The Belle Collaboration

#
Measurement of the Masses and Widths of the $\Sigma_{c}(2455)^{+}$ and
$\Sigma_{c}(2520)^{+}$ Baryons

J. Yelton  University of Florida, Gainesville, Florida 32611  I. Adachi  High
Energy Accelerator Research Organization (KEK), Tsukuba 305-0801  SOKENDAI
(The Graduate University for Advanced Studies), Hayama 240-0193  J. K. Ahn
Korea University, Seoul 02841  H. Aihara  Department of Physics, University of
Tokyo, Tokyo 113-0033  S. Al Said  Department of Physics, Faculty of Science,
University of Tabuk, Tabuk 71451  Department of Physics, Faculty of Science,
King Abdulaziz University, Jeddah 21589  D. M. Asner  Brookhaven National
Laboratory, Upton, New York 11973  H. Atmacan  University of Cincinnati,
Cincinnati, Ohio 45221  V. Aulchenko  Budker Institute of Nuclear Physics SB
RAS, Novosibirsk 630090  Novosibirsk State University, Novosibirsk 630090  T.
Aushev  National Research University Higher School of Economics, Moscow 101000
R. Ayad  Department of Physics, Faculty of Science, University of Tabuk, Tabuk
71451  V. Babu  Deutsches Electronen-Synchrotron, 22607 Hamburg  S. Bahinipati
Indian Institute of Technology Bhubaneswar, Satya Nagar 751007  P. Behera
Indian Institute of Technology Madras, Chennai 600036  K. Belous  Institute
for High Energy Physics, Protvino 142281  J. Bennett  University of
Mississippi, University, Mississippi 38677  M. Bessner  University of Hawaii,
Honolulu, Hawaii 96822  V. Bhardwaj  Indian Institute of Science Education and
Research Mohali, SAS Nagar, 140306  B. Bhuyan  Indian Institute of Technology
Guwahati, Assam 781039  T. Bilka  Faculty of Mathematics and Physics, Charles
University, 121 16 Prague  J. Biswal  J. Stefan Institute, 1000 Ljubljana  A.
Bozek  H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342  M.
Bračko  Faculty of Chemistry and Chemical Engineering, University of Maribor,
2000 Maribor  J. Stefan Institute, 1000 Ljubljana  P. Branchini  INFN -
Sezione di Roma Tre, I-00146 Roma  T. E. Browder  University of Hawaii,
Honolulu, Hawaii 96822  A. Budano  INFN - Sezione di Roma Tre, I-00146 Roma
M. Campajola  INFN - Sezione di Napoli, I-80126 Napoli  Università di Napoli
Federico II, I-80126 Napoli  D. Červenkov  Faculty of Mathematics and Physics,
Charles University, 121 16 Prague  M.-C. Chang  Department of Physics, Fu Jen
Catholic University, Taipei 24205  P. Chang  Department of Physics, National
Taiwan University, Taipei 10617  V. Chekelian  Max-Planck-Institut für Physik,
80805 München  A. Chen  National Central University, Chung-li 32054  B. G.
Cheon  Department of Physics and Institute of Natural Sciences, Hanyang
University, Seoul 04763  K. Chilikin  P.N. Lebedev Physical Institute of the
Russian Academy of Sciences, Moscow 119991  H. E. Cho  Department of Physics
and Institute of Natural Sciences, Hanyang University, Seoul 04763  K. Cho
Korea Institute of Science and Technology Information, Daejeon 34141  S.-J.
Cho  Yonsei University, Seoul 03722  S.-K. Choi  Gyeongsang National
University, Jinju 52828  Y. Choi  Sungkyunkwan University, Suwon 16419  S.
Choudhury  Indian Institute of Technology Hyderabad, Telangana 502285  D.
Cinabro  Wayne State University, Detroit, Michigan 48202  S. Cunliffe
Deutsches Electronen-Synchrotron, 22607 Hamburg  S. Das  Malaviya National
Institute of Technology Jaipur, Jaipur 302017  N. Dash  Indian Institute of
Technology Madras, Chennai 600036  G. De Nardo  INFN - Sezione di Napoli,
I-80126 Napoli  Università di Napoli Federico II, I-80126 Napoli  G. De Pietro
INFN - Sezione di Roma Tre, I-00146 Roma  R. Dhamija  Indian Institute of
Technology Hyderabad, Telangana 502285  F. Di Capua  INFN - Sezione di Napoli,
I-80126 Napoli  Università di Napoli Federico II, I-80126 Napoli  J.
Dingfelder  University of Bonn, 53115 Bonn  Z. Doležal  Faculty of Mathematics
and Physics, Charles University, 121 16 Prague  T. V. Dong  Key Laboratory of
Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern
Physics, Fudan University, Shanghai 200443  D. Epifanov  Budker Institute of
Nuclear Physics SB RAS, Novosibirsk 630090  Novosibirsk State University,
Novosibirsk 630090  T. Ferber  Deutsches Electronen-Synchrotron, 22607 Hamburg
D. Ferlewicz  School of Physics, University of Melbourne, Victoria 3010  B. G.
Fulsom  Pacific Northwest National Laboratory, Richland, Washington 99352  R.
Garg  Panjab University, Chandigarh 160014  V. Gaur  Virginia Polytechnic
Institute and State University, Blacksburg, Virginia 24061  N. Gabyshev
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090  Novosibirsk
State University, Novosibirsk 630090  A. Garmash  Budker Institute of Nuclear
Physics SB RAS, Novosibirsk 630090  Novosibirsk State University, Novosibirsk
630090  A. Giri  Indian Institute of Technology Hyderabad, Telangana 502285
P. Goldenzweig  Institut für Experimentelle Teilchenphysik, Karlsruher
Institut für Technologie, 76131 Karlsruhe  E. Graziani  INFN - Sezione di Roma
Tre, I-00146 Roma  T. Gu  University of Pittsburgh, Pittsburgh, Pennsylvania
15260  K. Gudkova  Budker Institute of Nuclear Physics SB RAS, Novosibirsk
630090  Novosibirsk State University, Novosibirsk 630090  C. Hadjivasiliou
Pacific Northwest National Laboratory, Richland, Washington 99352  T. Hara
High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801
SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193  O.
Hartbrich  University of Hawaii, Honolulu, Hawaii 96822  K. Hayasaka  Niigata
University, Niigata 950-2181  H. Hayashii  Nara Women’s University, Nara
630-8506  W.-S. Hou  Department of Physics, National Taiwan University, Taipei
10617  C.-L. Hsu  School of Physics, University of Sydney, New South Wales
