# Precision measurement of the $D^{*0}$ decay branching fractions

M. Ablikim1, M. N. Achasov8,a, X. C. Ai1, O. Albayrak4, M. Albrecht3, D. J.
Ambrose43, A. Amoroso47A,47C, F. F. An1, Q. An44, J. Z. Bai1, R. Baldini
Ferroli19A, Y. Ban30, D. W. Bennett18, J. V. Bennett4, M. Bertani19A, D.
Bettoni20A, J. M. Bian42, F. Bianchi47A,47C, E. Boger22,h, O. Bondarenko24, I.
Boyko22, R. A. Briere4, H. Cai49, X. Cai1, O. Cakir39A,b, A. Calcaterra19A, G.
F. Cao1, S. A. Cetin39B, J. F. Chang1, G. Chelkov22,c, G. Chen1, H. S. Chen1,
H. Y. Chen2, J. C. Chen1, M. L. Chen1, S. J. Chen28, X. Chen1, X. R. Chen25,
Y. B. Chen1, H. P. Cheng16, X. K. Chu30, G. Cibinetto20A, D. Cronin-
Hennessy42, H. L. Dai1, J. P. Dai33, A. Dbeyssi13, D. Dedovich22, Z. Y. Deng1,
A. Denig21, I. Denysenko22, M. Destefanis47A,47C, F. De Mori47A,47C, Y.
Ding26, C. Dong29, J. Dong1, L. Y. Dong1, M. Y. Dong1, S. X. Du51, P. F.
Duan1, J. Z. Fan38, J. Fang1, S. S. Fang1, X. Fang44, Y. Fang1, L.
Fava47B,47C, F. Feldbauer21, G. Felici19A, C. Q. Feng44, E. Fioravanti20A, M.
Fritsch13,21, C. D. Fu1, Q. Gao1, Y. Gao38, I. Garzia20A, K. Goetzen9, W. X.
Gong1, W. Gradl21, M. Greco47A,47C, M. H. Gu1, Y. T. Gu11, Y. H. Guan1, A. Q.
Guo1, L. B. Guo27, T. Guo27, Y. Guo1, Y. P. Guo21, Z. Haddadi24, A. Hafner21,
S. Han49, Y. L. Han1, F. A. Harris41, K. L. He1, Z. Y. He29, T. Held3, Y. K.
Heng1, Z. L. Hou1, C. Hu27, H. M. Hu1, J. F. Hu47A, T. Hu1, Y. Hu1, G. M.
Huang5, G. S. Huang44, H. P. Huang49, J. S. Huang14, X. T. Huang32, Y.
Huang28, T. Hussain46, Q. Ji1, Q. P. Ji29, X. B. Ji1, X. L. Ji1, L. L. Jiang1,
L. W. Jiang49, X. S. Jiang1, J. B. Jiao32, Z. Jiao16, D. P. Jin1, S. Jin1, T.
Johansson48, A. Julin42, N. Kalantar-Nayestanaki24, X. L. Kang1, X. S. Kang29,
M. Kavatsyuk24, B. C. Ke4, R. Kliemt13, B. Kloss21, O. B. Kolcu39B,d, B.
Kopf3, M. Kornicer41, W. Kuehn23, A. Kupsc48, W. Lai1, J. S. Lange23, M.
Lara18, P. Larin13, C. H. Li1, Cheng Li44, D. M. Li51, F. Li1, G. Li1, H. B.
Li1, J. C. Li1, Jin Li31, K. Li12, K. Li32, P. R. Li40, T. Li32, W. D. Li1, W.
G. Li1, X. L. Li32, X. M. Li11, X. N. Li1, X. Q. Li29, Z. B. Li37, H. Liang44,
Y. F. Liang35, Y. T. Liang23, G. R. Liao10, D. X. Lin13, B. J. Liu1, C. L.
Liu4, C. X. Liu1, F. H. Liu34, Fang Liu1, Feng Liu5, H. B. Liu11, H. H. Liu1,
H. H. Liu15, H. M. Liu1, J. Liu1, J. P. Liu49, J. Y. Liu1, K. Liu38, K. Y.
Liu26, L. D. Liu30, P. L. Liu1, Q. Liu40, S. B. Liu44, X. Liu25, X. X. Liu40,
Y. B. Liu29, Z. A. Liu1, Zhiqiang Liu1, Zhiqing Liu21, H. Loehner24, X. C.
Lou1,e, H. J. Lu16, J. G. Lu1, R. Q. Lu17, Y. Lu1, Y. P. Lu1, C. L. Luo27, M.
X. Luo50, T. Luo41, X. L. Luo1, M. Lv1, X. R. Lyu40, F. C. Ma26, H. L. Ma1, L.
L. Ma32, Q. M. Ma1, S. Ma1, T. Ma1, X. N. Ma29, X. Y. Ma1, F. E. Maas13, M.
Maggiora47A,47C, Q. A. Malik46, Y. J. Mao30, Z. P. Mao1, S. Marcello47A,47C,
J. G. Messchendorp24, J. Min1, T. J. Min1, R. E. Mitchell18, X. H. Mo1, Y. J.
Mo5, C. Morales Morales13, K. Moriya18, N. Yu. Muchnoi8,a, H. Muramatsu42, Y.
Nefedov22, F. Nerling13, I. B. Nikolaev8,a, Z. Ning1, S. Nisar7, S. L. Niu1,
X. Y. Niu1, S. L. Olsen31, Q. Ouyang1, S. Pacetti19B, P. Patteri19A, M.
