∎

11institutetext: L. Borsato 22institutetext: INAF-Osservatorio Astronomico di
Padova
Vicolo dell’Osservatorio 5, - 35122 - Padova - Italy
22email<EMAIL_ADDRESS>33institutetext: V. Nascimbeni 44institutetext:
INAF-Osservatorio Astronomico di Padova
Vicolo dell’Osservatorio 5, - 35122 - Padova - Italy 55institutetext: G.
Piotto 66institutetext: Università di Padova
Dipartimento di Fisica e Astronomia “Galileo Galilei”
Vicolo dell’Osservatorio 3, 35122 Padova - Italy 77institutetext: G. Szabó
88institutetext: ELTE Eötvös Loránd University
Gothard Astrophysical Observatory
Szent Imre h. u. 112, Szombathely, Hungary

# Exploiting the transit timing capabilities of Ariel

Luca Borsato  Valerio Nascimbeni  Giampaolo Piotto  Gyula Szabó

(Received: 2020 June 30 / Accepted: 2021 March 15)

###### Abstract

The Transit Timing Variation (TTV) technique is a powerful dynamical tool to
measure exoplanetary masses by analysing transit light curves. We assessed the
transit timing performances of the Ariel Fine Guidance Sensors (FGS1/2) based
on the simulated light curve of a bright, 55 Cnc, and faint, K2-24, planet-
hosting star. We estimated through a Markov-Chain Monte-Carlo analysis the
transit time uncertainty at the nominal cadence of $1$ second and, as a
comparison, at a 30 and 60-s cadence. We found that at the nominal cadence
Ariel will be able to measure the transit time with a precision of about 12s
and 34s, for a star as bright as 55 Cnc and K2-24, respectively. We then ran
dynamical simulations, also including the Ariel timing errors, and we found an
improvement on the measurement of planetary masses of about 20-30% in a
K2-24-like planetary system through TTVs. We also simulated the conditions
that allow us to detect the TTV signal induced by an hypothetical external
perturber within the mass range between Earth and Neptune using 10 transit
light curves by Ariel.

###### Keywords:

Arieltransit times TTV planetary dynamics

##  1 Introduction

The Transit Time Variation (TTV) technique is a powerful tool to discover
multi-bodies orbiting around a star, and can be used to characterise
exoplanetary systems by measuring changes in the orbital period due to
gravitational interaction between planets (Agol et al., 2005; Holman and
Murray, 2005; Miralda-Escudé, 2002). The amplitude of the TTV effect is
greatly boosted if the planets are near a mean-motion resonance (MMR, Agol et
al., 2005; Holman and Murray, 2005), allowing us to infer, in particular
configurations, even the presence of an exoplanet in the Earth-mass regime.
The Kepler mission (Borucki et al., 2011), and its extension Kepler/K2 (Howell
et al., 2014), demonstrated the potentiality of this technique, able to
characterise planets also for stars too faint for a spectroscopy analysis and
radial velocity measurement. Some examples of the application of the TTV
technique on multiple planet systems are: Kepler-9 (Holman et al., 2010;
Borsato et al., 2014, 2019), Kepler-11 (Lissauer et al., 2011, 2013),
Kepler-88 (Nesvorný et al., 2013; Weiss et al., 2020), K2-24 (Petigura et al.,
2016, 2018), and WASP-47 (Vanderburg et al., 2017; Weiss et al., 2017).
A TTV can be the result of other different physical sources, e.g. star spots,
oblateness of hosting star, orbital precession induced by tidal interactions,
and general relativity (for a general review see Perryman, 2018), and non-
physical sources such as binning or sampling of the data (e.g. Kipping, 2010a;
Mazeh et al., 2013; Szabó et al., 2013; Price and Rogers, 2014). In this work
we focus on TTV only due to gravitational interaction of exoplanets.

The European Space Agency (ESA) adopted Ariel (Atmospheric Remote sensing
Infrared Exoplanet Large survey; Pascale et al., 2018; Pilbratt, 2019; Puig et
al., 2018; Tinetti et al., 2018) as an M4 mission within the Cosmic Vision
programme, and its launch is scheduled for 2028. The Ariel mission aims to
study the atmospheres and the chemical compositions of exoplanets by surveying
about 1000 transiting exoplanets through fast-cadence high-precision
spectroscopy and photometry of transits, eclipses, and phase-curves in a wide
spectral range from the visible (VIS, 0.5 $\mu$m) to the infrared (IR, 7.8
$\mu$m; detailed description in Tinetti et al., 2018; Encrenaz et al., 2018;
Zingales et al., 2018; Pascale et al., 2018). The Ariel satellite mount two
spectrometers, the Ariel Infrared Spectrometer (AIRS, two prism-dispersed
channels that cover the band width 1.95–3.9$\mu$m with $R>100$ and
3.9–7.8$\mu$m with $R>30$) and NIRSpec (slit-less prism spectrometer with
spectral resolving power $R>15$ in spectral range of 1.1–1.95 $\mu$m), and
three photometers, namely VISPhot (1.1–1.95 $\mu$m) and two Ariel Fine
Guidance Sensors (FGS1 at 0.6–0.8 $\mu$m and FGS2 at 0.8–1.11 $\mu$m). See
Tinetti et al. (2018), Pascale et al. (2018), and Mugnai et al. (2020) for
further details on Ariel instruments. The fast-cadence photometric data will
allow us to measure the planetary transit time at precision and accuracy level
of a few seconds. This is crucial to extend the temporal baseline of TTV
signals of known planets in multiple-planet systems, breaking the degeneracy
on doubtful dynamical solutions and improving the precision on their masses
and orbital parameters (Petigura et al., 2018; Delrez et al., 2018).

In this work we present a study on the Ariel timing performances based on
simulations of real targets (Sec. 2) and some possible science cases (Sec. 3).
This analysis describes one of the possible extended uses of the Ariel’s Core
data and it has been developed within the Ariel Working Group High-Precision
Photometry (described in details in Szabo et al.; 2020, submitted and in
Haswell 2020, in preparation).

##  2 Transit Time analysis

We simulated two science cases, modelled after the real planet hosts 55 Cnc e
and K2-24 b, by analysing synthetic light curves assuming the nominal
performances of FGS1 and 2. In our analysis we simultaneously fitted the light
curves gathered from the two channels to get a single value of the parameters
that are not dependent on wavelength, such as the $T_{0}$. We simulated
photometric data at three different cadences: 1 s, that is the nominal cadence
of Ariel observations, 30 and 60 s as a comparison, in order to understand
when the sampling cadence becomes a limiting factor for our analysis.

For both targets we estimated the expected Ariel photometric noise per time
unit, and for each band-pass, by using the ArielRad code (Mugnai et al.,
2020). This program takes into account different sources of noise, such as
detector noise (dark current, gain and read-out noise), and other stationary
random processes modelled as Poisson noise, i.e. photon noise, Zodiacal noise,
and instrument emission). ArielRad cannot include non-stationary noise (time-
correlated noise), so it includes a jitter noise as the variance at different
wavelength on timescale of 1 hour, and it includes a margin noise to take into
account noise uncertainties and possible time-correlated effects (about 20% on
top of the photon noise, see Mugnai et al., 2020). We re-scaled the noise to
the actual sampling cadence and we added a noise floor of 20 ppm in quadrature
(as shown in eq. 17 of Mugnai et al., 2020). This noise floor is needed to
avoid to indefinitely integrate down the noise (Beichman et al., 2014; Greene
et al., 2017; Mollière et al., 2017), and it is 20 ppm at every integration
time (Mugnai et al., 2020). Due to the lack of time-correlated model in the
noise analysis of ArielRad, we also added a linear trend (as $0.2\%$ on the
transit time scale) to the light curve to mimic the presence of systematic
effects from astrophysical (e.g. stellar activity) or from instrumental
sources (e.g. due to stray light or pointing effects of the satellite). We
scaled the FGS2 trend as a random Gaussian with $\sigma=0.005)$. We also
created light curves with a quadratic term111We used coefficients
$c_{2}=-0.003$, $c_{1}=0.002$, $c_{0}=0.0$, from high to low order., and
scaled the FGS2 as before. We analysed the statistics of Table 4 of Holczer et
al. (2016) and we found that for 92.2% of the planets (on a sample of 2339)
the trend could be described by a polynomial of first order; the rest can be
detrendend with a second and third order polynomial (4.7% and 3.2%,
respectively). So, we can assume that in most cases a linear trend is a good
approximation of the out-of-transit on timescales of 2–3 transit duration.
However, the measurement of the transit time and of its uncertainty is
strongly affected by the sampling of the ingress and egress phases and by the
symmetry of the transit model, so, the trend (and the red noise) contributes
only at a second order. We decided to only fit a linear trend even if the
light curve has been created with a quadratic one and a red noise term.

We modelled the transit light curve with the batman package (Kreidberg, 2015)
and we ran a statistical analysis with the emcee222 We are aware that emcee
code should be used with caution when space of the parameters has a number of
dimension greater than 10, but it has been extensively used in exoplanet
literature showing great performances in different cases. Furthermore, using a
parameterization that reduces the correlation among parameters and that allows
the algorithm to evenly sample the parameter space can mitigate this issue.
package (Foreman-Mackey et al., 2013, 2019), a Markov-Chain Monte-Carlo (MCMC)
code with an affine-invariant sampler (Goodman and Weare, 2010).

