z
bin, while
somewhat smaller values are seen for
ππ
and
pairs.
In particular, at low (
z
1
, z
2
) bins
A
UL
for
ππ
pairs is
nonzero, in agreement with the behavior observed in [10].
The small differences between the two data sets are due
to the different kinematic region selected after the cut on
cos
θ
th
. The
A
UC
asymmetry is smaller than
A
UL
in all
cases, and, for the
KK
pairs, the rise of the asymmetry
with the hadron energies is not evident.
In summary, we have studied for the first time in
e
+
e
annihilation the Collins asymmetry for inclusive
production of
KK
and
pairs as a function of
(
z
1
, z
2
) in two distinct reference frames. We measure
the azimuthal modulation of the double ratios
U/L
and
U/C
, which are sensitive to the favored and disfavored
Collins FFs for light quarks. We simultaneously extract
also the Collins asymmetries for
ππ
pairs, which are
found to be in agreement with those obtained in previous
studies [10, 12]. The results reported in this Letter and
those obtained from SIDIS experiments can be used in
a global analysis to extract the favored contribution of
the strange quark, and to improve the knowledge on the
u
and
d
fragmentation processes [13–15].
We are grateful for the excellent luminosity and ma-
chine conditions provided by our PEP-II colleagues, and
for the substantial dedicated effort from the comput-
ing organizations that support
B
A
B
AR
. The collaborat-
ing institutions wish to thank SLAC for its support and
kind hospitality. This work is supported by DOE and
NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3
(France), BMBF and DFG (Germany), INFN (Italy),
FOM (The Netherlands), NFR (Norway), MES (Russia),
MEC (Spain), and STFC (United Kingdom). Individuals
have received support from the Marie Curie EIF (Euro-
pean Union) and the A. P. Sloan Foundation.
Now at: University of Tabuk, Tabuk 71491, Saudi Arabia
Also at: Universit`a di Perugia, Dipartimento di Fisica,
I-06123 Perugia, Italy
Now at: Laboratoire de Physique Nucl ́eaire et de Hautes
Energies, IN2P3/CNRS, F-75252 Paris, France
§
Now at: University of Huddersfield, Huddersfield HD1
3DH, UK
Deceased
∗∗
Now at: University of South Alabama, Mobile, Alabama
36688, USA
††
Also at: Universit`a di Sassari, I-07100 Sassari, Italy
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1
z
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z
0.9/0.15
0.9/0.15
0.9/0.15
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KK
,
, and
ππ
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z
1
, z
2
) bins are shown on the x-axis: in each interval between the da
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1
is chosen in the
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.
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.
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.
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8
KK
sample
z
1
h
z
1
i
z
2
h
z
2
i
h
sin
2
θ
th
i
h
1+cos
2
θ
th
i
A
UL
12
(10
4
)
A
UC
12
(10
4
)
[0
.
15
,
0
.
2] 0.175 [0
.
15
,
0
.
2] 0.175 0.797 0.88
±
1.43
±
0.73 0.62
±
1.02
±
0.51
[0
.
15
,
0
.
2] 0.175 [0
.
2
,
0
.
3] 0.247 0.794 1.96
±
1.32
±
0.67 0.88
±
0.92
±
0.43
[0
.
15
,
0
.
2] 0.175 [0
.
3
,
0
.
5] 0.381 0.794 3.38
±
1.23
±
0.73 1.08
±
0.81
±
0.43
[0
.
15
,
0
.
2] 0.175 [0
.
5
,
0
.
9] 0.608 0.786 7.32
±
1.06
±
0.97 2.06
±
0.72
±
0.59
[0
.
2
,
0
.
3] 0.246 [0
.
15
,
0
.
2] 0.175 0.794 2.06
±
1.33
±
0.68 0.95
±
0.93
±
0.44
[0
.
2
,
0
.
3] 0.247 [0
.
2
,
0
.
3] 0.247 0.792 3.78
±
1.22
±
0.58 1.30
±
0.84
±
0.36
[0
.
2
,
0
.
3] 0.247 [0
.
3
,
0
.
5] 0.382 0.792 7.44
±
1.14
±
0.59 2.06
±
0.72
±
0.35
[0
.
2
,
0
.
3] 0.247 [0
.
5
,
0
.
9] 0.608 0.783 10.91
±
0.98
±
0.91 2.63
±
0.58
±
0.48
[0
.
3
,
0
.
5] 0.381 [0
.
15
,
0
.
2] 0.175 0.794 5.34
±
1.28
±
0.74 1.73
±
0.84
±
0.44
[0
.
3
,
0
.
5] 0.381 [0
.
2
,
0
.
3] 0.247 0.792 8.74
±
1.17
±
0.59 2.45
±
0.74
±
0.35
[0
.
3
,
0
.
5] 0.382 [0
.
3
,
0
.
5] 0.382 0.792 10.97
±
1.31
±
0.63 2.41
±
0.65
±
0.34
[0
.
3
,
0
.
5] 0.383 [0
.
5
,
0
.