Pelizaeus3, H. P. Peng44, K. Peters9, J. L. Ping27, R. G. Ping1, R. Poling42,
Y. N. Pu17, M. Qi28, S. Qian1, C. F. Qiao40, L. Q. Qin32, N. Qin49, X. S.
Qin1, Y. Qin30, Z. H. Qin1, J. F. Qiu1, K. H. Rashid46, C. F. Redmer21, H. L.
Ren17, M. Ripka21, G. Rong1, X. D. Ruan11, V. Santoro20A, A. Sarantsev22,f, M.
Savrié20B, K. Schoenning48, S. Schumann21, W. Shan30, M. Shao44, C. P. Shen2,
P. X. Shen29, X. Y. Shen1, H. Y. Sheng1, M. R. Shepherd18, W. M. Song1, X. Y.
Song1, S. Sosio47A,47C, S. Spataro47A,47C, B. Spruck23, G. X. Sun1, J. F.
Sun14, S. S. Sun1, Y. J. Sun44, Y. Z. Sun1, Z. J. Sun1, Z. T. Sun18, C. J.
Tang35, X. Tang1, I. Tapan39C, E. H. Thorndike43, M. Tiemens24, D. Toth42, M.
Ullrich23, I. Uman39B, G. S. Varner41, B. Wang29, B. L. Wang40, D. Wang30, D.
Y. Wang30, K. Wang1, L. L. Wang1, L. S. Wang1, M. Wang32, P. Wang1, P. L.
Wang1, Q. J. Wang1, S. G. Wang30, W. Wang1, X. F. Wang38, Y. D. Wang19A, Y. F.
Wang1, Y. Q. Wang21, Z. Wang1, Z. G. Wang1, Z. H. Wang44, Z. Y. Wang1, T.
Weber21, D. H. Wei10, J. B. Wei30, P. Weidenkaff21, S. P. Wen1, U. Wiedner3,
M. Wolke48, L. H. Wu1, Z. Wu1, L. G. Xia38, Y. Xia17, D. Xiao1, Z. J. Xiao27,
Y. G. Xie1, G. F. Xu1, L. Xu1, Q. J. Xu12, Q. N. Xu40, X. P. Xu36, L. Yan44,
W. B. Yan44, W. C. Yan44, Y. H. Yan17, H. X. Yang1, L. Yang49, Y. Yang5, Y. X.
Yang10, H. Ye1, M. Ye1, M. H. Ye6, J. H. Yin1, B. X. Yu1, C. X. Yu29, H. W.
Yu30, J. S. Yu25, C. Z. Yuan1, W. L. Yuan28, Y. Yuan1, A. Yuncu39B,g, A. A.
Zafar46, A. Zallo19A, Y. Zeng17, B. X. Zhang1, B. Y. Zhang1, C. Zhang28, C. C.
Zhang1, D. H. Zhang1, H. H. Zhang37, H. Y. Zhang1, J. J. Zhang1, J. L. Zhang1,
J. Q. Zhang1, J. W. Zhang1, J. Y. Zhang1, J. Z. Zhang1, K. Zhang1, L. Zhang1,
S. H. Zhang1, X. J. Zhang1, X. Y. Zhang32, Y. Zhang1, Y. H. Zhang1, Z. H.
Zhang5, Z. P. Zhang44, Z. Y. Zhang49, G. Zhao1, J. W. Zhao1, J. Y. Zhao1, J.
Z. Zhao1, Lei Zhao44, Ling Zhao1, M. G. Zhao29, Q. Zhao1, Q. W. Zhao1, S. J.
Zhao51, T. C. Zhao1, Y. B. Zhao1, Z. G. Zhao44, A. Zhemchugov22,h, B. Zheng45,
J. P. Zheng1, W. J. Zheng32, Y. H. Zheng40, B. Zhong27, L. Zhou1, Li Zhou29,
X. Zhou49, X. K. Zhou44, X. R. Zhou44, X. Y. Zhou1, K. Zhu1, K. J. Zhu1, S.
Zhu1, X. L. Zhu38, Y. C. Zhu44, Y. S. Zhu1, Z. A. Zhu1, J. Zhuang1, B. S.
Zou1, J. H. Zou1 (BESIII Collaboration) 1 Institute of High Energy Physics,
Beijing 100049, People’s Republic of China
2 Beihang University, Beijing 100191, People’s Republic of China
3 Bochum Ruhr-University, D-44780 Bochum, Germany
4 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
5 Central China Normal University, Wuhan 430079, People’s Republic of China
6 China Center of Advanced Science and Technology, Beijing 100190, People’s
Republic of China
7 COMSATS Institute of Information Technology, Lahore, Defence Road, Off
Raiwind Road, 54000 Lahore, Pakistan
8 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090,
Russia
9 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
10 Guangxi Normal University, Guilin 541004, People’s Republic of China
11 GuangXi University, Nanning 530004, People’s Republic of China
12 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
13 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz,
Germany
