EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-175 LHCb-PAPER-2018-028 July 5, 2018

Measurement of the ${{\mathchar 28938\relax}^{0}_{c}}$ baryon lifetime

LHCb collaboration†††Authors are listed at the end of this paper.

We report a measurement of the lifetime of the ${{\mathchar
28938\relax}^{0}_{c}}$ baryon using proton-proton collision data at center-of-
mass energies of 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$, corresponding to an
integrated luminosity of 3.0$\mbox{\,fb}^{-1}$ collected by the LHCb
experiment. The sample consists of about 1000 ${{\mathchar
28938\relax}^{-}_{b}}\rightarrow{{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ signal decays, where
the ${{\mathchar 28938\relax}^{0}_{c}}$ baryon is detected in the
$p{{K}^{-}}{{K}^{-}}{{\pi}^{+}}$ final state and $X$ represents possible
additional undetected particles in the decay. The ${{\mathchar
28938\relax}^{0}_{c}}$ lifetime is measured to be $\tau_{{{\mathchar
28938\relax}^{0}_{c}}}=268\pm 24\pm 10\pm 2$ fs, where the uncertainties are
statistical, systematic, and from the uncertainty in the ${{D}^{+}}$ lifetime,
respectively. This value is nearly four times larger than, and inconsistent
with, the current world-average value.

Published in Phys. Rev. Lett. 121, 092003 (2018)

© 2024 CERN for the benefit of the LHCb collaboration, CC-BY-4.0 license.

Measurements of the lifetimes of hadrons containing heavy ($b$ or $c$) quarks
play an important role in testing theoretical approaches that are used to
predict Standard Model parameters. The validation of such tools is important,
as they can then be used to search for deviations from Standard Model
expectations in other processes. One of the most predictive tools in quark
flavor physics is the heavy quark expansion (HQE) [1, 2, 3, 4, 5, 6, 7, 8],
which describes the decay widths of hadrons containing heavy quarks, $Q$,
through an expansion in powers of $1/m_{Q}$, where $m_{Q}$ is the heavy quark
mass. While predictions for absolute lifetimes carry relatively large
uncertainties, ratios of lifetimes have smaller theoretical uncertainties [9].
Higher-order terms in the HQE are related to non-perturbative corrections, and
to effects due to the presence of the other light quark(s) (spectator) in the
heavy hadron. For beauty hadrons with a single heavy quark, these corrections
are typically at the few percent level or less, due to the large mass of the
$b$ quark [9]. For charm hadrons, since $m_{c}$ is significantly smaller than
$m_{b}$, these higher-order corrections can be sizable. Therefore measurements
of charm-hadron lifetimes provide a sensitive probe of their contributions
[10, 11, 12, 13, 14].

While charm-meson lifetimes have been measured precisely and provide useful
information on these higher-order terms, the knowledge of charm-baryon
lifetimes is much less accurate. The lifetimes of the ${{D}^{0}}$, ${{D}^{+}}$
and ${{D}^{+}_{s}}$ mesons are known to about 1% precision, whereas the
corresponding uncertainties for the ${{\mathchar 28931\relax}^{+}_{c}}$,
${{\mathchar 28932\relax}^{+}_{c}}$, ${{\mathchar 28932\relax}^{0}_{c}}$ and
${{\mathchar 28938\relax}^{0}_{c}}$ baryons are 3%, 6%, 10% and 17%,
respectively [15]. Improved measurements of the charm-baryon lifetimes provide
complementary information to what can be gleaned from charm mesons. For
example, contributions from $W$-exchange and constructive Pauli interference
effects are present in charm-baryon decays, but are small or absent in charm-
meson decays [11]. Moreover, for charm baryons, the spectator system may have
spin 0 (${{\mathchar 28931\relax}^{+}_{c}}$, ${{\mathchar
28932\relax}^{+}_{c}}$, ${{\mathchar 28932\relax}^{0}_{c}}$) or spin 1
(${{\mathchar 28938\relax}^{0}_{c}}$), whereas for charm mesons, the light
quark spin is always equal to 1/2.

It has been argued that the expected lifetime hierarchy, due to the higher
order contributions discussed above, should be [10, 11, 16, 17, 12, 18]

$\displaystyle\tau_{{{\mathchar 28932\relax}^{+}_{c}}}>\tau_{{{\mathchar
28931\relax}^{+}_{c}}}>\tau_{{{\mathchar
28932\relax}^{0}_{c}}}>\tau_{{{\mathchar 28938\relax}^{0}_{c}}}.$ (1)

The quark content of the ${{\mathchar 28938\relax}^{0}_{c}}$ baryon is $css$,
and the qualitative argument that the ${{\mathchar 28938\relax}^{0}_{c}}$
lifetime should be the shortest is predicated on large constructive
interference between the $s$ quark in the $c\rightarrow sW^{+}$ transition in
the ${{\mathchar 28938\relax}^{0}_{c}}$ decay and the spectator $s$ quarks in
the final state. However, it is also conceivable that the ${{\mathchar
28938\relax}^{0}_{c}}$ lifetime could be the largest, depending on the
treatment of higher-order terms in the HQE expansion [12].

Current measurements [15] are consistent with this hierarchy. The least well
measured lifetime is that of the ${{\mathchar 28938\relax}^{0}_{c}}$ baryon,
with a value of $\tau_{{{\mathchar 28938\relax}^{0}_{c}}}=69\pm 12$ fs,
obtained by fixed-target experiments using a small number of signal decays
[19, 20, 21].

In this Letter reports a new measurement of the ${{\mathchar
28938\relax}^{0}_{c}}$ baryon lifetime using a sample of semileptonic (SL)
${{\mathchar 28938\relax}^{-}_{b}}\rightarrow{{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ decays, where the
${{\mathchar 28938\relax}^{0}_{c}}$ baryons are detected in the
$p{{K}^{-}}{{K}^{-}}{{\pi}^{+}}$ final state and $X$ represents any additional
undetected particles. Semileptonic $b$-meson decays were used previously by
LHCb to make precise measurements of the ${{D}^{+}_{s}}$ and ${{B}^{0}_{s}}$
lifetimes [22]. Throughout the text, charge-conjugate processes are implicitly
included.

To reduce the uncertainties associated with systematic effects, the lifetime
ratio

$\displaystyle r_{{{\mathchar
28938\relax}^{0}_{c}}}\equiv\frac{\tau_{{{\mathchar
28938\relax}^{0}_{c}}}}{\tau_{{{D}^{+}}}}$ (2)

is measured, where the ${{D}^{+}}$ meson is detected in
$B\rightarrow{{D}^{+}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ decays, with
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$. In the following, the
symbols $H_{b}$ and $H_{c}$ are used to refer to the $b$ or $c$-hadron in
either of the two modes indicated above.

