11institutetext:  Department of Physics, Chungbuk National University,
Cheongju 28644, Republic of Korea, 22institutetext: Korea Astronomy and Space
Science Institute, Daejon 34055, Republic of Korea 33institutetext: Korea
University of Science and Technology, Korea, (UST), 217 Gajeong-ro, Yuseong-
gu, Daejeon, 34113, Republic of Korea 44institutetext: Institute of Natural
and Mathematical Science, Massey University, Auckland 0745, New Zealand
55institutetext: Max-Planck-Institute for Astronomy, Königstuhl 17, 69117
Heidelberg, Germany 66institutetext: Department of Astronomy, Ohio State
University, 140 W. 18th Ave., Columbus, OH 43210, USA 77institutetext: Center
for Astrophysics $|$ Harvard & Smithsonian, 60 Garden St., Cambridge, MA
02138, USA 88institutetext: University of Canterbury, Department of Physics
and Astronomy, Private Bag 4800, Christchurch 8020, New Zealand
99institutetext: Department of Particle Physics and Astrophysics, Weizmann
Institute of Science, Rehovot 76100, Israel 1010institutetext: Department of
Astronomy, Tsinghua University, Beijing 100084, China 1111institutetext:
School of Space Research, Kyung Hee University, Yongin, Kyeonggi 17104,
Republic of Korea 1212institutetext: Institute for Space-Earth Environmental
Research, Nagoya University, Nagoya 464-8601, Japan 1313institutetext: Code
667, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
1414institutetext: Department of Astronomy, University of Maryland, College
Park, MD 20742, USA 1515institutetext: Department of Earth and Planetary
Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-0033, Japan 1616institutetext: Instituto de Astrofísica
de Canarias, Vía Láctea s/n, E-38205 La Laguna, Tenerife, Spain
1717institutetext: Department of Earth and Space Science, Graduate School of
Science, Osaka University, Toyonaka, Osaka 560-0043, Japan 1818institutetext:
Department of Physics, The Catholic University of America, Washington, DC
20064, USA 1919institutetext: Department of Astronomy, Graduate School of
Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033,
Japan 2020institutetext: Sorbonne Université, CNRS, UMR 7095, Institut
d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France
2121institutetext: Department of Physics, University of Auckland, Private Bag
92019, Auckland, New Zealand 2222institutetext: University of Canterbury Mt.
John Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand

# KMT-2021-BLG-1150Lb: Microlensing planet detected through a densely covered
planetary-caustic signal

Cheongho Han 0101 Youn Kil Jung 02020303 Ian A. Bond 0404 Andrew Gould
(Leading authors)
Sun-Ju Chung 0505060602020707 Michael D. Albrow 0808 Kyu-Ha Hwang 0202 Yoon-
Hyun Ryu 0202 In-Gu Shin 0707 Yossi Shvartzvald 0909 Hongjing Yang 1010
Jennifer C. Yee 0707 Weicheng Zang 07071010 Sang-Mok Cha 02021111 Doeon Kim
0101 Dong-Jin Kim 0202 Seung-Lee Kim 0202 Chung-Uk Lee 0202 Dong-Joo Lee 0202
Yongseok Lee 02021111 Byeong-Gon Park 0202 Richard W. Pogge
(The KMTNet collaboration)
Fumio Abe 06061212 Richard Barry 1313 David P. Bennett 13131414 Aparna
Bhattacharya 13131414 Hirosame Fujii 1212 Akihiko Fukui 15151616 Ryusei Hamada
1717 Yuki Hirao 1717 Stela Ishitani Silva 13131818 Yoshitaka Itow 1212 Rintaro
Kirikawa 1717 Iona Kondo 1717 Naoki Koshimoto 1919 Yutaka Matsubara 1212 Sho
Matsumoto 1717 Shota Miyazaki 1717 Yasushi Muraki 1212 Arisa Okamura 1717 Greg
Olmschenk 1313 Clément Ranc 2020 Nicholas J. Rattenbury 2121 Yuki Satoh 1717
Takahiro Sumi 1717 Daisuke Suzuki 1717 Taiga Toda 1717 Mio Tomoyoshi 1717 Paul
J. Tristram 2222 Aikaterini Vandorou 13131414 Hibiki Yama 1717 Kansuke
Yamashita
(The MOA Collaboration)
1717

###### Abstract

Aims.  Recently, there have been reports of various types of degeneracies in
the interpretation of planetary signals induced by planetary caustics. In this
work, we check whether such degeneracies persist in the case of well-covered
signals by analyzing the lensing event KMT-2021-BLG-1150, for which the light
curve exhibits a densely and continuously covered short-term anomaly.

Methods.  In order to identify degenerate solutions, we thoroughly investigate
the parameter space by conducting dense grid searches for the lensing
parameters. We then check the severity of the degeneracy among the identified
solutions.

Results.  We identify a pair of planetary solutions resulting from the well-
known inner-outer degeneracy, and find that interpreting the anomaly is not
subject to any degeneracy other than the inner-outer degeneracy. The measured
parameters of the planet separation (normalized to the Einstein radius) and
mass ratio between the lens components are $(s,q)_{\rm
in}\sim(1.297,1.10\times 10^{-3})$ for the inner solution and $(s,q)_{\rm
out}\sim(1.242,1.15\times 10^{-3})$ for the outer solution. According to a
Bayesian estimation, the lens is a planetary system consisting of a planet
with a mass $M_{\rm p}=0.88^{+0.38}_{-0.36}\leavevmode\nobreak\ M_{\rm J}$ and
its host with a mass $M_{\rm h}=0.73^{+0.32}_{-0.30}\leavevmode\nobreak\
M_{\odot}$ lying toward the Galactic center at a distance $D_{\rm
L}=3.8^{+1.3}_{-1.2}$ kpc. By conducting analyses using mock data sets
prepared to mimic those obtained with data gaps and under various
observational cadences, it is found that gaps in data can result in various
degenerate solutions, while the observational cadence does not pose a serious
degeneracy problem as long as the anomaly feature can be delineated.