2006  K. Inami  Graduate School of Science, Nagoya University, Nagoya 464-8602
A. Ishikawa  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801  SOKENDAI (The Graduate University for Advanced Studies), Hayama
240-0193  R. Itoh  High Energy Accelerator Research Organization (KEK),
Tsukuba 305-0801  SOKENDAI (The Graduate University for Advanced Studies),
Hayama 240-0193  M. Iwasaki  Osaka City University, Osaka 558-8585  Y. Iwasaki
High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801  W. W.
Jacobs  Indiana University, Bloomington, Indiana 47408  S. Jia  Key Laboratory
of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern
Physics, Fudan University, Shanghai 200443  Y. Jin  Department of Physics,
University of Tokyo, Tokyo 113-0033  K. K. Joo  Chonnam National University,
Gwangju 61186  A. B. Kaliyar  Tata Institute of Fundamental Research, Mumbai
400005  K. H. Kang  Kyungpook National University, Daegu 41566  Y. Kato
Graduate School of Science, Nagoya University, Nagoya 464-8602  C. Kiesling
Max-Planck-Institut für Physik, 80805 München  C. H. Kim  Department of
Physics and Institute of Natural Sciences, Hanyang University, Seoul 04763  D.
Y. Kim  Soongsil University, Seoul 06978  K.-H. Kim  Yonsei University, Seoul
03722  S. H. Kim  Seoul National University, Seoul 08826  Y.-K. Kim  Yonsei
University, Seoul 03722  K. Kinoshita  University of Cincinnati, Cincinnati,
Ohio 45221  P. Kodyš  Faculty of Mathematics and Physics, Charles University,
121 16 Prague  T. Konno  Kitasato University, Sagamihara 252-0373  A. Korobov
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090  Novosibirsk
State University, Novosibirsk 630090  S. Korpar  Faculty of Chemistry and
Chemical Engineering, University of Maribor, 2000 Maribor  J. Stefan
Institute, 1000 Ljubljana  E. Kovalenko  Budker Institute of Nuclear Physics
SB RAS, Novosibirsk 630090  Novosibirsk State University, Novosibirsk 630090
P. Križan  Faculty of Mathematics and Physics, University of Ljubljana, 1000
Ljubljana  J. Stefan Institute, 1000 Ljubljana  R. Kroeger  University of
Mississippi, University, Mississippi 38677  P. Krokovny  Budker Institute of
Nuclear Physics SB RAS, Novosibirsk 630090  Novosibirsk State University,
Novosibirsk 630090  T. Kuhr  Ludwig Maximilians University, 80539 Munich  R.
Kulasiri  Kennesaw State University, Kennesaw, Georgia 30144  K. Kumara  Wayne
State University, Detroit, Michigan 48202  Y.-J. Kwon  Yonsei University,
Seoul 03722  J. S. Lange  Justus-Liebig-Universität Gießen, 35392 Gießen  M.
Laurenza  INFN - Sezione di Roma Tre, I-00146 Roma  Dipartimento di Matematica
e Fisica, Università di Roma Tre, I-00146 Roma  S. C. Lee  Kyungpook National
University, Daegu 41566  J. Li  Kyungpook National University, Daegu 41566  L.
K. Li  University of Cincinnati, Cincinnati, Ohio 45221  Y. B. Li  Peking
University, Beijing 100871  L. Li Gioi  Max-Planck-Institut für Physik, 80805
München  J. Libby  Indian Institute of Technology Madras, Chennai 600036  K.
Lieret  Ludwig Maximilians University, 80539 Munich  D. Liventsev  Wayne State
University, Detroit, Michigan 48202  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801  C. MacQueen  School of Physics,
University of Melbourne, Victoria 3010  M. Masuda  Earthquake Research
Institute, University of Tokyo, Tokyo 113-0032  Research Center for Nuclear
Physics, Osaka University, Osaka 567-0047  T. Matsuda  University of Miyazaki,
Miyazaki 889-2192  D. Matvienko  Budker Institute of Nuclear Physics SB RAS,
Novosibirsk 630090  Novosibirsk State University, Novosibirsk 630090  P.N.
Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991
J. T. McNeil  University of Florida, Gainesville, Florida 32611  M. Merola
INFN - Sezione di Napoli, I-80126 Napoli  Università di Napoli Federico II,
I-80126 Napoli  K. Miyabayashi  Nara Women’s University, Nara 630-8506  R.
Mizuk  P.N. Lebedev Physical Institute of the Russian Academy of Sciences,
Moscow 119991  National Research University Higher School of Economics, Moscow
101000  G. B. Mohanty  Tata Institute of Fundamental Research, Mumbai 400005
T. J. Moon  Seoul National University, Seoul 08826  R. Mussa  INFN - Sezione
di Torino, I-10125 Torino  M. Nakao  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801  SOKENDAI (The Graduate University for
Advanced Studies), Hayama 240-0193  Z. Natkaniec  H. Niewodniczanski Institute
of Nuclear Physics, Krakow 31-342  A. Natochii  University of Hawaii,
Honolulu, Hawaii 96822  L. Nayak  Indian Institute of Technology Hyderabad,
Telangana 502285  M. Nayak  School of Physics and Astronomy, Tel Aviv
University, Tel Aviv 69978  M. Niiyama  Kyoto Sangyo University, Kyoto
603-8555  N. K. Nisar  Brookhaven National Laboratory, Upton, New York 11973
S. Nishida  High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801  SOKENDAI (The Graduate University for Advanced Studies), Hayama
240-0193  S. Ogawa  Toho University, Funabashi 274-8510  H. Ono  Nippon Dental
University, Niigata 951-8580  Niigata University, Niigata 950-2181  Y. Onuki
Department of Physics, University of Tokyo, Tokyo 113-0033  P. Oskin  P.N.
Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991
P. Pakhlov  P.N. Lebedev Physical Institute of the Russian Academy of
Sciences, Moscow 119991  Moscow Physical Engineering Institute, Moscow 115409
G. Pakhlova  National Research University Higher School of Economics, Moscow
101000  P.N. Lebedev Physical Institute of the Russian Academy of Sciences,
Moscow 119991  S. Pardi  INFN - Sezione di Napoli, I-80126 Napoli  H. Park
Kyungpook National University, Daegu 41566  S.-H. Park  High Energy