The measurement uses proton-proton ($pp$) collision data samples, collected by
the LHCb experiment, corresponding to an integrated luminosity of
3.0$\mbox{\,fb}^{-1}$, of which 1.0$\mbox{\,fb}^{-1}$ was recorded at a
center-of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$ and
2.0$\mbox{\,fb}^{-1}$ at 8$\mathrm{\,Te\kern-1.00006ptV}$. The LHCb detector
[23, 24] is a single-arm forward spectrometer covering the pseudorapidity
range $2<\eta<5$, designed for the study of particles containing $b$ or $c$
quarks. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The minimum
distance of a track to a primary vertex (PV), the impact parameter (IP), is
measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Charged hadrons are identified using
information from two ring-imaging Cherenkov (RICH) detectors [25]. Muons are
identified by a system composed of alternating layers of iron and multiwire
proportional chambers [26]. The online event selection is performed by a
trigger [27], which consists of a hardware stage, based on information from
the calorimeter and muon systems, followed by a software stage, which applies
a full event reconstruction.

Simulation is required to model the effects of the detector acceptance and the
imposed selection requirements. Proton-proton collisions are simulated using
Pythia [28, *Sjostrand:2007gs] with a specific LHCb configuration [30]. Decays
of hadronic particles are described by EvtGen [31], in which final-state
radiation is generated using Photos [32]. The interaction of the generated
particles with the detector and its response are implemented using the Geant4
toolkit [33, *Agostinelli:2002hh] as described in Ref. [35].

Signal ${{\mathchar 28938\relax}^{-}_{b}}$ candidates are formed by combining
an ${{\mathchar 28938\relax}^{0}_{c}}\rightarrow
p{{K}^{-}}{{K}^{-}}{{\pi}^{+}}$ candidate with a ${\mu^{-}}$ candidate. Each
final-state particle in the decay is required to be detached from all PVs in
the event, and is associated to the one with the smallest
$\chi^{2}_{\text{IP}}$. Here, $\chi^{2}_{\text{IP}}$ is defined as the
difference in $\chi^{2}$ of the particle’s associated PV reconstructed with
and without the considered track. The muon is required to have
$\mbox{$p_{\mathrm{T}}$}>1{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$,
$p>6{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and have particle identification
(PID) information consistent with being a muon. The ${{\mathchar
28938\relax}^{0}_{c}}$ candidate’s decay products must have PID information
consistent with their assumed particle hypotheses, and have
$\mbox{$p_{\mathrm{T}}$}>0.25{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$p>2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, except for the proton, which is
required to have $p>8{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. To remove the
contribution from promptly produced ${{\mathchar 28938\relax}^{0}_{c}}$
baryons, each ${{\mathchar 28938\relax}^{0}_{c}}$ candidate’s reconstructed
trajectory must not point back to any PV in the event. Only ${{\mathchar
28938\relax}^{0}_{c}}$ candidates that have an invariant mass within
60${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known ${{\mathchar
28938\relax}^{0}_{c}}$ mass are retained.

The ${{\mathchar 28938\relax}^{0}_{c}}{\mu^{-}}$ combinations are required to
form a good quality vertex and satisfy the invariant mass requirement,
$m({{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}})<8.0$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$.
Random combinations of ${{\mathchar 28938\relax}^{0}_{c}}$ and ${\mu^{-}}$ are
suppressed by requiring the fitted $z$ coordinates of the ${{\mathchar
28938\relax}^{0}_{c}}$ and ${{\mathchar 28938\relax}^{-}_{b}}$ decay vertices
to satisfy $z({{\mathchar 28938\relax}^{0}_{c}})-z({{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}})>-0.05$ mm, where the $z$ axis is parallel to
the beam direction.

To ensure precise modeling of the decay-time acceptance from simulation, the
candidates must satisfy a well-defined set of hardware and software trigger
requirements. At the hardware level, candidates are required to pass the
single-muon trigger, and, at the software level, to pass specific triggers
designed to select multi-body final states containing a muon [27].

To improve the signal-to-background ratio in the ${{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}}$ sample, a boosted decision tree (BDT)
discriminant [36, 37] is built from 18 variables, which include the $\chi^{2}$
for the ${{\mathchar 28938\relax}^{-}_{b}}$ and ${{\mathchar
28938\relax}^{0}_{c}}$ decay-vertex fits, and $\chi^{2}_{\text{IP}}$, $p$,
$p_{\mathrm{T}}$, and a PID response variable for each final-state hadron. The
BDT is trained using simulated ${{\mathchar
28938\relax}^{-}_{b}}\rightarrow{{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ decays for the
signal, while background is taken from the ${{\mathchar 28938\relax}^{0}_{c}}$
mass sidebands, $30<|m(p{{K}^{-}}{{K}^{-}}{{\pi}^{+}})-m_{{{\mathchar
28938\relax}^{0}_{c}}}|<50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, where
$m_{{{\mathchar 28938\relax}^{0}_{c}}}$ is the known ${{\mathchar
28938\relax}^{0}_{c}}$ mass [15]. The requirement on the BDT response is
determined by optimizing the figure of merit $S/\sqrt{S+B}$, where $S$ and $B$
are the expected signal and background yields within a
$\pm$15${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ mass region centered on the
mass peak, respectively. The optimal BDT requirement provides a signal
(background) efficiency of 78% (16%).

The ${{D}^{+}}{\mu^{-}}$ candidates, used for normalization, are formed by
combining ${{{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}}$ and
${\mu^{-}}$ candidates. The selections are identical to those discussed above,
except the mass window is centered on the known ${{D}^{+}}$ mass and the BDT
requirement is eliminated. Only 10% of the ${{D}^{+}}{\mu^{-}}$ data, selected
at random, are used in the analysis, since the full sample is much larger than
needed for this measurement.

The invariant-mass distributions for the selected ${{\mathchar
28938\relax}^{0}_{c}}$ and ${{D}^{+}}$ candidates in the two $H_{c}{\mu^{-}}$
final states are shown in Fig. 1. Both distributions are fitted using the sum
of a signal component, defined as the sum of two Gaussian functions with a
common mean, and an exponential shape to represent the combinatorial
background. From a binned maximum-likelihood fit, the fitted ${{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}}$ and ${{D}^{+}}{\mu^{-}}$ yields are $978\pm
60$ and $(809\pm 1)\times 10^{3}$, respectively. The number of ${{\mathchar
28938\relax}^{0}_{c}}$ signal decays is at least an order of magnitude larger
than any previous sample used for an ${{\mathchar 28938\relax}^{0}_{c}}$
lifetime measurement.