###### Key Words.:

planets and satellites: detection – gravitational lensing: micro

##  1 Introduction

The microlensing signal of a planet generally appears as a short-term anomaly
to the lensing light curve produced by the host of the planet (Mao &
Paczyński, 1991; Gould & Loeb, 1992). The planetary signal is produced when a
source star approaches close to or passes over the lensing caustic induced by
the planet. A planetary companion induces two sets of caustics, in which one
tiny set forms near the host of the planetary system, and the other set forms
in the region away from the host with a separation $\sim{\bf s}-1/{\bf s}$,
where ${\bf s}$ denote the planet-host separation vector. The former and
latter caustics are referred to as ”central” and ”planetary” caustics,
respectively. Due to the caustic location, the planetary signal generated by
the central caustic appears near the peak of a high-magnification event, while
the signal produced by the planetary caustic can appear at any part of the
lensing light curve.

In the early phase of the planetary microlensing experiments, the majority of
microlensing planets were found from the observations of high-magnifications
events, for example, OGLE-2005-BLG-071Lb (Udalski et al., 2005),
OGLE-2005-BLG-169Lb (Gould et al., 2006), and MOA-2007-BLG-192Lb (Bennett et
al., 2008). This was because the observational cadence of the microlensing
surveys at that time was generally not high enough to detect short-term
planetary signals, and thus planet searches were carried out in a
survey+followup mode, in which survey groups mainly concentrated on event
detections, and followup groups conducted high-cadence followup observations
for a fraction of events found by the survey groups. In this observation mode,
high-magnification events were important targets because the chance for the
source stars of these events to pass the perturbation regions induced by the
central caustics was very high and the time of the event peak could be
predicted in advance for the preparation of followup observations (Griest &
Safizadeh, 1998).

With the launch of high-cadence microlensing surveys in the 2010s, not only
the total detection rate of microlensing planets but also the fraction of
planets detected via the perturbations induced by planetary caustics have
greatly increased, for example, KMT-2016-BLG-1105Lb, KMT-2017-BLG-1194Lb, and
OGLE-2017-BLG-1806 (Zang et al., 2023), KMT-2018-BLG-0173Lb (Jung et al.,
2022), KMT-2021-BLG-0712Lb and KMT-2021-BLG-0909Lb (Ryu et al., 2023). The
total planet detection rate has increased because all lensing events can be
densely monitored regardless of lensing magnifications without the need of
extra followup observations. The rate of planet detections via the signals
generated by planetary caustics has increased because all parts of lensing
light curves can be monitored with moderately-high to very-high cadences.

The classic type of degeneracy in the interpretations of the signals induced
by planetary caustics is the ”inner-outer” degeneracy, which was predicted by
Gaudi & Gould (1997) even before the detection of the first microlensing
planet OGLE 2003-BLG-235/MOA-2003-BLG-53Lb (Bond et al., 2004). This
degeneracy is intrinsic in the sense that it arises due to the intrinsic
similarity between the magnification patterns on the near (to the primary
lens) and far sides of the planetary caustic, and thus the planetary signal
resulting from the source trajectory passing on near side of the caustic would
be similar to the signal resulting from the trajectory passing on the far
side. The origins of this degeneracy have been further explored in Zhang et
al. (2022).

As the number of planets detected from actually observed signals generated by
planetary increases, various types of unexpected degeneracies have been
reported. From the analysis of the planetary lensing event OGLE-2017-BLG-0173,
Hwang et al. (2018) reported a new type of degeneracy between the solution in
which the source fully enveloped the caustic and the other solution in which
the source enveloped one side of the caustic. They also reported a degeneracy
between the solution in which the light-curve perturbation was generated by a
planetary caustic due to a ”close” planet and the one in which it was
generated by a ”wide” planet. Here the terms ”close” and ”wide” refer to the
cases in which the projected planet-host separation is less and greater than
the radius of the Einstein ring ($\theta_{\rm E}$), respectively. From the
analysis of the anomaly appearing in the planetary lensing event
OGLE-2017-BLG-0373, Skowron et al. (2018) also reported multiple degeneracies
that had not been known before. We note that these new types of degeneracies
were identified from the analyses of partially covered planetary signals, and
thus it is not yet clear whether these degeneracies persist in the
interpretations of continuously covered signals.

In this paper, we present the analysis of the lensing event KMT-2021-BLG-1150,
for which a short-term signal induced by a planetary caustic appears on the
lensing light curve. Despite the short duration, the anomaly was densely and
continuously covered including both the caustic entrance and exit, and thus
the event provides an important test bed that enables one to check whether
various types of recently-reported degeneracies persist even for well covered
planetary signals.

We present the analysis according to the following organization. In Sect. 2,
we describe the observations of the lensing event and the data acquired from
the observations. We mention the characteristics of the lensing event and the
anomaly appearing in the lensing light curve. In Sect. 3, we depict the
detailed procedure of the analysis and present the results found from the
analysis. In Sect. 4, we explain the source characterization procedure
conducted to estimate the angular Einstein radius and present the measured
value of $\theta_{\rm E}$. In Sect. 5, we detail the Bayesian analysis
conducted to estimate the physical parameters of the planetary system and
present the estimated parameters. In Sect. 6, we present the results of the
test conducted using mock data sets prepared to mimic those obtained with data
gaps and under various observational cadences. We summarize the results of the
analysis and conclude in Sect. 7.

Figure 1:  Light curve of KMT-2021-BLG-1150. The lower panel shows the whole
view and the upper panel shows the zoom of the region around the anomaly. The
curve drawn over the data point is a 1L1S model obtained by fitting the light
curve excluding the data points around the anomaly.

##  2 Observations and data

The source of the microlensing event KMT-2021-BLG-1150 lies toward the
Galactic bulge field at the equatorial coordinates $({\rm RA},{\rm DEC})_{\rm
J2000}=($17:55:09.63, -31:18:47.99), which correspond to the Galactic
coordinates $(l,b)=(-0^{\circ}\hskip-2.0pt.986,-2^{\circ}\hskip-2.0pt.989)$.
The extinction toward the field is $A_{I}=1.50$, and the baseline $I$-band
magnitude of the source is $I_{\rm base}=18.86$, as derived from the
calibrated OGLE-III catalog (Szymański et al., 2011). The magnification of the
source flux induced by lensing was first found by the EventFinder system (Kim
et al., 2018) of the KMTNet group (Kim et al., 2016) on 2021 June 4, which
corresponds to the abridged heliocentric Julian date ${\rm HJD}^{\prime}={\rm
HJD}-2450000=9369.56$. On 2021 June 21, the event was independently found by
the MOA group (Bond et al., 2001), who labeled the event as MOA-2021-BLG-197.
Hereafter we refer to the event as KMT-2021-BLG-1150 following the convention
of using the event ID reference of the first discovery group. The source lies
in the KMTNet prime fields BLG01 and BLG41, toward which observations were
conducted with a 0.5 hr cadence for each field and 0.25 hr in combination. The
MOA observations were carried out at a similar cadence.