Firstly, we generated the synthetic transit light curve with the physical
parameters reported in Table 1. Then, for each cadence, we fitted common
parameters (different parameterization with respect to Table 1) between the
two filters, i.e. the stellar density in solar units ($\rho_{\star}$), the
base-2 logarithm of the period ($\log_{2}P$, used in combination with
$\rho_{\star}$ to constraint the $a/R_{\star}$), the impact parameter333 In
the impact parameter we taken into account the eccentricity and the argument
of pericenter as in Winn (2010) and Kipping (2010b).  ($b$), a combination of
eccentricity $e$ and argument of pericenter $\omega$ ($\sqrt{e}\cos\omega$,
$\sqrt{e}\sin\omega$), and the transit time ($T_{0}$), while, for each filter,
we fitted the planet to stellar radius ratio ($k=R_{\mathrm{p}}/R_{\star}$),
the quadratic limb-darkening (LD) coefficients, $q_{1}$ and $q_{2}$, an
uninformative sampling of quadratic LD $u_{1}$ and $u_{2}$ in the form
$q_{1}=(u_{1}+u_{2})^{2}$ and $q_{2}=0.5u_{1}(u_{1}+u_{2})^{-1}$ as suggested
in Kipping (2013), a jitter factor in base-2 logarithm
($\log_{2}\sigma_{\mathrm{jit}}$), and linear trend. We selected the best (and
common) parameterization of the fitting model to reduce the correlation among
parameters and allowing the emcee code to properly, and as evenly as possible,
sample the parameter space. We wanted to simulate an Ariel transit
observation, i.e. different transit depth for each different band-pass
depending on different planetary radius that corresponds to different layers
of atmosphere. Given that the two FGS channels have different, almost non-
overlapping, band-pass (see Figure 2 in Mugnai et al., 2020), we decided to
fit different $k$, but we generated the synthetic light curves with a single
value. We used as priors the stellar density (computed from stellar mass and
radius), period $P$ , and eccentricity reported in Table 1, and we set very
tight prior if the parameter has a null error (i.e. eccentricity of 55 Cnc e).
We did not apply any priors on the LD coefficients.

The emcee code outputs the posterior distribution of the fitted parameters
from which we extract a best-fit solution and an uncertainty as the high
density interval (HDI at $68.27\%$, equivalent of 1-$\sigma$) for the transit
model parameters, including the most relevant here, i.e. the transit time
($T_{0}$) and its uncertainty ($\sigma_{T_{0}}$). As best-fit solution we
compared the median, the mode444As
$\mathrm{mode}=3\times\mathrm{median}-2\times\mathrm{mean}$, and the maximum
likelihood estimation (MLE, as the parameter sample that maximises the
likelihood within the HDI). In our cases the differences among these best-fit
parameter sets are negligible (in terms of values and uncertainties) and we
decided to use as representative of the best-fit solution the median of the
posterior distribution, because of its symmetry with respect to the HDI. We
want also to stress that finding the best-fit solution was out of the purpose
of this work and we wanted to focus on the determination of the uncertainty of
the parameters, mainly the $\sigma_{T_{0}}$.

###  2.1 55 Cnc e

The first case, 55 Cnc e, has been selected to assess the performances of
Ariel on transit timing at the bright end. The magnitude and spectral type of
the host star 55 Cnc (V = 5.95 mag, $M_{\star}=0.91\,M_{\odot}$,
$R_{\star}=0.94\,R_{\odot}$; von Braun et al., 2011) and the size of planet e,
$R_{\mathrm{e}}\sim 2\,R_{\oplus}$ (Demory et al., 2016) represent a perfect
case to assess the feasibility of a solar-like star with a small transiting
planet. Its transit has very short, and almost vertical, ingress and egress
phases, reducing the impact of the LD effect to the timing of the transit
model.

We obtained stellar and planetary parameters from von Braun et al. (2011) and
Demory et al. (2016) and available through the NASA Exoplanet
Archive555https://exoplanetarchive.ipac.caltech.edu/. We computed the
coefficients of a quadratic LD-law ($u_{1}$ and $u_{2}$) fitting the ATLAS
(Kurucz, 1979) and PHOENIX (Husser et al., 2013) models through the
tool666http://www.github.com/nespinoza/limb-darkening developed by Espinoza
and Jordán (2015). We assumed a box-shaped filter for both FGS1 and FGS2
within the spectral range of $0.8-1.0\,\mu$m and $1.05-1.2\,\mu$m,
respectively. We adopted the values of $u_{1}$ and $u_{2}$ for the fitting as
the average of the values computed for each combination of stellar parameters
and their extremal errors for both models, obtaining:
$u_{1}=0.33\,,u_{2}=0.23$ for the FGS1 and $u_{1}=0.26\,,u_{2}=0.25$ for the
FGS2. We also tested LD coefficients for band $I$ and $J$ computed with
exofast777http://astroutils.astronomy.ohio-state.edu/exofast/limbdark.shtml
(Eastman et al., 2013): $u_{1}=0.39\,,u_{2}=0.22$ for the $I$ band and
$u_{1}=0.22\,,u_{2}=0.29$ for the $J$ band. We used the LD coefficients of $I$
for FGS1 and those of $J$ for FGS2 and we found no difference with the results
obtained from the LD coefficients computed from the stellar models. See in
Table 1 the summary of the stellar and planetary parameters used to create the
synthetic light curves.

Table 1: Stellar and planetary parameters adopted in the synthetic light
curves. 55 Cnc e parameters from von Braun et al. (2011); Demory et al.
(2016), K2-24 b from Petigura et al. (2016, 2018).

Parameters | 55 Cnc e | K2-24 b
---|---|---
$T_{\mathrm{eff}}\,(\mathrm{K})$ | $5196\pm 24$ | $5625\pm 60$
$\log g\,(\mathrm{dex})$ | $4.45\pm 0.01$ | $4.29\pm 0.05$
$[Fe/H]\,(\mathrm{dex})$ | $0.31\pm 0.04$ | $0.34\pm 0.04$
$M_{\star}\,(M_{\odot})$ | $0.91\pm 0.02$ | $1.07\pm 0.06$
$R_{\star}\,(R_{\odot})$ | $0.94\pm 0.01$ | $1.16\pm 0.04$
$R_{\mathrm{p}}\,(R_{\oplus})$ | $1.91$ | $5.4$
$P\,(\mathrm{days})$ | $0.736539\pm 0.000007$ | $20.88977\pm 0.00035$
$T_{0}^{(a)}\,(\mathrm{days})$ | $5733.013$ | $6905.886$
$e$ | $0$ | $0.06\pm 0.01$
$\omega\,(^{\circ})$ | $90$ | $90$
$i\,(^{\circ})$ | $83.3$ | $89.25$
FGS1 |  |
$u_{1}$ | $0.33$ | $0.29$
$u_{2}$ | $0.23$ | $0.25$
noise (ppm/hr)(b) | $12.4$ | $54.0$
FGS2 |  |
$u_{1}$ | $0.26$ | $0.23$
$u_{2}$ | $0.25$ | $0.26$
noise (ppm/hr)(b) | $5.6$ | $43.5$

(a) $T_{0}$ expressed as $\mathrm{BJD_{TDB}}-2450000$. (b) Noise value from
ArielRad. We added in quadrature a noise floor of 20 ppm as described in the
text.

The analysis (see best-fit model for each cadence in Fig. 1) yields an
estimated uncertainty in the transit time ($\sigma_{T_{0}}$) of $12$ s, $12$
s, and $14$ s for cadence at $1$ s, $30$ s, and $60$ s respectively, that is
the sampling cadence for bright targets is not a limiting factor.

Figure 1: Transit light curves of 55 Cnc e with simulated Ariel noise (blue
dots with gray error bars) and quadratic trend (orange line) along with the
best-fit transit model with fitted linear trend (green line) for FGS1 (left)
and FGS2 (right). First row for $1$ s cadence, second and third row for $30$ s
and $60$ s, respectively.

###  2.2 K2-24 b

The second case, K2-24 b, is a Neptune-size transiting planet in a multiple-
planet system showing anti-correlated TTVs with another transiting planet
(K2-24 c). The star is much fainter than 55 Cnc ($V=11.28$, $K=9.18$) with a
mass and radius slightly bigger than the Sun ($M_{\star}=1.07\,M_{\odot}$,
$R_{\star}=1.16\,R_{\odot}$).

We studied the transit timing performances of Ariel with the same two FGS
channels as before and we also analysed the impact of a few Ariel observations
on the recovering of the planetary ephemeris and on the improvement of the
other orbital parameters (see Sec. 3). We used the stellar parameters from
Petigura et al. (2018) and we computed the quadratic LD coefficients, as we
did for 55 Cnc e. We found $u_{1}=0.29\,,u_{2}=0.25$ for the FGS1 and
$u_{1}=0.23\,,u_{2}=0.26$ for the FGS2. We also tested LD coefficients from
exofast: $u_{1}=0.32\,,u_{2}=0.27$ for the $I$ band and
$u_{1}=0.17\,,u_{2}=0.30$ for the $J$ band. A summary of the stellar and
planetary parameters are reported in Table 1.