Accelerator Research Organization (KEK), Tsukuba 305-0801  S. Paul  Department
of Physics, Technische Universität München, 85748 Garching  Max-Planck-
Institut für Physik, 80805 München  T. K. Pedlar  Luther College, Decorah,
Iowa 52101  R. Pestotnik  J. Stefan Institute, 1000 Ljubljana  L. E. Piilonen
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
24061  T. Podobnik  Faculty of Mathematics and Physics, University of
Ljubljana, 1000 Ljubljana  J. Stefan Institute, 1000 Ljubljana  E. Prencipe
Forschungszentrum Jülich, 52425 Jülich  M. T. Prim  University of Bonn, 53115
Bonn  A. Rostomyan  Deutsches Electronen-Synchrotron, 22607 Hamburg  N. Rout
Indian Institute of Technology Madras, Chennai 600036  G. Russo  Università di
Napoli Federico II, I-80126 Napoli  D. Sahoo  Tata Institute of Fundamental
Research, Mumbai 400005  Y. Sakai  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801  SOKENDAI (The Graduate University for
Advanced Studies), Hayama 240-0193  S. Sandilya  Indian Institute of
Technology Hyderabad, Telangana 502285  A. Sangal  University of Cincinnati,
Cincinnati, Ohio 45221  L. Santelj  Faculty of Mathematics and Physics,
University of Ljubljana, 1000 Ljubljana  J. Stefan Institute, 1000 Ljubljana
T. Sanuki  Department of Physics, Tohoku University, Sendai 980-8578  V.
Savinov  University of Pittsburgh, Pittsburgh, Pennsylvania 15260  G. Schnell
Department of Physics, University of the Basque Country UPV/EHU, 48080 Bilbao
IKERBASQUE, Basque Foundation for Science, 48013 Bilbao  J. Schueler
University of Hawaii, Honolulu, Hawaii 96822  C. Schwanda  Institute of High
Energy Physics, Vienna 1050  Y. Seino  Niigata University, Niigata 950-2181
K. Senyo  Yamagata University, Yamagata 990-8560  M. E. Sevior  School of
Physics, University of Melbourne, Victoria 3010  M. Shapkin  Institute for
High Energy Physics, Protvino 142281  C. Sharma  Malaviya National Institute
of Technology Jaipur, Jaipur 302017  C. P. Shen  Key Laboratory of Nuclear
Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan
University, Shanghai 200443  J.-G. Shiu  Department of Physics, National
Taiwan University, Taipei 10617  A. Sokolov  Institute for High Energy
Physics, Protvino 142281  E. Solovieva  P.N. Lebedev Physical Institute of the
Russian Academy of Sciences, Moscow 119991  M. Starič  J. Stefan Institute,
1000 Ljubljana  Z. S. Stottler  Virginia Polytechnic Institute and State
University, Blacksburg, Virginia 24061  M. Sumihama  Gifu University, Gifu
501-1193  K. Sumisawa  High Energy Accelerator Research Organization (KEK),
Tsukuba 305-0801  SOKENDAI (The Graduate University for Advanced Studies),
Hayama 240-0193  T. Sumiyoshi  Tokyo Metropolitan University, Tokyo 192-0397
M. Takizawa  Showa Pharmaceutical University, Tokyo 194-8543  J-PARC Branch,
KEK Theory Center, High Energy Accelerator Research Organization (KEK),
Tsukuba 305-0801  Meson Science Laboratory, Cluster for Pioneering Research,
RIKEN, Saitama 351-0198  U. Tamponi  INFN - Sezione di Torino, I-10125 Torino
K. Tanida  Advanced Science Research Center, Japan Atomic Energy Agency, Naka
319-1195  Y. Tao  University of Florida, Gainesville, Florida 32611  F.
Tenchini  Deutsches Electronen-Synchrotron, 22607 Hamburg  K. Trabelsi
Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay  M. Uchida  Tokyo
Institute of Technology, Tokyo 152-8550  T. Uglov  P.N. Lebedev Physical
Institute of the Russian Academy of Sciences, Moscow 119991  National Research
University Higher School of Economics, Moscow 101000  Y. Unno  Department of
Physics and Institute of Natural Sciences, Hanyang University, Seoul 04763  S.
Uno  High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801
SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193  P.
Urquijo  School of Physics, University of Melbourne, Victoria 3010  Y. Usov
Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090  Novosibirsk
State University, Novosibirsk 630090  S. E. Vahsen  University of Hawaii,
Honolulu, Hawaii 96822  R. Van Tonder  University of Bonn, 53115 Bonn  G.
Varner  University of Hawaii, Honolulu, Hawaii 96822  A. Vinokurova  Budker
Institute of Nuclear Physics SB RAS, Novosibirsk 630090  Novosibirsk State
University, Novosibirsk 630090  E. Waheed  High Energy Accelerator Research
Organization (KEK), Tsukuba 305-0801  C. H. Wang  National United University,
Miao Li 36003  D. Wang  University of Florida, Gainesville, Florida 32611  E.
Wang  University of Pittsburgh, Pittsburgh, Pennsylvania 15260  M.-Z. Wang
Department of Physics, National Taiwan University, Taipei 10617  P. Wang
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049
M. Watanabe  Niigata University, Niigata 950-2181  S. Watanuki  Université
Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay  E. Won  Korea University, Seoul
02841  B. D. Yabsley  School of Physics, University of Sydney, New South Wales
2006  W. Yan  Department of Modern Physics and State Key Laboratory of
Particle Detection and Electronics, University of Science and Technology of
China, Hefei 230026  S. B. Yang  Korea University, Seoul 02841  H. Ye
Deutsches Electronen-Synchrotron, 22607 Hamburg  J. H. Yin  Korea University,
Seoul 02841  C. Z. Yuan  Institute of High Energy Physics, Chinese Academy of
Sciences, Beijing 100049  Z. P. Zhang  Department of Modern Physics and State
Key Laboratory of Particle Detection and Electronics, University of Science
and Technology of China, Hefei 230026  V. Zhilich  Budker Institute of Nuclear
Physics SB RAS, Novosibirsk 630090  Novosibirsk State University, Novosibirsk
630090  V. Zhukova  P.N. Lebedev Physical Institute of the Russian Academy of
Sciences, Moscow 119991

