SLAC-PUB-16139
BABAR-PUB-14/008
Search for new
π
0
-like particles produced in association with a
τ
-lepton pair
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
M. Mandelkern,
10
B. Dey,
11
J. W. Gary,
11
O. Long,
11
C. Campagnari,
12
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, a
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, b
M. Piccolo,
22
M. Rama,
22
A. Zallo,
22
R. Contri
ab
,
23
M. Lo Vetere
ab
,
23
M. R. Monge
ab
,
23
S. Passaggio
a
,
23
C. Patrignani
ab
,
23
E. Robutti
a
,
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, c
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
J. Bougher,
36
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, d
G. D. Lafferty,
38
R. Cenci,
39
B. Hamilton,
39
A. Jawahery,
39
D. A. Roberts,
39
R. Cowan,
40
G. Sciolla,
40
R. Cheaib,
41
P. M. Patel,
41, e
S. H. Robertson,
41
N. Neri
a
,
42
F. Palombo
ab
,
42
L. Cremaldi,
43
R. Godang,
43, f
P. Sonnek,
43
D. J. Summers,
43
M. Simard,
44
P. Taras,
44
G. De Nardo
ab
,
45
G. Onorato
ab
,
45
C. Sciacca
ab
,
45
M. Martinelli,
46
G. Raven,
46
C. P. Jessop,
47
J. M. LoSecco,
47
K. Honscheid,
48
R. Kass,
48
E. Feltresi
ab
,
49
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
S. Pacetti
ab
,
51
A. Rossi
a
,
51
C. Angelini
ab
,
52
G. Batignani
ab
,
52
S. Bettarini
ab
,
52
M. Carpinelli
ab
,
52, g
G. Casarosa
ab
,
52
A. Cervelli
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
A. Perez
a
,
52
G. Rizzo
ab
,
52
J. J. Walsh
a
,
52
D. Lopes Pegna,
53
J. Olsen,
53
A. J. S. Smith,
53
R. Faccini
ab
,
54
F. Ferrarotto
a
,
54
F. Ferroni
ab
,
54
M. Gaspero
ab
,
54
L. Li Gioi
a
,
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
F. Anulli,
58, h
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
P. Lewis,
58
D. Lindemann,
58
S. Luitz,
58
V. Luth,
58
H. L. Lynch,
58
D. B. MacFarlane,
58
D. R. Muller,
58
H. Neal,
58
M. Perl,
58, e
T. Pulliam,
58
B. N. Ratcliff,
58
A. Roodman,
58
A. A. Salnikov,
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
R. M. White,
59, i
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
B. C. Wray,
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
P. Villanueva-Perez,
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
D. McKeen,
70, j
I. M. Nugent,
70
M. Pospelov,
70, k
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-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
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 California, Berkeley, California 94720, USA
6
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphysik 1, D-44780 Bochum, Germany
arXiv:1411.1806v2 [hep-ex] 28 Nov 2014
2
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090
a
,
Novosibirsk State University, Novosibirsk 630090
b
,
Novosibirsk State Technical University, Novosibirsk 630092
c
, Russia
10
University of California at Irvine, Irvine, California 92697, USA
11
University of California at Riverside, Riverside, California 92521, USA
12
University of California at Santa Barbara, Santa Barbara, California 93106, USA
13
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA
14
California Institute of Technology, Pasadena, California 91125, USA
15
University of Cincinnati, Cincinnati, Ohio 45221, USA
16
University of Colorado, Boulder, Colorado 80309, USA
17
Colorado State University, Fort Collins, Colorado 80523, USA
18
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44221 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, Italy
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-69120 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, Kingdom of Saudia 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, California 94550, USA
33
University of Liverpool, Liverpool L69 7ZE, United Kingdom
34
Queen Mary, University of London, London, E1 4NS, United Kingdom
35
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
36
University of Louisville, Louisville, Kentucky 40292, USA
37
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Kernphysik, D-55099 Mainz, Germany
38
University of Manchester, Manchester M13 9PL, United Kingdom
