of 20
Bottomonium spectroscopy and radiative transitions involving
the
χ
bJ
ð
1
P
;
2
P
Þ
states at
B
A
B
AR
J. P. Lees,
1
V. Poireau,
1
V. Tisserand,
1
E. Grauges,
2
A. Palano,
3a,3b
G. Eigen,
4
B. Stugu,
4
D. N. Brown,
5
L. T. Kerth,
5
Yu. G. Kolomensky,
5
M. 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,
9a,9b,9c
A. R. Buzykaev,
9a
V. P. Druzhinin,
9a,9b
V. B. Golubev,
9a,9b
E. A. Kravchenko,
9a,9b
A. P. Onuchin,
9a,9b,9c
S. I. Serednyakov,
9a,9b
Yu. I. Skovpen,
9a,9b
E. P. Solodov,
9a,9b
K. Yu. Todyshev,
9a,9b
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. Roehrken,
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,
21a
C. Bozzi,
21a
R. Calabrese,
21a,21b
G. Cibinetto,
21a,21b
E. Fioravanti,
21a,21b
I. Garzia,
21a,21b
E. Luppi,
21a,21b
L. Piemontese,
21a
V. Santoro,
21a
A. Calcaterra,
22
R. de Sangro,
22
G. Finocchiaro,
22
S. Martellotti,
22
P. Patteri,
22
I. M. Peruzzi,
22
,
M. Piccolo,
22
M. Rama,
22
A. Zallo,
22
R. Contri,
23a,23b
M. Lo Vetere,
23a,23b
M. R. Monge,
23a,23b
S. Passaggio,
23a
C. Patrignani,
23a,23b
E. Robutti,
23a
B. Bhuyan,
24
V. Prasad,
24
A. Adametz,
25
U. Uwer,
25
H. M. Lacker,
26
P. D. Dauncey,
27
U. Mallik,
28
C. Chen,
29
J. Cochran,
29
S. Prell,
29
H. Ahmed,
30
A. V. Gritsan,
31
N. Arnaud,
32
M. Davier,
32
D. Derkach,
32
G. Grosdidier,
32
F. Le Diberder,
32
A. M. Lutz,
32
B. Malaescu,
32
P. Roudeau,
32
A. Stocchi,
32
G. Wormser,
32
D. J. Lange,
33
D. M. Wright,
33
J. P. Coleman,
34
J. R. Fry,
34
E. Gabathuler,
34
D. E. Hutchcroft,
34
D. J. Payne,
34
C. Touramanis,
34
A. J. Bevan,
35
F. Di Lodovico,
35
R. Sacco,
35
G. Cowan,
36
J. Bougher,
37
D. N. Brown,
37
C. L. Davis,
37
A. G. Denig,
38
M. Fritsch,
38
W. Gradl,
38
K. Griessinger,
38
A. Hafner,
38
K. R. Schubert,
38
R. J. Barlow,
39
G. D. Lafferty,
39
R. Cenci,
40
B. Hamilton,
40
A. Jawahery,
40
D. A. Roberts,
40
R. Cowan,
41
G. Sciolla,
41
R. Cheaib,
42
P. M. Patel,
42
,*
S. H. Robertson,
42
N. Neri,
43a
F. Palombo,
43a,43b
L. Cremaldi,
44
R. Godang,
44
,**
P. Sonnek,
44
D. J. Summers,
44
M. Simard,
45
P. Taras,
45
G. De Nardo,
46a,46b
G. Onorato,
46a,46b
C. Sciacca,
46a,46b
M. Martinelli,
47
G. Raven,
47
C. P. Jessop,
48
J. M. LoSecco,
48
K. Honscheid,
49
R. Kass,
49
E. Feltresi,
50a,50b
M. Margoni,
50a,50b
M. Morandin,
50a
M. Posocco,
50a
M. Rotondo,
50a
G. Simi,
50a,50b
F. Simonetto,
50a,50b
R. Stroili,
50a,50b
S. Akar,
51
E. Ben-Haim,
51
M. Bomben,
51
G. R. Bonneaud,
51
H. Briand,
51
G. Calderini,
51
J. Chauveau,
51
Ph. Leruste,
51
G. Marchiori,
51
J. Ocariz,
51
M. Biasini,
52a,52b
E. Manoni,
52a
S. Pacetti,
52a,52b
A. Rossi,
52a
C. Angelini,
53a,53b
G. Batignani,
53a,53b
S. Bettarini,
53a,53b
M. Carpinelli,
53a,53b
,
††
G. Casarosa,
53a,53b
A. Cervelli,
53a,53b
M. Chrzaszcz,
53a
F. Forti,
53a,53b
M. A. Giorgi,
53a,53b
A. Lusiani,
53a,53c
B. Oberhof,
53a,53b
E. Paoloni,
53a,53b
A. Perez,
53a
G. Rizzo,
53a,53b
J. J. Walsh,
53a
D. Lopes Pegna,
54
J. Olsen,
54
A. J. S. Smith,
54
R. Faccini,
55a,55b
F. Ferrarotto,
55a
F. Ferroni,
55a,55b
M. Gaspero,
55a,55b
L. Li Gioi,
55a
A. Pilloni,
55a,55b
G. Piredda,
55a
C. Bünger,
56
S. Dittrich,
56
O. Grünberg,
56
M. Hess,
56
T. Leddig,
56
C. Voß,
56
R. Waldi,
56
T. Adye,
57
E. O. Olaiya,
57
F. F. Wilson,
57
S. Emery,
58
G. Vasseur,
58
F. Anulli,
59
,
‡‡
D. Aston,
59
D. J. Bard,
59
C. Cartaro,
59
M. R. Convery,
59
J. Dorfan,
59
G. P. Dubois-Felsmann,
59
W. Dunwoodie,
59
M. Ebert,
59
R. C. Field,
59
B. G. Fulsom,
59
M. T. Graham,
59
C. Hast,
59
W. R. Innes,
59
P. Kim,
59
D. W. G. S. Leith,
59
P. Lewis,
59
D. Lindemann,
59
S. Luitz,
59
V. Luth,
59
H. L. Lynch,
59
D. B. MacFarlane,
59
D. R. Muller,
59
H. Neal,
59
M. Perl,
59
T. Pulliam,
59
B. N. Ratcliff,
59
A. Roodman,
59
A. A. Salnikov,
59
R. H. Schindler,
59
A. Snyder,
59
D. Su,
59
M. K. Sullivan,
59
J. Va
vra,
59
W. J. Wisniewski,
59
H. W. Wulsin,
59
M. V. Purohit,
60
R. M. White,
60
,§§
J. R. Wilson,
60
A. Randle-Conde,
61
S. J. Sekula,
61
M. Bellis,
62
P. R. Burchat,
62
E. M. T. Puccio,
62
M. S. Alam,
63
J. A. Ernst,
63
R. Gorodeisky,
64
N. Guttman,
64
D. R. Peimer,
64
A. Soffer,
64
S. M. Spanier,
65
J. L. Ritchie,
66
A. M. Ruland,
66
R. F. Schwitters,
66
B. C. Wray,
66
J. M. Izen,
67
X. C. Lou,
67
F. Bianchi,
68a,68b
F. De Mori,
68a,68b
A. Filippi,
68a
D. Gamba,
68a,68b
L. Lanceri,
69a,69b
L. Vitale,
69a,69b
F. Martinez-Vidal,
70
A. Oyanguren,
70
P. Villanueva-Perez,
70
J. Albert,
71
Sw. Banerjee,
71
A. Beaulieu,
71
F. U. Bernlochner,
71
H. H. F. Choi,
71
G. J. King,
71
R. Kowalewski,
71
M. J. Lewczuk,
71
T. Lueck,
71
I. M. Nugent,
71
J. M. Roney,
71
R. J. Sobie,
71
N. Tasneem,
71
T. J. Gershon,
72
P. F. Harrison,
72
T. E. Latham,
72
H. R. Band,
73
S. Dasu,
73
Y. Pan,
73
R. Prepost,
73
and S. L. Wu
73
(
B
A
B
AR
Collaboration)
1
Laboratoire d
Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie,
CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain
3a