Figure 1: Invariant-mass distributions for (left) ${{D}^{+}}$ candidates in
$B\rightarrow{{D}^{+}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ decays and (right)
${{\mathchar 28938\relax}^{0}_{c}}$ candidates in ${{\mathchar
28938\relax}^{-}_{b}}\rightarrow{{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ decays. The results
of the fits, as described in the text, are overlaid.

The decay time of each $H_{c}$ candidate is determined from the positions of
the $H_{b}$ and $H_{c}$ decay vertices, and the measured $H_{c}$ momentum. The
background-subtracted decay-time spectra are obtained using the sPlot
technique [38], where the measured $H_{c}$ mass is used as the discriminating
variable. The uncertainties in the bin-by-bin signal yields reflect both the
finite signal yield and the statistical uncertainty due to the background
subtraction.

Potential backgrounds from (i) random $H_{c}{\mu^{-}}$ combinations, (ii)
$H_{b}\rightarrow H_{c}{\tau^{-}}{{\overline{\nu}}_{\tau}}$,
${\tau^{-}}\rightarrow{\mu^{-}}{{\nu}_{\tau}}{{\overline{\nu}}_{\mu}}$ decays,
and (iii) $H_{b}\rightarrow H_{c}{\kern
1.99997pt\overline{\kern-1.99997ptD}{}},~{}{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}\rightarrow{\mu^{-}}X$, where ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}$ represents a ${{D}^{-}_{s}}$,
${{D}^{-}}$ or ${{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}$ meson,
could lead to a bias on the lifetime, since the muon is not produced directly
at the $H_{b}$ decay vertex. These backgrounds have been investigated and
constitute a small fraction of the observed signal, about 3% in total, and
have decay-time spectra that are similar to the true
$H_{c}{\mu^{-}}{{\overline{\nu}}_{\mu}}$ final state due to the $\chi^{2}$
requirements on the $H_{b}$ vertex fit. Moreover, these backgrounds affect the
signal and the normalization mode similarly, thus leading to at least a
partial cancellation of any bias. Contamination in the ${{\mathchar
28938\relax}^{-}_{b}}\rightarrow{{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ sample from
misidentified four-body ${{D}^{0}}$ final states in
$B\rightarrow{{D}^{0}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ decays has been
investigated, and none are found to peak in the ${{\mathchar
28938\relax}^{0}_{c}}$ signal region.

The decay-time spectra for the ${{\mathchar 28938\relax}^{0}_{c}}$ and
${{D}^{+}}$ signals are shown in Fig. 2, along with the results of the fits
described below. The decrease in the signal yield as the decay time approaches
zero is mainly due to the effects of the $H_{c}$ decay-time resolution, which
is in the range of $85-100$ fs, and the $z(H_{c})-z(H_{c}{\mu^{-}})>-0.05$ mm
requirement.

Figure 2: Decay-time spectra for (left) ${{D}^{+}}$ signal in
$B\rightarrow{{D}^{+}}{\mu^{-}}X$ events and (right) ${{\mathchar
28938\relax}^{0}_{c}}$ signal in ${{\mathchar
28938\relax}^{-}_{b}}\rightarrow{{\mathchar 28938\relax}^{0}_{c}}{\mu^{-}}X$
events. Overlaid are the fit results, as described in the text, along with the
uncertainties due to finite simulated sample sizes.

The decay-time signal model, $S(t_{\rm rec})$, takes the form

$\displaystyle S(t_{\rm rec})=f(t_{\rm rec})g(t_{\rm rec})\beta(t_{\rm rec}).$
(3)

Here, $f(t_{\rm rec})$ is a signal template of reconstructed decay times,
obtained from the full LHCb simulation, after all selections have been applied
as in the data. The signal template is multiplied by $g(t_{\rm
rec})=\exp(-t_{\rm rec}/\tau_{\rm fit}^{H_{c}})/\exp(-t_{\rm rec}/\tau_{\rm
sim}^{H_{c}})$, where $\tau_{\rm sim}^{{{D}^{+}}}=1040$ fs and $\tau_{\rm
sim}^{{{\mathchar 28938\relax}^{0}_{c}}}=250$ fs are the lifetimes used in the
simulation, and $\tau_{\rm fit}^{H_{c}}$ is the signal lifetime to be fitted.
The function $\beta(t_{\rm rec})$ is a correction that accounts for a small
difference in the efficiency between data and simulation for reconstructing
tracks in the vertex detector that originate far from the beamline [39].

Given the precise knowledge of the ${{D}^{+}}$ meson lifetime ($1040\pm 7$ fs)
[15], the ${{D}^{+}}{\mu^{-}}$ sample is used to calibrate $\beta(t_{\rm
rec})$ and validate the fit. The signal template is obtained from simulated
$B\rightarrow{{D}^{+}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ decays, where
contributions from $B\rightarrow{{D}^{+}}{\tau^{-}}{{\overline{\nu}}_{\tau}}X$
decays are included. The function $\beta(t_{\rm rec})$ is obtained by taking
the ratio between the ${{D}^{+}}$ decay-time spectrum in data (obtained via
the sPlot technique) and that obtained from simulation. The ratio shows a
linear dependence, and a fit to the function $\beta(t_{\rm
rec})=1+\beta_{0}t_{\rm rec}$ yields $\beta_{0}=(-0.89\pm 0.32)\times 10^{-2}$
ps-1. If the $\beta(t_{\rm rec})$ function is excluded from the fit,
$\tau^{{{D}^{+}}}_{\rm fit}$ is $10$ fs below the world average. The result of
the binned $\chi^{2}$ fit after this correction is applied is shown in Fig. 2
(left), where the fitted lifetime is found to be $\tau_{\rm
fit}^{{{D}^{+}}}=1042.0\pm 1.7\mathrm{\,(stat)}$ fs.

The ${{\mathchar 28938\relax}^{0}_{c}}$ lifetime is determined from a
simultaneous fit to the ${{\mathchar 28938\relax}^{0}_{c}}$ and ${{D}^{+}}$
decay-time spectra, for which the free parameters in the fit are
$r_{{{\mathchar 28938\relax}^{0}_{c}}}$ (see Eq. 2) and $\tau_{\rm
fit}^{{{D}^{+}}}$. By fitting for the ratio $r_{{{\mathchar
28938\relax}^{0}_{c}}}$, correlated systematic uncertainties partially cancel.
In the ${{\mathchar 28938\relax}^{0}_{c}}$ decay-time fit, $\beta_{0}$ is
scaled by 4/3 since the effect is expected to scale with the number of charged
final state particles in the $H_{c}$ decay [39]. The simulation includes
contributions from ${{\mathchar
28938\relax}^{0}_{c}}{\tau^{-}}{{\overline{\nu}}_{\tau}}X$ final states. The
results of the fit to the ${{\mathchar 28938\relax}^{0}_{c}}$ decay-time
distribution are shown in Fig. 2 (right), where the value $r_{{{\mathchar
28938\relax}^{0}_{c}}}=0.258\pm 0.023\mathrm{\,(stat)}$ is obtained.
Multiplying this value by $\tau^{{{D}^{+}}}=1040$ fs [15], the ${{\mathchar
28938\relax}^{0}_{c}}$ lifetime is measured to be $268\pm 24$ fs. This is
about four times larger than, and incompatible with, the current world average
value of $69\pm 12$ fs [15].

