arXiv:1410.3902v2 [hep-ex] 16 Oct 2014
B
A
B
AR
-PUB-14/005
SLAC-PUB-16123
Bottomonium spectroscopy and radiative transitions invol
ving the
χ
bJ
(
1
P,
2
P
)
states
at
B
A
B
AR
J. P. Lees, V. Poireau, and V. Tisserand
Laboratoire d’Annecy-le-Vieux de Physique des Particules
(LAPP),
Universit ́e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vie
ux, France
E. Grauges
Universitat de Barcelona, Facultat de Fisica, Departament
ECM, E-08028 Barcelona, Spain
A. Palano
ab
INFN Sezione di Bari
a
; Dipartimento di Fisica, Universit`a di Bari
b
, I-70126 Bari, Italy
G. Eigen and B. Stugu
University of Bergen, Institute of Physics, N-5007 Bergen,
Norway
D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, M. J. Lee, and G. Lyn
ch
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, California 94720, USA
H. Koch and T. Schroeder
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. So
University of British Columbia, Vancouver, British Columb
ia, Canada V6T 1Z1
A. Khan
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kin
gdom
V. E. Blinov
abc
, A. R. Buzykaev
a
, V. P. Druzhinin
ab
, V. B. Golubev
ab
, E. A. Kravchenko
ab
,
A. P. Onuchin
abc
, S. I. Serednyakov
ab
, Yu. I. Skovpen
ab
, E. P. Solodov
ab
, and K. Yu. Todyshev
ab
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
A. J. Lankford and M. Mandelkern
University of California at Irvine, Irvine, California 926
97, USA
B. Dey, J. W. Gary, and O. Long
University of California at Riverside, Riverside, Califor
nia 92521, USA
C. Campagnari, M. Franco Sevilla, T. M. Hong, D. Kovalskyi, J. D. Rich
man, and C. A. West
University of California at Santa Barbara, Santa Barbara, C
alifornia 93106, USA
A. M. Eisner, W. S. Lockman, W. Panduro Vazquez, B. A. Schumm, a
nd A. Seiden
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, California 95064, USA
D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin,
T. S. Miyashita, P. Ongmongkolkul, F. C. Porter, and M. Roehrken
California Institute of Technology, Pasadena, California
91125, USA
R. Andreassen, Z. Huard, B. T. Meadows, B. G. Pushpawela, M. D.
Sokoloff, and L. Sun
University of Cincinnati, Cincinnati, Ohio 45221, USA
P. C. Bloom, W. T. Ford, A. Gaz, J. G. Smith, and S. R. Wagner
University of Colorado, Boulder, Colorado 80309, USA
R. Ayad
∗
and W. H. Toki
Colorado State University, Fort Collins, Colorado 80523, U
SA
B. Spaan
Technische Universit ̈at Dortmund, Fakult ̈at Physik, D-44
221 Dortmund, Germany
D. Bernard and M. Verderi
Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS
/IN2P3, F-91128 Palaiseau, France
S. Playfer
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
D. Bettoni
a
, C. Bozzi
a
, R. Calabrese
ab
, G. Cibinetto
ab
, E. Fioravanti
ab
,
I. Garzia
ab
, E. Luppi
ab
, L. Piemontese
a
, and V. Santoro
a
INFN Sezione di Ferrara
a
; Dipartimento di Fisica e Scienze della Terra, Universit`a
di Ferrara
b
, I-44122 Ferrara, Italy
A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Martellotti,
P. Patteri, I. M. Peruzzi,
†
M. Piccolo, M. Rama, and A. Zallo
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, I
taly
R. Contri
ab
, M. Lo Vetere
ab
, M. R. Monge
ab
, S. Passaggio
a
, C. Patrignani
ab
, and E. Robutti
a
INFN Sezione di Genova
a
; Dipartimento di Fisica, Universit`a di Genova
b
, I-16146 Genova, Italy
B. Bhuyan and V. Prasad
Indian Institute of Technology Guwahati, Guwahati, Assam,
781 039, India
A. Adametz and U. Uwer
Universit ̈at Heidelberg, Physikalisches Institut, D-691
20 Heidelberg, Germany
H. M. Lacker
Humboldt-Universit ̈at zu Berlin, Institut f ̈ur Physik, D-
12489 Berlin, Germany
P. D. Dauncey
Imperial College London, London, SW7 2AZ, United Kingdom
U. Mallik
University of Iowa, Iowa City, Iowa 52242, USA
C. Chen, J. Cochran, and S. Prell
Iowa State University, Ames, Iowa 50011-3160, USA
H. Ahmed
Physics Department, Jazan University, Jazan 22822, Kingdo
m of Saudia Arabia
A. V. Gritsan
Johns Hopkins University, Baltimore, Maryland 21218, USA
N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder,
A. M. Lutz, B. Malaescu,
‡
P. Roudeau, A. Stocchi, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, IN2P3/CNRS et
Universit ́e Paris-Sud 11,
Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France
D. J. Lange and D. M. Wright
Lawrence Livermore National Laboratory, Livermore, Calif
ornia 94550, USA
J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. P
ayne, and C. Touramanis
2
University of Liverpool, Liverpool L69 7ZE, United Kingdom
A. J. Bevan, F. Di Lodovico, and R. Sacco
Queen Mary, University of London, London, E1 4NS, United Kin
gdom
G. Cowan
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
J. Bougher, D. N. Brown, and C. L. Davis
University of Louisville, Louisville, Kentucky 40292, USA
A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, and K.