14 Henan Normal University, Xinxiang 453007, People’s Republic of China
15 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
16 Huangshan College, Huangshan 245000, People’s Republic of China
17 Hunan University, Changsha 410082, People’s Republic of China
18 Indiana University, Bloomington, Indiana 47405, USA
19 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN
and University of Perugia, I-06100, Perugia, Italy
20 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of
Ferrara, I-44122, Ferrara, Italy
21 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
22 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
23 Justus Liebig University Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
24 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands
25 Lanzhou University, Lanzhou 730000, People’s Republic of China
26 Liaoning University, Shenyang 110036, People’s Republic of China
27 Nanjing Normal University, Nanjing 210023, People’s Republic of China
28 Nanjing University, Nanjing 210093, People’s Republic of China
29 Nankai University, Tianjin 300071, People’s Republic of China
30 Peking University, Beijing 100871, People’s Republic of China
31 Seoul National University, Seoul, 151-747 Korea
32 Shandong University, Jinan 250100, People’s Republic of China
33 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
34 Shanxi University, Taiyuan 030006, People’s Republic of China
35 Sichuan University, Chengdu 610064, People’s Republic of China
36 Soochow University, Suzhou 215006, People’s Republic of China
37 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
38 Tsinghua University, Beijing 100084, People’s Republic of China
39 (A)Istanbul Aydin University, 34295 Sefakoy, Istanbul, Turkey; (B)Dogus
University, 34722 Istanbul, Turkey; (C)Uludag University, 16059 Bursa, Turkey
40 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
41 University of Hawaii, Honolulu, Hawaii 96822, USA
42 University of Minnesota, Minneapolis, Minnesota 55455, USA
43 University of Rochester, Rochester, New York 14627, USA
44 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
45 University of South China, Hengyang 421001, People’s Republic of China
46 University of the Punjab, Lahore-54590, Pakistan
47 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern
Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy
48 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
49 Wuhan University, Wuhan 430072, People’s Republic of China
50 Zhejiang University, Hangzhou 310027, People’s Republic of China
51 Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
b Also at Ankara University, 06100 Tandogan, Ankara, Turkey
c Also at the Moscow Institute of Physics and Technology, Moscow 141700,
Russia and at the Functional Electronics Laboratory, Tomsk State University,
Tomsk, 634050, Russia
d Currently at Istanbul Arel University, Kucukcekmece, Istanbul, Turkey
e Also at University of Texas at Dallas, Richardson, Texas 75083, USA
f Also at the PNPI, Gatchina 188300, Russia
g Also at Bogazici University, 34342 Istanbul, Turkey
h Also at the Moscow Institute of Physics and Technology, Moscow 141700,
Russia