Several cross-checks have been performed to ensure the robustness of this
result. To confirm that the signal events are from SL ${{\mathchar
28938\relax}^{-}_{b}}$ decays, a number of distributions, such as the
${{\mathchar 28938\relax}^{0}_{c}}{\mu^{-}}$ mass spectrum, $p_{\mathrm{T}}$
and decay time have been compared between data (using sPlot) and the
${{\mathchar 28938\relax}^{-}_{b}}\rightarrow{{\mathchar
28938\relax}^{0}_{c}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ simulation. In all
cases, good agreement is found. The lifetime measurement has also been
performed using a simple subtraction of the ${{\mathchar
28938\relax}^{0}_{c}}$ mass sidebands, and we find good agreement with the
value obtained by the sPlot technique. The ${{\mathchar 28938\relax}^{0}_{c}}$
decay-time distribution obtained from an independent and comparably sized data
sample of semileptonic decays collected at 13$\mathrm{\,Te\kern-1.00006ptV}$
center-of-mass energy has been examined, and the distribution is consistent
with the one observed here. The procedure has also been checked using a sample
of about 88,000
${{{B}^{-}}}\rightarrow{{D}^{0}}(\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}){\mu^{-}}X$
decays to measure the ${{D}^{0}}$ meson lifetime. The obtained lifetime is
consistent with the expected value within about one standard deviation. The
analysis has also been carried out with either tighter PID or tighter BDT
requirements, and the fitted ${{\mathchar 28938\relax}^{0}_{c}}$ lifetime in
each case is consistent with the value from the default fit. The analysis has
also been checked with the ${{\mathchar 28931\relax}^{+}_{c}}$ baryon, and the
lifetime is consistent with expectations.

A number of sources of systematic uncertainty on the measured ratio
$r_{{{\mathchar 28938\relax}^{0}_{c}}}$ have been investigated, and are
summarized in Table 1. The decay time acceptance correction, $\beta(t_{\rm
rec})$, leads to an uncertainty of 0.5% on $r_{{{\mathchar
28938\relax}^{0}_{c}}}$, which includes a contribution from the finite sample
sizes and the choice of fit function.

Studies of the ${{D}^{+}}$ calibration mode show a small dependence of the
$\beta_{0}$ parameter on the $p_{\mathrm{T}}$ and $\eta$ of the $H_{b}$
hadron. In the case that the $p_{\mathrm{T}}$ and $\eta$ spectra in data and
simulation differ, it could cause a shift in the average $\beta_{0}$. The
uncertainty on $r_{{{\mathchar 28938\relax}^{0}_{c}}}$ is obtained by taking
into account the variation of $\beta_{0}$ in different $p_{\mathrm{T}}$ and
$\eta$ ranges, and the extent to which the $p_{\mathrm{T}}$ and $\eta$ spectra
may differ between data and simulation.

The world-average value of the ${{\mathchar 28938\relax}^{-}_{b}}$ lifetime is
$1.64^{+0.18}_{-0.17}$ ps [15], whereas the simulation uses 1.60 ps. To assess
the potential impact on the ${{\mathchar 28938\relax}^{0}_{c}}$ lifetime, we
weight $f(t_{\rm rec})$ to replicate an ${{\mathchar 28938\relax}^{-}_{b}}$
lifetime of either 1.50 ps or 1.70 ps. The changes in $r_{{{\mathchar
28938\relax}^{0}_{c}}}$ are assigned as a systematic uncertainty.

The decay-time resolution has been checked by comparing the ${{D}^{0}}$ decay-
time spectra in ${{{B}^{-}}}\rightarrow{{D}^{0}}{{\pi}^{-}}$ decays, where no
explicit requirement on the flight distance of the ${{D}^{0}}$ is applied.
Negative decay times are entirely due to the decay-time resolution, and
simulation is found to agree well with data. To assess a potential impact of a
small difference in decay-time resolution between simulation and data, new
${{\mathchar 28938\relax}^{0}_{c}}$ and ${{D}^{+}}$ signal templates are
formed where the reconstructed decay time is smeared by an additional 15%,
beyond what is produced by the full simulation. The fit is redone, and the
difference in $r_{{{\mathchar 28938\relax}^{0}_{c}}}$ from the nominal value
is assigned as a systematic uncertainty.

The method for background subtraction uses the sPlot technique, which has some
dependence on the choice of signal and background functions. To assess a
potential systematic effect, the decay-time spectra are obtained using a
sideband subtraction of the $H_{c}$ mass spectra for both the signal and the
normalization modes. The sideband-subtracted decay-time spectra are then
fitted using the decay-time fit described above. The difference between this
result and the nominal one is assigned as a systematic uncertainty.

The decay-time spectra in both ${{\mathchar 28938\relax}^{0}_{c}}{\mu^{-}}$
and ${{D}^{+}}{\mu^{-}}$ samples, have small contributions from random
combinations of $H_{c}$ and ${\mu^{-}}$ candidates [($0.8\pm 0.2)$% of the
signal], as well as physics backgrounds where the ${\mu^{-}}$ comes from
either a ${\tau^{-}}$ [($1.8\pm 0.3$%)] or a SL $D$ decay [($0.5\pm 0.2)$%].
From simulation and data control samples, we find that the effective lifetimes
of these backgrounds are within 10% of the true signal lifetime; this is due
to the requirement that the muon candidate must form a good vertex with the
$H_{c}$ candidate. The impact on the ${{\mathchar 28938\relax}^{0}_{c}}$
lifetime is evaluated using pseudoexperiments, where mixtures of these
backgrounds (with different decay-time spectra) and signal decays are formed
and fitted assuming a single lifetime for the sample. The difference in the
mean value of $r_{{{\mathchar 28938\relax}^{0}_{c}}}$ between the nominal fit,
and that with the backgrounds added is assigned as the systematic uncertainty.

The systematic uncertainty due to the finite size of the simulated samples is
assessed by repeating the fit to the data many times, where in each fit the
simulated-template bin contents are fluctuated within their uncertainties. The
standard deviation of the distribution of the fitted $r_{{{\mathchar
28938\relax}^{0}_{c}}}$ values is assigned as a systematic uncertainty.