R. Schubert
Johannes Gutenberg-Universit ̈at Mainz, Institut f ̈ur Ker
nphysik, D-55099 Mainz, Germany
R. J. Barlow
§
and G. D. Lafferty
University of Manchester, Manchester M13 9PL, United Kingd
om
R. Cenci, B. Hamilton, A. Jawahery, and D. A. Roberts
University of Maryland, College Park, Maryland 20742, USA
R. Cowan and G. Sciolla
Massachusetts Institute of Technology, Laboratory for Nuc
lear Science, Cambridge, Massachusetts 02139, USA
R. Cheaib, P. M. Patel,
¶
and S. H. Robertson
McGill University, Montr ́eal, Qu ́ebec, Canada H3A 2T8
N. Neri
a
and F. Palombo
ab
INFN Sezione di Milano
a
; Dipartimento di Fisica, Universit`a di Milano
b
, I-20133 Milano, Italy
L. Cremaldi, R. Godang,
∗∗
P. Sonnek, and D. J. Summers
University of Mississippi, University, Mississippi 38677
, USA
M. Simard and P. Taras
Universit ́e de Montr ́eal, Physique des Particules, Montr ́
eal, Qu ́ebec, Canada H3C 3J7
G. De Nardo
ab
, G. Onorato
ab
, and C. Sciacca
ab
INFN Sezione di Napoli
a
; Dipartimento di Scienze Fisiche,
Universit`a di Napoli Federico II
b
, I-80126 Napoli, Italy
M. Martinelli and G. Raven
NIKHEF, National Institute for Nuclear Physics and High Ene
rgy Physics, NL-1009 DB Amsterdam, The Netherlands
C. P. Jessop and J. M. LoSecco
University of Notre Dame, Notre Dame, Indiana 46556, USA
K. Honscheid and R. Kass
Ohio State University, Columbus, Ohio 43210, USA
E. Feltresi
ab
, M. Margoni
ab
, M. Morandin
a
, M. Posocco
a
, M. Rotondo
a
, G. Simi
ab
, F. Simonetto
ab
, and R. Stroili
ab
INFN Sezione di Padova
a
; Dipartimento di Fisica, Universit`a di Padova
b
, I-35131 Padova, Italy
S. Akar, E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand,
G. Calderini, J. Chauveau, Ph. Leruste, G. Marchiori, and J. Ocariz
Laboratoire de Physique Nucl ́eaire et de Hautes Energies,
IN2P3/CNRS, Universit ́e Pierre et Marie Curie-Paris6,
Universit ́e Denis Diderot-Paris7, F-75252 Paris, France
M. Biasini
ab
, E. Manoni
a
, S. Pacetti
ab
, and A. Rossi
a
3
INFN Sezione di Perugia
a
; Dipartimento di Fisica, Universit`a di Perugia
b
, I-06123 Perugia, Italy
C. Angelini
ab
, G. Batignani
ab
, S. Bettarini
ab
, M. Carpinelli
ab
,
††
G. Casarosa
ab
, A. Cervelli
ab
, M. Chrzaszcz
a
,
F. Forti
ab
, M. A. Giorgi
ab
, A. Lusiani
ac
, B. Oberhof
ab
, E. Paoloni
ab
, A. Perez
a
, G. Rizzo
ab
, and J. J. Walsh
a
INFN Sezione di Pisa
a
; Dipartimento di Fisica, Universit`a di Pisa
b
; Scuola Normale Superiore di Pisa
c
, I-56127 Pisa, Italy
D. Lopes Pegna, J. Olsen, and A. J. S. Smith
Princeton University, Princeton, New Jersey 08544, USA
R. Faccini
ab
, F. Ferrarotto
a
, F. Ferroni
ab
, M. Gaspero
ab
, L. Li Gioi
a
, A. Pilloni
ab
, and G. Piredda
a
INFN Sezione di Roma
a
; Dipartimento di Fisica,
Universit`a di Roma La Sapienza
b
, I-00185 Roma, Italy
C. B ̈unger, S. Dittrich, O. Gr ̈unberg, M. Hess, T. Leddig, C. Voß
, and R. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
T. Adye, E. O. Olaiya, and F. F. Wilson
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
S. Emery and G. Vasseur
CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, F
rance
F. Anulli,
‡‡
D. Aston, D. J. Bard, C. Cartaro, M. R. Convery, J. Dorfan, G. P
. Dubois-Felsmann,
W. Dunwoodie, M. Ebert, R. C. Field, B. G. Fulsom, M. T. Graham, C. H
ast, W. R. Innes, P. Kim,
D. W. G. S. Leith, P. Lewis, D. Lindemann, S. Luitz, V. Luth, H. L. Ly