###### Abstract

Using 482 pb-1 of data taken at $\sqrt{s}=4.009$ GeV, we measure the branching
fractions of the decays of $D^{*0}$ into $D^{0}\pi^{0}$ and $D^{0}\gamma$ to
be ${\cal B}(D^{*0}\to D^{0}\pi^{0})=(65.5\pm 0.8\pm 0.5)\%$ and ${\cal
B}(D^{*0}\to D^{0}\gamma)=(34.5\pm 0.8\pm 0.5)\%$ respectively, by assuming
that the $D^{*0}$ decays only into these two modes. The ratio of the two
branching fractions is ${\cal B}(D^{*0}\to D^{0}\pi^{0})/{\cal B}(D^{*0}\to
D^{0}\gamma)=1.90\pm 0.07\pm 0.05$, which is independent of the assumption
made above. The first uncertainties are statistical and the second ones
systematic. The precision is improved by a factor of three compared to the
present world average values.

###### pacs:

13.20.Fc, 13.25.Ft, 14.40.Lb

##  I Introduction

Quantum chromodynamics (QCD) Fritzsch:1973pi  is widely accepted as the
correct theory for the strong interaction. In the framework of QCD, the
building blocks of matter, colored quarks, interact with each other by
exchanging $SU(3)$ Yang-Mills gauge bosons, gluons, which are also colored.
Consequently, the quark-gluon dynamics becomes nonperturbative in the low
energy regime. Many effective models (EMs), such as the potential model, heavy
quark and chiral symmetries, and QCD sum rules, have been developed to deal
with the nonperturbative effects, as described in a recent review review . The
charmed meson, described as a hydrogen-like hadronic system consisting of a
heavy quark ($c$ quark) and a light quark ($u$, $d$, or $s$ quark), is a
particularly suited laboratory to test the EMs mentioned above. The decay
branching fractions of $D^{*0}$ to $D^{0}\pi^{0}$ (hadronic decay) and
$D^{0}\gamma$ (radiative decay) have been studied by a number of authors based
on EMs Eichten:1979ms ; Cheng:1993gc ; Aliev:1994nq ; Miller:1988tz . A
precise measurement of the branching fractions will constrain the model
parameters and thereby help to improve the EMs. On the experimental side,
these two branching fractions are critical input values for many measurements
such as the open charm cross section in $e^{+}e^{-}$ annihilation
CroninHennessy:2008yi  and the semileptonic decays of $B^{\pm}$ Bozek:2010xy .

These branching fractions have been measured in many electron-positron
collision experiments, such as CLEO cleo , ARGUS argus , BABAR babar  etc.,
but the uncertainties of the averaged branching fractions by the Particle Data
Group (PDG) pdg  are large (about 8%). The data sample used in this analysis
of 482 pb-1 collected at a center-of-mass (CM) energy $\sqrt{s}=4.009$ GeV
with the BESIII detector provides an opportunity for significant improvement.

##  II BESIII detector and Monte Carlo

BESIII is a general purpose detector which covers 93% of the solid angle, and
operates at the $e^{+}e^{-}$ collider BEPCII. Its construction is described in
great detail in Ref. BESIII . It consists of four main components: (a) A
small-cell, helium-based main drift chamber (MDC) with 43 layers providing an
average single-hit resolution of 135 $\mu$m, and a momentum resolution of 0.5%
for charged-particle at 1 GeV/$c$ in a 1 T magnetic field. (b) An electro-
magnetic calorimeter (EMC) consisting of 6240 CsI(Tl) crystals in a
cylindrical structure (barrel and two end-caps). The energy resolution for 1
GeV photons is 2.5% (5%) in the barrel (end-caps), while the position
resolution is 6 mm (9 mm) in the barrel (end-caps). (c) A time-of-fight system
(TOF), which is constructed of 5-cm-thick plastic scintillators and includes
88 detectors of 2.4 m length in two layers in the barrel and 96 fan-shaped
detectors in the end-caps. The barrel (end-cap) time resolution of 80 ps (110
ps) provides 2$\sigma$ $K/\pi$ separation for momenta up to about 1 GeV/$c$.
(d) The muon counter (MUC), consisting of Resistive Plate Chambers (RPCs) in
nine barrel and eight end-cap layers, is incorporated in the return iron of
the super-conducting magnet, and provides a position resolution of about 2 cm.

To investigate the event selection criteria, calculate the selection
efficiency, and estimate the background, Monte Carlo (MC) simulated samples
including 1,000,000 signal MC events and 500 pb-1 inclusive MC events are
generated. The event generator kkmc Jadach:1999vf  is used to generate the
charmonium state including initial state radiation (ISR) and the beam energy
spread; evtgen Ping:2008zz  is used to generate the charmonium decays with
known branching ratios pdg ; the unknown charmonium decays are generated based
on the lundcharm model Chen:2000tv ; and continuum events are generated with
pythia Sjostrand:2006za . In simulating the ISR events, the $e^{+}e^{-}\to
D^{*0}\bar{D}^{0}$ cross section measured with BESIII data at CM energies from
threshold to 4.009 GeV is used as input. A geant4 geant41 ; geant42  based
detector simulation package is used to model the detector response.

##  III Methodology and event selection

At $\sqrt{s}=4.009$ GeV, $e^{+}e^{-}\to D^{*0}\bar{D}^{0}+c.c.$ is produced
copiously. Assuming that there are only two decay modes for $D^{*0}$, i.e.,
$D^{*0}\to D^{0}\pi^{0}$ and $D^{*0}\to D^{0}\gamma$, the final states of
$D^{*0}\bar{D}^{0}$ decays will be either $D^{0}\bar{D}^{0}\pi^{0}$ or
$D^{0}\bar{D}^{0}\gamma$. Such an assumption is reasonable, since as shown in
Ref. next , the next largest branching fraction mode $D^{*0}\to
D^{0}\gamma\gamma$ is expected to be less than $3.3\times 10^{-5}$. The CM
energy is not high enough for $D^{*0}\bar{D}^{*0}$ production. To select
$e^{+}e^{-}\to D^{*0}\bar{D}^{0}$ signal events, we first reconstruct the
$D^{0}\bar{D}^{0}$ pair, and then require that the mass recoiling against the
$D^{0}\bar{D}^{0}$ system corresponds to a $\pi^{0}$ at its nominal mass pdg
or a photon with a mass of zero. This approach allows us to measure the
$D^{*0}$ decay branching ratios from the numbers of $D^{*0}\to D^{0}\pi^{0}$
and $D^{*0}\to D^{0}\gamma$ events in the $D^{0}\bar{D}^{0}$ recoil mass
spectra without reconstructing the $\pi^{0}$ or $\gamma$.