Observations by the KMTNet group were done utilizing the three identical 1.6 m
telescopes that are globally distributed in the Southern Hemisphere at the
Cerro Tololo Inter-American Observatory in Chile (KMTC), the South African
Astronomical Observatory in South Africa (KMTS), and the Siding Spring
Observatory in Australia (KMTA). The MOA group used the 1.8 m telescope
located at the Mt. John Observatory in New Zealand. Images were acquired
mainly in the $I$ band for the KMTNet survey and in the customized MOA-$R$
band for the MOA survey. For both surveys, subsets of images were taken in the
$V$ band for the purpose of measuring the color of the source.

Figure 2:  Map of $\Delta\chi^{2}$ in the space of the binary-lens parameters
$s$ and $q$. The vertical dashed line indicates the geometric mean of $s_{\rm
in}$ and $s_{\rm out}$, which represent the binary separations of the inner
and outer solutions, respectively. The color coding is set to represent points
with $\leq 1n\sigma$ (red), $\leq 2n\sigma$ (yellow), $\leq 3n\sigma$ (green),
$\leq 4n\sigma$ (cyan) and, $\leq 5n\sigma$ (blue), where $n=3$.

Figure 1 shows the lensing light curve of KMT-2021-BLG-1150 constructed by
combining the data from the KMTNet and MOA surveys. It displays a short-term
anomaly appearing near the peak of the event. The curve drawn over the data
points is the single-lens single-source (1L1S) model obtained by fitting the
data excluding those around the anomaly. From the zoom-in view of the anomaly
region presented in the top panel, it is found that the anomaly exhibits two
caustic-crossing features at $t_{\rm c,1}\sim 9386.9$ (caustic entrance) and
$t_{\rm c,2}\sim 9387.7$ (caustic exit) with a time gap $\Delta t_{\rm
c}=t_{\rm c,2}-t_{\rm c,1}\sim 0.8$ day between the caustic features. Besides
these caustic features, the anomaly exhibits negative deviations of $\sim 0.1$
mag level from the 1L1S model just before the caustic entrance and after the
caustic exit. We note that all these anomaly features were densely resolved by
the data from the combined high-cadence observations of the survey groups.

In the analysis of the event, we used the data prepared by reducing the images
and conducting photometry of the source with the use of the pipelines of the
individual groups. The pySIS pipeline of the KMTNet group was developed by
Albrow et al. (2009), and that of the MOA survey was developed by Bond et al.
(2001). Both pipelines commonly applied the difference image technique
(Tomaney & Crotts, 1996; Alard & Lupton, 1998) that was developed for the
optimal photometry of stars lying in very dense fields. Following the Yee et
al. (2012) routine, we readjusted the error bars estimated by the pipelines so
that the scatter of data is consistent with the error bars and the $\chi^{2}$
value per degree of freedom (dof) for each data becomes unity.

Table 1: Model parameters

Parameter | Inner | Outer
---|---|---
$\chi^{2}$/dof | $8139.7/8152$ | $8133.4/8152$
$t_{0}$ (HJD′) | $9387.077\pm 0.055$ | $9387.086\pm 0.055$
$u_{0}$ | $0.502\pm 0.010$ | $0.464\pm 0.010$
$t_{\rm E}$ (days) | $41.55\pm 0.58$ | $43.75\pm 0.65$
$s$ | $1.297\pm 0.005$ | $1.242\pm 0.007$
$q$ ($10^{-3}$) | $1.10\pm 0.05$ | $1.15\pm 0.05$
$\alpha$ (rad) | $4.703\pm 0.003$ | $4.703\pm 0.003$
$\rho$ ($10^{-3}$) | $0.956\pm 0.015$ | $0.899\pm 0.016$

111 ${\rm HJD}^{\prime}={\rm HJD}-2450000$.

##  3 Interpretation of the anomaly

The anomaly in the lensing light curve of KMT-2021-BLG-1150 is characterized
by a near-peak caustic feature. Such an anomaly feature is known to be
produced by 3 major channels. The first is the ”high-magnification” channel,
in which an anomaly near the peak is produced when a source approaches close
to the central caustic induced either by a planetary companion lying around
the Einstein ring ($s\sim 1$) or a binary companion with a very small ($s\ll
1$) or large ($s\gg 1$) separation from the primary (Han & Hwang, 2009). The
anomaly produced via this channel arises for a high-magnification event
because the central caustic is very tiny (Chung et al., 2005), and thus the
source should approach very close to the primary for the production of a near-
peak anomaly. The second is the ”right-angle” channel, in which a near-peak
anomaly is generated when a source passes the perturbation region around the
caustic at an approximately right angle with respect to the planet-host axis,
for example, KMT-2021-BLG-0748 (Ryu et al., 2022) and KMT-2021-BLG-1554 (Han
et al., 2022). In this case, the anomaly can arise regardless of the peak
magnification because the caustic can appear at any part around the Einstein
ring. The third is the ”off-axis” channel, in which a near-peak anomaly is
produced by the source passage through the anomaly region around the caustic
lying away from the binary axis, for example, OGLE-2016-BLG-1266 (Albrow et
al., 2018) and the off-axis solution of KMT-2018-BLG-1497 (Jung et al., 2022).
Among these channels, the anomaly in KMT-2021-BLG-1150 is unlikely to be
produced by the high-magnification channel because it appears when the
magnification $A_{\rm anom}\sim 2.4$ is not very high.

Figure 3:  Enlarged view around the region of the anomaly. The dashed, dotted,
and solid curves represent the models of the 1L1S, inner 2L1S, and outer 2L1S
solutions, respectively. We note that the model curves of the inner and outer
2L1S solutions are so similar that it is difficult to resolve them with the
given line width.