INFN Sezione di Bari, I-70126 Bari, Italy
3b
Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
6
Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany
7
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
PHYSICAL REVIEW D
90,
112010 (2014)
1550-7998
=
2014
=
90(11)
=
112010(20)
112010-1
© 2014 American Physical Society
8
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
9a
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
9b
Novosibirsk State University, Novosibirsk 630090, Russia
9c
Novosibirsk State Technical University, Novosibirsk 630092, 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 Universität Dortmund, Fakultät 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
21a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
21b
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy
22
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
23a
INFN Sezione di Genova, I-16146 Genova, Italy
23b
Dipartimento di Fisica, Università di Genova, I-16146 Genova, Italy
24
Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India
25
Universität Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany
26
Humboldt-Universität zu Berlin, Institut für Physik, D-12489 Berlin, Germany
27
Imperial College London, London, SW7 2AZ, United Kingdom
28
University of Iowa, Iowa City, Iowa 52242, USA
29
Iowa State University, Ames, Iowa 50011-3160, USA
30
Physics Department, Jazan University, Jazan 22822, Kingdom of Saudia Arabia
31
Johns Hopkins University, Baltimore, Maryland 21218, USA
32
Laboratoire de l
Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11,
Centre Scientifique d
Orsay, F-91898 Orsay Cedex, France
33
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
34
University of Liverpool, Liverpool L69 7ZE, United Kingdom
35
Queen Mary, University of London, London, E1 4NS, United Kingdom
36
University of London, Royal Holloway and Bedford New College, Egham,
Surrey TW20 0EX, United Kingdom
37
University of Louisville, Louisville, Kentucky 40292, USA
38
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany
39
University of Manchester, Manchester M13 9PL, United Kingdom
40
University of Maryland, College Park, Maryland 20742, USA
41
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge,
Massachusetts 02139, USA
42
McGill University, Montréal, Québec, Canada H3A 2T8
43a
INFN Sezione di Milano, I-20133 Milano, Italy
43b
Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy
44
University of Mississippi, University, Mississippi 38677, USA
45
Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7
46a
INFN Sezione di Napoli, I-80126 Napoli, Italy
46b
Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
47
NIKHEF, National Institute for Nuclear Physics and High Energy Physics,
NL-1009 DB Amsterdam, The Netherlands
48
University of Notre Dame, Notre Dame, Indiana 46556, USA
49
Ohio State University, Columbus, Ohio 43210, USA
50a
INFN Sezione di Padova, I-35131 Padova, Italy
50b
Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
51
Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie
Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France
52a
INFN Sezione di Perugia, I-06123 Perugia, Italy
52b
Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
53a
INFN Sezione di Pisa, I-56127 Pisa, Italy
53b
Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
J. P. LEES
et al.
PHYSICAL REVIEW D
90,
112010 (2014)
112010-2
53c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy
54
Princeton University, Princeton, New Jersey 08544, USA
55a
INFN Sezione di Roma, I-00185 Roma, Italy
55b
Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy
56
Universität Rostock, D-18051 Rostock, Germany
57
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
58
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France
59
SLAC National Accelerator Laboratory, Stanford, California 94309, USA
60
University of South Carolina, Columbia, South Carolina 29208, USA
61
Southern Methodist University, Dallas, Texas 75275, USA
62
Stanford University, Stanford, California 94305-4060, USA
63
State University of New York, Albany, New York 12222, USA
64
Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
65
University of Tennessee, Knoxville, Tennessee 37996, USA
66
University of Texas at Austin, Austin, Texas 78712, USA
67
University of Texas at Dallas, Richardson, Texas 75083, USA
68a
INFN Sezione di Torino, I-10125 Torino, Italy
68b
Dipartimento di Fisica, Università di Torino, I-10125 Torino, Italy
69a
INFN Sezione di Trieste, I-34127 Trieste, Italy
69b
Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy
70
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain
71
University of Victoria, Victoria, British Columbia, Canada V8W 3P6
72
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
73
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 15 October 2014; published 24 December 2014)
We use
ð
121