39
University of Maryland, College Park, Maryland 20742, USA
40
Massachusetts Institute of Technology, Laboratory for Nuclear 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 Energy 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, OX11 0QX, United Kingdom
57
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
58
SLAC National Accelerator Laboratory, Stanford, California 94309 USA
59
University of South Carolina, Columbia, South Carolina 29208, USA
60
Southern Methodist University, Dallas, Texas 75275, USA
61
Stanford University, Stanford, California 94305-4060, USA
62
State University of New York, Albany, New York 12222, USA
3
63
Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 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, Spain
70
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
71
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
72
University of Wisconsin, Madison, Wisconsin 53706, USA
We report on a search in
e
+
e
−
annihilations for new
π
0
-like particles produced in association
with a
τ
-lepton pair. These objects, with a similar mass and similar decay modes to
π
0
mesons,
could provide an explanation for the non-asymptotic behavior of the pion-photon transition form
factor observed by the
B
A
B
AR
Collaboration. No significant signal is observed, and limits on the
production cross section at the level of 73 fb or 370 fb, depending on the model parameters, are
determined at 90% confidence level. These upper limits lie below the cross section values needed to
explain the
B
A
B
AR
form factor data.
PACS numbers: 14.40.Rt, 14.60.Fg
I. INTRODUCTION
The measurement of the pion-photon transition form
factor
F
π
0
(
Q
2
)
reported by the
B
A
B
AR
Collaboration [1]
has given rise to much discussion [2–5]. The result does
not exhibit convergence towards the Brodsky-Lepage
limit of 185 MeV
/Q
2
[6] even for large values of the
squared momentum transfer, viz.,
Q
2
>
15 GeV
2
, where
the data are expected to be well described by perturba-
tive QCD. Results from the Belle Collaboration [7] show
better agreement with the perturbative predictions but
are consistent with the
B
A
B
AR
data within the uncertain-
ties.
A recent suggestion [8] proposes that the observed lack
of asymptotic behavior might be due to the production of
new particles or states, tentatively named “pion impos-
tors” and generically denoted
φ
[9]. Two classes of models
are considered. In the first, scalar
φ
S
or pseudoscalar
φ
P
particles are introduced with a mass within 10 MeV
/c
2
of
the
π
0
mass, and with similar decay modes to the
π
0
,
such that they thereby contribute to the
F
π
0
(
Q
2
)
mea-
surement. In the second, a new light pseudoscalar state
a
Now at: University of Tabuk, Tabuk 71491, Saudi Arabia
b
Also at: Universit`a di Perugia, Dipartimento di Fisica, I-06123
Perugia, Italy
c
Now at: Laboratoire de Physique Nucl ́eaire et de Hautes Ener-
gies, IN2P3/CNRS, F-75252 Paris, France
d
Now at: University of Huddersfield, Huddersfield HD1 3DH, UK
e
Deceased
f
Now at: University of South Alabama, Mobile, Alabama 36688,
USA
g
Also at: Universit`a di Sassari, I-07100 Sassari, Italy
h
Also at: INFN Sezione di Roma, I-00185 Roma, Italy
i
Now at: Universidad T ́ecnica Federico Santa Maria, 2390123
Valparaiso, Chile
j
Now at: University of Washington, Seattle, Washington 98195,
USA
k
Also at: Perimeter Institute for Theoretical Physics, Waterloo,
Ontario, Canada N2J 2W9
mixes with the
π
0
to produce a so-called “hardcore pion”
π
0
HC
. The
φ
P
and
π
0
HC
have similar experimental signa-
tures and the related processes only differ in their produc-
tion rates. These models predict large coupling strengths
between the new objects and the
τ
lepton, comparable to
the strength of the strong force, leading to an observable
increase of
F
π
0
(
Q
2
)
through virtual loops with
τ
leptons.
The couplings of the new particles to heavy quarks and
other Standard Model (SM) particles are constrained by
experimental data to be an order of magnitude or more
smaller [8].