For the interpretation of the anomaly, we conducted modeling of the observed
lensing light curve. In the modeling, we searched for a lensing solution
representing a set of the lensing parameters that best described the observed
anomaly. Considering that caustic features are produced by the multiplicity of
a lens, we conducted a binary-lens single-source (2L1S) modeling. The lensing
parameters of the 2L1S model include $(t_{0},u_{0},t_{\rm
E},s,q,\alpha,\rho)$. The first three of these parameters describe the source
approach to the lens, and they represent the time of the closest lens-source
approach, the separation at that time, and the event time scale, respectively.
The next three parameters describe the binarity of the lens, and the
individual parameters denote the projected separation (scaled to $\theta_{\rm
E}$) and mass ratio between the lens components, and the source trajectory
angle defined as the angle between the source trajectory and the binary axis.
The last parameter denotes the ratio of the angular source radius $\theta_{*}$
to the Einstein radius, that is, $\rho=\theta_{*}/\theta_{\rm E}$ (normalized
source radius), and this parameters is needed to describe the deformation of
the caustic-crossing features by finite-source effects.

Considering that various types of degeneracies had been reported from the
recent analyses of microlensing planets detected through the signals generated
by planetary caustics, we thoroughly investigated the parameter space to check
all possible degenerate solutions. Figure 2 shows the $\Delta\chi^{2}$ map
constructed by conducting dense grid searches for the binary-lens parameters
$s$ and $q$. The map shows two distinct local solutions resulting from the
inner-outer degeneracy with planetary parameters $(s,q)_{\rm
in}\sim(1.297,1.10\times 10^{-3})$ for the inner solution and $(s,q)_{\rm
out}\sim(1.242,1.15\times 10^{-3})$ for the outer solution. The degeneracy
between the two solutions is fairly severe, although the outer solution is
slightly preferred over the inner solution by $\Delta\chi^{2}=6.3$.

Figure 4:  Zoom-in views around the caustic entrance (left panel) and exit
(right panel). The solid curve is the model curve of the outer 2L1S solution.

We list the full lensing parameters of the inner and outer 2L1S solutions in
Table 1 together with the $\chi^{2}$ values of the fits and degrees of
freedom. The two degenerate solutions result in similar mass ratios of $q\sim
1.1\times 10^{-3}$, and the low value of $q$ indicates that the companion to
the lens is a planetary mass object. The planet separations of the inner and
outer solutions are slightly different from each other, and the separation of
the inner solution $s_{\rm in}=1.297\pm 0.005$ is slightly larger than the
separation of the outer solution of $s_{\rm out}=1.242\pm 0.007$. Besides
these two solutions, we found no other degenerate solutions. For a double
check, we investigated a degenerate solution resulting from the off-axis
channel by restricting the source trajectory to pass the off-axis cusps, and
found that the best-fit off-axis solution resulted in a model that yielded a
poorer fit than the outer solution by $\Delta\chi^{2}=2320$.

In Figure 3, we present the model curves of the inner (dotted curve) and outer
(solid curve) solutions around the region of the anomaly. It shows that both
models well describe the anomaly including the positive deviations caused by
caustic crossings and the negative deviations before the caustic entrance and
after the caustic exit. As shown in the zoom-in views around the caustic
entrance and exit presented in Figure 4, both caustic crossings were densely
resolved despite the short duration of each caustic crossing of $\Delta t_{\rm
c}\sim 2\rho t_{\rm E}/\sin\psi\sim 2$ hr, where $\psi\sim 70^{\circ}$
represents the incidence angle of the source to the fold of the caustic. With
the well resolved caustic crossings, the normalized source radius was
precisely measured.

The lens-system configurations of the inner and outer 2L1S solutions are
presented in Figure 5, which shows the trajectory of the source with respect
to the lens caustic. It shows that the anomaly was produced by the crossings
of the source over the planetary caustic formed by a planetary companion, and
the source crossed the near and far side according to the inner and outer
solutions, respectively. The source crossed the planet-host axis at a very
nearly right angle, 89.4 deg, and this explains the near-peak location of the
anomaly. The lens-source separation (scaled to $\theta_{\rm E}$) at the time
of the anomaly, $u_{\rm anom}\sim 0.5$, is not small, and this explains the
low lensing magnification at the time of the anomaly.

Figure 5:  Lens-system configurations of the inner (upper panel) and outer
(lower panel) solutions. The inset in each panel shows the whole view of the
caustic (red figures), and the main panel shows the zoom-in view around the
planetary caustic. The arrowed line represents the source trajectory, and the
grey curves encompassing the caustic are equi-magnification contours.

We found that the pair of the planet separations of the inner and outer
solutions, $(s_{\rm in},s_{\rm out})$, well obeyed the analytic relation
introduced by Hwang et al. (2022). The relation is expressed as

$s^{\dagger}=\sqrt{s_{\rm in}\times s_{\rm out}}={\sqrt{u_{\rm
anom}^{2}+4}+u_{\rm anom}\over 2},$ (1)

where $u^{2}_{\rm anom}=\tau^{2}_{\rm anom}+u_{0}^{2}$, $\tau_{\rm
anom}=(t_{\rm anom}-t_{0})/t_{\rm E}$, and $t_{\rm anom}$ represents the time
of the anomaly. We note that the second term in Equation (1) was originally
expressed as the arithmetic mean of $s_{\rm in}$ and $s_{\rm out}$, that is,
$(s_{\rm in}+s_{\rm out})/2$, and Gould et al. (2022) found that the geometric
mean, this is, $(s_{\rm out}\times s_{\rm in})^{1/2}$, proved to be a better
approximation than the arithmetic mean. The $s^{\dagger}$ value estimated from
$s_{\rm in}$ and $s_{\rm out}$ is $s^{\dagger}=(s_{\rm out}\times s_{\rm
in})^{1/2}=1.269$. From the lensing parameters $(t_{0},t_{\rm anom},t_{\rm
E})\sim(9387.1,9387.3,43.5)$, it is estimated that $\tau_{\rm anom}=(t_{\rm
anom}-t_{0})/t_{\rm E}=0.005$, $u_{\rm anom}=(\tau_{\rm
anom}^{2}+u_{0}^{2})^{1/2}=0.480$, and $s^{\dagger}=[(u_{\rm
anom}^{2}+4)^{1/2}+u_{\rm anom}]/2=1.269$. Therefore, the $s^{\dagger}$ values
estimated from the planet separations $(s_{\rm in},s_{\rm out})$ and from the
planetary parameters $(t_{0},t_{\rm anom},u_{0},t_{\rm E})$ match very well
down to 3 digits after the decimal point, proving the validity of the analytic
relation. In Figure 2, we mark the geometric mean of $s_{\rm in}$ and $s_{\rm
out}$ as a dashed vertical line.