To increase the statistics and limit backgrounds, three $D^{0}$ decay modes
with large branching fractions and simple topologies are used, as shown in
Table 1. The corresponding five combinations are labeled as modes I to V.
Combinations with more than one $\pi^{0}$ or more than 6 charged tracks are
not used in this analysis.

Table 1: The charmed meson tag modes. Mode | Decay of $D^{0}$ | Decay of $\bar{D}^{0}$
---|---|---
I | $D^{0}\to K^{-}\pi^{+}$ | $\bar{D}^{0}\to K^{+}\pi^{-}$
II | $D^{0}\to K^{-}\pi^{+}$ | $\bar{D}^{0}\to K^{+}\pi^{-}\pi^{0}$
III | $D^{0}\to K^{-}\pi^{+}\pi^{0}$ | $\bar{D}^{0}\to K^{+}\pi^{-}$
IV | $D^{0}\to K^{-}\pi^{+}$ | $\bar{D}^{0}\to K^{+}\pi^{-}\pi^{+}\pi^{-}$
V | $D^{0}\to K^{-}\pi^{+}\pi^{+}\pi^{-}$ | $\bar{D}^{0}\to K^{+}\pi^{-}$

To select a good charged track, we require that it must originate within 10 cm
to the interaction point in the beam direction and 1 cm in the plane
perpendicular to the beam. In addition, a good charged track should be within
$|\cos\theta|<0.93$, where $\theta$ is its polar angle in the MDC. Information
from the TOF and energy loss ($dE/dx$) measurements in the MDC are combined to
form a probability $P_{\pi}$ ($P_{K}$) with a pion (kaon) assumption. To
identify a pion (kaon), the probability $P_{\pi}$ ($P_{K}$) is required to be
greater than 0.1%, and $P_{\pi}>P_{K}$ ($P_{K}>P_{\pi}$). In modes I-III, one
oppositely charged kaon pair and one oppositely charged pion pair are required
in the final state; while in modes IV and V, one oppositely charged kaon pair
and two oppositely charged pion pairs are required.

Photons, which are reconstructed from isolated showers in the EMC, are
required to be at least 20 degrees away from charged tracks and to have energy
greater than 25 MeV in the barrel EMC or 50 MeV in the end-cap EMC. To
suppress electronic noise and energy deposits unrelated to the signal event,
the EMC time ($t$) of the photon candidate should be coincident with the
collision event time, namely 0 $\leq t\leq$ 700 ns. We require at least two
good photons in modes II and III.

In order to improve the resolution of the $D^{0}\bar{D}^{0}$ recoil mass, a
kinematic fit is performed with the $D^{0}$ and $\bar{D}^{0}$ candidates
constrained to the nominal $D^{0}$ mass pdg . In modes II and III, after
requiring the invariant mass of the two photons be within $\pm 15$ MeV/$c^{2}$
of the nominal $\pi^{0}$ mass, a $\pi^{0}$ mass constraint is also included in
the fit. The total $\chi^{2}$ is calculated for the fit, and when there is
more than one $D^{0}\bar{D}^{0}$ combinations satisfying the selection
criteria above, the one with the least total $\chi^{2}$ is selected. Figure 1
shows comparisons of some interesting distributions between MC simulation and
data after applying the selection criteria above. Reasonable agreement between
data and MC simulation is observed, and the differences are considered in the
systematic uncertainty estimation. Figure 1 shows the total $\chi^{2}$
distribution; $\chi^{2}$ less than 30 is required to increase the purity of
the signal. Figures 1 and 1 show the distributions of $D^{0}$ momentum and
$\bar{D^{0}}$ momentum in the $e^{+}e^{-}$ center-of-mass system. The small
peaks at 0.75 GeV/$c$ are from direct $e^{+}e^{-}\to D^{0}\bar{D}^{0}$
production. To suppress such background events, we require that the momenta of
both $D^{0}$ and $\bar{D}^{0}$ to be less than 0.65 GeV/$c$. Another source of
background events is ISR production of $\psi(3770)$ with subsequent decay
$\psi(3770)\to D^{0}\bar{D}^{0}$, the number of which is obtained from MC
simulation. As shown in Fig. 1, the right and left peaks in the distribution
of the square of the $D^{0}\bar{D}^{0}$ recoil mass correspond to $D^{*0}\to
D^{0}\pi^{0}$ and $D^{*0}\to D^{0}\gamma$ events respectively; the respective
signal regions are defined by $[0.01,0.04]$ and $[-0.01,0.01]~{}({\rm
GeV}/c^{2})^{2}$ in the further analysis.