Table 1: Summary of systematic uncertainties on the lifetime ratio, $r_{{{\mathchar 28938\relax}^{0}_{c}}}$, in units of $10^{-4}$. Source |  $r_{{{\mathchar 28938\relax}^{0}_{c}}}$ ($10^{-4}$)
---|---
Decay-time acceptance |  13
${{\mathchar 28938\relax}^{-}_{b}}$ prod. spectrum |  3
${{\mathchar 28938\relax}^{-}_{b}}$ lifetime |  4
Decay-time resolution |  3
Background subtraction |  18
$H_{c}({\tau^{-}},D)$, random ${\mu^{-}}$ |  8
Simulated sample size |  98
Total systematic | 101
Statistical uncertainty | 230

In summary, we use $pp$ collision data samples at
7$\mathrm{\,Te\kern-1.00006ptV}$ and 8$\mathrm{\,Te\kern-1.00006ptV}$ center
of mass energies, corresponding to 3.0$\mbox{\,fb}^{-1}$ of integrated
luminosity, to measure the lifetime of the ${{\mathchar 28938\relax}^{0}_{c}}$
baryon. The measured ratio of lifetimes and absolute ${{\mathchar
28938\relax}^{0}_{c}}$ lifetime are

$\displaystyle\frac{\tau_{{{\mathchar
28938\relax}^{0}_{c}}}}{\tau_{{{D}^{+}}}}$ $\displaystyle=0.258\pm 0.023\pm
0.010$ $\displaystyle\tau_{{{\mathchar 28938\relax}^{0}_{c}}}$
$\displaystyle=268\pm 24\pm 10\pm 2~{}{\rm fs},$

where the first uncertainty is statistical, the second is systematic, and the
third is due to the uncertainty in the ${{D}^{+}}$ lifetime [15]. The measured
${{\mathchar 28938\relax}^{0}_{c}}$ lifetime is about four times larger than,
and inconsistent with, the world average value of $69\pm 12$ fs [15].

With this measurement, the lifetime hierarchy places the ${{\mathchar
28938\relax}^{0}_{c}}$ baryon as having the second largest lifetime after the
${{\mathchar 28932\relax}^{+}_{c}}$ baryon,

$\displaystyle\tau_{{{\mathchar 28932\relax}^{+}_{c}}}>\tau_{{{\mathchar
28938\relax}^{0}_{c}}}>\tau_{{{\mathchar
28931\relax}^{+}_{c}}}>\tau_{{{\mathchar 28932\relax}^{0}_{c}}}.$

The result presented here may suggest that the constructive interference
between the $s$ quark in the $c\rightarrow sW^{+}$ transition in the
${{\mathchar 28938\relax}^{0}_{c}}$ decay and the spectator $s$ quarks in the
final state is smaller than expected, that the spin of the $ss$ system plays a
larger role, or that additional or higher order contributions in the heavy
quark expansion need to be considered.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES
and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine);
STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC
(Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID
(Poland) and OSC (USA). We are indebted to the communities behind the multiple
open-source software packages on which we depend. Individual groups or members
have received support from AvH Foundation (Germany); EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union); ANR, Labex P2IO and OCEVU,
and Région Auvergne-Rhône-Alpes (France); Key Research Program of Frontier
Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF
and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); Herchel Smith Fund,
the Royal Society, the English-Speaking Union and the Leverhulme Trust (United
Kingdom); Laboratory Directed Research and Development program of LANL (USA).