nch, D. B. MacFarlane,
D. R. Muller, H. Neal, M. Perl, T. Pulliam, B. N. Ratcliff, A. Roodman, A. A
. Salnikov,
R. H. Schindler, A. Snyder, D. Su, M. K. Sullivan, J. Va’vra, W. J. Wisn
iewski, and H. W. Wulsin
SLAC National Accelerator Laboratory, Stanford, Californ
ia 94309 USA
M. V. Purohit, R. M. White,
§§
and J. R. Wilson
University of South Carolina, Columbia, South Carolina 292
08, USA
A. Randle-Conde and S. J. Sekula
Southern Methodist University, Dallas, Texas 75275, USA
M. Bellis, P. R. Burchat, and E. M. T. Puccio
Stanford University, Stanford, California 94305-4060, US
A
M. S. Alam and J. A. Ernst
State University of New York, Albany, New York 12222, USA
R. Gorodeisky, N. Guttman, D. R. Peimer, and A. Soffer
Tel Aviv University, School of Physics and Astronomy, Tel Av
iv, 69978, Israel
S. M. Spanier
University of Tennessee, Knoxville, Tennessee 37996, USA
J. L. Ritchie, A. M. Ruland, R. F. Schwitters, and B. C. Wray
University of Texas at Austin, Austin, Texas 78712, USA
J. M. Izen and X. C. Lou
University of Texas at Dallas, Richardson, Texas 75083, USA
F. Bianchi
ab
, F. De Mori
ab
, A. Filippi
a
, and D. Gamba
ab
INFN Sezione di Torino
a
; Dipartimento di Fisica, Universit`a di Torino
b
, I-10125 Torino, Italy
L. Lanceri
ab
and L. Vitale
ab
INFN Sezione di Trieste
a
; Dipartimento di Fisica, Universit`a di Trieste
b
, I-34127 Trieste, Italy
4
F. Martinez-Vidal, A. Oyanguren, and P. Villanueva-Perez
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spa
in
J. Albert, Sw. Banerjee, A. Beaulieu, F. U. Bernlochner, H. H. F. C
hoi, G. J. King, R. Kowalewski,
M. J. Lewczuk, T. Lueck, I. M. Nugent, J. M. Roney, R. J. Sobie, a
nd N. Tasneem
University of Victoria, Victoria, British Columbia, Canad
a V8W 3P6
T. J. Gershon, P. F. Harrison, and T. E. Latham
Department of Physics, University of Warwick, Coventry CV4
7AL, United Kingdom
H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu
University of Wisconsin, Madison, Wisconsin 53706, USA
We use (121
±
1) million
Υ
(3
S
) and (98
±
1) million
Υ
(2
S
) mesons recorded by the
B
A
B
AR
detec-
tor at the PEP-II
e
+
e
−
collider at SLAC to perform a study of radiative transitions
involving the
χ
b
J
(1
P,
2
P
) states in exclusive decays with
μ
+
μ
−
γγ
final states. We reconstruct twelve channels in
four cascades using two complementary methods. In the first w
e identify both signal photon candi-
dates in the Electromagnetic Calorimeter (EMC), employ a ca
lorimeter timing-based technique to
reduce backgrounds, and determine branching-ratio produc
ts and fine mass splittings. These results
include the best observational significance yet for the
χ
b
0
(2
P
)
→
γΥ
(2
S
) and
χ
b
0
(1
P
)
→
γΥ
(1
S
)
transitions. In the second method, we identify one photon ca
ndidate in the EMC and one which
has converted into an
e
+
e
−
pair due to interaction with detector material, and we measu
re absolute
product branching fractions. This method is particularly u
seful for measuring
Υ
(3
S
)
→
γχ
b
1
,
2
(1
P
)
decays. Additionally, we provide the most up-to-date deriv
ed branching fractions, matrix elements
and mass splittings for
χ
b
transitions in the bottomonium system. Using a new techniqu
e, we also
measure the two lowest-order spin-dependent coefficients in
the nonrelativistic QCD Hamiltonian.