###### Abstract

Using 980 ${\rm fb}^{-1}$ of data collected with the Belle detector operating
at the KEKB asymmetric-energy $e^{+}e^{-}$ collider, we report the
measurements of the masses, and the first measurements of the instrinsic
widths, of the $\Sigma_{c}(2455)^{+}$ and $\Sigma_{c}(2520)^{+}$ charmed
baryons. We find $M(\Sigma_{c}(2455)^{+})-M(\Lambda_{c}^{+})=166.17\pm
0.05^{+0.16}_{-0.07}\ {\rm MeV}/c^{2}$, $\Gamma(\Sigma_{c}(2455)^{+})=2.3\pm
0.3\pm 0.3\ {\rm MeV/c^{2}}$,
$M(\Sigma_{c}(2520)^{+})-M(\Lambda_{c}^{+})=230.9\pm 0.5^{+0.5}_{-0.1}\ {\rm
MeV}/c^{2}$, and $\Gamma(\Sigma_{c}(2520)^{+})=17.2^{+2.3\ +3.1}_{-2.1\ -0.7}\
{\rm MeV}/c^{2}$, where the uncertainties are statistical and systematic,
respectively. These measurements can be used to test models of the underlying
quark structure of the $\Sigma_{c}$ states.

## Introduction

The $\Sigma_{c}$ charmed baryons consist of a charm quark in combination with
a spin-1 light ($uu$, $ud$ or $dd$) diquark. The lowest of these states are
the $\Sigma_{c}(2455)$ isotriplet which have $J^{P}=\frac{1}{2}^{+}$, with the
next most massive being the $J^{P}=\frac{3}{2}^{+}$ $\Sigma_{c}(2520)$
isotriplet. All these six states decay strongly to $\Lambda_{c}^{+}\pi$. The
doubly-charged and neutral states, both of which decay with the emission of a
charged pion, have been well studied. The most precise measurements of their
masses and widths have been made SIGC  by the Belle Collaboration using the
same dataset as the analysis presented here. However, $\pi^{0}$ transitions
have lower efficiency, higher backgrounds and inferior resolution to
$\pi^{\pm}$ transitions, so there is comparatively little experimental
information on the singly-charged $\Sigma_{c}^{+}$ states CC .

All mass measurements of the $\Sigma_{c}$ baryons have been made with respect
to the $\Lambda_{c}^{+}$ mass, as the resolution of these mass differences
(denoted $\Delta(M)$) is superior to that of the individual baryons. The CLEO
Collaboration has measured $\Delta(M)$ for both the $\Sigma_{c}(2455)^{+}$ and
$\Sigma_{c}(2520)^{+}$ states CLEO , but were only able to set limits on their
intrinsic widths. The large Belle dataset allows for much more precise
measurements of the masses of these particles than has been possible hitherto,
and also the first measurements of their widths.