The largeness of the predicted couplings of the pion
impostors to the
τ
lepton, and the absence of correspond-
ing experimental constraints, motivate a search for pion
impostors radiated from
τ
leptons in
e
+
e
−
→
τ
+
τ
−
φ
,
φ
→
γγ
interactions. This process is particularly com-
pelling because the rate of such events must be consider-
able in order to explain the
B
A
B
AR
F
π
0
(
Q
2
)
data, making
it potentially observable. The production cross sections
required to describe the
B
A
B
AR
measurements are listed
in Table I. The corresponding results for the combined
B
A
B
AR
and Belle data are also given. Based on the cross
sections derived from the
B
A
B
AR
data alone, on the order
of 10
5
events are expected in the
B
A
B
AR
data sample.
TABLE I. Production cross sections of
e
+
e
−
→
τ
+
τ
−
π
0
HC
,
τ
+
τ
−
φ
P
, and
τ
+
τ
−
φ
S
at
√
s
= 10
.
58 GeV needed to ac-
commodate the pion-photon transition form factor reported
by
B
A
B
AR
, as well as the combination of
B
A
B
AR
and Belle
measurements. Confidence intervals at 95% confidence level
are provided in brackets.
Model
σ
(pb)
σ
(pb)
B
A
B
AR
[1]
B
A
B
AR
+ Belle [7]
π
0
HC
0.62
[0.25 – 0.84]
0.44
[0.15 – 0.59]
φ
P
4.8
[2.5 – 6.9]
3.4
[ 2.5 – 5.1]
φ
S
130
[70 – 180]
90
[ 50 – 140]
4
τ
−
π
0
τ
−
FIG. 1. Diagram of the leading order SM process for
π
0
ra-
diation from a
τ
lepton.
The SM production of genuine
π
0
meson in association
with a
τ
-lepton pair is expected to be highly suppressed.
To lowest order, the SM process in which a
π
0
is radi-
ated from a
τ
lepton is depicted in Fig. 1. The matrix
element involves the pseudoscalar to two-photon tran-
sition amplitude as well as a suppression factor arising
from the two-photon loop and the
τ
-lepton propagator.
The matrix element for this diagram [10, 11] yields an
effective coupling between the
π
0
and the
τ
lepton of the
form
g
e.m.
ττ
=
−
1
√
2
m
τ
f
π
(
α
π
)
2
R
,
(1)
where
m
τ
is the mass of the
τ
lepton,
f
π
'
0
.
130 GeV
is the pion decay constant, and
α
is the fine-structure
constant.
The factor
R
is a dimensionless complex
amplitude that is a function of the pion form factor
F
π
0
(
k
2
,
(
p
π
0
−
k
)
2
)
, integrated over the virtual photon
four-momentum
k
, and of the mass ratio
m
τ
/m
π
0
be-
tween the
τ
lepton and the neutral pion. Using a sim-
plified analytical expression for the form factor [10], the
magnitude of
R
is estimated to be around 0.2. The SM
electromagnetic
τ
-
π
0
coupling is therefore
|
g
e.m.
ττ
|∼O
(
10
−
5
)
,
(2)
which is approximately four orders of magnitude smaller
than the coupling strength expected for the impostor
model.
A second potential SM background arises from events
in which the
π
0
meson is created through the
s
-channel
virtual photon from the
e
+
e
−
annihilation, together with
another photon that converts to a
τ
-lepton pair. This
process is highly suppressed by the form factor at
Q
2
=
(10
.
58 GeV)
2
. Compared to the
τ
-lepton pair rate, it is
further suppressed by a factor of
α
.
The total combined expected background yield from
the two SM background processes described above corre-
sponds to less than around 0.01 events, which is negligible
compared to the number of pion impostor events required
to explain the
F
π
0
(
Q
2
)
anomaly.