PACS numbers: 13.20.Gd, 14.40.Pq, 14.65.Fy
I. INTRODUCTION
The strongly bound
b
b
meson system – bottomonium
– exhibits a rich positronium-like structure that is a lab-
oratory for verifying perturbative and nonperturbative
QCD calculations [1]. Potential models and lattice cal-
culations provide good descriptions of the mass structure
and radiative transitions below the open-flavor threshold.
Precision spectroscopy probes spin-dependent and rela-
tivistic effects. Quark-antiquark potential formulations
have been successful at describing the bottomonium sys-
tem phenomenologically [1]. These potentials are gen-
erally perturbative in the short range in a Coulomb-like
single-gluon exchange, and transition to a linear nonper-
turbative confinement term at larger inter-quark sepa-
ration. The various observed bottomonium states span
∗
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 Ener
gies,
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
‡‡
Also at: INFN Sezione di Roma, I-00185 Roma, Italy
§§
Now at: Universidad T ́ecnica Federico Santa Maria, 2390123
Val-
paraiso, Chile
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 transi-
tions couple the
S
-wave
Υ
(
nS
) states produced in
e
+
e
−
collisions to the spin-one
P
-wave
χ
b
J
(
mP
) states; sup-
pressed
M
1 transitions are required to reach the spin-
singlet states such as the ground-state
η
b
(1
S
).
The partial width for an
E
1 transition from initial state
i
to final state
f
is calculated in effective theories us-
ing [2]:
Γ
i
→
f
=
4
3
e
2
b
αC
if
(2
J
f
+ 1)
E
3
γ
|h
n
f
L
f
|
r
|
n
i
L
i
i|
2
,
(1)
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 an-
gular momentum quantum numbers, respectively. Mea-
surements of
E
1 transition rates directly probe potential-
model calculations of the matrix elements and inform rel-
ativistic corrections.
Nonrelativistic QCD (NRQCD) calculations on the lat-
tice have been used with success to describe the bottomo-
nium mass spectrum in the nonperturbative regime [3–7],
5
including splittings in the spin-triplet
P
-wave states due
to spin-orbit and tensor interactions. Experimental split-
ting 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 tran-
sitions involving the
χ
bJ
(2
P
) and
χ
bJ
(1
P
) spin triplets,
as displayed in Fig. 1. We also provide relevant matrix
elements and NRQCD coefficients for use in relativis-
tic corrections and lattice calculations. These measure-
ments are performed using two different strategies: in the
first, we reconstruct the transition photons using only the
B
A
B
AR
Electromagnetic Calorimeter (EMC); in the sec-
ond, we consider a complementary set of such transitions
in which one of the photons has converted into an
e
+
e
−
pair within detector material.
Following an introduction of the analysis strategy in
Sec. II, we describe relevant
B
A
B
AR
detector and dataset
details in Sec. III. The event reconstruction and selec-
tion, energy spectrum fitting, and the corresponding
uncertainties for the calorimeter-based analysis are de-
scribed in Sec. IV. Sec. 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
splittings of the
P
-wave bottomonium states are not re-
solvable for the “hard” (
>
∼
200 MeV)
P
→
S
transitions
but have been resolved successfully in “soft” (
<
∼
200 MeV)
nS
→
(
n
−
1)
P
transitions by many experiments, includ-
ing in high-statistics inclusive [8–13] and high-resolution
converted [14, 15] photon spectra. The hard transition
rates are therefore less well-known, particularly for the
J
= 0 states, which have large hadronic branching frac-
tions. In particular, the individual
J
= 0 hard transitions
have been observed only by single experiments [16–18]
and have yet to be confirmed by others. The
Υ
(3
S
)
→
γχ
b
J
(1
P
)
, χ
b
J
(1
P
)
→
γΥ
(1
S
) transitions are also exper-
imentally difficult to measure because the soft and hard
transition energies are nearly the same, and thus overlap.
Previous measurements of
B
(
Υ
(3
S
)
→
γχ
b
1
,
2
(1
P
)) agree
only marginally [18, 19].