Measurements of the masses of all members of the two isotriplets allow tests
of models of isospin mass splittings. In the model of Yang and Kim YK , for
instance, the mass splittings from the following four sources add: the
electromagnetic corrections due to the light quarks, the differences of the
masses of the $u$ and $d$ quarks, the hyperfine interactions between the light
quarks, and the Coulomb interactions between the soliton and charm quark. Most
mass models predict that the singly-charged states should have masses a little
lower than their doubly-charged and neutral analogs theories  and this is true
in the limited precision measurements made to date PDG .

The natural width of the $\Sigma_{c}(2455)^{+}$ is predicted to be somewhat
larger than its isospin partners; this is mostly because of the effect of the
$\pi^{\pm}/\pi^{0}$ mass difference on the available phase space for the
decay. There is also a possibility that electromagnetic decays are non-
negligible. Cheng and Chua Cheng  predict
$\Gamma(\Sigma_{c}(2455)^{+})=2.3^{+0.1}_{-0.2}\ {\rm MeV}/c^{2}$ using the
experimental value of $\Gamma(\Sigma_{c}(2455)^{++})=1.94^{+0.08}_{-0.16}\
{\rm MeV}/c^{2}$ as input. For the $\Sigma_{c}(2520)$, it is expected that the
instrinsic width of the $\Sigma_{c}^{+}$ will be similar to those measured for
its isospin partners of $\Gamma(\Sigma_{c}(2520)^{++})=14.8^{+0.3}_{-0.4}\
{\rm MeV}/c^{2}$ and $\Gamma(\Sigma_{c}(2520)^{0})=15.3^{+0.4}_{-0.5}\ {\rm
MeV}/c^{2}$, respectively; the two effects listed above are expected to be
small compared with these values.

In addition to checking the quark model predictions, the parameters of the
$\Sigma_{c}(2455)^{+}$ are vital in studies of the $\Lambda_{c}(2595)^{+}$,
whose pole mass appears to be between the $\Sigma_{c}(2455)^{+}\pi^{0}$ and
$\Sigma_{c}(2455)^{++}\pi^{-}$ thresholds. This particle, although generally
considered to be an orbitally excited heavy-quark light-diquark state, has
been conjectured to have different underlying quark structure 2593 . The
threshold behavior, and thus measurement of the pole mass and width, of the
$\Lambda_{c}(2595)^{+}$ is critically dependent on the masses and widths of
the $\Sigma_{c}$ particles.

Table 1: Parameters of the double-Gaussian resolution function derived from the Monte Carlo program. Particle | $\sigma_{\rm narrow}\ ({\rm MeV}/c^{2})$ | $\sigma_{\rm wide}\ ({\rm MeV}/c^{2})$ | ${\rm Area}_{\rm wide}/{\rm Area}_{\rm narrow}$ | Mass Offset $({\rm MeV}/c^{2})$
---|---|---|---|---
$\Sigma_{c}(2455)^{+}$ | 1.473 | 2.932 | 0.97 | 0.078
$\Sigma_{c}(2520)^{+}$ | 2.23 | 4.22 | 3.06 | 0.08

## Detector and Dataset

This analysis uses a data sample of $e^{+}e^{-}$ annihilations recorded by the
Belle detector Belle  operating at the KEKB asymmetric-energy $e^{+}e^{-}$
collider KEKB . It corresponds to an integrated luminosity of 980 ${\rm
fb}^{-1}$. The majority of these data were taken with the accelerator energy
tuned for production of the $\Upsilon(4S)$ resonance, as this is optimum for
investigation of $B$ decays. However, the $\Sigma_{c}$ particles in this
analysis are produced in continuum charm production and are of higher momentum
than those that are decay products of $B$ mesons. This allows the use of the
complete Belle data set which includes data taken at beam energies
corresponding to the other $\Upsilon$ resonances and the nearby continuum. The
Belle detector is a large solid-angle spectrometer comprising six sub-
detectors: the Silicon Vertex Detector (SVD), the 50-layer Central Drift
Chamber (CDC), the Aerogel Cherenkov Counter (ACC), the Time-of-Flight
scintillation counter (TOF), the electromagnetic calorimeter (ECL), and the
$K_{L}$ and muon detector. A superconducting solenoid produces a 1.5 T
magnetic field throughout the first five of these sub-detectors. The detector
is described in detail elsewhere Belle . Two inner detector configurations
were used. The first comprised a 2.0 cm radius beampipe and a 3-layer silicon
vertex detector, and the second a 1.5 cm radius beampipe and a 4-layer silicon
detector and a small-cell inner drift chamber.