We present a search for new
π
0
-like particles in the
e
+
e
−
→
τ
+
τ
−
φ
final state, where
φ
can be any of the
φ
P
,
φ
S
, or
π
0
HC
states. The paper is organized as follows:
Section II describes the detector and data samples used
in this analysis, while Section III presents the signal se-
lection and the yield extraction methodology. The main
contributions to the systematic uncertainty are described
in Section IV and the results are presented in Section V.
Section VI contains a summary.
II. THE
B
A
B
AR
DETECTOR, DATA AND
SIMULATION
The data used in this analysis were collected with the
B
A
B
AR
detector at the PEP-II asymmetric-energy
e
+
e
−
storage rings between 1999 and 2007. The
B
A
B
AR
de-
tector is described in detail elsewhere [12, 13]. Here we
provide a brief overview of the two subdetectors most
relevant to this analysis.
The energy of photons and electrons is measured with
an electromagnetic calorimeter (EMC) composed of a
cylindrical array of CsI(Tl) crystals. The resolution for
the polar and azimuthal angles is
∼
4 mrad, and the en-
ergy resolution is
∼
3% for 1 GeV photons [12]. The
EMC also serves as a particle identification (PID) device
for electrons. The drift chamber is used to determine
the momentum of the charged tracks by measuring their
curvature in a 1.5 T magnetic field. The transverse mo-
mentum resolution is a linear function of the transverse
momentum
p
T
and is 0.67% for
p
T
= 1
.
7 GeV
/c
, which is
the mean laboratory
p
T
value of charged tracks expected
in signal events.
This analysis is based on 424 fb
−
1
of data collected at
a center-of-mass (CM) energy
√
s
= 10
.
58 GeV and on
44 fb
−
1
collected at
√
s
= 10
.
54 GeV [14], corresponding
to a total production of approximately 430
×
10
6
τ
+
τ
−
pairs.
Simulated signal events are created using the
EvtGen
[15] generator. First, large samples of
e
+
e
−
→
τ
+
τ
−
π
0
events are generated, based on three-body phase
space and nominal decay modes for the
τ
leptons and
π
0
meson. Then the events are reweighted to reflect the
production rate of
e
+
e
−
→
τ
+
τ
−
φ
processes using the
analytical matrix elements corresponding to the pion im-
postor process illustrated in Fig. 2, assuming either the
scalar or pseudoscalar hypothesis.
e
+
e
−
τ
∓
φ
τ
±
FIG. 2. Diagram of the pion impostor production process in
e
+
e
−
annihilations. The
φ
can be any of the
φ
P
,
φ
S
, or
π
0
HC
particles.
The following backgrounds are considered:
e
+
e
−
→
B
B
events, generated with the
EvtGen
[15] program, con-
tinuum hadronic
e
+
e
−
→
q
q
(
q
=
u,d,s,c
) events, gen-
5
erated with the
JETSET
[16] program,
e
+
e
−
→
μ
+
μ
−
and
e
+
e
−
→
τ
+
τ
−
events, generated with the
KK
[17] pro-
gram, with the decay of the
τ
leptons described using
the
TAUOLA
[18] library, and
e
+
e
−
→
e
+
e
−
events are
simulated with the
BHWIDE
[19] program. Radiative cor-
rections are modeled with the
PHOTOS
[20] algorithm and
the detector response with the
GEANT4
[21] toolkit.
III. ANALYSIS METHOD
The signal consists of a
τ
+
τ
−
pair and a single pion
impostor
φ
. The pion impostor decays to a pair of pho-
tons with diphoton invariant mass close to the
π
0
mass.
The selection criteria are optimized using simulated sig-
nal and background events. Simulated samples are also
used to evaluate the selection efficiency and systematic
uncertainties. These quantities are evaluated using an
impostor mass set equal to the mass of the
π
0
.
A. Signal selection
For the selection of
e
+
e
−
→
τ
+
τ
−
φ
signal events, we
require one
τ
lepton to decay leptonically to an elec-
tron and the other to a muon. This requirement sup-
presses background from radiative Bhabha and dimuon
events. We thus require events to contain exactly two
charged tracks, one identified as an electron and the
other as a muon. To reduce background from two-photon
e
+
e
−
→
e
+
e
−
X
events, signal event candidates are re-
quired to have a missing transverse momentum larger
than 0
.