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LHCb collaboration

R. Aaij27, B. Adeva41, M. Adinolfi48, C.A. Aidala74, Z. Ajaltouni5, S. Akar59,
P. Albicocco18, J. Albrecht10, F. Alessio42, M. Alexander53, A. Alfonso
Albero40, S. Ali27, G. Alkhazov33, P. Alvarez Cartelle55, A.A. Alves Jr41, S.
Amato2, S. Amerio23, Y. Amhis7, L. An3, L. Anderlini17, G. Andreassi43, M.
Andreotti16,g, J.E. Andrews60, R.B. Appleby56, F. Archilli27, P. d’Argent12,
J. Arnau Romeu6, A. Artamonov39, M. Artuso61, K. Arzymatov37, E. Aslanides6,
M. Atzeni44, B. Audurier22, S. Bachmann12, J.J. Back50, S. Baker55, V.
Balagura7,b, W. Baldini16, A. Baranov37, R.J. Barlow56, S. Barsuk7, W.
Barter56, F. Baryshnikov71, V. Batozskaya31, B. Batsukh61, V. Battista43, A.
Bay43, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61, L.J. Bel27, S.
Belin22, N. Beliy63, V. Bellee43, N. Belloli20,i, K. Belous39, I.
Belyaev34,42, E. Ben-Haim8, G. Bencivenni18, S. Benson27, S. Beranek9, A.
Berezhnoy35, R. Bernet44, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt44, F. Betti15,42, M.O. Bettler49, M. van Beuzekom27, Ia.
Bezshyiko44, S. Bhasin48, J. Bhom29, S. Bifani47, P. Billoir8, A. Birnkraut10,
A. Bizzeti17,v, M. Bjørn57, M.P. Blago42, T. Blake50, F. Blanc43, S. Blusk61,
D. Bobulska53, V. Bocci26, O. Boente Garcia41, T. Boettcher58, A. Bondar38,x,
N. Bondar33, S. Borghi56,42, M. Borisyak37, M. Borsato41, F. Bossu7, M.
Boubdir9, T.J.V. Bowcock54, C. Bozzi16,42, S. Braun12, M. Brodski42, J.
Brodzicka29, A. Brossa Gonzalo50, D. Brundu22, E. Buchanan48, A. Buonaura44,
C. Burr56, A. Bursche22, J. Buytaert42, W. Byczynski42, S. Cadeddu22, H.
Cai64, R. Calabrese16,g, R. Calladine47, M. Calvi20,i, M. Calvo Gomez40,m, A.
Camboni40,m, P. Campana18, D.H. Campora Perez42, L. Capriotti56, A.
Carbone15,e, G. Carboni25, R. Cardinale19,h, A. Cardini22, P. Carniti20,i, L.
Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina20, M. Cattaneo42, G.
Cavallero19,h, R. Cenci24,q, D. Chamont7, M.G. Chapman48, M. Charles8, Ph.
Charpentier42, G. Chatzikonstantinidis47, M. Chefdeville4, V. Chekalina37, C.
Chen3, S. Chen22, S.-G. Chitic42, V. Chobanova41, M. Chrzaszcz42, A.
Chubykin33, P. Ciambrone18, X. Cid Vidal41, G. Ciezarek42, P.E.L. Clarke52, M.
Clemencic42, H.V. Cliff49, J. Closier42, V. Coco42, J.A.B. Coelho7, J. Cogan6,
E. Cogneras5, L. Cojocariu32, P. Collins42, T. Colombo42, A. Comerma-
Montells12, A. Contu22, G. Coombs42, S. Coquereau40, G. Corti42, M. Corvo16,g,
C.M. Costa Sobral50, B. Couturier42, G.A. Cowan52, D.C. Craik58, A.
Crocombe50, M. Cruz Torres1, R. Currie52, C. D’Ambrosio42, F. Da Cunha
Marinho2, C.L. Da Silva75, E. Dall’Occo27, J. Dalseno48, A. Danilina34, A.
Davis3, O. De Aguiar Francisco42, K. De Bruyn42, S. De Capua56, M. De Cian43,
J.M. De Miranda1, L. De Paula2, M. De Serio14,d, P. De Simone18, C.T. Dean53,
D. Decamp4, L. Del Buono8, B. Delaney49, H.-P. Dembinski11, M. Demmer10, A.
Dendek30, D. Derkach37, O. Deschamps5, F. Desse7, F. Dettori54, B. Dey65, A.
Di Canto42, P. Di Nezza18, S. Didenko71, H. Dijkstra42, F. Dordei42, M.
Dorigo42,z, A. Dosil Suárez41, L. Douglas53, A. Dovbnya45, K. Dreimanis54, L.
Dufour27, G. Dujany8, P. Durante42, J.M. Durham75, D. Dutta56, R.
Dzhelyadin39, M. Dziewiecki12, A. Dziurda29, A. Dzyuba33, S. Easo51, U.
Egede55, V. Egorychev34, S. Eidelman38,x, S. Eisenhardt52, U. Eitschberger10,
R. Ekelhof10, L. Eklund53, S. Ely61, A. Ene32, S. Escher9, S. Esen27, T.
Evans59, A. Falabella15, N. Farley47, S. Farry54, D. Fazzini20,42,i, L.
Federici25, P. Fernandez Declara42, A. Fernandez Prieto41, F. Ferrari15, L.
Ferreira Lopes43, F. Ferreira Rodrigues2, M. Ferro-Luzzi42, S. Filippov36,
R.A. Fini14, M. Fiorini16,g, M. Firlej30, C. Fitzpatrick43, T. Fiutowski30, F.
Fleuret7,b, M. Fontana22,42, F. Fontanelli19,h, R. Forty42, V. Franco Lima54,
M. Frank42, C. Frei42, J. Fu21,r, W. Funk42, C. Färber42, M. Féo Pereira
Rivello Carvalho27, E. Gabriel52, A. Gallas Torreira41, D. Galli15,e, S.
Gallorini23, S. Gambetta52, Y. Gan3, M. Gandelman2, P. Gandini21, Y. Gao3,
L.M. Garcia Martin73, B. Garcia Plana41, J. García Pardiñas44, J. Garra
Tico49, L. Garrido40, D. Gascon40, C. Gaspar42, L. Gavardi10, G. Gazzoni5, D.
Gerick12, E. Gersabeck56, M. Gersabeck56, T. Gershon50, D. Gerstel6, Ph.
Ghez4, S. Gianì43, V. Gibson49, O.G. Girard43, L. Giubega32, K. Gizdov52, V.V.
Gligorov8, D. Golubkov34, A. Golutvin55,71, A. Gomes1,a, I.V. Gorelov35, C.
Gotti20,i, E. Govorkova27, J.P. Grabowski12, R. Graciani Diaz40, L.A. Granado
Cardoso42, E. Graugés40, E. Graverini44, G. Graziani17, A. Grecu32, R.
Greim27, P. Griffith22, L. Grillo56, L. Gruber42, B.R. Gruberg Cazon57, O.
Grünberg67, C. Gu3, E. Gushchin36, Yu. Guz39,42, T. Gys42, C. Göbel62, T.
Hadavizadeh57, C. Hadjivasiliou5, G. Haefeli43, C. Haen42, S.C. Haines49, B.
Hamilton60, X. Han12, T.H. Hancock57, S. Hansmann-Menzemer12, N. Harnew57,
S.T. Harnew48, T. Harrison54, C. Hasse42, M. Hatch42, J. He63, M. Hecker55, K.
Heinicke10, A. Heister10, K. Hennessy54, L. Henry73, E. van Herwijnen42, M.
Heß67, A. Hicheur2, R. Hidalgo Charman56, D. Hill57, M. Hilton56, P.H.
Hopchev43, W. Hu65, W. Huang63, Z.C. Huard59, W. Hulsbergen27, T. Humair55, M.
Hushchyn37, D. Hutchcroft54, D. Hynds27, P. Ibis10, M. Idzik30, P. Ilten47, K.
Ivshin33, R. Jacobsson42, J. Jalocha57, E. Jans27, A. Jawahery60, F. Jiang3,
M. John57, D. Johnson42, C.R. Jones49, C. Joram42, B. Jost42, N. Jurik57, S.
Kandybei45, M. Karacson42, J.M. Kariuki48, S. Karodia53, N. Kazeev37, M.
Kecke12, F. Keizer49, M. Kelsey61, M. Kenzie49, T. Ketel28, E. Khairullin37,
B. Khanji12, C. Khurewathanakul43, K.E. Kim61, T. Kirn9, S. Klaver18, K.
Klimaszewski31, T. Klimkovich11, S. Koliiev46, M. Kolpin12, R. Kopecna12, P.
Koppenburg27, I. Kostiuk27, S. Kotriakhova33, M. Kozeiha5, L. Kravchuk36, M.
Kreps50, F. Kress55, P. Krokovny38,x, W. Krupa30, W. Krzemien31, W.
Kucewicz29,l, M. Kucharczyk29, V. Kudryavtsev38,x, A.K. Kuonen43, T.
Kvaratskheliya34,42, D. Lacarrere42, G. Lafferty56, A. Lai22, D. Lancierini44,
G. Lanfranchi18, C. Langenbruch9, T. Latham50, C. Lazzeroni47, R. Le Gac6, A.
Leflat35, J. Lefrançois7, R. Lefèvre5, F. Lemaitre42, O. Leroy6, T. Lesiak29,
B. Leverington12, P.-R. Li63, T. Li3, Z. Li61, X. Liang61, T. Likhomanenko70,
R. Lindner42, F. Lionetto44, V. Lisovskyi7, X. Liu3, D. Loh50, A. Loi22, I.
Longstaff53, J.H. Lopes2, G.H. Lovell49, D. Lucchesi23,p, M. Lucio Martinez41,
A. Lupato23, E. Luppi16,g, O. Lupton42, A. Lusiani24, X. Lyu63, F. Machefert7,
F. Maciuc32, V. Macko43, P. Mackowiak10, S. Maddrell-Mander48, O. Maev33,42,
K. Maguire56, D. Maisuzenko33, M.W. Majewski30, S. Malde57, B. Malecki29, A.
Malinin70, T. Maltsev38,x, G. Manca22,f, G. Mancinelli6, D. Marangotto21,r, J.
Maratas5,w, J.F. Marchand4, U. Marconi15, C. Marin Benito7, M. Marinangeli43,
P. Marino43, J. Marks12, P.J. Marshall54, G. Martellotti26, M. Martin6, M.
Martinelli42, D. Martinez Santos41, F. Martinez Vidal73, A. Massafferri1, M.
Materok9, R. Matev42, A. Mathad50, Z. Mathe42, C. Matteuzzi20, A. Mauri44, E.
Maurice7,b, B. Maurin43, A. Mazurov47, M. McCann55,42, A. McNab56, R.
McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6, F. Meier10, N. Meinert67, D.
Melnychuk31, M. Merk27, A. Merli21,r, E. Michielin23, D.A. Milanes66, E.
Millard50, M.-N. Minard4, L. Minzoni16,g, D.S. Mitzel12, A. Mogini8, J. Molina
Rodriguez1,aa, T. Mombächer10, I.A. Monroy66, S. Monteil5, M. Morandin23, G.
Morello18, M.J. Morello24,u, O. Morgunova70, J. Moron30, A.B. Morris6, R.
Mountain61, F. Muheim52, M. Mulder27, C.H. Murphy57, D. Murray56, A. Mödden
10, D. Müller42, J. Müller10, K. Müller44, V. Müller10, P. Naik48, T.
Nakada43, R. Nandakumar51, A. Nandi57, T. Nanut43, I. Nasteva2, M. Needham52,
N. Neri21, S. Neubert12, N. Neufeld42, M. Neuner12, T.D. Nguyen43, C. Nguyen-
Mau43,n, S. Nieswand9, R. Niet10, N. Nikitin35, A. Nogay70, N.S. Nolte42, D.P.
O’Hanlon15, A. Oblakowska-Mucha30, V. Obraztsov39, S. Ogilvy18, R.
Oldeman22,f, C.J.G. Onderwater69, A. Ossowska29, J.M. Otalora Goicochea2, P.
Owen44, A. Oyanguren73, P.R. Pais43, T. Pajero24,u, A. Palano14, M.
Palutan18,42, G. Panshin72, A. Papanestis51, M. Pappagallo52, L.L.
Pappalardo16,g, W. Parker60, C. Parkes56, G. Passaleva17,42, A. Pastore14, M.
Patel55, C. Patrignani15,e, A. Pearce42, A. Pellegrino27, G. Penso26, M. Pepe
Altarelli42, S. Perazzini42, D. Pereima34, P. Perret5, L. Pescatore43, K.
Petridis48, A. Petrolini19,h, A. Petrov70, S. Petrucci52, M. Petruzzo21,r, B.
Pietrzyk4, G. Pietrzyk43, M. Pikies29, M. Pili57, D. Pinci26, J. Pinzino42, F.
Pisani42,o, A. Piucci12, V. Placinta32, S. Playfer52, J. Plews47, M. Plo
Casasus41, F. Polci8, M. Poli Lener18, A. Poluektov50, N. Polukhina71,c, I.
Polyakov61, E. Polycarpo2, G.J. Pomery48, S. Ponce42, A. Popov39, D.
Popov47,11, S. Poslavskii39, C. Potterat2, E. Price48, J. Prisciandaro41, C.
Prouve48, V. Pugatch46, A. Puig Navarro44, H. Pullen57, G. Punzi24,q, W.
Qian63, J. Qin63, R. Quagliani8, B. Quintana5, B. Rachwal30, J.H.
Rademacker48, M. Rama24, M. Ramos Pernas41, M.S. Rangel2, F. Ratnikov37,y, G.
Raven28, M. Ravonel Salzgeber42, M. Reboud4, F. Redi43, S. Reichert10, A.C.
dos Reis1, F. Reiss8, C. Remon Alepuz73, Z. Ren3, V. Renaudin7, S.
Ricciardi51, S. Richards48, K. Rinnert54, P. Robbe7, A. Robert8, A.B.
Rodrigues43, E. Rodrigues59, J.A. Rodriguez Lopez66, M. Roehrken42, A.
Rogozhnikov37, S. Roiser42, A. Rollings57, V. Romanovskiy39, A. Romero
Vidal41, M. Rotondo18, M.S. Rudolph61, T. Ruf42, J. Ruiz Vidal73, J.J.
Saborido Silva41, N. Sagidova33, B. Saitta22,f, V. Salustino Guimaraes62, C.
Sanchez Gras27, C. Sanchez Mayordomo73, B. Sanmartin Sedes41, R.
Santacesaria26, C. Santamarina Rios41, M. Santimaria18, E. Santovetti25,j, G.
Sarpis56, A. Sarti18,k, C. Satriano26,t, A. Satta25, M. Saur63, D.
Savrina34,35, S. Schael9, M. Schellenberg10, M. Schiller53, H. Schindler42, M.
Schmelling11, T. Schmelzer10, B. Schmidt42, O. Schneider43, A. Schopper42,
H.F. Schreiner59, M. Schubiger43, M.H. Schune7, R. Schwemmer42, B. Sciascia18,
A. Sciubba26,k, A. Semennikov34, E.S. Sepulveda8, A. Sergi47,42, N. Serra44,
J. Serrano6, L. Sestini23, A. Seuthe10, P. Seyfert42, M. Shapkin39, Y.
Shcheglov33,†, T. Shears54, L. Shekhtman38,x, V. Shevchenko70, E. Shmanin71,
B.G. Siddi16, R. Silva Coutinho44, L. Silva de Oliveira2, G. Simi23,p, S.
Simone14,d, N. Skidmore12, T. Skwarnicki61, J.G. Smeaton49, E. Smith9, I.T.
Smith52, M. Smith55, M. Soares15, l. Soares Lavra1, M.D. Sokoloff59, F.J.P.
Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, F. Stagni42, M.
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S. Strokov72, J. Sun3, L. Sun64, K. Swientek30, V. Syropoulos28, T. Szumlak30,
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R. Tourinho Jadallah Aoude1, E. Tournefier4, M. Traill53, M.T. Tran43, A.
Trisovic49, A. Tsaregorodtsev6, G. Tuci24, A. Tully49, N. Tuning27,42, A.
Ukleja31, A. Usachov7, A. Ustyuzhanin37, U. Uwer12, A. Vagner72, V. Vagnoni15,
A. Valassi42, S. Valat42, G. Valenti15, R. Vazquez Gomez42, P. Vazquez
Regueiro41, S. Vecchi16, M. van Veghel27, J.J. Velthuis48, M. Veltri17,s, G.
Veneziano57, A. Venkateswaran61, T.A. Verlage9, M. Vernet5, M. Veronesi27,
N.V. Veronika13, M. Vesterinen57, J.V. Viana Barbosa42, D. Vieira63, M.
Vieites Diaz41, H. Viemann67, X. Vilasis-Cardona40,m, A. Vitkovskiy27, M.
Vitti49, V. Volkov35, A. Vollhardt44, B. Voneki42, A. Vorobyev33, V.
Vorobyev38,x, J.A. de Vries27, C. Vázquez Sierra27, R. Waldi67, J. Walsh24, J.
Wang61, M. Wang3, Y. Wang65, Z. Wang44, D.R. Ward49, H.M. Wark54, N.K.
Watson47, D. Websdale55, A. Weiden44, C. Weisser58, M. Whitehead9, J. Wicht50,
G. Wilkinson57, M. Wilkinson61, I. Williams49, M.R.J. Williams56, M.
Williams58, T. Williams47, F.F. Wilson51,42, J. Wimberley60, M. Winn7, J.
Wishahi10, W. Wislicki31, M. Witek29, G. Wormser7, S.A. Wotton49, K. Wyllie42,
D. Xiao65, Y. Xie65, A. Xu3, M. Xu65, Q. Xu63, Z. Xu3, Z. Xu4, Z. Yang3, Z.
Yang60, Y. Yao61, L.E. Yeomans54, H. Yin65, J. Yu65,ac, X. Yuan61, O.
Yushchenko39, K.A. Zarebski47, M. Zavertyaev11,c, D. Zhang65, L. Zhang3, W.C.
Zhang3,ab, Y. Zhang7, A. Zhelezov12, Y. Zheng63, X. Zhu3, V. Zhukov9,35, J.B.
Zonneveld52, S. Zucchelli15.