We checked whether the microlens parallax $\mbox{\boldmath$\pi$}_{\rm E}$
could be measured by conducting an additional modeling including the two
microlens-parallax parameters $(\pi_{{\rm E},N},\pi_{{\rm E},E})$, which
denote the north and east components of the microlens-parallax vector
$\mbox{\boldmath$\pi$}_{\rm E}=(\mbox{\boldmath$\pi$}_{\rm rel}/\theta_{\rm
E})(\mbox{\boldmath$\mu$}/\mu)$, respectively (Gould, 1992, 2000, 2004). Here
$\mu$ represents the relative lens-source proper motion vector, $\pi_{\rm
rel}=\pi_{\rm L}-\pi_{\rm S}={\rm AU}(1/D_{\rm L}-1/D_{\rm S})$ is the
relative lens-source parallax, and $(D_{\rm L},D_{\rm S})$ denote the
distances to the lens and source, respectively. We found that it was difficult
to measure the parallax parameters because the lensing magnification of the
event was low, and thus the light curve was not susceptible to the subtle
variation induced by higher-order effects.

Figure 6:  Locations of the source, blend, and red giant clump (RGC) centroid
in the instrumental color-magnitude diagram.

##  4 Source star and Einstein radius

In this section, we characterize the source star of the event and estimate the
angular Einstein radius. We estimated $\theta_{\rm E}$ from the relation

$\theta_{\rm E}={\theta_{*}\over\rho},$ (2)

where the angular source radius $\theta_{*}$ was deduced from the source type,
and the normalized source radius $\rho$ was measured from modeling the light
curve. For the specification of the source type, we estimated the reddening-
and extinction-corrected (de-reddened) color and magnitude of the source,
$(V-I,I)_{{\rm S},0}$.

We used the Yoo et al. (2004) method for the estimation of $(V-I,I)_{{\rm
S},0}$. Following the routine procedure of the method, we first measured the
instrumental color and magnitude of the source, placed the source in the
instrumental color-magnitude diagram (CMD), and then calibrated the source
color and magnitude using the centroid of the red giant clump (RGC) in the CMD
as a reference. The RGC centroid can serve as a reference for calibration
because of its known de-reddened color and magnitude.

In Figure 6, we mark the source position with respect to the RGC centroid in
the instrumental CMD constructed using the pyDIA photometry of stars lying
around the source. The $I$\- and $V$-band magnitudes of the source were
measured by regressing the pyDIA photometry data of the individual passbands
with respect to the model light curve. The measured colors and magnitudes of
the source and RGC centroid are $(V-I,I)_{\rm S}=(2.129\pm 0.113,19.619\pm
0.008)$ and $(V-I,I)_{\rm RGC}=(2.463\pm 0.020,16.377\pm 0.040)$,
respectively. We note that the magnitude of the instrumental CMD is
approximately scaled, and thus the extinction toward field measured from
$I_{\rm RGC}-I_{\rm RGC,0}=1.87$ does not match the value $A_{I}=1.50$ that is
estimated from the calibrated magnitude. The measurement uncertainty of $V-I$
is fairly big because the source color was measured mainly on a single
$V$-band point inside the caustic trough taken at ${\rm
HJD}^{\prime}=9387.584$. With the known de-reddened values of the RGC
centroid, $(V-I,I)_{\rm RGC,0}=(1.060,14.502)$ (Bensby et al., 2013; Nataf et
al., 2013), then the de-reddened source color and magnitude were estimated as

$\displaystyle{(V-I,I)_{\rm 0}=}$ | $\displaystyle{{}\ (V-I,I)_{{\rm RGC},0}+\Delta(V-I,I)}$
---|---
$\displaystyle{=}$ | $\displaystyle{{}\ (0.726\pm 0.120,17.744\pm 0.021),}$
(3)

where $\Delta(V-I,I)=(V-I,I)_{\rm S}-(V-I,I)_{\rm RGC}$ represents the offset
of the source from the RGC centroid. According to the estimated color and
magnitude, the source is a G-type main-sequence star. We note that the error
of the dereddened $I$-band magnitude, that is, $\sigma(I_{0})=0.021$ mag, is
based purely on the fractional error of the source flux measured from the
modeling. Gould (2014) pointed out that the $\theta_{*}$ measurement is
subject to additional errors originating from the uncertain dereddened RGC
color of Bensby et al. (2013) and the uncertain position of the RGC, and these
two errors combined yield a 7% error in the estimation of $\theta_{*}$. In our
estimation of $\theta_{*}$, we add this fractional error.

Once the source type was specified, we then estimated the source radius. For
the $\theta_{\rm E}$ estimation, we use the Adams et al. (2018) relation of

$\theta_{*}=0.5\times
10^{[-0.2I_{0}+c_{0}+c_{1}(V-I)_{0}+3]}\leavevmode\nobreak\ \mu{\rm as},$ (4)

where the values of the coefficients are $c_{0}=0.542\pm 0.007$ and
$c_{1}=0.378\pm 0.011$. The measured source radius is

$\theta_{*}=0.93\pm 0.13\leavevmode\nobreak\ \mu{\rm as},$ (5)

and this yields the angular Einstein radius

$\theta_{\rm E}=1.03\pm 0.14\leavevmode\nobreak\ {\rm mas}.$ (6)

With the measured value of $\theta_{\rm E}$ together with the event time scale
$t_{\rm E}$, we estimated the relative lens-source proper motion as

$\mu={\theta_{\rm E}\over t_{\rm E}}=8.59\pm 1.20\leavevmode\nobreak\ {\rm
mas}/{\rm yr}.$ (7)

Also marked in Figure 6 is the position of the blend (green filled dot), which
lies at $(V-I,I)_{\rm b}=(1.76,19.50)$. We checked the possibility that the
lens would be the main source of the blended flux by measuring the astrometric
offset between the centroid of the source image obtained before the lensing
magnification and the centroid of the image obtained at the peak of the
lensing magnification. The measured offset is $\delta\theta=(275.95\pm
129.60)$ mas. Considering that the offset is greater than the measurement
uncertainty by a factor 2.1, it is unlikely that the main origin of the
blended flux is the lens.