3 GeV
/c
, where the missing transverse momen-
tum is the magnitude of the vector sum of the
p
T
values
of both tracks and of all reconstructed neutral particles,
evaluated in the event CM frame.
The pion-impostor candidates
φ
are reconstructed by
combining two photons, each with a CM energy larger
than 250 MeV. To reduce the contribution of radiative
events, we require the sum of the CM energies of all pho-
tons in the event not associated with the
φ
candidate to
be less than 300 MeV. The latter requirement also has
the effect of rejecting events containing more than one
φ
candidate. The photons associated with a
φ
candidate
must be separated from the electron track by at least 30
◦
to further suppress radiative events. Control samples of
τ
±
→
X
±
(
π
0
)
ν
τ
events with
X
±
=
π
±
,
K
±
,
μ
±
ν
μ
are
used to determine momentum-dependent corrections for
the
φ
selection efficiency [22].
Kinematic constraints are used to ensure that the
φ
candidate does not arise from events in which one
τ
lep-
ton decays leptonically, while the other decays through
τ
±
→
ρ
±
ν
followed by
ρ
±
→
π
±
π
0
, where the
π
±
is
misidentified as a lepton. We form the invariant mass
between each track and the
φ
candidate, assuming a
π
±
mass hypothesis for the track, and require the combined
mass to be greater than the
τ
-lepton mass. To further
suppress neutral pions from
τ
-lepton decays, the sum of
(GeV)
φ
+ E
small
E
2
3
4
5
6
7
Counts / 0.2 GeV
0
10
20
30
40
50
60
Data
MC
HC
φ
-
τ
+
τ
→
-
e
+
e
MC
-
τ
+
τ
→
-
e
+
e
MC
-
μ
+
μ
→
-
e
+
e
MC
b
b
→
-
e
+
e
MC
c
c
→
-
e
+
e
σ
(Data - SM MC) /
-1
-0.5
0
0.5
1
1.5
2
FIG. 3. (color online) Top: sum of the smaller of the track
energies
E
small
and of the
φ
candidate energy
E
φ
, evaluated
in the event CM, after applying all other selection criteria and
requiring
m
γγ
∈
[100
,
160] MeV
/c
2
. The data to the right of
the vertical line at 5.29 GeV are in the signal region. The
predicted hardcore pion
e
+
e
−
→
τ
+
τ
−
π
0
HC
distribution, as-
suming a production cross section of 0.254 pb, is included for
reference. Bottom: Difference between data and Standard
Model simulation (SM MC), divided by combined statistical
uncertainty.
the CM energy of the
φ
candidate,
E
φ
, and that of the
track with the lower energy,
E
small
, must be greater than
√
s/
2. The distribution of
E
small
+
E
φ
for events with
m
γγ
∈
[100
,
160] MeV
/c
2
, after all other selection criteria
have been applied, is shown in Fig. 3.
The resulting diphoton mass spectrum after applying
all other selection criteria is displayed in Fig. 4. The data
are seen to agree with the SM simulation to within the
uncertainties.
B. Yield extraction, background evaluation, and
selection efficiency
The signal yield is extracted by performing a series of
extended unbinned maximum likelihood fits to the dipho-
ton invariant mass distribution in the [50
,
300] MeV
/c
2
range, scanning
φ
mass hypotheses as explained below.