9] 0.610 0.784 9.84
±
1.16
±
0.92 1.71
±
0.52
±
0.45
[0
.
5
,
0
.
9] 0.609 [0
.
15
,
0
.
2] 0.175 0.785 6.15
±
1.09
±
0.98 1.78
±
0.74
±
0.60
[0
.
5
,
0
.
9] 0.608 [0
.
2
,
0
.
3] 0.248 0.783 11.75
±
1.03
±
0.91 2.81
±
0.60
±
0.48
[0
.
5
,
0
.
9] 0.610 [0
.
3
,
0
.
5] 0.383 0.784 7.40
±
1.13
±
0.91 1.11
±
0.52
±
0.45
[0
.
5
,
0
.
9] 0.615 [0
.
5
,
0
.
9] 0.615 0.776 22.36
±
2.09
±
1.69 2.63
±
0.61
±
0.62
z
1
h
z
1
i
z
2
h
z
2
i
h
sin
2
θ
2
i
h
1+cos
2
θ
2
i
A
UL
0
(10
4
)
A
UC
0
(10
4
)
[0
.
15
,
0
.
2] 0.175 [0
.
15
,
0
.
2] 0.175 0.739 2.41
±
1.44
±
1.25 0.82
±
1.02
±
0.58
[0
.
15
,
0
.
2] 0.175 [0
.
2
,
0
.
3] 0.247 0.736 1.66
±
1.31
±
0.74 0.53
±
0.92
±
0.40
[0
.
15
,
0
.
2] 0.175 [0
.
3
,
0
.
5] 0.381 0.750 1.33
±
1.24
±
0.71 0.23
±
0.81
±
0.39
[0
.
15
,
0
.
2] 0.175 [0
.
5
,
0
.
9] 0.608 0.751 0.24
±
1.02
±
0.90 -0.13
±
0.71
±
0.55
[0
.
2
,
0
.
3] 0.246 [0
.
15
,
0
.
2] 0.175 0.739 1.95
±
1.32
±
0.75 0.61
±
0.93
±
0.41
[0
.
2
,
0
.
3] 0.247 [0
.
2
,
0
.
3] 0.247 0.736 3.28
±
1.21
±
0.69 1.00
±
0.84
±
0.33
[0
.
2
,
0
.
3] 0.247 [0
.
3
,
0
.
5] 0.382 0.749 3.69
±
1.14
±
0.67 0.90
±
0.72
±
0.31
[0
.
2
,
0
.
3] 0.247 [0
.
5
,
0
.
9] 0.608 0.750 6.05
±
0.96
±
0.88 1.49
±
0.58
±
0.44
[0
.
3
,
0
.
5] 0.381 [0
.
15
,
0
.
2] 0.175 0.738 2.62
±
1.27
±
0.72 0.67
±
0.84
±
0.39
[0
.
3
,
0
.
5] 0.381 [0
.
2
,
0
.
3] 0.247 0.736 4.76
±
1.17
±
0.67 1.21
±
0.74
±
0.31
[0
.
3
,
0
.
5] 0.382 [0
.
3
,
0
.
5] 0.382 0.749 2.99
±
1.18
±
0.78 0.73
±
0.63
±
0.31
[0
.
3
,
0
.
5] 0.383 [0
.
5
,
0
.
9] 0.610 0.750 4.18
±
1.06
±
0.92 0.77
±
0.52
±
0.41
[0
.
5
,
0
.
9] 0.609 [0
.
15
,
0
.
2] 0.175 0.731 3.30
±
1.10
±
0.91 0.90
±
0.74
±
0.56
[0
.
5
,
0
.
9] 0.608 [0
.
2
,
0
.
3] 0.248 0.728 5.83
±
1.00
±
0.88 1.42
±
0.60
±
0.44
[0
.
5
,
0
.
9] 0.610 [0
.
3
,
0
.
5] 0.383 0.743 2.52
±
1.04
±
0.92 0.38
±
0.51
±
0.41
[0
.
5
,
0
.
9] 0.615 [0
.
5
,
0
.
9] 0.615 0.743 6.81
±
1.72
±
1.26 0.74
±
0.59
±
0.57
TABLE I. Light quark (
uds
) Collins asymmetries obtained by fitting the U/L and U/C doub
le ratios as a function of (
z
1
, z
2
)
for kaon pairs. In the first two columns, the
z
bins and their respective mean values for the kaon in one hemi
sphere are
reported; in the following two columns, the same variables f
or the second kaon are shown; in the fifth column the mean value
of sin
2
θ
th
(2)
/
(1 + cos
2
θ
th
(2)
) is summarized, calculated in the RF12 (upper table) or RF0 (
lower table) frames; in the last
two columns the asymmetry results are summarized. The quote
d errors are statistical and systematic, respectively. The
mean
values of the quantities reported in the table are calculate
d by summing the corresponding values for each
KK
pair and dividing
by the number of
KK
pairs that fall into each (
z
1
, z
2
) interval. Note that the
A
UL
and
A
UC
results are strongly correlated
since they are obtained by using the same data set.