Figure 1: Comparisons between data and MC simulation, summing the five modes
listed in Table 1: (a) the $\chi^{2}$ distribution, (b) the momentum of
$D^{0}$, (c) the momentum of $\bar{D}^{0}$, and (d) the square of the
$D^{0}\bar{D}^{0}$ recoil mass. Dots with error bars are data, the open red
histograms are MC simulations, and the filled green histograms are background
events from the inclusive MC sample. The signal MCs are normalized to data
according to the number of events, and background events from inclusive MC
sample are normalized to data by luminosity.

##  IV Branching fractions

We calculate the branching fraction of $D^{*0}\to D^{0}\pi^{0}$ using ${\cal
B}(D^{*0}\to D^{0}\pi^{0})=\frac{N_{\pi^{0}}^{\rm prod}}{N_{\gamma}^{\rm
prod}+N_{\pi^{0}}^{\rm prod}}$, where $N_{\gamma}^{\rm prod}$ and
$N_{\pi^{0}}^{\rm prod}$ are the numbers of produced $D^{*0}\to D^{0}\gamma$
and $D^{*0}\to D^{0}\pi^{0}$ events, respectively, which are obtained by
solving the following equations

$\left(\begin{array}[]{l}N_{\pi^{0}}^{\rm obs}-N_{\pi^{0}}^{\rm bkg}\\\
N_{\gamma}^{\rm obs}-N_{\gamma}^{\rm
bkg}\end{array}\right)=\left(\begin{array}[]{cc}\epsilon_{\pi^{0}\pi^{0}}&\epsilon_{\gamma\pi^{0}}\\\
\epsilon_{\pi^{0}\gamma}&\epsilon_{\gamma\gamma}\end{array}\right)\left(\begin{array}[]{l}N_{\pi^{0}}^{\rm
prod}\\\ N_{\gamma}^{\rm prod}\end{array}\right),$ (1)

where $N_{i}^{\rm obs}$ and $N_{i}^{\rm bkg}$ are the number of selected
events in data and the number of background events estimated from MC
simulation in the $D^{*0}\to D^{0}+i$ mode, respectively; $\epsilon_{ij}$ is
the efficiency of selecting the generated $D^{*0}\to D^{0}+i$ events as
$D^{*0}\to D^{0}+j$, determined from MC simulation. Here, $i$ and $j$ denote
$\pi^{0}$ or $\gamma$. In the simulation, all decay channels of the $\pi^{0}$
from $D^{*0}$ decays are taken into account.

The numbers used in the calculation and the measured branching fractions are
listed in Table 2. For mode II and III, the final state used to reconstruct
the charm meson contains a $\pi^{0}$, so the efficiency for $D^{*0}\to
D^{0}\pi^{0}$ will be higher when the $\pi^{0}$ outside the charm meson is
misidentified as the $\pi^{0}$ from charm meson decays; for the other three
modes, the efficiency difference is caused by the dividing line, this can be
illustrated by the fact that
$\epsilon_{\pi^{0}\pi^{0}}$+$\epsilon_{\pi^{0}\gamma}$ almost equals to
$\epsilon_{\gamma\gamma}$+$\epsilon_{\gamma\pi^{0}}$. The results from each
mode and their weighted average are shown in Fig. 2; the goodness of the fit
determined with respect to the weighted average is $\rm\chi^{2}/n.d.f.=3.6/4$,
which means that the results from these five modes are consistent with each
other. Here $\rm n.d.f.$ is the number of degrees of freedom. The combined
result (${\cal B}(D^{*0}\to D^{0}\pi^{0})=65.7\pm 0.8\%$), which is calculated
by directly summing the number of events for the five modes together, is
consistent with the weighted average (${\cal B}(D^{*0}\to
D^{0}\pi^{0})=65.5\pm 0.8\%$). The weighted average is taken as the nominal
result. A cross check is performed by fitting the square of the
$D^{0}\bar{D}^{0}$ recoil mass from data with the MC simulated signal shapes,
and the results agree well with those in Table 2.