1
Þ
million
Υ
ð
3
S
Þ
and
ð
98

1
Þ
million
Υ
ð
2
S
Þ
mesons recorded by the
BABAR
detector at
the PEP-II
e
þ
e
collider at SLAC to perform a study of radiative transitions involving the
χ
b
J
ð
1
P;
2
P
Þ
states in exclusive decays with
μ
þ
μ
γγ
final states. We reconstruct twelve channels in four cascades using
two complementary methods. In the first we identify both signal photon candidates in the electromagnetic
calorimeter (EMC), employ a calorimeter timing-based technique to reduce backgrounds, and determine
branching-ratio products and fine mass splittings. These results include the best observational significance
yet for the
χ
b
0
ð
2
P
Þ
γ
Υ
ð
2
S
Þ
and
χ
b
0
ð
1
P
Þ
γ
Υ
ð
1
S
Þ
transitions. In the second method, we identify one
photon candidate in the EMC and one which has converted into an
e
þ
e
pair due to interaction with
detector material, and we measure absolute product branching fractions. This method is particularly useful
for measuring
Υ
ð
3
S
Þ
γχ
b
1
;
2
ð
1
P
Þ
decays. Additionally, we provide the most up-to-date derived
branching fractions, matrix elements and mass splittings for
χ
b
transitions in the bottomonium system.
Using a new technique, we also measure the two lowest-order spin-dependent coefficients in the
nonrelativistic QCD Hamiltonian.
DOI:
10.1103/PhysRevD.90.112010
PACS numbers: 13.20.Gd, 14.40.Pq, 14.65.Fy
I. INTRODUCTION
The strongly bound
b
̄
b
meson system
bottomonium
exhibits a rich positroniumlike structure that is a laboratory
for verifying perturbative and nonperturbative QCD cal-
culations
[1]
. Potential models and lattice calculations
provide good descriptions of the mass structure and
radiative transitions below the open-flavor threshold.
Precision spectroscopy probes spin-dependent and relativ-
istic effects. Quark-antiquark potential formulations have
been successful at describing the bottomonium system
phenomenologically
[1]
. These potentials are generally
perturbative in the short range in a Coulomb-like single-
gluon exchange, and transition to a linear nonperturbative
confinement term at larger inter-quark separation. The
*
Deceased.
Now at University of Tabuk, Tabuk 71491, Saudi Arabia.
Also at Università di Perugia, Dipartimento di Fisica, I-06123
Perugia, Italy.
§
Now at Laboratoire de Physique Nucléaire et de Hautes
Energies, IN2P3/CNRS, F-75252 Paris, France.
Now at University of Huddersfield, Huddersfield HD1
3DH, UK.
**
Now at University of South Alabama, Mobile, Alabama
36688, USA.
††
Also at Università di Sassari, I-07100 Sassari, Italy.
‡‡
Also at INFN Sezione di Roma, I-00185 Roma, Italy.
§§
Now at Universidad Técnica Federico Santa Maria, 2390123
Valparaiso, Chile.
BOTTOMONIUM SPECTROSCOPY AND RADIATIVE
...
PHYSICAL REVIEW D
90,
112010 (2014)
112010-3
various observed bottomonium states span these two
regions and so present a unique opportunity to probe these
effective theories.
Radiative transition amplitudes between the long-lived
bottomonium states are described in potential models in
a multipole expansion with leading-order electric and
magnetic dipole
E
1
and
M
1
terms. The
E
1
transitions
couple the
S
-wave
Υ
ð
nS
Þ
states produced in
e
þ
e
colli-
sions to the spin-one
P
-wave
χ
b
J
ð
mP
Þ
states; suppressed
M
1
transitions are required to reach the spin-singlet states
such as the ground-state
η
b
ð
1
S
Þ
.
The partial width for an
E
1
transition from initial state
i
to final state
f
is calculated in effective theories using
[2]
Γ
i
f
¼
4
3
e
2
b
α
C
if
ð
2
J
f
þ
1
Þ
E
3
γ
jh
n
f
L
f
j
r
j
n
i
L
i
ij
2
;
ð
1
Þ
where
e
b
is the charge of the
b
quark,
α
is the fine-structure
constant,
C
if
is a statistical factor that depends on the
initial- and final-state quantum numbers (equal to
1
=
9
for
transitions between
S
and
P
states),
E
γ
is the photon energy
in the rest frame of the decaying state,
r
is the inter-quark
separation, and
n
,
L
and
J
refer to the principal, orbital
angular momentum and total angular momentum quantum
numbers, respectively. Measurements of
E
1
transition rates
directly probe potential-model calculations of the matrix
elements and inform relativistic corrections.
Nonrelativistic QCD (NRQCD) calculations on the
lattice have been used with success to describe the
bottomonium mass spectrum in the nonperturbative regime
[3
7]
, including splittings in the spin-triplet
P
-wave states
due to spin-orbit and tensor interactions. Experimental
splitting results can be used as an independent check of the
leading-order spin-dependent coefficients in the NRQCD
Hamiltonian
[3,4]
.
In the present analysis we measure radiative transition
branching-ratio products and fine splittings in
E
1
transi-
tions involving the
χ
bJ
ð
2
P
Þ
and
χ
bJ
ð
1
P
Þ
spin triplets, as
displayed in Fig.
1
. We also provide relevant matrix
elements and NRQCD coefficients for use in relativistic
corrections and lattice calculations. These measurements
are performed using two different strategies: in the first, we
reconstruct the transition photons using only the
BABAR
electromagnetic calorimeter (EMC); in the second, we
consider a complementary set of such transitions in which
one of the photons has converted into an
e
þ
e
pair within
detector material.
Following an introduction of the analysis strategy in
Sec.
II
, we describe relevant
BABAR
detector and data-
set details in Sec.
III
. The event reconstruction and
selection, energy spectrum fitting, and the corresponding
uncertainties for the calorimeter-based analysis are
described in Sec.
IV
. Section
V
similarly describes the
photon-conversion-based analysis. Finally, we present
results in Sec.
VI
, and a discussion and summary in Sec.
VII
.