This region is chosen because it includes the predicted
mass range for the signal, and also because the back-
ground distribution is relatively flat. The
m
γγ
distribu-
tion is fitted with the sum of a Gaussian function, de-
scribing the contribution of the signal and peaking back-
ground components, and a first-order polynomial repre-
senting the combinatorial background. The number of
events in the Gaussian peak is denoted
N
g
. The slope
6
)
2
(GeV/c
γ
γ
m
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
2
Counts / 0.2 GeV/c
0
10
20
30
40
50
60
70
Data
MC
HC
φ
-
τ
+
τ
→
-
e
+
e
MC
-
τ
+
τ
→
-
e
+
e
MC
-
μ
+
μ
→
-
e
+
e
MC
b
b
→
-
e
+
e
MC
c
c
→
-
e
+
e
)
2
(GeV/c
γ
γ
m
0
0.05
0.1
0.15
0.2
0.25
0.3
0
2
4
6
8
10
12
FIG. 4. (color online) Distribution of
m
γγ
after applying all
other selection criteria. The insert shows the low mass range
with bin size of 10 MeV
/c
2
and normalization of the polynomial as well as the value
of
N
g
are determined in the fit. The mean
μ
g
and width
σ
g
of the Gaussian function are fixed to values deter-
mined as explained below.
The value of
σ
g
is evaluated using control samples.
These samples are selected, for both data and simula-
tion, using criteria similar to those described above, but
reversing the requirements on the invariant mass formed
from the charged track and the
π
0
candidate, and re-
moving the requirement on
E
small
+
E
φ
. The reason this
latter requirement is removed is to increase the statisti-
cal precision. The
m
γγ
spectra are then fitted using the
signal model described above except with
σ
g
a fitted pa-
rameter. We find
σ
g
= 10
.
6
±
1
.
8 MeV
/c
2
for the data
and
σ
g
= 11
.
2
±
0
.
8 MeV
/c
2
for the simulation. For the
subsequent fits, we fix
σ
g
to 11
.
1 MeV
/c
2
, which is the
average of the results from data and simulation.
The value of
μ
g
represents the mass of the hypothetical
φ
particle. It is is fixed in the fit and scanned between 110
and 160 MeV
/c
2
, covering the expected range of impostor
mass values [8]. The step size is 0.5 MeV
/c
2
, correspond-
ing to less than half the estimated mass resolution.
We select the scan point that yields the largest value
N
max
g
of
N
g
. The signal yield
N
sig
is obtained by sub-
tracting the estimated number of peaking background
events from
N
max
g
and correcting for the signal yield bias.
The number of peaking background events predicted
by the simulation is 0
.
38
±
0
.
09, where the uncertainty
accounts for uncertainties in the PID as well as for the
difference between the data and simulation rates in the
sidebands, which is visible in Fig. 3 for values of
E
small
+
E
φ
above 4.8 GeV
/c
2
.
We also consider potential peaking backgrounds that
are not present in the simulation. Specifically, we con-
sider two-photon
e
+
e
−
→
e
+
e
−
π
+
π
−
π
0
events, for which
either the
e
+
or
e
−
, and one of the charged pions, are un-
detected, while the other charged pion is misidentified as
a muon. The events are selected using the same crite-
ria as described above except requiring the presence of
a charged pion rather than a muon. The
m
γγ
spectrum
of the selected events is fitted as described above, and
the resulting value of
N
g
is scaled by the muon-to-pion
misidentification rate of (3
.
0
±
1
.
0)%. Adding the result-
ing value to the number of peaking events determined
from simulation yields an estimate of 1
.
24
±
0
.
37 events.
This number is subtracted from
N
max
g
as described above.
The evaluation of the fit bias is performed using a
large ensemble of pseudo-experiments. For this purpose,
diphoton invariant mass spectra are generated to repro-
duce the combinatorial background with the number of
combinatorial events drawn from a Poisson distribution
whose mean equals the simulated result. A peaking com-
ponent centered at the
π
0
mass is added. The number of
peaking events is drawn from a Poisson distribution with
mean equal to one. Each peaking background event is
then weighted by a number drawn from a Gaussian dis-
tribution whose mean and width are 1.24 and 0.37 events,
respectively. We determine the bias for several values of
the signal yield by further adding a known number of
signal-like events to each experiment. Between 0 and
25 signal events are added to each pseudo-experiment,
yielding an average fit bias of
−
0
.