In the K2-24 b case, when using LD for $I$ and $J$ we obtained for each
cadence the same $\sigma_{T_{0}}$ of $35$ s. This result suggests us that in
this situation we are photon noise dominated. In the analysis with the LD from
box-shaped FGS1 and 2 filters we obtained $\sigma_{T_{0}}$ of $34$ s, $29$ s,
and $32$ s for cadence at $1$ s, $30$ s, and $60$ s respectively. In both
analysis the $\sigma_{T_{0}}$, obtained with only one transit, is about half
the best timing uncertainty ($\sim 78$ s) obtained with Kepler/K2 observations
(Petigura et al., 2018).

Figure 2: Same as in Fig. 1, but for K2-24 b.

We also analysed the case of K2-24 b observed by Ariel with only one channel,
i.e. the FGS1. This could mimic the possible failure of one of the
instruments, reducing the number of light curves per transit. We generated the
synthetic light curve with the parameters in Table 1 with LD coefficients of
FGS1 in $I$ band. We repeated the analysis as before and we obtained a
$\sigma_{T_{0}}$ of about 53 seconds, that is still better than Kepler/K2
timing obtained from the simultaneous analysis of four transits for this
target. This could be due to the high cadence photometry that is able to
homogeneously sample the ingress and egress, the transit phases that have the
greatest impact on determining the transit time.

##  3 Dynamical analysis

###  3.1 Impact of Ariel observations

K2-24 is a multiple-planet system showing anti-correlated TTVs by the
transiting planet b and c, but with a poor sampling of the TTV period on K2
data (Petigura et al., 2016, 2018). This can lead to an imprecise or ambiguous
determination of masses and orbital parameters of the planets (see the
Kepler-9 case by Holman et al., 2010; Borsato et al., 2014, 2019). Petigura et
al. (2018) found a possible candidate planet d, from the radial velocity (RV)
analysis, with a mass of $54\pm 14\,M_{\oplus}$ and a period of about 427
days.

We simulates the K2-24 system with the dynamical integrator within the TRADES
code888https://github.com/lucaborsato/trades (Borsato et al., 2014; Malavolta
et al., 2017; Borsato et al., 2019). We integrated the orbits for the same
time range spanning the observations by Kepler/K2 and follow-up (radial
velocities, RVs, and additional transits) and computed all the transit times
($T_{0}$s) and RVs within the same range. We then selected the corresponding
$T_{0}$s and RVs analysed by Petigura et al. (2018) and we added white noise,
based on the actual error bars from the same work. We used TRADES with the
emcee module to get masses and orbital parameters from this synthetic data set
and to compute the so-called “Observed - Calculated” ($O-C$) plot, where the
residuals of the observed $T_{0}$ with respect to the reference linear
ephemeris are shown as a function of time (see Fig. 3).

Figure 3: Top panel: Observed - Calculated ($O-C$) plot of K2-24 b (left) and
c (right) synthetic transit times for the baseline of the observations. The
Observed is given by the synthetic $T_{0}$s (open-black dots) or simulated
$T_{0}$s (filled-blue dots), while Calculated is given by the $T_{0}$s
computed from linear ephemeris (from synthetic $T_{0}$s). The gray lines are
100 drawn from the posterior distribution. Bottom panel: residuals between
observed and simulated $O-C$. The x-axis is in unit of days, starting from a
reference time $\mathrm{BJD_{TDB}}-2454833=2071.0$ to match the transit times
from Petigura et al. (2018).

If we integrate for 10 years further the orbital solution obtained, we have
two main effects on the prediction of the transit times. The accumulating
errors of the linear ephemeris produce a shift of the transit time with
respect to the predicted one. Another source of error on the transit time is
due to the uncertainty on the orbital parameters of the planetary system (see.
Fig. 4). In 2028, when the Ariel launch is supposed to take place, the shift
from the linear ephemeris could lead to almost one day of uncertainty on the
transit times. Even if we could recover the ephemeris, we still have more than
three hours of uncertainty on transit times due to the errors on the orbital
parameters.

Figure 4: Same as Fig. 3, but extending the orbital integration to almost 10
years in the future. The linear trend of the departure from $O-C=0$ is due to
the short time coverage of the linear ephemeris computed from the synthetic
$T_{0}$s.

We simulated the K2-24 system and ran a dynamical retrieval with TRADES+emcee
in the case of our synthetic data set with two observations with Ariel, one
for planet b and one for c. We assumed the same error bar for the two transit
times $\sigma_{T_{0}}=35$ s, that is the highest (conservative) value obtained
from the previous analysis (see Sec. 2.2). We built the $O-C$ plots (see Fig.
5) from the best-fit solution extracted from the posterior distribution and we
found that just one transit per planet is enough to recover the ephemeris and
to greatly improve the knowledge of orbital parameters of the system. This can
be easily achieved taking advantage of existing ground-based transit survey,
such as the The Asiago Search for Transit timing variations of Exoplanets
project (TASTE, Nascimbeni et al., 2011; Granata et al., 2014), the Next-
Generation Transit Survey (NGTS, Wheatley et al., 2018), and the ExoClock
Project999https://www.exoclock.space/ (within the Ariel Ephemerides Working
Group), or space missions, i.e. Transiting Exoplanet Survey Satellite (TESS,
Ricker et al., 2014), CHaracterizing ExOPlanets Satellite (CHEOPS, Broeg et
al., 2014; Benz et al., 2020), PLAnetary Transits and Oscillations of stars
(PLATO, Rauer et al., 2014). Thanks to TESS and to the extended operations
TESS will also be of great advantage for the ephemeris recovery of almost all
the Kepler/K2 targets on the ecliptic and most of the targets on the sky. With
only two transit times from Ariel we get an improvement on the uncertainty of
the mass of about $22\%$ and $31\%$ for planet b and c, respectively.

Figure 5: Same as Fig. 4, but for the analysis with two $T_{0}$s by Ariel, one
for planet b (left) and one for planet c (right). The thin gray area is the
result of 100 random draws from the posterior distribution; this area is
thinner than in Fig. 4 as the result of better determination of orbital
parameters.

###  3.2 Possible TTV signal from Ariel observations

In the most favourable case Ariel will be able to observe 10 transits of the
same planet (Puig et al., 2018; Tinetti et al., 2018). We wanted to determine
the amplitude of the TTV signal ($A_{\mathrm{TTV}}$) produced by an external
perturber. We decided to consider as transiting planet the K2-24 b (orbital
parameters from Petigura et al., 2016, 2018) and we used TRADES, by choosing
the mass and period of an hypothetical outer perturber from a grid with 30
log-spaced values of mass, ranging from $1\,M_{\oplus}$ to
$4\,M_{\mathrm{Nep}}$, and 30 log-spaced values of orbital period, from 25 to
100 days. For each simulation the code integrates the orbits for 4 years (as
the nominal duration of the Ariel mission), selects the transit times, with
associated error of $35$ s determined in Sec.2.2, and it computes the linear
ephemeris. Then it selects 10 random transits (without replacement), re-
computes the linear ephemeris, and calculates the $A_{\mathrm{TTV}}$ as the
semi-amplitude of the $O-C$ (selected transit times minus the newly computed
linear ephemeris). It repeats this for 100 times and computes the median of
$A_{\mathrm{TTV}}$. We obtained a map of the $A_{\mathrm{TTV}}$ as a function
of the mass ($M_{\mathrm{perturber}}$) and of the period
($P_{\mathrm{perturber}}$). It is well known that the eccentricity of the
perturber ($e_{\mathrm{perturber}}$) boosts the $A_{\mathrm{TTV}}$, so we did
the same analysis three times, with three different initial values of
$e_{\mathrm{perturber}}$: 0.0, 0.05, and 0.1 (see Figures 6, 7, and 8).

Figure 6: TTV amplitude ($A_{\mathrm{TTV}}$) for K2-24 b as a function of mass
and period of the perturber. Each gray dot is the combination of mass-period
in a grid of 900 simulations, where
$M_{\mathrm{perturber}}=[1\,M_{\oplus},4\,M_{\mathrm{Nep}}]$ and
$P_{\mathrm{perturber}}=[25,100]$ days, both in 30 logarithmic steps. For each
simulation we selected 10 transit times within 4 years of orbital integration,
we repeated the selection 100 times and computed the $A_{\mathrm{TTV}}$ as the
the median value of the semi-amplitude of the $O-C$ with respect to a linear
ephemeris. In these simulations the initial $e_{\mathrm{perturber}}$ was set
to 0.0. The white contour lines are the RV semi-amplitude due to the
perturber.  Figure 7: Same as Fig. 6, but with initial
$e_{\mathrm{perturber}}=0.05$. It is evident that a perturber with non-zero
eccentricity extend the possible TTV signal regions and increase their
amplitudes. Figure 8: Same as Fig. 6, but with initial
$e_{\mathrm{perturber}}=0.1$. In this case, the effect of the eccentricity of
the perturber is even stronger than that in Fig. 7.