Two methods have been used to disentangle the
P
-
wave spin states in the hard transitions: inclusive con-
verted photon searches, used in a recent
B
A
B
AR
analy-
sis [19]; and exclusive reconstruction of a two-photon
cascade
S
→
P
→
S
with dileptonic decay of the ter-
minal
Υ
[16–18, 20–22]. 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 lat-
ter strategy in an analysis of
E
1 transitions between
Υ
(3S)
Υ
(2S)
Υ
(1S)
3S
2P
2S
2S
1P
1S
3S
2P
1S
3S
1P
1S
10.023
10.023
9.460
10.355
9.859
9.893
χ
bJ
(1P)
χ
bJ
(1P)
10.232
10.259
10.255
10.232
10.259
10.255
9.912
χ
bJ
(2P)
χ
bJ
(2P)
FIG. 1: Schematic representation of the twelve
E
1 chan-
nels in the four radiative cascades measured in this analy-
sis: 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 anni-
hilation
Υ
(
nS
)
→
μ
+
μ
−
, not shown. The numbers give the
masses [23] 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 photo
n
spectra for these cascades are due to the mass splittings in
the intermediate states
χ
bJ
with
J
= 0, 1 or 2.
bottomonium states below the open-flavor threshold in
exclusive reconstruction of
μ
+
μ
−
γγ
final states. We
use a large-statistics sample obtained by reconstruct-
ing the two photons in the cascade with the EMC to
measure
Υ
(2
S
)
→
γχ
bJ
(1
P
),
χ
bJ
(1
P
)
→
γΥ
(1
S
) and
Υ
(3
S
)
→
γχ
bJ
(2
P
),
χ
bJ
(2
P
)
→
γΥ
(1
S,
2
S
) decays. We
employ a background-reduction technique, new to
B
A
B
AR
analyses, that utilizes EMC timing information. Further-
more, we reconstruct these same decay chains with one
converted and one calorimeter-identified photon as a con-
firmation, and then extend this analysis to obtain a new
measurement of
Υ
(3
S
)
→
γχ
bJ
(1
P
),
χ
bJ
(1
P
)
→
γΥ
(1
S
).
To simplify the notation, we hereinafter refer to
the cascade
Υ
(2
S
)
→
γχ
bJ
(1
P
),
χ
bJ
(1
P
)
→
γΥ
(1
S
),
Υ
(1
S
)
→
μ
+
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 ener-
6
gies
E
γ
are in the center-of-mass frame. The cascades
measured in this analysis are shown in Fig. 1.
III. THE
B
A
B
AR
DETECTOR AND DATASET
The
B
A
B
AR
detector is described elsewhere [24], with
the techniques associated with photon conversions de-
scribed in Ref. [19]. 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 digitiza-
tion 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 suffi-
ciently large. For surviving waveforms, the moment time
is bundled with the crystal energy and called a “digi”.
A collection of neighboring digis constitutes a “cluster”
which can be associated with a neutral or charged parti-
cle 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 signa-
ture of an EMC cluster associated with an in-time event
should be distinct from those for out-of-time events (pri-
marily “beam” photons originating from interactions be-
tween the beam with stray gas or beam-related equip-
ment, which are uncorrelated in time with events of
physical interest). However, crystal-to-crystal differences
(such as the shaping circuitry or crystal response proper-
ties) 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 non-physics 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 cor-
rected timing data in Sec. IV A.
The data analyzed include (121
±
1) million
Υ
(3
S
) and
(98
±
1) million
Υ
(2
S
) [25] mesons produced by the PEP-
II asymmetric-energy
e
+
e
−
collider, corresponding to in-
tegrated luminosities of 27
.
9
±
0
.
2fb
−
1
and 13
.
6
±
0
.
1fb
−
1
,
respectively. Large Monte Carlo (MC) datasets, includ-
ing simulations of the signal and background processes,
are used for determining efficiency ratios and studying
photon line shape behavior. Event production and de-
cays are simulated using
Jetset7.4
[26] and
EvtGen
[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
→
(
m
−
1)
P
→
nS
cascades, with
m > n
(that is, all cascades in Fig. 1 except 3
S
→
1
P
→
1
S
), include
μ
+
μ
−
γγ
final states in data obtained at the
Υ
(
mS
) resonance, with both photons reconstructed us-
ing the EMC, and the four-particle invariant mass re-
quired to be within 300 MeV
/c
2
of the nominal
Υ
(
mS
)
mass. Photon candidates are required to have a min-
imum 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 hy-
pothesis is performed with the collision energy and loca-
tion of the interaction point fixed. The dimuon mass is
constrained to the
Υ
(
nS
) mass, and the
μ
+
μ
−
γγ
invari-
ant mass is constrained to the
Υ
(
mS
) mass, both taken
from the Particle Data Group [23]. These constraints im-
prove the soft photon resolution and allow better rejec-
tion of background from the decay
Υ
(
mS
)
→
π
0
π
0
Υ
(
nS
),
in which four final-state photons share the energy differ-
ence 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 each event; the
χ
2
proba-
bility 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
→
(
m
−
1)
P
in selected candidate cascades.