II. ANALYSIS OVERVIEW
Since the energy resolution of a calorimeter typically
degrades with photon energy, the
20
MeV
=c
2
mass split-
tings of the
P
-wave bottomonium states are not resolvable
for the
hard
(
200
MeV)
P
S
transitions but have
been resolved successfully in
soft
(
200
MeV)
nS
ð
n
1
Þ
P
transitions by many experiments, including in
high-statistics inclusive
[9
14]
and high-resolution con-
verted
[15,16]
photon spectra. The hard transition rates are
therefore less well known, particularly for the
J
¼
0
states,
which have large hadronic branching fractions. In particular,
the individual
J
¼
0
hard transitions have been observed
only by single experiments
[17
19]
and have yet to be
confirmed by others. The
Υ
ð
3
S
Þ
γχ
b
J
ð
1
P
Þ
;
χ
b
J
ð
1
P
Þ
γ
Υ
ð
1
S
Þ
transitions are also experimentally difficult to
measure because the soft and hard transition energies are
FIG. 1 (color online). Schematic representation of the twelve
E
1
channels in the four radiative cascades measured in this
analysis:
2
S
1
P
1
S
,
3
S
2
P
2
S
,
3
S
1
P
1
S
, and
3
S
2
P
1
S
. Each cascade terminates in the annihilation
Υ
ð
nS
Þ
μ
þ
μ
, not shown. The numbers give the masses
[8]
of the relevant bottomonium states in GeV
=c
2
. The first and
second transitions in each cascade (except the
3
S
1
P
1
S
)
are referred to in the text as
soft
and
hard
transitions,
respectively. Splittings in the photon spectra for these cascades
are due to the mass splittings in the intermediate states
χ
bJ
with
J
¼
0
, 1 or 2.
J. P. LEES
et al.
PHYSICAL REVIEW D
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112010-4
nearlythesame, andthusoverlap.Previousmeasurementsof
B
ð
Υ
ð
3
S
Þ
γχ
b
1
;
2
ð
1
P
ÞÞ
agree only marginally
[19,20]
.
Two methods have been used to disentangle the
P
-wave
spin states in the hard transitions: inclusive converted
photon searches, used in a recent
BABAR
analysis
[20]
;
and exclusive reconstruction of a two-photon cascade
S
P
S
with dileptonic decay of the terminal
Υ
[17
19,21
23]
. In the first method, excellent energy
resolution is achieved with a significant penalty in statistics.
In the second method, the hard photon transitions are only
indirectly measured, through their effect on the exclusive
process. Here, we follow the latter strategy in an analysis of
E
1
transitions between bottomonium states below
the open-flavor threshold in exclusive reconstruction of
μ
þ
μ
γγ
final states. We use a large-statistics sample
obtained by reconstructing the two photons in the cascade
with the EMC to measure
Υ
ð
2
S
Þ
γχ
bJ
ð
1
P
Þ
,
χ
bJ
ð
1
P
Þ
γ
Υ
ð
1
S
Þ
and
Υ
ð
3
S
Þ
γχ
bJ
ð
2
P
Þ
,
χ
bJ
ð
2
P
Þ
γ
Υ
ð
1
S;
2
S
Þ
decays. We employ a background-reduction technique,
new to
BABAR
analyses, that utilizes EMC timing informa-
tion. Furthermore, we reconstruct these same decay chains
with one converted and one calorimeter-identified photon as
a confirmation, and then extend this analysis to obtain a new
measurement of
Υ
ð
3
S
Þ
γχ
bJ
ð
1
P
Þ
,
χ
bJ
ð
1
P
Þ
γ
Υ
ð
1
S
Þ
.
To simplify the notation, we hereinafter refer to
the cascade
Υ
ð
2
S
Þ
γχ
bJ
ð
1
P
Þ
,
χ
bJ
ð
1
P
Þ
γ
Υ
ð
1
S
Þ
,
Υ
ð
1
S
Þ
μ
þ
μ
as
2
S
1
P
1
S
(and analogously for
other cascades) where the muonic decay of the final state is
implicit. Radiative photons are labeled based on the states
that they connect:
γ
2
S
1
P
and
γ
1
P
1
S
for the example
above. Unless noted otherwise all photon energies
E
γ
are in
the center-of-mass frame. The cascades measured in this
analysis are shown in Fig.
1
.
III. THE
BABAR
DETECTOR AND DATA SET
The
BABAR
detector is described elsewhere
[24]
, with
the techniques associated with photon conversions
described in Ref.
[20]
. Only relevant details regarding
the timing pipeline of the EMC are summarized here.
Energy deposited in one of the 6580 CsI(Tl) crystals
comprising the detector material of the EMC produces a
light pulse that is detected by a photodiode mounted to the
rear of the crystal. After amplification and digitization the
pulse is copied onto a circular buffer which is read out upon
arrival of a trigger signal. The energy-weighted mean of the
waveform within a window encompassing the expected
time of arrival of pulses is calculated and called the moment
time. This moment time is compared to the event time
the energy-weighted mean of all bins in the waveform
above a threshold energy
and the pulse is discarded if the
difference between the two times is sufficiently large. For
surviving waveforms, the moment time is bundled with the
crystal energy and called a
digi.
A collection of neigh-
boring digis constitutes a
cluster
which can be associated
with a neutral or charged particle candidate. The cluster
time is a weighted mean of the digi times for all digis
associated with a single cluster.
Particle candidates are called
in-time
if they are part of
an event that generates a trigger. The timing signature of an
EMC cluster associated with an in-time event should be
distinct from those for out-of-time events (primarily
beam
photons originating from interactions between
the beam with stray gas or beam-related equipment, which
are uncorrelated in time with events of physical interest).
However, crystal-to-crystal differences (such as the shaping
circuitry or crystal response properties) cause the quality of
the EMC timing information to be low, and consequently it
has been used only rarely to reject out-of-time backgrounds
from nonphysics sources. As a part of this analysis, we
perform a calibration and correction of the EMC timing
information. We present the results of an analysis of the
performance of the corrected timing data in Sec.
IVA
.
The data analyzed include
ð
121