The darkest regions of the P-M parameter space (shown in Fig. 5, 6, and 7)
where the amplitude $A_{\mathrm{TTV}}$ is much larger than the timing error
$\sigma_{T_{0}}$ for the individual transit observations ($\sim 35$ s, Sec.
2.2) are those where the TTV signal could be detected at high confidence with
Ariel. At least in some orbital configurations close to a MMR, and especially
for eccentric orbits, it will be possible for Ariel to robustly detect a TTV
signal induced by an outer pertuber with one Earth mass (or greater) with just
10 transit observations.

##  4 Conclusions

According to our simulations, the Ariel photometric and timing precision is
suitable to study known multiple-planet systems showing TTV signals in order
to extend the TTV phase coverage, breaking the degeneracy on the retrieved
orbital parameters, and in particular to improve the mass estimation. The
latter is fundamental to put strong constraints on planetary formation,
migration, and evolution processes (e.g. Mordasini et al., 2012). However, to
avoid losing transits within the Ariel observing window due to lack of
precision on the ephemeris and/or on the orbital parameters, it will be
necessary to constrain the ephemeris by taking advantage of ground- (e.g.
ExoClock Project, TASTE, and NGTS) and space-based telescopes (e.g. TESS,
CHEOPS, and PLATO).

We warn the reader that even if ArielRad takes into account different sources
of stationary noise and includes a noise margin, it cannot model time-
correlated noise. So, we can consider the values of the uncertainty on the
$T_{0}$ obtained in our analysis as optimistic. As soon as the on-flight
performances of the satellite and of instruments will be precisely evaluated
we will be able to perform a deeper and more robust analysis of the impact of
correlated noise on the determination of the transit time and of its
uncertainty. A possible way to model correlated noise (or coloured noise, such
as pink and red noise) would be to use non-parametric models such as ARMA or
ARIMA processes, creating, for example, a common coloured noise for both FGS1
and FGS2 and an additional coloured noise different for each filter. We want
to stress that currently the instrumental correlated noise is unknown and
unpredictable and also the stellar noise can vary star-by-star, so it is not
so trivial to properly model these noise components.

In the future it would be interesting to repeat the analysis taking into
account multiple transits of the same planet observed with Ariel (e.g. Tier 3
targets, about $\sim 10\%$ of Tier 1) and assess the improvement on
$\sigma_{T_{0}}$, even if the main contribution derives from the sampling rate
of the transit ingress and egress. Furthermore, an MCMC analysis with a
different algorithm, such as Nested and Dynamic Nested Sampling (Skilling,
2004, 2006; Higson et al., 2019) implemented in dynesty (Speagle, 2020) would
help to sample in a more efficient and robust way a high dimensional space as
in the modelling of many transit light curves in different bands and modelling
the dynamics of multi-planet systems.

Furthermore, Ariel will be able for some orbital configurations to
independently detect TTV signals with about 10 transit observations, allowing
us to identify perturbing planets with masses spanning the Earth-Neptune
range. Combining RV data with transit times helps to put strong constraints on
bulk density and orbital parameters of the transiting planet (e.g. Kepler-19
and Kepler-9, Malavolta et al., 2017; Borsato et al., 2019, , respectively).
However, if the RV data have not enough precision to detect the external
perturber, and taking into account the precision in the mass measurement of
$~{}17\%$ for K2-24 c in Petigura et al. (2018), we can say that “in any case”
the detection of a TTV signal in Ariel data will allow us to determine
planetary masses of perturber with a precision better than $20\%$ in the
Earth-Neptune regime.

The Ariel target list is evolving with time and with new discoveries, so at
the moment is very difficult to give a quantitative estimates of the number of
known multi-planet system with TTV that Ariel will observe and characterise.
We can expect about several tens of planets with significant TTV improvements,
and a similar number of targets with TTV, whose contribution from Ariel will
be important. Hadden et al. (2019) predicted that about less than 4000 planet
systems will be discovered during the nominal mission of TESS and about half
of these will be in multi-planet systems. 30 of these multi-planet systems
will have a measurable TTV signal and only 10 will be characterised with
precise mass measurement from TTV only. Differently from missions like TESS or
PLATO, Ariel will point a single target, as CHEOPS, and it will observe about
1000 targets, roughly a quarter of the TESS predicted value. So, we can assume
for Ariel a similar number of the predicted TTV systems for TESS, but only
before launch we will know which planets will be observed and how many of
these will be systems with TTV, and it will mostly depend on the selection
process and on the schedulability of the targets.

###### Acknowledgements.

LBo, VNa, and GPi acknowledge the funding support from Italian Space Agency
(ASI) regulated by “Accordo ASI-INAF n. 2013-016-R.0 del 9 luglio 2013 e
integrazione del 9 luglio 2015”.

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#  Study of intermediate two-body decays in
$\bar{B}^{0}\to\Sigma_{c}(2455)^{0}\bar{p}\pi^{+}$

H. O. Kim<EMAIL_ADDRESS>H. Kichimi<EMAIL_ADDRESS>Corresponding
author. I. Adachi  H. Aihara  K. Arinstein  V. Aulchenko  T. Aushev  A. M.
Bakich  V. Balagura  I. Bedny  A. Bondar  A. Bozek  M. Bračko  T. E. Browder
P. Chang  Y. Chao  B. G. Cheon  R. Chistov  I.-S. Cho  Y. Choi  J. Dalseno  M.
Dash  S. Eidelman  D. Epifanov  N. Gabyshev  H. Ha  K. Hayasaka  M. Hazumi  D.
Heffernan  Y. Hoshi  W.-S. Hou  H. J. Hyun  T. Iijima  K. Inami  A. Ishikawa
R. Itoh  M. Iwasaki  Y. Iwasaki  D. H. Kah  J. H. Kang  N. Katayama  H. Kawai
T. Kawasaki  H. J. Kim  Y. I. Kim  Y. J. Kim  S. Korpar  P. Križan  P.
Krokovny  R. Kumar  A. Kuzmin  Y.-J. Kwon  J. S. Lee  M. J. Lee  T. Lesiak
S.-W. Lin  D. Liventsev  A. Matyja  S. McOnie  K. Miyabayashi  H. Miyata  Y.
Miyazaki  M. Nakao  H. Nakazawa  Z. Natkaniec  S. Nishida  O. Nitoh  S. Ogawa
T. Ohshima  S. Okuno  C. W. Park  H. Park  H. K. Park  K. S. Park  L. S. Peak
R. Pestotnik  L. E. Piilonen  A. Poluektov  H. Sahoo  Y. Sakai  O. Schneider
K. Senyo  M. E. Sevior  M. Shapkin  V. Shebalin  J.-G. Shiu  B. Shwartz  J. B.
Singh  A. Somov  S. Stanič  M. Starič  T. Sumiyoshi  M. Tanaka  G. N. Taylor
Y. Teramoto  S. Uehara  Y. Unno  S. Uno  P. Urquijo  Y. Usov  G. Varner  A.
Vinokurova  C. H. Wang  M.-Z. Wang  P. Wang  X. L. Wang  Y. Watanabe  E. Won
Y. Yamashita  M. Yamauchi  Z. P. Zhang  V. Zhilich  V. Zhulanov  T. Zivko  A.
Zupanc  O. Zyukova  Budker Institute of Nuclear Physics, Novosibirsk, Russia
Chiba University, Chiba, Japan  University of Cincinnati, Cincinnati, OH, USA
T. Kościuszko Cracow University of Technology, Krakow, Poland  The Graduate
University for Advanced Studies, Hayama, Japan  Hanyang University, Seoul,
South Korea  University of Hawaii, Honolulu, HI, USA  High Energy Accelerator
Research Organization (KEK), Tsukuba, Japan  Institute of High Energy Physics,
Chinese Academy of Sciences, Beijing, PR China  Institute for High Energy
Physics, Protvino, Russia  Institute for Theoretical and Experimental Physics,
Moscow, Russia  J. Stefan Institute, Ljubljana, Slovenia  Kanagawa University,
Yokohama, Japan  Korea University, Seoul, South Korea  Kyungpook National
University, Taegu, South Korea  École Polytechnique Fédérale de Lausanne,
EPFL, Lausanne, Switzerland  Faculty of Mathematics and Physics, University of
Ljubljana, Ljubljana, Slovenia  University of Maribor, Maribor, Slovenia
University of Melbourne, Victoria, Australia  Nagoya University, Nagoya, Japan
Nara Women’s University, Nara, Japan  National Central University, Chung-li,
Taiwan  National United University, Miao Li, Taiwan  Department of Physics,
National Taiwan University, Taipei, Taiwan  H. Niewodniczanski Institute of
Nuclear Physics, Krakow, Poland  Nippon Dental University, Niigata, Japan
Niigata University, Niigata, Japan  University of Nova Gorica, Nova Gorica,
Slovenia  Osaka City University, Osaka, Japan  Osaka University, Osaka, Japan
Panjab University, Chandigarh, India  Saga University, Saga, Japan  University
of Science and Technology of China, Hefei, PR China  Seoul National
University, Seoul, South Korea  Sungkyunkwan University, Suwon, South Korea
University of Sydney, Sydney, NSW, Australia  Toho University, Funabashi,
Japan  Tohoku Gakuin University, Tagajo, Japan  Department of Physics,
University of Tokyo, Tokyo, Japan  Tokyo Metropolitan University, Tokyo, Japan
Tokyo University of Agriculture and Technology, Tokyo, Japan  Virginia
Polytechnic Institute and State University, Blacksburg, VA, USA  Yonsei
University, Seoul, South Korea