Based on MC simulation of the soft photon spec-
trum, two significant background processes contribute:
“
π
0
π
0
” (
Υ
(
mS
)
→
π
0
π
0
Υ
(
nS
);
Υ
(
nS
)
→
μ
+
μ
−
) and
“
μμ
(
γ
)” (continuum
μ
+
μ
−
production with initial- or
final-state radiation or, rarely,
Υ
(
mS
)
→
μ
+
μ
−
with
QED bremsstrahlung photons). Regardless of the physics
process, beam sources dominate the soft photon back-
ground.
To reject beam background we utilize the cluster tim-
ing information of the EMC. This is a novel technique not
used in previous
B
A
B
AR
analyses. We define the EMC
cluster timing difference significance between two clus-
ters 1 and 2 as
S
1
−
2
≡ |
t
1
−
t
2
|
/
√
σ
2
1
+
σ
2
2
, 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 allow-
able difference in standard 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 cal-
ibrated 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
(2
S
)
→
π
0
proxy
π
0
spare
Υ
(1
S
),
Υ
(1
S
)
→
μ
+
μ
−
cascades with final-
state particles
γ
soft
proxy
γ
hard
proxy
γ
1
spare
γ
2
spare
μ
+
μ
−
. The proxy
7
(signal fit probability)
10
log
-45 -40 -35 -30 -25 -20 -15 -10 -5 0
Timing difference significance S
0
20
40
60
80
100
12
10
8
6
4
2
0
FIG. 2: 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 clu
s-
ter of in-time and high-probability events in the lower righ
t
corner is from the signal process, with a residue at lower pro
b-
abilities due to tail events. The lack of structure in the sca
t-
ter plot confirms the complementarity of these two selection
s.
Events with
S
soft
−
hard
>
2
.
0 or fit probability below 10
−
5
are
excluded, as shown by the white dashed lines.
π
0
proxy
candidate is reconstructed from the proxy soft pho-
ton
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 mis-labeled cascades
we reject events where the invariant mass of any combina-
tion 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 contribu-
tions: a peak at the nominal
π
0
mass corresponding to
in-time photon pairs and a continuous background corre-
sponding 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(
S
max
). With an EMC timing
selection of
S
max
= 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 signifi-
cance between the two signal photon candidates below
2
.
0
σ
are retained:
S
soft
−
hard
< S
max
= 2
.
0 (3
.
0
σ
for
3
S
→
2
P
→
1
S
to compensate for poorly-known tim-
ing 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
(
γ
) events according to re-
constructions 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 col-
lected by the calorimeter. Excluding these events lowers
the signal efficiency but improves our ability to disen-
tangle the overlapping signal peaks during fitting. The
highest-probability cascade candidate remaining in each
event is then chosen. Fig. 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 dif-
ferences from the
E
mS
→
(
m
−
1)
P
spectra using unbinned
maximum likelihood fits with three incoherent overlap-
ping signal components corresponding to the
J
= 0, 1
and 2 decay channels and a smooth incoherent back-
ground. Simulated signal, and
μμ
(
γ
) and
π
0
π
0
back-
ground MC collections are subjected to the same recon-
struction 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 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 [32]
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 de-
caying exponential component with power
λ
and a linear
component with slope
a
1
. The simplest approach to fit-
ting 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 float-
ing independently perform equally poorly; in particular,
the
J
= 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
= 1 peak
to float, and we fix the corresponding
J
= 0 and
J
= 2
parameters with a linear extrapolation from the
J
= 1
values using slopes derived from fits to the MC signal
8
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
=
N
J
/N
1
and
peak mean offsets
δ
J
=
μ
J
−
μ
1
, which both float in
the fit, as well as the
J
= 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 in-
volving
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
(
J
)
→
nS
=
B
(
mS
→
P
(
J
))
B
(
P
(
J
)
→
nS
)
B
(
mS
→
P
(1))
B
(
P
(1)
→
nS
)
=
f
J
ǫ
1
ǫ
J
(2)
where
ǫ
J
is the signal efficiency of the
J
channel and the
measured yield ratio
f
J
has systematic corrections ap-
plied. The branching fraction of the terminal
Υ
(
nS
)
→
μ
+
μ
−
decay appears in both the numerator and denom-
inator and thus cancels. We also measure the mass split-
tings ∆
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 associ-
ated with determining the absolute photon energies. Sys-
tematic effects and uncertainties on the yield ratio
f
J
,
line energy differences
δ
J
, and efficiency ratio
ǫ
1
/ǫ
J
are
discussed below.