1
Þ
million
Υ
ð
3
S
Þ
and
ð
98

1
Þ
million
Υ
ð
2
S
Þ
[25]
mesons produced by the PEP-II
asymmetric-energy
e
þ
e
collider, corresponding to inte-
grated luminosities of
27
.
9

0
.
2
fb
1
and
13
.
6

0
.
1
fb
1
,
respectively. Large Monte Carlo (MC) data sets, including
simulations of the signal and background processes, are
used for determining efficiency ratios and studying photon
line shape behavior. Event production and decays are
simulated using J
ETSET
7.4
[26]
and E
VT
G
EN
[27]
.We
use theoretically predicted helicity amplitudes
[28]
to model
the angular distribution for each simulated signal channel,
and we simulate the interactions of the final-state particles
with the detector materials with Geant4
[29]
.
IV. CALORIMETER-BASED ANALYSIS
A. Event selection and reconstruction
Candidate
mS
ð
m
1
Þ
P
nS
cascades, with
m>n
(that is, all cascades in Fig.
1
except
3
S
1
P
1
S
),
include
μ
þ
μ
γγ
final states in data obtained at the
Υ
ð
mS
Þ
resonance, with both photons reconstructed using the
EMC, and the four-particle invariant mass required to be
within
300
MeV
=c
2
of the nominal
Υ
ð
mS
Þ
mass. Photon
candidates are required to have a minimum laboratory-
frame energy of 30 MeV and a lateral moment
[30]
less
than 0.8. A least-squares kinematic fit of the final-state
particles under the signal cascade hypothesis is performed
with the collision energy and location of the interaction
point fixed. The dimuon mass is constrained to the
Υ
ð
nS
Þ
mass, and the
μ
þ
μ
γγ
invariant mass is constrained to the
Υ
ð
mS
Þ
mass, both taken from the Particle Data Group
(PDG)
[8]
. These constraints improve the soft photon
resolution and allow better rejection of background from
the decay
Υ
ð
mS
Þ
π
0
π
0
Υ
ð
nS
Þ
, in which four final-state
photons share the energy difference between the two
Υ
states, in contrast to the signal cascade which shares the
same energy between only two photons. At this stage of
reconstruction there are often many cascade candidates in
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...
PHYSICAL REVIEW D
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each event; the
χ
2
probability from the kinematic fit is used
to select the
best
candidate cascade in each event. The
signal yields are obtained from a fit to the spectrum of the soft
photon energy
E
mS
ð
m
1
Þ
P
in selected candidate cascades.
Based on MC simulation of the soft photon spectrum,
two significant background processes contribute:
π
0
π
0
(
Υ
ð
mS
Þ
π
0
π
0
Υ
ð
nS
Þ
;
Υ
ð
nS
Þ
μ
þ
μ
) and
μμ
ð
γ
Þ
(con-
tinuum
μ
þ
μ
production with initial- or final-state radiation
or, rarely,
Υ
ð
mS
Þ
μ
þ
μ
with QED bremsstrahlung
photons). Regardless of the physics process, beam sources
dominate the soft photon background.
To reject beam background we utilize the cluster timing
information of the EMC. This is a novel technique not used
in previous
BABAR
analyses. We define the EMC cluster
timing difference significance between two clusters 1 and 2
as
S
1
2
j
t
1
t
2
j
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
σ
2
1
þ
σ
2
2
p
, where
t
i
are the cluster times
with associated timing uncertainties
σ
i
. For background
rejection we require
S
soft-hard
<S
max
, where
S
max
can be
interpreted as the maximum allowable difference in stan-
dard deviations between the EMC timing of the soft and
hard signal photon candidates.
In conjunction with this analysis we have corrected
several large nonuniformities in the EMC timing and
calibrated the timing uncertainties; therefore characteriza-
tion of the accuracy and precision of the timing infor-
mation is required. To this end we use a proxy cascade
mode which provides a precise and independent analog
of the signal mode. Specifically, we reconstruct
Υ
ð
2
S
Þ
π
0
proxy
π
0
spare
Υ
ð
1
S
Þ
,
Υ
ð
1
S
Þ
μ
þ
μ
cascades with final-state
particles
γ
soft
proxy
γ
hard
proxy
γ
1
spare
γ
2
spare
μ
þ
μ
. The proxy
π
0
candi-
date,
π
0
proxy
, is reconstructed from the proxy soft photon,
γ
soft
proxy
, and the proxy hard photon,
γ
hard
proxy
, candidates, which
are required to pass the energy selections of the soft and
hard signal photons. To remove mislabeled cascades we
reject events where the invariant mass of any combination
of one proxy and one spare photon is in the
π
0
mass range
100
155
MeV
=c
2
. A plot of the invariant mass of the
π
0
proxy
candidates now includes only two contributions: a peak at
the nominal
π
0
mass corresponding to in-time photon pairs
and a continuous background corresponding to out-of-time
photon pairs, almost exclusively the result of
γ
soft
proxy
coming
from beam background. We then measure the effect of the
timing selection on in-time and out-of-time clusters by
extracting the yields of these two contributions from fits
over a range of
S
max
values. We observe that the out-of-time
rejection is nearly linear in
S
max
and the functional form of
the in-time efficiency is close to the ideal erf
ð
S
max
Þ
. With an
EMC timing selection of
S
max
¼
2
.
0
we observe a signal
efficiency of
0
.
92