###### Abstract

We present results of a detailed study of the three-body
$\bar{B}^{0}\to\Sigma_{c}(2455)^{0}\bar{p}\pi^{+}$ decay. A significant
enhancement of signal events is observed in the $\bar{p}\pi^{+}$ mass system
near $1.5\,{\rm GeV}/c^{2}$ that is consistent with the presence of an
intermediate baryonic resonance $\bar{N}^{0}$, where $\bar{N}^{0}$ is the
$\bar{N}(1440)^{0}P_{11}$ or $\bar{N}(1535)^{0}S_{11}$ state, or an admixture
of the two states. We measure the product ${\cal
B}(\bar{B}^{0}\to\Sigma_{c}(2455)^{0}\bar{N}^{0})\times{\cal
B}(\bar{N}^{0}\to\bar{p}\pi^{+})$=($0.80\pm 0.15\rm{(stat.)}\pm
0.14\rm{(syst.)}\pm 0.21$)$\times 10^{-4}$, where the last error is due to the
uncertainty in ${\cal B}(\Lambda_{c}^{+}\to pK^{-}\pi^{+})$. The significance
of the signal is 6.1 standard deviations. This analysis is based on a data
sample of 357 fb-1, accumulated at the $\Upsilon(4S)$ resonance with the Belle
detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider.

###### keywords:

B-meson, Charmed baryon, $N^{0}$ $P_{11}$ and $S_{11}$ resonaces.

###### PACS:

13.20.H

††journal: Physics Letters B

Belle Preprint 2008-23

KEK Preprint 2008-23

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Various charmed baryonic $B$ decays into four-, three- and two-body final
states have been reported [1, 2, 3, 4, 5, 6, 7], and the measured branching
fractions show clearly that the branching fraction increases with the
multiplicity of the final state [8, 3]. To understand this hierarchy, it is
interesting to study decays of
$\bar{B}^{0}\to\Lambda_{c}^{+}{\bar{p}}\pi^{+}\pi^{-}$ into three- and two-
body final states. The branching fractions are predicted from CKM matrix
elements [9], while the form factors of the decay vertices depend on the decay
mechanism. Experimental studies provide stringent constraints on the
theoretical models [10, 11, 12].

In this report, we perform a detailed study of the intermediate three-body
decay $\bar{B}^{0}\to\Sigma_{c}(2455)^{0}\bar{p}\pi^{+}$ observed in the
previous analysis of $\bar{B}^{0}\to\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}$ [1],
using a data sample of $388\times 10^{6}$ $B\bar{B}$ events, corresponding to
357 fb-1 accumulated at the $\Upsilon(4S)$ resonance with the Belle detector
at the KEKB asymmetric-energy $e^{+}e^{-}$ collider [13].

The Belle detector is a large-solid-angle spectrometer based on a 1.5 Tesla
superconducting solenoid magnet. It consists of a silicon vertex detector
(SVD) (a three-layer SVD for the first sample of $(152.0\pm 1.2)\times 10^{6}$
$B\bar{B}$ events and a four-layer SVD for the latter $(235.8\pm 3.6)\times
10^{6}$ $B\bar{B}$ events), a 50-layer central drift chamber (CDC), an array
of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of
time-of-flight scintillation counters (TOF), and an electromagnetic
calorimeter (ECL) comprised of CsI (Tl) crystals located inside the
superconducting solenoid coil. An iron flux return located outside the coil is
instrumented to detect $K_{L}^{0}$ mesons and to identify muons (KLM). The
detector is described in detail elsewhere [14]. We simulate the detector
response and estimate the efficiency for signal reconstruction by Monte Carlo
simulation (MC). We use the EvtGen program [15] for signal event generation
and a GEANT-based [16] detector simulation program to model the Belle detector
response for the signal.

We first describe briefly the previous analysis of
${\bar{B}}^{0}\to\Lambda_{c}^{+}{\bar{p}}\pi^{+}\pi^{-}$ [1], We select
$\bar{B}^{0}\to\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}$ events by reconstructing
$\Lambda_{c}^{+}\to pK^{-}\pi^{+}$ decays, using charged tracks reconstructed
by the SVD and CDC, and hadron identification information (such as protons,
kaons and pions) provided from the CDC $dE/dx$, TOF and ACC (PID) [17], and
ECL and KLM information to veto electron and $\mu$ tracks. Charge-conjugate
modes are implicitly included throughout this paper unless noted otherwise.
After the event selection, we fit the $\Delta{E}$ distribution for the $B$
candidate events with $5.27\,{\rm GeV}/c^{2}<M_{\rm bc}<5.29\,{\rm
GeV}/c^{2}$, with a double Gaussian fixed to the signal MC shape ($\sigma_{\rm
core}=7\,{\rm MeV}/c^{2}$, $\sigma_{\rm tail}=16\,{\rm MeV}/c^{2}$) plus a
linear background. The variable $\Delta{E}=E_{B}-E_{\rm{beam}}$ is the
difference between the reconstructed $B$ meson energy ($E_{B}$) and the beam
energy ($E_{\rm beam}$) evaluated in the center-of-mass system (CMS), while
$M_{\rm bc}=\sqrt{E_{\rm beam}^{2}-P_{B}^{2}}$ is the beam-energy-constrained
$B$ meson mass and ${P_{B}}$ is the momentum of the $B$ meson also evaluated
in the CMS. We obtain a $B$ signal of $1400\pm 49$ events for
${\bar{B}}^{0}\to\Lambda_{c}^{+}{\bar{p}}\pi^{+}\pi^{-}$. Figure 1 shows the
$\Lambda_{c}^{+}\pi^{+}$ and $\Lambda_{c}^{+}\pi^{-}$ mass distributions for
the events in the $B$ signal region $|\Delta{E}|<0.03{\,\rm GeV}$ ($\pm
4\sigma$) and $5.27{\,\rm GeV}/c^{2}<M_{\rm bc}<5.29{\,\rm GeV}/c^{2}$ ($\pm
4\sigma$). We focus our discussion on the $\Sigma_{c}(2455)^{++}$ and
$\Sigma_{c}(2455)^{0}$ resonances clearly observed in figure [1]; $(182\pm
15)$ events for $\bar{B}^{0}\rightarrow\Sigma_{c}(2455)^{++}\bar{p}\pi^{-}$
and $(122\pm 14)$ events for
$\bar{B}^{0}\rightarrow\Sigma_{c}(2455)^{0}\bar{p}\pi^{+}$, corresponding to
branching fractions of ($2.1\pm 0.2\rm{(stat.)}\pm 0.3\rm{(syst.)}\pm
0.5$)$\times 10^{-4}$ and ($1.4\pm 0.2\rm{(stat.)}\pm 0.2\rm{(syst.)}\pm
0.4$)$\times 10^{-4}$, respectively. Hereafter, we denote $\Sigma_{c}(2455)$
as $\Sigma_{c}$.

Figure 1:  The mass distributions of (a) $\Lambda_{\mathrm{c}}^{+}\pi^{+}$ and
(b) $\Lambda_{\mathrm{c}}^{+}\pi^{-}$ in
$\bar{B}^{0}\rightarrow\Lambda_{\mathrm{c}}^{+}\bar{p}\pi^{+}\pi^{-}$. The
points with error bars show the mass distribution for the events in the $B$
signal box, and the shaded histogram indicates that for the background. The
solid and dashed curves represent the signal and the background, respectively,
obtained from a simultaneous binned likelihood fit.

Figure 2 shows (a) the Dalitz plot and (b) the $M^{2}(\bar{p}\pi^{-})$
distribution for the $\bar{B}^{0}\to\Sigma_{c}^{++}\bar{p}\pi^{-}$ events, and
(c) the Dalitz plot and (d) the $M^{2}(\bar{p}\pi^{+})$ distribution for the
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ events. Here we require the
$\Sigma_{c}$ candidates satisfy the invariant mass requirement $2.447\,{\rm
GeV}/c^{2}<M(\Lambda_{c}^{+}\pi^{\pm})<2.461\,{\rm GeV}/c^{2}$ ($\pm
2\sigma$). We find that the $M^{2}(\bar{p}\pi^{-})$ distribution for
$\bar{B}^{0}\rightarrow\Sigma_{c}^{++}{\bar{p}}\pi^{-}$ is consistent with
three-body phase space, while the $M^{2}(\bar{p}\pi^{+})$ distribution for
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ has a significant peak. In what
follows, we present a detailed study of the
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ decay.