Figure 7:  Bayesian posteriors of the primary lens mass and distances to the
lens and source. In each panel, the solid vertical line represent the median
value, and the two dotted lines represent the 16% and 84% of the distribution.

##  5 Physical lens parameters

In this section, we estimate the physical parameters of the mass and distance
to the lens. For the unique determinations of these parameters, it is required
to simultaneously measure the three lensing observables $(t_{\rm
E},\theta_{\rm E},\pi_{\rm E})$, from which the parameters are determined by
the relations

$M={\theta_{\rm E}\over\kappa\pi_{\rm E}};\qquad D_{\rm L}={{\rm
AU}\over\pi_{\rm E}\theta_{\rm E}+\pi_{\rm S}},$ (8)

where $\kappa=4G/(c^{2}{\rm AU})\simeq 8.14\leavevmode\nobreak\ {\rm
mas}/M_{\odot}$, and $\pi_{\rm S}={\rm AU}/D_{\rm S}$ denotes the parallax of
the source (Gould, 2000). For KMT-2021-BLG-1150, the lensing observables
$t_{\rm E}$ and $\theta_{\rm E}$ were securely measured, but the other
parameter $\pi_{\rm E}$ could not be measured, making it difficult to uniquely
determine $M$ and $D_{\rm L}$ using the analytic relations in Equation (8).
We, therefore, estimated the physical parameters of the planetary system by
conducting a Bayesian analysis based on the measured observables and using a
Galactic model. In the analysis, we additionally imposed the lens-brightness
constraint given by the fact that the lens cannot be brighter than the blend.
It turned out that this constraint had little effect on the Bayesian
posteriors.

Table 2: Physical lens parameters Parameter | Value
---|---
$M_{\rm h}$ ($M_{\odot}$) | $0.73^{+0.32}_{-0.30}$
$M_{\rm p}$ ($M_{\rm J}$) | $0.88^{+0.38}_{-0.36}$
$D_{\rm L}$ (kpc) | $3.8^{+1.3}_{-1.2}$
$a_{\perp}$ (AU) | $4.5^{+1.6}_{-1.4}$
Table 3: Variation of planet parameters depending on data Cadence | Inner | Outer
---|---|---
| $s$ |  $q$ ($10^{-3}$) | $s$ |  $q$ ($10^{-3}$)
0.25 hr | $1.297\pm 0.005$ | $1.10\pm 0.05$ | $1.242\pm 0.007$ | $1.15\pm 0.05$
1.0 hr | $1.280\pm 0.008$ | $1.29\pm 0.08$ | $1.227\pm 0.010$ | $1.26\pm 0.06$
2.5 hr | $1.297\pm 0.009$ | $1.30\pm 0.09$ | $1.273\pm 0.017$ | $1.00\pm 0.15$
5.0 hr | $1.297\pm 0.013$ | $1.35\pm 0.12$ | $1.278\pm 0.024$ | $1.08\pm 0.18$

In the Bayesian analysis, we started by generating a large number ($2\times
10^{6}$) of artificial lensing events from the Monte Carlo simulation
conducted using a Galactic model and a mass function model of lens objects.
The Galactic model defines the physical and dynamical distributions of
Galactic objects. In the simulation, we adopted the Galactic and mass function
models described in Jung et al. (2021). For each simulated event with
$(M_{i},D_{{\rm L},i},\mu_{i})$, we computed the lensing observables using the
relations $t_{{\rm E},i}=\theta_{{\rm E},i}/\mu_{i}$ and $\theta_{{\rm
E},i}=(\kappa M_{i}\pi_{{\rm rel},i})^{1/2}$, where $\pi_{{\rm rel},i}={\rm
AU}(1/D_{{\rm L},i}-1/D_{{\rm S},i})$. Based on the simulated events,
posterior distributions of $M$ and $D_{\rm L}$ were constructed by imposing a
weight $w_{i}=\exp(-\chi^{2}/2)$ to each artificial event. Here the $\chi^{2}$
value is computed by $\chi^{2}=(t_{{\rm E},i}-t_{\rm E})^{2}/\sigma(t_{\rm
E})^{2}+(\theta_{{\rm E},i}-\theta_{\rm E})^{2}/\sigma(\theta_{\rm E})^{2}$,
where $(t_{\rm E},\theta_{\rm E})$ represent the measured observables and
$[\sigma(t_{\rm E}),\sigma(\theta_{\rm E})]$ denote their measurement
uncertainties.

Figure 7 shows the Bayesian posteriors of the mass of the planet host and
distances to the lens and source. The physical parameters of the planetary
system, including the masses of the host ($M_{\rm h}$) and planet ($M_{\rm
p}$), distance, and projected physical separation ($a_{\perp}$) between the
planet and host, are listed in Table 2. According to the Bayesian estimation,
the lens is a planetary system consisting of a giant planet with a mass
$M_{\rm p}=0.88^{+0.38}_{-0.36}\leavevmode\nobreak\ M_{\rm J}$ and its host
with a mass $M_{\rm h}=0.73^{+0.32}_{-0.30}\leavevmode\nobreak\ M_{\odot}$
lying toward the Galactic center at a distance $D_{\rm L}=3.8^{+1.3}_{-1.2}$
kpc. Here we adopted the median values of the posterior distributions as
representative parameters and the uncertainties were estimated as the 16% and
84% of the distributions. The projected separations estimated from the inner
and outer solutions are $a_{\perp,{\rm in}}\sim 4.4$ AU and $a_{\perp,{\rm
out}}\sim 4.6$ AU, respectively, and this indicates that the planet lies
beyond the snow line, $a_{\rm sl}\sim 2.7(M_{\rm h}/M_{\odot}){\rm AU}\sim
2.0$ AU, of the planetary system regardless of the solutions. Although
slightly different, the difference between $a_{\perp,{\rm in}}$ and
$a_{\perp,{\rm out}}$ is within the uncertainty of each, and thus we present
the mean value in Table 2. We found that the probabilities for the lens to be
in the disk and bulge are 93% and 7%, respectively, and thus the host of the
planetary system is very likely to be a disk star.