## Analysis

We study $\Sigma_{c}^{+}$ baryons from the decay chain
$\Sigma_{c}^{+}\to\Lambda_{c}^{+}\pi^{0},\Lambda_{c}^{+}\to pK^{-}\pi^{+}$.
The decays are reconstructed from combinations of charged particles measured
using the tracking system, and neutral particles measured in the ECL. Final-
state charged particles, $\pi^{+},K^{-}$, and $p$, are selected using the
likelihood information from the tracking (SVD, CDC) and charged-hadron
identification (CDC, ACC, TOF) systems into a combined likelihood, ${\cal
L}(h1:h2)={\cal L}_{h1}/({\cal L}_{h1}+{\cal L}_{h2})$ where $h1$ and $h2$ are
$p$, $K$, and $\pi$ as appropriate Nakano . We require proton candidates to
have ${\cal L}(p:K)>0.6$ and ${\cal L}(p:\pi)>0.6$, kaon candidates to have
${\cal L}(K:p)>0.6$ and ${\cal L}(K:\pi)>0.6$, and pions to have requirements
of ${\cal L}(\pi:K)>0.6$ and ${\cal L}(\pi:p)>0.6$. The efficiencies of thse
hadron identification requirements are about 90%, 90%, and 93% for pions,
kaons and protons, respectively. The probability to misidentify a pion (kaon)
track as a kaon (pion) track is about 9 (10)%, and the momentum averaged
probability to misidentify a pion or kaon track as a proton track is about 5%.
Combinations of $pK^{-}\pi^{+}$ candidates with an invariant mass within 3.9
${\rm MeV}/c^{2}$ (approximately two standard deviations ($\sigma$)) of the
$\Lambda_{c}^{+}$ were retained as $\Lambda_{c}^{+}$ candidates. The number of
events having more than one $\Lambda_{c}^{+}$ candidate which share a daughter
particle is approximately 1%.

The $\pi^{0}$ candidates are reconstructed from two detected neutral clusters
in the ECL each consistent with being due to a photon and each with an energy
greater than 50 ${\rm MeV}$ in the laboratory frame. The invariant mass of the
photon pair is required to be within $5.4\ {\rm MeV}/c^{2}$ ($\approx\
2\sigma$) of the nominal $\pi^{0}$ mass. The two photons are then constrained
to this mass to improve the momentum resolution of the $\pi^{0}$.

To optimize the requirements specific to this analysis, a simulated data set
is constructed using a combination of the decays under study and $e^{+}e^{-}$
hadronic events generated by PYTHIA PYTHIA . We find that the following
requirements are optimal for the highest $\Sigma_{c}(2455)^{+}$ signal
significance: the momentum of the $\Sigma_{c}^{+}$ candidate in the
$e^{+}e^{-}$ center-of-mass frame, $p^{*}\ >\ 2.6\ {\rm GeV}/c$; the momentum
of the $\pi^{0}$ in laboratory frame, $p\ >\ 200\ {\rm MeV}/c$.

The Monte Carlo (MC) simulation is performed using a GEANT-based MC simulation
Geant  to model the response of the detector. The photon energy response in
the simulation is corrected to take into account the data-MC difference of
resolution based on studies of mass resolution in the decays
$\pi^{0}\to\gamma\gamma$, $\eta\to\gamma\gamma$, and $D^{*0}\to D^{0}\gamma$
Umberto ; Mizuk . The resolution of the $\Sigma_{c}(2455,2520)^{+}$ mass peaks
is parameterized by double-Gaussian resolution functions with a small offset
in the peak mass allowed. The parameters of these functions are shown in Table
1 and the statistical uncertainties in these values are negligible. It is
immediately clear that knowledge of the $\Sigma_{c}(2455)^{+}$ signal
resolution is vital as it is similar to the expected intrinsic width. To
further check the MC simulation, a study was made of the decay $D^{*+}\to
D^{+}\pi^{0}$, where $D^{+}\to K^{-}\pi^{+}\pi^{+}$. This decay has almost the
same final state as the one under consideration, similar momentum
distribution, is much more copiously produced, and has a very small and well-
known intrinsic width. The resolution of this mode is found to be 3% larger in
data than in MC simulations, and the reconstructed mass was found to be
$0.020\pm 0.015\ {\rm MeV}/c^{2}$ lower, where the uncertainty is due to the
Particle Data Group value PDG  as our statistical uncertainties are
negligible. We take these comparisons into account in the considerations of
the systematic uncertainties of our $\Sigma_{c}^{+}$ measurements.

Figure 1: The mass difference $M(\Lambda_{c}^{+}\pi^{0})-M(\Lambda_{c}^{+})$
for the entire mass range of interest. The line shows the expected
contribution from $\Lambda_{c}(2625)^{+}\to\Lambda_{c}^{+}\pi^{0}\pi^{0}$
decays assuming uniform 3-body phase-space.  Figure 2: The mass difference
$M(\Lambda_{c}^{+}\pi^{0})-M(\Lambda_{c}^{+})$ in the region of the
$\Sigma_{c}(2455)^{+}$. The fit to the data is described in the text, and the
lower line shows its contribution from the background function.  Figure 3: The
mass difference $M(\Lambda_{c}^{+}\pi^{0})-M(\Lambda_{c}^{+})$ in the region
of the $\Sigma_{c}(2520)^{+}$. The fit to the data is described in the text,
and the lower line shows its contribution from the background function.