Figure 3 shows the $\Delta{E}$ distribution for the
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ events, which are selected from
the $\bar{B}^{0}\to\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}$ sample with the
additional requirement that the $\Lambda_{c}^{+}\pi^{-}$ mass be consistent
with the $\Sigma_{c}^{0}$. The curves show fits to the data with a double
Gaussian function with shape parameters fixed to the values from signal MC and
a linear background. We obtain a $B$ signal yield of $(102\pm 11)$ events and
a background of $(17\pm 3)$ events. The signal reduction of 16% is consistent
with the MC estimation of the effect due to the ${\Sigma_{c}^{0}}$ mass
requirement. We estimate a non-$\Sigma_{c}^{0}$ background of $(8\pm 4)$
events from a fit to the $\Delta{E}$ distribution in the $\Sigma_{c}$ mass
sideband $2.435{\,\rm GeV}/c^{2}<M(\Lambda_{c}^{+}\pi^{-})<2.442{\,\rm
GeV}/c^{2}$ and $2.466{\,\rm GeV}/c^{2}<M(\Lambda_{c}^{+}\pi^{-})<2.473{\,\rm
GeV}/c^{2}$. This can be compared with $(2.5\pm 0.5)$ events estimated from MC
simulation of $\bar{B}^{0}\rightarrow\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}$
decay with four-body phase space normalized to the total of 1400 events [1].
Here the error is due to the statistics of the simulation. We do not take into
account the non-$\Sigma_{c}^{0}$ background in the analysis that follows.

Figure 2:  (a) Dalitz plot and (b) $M^{2}(\bar{p}\pi^{-})$ distribution for
$\bar{B}^{0}\to\Sigma_{c}^{++}\bar{p}\pi^{-}$. (c) Dalitz plot and (d)
$M^{2}(\bar{p}\pi^{+})$ distribution for
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$. Points with error bars indicate
the data, and histograms are the decays simulated according to three-body
phase space.  Figure 3:  $\Delta{E}$ distribution for the
$\bar{B}^{0}\to\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}$ events in the $M_{\rm
bc}$ signal region with
$2.447\,\rm{GeV}/c^{2}<M(\Lambda_{c}^{+}\pi^{\pm})<2.461\,\rm{GeV}/c^{2}$. The
curves indicate the fit with a double Gaussian for the signal and a linear
background.

Figure 4 shows (a) the $\bar{p}\pi^{+}$ mass, (b) $\cos\theta_{p}$ and (c)
$\Sigma_{c}^{0}\pi^{+}$ mass distributions for the selected
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ events. Here, $\cos\theta_{p}$ is
the cosine of the angle between the $\bar{p}$ momentum and the direction
opposite to the $B$ momentum in the $\bar{p}\pi^{+}$ rest frame. The shaded
histograms indicate the distributions for the background discussed above. The
background shapes are obtained by fits to the data in the sideband region
$|\Delta{E}|<0.1\,{\rm GeV}$ and $5.26\,{\rm GeV}/c^{2}<M_{\rm bc}<5.29\,{\rm
GeV}/c^{2}$ outside the $B$ signal region, and the yield is fixed to 17
events. Here, the $M(\bar{p}\pi^{+})$ distribution is parameterized by the
function $P_{\rm bkg}(M)=c\cdot\sqrt{t_{\rm min}\cdot t_{\rm
max}}\cdot(1+c_{1}\cdot t_{\rm min})(1+c_{2}\cdot t_{\rm max})$ with $t_{\rm
min}=(M^{2}-M^{2}_{\rm min})$ and $t_{\rm max}=(M^{2}_{\rm max}-M^{2})$.
$M_{\rm min}$ and $M_{\rm max}$ are the minimum and maximum masses. The
variable $c$ is a normalization constant, and $c_{1}$ and $c_{2}$ are shape
parameters. The $\cos\theta_{p}$ distribution is modeled by a second-order
Chebyshev polynomial.

Figure 4:  Data distributions for (a) $M(\bar{p}\pi^{+})$, (b)
$\cos\theta_{p}$ and (c) $M(\Sigma_{c}^{0}\pi^{+})$. The shaded histograms
indicate the normalized background.

We find a significant structure in the $\bar{p}\pi^{+}$ mass distribution, and
a forward peak in the $\cos\theta_{p}$ distribution, and a low mass
$\Sigma_{c}^{0}\pi^{+}$ enhancement, denoted as $(\Sigma_{c}^{0}\pi^{+})_{\rm
X}$. The $\bar{p}\pi^{+}$ mass structure has a mass near $1.5\,{\rm
GeV}/c^{2}$ and a width of about $0.3\,{\rm GeV}$. We denote it as
$\bar{N}^{0}$, and investigate its characteristics in detail. In order to
describe the $\bar{p}\pi^{+}$ mass structure, which is not explained by a
simple phase space non-resonant $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$
decay, we consider an intermediate two-body decay
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ with a resonant state
${\bar{N}}^{0}\to{\bar{p}}\pi^{+}$. However, we still cannot reproduce the
forward $\cos\theta_{p}$ peak and the $\Sigma_{c}^{0}\pi^{+}$ low mass
structure with these two modes only. Therefore, we introduce one additional
mode $\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ to account for
the observed features. As the low mass $\Sigma_{c}^{0}\pi^{+}$ structure is
close to threshold, it produces a forward peak in the $\cos\theta_{p}$
distribution. In the low $\Sigma_{c}^{0}\pi^{+}$ mass region, we search for
known $\Sigma_{c}^{0}\pi^{+}$ resonant states [18] in finer mass bins, but
find no signals. So far, there is no good candidate to interpret this broad
structure as a resonance. Therefore we assume that there is a threshold mass
enhancement with a mass of $2800\,{\rm MeV/}c^{2}$ and a width of $350\,{\rm
MeV}$ obtained from a fit to the $\Sigma_{c}^{0}\pi^{+}$ mass distribution
using a relativistic Breit-Wigner (S-wave) function.

Figure 5 compares binned Probability Density Functions (PDF) of the MC
simulated events for the three assumed decay modes. The histograms show the
PDFs for (a) the $M(\bar{p}\pi^{+})$, (b) $\cos\theta_{p}$ and (c) the
$M(\Sigma_{c}^{0}\pi^{+})$ distributions. The solid histograms show the
distributions of the mode $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$, assuming
a P-wave relativistic Breit-Wigner amplitude with a mass of $1530\,{\rm
MeV/}c^{2}$ and a width of $340\,{\rm MeV}$.

Figure 5:  Binned probability distributions of (a) $M(\bar{p}\pi^{+})$, (b)
$\cos\theta_{p}$ and (c) $M(\Sigma_{c}^{0}\pi^{+})$, where we compare MC
simulated distributions for $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ (solid
lines), $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ (dashed lines), and
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ (dotted lines). We
make a simultaneous fit to the distributions in (a) and (b).

To determine the $N^{0}$ mass, width and the yields of the three modes, we
perform a maximum likelihood fit to the observed $M({\bar{p}}\pi^{+})$ and
$\cos\theta_{p}$ distributions shown in Fig. 4. These two distributions are
sufficient to fully describe the three-body decay
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$. To model the observed
distribution, we construct a function $F(M(\bar{p}\pi^{+}),\cos\theta_{p})$
from the sum of PDFs of the three decay modes and the background.

$\begin{split}F=\nu_{1}P_{\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}}+\nu_{2}P_{\bar{B}^{0}\to(\Sigma_{c}^{0}\pi^{+})_{\rm
X}\,\bar{p}}\\\
+\nu_{3}P_{\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}}+\nu_{4}P_{\rm
bkg},\end{split}$

where $P_{i}$ denotes a product of the normalized PDFs,
$Q_{i}(M(\bar{p}\pi^{+}))$ (20 bins) and $R_{i}(\cos\theta_{p})$ (16 bins),
and $\nu_{i}$ stands for the yield of the $i$-th mode. We plot
$Q(M(\bar{p}\pi^{+}))$ and $R(\cos\theta_{p})$ distributions from the detector
MC simulation for $\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ and
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ modes, as shown in Figs 5(a) and
(b), respectively. For the $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ mode, we
use the MC simulated $R(\cos\theta_{p})$ distribution and a Breit-Wigner for
$Q(M({\bar{p}}\pi^{+}))$ with the ${\bar{N}}^{0}$ mass and width ($m_{R}$,
$\Gamma$) as free parameters. A small systematic error due to the use of the
$Q(M({\bar{p}}\pi^{+}))$ distribution without the MC detector simulation is
discussed later. We use a P-wave (S-wave) relativistic Breit-Wigner shape.