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
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14INFN Sezione di Bari, Bari, Italy
15INFN Sezione di Bologna, Bologna, Italy
16INFN Sezione di Ferrara, Ferrara, Italy
17INFN Sezione di Firenze, Firenze, Italy
18INFN Laboratori Nazionali di Frascati, Frascati, Italy
19INFN Sezione di Genova, Genova, Italy
20INFN Sezione di Milano-Bicocca, Milano, Italy
21INFN Sezione di Milano, Milano, Italy
22INFN Sezione di Cagliari, Monserrato, Italy
23INFN Sezione di Padova, Padova, Italy
24INFN Sezione di Pisa, Pisa, Italy
25INFN Sezione di Roma Tor Vergata, Roma, Italy
26INFN Sezione di Roma La Sapienza, Roma, Italy
27Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
28Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
29Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
30AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
31National Center for Nuclear Research (NCBJ), Warsaw, Poland
32Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
33Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
34Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
35Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
36Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
37Yandex School of Data Analysis, Moscow, Russia
38Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
39Institute for High Energy Physics (IHEP), Protvino, Russia
40ICCUB, Universitat de Barcelona, Barcelona, Spain
41Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
42European Organization for Nuclear Research (CERN), Geneva, Switzerland
43Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
44Physik-Institut, Universität Zürich, Zürich, Switzerland
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68INFN Sezione di Bologna, Bologna, Italy, Bologna, Italy
69Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 27
70National Research Centre Kurchatov Institute, Moscow, Russia, associated to
34
71National University of Science and Technology ”MISIS”, Moscow, Russia,
associated to 34
72National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
34
73Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 40
74University of Michigan, Ann Arbor, United States, associated to 61
75Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Vietnam
oINFN Sezione di Bologna, Bologna, Italy
pUniversità di Padova, Padova, Italy
qUniversità di Pisa, Pisa, Italy
rUniversità degli Studi di Milano, Milano, Italy
sUniversità di Urbino, Urbino, Italy
tUniversità della Basilicata, Potenza, Italy
uScuola Normale Superiore, Pisa, Italy
vUniversità di Modena e Reggio Emilia, Modena, Italy
wMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
xNovosibirsk State University, Novosibirsk, Russia
yNational Research University Higher School of Economics, Moscow, Russia
zSezione INFN di Trieste, Trieste, Italy
aaEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras
abSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
acPhysics and Micro Electronic College, Hunan University, Changsha City, China
†Deceased