06
±
0
.
02 events.
The signal selection efficiency is determined by ap-
plying the analysis procedures to the simulated signal
events. After accounting for the
τ
−
→
μ
−
ν
μ
ν
τ
and the
τ
−
→
e
−
ν
e
ν
τ
branching fractions [23], the efficiencies
are found to be
ε
φ
P
=
ε
π
0
HC
= (0
.
455
±
0
.
017)% and
ε
φ
S
= (0
.
0896
±
0
.
0033)%, where the uncertainties are
statistical. The efficiency to reconstruct the
φ
S
is smaller
than that to reconstruct the
φ
P
and
π
0
HC
because the
scalar particle tends to produce lower-energy impostor
candidates that do not satisfy the selection criteria.
IV. SYSTEMATIC UNCERTAINTIES
Sources of systematic uncertainty affecting the effi-
ciency measurement include those associated with the
π
0
and PID efficiency corrections, as well as differences
between the data and simulation in the track momentum
scale and resolution, and in the photon energy scale and
resolution. These multiplicative uncertainties are sum-
marized in Table II. The additive uncertainty contribu-
tions to the signal yield measurement are associated with
the peaking background estimate and potential biases in
the fit procedure. For the latter, we assign the full bias
correction as a systematic uncertainty.
The uncertainty related to the
π
0
reconstruction effi-
ciency is evaluated by performing the analysis while vary-
ing the
π
0
efficiency correction within its uncertainties.
The PID uncertainty is 0
.
5%, estimated using high-purity
control samples.
The uncertainties associated with the differences be-
tween the data and simulation for the track momentum
scale and resolution are measured using
e
+
e
−
→
μ
+
μ
−
γ
events. These samples are also used to determine the
7
)
2
(GeV/c
g
μ
0.11
0.12
0.13
0.14
0.15
0.16
g
N
-2
0
2
4
6
8
FIG. 5. Number
N
g
of events in the Gaussian peak as a
function of the
φ
mass hypothesis
μ
g
. The shaded region
indicates the statistical uncertainty.
uncertainties related to the photon energy scale and res-
olution [24].
TABLE II. Contributions to the uncertainty of the efficiency
(%) for the three models considered.
Source of uncertainty
φ
P
,π
0
HC
φ
S
(%)
(%)
MC sample size
3
.
5
3
.
7
π
0
efficiency
1
.
0
1
.
0
PID
0
.
5
0
.
5
Momentum scale
0
.
2
0
.
2
Momentum resolution
0
.
1
<
0
.
1
Energy scale
2
.
0
2
.
0
Energy resolution
0
.
6
0
.
6
Total systematic uncertainty
4
.
2
4
.
4
V. RESULTS
A. Data
m
γγ
spectrum
Figure 5 shows the yield
N
g
of events in the Gaussian
peak, with its statistical uncertainty, as a function of the
φ
particle mass hypothesis. The largest value,
N
max
g
=
6
.
2
±
2
.
7
(stat.)
events, arises for
μ
g
= 136 MeV
/c
2
. The
fit result with this mass hypothesis is shown in the dipho-
ton mass distribution of Fig. 6, where the contribution
from the expected background is also presented. The
probability of observing a signal of at least 6.2 events as-
suming a background-only hypothesis is estimated from
the pseudo-experiments described in Section IV, which
assume a mass
μ
g
∈
[110
,
160] MeV
/c
2
. The
p
-value is
found to be
p
0
= 3
.
71
×
10
−
2
.
After subtraction of the peaking background and cor-
rection for the fit bias, the number of signal candidate
)
2
(GeV/c
γ
γ
m
0
0.05
0.1
0.15
0.2
0.25
0.3
2
Counts / 0.01 GeV/c
0
1
2
3
4
5
Data
Data fit
Background model
MC
-
τ
+
τ
→
-
e
+
e
MC
-
μ
+
μ
→
-
e
+
e
MC
b
b
→
-
e
+
e
MC
c
c
→
-
e
+
e
FIG. 6. (color online) Results for the
m
γγ
spectrum of the
signal candidates. The solid line shows fit result for the signal
and background model. The dotted line represents the con-
tribution from background only using the linear component
of the fit result added to the estimated peaking background
of 1.24 events.
events at
μ
g
= 136 MeV
/c
2
is found to be
N
sig
= 5
.