0
.
02
and background efficiency of
0
.
41

0
.
06
in the proxy mode, and expect the same in the
signal mode.
To choose the
best
signal cascade candidate in an event
we first require that the two photon energies fall within the
windows 40
160 MeV for
3
S
2
P
, 160
280 MeV for
2
P
2
S
, 620
820 MeV for
2
P
1
S
,40
240 MeV for
2
S
1
P
or 300
480 MeV for
1
P
1
S
. Of these, only
cascades with a timing difference significance between
the two signal photon candidates below
2
.
0
σ
are retained:
S
soft-hard
<S
max
¼
2
.
0
(
3
.
0
σ
for
3
S
2
P
1
S
to com-
pensate for poorly known timing uncertainties for higher
photon energies). The best cascade candidate is further
required to have a cascade fit probability in excess of
10
5
,
rejecting 90% and 82% of the passing
π
0
π
0
and
μμ
ð
γ
Þ
events according to reconstructions on MC simulations of
those processes. The large majority of signal events lost
in this selection have anomalously low-energy photon
candidates which have deposited energy in the detector
material that is not collected by the calorimeter. Excluding
these events lowers the signal efficiency but improves our
ability to disentangle the overlapping signal peaks during
fitting. The highest-probability cascade candidate remain-
ing in each event is then chosen. Figure
2
demonstrates the
selections on reconstructed
2
S
1
P
1
S
cascades.
B. Fitting the photon energy spectra
We extract peak yield ratios and mean energy differences
from the
E
mS
ð
m
1
Þ
P
spectra using unbinned maximum
likelihood fits with three incoherent overlapping signal
components corresponding to the
J
¼
0
, 1 and 2 decay
channels and a smooth incoherent background. Simulated
signal, and
μμ
ð
γ
Þ
and
π
0
π
0
background MC collections are
subjected to the same reconstruction and selection criteria
as the data, scaled to expected cross sections, and combined
to constitute the
MC ensemble
which is representative of
the expected relevant data. Qualitative agreement between
the MC ensemble and data spectra is good, although the
FIG. 2 (color online). Scatter plot of reconstructed
2
S
1
P
1
S
events in the two selection variables
S
soft-hard
and cascade
kinematic fit probability for the calorimeter-based analysis. The
cluster of in-time and high-probability events in the lower right
corner is from the signal process, with a residue at lower
probabilities due to tail events. The lack of structure in the
scatter plot confirms the complementarity of these two selections.
Events with
S
soft-hard
>
2
.
0
or fit probability below
10
5
are
excluded, as shown by the white dashed lines.
J. P. LEES
et al.
PHYSICAL REVIEW D
90,
112010 (2014)
112010-6
MC line shapes deviate from the data line shapes enough
that fit solutions to the individual MC lines cannot be
imposed on the corresponding fits to the data.
A fit to an individual peak from a signal MC collection
requires the flexibility of a double-sided Crystal Ball
[31]
fitting function. This function has a Gaussian core of width
σ
and mean
μ
which transitions at points
α
1
and
α
2
to
power-law tails with powers
n
1
and
n
2
on the low- and
high-energy sides, respectively, with the requirement that
the function and its first derivative are continuous at the
transition points. The background spectrum of the MC
ensemble is described well by the sum of a decaying
exponential component with power
λ
and a linear compo-
nent with slope
a
1
. The simplest approach to fitting the
spectrum is to float both background parameters
λ
and
a
1
and float Gaussian means for the three signal peaks
μ
0
,
μ
1
and
μ
2
separately while sharing the floated signal shape
parameters
σ
,
α
1
,
α
2
,
n
1
and
n
2
between all three signal
peaks. This approach assumes that the line shape does not
vary in the limited photon energy range of this spectrum.
However, fits of this nature on the MC ensemble spectrum
perform poorly, indicating that line shape variation cannot
be ignored. Conversely, fits with all twenty signal and
background parameters floating independently perform
equally poorly; in particular, the
J
¼
0
peak tends to
converge to a width well above or below the detector
resolution. A more refined fitting strategy is required.
To obtain stable fits to the data spectrum, we allow the
parameters
σ
,
α
1
and
α
2
of the dominant
J
¼
1
peak to
float, and we fix the corresponding
J
¼
0
and
J
¼
2
parameters with a linear extrapolation from the
J
¼
1
values using slopes derived from fits to the MC signal
FIG. 3 (color online). (a) Fit to the soft photon energy
E
2
S
1
P
in the
2
S
1
P
1
S
cascade with individual signal (dot-dashed) and
background (dash) components for the calorimeter-based analysis. The targeted
χ
b
0
ð
1
P
Þ
signal corresponds to the small bump on the
right; the integral ratio and mean offset of the fit to this peak compared to the
J
¼
1
peak (center), are defined as
f
0
and
δ
0
, respectively.
Similarly,
f
2
and
δ
2
are the integral ratio and mean offset for the fit to the
J
¼
2
peak (left), also compared to the
J
¼
1
peak. (b) A
zoomed-in view of the
χ
b
0
ð
1
P
Þ
peak on the same energy scale.
BOTTOMONIUM SPECTROSCOPY AND RADIATIVE
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PHYSICAL REVIEW D
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spectra. The fit is insensitive to the power of the tails, so
n
1
and
n
2
are fixed to solutions from fits to signal MC. The
background parameters
λ
and
a
1
are fixed to MC solutions
but the ratio of background contributions floats, as does the
absolute background yield
N
bkg
. The signal component
functions are expressed in terms of the desired observables:
signal yield ratios
f
J
¼
N
J
=N
1
and peak mean offsets
δ
J
¼
μ
J
μ
1
, which both float in the fit, as well as the
J
¼
1
yield,
N
1
, and mean,
μ
1
. Figures
3
,
4
and
5
show the
results of the fits to the three data spectra.
C. Systematic studies
We measure branching-ratio products for cascades
involving
χ
b
J
normalized to the
χ
b
1
channel and denote
them
F
J=
1
. In this way we avoid the systematic uncer-
tainty associated with estimating absolute reconstruction
and selection efficiencies, which cancel in the ratio. In
terms of measured values, the exclusive branching ratio is
given by
F
J=
1
mS
P
ð
J
Þ
nS
¼
B
ð
mS
P
ð
J
ÞÞ
B
ð
P
ð
J
Þ
nS
Þ
B
ð
mS
P
ð
1
ÞÞ
B
ð
P
ð
1
Þ
nS
Þ
¼
f
J
ε
1
ε
J
;
ð
2
Þ
where
ε
J
is the signal efficiency of the
J
channel and the
measured yield ratio
f
J
has systematic corrections
applied. The branching fraction of the terminal
Υ
ð
nS
Þ
μ
þ
μ
decay appears in both the numerator and denom-
inator and thus cancels. We also measure the mass
splittings
Δ
M
J
1
, which are simply equal to the measured
peak energy differences

δ
J
with systematic corrections.
In this way we avoid the systematic uncertainties asso-
ciated with determining the absolute photon energies.
FIG. 4 (color online). (a) Fit to the soft photon energy
E
3
S
2
P
in the
3
S
2
P
2
S
cascade with individual signal (dot-dashed) and
background (dash) components for the calorimeter-based analysis. (b) A zoomed-in view of the
χ
b
0
ð
2
P
Þ
peak on the same energy scale.
Discussion of the significance of the
J
¼
0
peak is contained in Sec.
IV C
.
J. P. LEES
et al.
PHYSICAL REVIEW D
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112010 (2014)
112010-8
Systematic effects and uncertainties on the yield ratio
f
J
,
line energy differences
δ
J
, and efficiency ratio
ε
1
=
ε
J
are
discussed below.
Constraining the line shape parameters to fixed linear
slopes introduces unknown systematic biases in the
extracted yield and mean values, resulting in systematic
uncertainties. To measure these uncertainties, a collection
of 50,000 model spectra is generated that violates these
assumptions; each spectrum is fit with the same fitting
procedure as for the data spectrum. The behavior of the fits
to these generic model spectra constrains the uncertainty of
the fit to the data spectrum. The functions used to generate
the model spectra are taken from the fit to the data spectrum
with all parameters varying in a flat distribution within

3
σ
of their fitted values, with these exceptions: the tail power
parameters are varied in the range 5.0
100.0 and the
parameter slopes, taken from MC, are varied within

5
σ
of their nominal values. The three peaks are decoupled to
violate the single-slope fitting constraint.
The fitting procedure fails to converge for some of the
generated spectra. These spectra are evidently not suffi-
ciently similar to the data spectrum and can be discarded
without biasing the set of generated spectra. We further
purify the model spectrum collection by rejecting models
with fitted parameters outside