Table 2:  Numbers used for the calculation of the branching fractions and the results. ${\cal B}_{\pi^{0}}$ and ${\cal B}_{\gamma}$ are the the branching fractions of $D^{*0}\to D^{0}\pi^{0}$ and $D^{*0}\to D^{0}\gamma$, respectively. “Combined” is the result obtained by summing the number of events for the five modes together; “weighted” averaged is the result from averaging the results from the five modes by taking the error in each mode as weighted factor. The uncertainties are statistical only. Mode | $N^{\rm obs}_{\pi^{0}}$ | $N^{\rm obs}_{\gamma}$ | $N^{\rm bkg}_{\pi^{0}}$ | $N^{\rm bkg}_{\gamma}$ |  $\epsilon_{\pi^{0}\pi^{0}}$ (%) |  $\epsilon_{\gamma\gamma}$ (%) |  $\epsilon_{\pi^{0}\gamma}$ (%) |  $\epsilon_{\gamma\pi^{0}}$ (%) |  ${\cal B}_{\pi^{0}}$ (%) |  ${\cal B}_{\gamma}$ (%)
---|---|---|---|---|---|---|---|---|---|---
I | 504$\pm$23 | 281$\pm$17 | 4$\pm$2 | 24$\pm$5 | 36.19 | 35.22 | 0.11 | 0.99 | 65.2$\pm$1.9 | 34.8$\pm$1.9
II | 831$\pm$29 | 419$\pm$21 | 5$\pm$2 | 36$\pm$6 | 15.54 | 14.46 | 0.47 | 0.65 | 67.8$\pm$1.6 | 32.2$\pm$1.6
III | 780$\pm$28 | 441$\pm$21 | 6$\pm$3 | 38$\pm$6 | 15.37 | 14.60 | 0.43 | 0.51 | 65.4$\pm$1.6 | 34.6$\pm$1.6
IV | 538$\pm$24 | 301$\pm$18 | 10$\pm$3 | 30$\pm$6 | 19.04 | 18.34 | 0.09 | 0.51 | 65.1$\pm$1.9 | 34.9$\pm$1.9
V | 518$\pm$23 | 320$\pm$18 | 11$\pm$3 | 35$\pm$6 | 19.05 | 18.48 | 0.11 | 0.53 | 63.2$\pm$1.9 | 36.8$\pm$1.9
Combined |  |  |  |  |  |  |  |  | 65.7$\pm$0.8 | 34.3$\pm$0.8
Weighted average |  |  |  |  |  |  |  |  | 65.5$\pm$0.8 | 34.5$\pm$0.8

Figure 2: The branching fraction of $D^{*0}\to D^{0}\pi^{0}$. The dots with
error bars are the results from the five modes; the band represents the
weighted average. Only statistical uncertainties are included.

##  V Systematic uncertainties

In this analysis, the reconstruction of the photon or the $\pi^{0}$ is not
required. The branching fractions are obtained from the ratio of the numbers
of events in the ranges defined above, so many of the systematic uncertainties
related to the $D^{0}\bar{D}^{0}$ reconstruction, such as the tracking
efficiencies, particle identification efficiencies, etc., cancel.

We use $M^{2}_{Recoil_{D^{0}\bar{D^{0}}}}=0.01~{}({\rm GeV}/c^{2})^{2}$ as the
dividing line between $D^{*0}\to D^{0}\pi^{0}$ and $D^{*0}\to D^{0}\gamma$, as
shown in Fig. 1. The systematic uncertainty due to this selection is estimated
by comparing the branching fractions via changing this requirement from 0.01
to 0.008 or 0.012 $({\rm GeV}/c^{2})^{2}$.

The $D^{*0}\to D^{0}\pi^{0}$ and $D^{*0}\to D^{0}\gamma$ signal regions in the
$D^{0}\bar{D^{0}}$ recoil mass squared spectrum are in the combined range of
$[-0.01,0.04]~{}({\rm GeV}/c^{2})^{2}$; the associated systematic uncertainty
is estimated by removing this requirement.

The corrected track parameters are used in the nominal MC simulation according
to the procedure described in Ref. Ablikim:2012pg , and the difference in the
branching fractions measured with and without this correction are taken as the
systematic uncertainty caused by the requirement on the $\chi^{2}$ of the
kinematic fit.

The fraction of events with final state radiation (FSR) photons from charged
pions in data is found to be 20% higher than that in MC simulation
BESIII:2011ac , and the associated systematic uncertainty is estimated by
enlarging the ratio of FSR events in MC simulation by a factor of $1.2^{X}$,
where $X$ is the number of charged pion in the final state, and taking the
difference in the final result as systematic uncertainty.

The number of background events is calculated from the inclusive MC sample;
the corresponding systematic uncertainty is estimated from the uncertainties
of cross sections used in generating this sample. The dominant background
events are from open charm processes and ISR production of $\psi(3770)$ with
subsequent $\psi(3770)\to D^{0}\bar{D}^{0}$. The cross section for open charm
processes is 7.1 nb, with an uncertainty of 0.31 nb or about 5%
CroninHennessy:2008yi . The cross section for ISR production of $\psi(3770)$
is 0.114 nb, with an uncertainty of 0.011 nb or about 9% which is calculated
by varying $\Gamma_{ee}$ and $\Gamma_{\rm total}$ of $\psi(3770)$ by
$1\sigma$. The systematic uncertainty related to the number of background
events is conservatively estimated by changing the background level in Table 2
by 10% (larger than 5% and 9% mentioned above).