0
±
2
.
7
(stat.)
±
0
.
4
(syst.)
.
(3)
Correcting this result for the signal selection efficiency
leads to the following production cross sections:
σ
=
{
38
±
21
(stat.)
±
3
(syst.)
fb for
φ
P
and
π
0
HC
,
190
±
100
(stat.)
±
20
(syst.)
fb for
φ
S
.
(4)
Statistical uncertainties dominate in both cases. The
main source of systematic uncertainty is the peaking
background estimation and subtraction procedure.
B. Upper limits on the cross sections
No significant signal is observed.
Upper limits on
the production cross sections are set using the
CL
s
method [25]. The 90% confidence level (CL) upper limit
on the number of signal events,
N
sig
≤
9
.
6, translates
into the following bounds on the cross section
σ
≤
{
73 fb for the
φ
P
and
π
0
HC
models,
370 fb for the
φ
S
model.
(5)
C. Compatibility of the measurement with the
π
0
impostor theories
The compatibility of the measured production cross
sections with the impostor theories is studied by includ-
ing this measurement as an additional term in the
χ
2
when calculating the optimal coupling values needed to
describe the
B
A
B
AR
measurement of
F
π
0
(
Q
2
)
. The in-
crease in
χ
2
obtained when adding the couplings corre-
sponding to our cross section measurements follows a
χ
2
8
distribution with one degree of freedom. This is used to
determine the
p
-values corresponding to a fluctuation of
the
e
+
e
−
→
τ
+
τ
−
φ
event rate from the level seen in the
present study to the level required to explain the
B
A
B
AR
F
π
0
(
Q
2
)
measurements.
The results are reported in Table III. As an example,
the
p
-value for the hardcore pion model is found to be
5
.
9
×
10
−
4
, corresponding to a required fluctuation of 3.4
standard deviations. The
p
-values for the
φ
P
and
φ
S
models are on the order of 10
−
9
. Thus the pion impostor
models do not provide a likely explanation for the ex-
cess seen in the
B
A
B
AR
pion-photon transition form factor
data.
TABLE III. Consistency (
p
-value) of the measured produc-
tion cross sections with the impostor theories adjusted to the
B
A
B
AR
F
π
0
(
Q
2
)
data.
Model
χ
2
min
/
n.d.f.
∆
χ
2
/
n.d.f.
p
-value
F
π
0
(
Q
2
)
and
F
π
0
(
Q
2
)
σ
e
+
e
−
→
τ
+
τ
−
φ
only
π
0
HC
23.7/10
11.9/9
11.8/1
5
.
9
×
10
−
4
φ
P
48.4/10
10.8/9
37.6/1
8
.
8
×
10
−
10
φ
S
49.2/10
13.4/9
35.8/1
2
.
2
×
10
−
9
VI. SUMMARY
A search for
π
0
impostors is conducted with the
B
A
B
AR
data set. At 90% confidence level, the limit on the pro-
duction cross section in association with a
τ
+
τ
−
pair is
73 fb for the pseudoscalar impostor and the hardcore pion
models, and 370 fb for the scalar impostor model. The
p
-values of our measurements under these hypotheses are
5
.
9
×
10
−
4
or smaller. The pion impostor hypotheses are
disfavored as explanations for the non-asymptotic behav-
ior of the pion-photon transition form factor observed
with the
B
A
B
AR
data.
ACKNOWLEDGMENTS
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),
MINECO (Spain), STFC (United Kingdom), BSF (USA-
Israel). Individuals have received support from the Marie
Curie EIF (European Union) and the A. P. Sloan Foun-
dation (USA).
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