3
σ
of the data fit solution.
For the successful fits we define the pull for a parameter
X
(
N
or
μ
)as
ð
X
generated
X
fit
Þ
=
σ
X
, where
σ
X
is the parameter
uncertainty in the fit. We fit a Gaussian function to each
pull distribution for the surviving model fits and observe a
modest shift in central value and increase in width (see
Table
II
). We use this shift to correct the data fit parameter
values, and scale the parameter uncertainties by the width
of the pull distribution. In this way we have used the model
spectra to measure systematic uncertainties and biases
FIG. 5 (color online). (a) Fit to the soft photon energy
E
3
S
2
P
in the
3
S
2
P
1
S
cascade with individual signal (signal corresponds
to the small bump) and background (dash) components for the calorimeter-based analysis. (b) A zoomed-in view of the
χ
b
0
ð
2
P
Þ
peak on
the same energy scale. Discussion of the significance of the
J
¼
0
peak is contained in Sec.
IV C
.
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associated with the fitting procedure, and used these to
correct the data fit results.
Two considerations arise in interpreting these scaled
uncertainties. First, statistical and systematic sources of
uncertainty are admixed and cannot be disentangled.
Second, all of the uncertainties are necessarily over-
estimated. However, the overestimation of uncertainty is
smaller than the difference between scaled and unscaled
uncertainty, which is itself much less than one standard
deviation (see Table
II
). The model spectrum selection
procedure guarantees further that the overestimation is
limited, and in fact further tightening the selections does
not decrease the width of the pull distributions, indicating
convergence. We conclude that the overestimation of
uncertainties is negligible.
The absolute signal efficiencies are a combination of
unknown reconstruction and selection efficiencies with
attendant systematic uncertainties which cancel in the ratio.
The efficiency ratio in Eq.
(2)
deviates from unity due to
spin-dependent angular distributions in a detector with
nonisotropic acceptance. The signal MC collections sim-
ulate the model-independent angular distributions of the
decay products in the signal cascades for the three
1
P
spin
states
[28]
as well as the detector response. Uncertainties in
the ratio come from two sources: MC sample size and the
effect of the fit probability selection on the ratio. We
measure the ratio in signal MC and add in quadrature the
standard deviation of the ratio taken over a variety of fit
probability selections as an estimation of the efficiency
ratio uncertainty (see Table
I
).
V. CONVERTED PHOTON ANALYSIS
A. Event selection and reconstruction
In the conversion-based analysis the
μ
þ
μ
γγ
final state is
reconstructed by requiring one of the photons to be
identified in the EMC and the other to be reconstructed
after converting into an
e
þ
e
pair in detector material.
Although it shares the same underlying physics as the
calorimeter-based analysis, the presence of a displaced
vertex and lack of calorimeter timing information neces-
sitate some differences in approach.
We reconstruct the
Υ
ð
1
S;
2
S
Þ
final states with two
opposite-sign muons within
100
MeV
=c
2
of the relevant
Υ
ð
nS
Þ
mass, satisfying a vertex probability
χ
2
of greater
than 0.0001. The
χ
bJ
ð
mP
Þ
candidates are formed by
constraining the
Υ
ð
nS
Þ
to its nominal mass
[8]
and adding
a converted photon (as described in detail in Ref.
[20]
). The
initial
Υ
ð
2
S;
3
S
Þ
candidate is reconstructed by combining a
calorimeter-identified photon candidate with the
χ
bJ
ð
mP
Þ
candidate. This photon is required to have a minimum
laboratory-frame energy of 30 MeVand lateral moment less
than 0.8. The center-of-mass energy of the calorimeter
photon is required to be in the range
300
<E
γ
<
550
MeV
for the
3
S
1
P
1
S
decay chain, while for the other
transitions it must be within
E
γ
ð
low
Þ
40
<E
γ
<E
γ
ð
high
Þ
þ
40
MeV, where
E
γ
ð
low
Þ
and
E
γ
ð
high
Þ
represent the lowest and
highest energy transition for the intermediate
χ
bJ
ð
mP
Þ
triplet in question.
TABLE I. MC efficiency ratios for the calorimeter-based
analysis.
Cascade
J
ε
1
=
ε
J
2
S
1
P
1
S
0
1
.
062

0
.
009
2
1
.
013

0
.
004
3
S
2
P
2
S
0
1
.
059

0
.
005
2
0
.
988

0
.
003
3
S
2
P
1
S
0
1
.
059

0
.
009
2
1
.
027

0
.
009
TABLE II. Results of systematic studies on 50,000 model spectra for each of the three signal channels in the calorimeter-based
analysis, with parameter values in units of
10
2
for
f
J
and MeV for
δ
J
. For the
3
S
2
P
2
S
and
3
S
2
P
1
S
analyses negative-
and zero-yield models for the
J
¼
0
peaks are inconsistent with the fit results with a significance of
5
.
1
σ
and
2
.
1
σ
, respectively. The
efficiency ratio corrections have not been applied.
Cascade
Parameter
Fit value
Pull shift
ð
σ
Þ
Pull width
ð
σ
Þ
Corrected
2
S
1
P
1
Sf
0
2
.
83

0
.
31
þ
0
.
82
1.12
3
.
09

0
.
35
f
2
54
.
8

1
.
3
þ
0
.
078
1.15
54
.
9

1
.
5
δ
0
32
.
00

0
.
91
þ
0
.
54
1.03
32
.
5

0
.
93
δ
2
19
.
00

0
.
22
0
.
036
1.06
19
.
01

0
.
24
3
S
2
P
2
Sf
0
1
.
66

0
.
39
þ
1
.
5
1.13
2
.
25

0
.
44
f
2
47
.
7

1
.
3
0
.
47
1.29
47
.
0

1
.
7
δ
0
22
.
60

0
.
20
þ
0
.
54
1.03
23
.
7

2
.
1
δ
2
13
.
30

0
.
22
0
.
036
1.06
13
.
3

0
.
24
3
S
2
P
1
Sf
0
1
.
05

0
.
52
þ
1
.
1
1.44
1
.
62

0
.
75
f
2
66
.
3

2
.
3
0
.
63
1.27
64
.
9

2
.
9
δ
0
21
.
60

0
.
30
þ
0
.
80
1.13
24
.
0

3
.
4
δ
2
12
.
80

0
.
22
þ
0
.
032
1.03
12
.
79

0
.
23
J. P. LEES
et al.
PHYSICAL REVIEW D
90,
112010 (2014)
112010-10
Because this reconstruction lacks a sufficient second
EMC timing measurement to take advantage of the tim-
ing-based selection described in Sec.
IVA
,
π
0
π
0
and
μ
þ
μ
ð
γ
Þ
backgrounds, which are also the dominant back-
ground sources for this analysis technique, are reduced
via more conventional means. The number of charged-
particle tracks in the event, as identified by the
BABAR
drift
chamber and silicon vertex tracker
[24]
, is required to be
equal to four, incidentally removing all events used in the
calorimeter-based analysis and resulting in mutually exclu-
sive data sets. This selection also makes this data set
independent from the previous inclusive converted photon
analysis
[20]
, with the only commonality being shared
uncertainties on the luminosity measurement and the con-
version efficiency (described in Sec.
VC
). Events with an
initial
Υ
ð
nS
Þ
mass,
M
Υ
ð
nS
Þ
, in the range
10
.
285
<M
Υ
ð
3
S
Þ
<
10
.
395
GeV
=c
2
or
M
Υ
ð
2
S
Þð
PDG
Þ