##  6 Discussion

Degeneracies in the interpretation of a planetary signal may be caused due to
either the sparse coverage of the signal or data gaps in the signal. Data gaps
can arise when observations cannot be done due to bad weather or when there
are gaps between the end of the night at one telescope site and the beginning
of the night at another site. In this section, we investigate how the
observational cadence and data gaps in microlensing data affect the
interpretation of planetary signals by conducting analyses based on mock data
sets prepared using those of KMT-2021-BLG-1150 to mimic events with sparse and
incomplete data coverage.

Figure 8 shows the anomaly regions of 4 data sets, in which the first 3 sets
are generated to mimic data obtained with a 1.0 hr, a 2.5 hr, and a 5.0 hr
cadence, and the last one was created to mimic a data set that misses the
negative deviations that occur just before the caustic entrance and just after
the caustic exit. The three tested observational cadences correspond to those
of the KMTNet sub-prime fields, and the assumed 0.25 hr cadence of the last
data set corresponds to the cadence of the KMTNet prime field. We note that
the anomaly feature is still delineated in the 5-hr-cadence data set.

Figure 8:  Four sets of mock data. The data sets in the top three panels mimic
those obtained with a 1.0 hr, a 2.5 hr, and a 5.0 hr cadence, and the data set
in the bottom panel simulate partially covered data. The inset in each panel
shows the lens-system configuration of the solution found from modeling, and
the solid curve drawn on the data points is the model curve.

In Table 3, we list the planet parameters $(s,q)$ obtained by conducting
modeling using the individual mock data sets. It shows that the inner and
outer solutions are identified and the variation in the planet parameters
among the solutions is not very big, although the measurement uncertainties of
the lensing parameters increase as the observational cadence increases. The
result of the simulation indicates that the observational cadence does not
pose a serious degeneracy problem as long as the anomaly feature is
delineated. In the insets of top three panels of Figure 8, we present the
lens-system configurations of the outer solutions corresponding to the
individual data sets. From the analysis of the partially-covered data set, on
the other hand, we were able to identify an off-axis solution, which was
decisively rejected in the analysis conducted using the full data set. The
planet parameters of the off-axis solution are $(s,q)\sim(0.961\pm
0.001,0.047\pm 0.001)$, which are substantially different from those of the
correct solution. The lens system configuration of the off-axis solution is
shown in the inset of the bottom panel in Figure 8. Although the fit of the
off-axis solution is still substantially worse than the outer solution by
$\Delta\chi^{2}\sim 1054$, one finds that the model curve of the off-axis
solution appears to approximately describe the caustic features. The
identification of the degenerate off-axis solution illustrates that gaps in
data can cause degeneracy problems, and this conclusion is further supported
by the fact that the recently reported various types of degeneracies were
identified from the analyses of partially-covered data sets.

Although the inner and outer solutions are distinct, the effect of the
degeneracy on the planet parameters is relatively not severe. This is because
the planet parameters of the pair of the inner and outer solutions are similar
to each other except for the planetary separation $s$, and even for $s$, the
difference between the separations estimated by the two solutions is minor. In
the case of KMT-2021-BLG-1150, this difference is $\Delta s=|s_{\rm in}-s_{\rm
out}|=0.055$. The difference becomes smaller for lower-mass planets because
the size of the planetary caustic decreases as the planet/host mass ratio
becomes smaller (Han, 2006). By contrast, the variations in the planet
parameters among the lensing solutions resulting from other degeneracy types
can be substantial as illustrated by the above off-axis solution and by the
recently-reported events with various types of degeneracies found from the
analyses of partially covered planetary signals.

We note that the above test has been conducted on an event, that is,
KMT-2021-BLG-1150, with a relatively large mass ratio, $q\sim 10^{-3}$. The
fact that the event parameters are recovered even when the cadence is greatly
reduced supports the original decision of the KMTNet group to survey the
majority of the bulge at a 2.5 hour cadence. By contrast, the 10-times higher-
cadence observations of the prime fields are designed to capture $q\sim
10^{-5}$ planets, which are 100 times less massive and so have planetary-
caustic anomalies that evolve $100^{1/2}=10$ times faster. What is surprising,
however, is that even modest gaps in high cadence observations can lead to
major degeneracies, even when most of the caustic structure is densely
covered.

##  7 Summary and conclusion

We analyzed the microlensing event KMT-2021-BLG-1150, for which a densely and
continuously resolved short-term anomaly appeared in the lensing light curve.
From the thorough investigation of the parameter space, we identified a pair
of planetary solutions resulting from the well-known inner-outer degeneracy,
and found that interpreting the anomaly was not subject to any degeneracy
other than the inner-outer degeneracy. The measured planet parameters are
$(s,q)_{\rm in}\sim(1.297,1.10\times 10^{-3})$ for the inner solution and
$(s,q)_{\rm out}\sim(1.242,1.15\times 10^{-3})$ for the outer solution. We
found that the pair of the planet separations of the inner and outer solutions
well obeyed the analytic relation introduced by Hwang et al. (2022). According
to the physical parameters estimated from a Bayesian analysis, it was found
that the lens is a planetary system consisting of a planet with a mass $M_{\rm
p}=0.88^{+0.38}_{-0.36}\leavevmode\nobreak\ M_{\rm J}$ and its host with a
mass $M_{\rm h}=0.73^{+0.32}_{-0.30}\leavevmode\nobreak\ M_{\odot}$ lying
toward the Galactic center at a distance $D_{\rm L}=3.8^{+1.3}_{-1.2}$ kpc.
From the analyses conducted using mock data sets prepared to mimic those
obtained with data gaps and under various observational cadences, it was found
that gaps in data could result in various degenerate solutions, while the
observational cadence would not pose a serious degeneracy problem as long as
the anomaly feature were be delineated.