$BW_{P}(m^{2})=\frac{p^{2}}{(m^{2}-m_{R}^{2})^{2}+m_{R}^{2}{\Gamma^{2}(m)}}{\left[\frac{B(p)}{B(p_{0})}\right]}^{2},$
$BW_{S}(m^{2})=\frac{m_{R}\Gamma(m)}{[(m^{2}-{m_{R}}^{2})^{2}+{m_{R}}^{2}\Gamma^{2}(m)]},$
$\Gamma(m)=\left(\frac{p}{p_{0}}\right)^{2L+1}\left(\frac{m_{R}}{m}\right)\Gamma_{0}{\left[\frac{B(p)}{B(p_{0})}\right]^{2}}.$

Here $m$ is the mass of the $\bar{p}\pi^{+}$ system, and $m_{R}$ is the
nominal $\bar{N}^{0}$ mass, and $\Gamma(m)$ is the width. The variable $p$ is
the momentum of a daughter particle in the $\bar{N}^{0}$ rest frame, and
$p_{0}$ is that for the nominal $\bar{N}^{0}$ mass.
$B(p)=1/{\sqrt{1+(Rp)^{2}}}$ is the Blatt-Weisskopf form factor [19]. The
value $R$, called the centrifugal barrier penetration factor, is set to
$3\,{\rm(GeV}/c)^{-1}$ for a P-wave, and is zero for an S-wave. $L$ indicates
the orbital angular momentum. For the S-wave Breit-Wigner amplitude [20] we
use $\Gamma(m)$ with $m=m_{R}$ and $L=0$ to parameterize the smooth shape near
the mass threshold.

We define an extended unbinned likelihood with coarse bins, and carry out a
maximum likelihood fit.

$L=\frac{e^{-(\nu_{1}+\nu_{2}+\nu_{3}+\nu_{4})}}{N!}\prod
F(m_{R},\Gamma,\nu_{1},\nu_{2},\nu_{3},\nu_{4})$

We fit the ${\bar{N}}^{0}$ mass and width $(m_{R},\Gamma)$ and the yields
$\nu_{1},\nu_{2}$ and $\nu_{3}$ as free parameters, while the background yield
$\nu_{4}$ is fixed to 17 events. Table 1 summarizes the fit results with
various model assumptions. We calculate the statistical significance from the
quality -2${\rm ln}({L}_{0}/{L}_{\rm max})$, where $L_{\max}$ is the maximum
likelihood returned from the fit, and $L_{0}$ is the likelihood with the
signal yield fixed to zero, and taking into account the reduction of the
degrees of freedom. We obtain a significance of 7.0$\,\sigma$ for the
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ contribution. The signal in the mode
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ has a statistical
significance of 4.6$\,\sigma$, while that for
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ is not significant (0.8
$\sigma$). Here, we calculate the goodness-of-fit from the likelihood ratio
$\lambda$ [18],

$\begin{split}\chi^{2}\approx-2{\rm ln}\lambda=2\sum_{j=1}^{36}[{\cal
F}_{j}(m_{R},\Gamma,\nu_{1},\nu_{2},\nu_{3},\nu_{4})-F_{j}\\\ +F_{j}{\rm
ln}(\frac{F_{j}}{{\cal
F}_{j}(m_{R},\Gamma,\nu_{1},\nu_{2},\nu_{3},\nu_{4})})],\end{split}$

where $F_{j}$ and ${\cal F}_{j}$ are the observed and the fitted yields,
respectively, in the $j$-th bin: $j=1,20$ for 20 bins in
$Q(M(\bar{p}\pi^{+}))$ and $j=21,36$ for 16 bins in $R(cos\theta_{p})$.

The small contribution ($\nu_{3}=-11\pm 10$) can be understood from Fig. 5.
The mode $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ has a broad
$\bar{p}\pi^{+}$ mass distribution similar to
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$, while it does not
reproduce the forward $\cos\theta_{\bar{p}}$ peak. On the other hand, the
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ mode can reproduce the
${\bar{p}}\pi^{+}$ mass bump structure and the uniform $\cos\theta_{\bar{p}}$
distribution. Hence, we fix $\nu_{3}=0$ in the subsequent fit and the
uncertainty of this contribution is taken into account in the systematic
error.

Table 1:  Summary of the simultaneous fits to the $M(\bar{p}\pi^{+})$ and $\cos\theta_{\bar{p}}$ distributions with the three decay modes $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$, $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ and $\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$. (a) - (d) represent fits with various assumed contributions. Here, we show the fit results with the P-wave assumption, as we find no significant difference from the S-wave assumption.  Decay mode | (a) | (b) | (c) | (d) | Signif. |
---|---|---|---|---|---|---
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ | free | free | free | 0 | 7.0 |
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ | free | free | 0 | free | 4.6 |
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ | free | 0 | free | free | 0.8 |
$\chi^{2}$/ndf | 31.7/31 |  32.4/32 |  52.8/32 |  88.4/34 |  |

Figure 6:  Simultaneous fit to (a) $M({\bar{p}}\pi^{+})$ and (b)
$\cos\theta_{p}$ distributions with a P-wave Breit-Wigner. The points with
error bars are the data, and the curves are the contributions from
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ (dashed),
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ (dotted), the
background (shaded) and their sum (solid). (c) $M(\Sigma_{c}^{0}\pi^{+})$
distribution, where the curves represent their contributions obtained by the
fit to (a) and (b).

Figure 6 shows the results of a fit to (a) the $M({\bar{p}}\pi^{+})$ and (b)
$\cos\theta_{\bar{p}}$ distributions under the P-wave assumption. The data are
the points with error bars. The curves are the contributions from
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ (dashed),
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ (dotted), the
background (shaded) and their sum (solid). We obtain yields of ($70\pm 11$)
and ($32\pm 9$) for the modes $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ and
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$, respectively. Figure
6(c) shows that the $M(\Sigma_{c}^{0}\pi^{+})$ distribution is consistently
represented by the fitted parameters even though the
$M(\Sigma_{c}^{0}\pi^{+})$ distribution is not included in the fit.

Table 2:  The fitted ${\bar{N}}^{0}$ mass and width with relativistic S-wave and P-wave Breit-Wigners. The first errors are statistical and the second are systematic including the uncertainties in the yields of $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ and the background, and the assumption of a low mass $(\Sigma_{c}^{0}\pi^{+})_{\rm X}$ structure.  Item | Yield | Mass | $\Gamma$ |  $\chi^{2}$/ndf
---|---|---|---|---
| Events | $\rm{MeV}/c^{2}$ | $\rm{MeV}$ |
S-wave | $71\pm 11\pm 10$ |  $1473\pm 31\pm 2$ |  $315\pm 72\pm 53$ |  32.9/32
P-wave | $70\pm 11\pm 10$ |  $1516\pm 29\pm 14$ |  $365\pm 97\pm 90$ |  32.4/32
$\Sigma_{c}^{0}\pi^{+}$ sys. | $\pm 5$ | $\pm 8$ | $\pm 50$ |

Table 2 compares the fit results for the ${\bar{N}}^{0}$ yield, mass and width
with P-wave and S-wave assumptions. The fitted yields are found to be
comparable with each other, while the mass and width show a systematic
difference. We estimate systematic errors by varying the fitted yields by
$\pm\sigma$ for the background ($\pm 3$) and
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ ($\pm 11$), and by taking into
account the uncertainty in modeling the low mass $(\Sigma_{c}^{0}\pi^{+})_{\rm
X}$ structure as discussed in the following.

The simulated $R(\cos\theta_{p})$ distribution for
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ is almost flat, as the generated
$\cos\theta_{p}$ distribution is uniform for $P$\- and $S$-waves. However, the
$R(cos\theta_{p})$ distribution is slightly affected by the assumed BW
parameters due to efficiency changes in $\cos\theta_{p}$. We study the
systematics of the fitted ${\bar{N}}^{0}$ mass and width due to the assumption
on $R(\cos\theta_{p})$, by changing the mass and the width in EvtGen in ranges
between $1400\,{\rm MeV}/c^{2}$ and $1620\,{\rm MeV}/c^{2}$, and between
$200\,{\rm MeV}$ and $450\,{\rm MeV}$, respectively. We find variations of
$\pm 1\,{\rm MeV}/c^{2}$ in the fitted mass and $\pm 5\,{\rm MeV}/c^{2}$ in
the width. We also study the systematic errors due to the parameterization of
the $(\Sigma_{c}^{0}\pi^{+})$ low mass structure. Instead of assuming a model
with a single Breit-Wigner $(\Sigma_{c}^{0}\pi^{+})_{\rm X}$, we consider a
combination of known states $\Lambda_{c}^{*}\to\Sigma_{c}(2455)^{0}\pi^{+}$;
$\Lambda_{c}^{+}(2625)$ ($\Gamma_{\rm total}<1.9\,{\rm MeV}$) [18],
$\Lambda_{c}^{+}(2765)\to\Lambda_{c}^{+}\pi^{+}\pi^{-}$ ($\Gamma\sim 50\,{\rm
MeV}/c^{2}$), $\Lambda_{c}^{+}(2880)$ ($\Gamma=5.8\pm 1.3\,{\rm MeV}$), and
$\Lambda_{c}^{+}(2940)$ ($\Gamma=13^{+28}_{-9}\,{\rm MeV}$). Here we use the
partial widths for $\Sigma_{c}^{0}\pi^{+}$ decay of the last three states
given by Ref. [21]. We make a fit to the $\bar{N}^{0}$ mass, width and the
yield of $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ with the individual
$\Lambda_{c}^{*+}$ yields floated and with the background fixed as mentioned
previously. We obtain $N({\bar{p}}\pi^{+})$ mass and width values in good
agreement with those obtained by the fit with the
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ model.