Figure 1 shows the invariant mass distribution for the
$\Lambda_{c}^{+}\pi^{0}$ candidates. Clear signals are seen corresponding to
$\Sigma_{c}(2455)^{+}$ and $\Sigma_{c}(2520)^{+}$ production. In addition, we
see the large enhancement up to a mass difference of $\approx 200\ {\rm
MeV}/c^{2}$ due to $\Lambda_{c}(2625)^{+}\to\Lambda_{c}^{+}\pi^{0}\pi^{0}$
decays as they produce $\Lambda_{c}^{+}\pi^{0}$ combinations with mass
differences up to the kinematic limit of
$M(\Lambda_{c}^{+}(2625))-M(\Lambda_{c}^{+})-M(\pi^{0})=207\ {\rm MeV}/c^{2}$.
The simulated shape of this component is shown in Fig.1. There is also a
possible enhancement due to $\Lambda_{c}(2625)^{+}\to\Sigma_{c}^{+}\pi^{0}$
decays that may produce an enhancement at around $194\ {\rm MeV}/c^{2}$. These
enhancements were anticipated because of isospin symmetry, but these
particular decays have never been studied. The “cusp” behavior at around $200\
{\rm MeV/c^{2}}$ is particularly problematic as its shape depends on the
relative contributions of 3-body decays, decays proceeding through virtual
$\Sigma_{c}(2520)$ production, and the interference between these two Arifi .
Rather than fitting the entire spectrum, we decided to find the signal
parameters from fits performed to limited-range subsets of this data which do
not include this cusp region. These are shown in Fig. 2 and Fig. 3 for the
$\Sigma_{c}(2455)^{+}$ and $\Sigma_{c}(2520)^{+}$ regions, respectively. The
results of a global fit to Fig. 1 will be taken into account in the systematic
uncertainty determination.

A fit is made to Fig. 2 using a third-order Chebychev polynomial function to
represent the background, and a P-wave relativistic Breit-Wigner function
convolved with the previously described double-Gaussian resolution function,
taking into account the small mass offset. The Breit-Wigner signal function
includes a Blatt-Weisskopf barrier factor BW , with radius parameter of
$R=3~{}{\rm GeV}^{-1}$ BW2 . The results of this fit are a mass difference of
$\Delta(M)=166.17\pm 0.05\ {\rm MeV}/c^{2}$ and $\Gamma=2.3\pm 0.3\ {\rm
MeV}/c^{2}$. The fit is made using a maximum-likelihood method to a large
number of small bins so that any uncertainty due to bin size is negligible. A
convenient test of the goodness-of-fit is the $\chi^{2}$ per degree of freedom
(reduced $\chi^{2}$) for the distribution as shown, and for Fig. 2 this
reduced $\chi^{2}$ is $49.2/43=1.14$.

A fit is made to Fig. 3 using a second-order Chebychev polynomial function to
represent the background, and a P-wave relativistic Breit-Wigner function
convolved with the double-Gaussian resolution function described above. The
results of this fit are a mass difference of $\Delta(M)=230.9\pm 0.5\ {\rm
MeV}/c^{2}$ and $\Gamma=17.2^{+2.3}_{-2.1}\ {\rm MeV}/c^{2}$. The reduced
$\chi^{2}$ of the fit for the plot as shown is $52.8/44=1.20$.

## Systematic uncertainties

In all four measurements, we take the systematic uncertainty due to fitting as
the maximum variation of the measured parameters using different fitting
functions which produce acceptable fits to the data. For the
$\Sigma_{c}(2455)^{+}$ we vary the power of the polynomial background function
from 2 to 4, allow the possibility of a satellite peak due to
$\Lambda_{c}(2625)^{+}\to\Sigma_{c}^{+}\pi^{0}$ decays as such decays are
expected at a low level, investigate the changes in parameters with small
changes to the fitting ranges, and also compare the results of the fit shown
in Fig. 2 with the results of a global fit to Fig. 1 which includes
contributions from $\Lambda_{c}(2595)^{+}$ and $\Lambda_{c}(2625)^{+}$ decays.

The differences in the values obtained using reasonable variations of the
Blatt-Weisskopf barrier parameter, $R$, were found to be small. As the
measurement of the $D^{*+}$ width indicates a possible underestimation of the
detector resolution by 3%, we also perform a fit using a resolution 6% higher
than that found from MC simulations and conservatively take the change in the
parameters as the systemetic uncertainty arising from the uncertainty in the
mass resolution. We similarly study the variation of the
$\Sigma_{c}(2520)^{+}$ measured parameters to estimate the associated
systematic uncertainties, but here we cannot reduce the order of the
polynomial background function as a first order polynomial does not produce a
satistfactory fit to the data.

For the systematic uncertainty due to the energy scale, we allow for the
possibility that the $D^{*+}$ mass is measured up to $0.035\ {\rm MeV}/c^{2}$
lower than the true mass. We make the conservative assumption that the
difference between the measured and canonical masses of the $D^{*+}$ is
entirely due to a miscalibration of our photon energy scale, and use MC
simulation to estimate how a change in the $D^{*+}$ mass, which is a decay
with a very small four-momentum-squared $(q^{2})$ associated with it,
translates to a change in mass for a particle decaying with a larger $q^{2}$.
The result of this study is a possible upward shift of $0.15\ {\rm MeV}/c^{2}$
in the mass of the $\Sigma_{c}(2455)^{+}$ and $0.3\ {\rm MeV}/c^{2}$ for the
$\Sigma_{c}(2520)^{+}$. The systematic uncertainty estimations are tabulated
in Table 2.