Constraining the line shape parameters to fixed linear
slopes introduces unknown systematic biases in the ex-
tracted yield and mean values, resulting in systematic
uncertainties. To measure these uncertainties, a collec-
tion of 50
,
000 model spectra is generated that violates
these assumptions; each spectrum is fit with the same fit-
ting procedure as for the data spectrum. The behavior of
the fits to these generic model spectra constrains the un-
certainty 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 mod-
els 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 (
X
generated
−
X
fit
)
/σ
X
, where
σ
X
is the parameter uncertainty in the fit. We fit a Gaus-
sian 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 distri-
bution. In this way we have used the model spectra to
measure systematic uncertainties and biases 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, indicat-
ing 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 non-isotropic acceptance. The signal MC collections
simulate 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. Un-
certainties in the ratio come from two sources: MC sam-
ple 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
+
μ
−
γγ
final
state is reconstructed by requiring one of the photons
to be identified in the EMC and the other to be recon-
structed after converting into an
e
+
e
−
pair in detector
material. Although it shares the same underlying physics
as the calorimeter-based analysis, the presence of a dis-
placed vertex and lack of calorimeter timing information
necessitate some differences in approach.
9
(
GeV)
1P→2S
γ
E
Events / ( 0.002 GeV )
(a)
(b)
0.04 0.06
0
0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24
10
40
20
30
80
70
60
50
0
400
200
600
800
1000
1200
χ (1P)
b
0
χ (1P)
b
2
χ (1P)
b
1
FIG. 3: (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 an
alysis. The targeted
χ
b
0
(1
P
) signal corresponds to the small bump
on the right; the integral ratio and mean offset of the fit to thi
s peak compared to the
J
= 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
= 2 peak (left), also
compared to the
J
= 1 peak. (b) A zoomed-in view of the
χ
b
0
(1
P
) peak on the same energy scale.
TABLE I: MC efficiency ratios for the calorimeter-based anal-
ysis.
Cascade
J ǫ
1
/ǫ
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
We reconstruct the
Υ
(1
S,
2
S
) final states with two
opposite-sign muons within 100 MeV
/c
2
of the relevant
Υ
(
nS
) mass, satisfying a vertex probability
χ
2
of greater
than 0.0001. The
χ
bJ
(
mP
) candidates are formed by con-
straining the
Υ
(
nS
) to its nominal mass [23] and adding
a converted photon (as described in detail in Ref. [19]).
The initial
Υ
(2
S,
3
S
) candidate is reconstructed by com-
bining a calorimeter-identified photon candidate with the
χ
bJ
(
mP
) candidate. This photon is required to have a
minimum laboratory-frame energy of 30 MeV and lat-
eral 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
(low)
−
40
< E
γ
< E
γ
(high)
+40 MeV, where
E
γ
(low)
and
E
γ
(high)
represent the lowest and highest energy transi-
tion for the intermediate
χ
bJ
(
mP
) triplet in question.
Because this reconstruction lacks a sufficient second
10
(GeV)
2P→3S
γ
E
Events / ( 0.0012 GeV )
0.04
0.06
0.08
0.10
0.12
0.14
0.16
10
20
30
40
50
60
0
70
80
90
100
200
400
600
0
(a)
(b)
800
1000
χ (2P)
b
0
χ (2P)
b
2
χ (2P)
b
1
FIG. 4: (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 an
alysis. (b) A zoomed-in view of the
χ
b
0
(2
P
) peak on the same
energy scale. Discussion of the significance of the
J
= 0 peak is contained in Section IV C.
EMC timing measurement to take advantage of the
timing-based selection described in Sec.IV A,
π
0
π
0
and
μ
+
μ
−
(
γ
) backgrounds, which are also the dominant
background sources for this analysis technique, are re-
duced via more conventional means. The number of
charged-particle tracks in the event, as identified by the
B
A
B
AR
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 re-
sulting in mutually exclusive datasets. This selection
also makes this dataset independent from the previous
inclusive converted photon analysis [19], with the only
commonality being shared uncertainties on the lumi-
nosity measurement and the conversion efficiency (de-
scribed in Sec. V C). Events with an initial
Υ
(
nS
) mass,
M
Υ
(
nS
)
, in the range 10
.