The branching fraction product ${\cal
B}$($\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$)$\times{\cal
B}(\bar{N}^{0}\to\bar{p}\pi^{+})$ is calculated as
$N_{s}/(N_{B\bar{B}}\cdot\epsilon\cdot CF\cdot{\cal B}_{\Lambda_{c}^{+}\to
pK^{-}\pi^{+}})$ assuming $N_{B^{+}B^{-}}=N_{B^{0}\bar{B}^{0}}$. For $N_{s}$
we use the P-wave yield in Table 2 as it gives a better confidence level than
an S-wave fit. We use $N_{B\bar{B}}=(387.7\pm 4.8)\times 10^{6}$ for the
integrated luminosity of 357 fb-1, and the signal efficiency
$\epsilon=(5.18\pm 0.13$)% from the MC simulation of
$\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$. We apply a correction factor
$CF=(86.7\pm 7.9)$%, which takes into account the systematic difference in
particle identification (PID) between data and MC simulation. Correction
factors for proton, kaon and pion tracks are determined from a comparison of
data and MC simulation for large samples of $D^{*+}\to D^{0}(K\pi)\pi^{+}$ and
$\Lambda\to p\pi^{-}$ decays. The overall PID correction factor is then
calculated as a linear sum over the six tracks for the selected $B$ signal
events. We assign an error of 7.2% due to track reconstruction efficiency for
the six charged tracks in the final state. The systematic error on the
branching fraction arising from a quadratic sum of the uncertainties on
$N_{B\bar{B}}$, the signal efficiency $\epsilon$, and particle identification
$CF$ and track reconstruction, is found to be 12%. Including the systematic
error in the $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ yield, we arrive at the
total systematic uncertainty in the branching fraction of 17.6 %. Thus, we
obtain the branching fraction product of ${\cal
B}(\bar{B}^{0}\to\Sigma_{c}(2455)^{0}\bar{N}^{0})\times{\cal
B}(\bar{N}^{0}\to\bar{p}\pi^{+})$=($0.80\pm 0.15\rm{(stat.)}\pm
0.14\rm{(syst.)}\pm 0.21$)$\times 10^{-4}$, and a significance of 6.1 standard
deviations including systematics. The last error is due to an uncertainty in
${\cal B}(\Lambda_{c}^{+}\to pK^{-}\pi^{+})=(5.0\pm 1.3)\%$ [18].

Next, we investigate goodness-of-fits with the masses and widths fixed to
representative values for $N({\bar{p}}\pi^{+})$ states [18], and by floating
the yields for $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$ and
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$. The fit results are
summarized in Table 3. Here $L_{2I,2S}$ stands for a resonance of isospin $I$
and spin $S$ with an orbital angular momentum of $L$=S, P and D for $L$=0, 1
and 2, respectively. We exclude $\Delta$ states such as $\Delta(1600)P_{33}$
and $\Delta(1620)S_{31}$, as we have no significant structure in the
$\bar{p}\pi^{-}$ mass distribution in
$\bar{B}^{0}\to\Sigma_{c}^{++}\bar{p}\pi^{-}$ decay. The fits favor
$N(1440)P_{11}$ and $N(1535)S_{11}$, while they disfavor $N(1520)D_{13}$ and
$N(1650)S_{11}$. In the decay $\bar{B}^{0}\to\Sigma^{0}_{c}\bar{N}^{0}$
(assuming $S(\Sigma^{0}_{c})=\frac{1}{2}$), one expects a uniform
$\cos\theta_{p}$ distribution for the $N(1440)P_{11}$ state, $N(1535)S_{11}$
state and $N(1650)S_{11}$ state, and a $(1+3\cos^{2}\theta)$ distribution for
the $N(1520)D_{13}$ state. As shown in Fig. 6(b), the distribution has a peak
only in the forward direction, which is well reproduced by the mode
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$. The remaining
uniform distribution is due to $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$.
Thus, the observed $\cos\theta_{\bar{p}}$ distribution is consistent with
both, $\bar{N}(1440)P_{11}$ and $\bar{N}(1535)S_{11}$ states, with a
preference for the former due to the width of the state.

Table 3:  Results of the fits using the parameters of known $N({\bar{p}}\pi^{+})$ resonances [18].  States |  | Mass | $\Gamma$ | $\Sigma_{c}^{0}\bar{N}^{0}$ | $(\Sigma_{c}^{0}\pi^{+})_{X}\bar{p}$ |  $\chi^{2}$/ndf
---|---|---|---|---|---|---
|  |  ${\rm MeV}/c^{2}$ | $~{}{\rm MeV}$ |  Events | Events |
N(1440) | $P_{11}$ | 1440 | 300 | $65\pm 10$ | $39\pm 9$ | 37.6/34
N(1520) | $D_{13}$ | 1520 | 115 | $46\pm 9$ | $53\pm 10$ | 53.5/34
N(1535) | $S_{11}$ | 1535 | 150 | $58\pm 10$ | $43\pm 10$ | 40.1/34
N(1650) | $S_{11}$ | 1655 | 165 | $44\pm 10$ | $55\pm 11$ | 74.2/34

Finally, we try to perform a fit with an incoherent sum of the two Breit-
Wigners, as we find that the fit results favor $N(1440)P_{11}$ and
$N(1535)S_{11}$, and both give a distribution uniform in $\cos\theta_{p}$.
Figure 7 shows the result of a fit to (a) the $M(\bar{p}\pi^{+})$ and (b)
$\cos{\theta}_{\bar{p}}$ distributions, where the $N$ masses and widths are
fixed to the values in Ref. [18], and the individual yields are floated. The
histograms show the contributions from $N(1440)$ (solid), $N(1535)$ (dashed)
states, $\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ (dotted), and
the background (shaded). The yields are $(37\pm 12)$ for the $N(1440)$ and
$(30\pm 11)$ for the $N(1535)$, while the
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ yield is $(35\pm 9)$.
We obtain the goodness of fit $\chi^{2}$/ndf=30.3/33, which indicates a slight
preference (by 2.7 $\sigma$) for a mixed state of $N(1440)$ and $N(1535)$
[18].

Figure 7:  Simultaneous fit to the $M(\bar{p}\pi^{+})$ and
$\cos{\theta}_{\bar{p}}$ distributions with the $N(1440)P_{11}$ and
$N(1535)S_{11}$ Breit-Wigners. The histograms indicate the contributions from
the $P_{11}$ (solid) and $S_{11}$ (dashed) states,
$\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ (dotted), and the
background (shaded).

In summary, we study the three-body decay
$\bar{B}^{0}\rightarrow\Sigma_{c}(2455)^{0}\bar{p}\pi^{+}$ with the same data
set used for the analysis of the four-body decay
$\bar{B}^{0}\rightarrow\Lambda_{c}^{+}\bar{p}\pi^{+}\pi^{-}$ [1]. We observe a
broad $\bar{p}\pi^{+}$ mass structure near $1.5\,{\rm GeV}/c^{2}$, and a
uniform $\cos{\theta}_{\bar{p}}$ distribution with a sharp forward peak. To
explain these structures, we find that contributions from an intermediate two-
body decay $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$, non-resonant three-body
decay $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{p}\pi^{+}$ and a low mass structure
near threshold $\bar{B}^{0}\to(\Sigma^{0}_{c}\pi^{+})_{\rm X}\,\bar{p}$ are
needed. We perform a simultaneous fit to the $M(\bar{p}\pi^{+})$ and
$\cos{\theta}_{\bar{p}}$ distributions with those three modes, and determine
the yield and the relativistic Breit-Wigner parameters of the ${\bar{N}}^{0}$
state for $\bar{B}^{0}\to\Sigma_{c}^{0}\bar{N}^{0}$. We obtain the branching
fraction product of ${\cal
B}(\bar{B}^{0}\to\Sigma_{c}(2455)^{0}\bar{N}^{0})\times{\cal
B}(\bar{N}^{0}\to\bar{p}\pi^{+})$=($0.80\pm 0.15\rm{(stat.)}\pm
0.14\rm{(syst.)}\pm 0.21$)$\times 10^{-4}$ with a signal significance of 6.1
standard deviations including systematics. The fitted mass and width are
consistent with $\bar{N}(1440)$$P_{11}$ and $\bar{N}(1535)S_{11}$; both states
also produce a uniform helicity distribution that is in good agreement with
the data. The structure is also consistent with an interpretation in terms of
an admixture of these two states.

ACKNOWLEDGMENT

We thank the KEKB group for excellent operation of the accelerator, the KEK
cryogenics group for efficient solenoid operations, and the KEK computer group
and the NII for valuable computing and Super-SINET network support. We
acknowledge support from MEXT and JSPS (Japan); ARC and DEST (Australia); NSFC
(China); DST (India); MOEHRD, KOSEF and KRF (Korea); KBN (Poland); MES and
RFAAE (Russia); ARRS (Slovenia); SNSF (Switzerland); NSC and MOE (Taiwan); and
DOE (USA).

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