Table 2: Contributions to the systematic uncertainties of the mass difference and width measurements of the two states in ${\rm MeV}/c^{2}$. | $\Sigma_{c}(2455)^{+}$ | $\Sigma_{c}(2520)^{+}$
---|---|---
| $\Delta(M)$ | $\Gamma$ | $\Delta(M)$ | $\Gamma$
Background Function | ${}^{+0.00}_{-0.07}$ | ${}^{+0.30}_{-0.04}$ | ${}^{+0.4}_{-0.0}$ | ${}^{+3.0}_{-0.5}$
Signal Function | ${}^{+0.06}_{-0.01}$ | ${}^{+0.01}_{-0.33}$ | ${}^{+0.0}_{-0.1}$ | ${}^{+0.7}_{-0.5}$
Photon Energy Scale | ${}^{+0.15}_{-0.00}$ | ${}^{+0.00}_{-0.00}$ | ${}^{+0.3}_{-0.0}$ | ${}^{+0.0}_{-0.0}$

## Discussion

The measured instrinsic widths are consistent with the quark model predictions
Cheng , namely that it is the same as the widths of their isospin partners,
except for a small change due to the increased phase-space available. The
measured mass differences are consistent with, but more precise than, the
previous measurements PDG  and confirm the picture in which the singly-charged
states are slightly lower in mass than their isospin partners. According to
the model first proposed by Franklin Franklin  the value of the mass
relationship $M(\Sigma_{c}^{++})+M(\Sigma_{c}^{0})-2\times M(\Sigma_{c}^{+})$
should be the same for the $\Sigma_{c}(2455)$ and $\Sigma_{c}(2520)$
isotriplets. Combining our measurements for the singly-charged $\Sigma_{c}$
states with those of the Particle Data Group PDG  for the others, we find
values of $2.46^{+0.17}_{-0.34}$ and $2.2^{+1.0}_{-1.4}\ {\rm MeV}/c^{2}$ for
the two systems, respectively, consistent with the model. Yang and Kim YK
further predict the mass difference between the singly-charged and neutral
$\Sigma_{c}$ baryons should be the same as those between the analogous
$\Xi_{c}^{\prime}$ and $\Xi_{c}^{*}$ states, and our results are also
consistent with this prediction.

## Conclusions

We measure the mass difference of the $\Sigma_{c}(2455)^{+}$ with respect to
the $\Lambda_{c}^{+}$ to be $\Delta(M)=166.17\pm 0.05^{+0.16}_{-0.07}\ {\rm
MeV}/c^{2}$ and its instrinsic width $\Gamma=2.3\pm 0.3\pm 0.3\ {\rm
MeV}/c^{2}$. For the $\Sigma_{c}(2520)^{+}$ the analogous values are
$\Delta(M)=230.9\pm 0.5^{+0.5}_{-0.1}\ {\rm MeV}/c^{2}$ and
$\Gamma=17.2^{+2.3+3.1}_{-2.1-0.7}\ {\rm MeV}/c^{2}$. These are the first non-
zero measurements of the instrinsic widths of these particles and show no
deviation from the expectations based upon the precise measurements of their
isospin partners made using the standard quark model.

## Acknowledgments

We thank the KEKB group for the excellent operation of the accelerator; the
KEK cryogenics group for the efficient operation of the solenoid; and the KEK
computer group, and the Pacific Northwest National Laboratory (PNNL)
Environmental Molecular Sciences Laboratory (EMSL) computing group for strong
computing support; and the National Institute of Informatics, and Science
Information NETwork 5 (SINET5) for valuable network support. We acknowledge
support from the Ministry of Education, Culture, Sports, Science, and
Technology (MEXT) of Japan, the Japan Society for the Promotion of Science
(JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the
Australian Research Council including grants DP180102629, DP170102389,
DP170102204, DP150103061, FT130100303; Austrian Federal Ministry of Education,
Science and Research (FWF) and FWF Austrian Science Fund No. P 31361-N36; the
National Natural Science Foundation of China under Contracts No. 11435013, No.
11475187, No. 11521505, No. 11575017, No. 11675166, No. 11705209; Key Research
Program of Frontier Sciences, Chinese Academy of Sciences (CAS), Grant No.
QYZDJ-SSW-SLH011; the CAS Center for Excellence in Particle Physics (CCEPP);
the Shanghai Pujiang Program under Grant No. 18PJ1401000; the Shanghai Science
and Technology Committee (STCSM) under Grant No. 19ZR1403000; the Ministry of
Education, Youth and Sports of the Czech Republic under Contract No. LTT17020;
Horizon 2020 ERC Advanced Grant No. 884719 and ERC Starting Grant No. 947006
“InterLeptons” (European Union); the Carl Zeiss Foundation, the Deutsche
Forschungsgemeinschaft, the Excellence Cluster Universe, and the
VolkswagenStiftung; the Department of Atomic Energy (Project Identification
No. RTI 4002) and the Department of Science and Technology of India; the
Istituto Nazionale di Fisica Nucleare of Italy; National Research Foundation
(NRF) of Korea Grant Nos. 2016R1D1A1B01010135, 2016R1D1A1B02012900,
2018R1A2B3003643, 2018R1A6A1A06024970, 2018R1D1A1B07047294,
2019K1A3A7A09033840, 2019R1I1A3A01058933; Radiation Science Research
Institute, Foreign Large-size Research Facility Application Supporting
project, the Global Science Experimental Data Hub Center of the Korea
Institute of Science and Technology Information and KREONET/GLORIAD; the
Polish Ministry of Science and Higher Education and the National Science
Center; the Ministry of Science and Higher Education of the Russian
Federation, Agreement 14.W03.31.0026, and the HSE University Basic Research
Program, Moscow; University of Tabuk research grants S-1440-0321, S-0256-1438,
and S-0280-1439 (Saudi Arabia); the Slovenian Research Agency Grant Nos.
J1-9124 and P1-0135; Ikerbasque, Basque Foundation for Science, Spain; the
Swiss National Science Foundation; the Ministry of Education and the Ministry
of Science and Technology of Taiwan; and the United States Department of
Energy and the National Science Foundation.

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