40
MeV
=c
2
are retained.
A requirement that the ratio of the second and zeroth Fox-
Wolfram moments
[32]
of each event,
R
2
, be less than 0.95 is
also applied. These selection criteria were determined by
maximizing the ratio of expected
3
S
1
P
1
S
signal
events to the square root of the sum of the expected number
of signal and background events, as determined by MC
simulation.
We calculate the signal efficiency by counting the number
of MC signal events remaining after reconstruction and the
application of event selection criteria. The efficiency is
highly dependent upon the conversion photon energy (as
seen in Ref.
[20]
), and ranges from 0.1% at
E
γ
200
MeV
to 0.8% at
E
γ
800
MeV. This drop in efficiency at lower
energies makes a measurement of the soft photon transitions
impractical with converted photons, which is why this
analysis is restricted to conversion of the hard photon.
Once the full
Υ
ð
nS
Þ
reconstruction is considered, the overall
efficiency ranges from 0.07
0.90% depending on the decay
chain. While the efficiency for the reconstruction with a
converted photon is low, this technique leads to a large
improvement in energy resolution from approximately 15 to
2.5 MeV. This is necessary in order to disentangle the
transition energy of the hard photon from the overlapping
signals for the
3
S
1
P
1
S
transitions. However, despite
this improvement in energy resolution, the mass splittings
are not measured with this technique because of line shape
complications described in the following section.
B. Fitting
We use an unbinned maximum likelihood fit to the hard
converted photon spectrum to extract the total number of
events for each signal cascade. In the case of
3
S
1
P
1
S
transitions, the first and second transitions overlap
in energy and either photon may be reconstructed as
the converted one. Therefore both components are fit
simultaneously. Because we analyze the photon energy
in the center-of-mass frame of the initial
Υ
ð
nS
Þ
system,
the photon spectra from subsequent boosted decays
(e.g.
χ
bJ
ð
mP
Þ
γ
Υ
ð
nS
Þ
) are affected by Doppler broad-
ening due to the motion of the parent state in the center-of-
mass frame. Due to this effect, variation of efficiency over
the photon angular distribution, and a rapidly changing
converted photon reconstruction efficiency, the signal line
shapes are most effectively modeled using a kernel esti-
mation of the high statistics MC samples. This is most
relevant for the
3
S
1
P
1
S
transitions, which are the
focus of this part of the analysis, and for which the signal
line shape for the
1
P
1
S
transition in
3
S
1
P
1
S
is
so significantly Doppler-broadened that its shape can be
qualitatively described by the convolution of a step-
function with a Crystal Ball function. Alternative param-
eterizations using variations of the Crystal Ball function as
described in Sec.
IV B
, give a good description of the other
transition data, but are reserved for evaluation of systematic
uncertainties in this analysis.
The MC simulation indicates the presence of a smooth
π
0
π
0
and
μ
þ
μ
ð
γ
Þ
background below the signal peaks.
This primarily affects the
3
S
2
P
ð
1
S;
2
S
Þ
cascades,
but is also present for
2
S
1
P
1
S
. The background is
modeled by a Gaussian with a large width and a mean
above the highest transition energy for each triplet. For
3
S
1
P
1
S
, both photons are hard and therefore the
background is expected to be much smaller, and to have a
flatter distribution. It is modeled with a linear function.
To allow for potential line shape differences between the
simulation and data, energy scale and resolution effects are
considered both by allowing the individual signal peak
positions to shift and by applying a variable Gaussian
smearing to the line shape. These effects are determined
from the fit to the higher-statistics
J
¼
1
and
J
¼
2
peaks in
the
3
S
2
P
1
S;
2
S
and
2
S
1
P
1
S
analysis energy
regions, and the yield-weighted average for the energy
scale shift and resolution smearing are applied to the
3
S
1
P
1
S
fit. The applied peak shift correction is
0
.
1
MeV, with maximal values ranging from
1
.
5
to
0.9 MeV, and the required energy resolution smearing is
less than 0.2 MeV. These energy scale values are consistent
with those found in the previous, higher-statistics,
BABAR
inclusive converted photon analysis
[20]
, and the resolution
smearing is small compared to the predicted resolution,
which is of the order of a few MeV.
Figures
6
,
7
,
8
, and
9
show the results of the fits to the data.
Compared to the calorimeter-based analysis, the statistical
uncertainty in the converted-photon analysis is large and the
systematic uncertainties do not readily cancel. Therefore, we
quote the full product of branching fractions without
normalization. The following section outlines the systematic
uncertainties associated with these measurements.
C. Systematic Uncertainties
The uncertainty on the luminosity is taken from the
standard
BABAR
determination
[25]
, which amounts to
0.58% (0.68%) for
Υ
ð
3
S
Þð
Υ
ð
2
S
ÞÞ
. The derivation of
BOTTOMONIUM SPECTROSCOPY AND RADIATIVE
...
PHYSICAL REVIEW D
90,
112010 (2014)
112010-11
branching fractions relies on efficiencies derived from MC
simulation. There are several corrections (e.g. related to
particle identification, reconstruction efficiency, etc.), with
accompanying uncertainties, necessary to bring simulation
and data into agreement. These are determined separately
from this analysis, and are employed generally by all
BABAR
analyses. For muon identification, decay chain-
dependent correction factors were estimated for each
measurement, and found to be no larger than 1.3%, with
fractional uncertainties of up to 3.3%. An efficiency
uncertainty of 1.8% is used for the calorimeter photon,
and 3.3% for the converted photon with a correction of
3.8% (as determined in Ref.
[20]
). Uncertainty due to
applying the energy scale shift and resolution smearing to
the
3
S
1
P
1
S
cascades is estimated by varying the
shift and smearing over the full range of values measured
by the other decay modes. The largest deviations from
the nominal fit yields are taken as the uncertainty. For the
J
¼
2
ð
1
Þ
signal, the values are
þ
2
.
0
1
.
7
%
ð
þ
8
.
7
11
.
5
%
Þ
.
The largest source of systematic uncertainty comes from
the line shape used in the fit. To account for the possibility
that the MC simulation does not represent the data, the data
FIG. 6 (color online). Fit to the photon energy
E
1
P
1
S
in the
2
S
1
P
1
S
cascade for the conversions-based analysis. The data are
represented by points, the total fit by a solid curve, the background component with a dashed curve, and the individual signal
components of the fit by peaking dot-dashed curves in progressively darker shades for
J
¼
0
;
1
;
2
. Clear evidence is seen for the
J
¼
2
and
J
¼
1
signals.
FIG. 7 (color online). Fit to the photon energy
E
3
S
1
S
in the
3
S
1
P
1
S
cascade for the conversions-based analysis. The data are
represented by points, the total fit by a solid curve, the background component with a dotted curve, and the individual signal components
of the fit by peaking dot-dashed curves for
J
¼
2
(darker shade) and
J
¼
1
(lighter shade). There is clear evidence for the
J
¼
2
transition, but the
J
¼
1
signal is not statistically significant.
J. P. LEES
et al.
PHYSICAL REVIEW D
90,
112010 (2014)
112010-12