285
< M
Υ
(3
S
)
<
10
.
395 GeV
/c
2
or
M
Υ
(2
S
)(PDG)
±
40 MeV
/c
2
are retained. A requirement
that the ratio of the second and zeroth Fox-Wolfram mo-
ments [33] of each event,
R
2
, be less than 0.95 is also ap-
plied. These selection criteria were determined by maxi-
mizing 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 sim-
ulation.
We calculate the signal efficiency by counting the num-
ber of MC signal events remaining after reconstruction
and the application of event selection criteria. The effi-
ciency is highly dependent upon the conversion photon
energy (as seen in Ref. [19]), and ranges from 0
.
1% at
E
γ
∼
200 MeV to 0
.
8% at
E
γ
∼
800 MeV. This drop in effi-
ciency 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
(
nS
) reconstruction is
considered, the overall efficiency ranges from 0
.
07
−
0
.
90%
depending on the decay chain. While the efficiency for
11
(a)
(GeV)
2P→3S
γ
E
(b)
Events / ( 0.0012 GeV )
0.04
0.06
0.08
0.10
0.12
0.14
0.16
10
20
30
40
50
60
0
100
200
300
400
500
600
0
χ (2P)
b
0
χ (2P)
b
2
χ (2P)
b
1
FIG. 5: (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 cal
orimeter-based analysis. (b) A zoomed-in view of the
χ
b
0
(2
P
)
peak on the same energy scale. Discussion of the significance
of the
J
= 0 peak is contained in Section IV C.
the reconstruction with a converted photon is low, this
technique leads to a large improvement in energy reso-
lution from approximately 15 MeV 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 im-
provement 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 tran-
sitions overlap in energy and either photon may be re-
constructed as the converted one. Therefore both com-
ponents are fit simultaneously. Because we analyze the
photon energy in the center-of-mass frame of the ini-
tial
Υ
(
nS
) system, the photon spectra from subsequent
boosted decays (
e.g.
χ
bJ
(
mP
)
→
γΥ
(
nS
)) are affected
by Doppler broadening due to the motion of the parent
state in the center-of-mass frame. Due to this effect, vari-
ation of efficiency over the photon angular distribution,
and a rapidly changing converted photon reconstruction
efficiency, the signal line shapes are most effectively mod-
eled using a kernel estimation 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 analy-
sis, 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 parameterizations using variations
12
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
= 0 peaks are inconsistent with the fit results with a significa
nce of 5
.
1
σ
and 2
.
1
σ
,
respectively. The efficiency ratio corrections have not been
applied.
Cascade
Parameter Fit value Pull shift (
σ
) Pull width (
σ
) Corrected
2
S
→
1
P
→
1
S
f
0
2
.
83
±
0
.
31
+0
.
82
1
.
12
3
.
09
±
0
.
35
f
2
54
.
8
±
1
.
3
+0
.
078
1
.
15
54
.
9
±
1
.
5
δ
0
32
.
00
±
0
.
91
+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
S
f
0
1
.
66
±
0
.
39
+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
+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
S
f
0
1
.
05
±
0
.
52
+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
+0
.
80
1
.
13
24
.
0
±
3
.
4
δ
2
−
12
.
80
±
0
.
22
+0
.
032
1
.
03
−
12
.
79
±
0
.
23
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
+
μ
−
(
γ
) background below the signal peaks.
This primarily affects the 3
S
→
2
P
→
(1
S,
2
S
) 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 ef-
fects are considered both by allowing the individual sig-
nal 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
= 1
and
J
= 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 ap-
plied 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,
B
A
B
AR
inclusive converted
photon analysis [19], and the resolution smearing is small
compared to the predicted resolution, which is of the or-
der 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 branch-
ing fractions without normalization. The following sec-
tion outlines the systematic uncertainties associated with
these measurements.
C. Systematic Uncertainties
The uncertainty on the luminosity is taken from the
standard
B
A
B
AR
determination [25], which amounts to
0
.
58% (0
.
68%) for
Υ
(3
S
) (
Υ
(2
S
)). The derivation of
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 sim-
ulation and data into agreement. These are determined
separately from this analysis, and are employed gener-
ally by all
B
A
B
AR
analyses. For muon identification, de-
cay 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. [19]). 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 mea-
sured by the other decay modes. The largest deviations
from the nominal fit yields are taken as the uncertainty.
For the
J
= 2(1) signal, the values are
+2
.
0
−
1
.
7
% (
+8
.
7
−
11
.
5
%).
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 are refit using double-sided Crystal Ball
13