The efficiency in Table 2 is calculated using 200,000 signal MC events for
each mode, but only the ratio of the efficiencies for $D^{*0}\to D^{0}\pi^{0}$
and $D^{*0}\to D^{0}\gamma$ is needed in the branching fraction measurement.
The systematic error caused by the statistical uncertainty of the MC samples
is estimated by varying the efficiency for $D^{*0}\to D^{0}\gamma$ by
$1\sigma$ of its statistical uncertainty, and the difference of the branching
fraction is taken as the systematic uncertainty.

Other possible systematic uncertainty sources, such as from the simulation of
ISR, the requirement on the charmed meson momentum, and the tracking
efficiency difference caused by the tiny phase space difference between the
two decay modes of $D^{*0}$, are investigated and are negligible.

The summary of the systematic uncertainties considered is shown in Table 3.
Assuming the systematic uncertainties from the different sources are
independent, the total systematic uncertainty is found to be 0.5% by adding
all the sources in quadrature.

Table 3: The summary of the absolute systematic uncertainties in ${\cal B}(D^{*0}\to D^{0}\pi^{0})$ and ${\cal B}(D^{*0}\to D^{0}\gamma)$. Source | (%)
---|---
Dividing line between $D^{*0}\to D^{0}\pi^{0}$ and $D^{*0}\to D^{0}\gamma$ | 0.2
Choice of signal regions | 0.2
Kinematic fit | 0.2
FSR simulation | 0.1
Background | 0.2
Statistics of MC samples | 0.2
Sum | 0.5

##  VI Summary

By assuming that there are only two modes of $D^{*0}$, we measure the
branching fractions of $D^{*0}$ to be ${\cal B}(D^{*0}\to
D^{0}\pi^{0})=(65.5\pm 0.8\pm 0.5)\%$ and ${\cal B}(D^{*0}\to
D^{0}\gamma)=(34.5\pm 0.8\pm 0.5)\%$, where the first uncertainties are
statistical and the second ones are systematic. It should be noted that both
the statistical and the systematic uncertainties of these two branching
fractions are fully anti-correlated. Taking the correlations into account, the
branching ratio ${\cal B}(D^{*0}\to D^{0}\pi^{0})/{\cal B}(D^{*0}\to
D^{0}\gamma)=1.90\pm 0.07\pm 0.05$ is obtained. This ratio does not depend on
any assumptions in the $D^{*0}$ decays, so it can be used in calculating the
$D^{*0}$ decay branching fractions if more decay modes are discovered.

Figure 3 shows a comparison of the measured branching fraction of $D^{*0}\to
D^{0}\pi^{0}$ with other experiments and the world average value pdg . Our
measurement is consistent with the previous ones within about 1$\sigma$ but
with much better precision. These much improved results can be used to update
the parameters in the effective models mentioned above, such as the mass of
the charm quark Eichten:1979ms ; Aliev:1994nq , the effective coupling
constant Cheng:1993gc , and the magnetic moment of the charm quark
Miller:1988tz . With these new results as input, the uncertainty in the
semileptonic decay branching fraction of $B^{\pm}$ Bozek:2010xy  can be
reduced, thus leading to a tighter constraint on the standard model (SM) and
its extensions.

Figure 3: Comparison of the branching fraction of $D^{*0}\to D^{0}\pi^{0}$
from this work and from previous experiments. Dots with error bars are results
from different experiments, and the band is the result from this work with
both statistical and systematic uncertainties.

###### Acknowledgements.

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing
center for their strong support. This work is supported in part by National
Key Basic Research Program of China under Contract No. 2015CB856700; Joint
Funds of the National Natural Science Foundation of China under Contracts Nos.
11079008, 11179007, U1232201, U1332201; National Natural Science Foundation of
China (NSFC) under Contracts Nos. 10935007, 11121092, 11125525, 11235011,
11322544, 11335008; the Chinese Academy of Sciences (CAS) Large-Scale
Scientific Facility Program; CAS under Contracts Nos. KJCX2-YW-N29,
KJCX2-YW-N45; 100 Talents Program of CAS; INPAC and Shanghai Key Laboratory
for Particle Physics and Cosmology; German Research Foundation DFG under
Contract No. Collaborative Research Center CRC-1044; Istituto Nazionale di
Fisica Nucleare, Italy; Ministry of Development of Turkey under Contract No.
DPT2006K-120470; Russian Foundation for Basic Research under Contract No.
14-07-91152; U.S. Department of Energy under Contracts Nos. DE-FG02-04ER41291,
DE-FG02-05ER41374, DE-FG02-94ER40823, DESC0010118; U.S. National Science
Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer
Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research
Foundation of Korea under Contract No. R32-2008-000-10155-0.

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