###### Acknowledgements.

Work by C.H. was supported by the grants of National Research Foundation of
Korea (2020R1A4A2002885 and 2019R1A2C2085965). This research has made use of
the KMTNet system operated by the Korea Astronomy and Space Science Institute
(KASI) at three host sites of CTIO in Chile, SAAO in South Africa, and SSO in
Australia. Data transfer from the host site to KASI was supported by the Korea
Research Environment Open NETwork (KREONET). This research was supported by
the Korea Astronomy and Space Science Institute under the R&D program (Project
No. 2023-1-832-03) supervised by the Ministry of Science and ICT. The MOA
project is supported by JSPS KAKENHI Grant Number JSPS24253004, JSPS26247023,
JSPS23340064, JSPS15H00781, JP16H06287, and JP17H02871. J.C.Y., I.G.S., and
S.J.C. acknowledge support from NSF Grant No. AST-2108414. Y.S. acknowledges
support from NSF Grant No. 2020740. W.Zang acknowledges the support from the
Harvard-Smithsonian Center for Astrophysics through the CfA Fellowship. C.R.
was supported by the Research fellowship of the Alexander von Humboldt
Foundation.

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Henry8, E. van Herwijnen38, M. Heß63, A. Hicheur2, D. Hill55, M. Hoballah5, C.
Hombach54, W. Hulsbergen41, T. Humair53, N. Hussain55, D. Hutchcroft52, D.
Hynds51, M. Idzik27, P. Ilten56, R. Jacobsson38, A. Jaeger11, J. Jalocha55, E.
Jans41, A. Jawahery58, F. Jing3, M. John55, D. Johnson38, C.R. Jones47, C.
Joram38, B. Jost38, N. Jurik59, S. Kandybei43, W. Kanso6, M. Karacson38, T.M.
Karbach38,†, S. Karodia51, M. Kecke11, M. Kelsey59, I.R. Kenyon45, M.
Kenzie38, T. Ketel42, E. Khairullin65, B. Khanji20,38,j, C. Khurewathanakul39,
S. Klaver54, K. Klimaszewski28, O. Kochebina7, M. Kolpin11, I. Komarov39, R.F.
Koopman42, P. Koppenburg41,38, M. Kozeiha5, L. Kravchuk33, K. Kreplin11, M.
Kreps48, G. Krocker11, P. Krokovny34, F. Kruse9, W. Krzemien28, W.
Kucewicz26,n, M. Kucharczyk26, V. Kudryavtsev34, A. K. Kuonen39, K. Kurek28,
T. Kvaratskheliya31, D. Lacarrere38, G. Lafferty54,38, A. Lai15, D. Lambert50,
G. Lanfranchi18, C. Langenbruch48, B. Langhans38, T. Latham48, C. Lazzeroni45,
R. Le Gac6, J. van Leerdam41, J.-P. Lees4, R. Lefèvre5, A. Leflat32,38, J.
Lefrançois7, E. Lemos Cid37, O. Leroy6, T. Lesiak26, B. Leverington11, Y. Li7,
T. Likhomanenko65,64, M. Liles52, R. Lindner38, C. Linn38, F. Lionetto40, B.
Liu15, X. Liu3, D. Loh48, I. Longstaff51, J.H. Lopes2, D. Lucchesi22,q, M.
Lucio Martinez37, H. Luo50, A. Lupato22, E. Luppi16,f, O. Lupton55, A.
Lusiani23, F. Machefert7, F. Maciuc29, O. Maev30, K. Maguire54, S. Malde55, A.
Malinin64, G. Manca7, G. Mancinelli6, P. Manning59, A. Mapelli38, J. Maratas5,
J.F. Marchand4, U. Marconi14, C. Marin Benito36, P. Marino23,38,s, J. Marks11,
G. Martellotti25, M. Martin6, M. Martinelli39, D. Martinez Santos37, F.
Martinez Vidal66, D. Martins Tostes2, A. Massafferri1, R. Matev38, A.
Mathad48, Z. Mathe38, C. Matteuzzi20, A. Mauri40, B. Maurin39, A. Mazurov45,
M. McCann53, J. McCarthy45, A. McNab54, R. McNulty12, B. Meadows57, F. Meier9,
M. Meissner11, D. Melnychuk28, M. Merk41, E Michielin22, D.A. Milanes62, M.-N.
Minard4, D.S. Mitzel11, J. Molina Rodriguez60, I.A. Monroy62, S. Monteil5, M.
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G.D. Patel52, M. Patel53, C. Patrignani19,i, A. Pearce54,49, A. Pellegrino41,
G. Penso25,l, M. Pepe Altarelli38, S. Perazzini14,d, P. Perret5, L.
Pescatore45, K. Petridis46, A. Petrolini19,i, M. Petruzzo21, E. Picatoste
Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, A. Piucci11, S.
Playfer50, M. Plo Casasus37, T. Poikela38, F. Polci8, A. Poluektov48,34, I.
Polyakov31, E. Polycarpo2, A. Popov35, D. Popov10,38, B. Popovici29, C.
Potterat2, E. Price46, J.D. Price52, J. Prisciandaro37, A. Pritchard52, C.
Prouve46, V. Pugatch44, A. Puig Navarro39, G. Punzi23,r, W. Qian4, R.
Quagliani7,46, B. Rachwal26, J.H. Rademacker46, M. Rama23, M.S. Rangel2, I.
Raniuk43, N. Rauschmayr38, G. Raven42, F. Redi53, S. Reichert54, M.M. Reid48,
A.C. dos Reis1, S. Ricciardi49, S. Richards46, M. Rihl38, K. Rinnert52,38, V.
Rives Molina36, P. Robbe7,38, A.B. Rodrigues1, E. Rodrigues54, J.A. Rodriguez
Lopez62, P. Rodriguez Perez54, S. Roiser38, V. Romanovsky35, A. Romero
Vidal37, J. W. Ronayne12, M. Rotondo22, J. Rouvinet39, T. Ruf38, P. Ruiz
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1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
63Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
64National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
65Yandex School of Data Analysis, Moscow, Russia, associated to 31
66Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
67Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 41

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
oLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
pHanoi University of Science, Hanoi, Viet Nam
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy
tUniversità degli Studi di Milano, Milano, Italy
†Deceased