# XAI in Computational Linguistics:
Understanding Political Leanings in the Slovenian Parliament

###### Abstract

The work covers the development and explainability of machine learning models
for predicting political leanings through parliamentary transcriptions. We
concentrate on the Slovenian parliament and the heated debate on the European
migrant crisis, with transcriptions from 2014 to 2020. We develop both
classical machine learning and transformer language models to predict the
left- or right-leaning of parliamentarians based on their given speeches on
the topic of migrants. With both types of models showing great predictive
success, we continue with explaining their decisions. Using explainability
techniques, we identify keywords and phrases that have the strongest influence
in predicting political leanings on the topic, with left-leaning
parliamentarians using concepts such as people and unity and speak about
refugees, and right-leaning parliamentarians using concepts such as
nationality and focus more on illegal migrants. This research is an example
that understanding the reasoning behind predictions can not just be beneficial
for AI engineers to improve their models, but it can also be helpful as a tool
in the qualitative analysis steps in interdisciplinary research.

XAI in Computational Linguistics:
Understanding Political Leanings in the Slovenian Parliament

Bojan Evkoski∗†, Senja Pollak∗
---
∗Jozef Stefan Institute
† Jozef Stefan International Postgraduate School
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>

Abstract content

The final formatted version of this publication was published in Proceedings
of the 10th Language and Technology Conference (LTC 2023), April 2023, and is
available online at dx.doi.org/10.14746/amup.9788323241775.

##  1\. Introduction

Artificial intelligence, in particular machine learning, is extensively used
for solving many real-world problems both in research Jordan and Mitchell,
(2015) and industry Shinde and Shah, (2018). In recent years, with AI being
more present and the introduction of stricter guidelines Interpol, (2019) and
regulations Sartor and Lagioia, (2020), it became apparent that the sheer
power of machine learning models for predicting tasks does not justify their
widespread potentially inconsiderate usage. Today, understanding and
explaining the previously considered black-box models is equally important as
developing and training them. This process enables engineers to detect biases
in the model, come up with ideas for improvement, and most importantly examine
the security of the system. Explainable AI (or simply XAI) is gradually
becoming a must both in industry and research.

Another aspect of AI interpretability is its effect of bridging the gap
between heavy quantitative black-box research and qualitative research more
common among humanities and social sciences scholars. As machine learning
engineers get feedback from a model on why it makes a particular prediction,
humanities and social sciences scholars would take these signals to further
examinations that can lead to more qualitative explanations of why certain
features play a significant role in a particular problem.

This work covers a case of interdisciplinary research between computational
linguistics (or natural language processing) and political science where we
explain AI models to gain insight from a political linguistics perspective. We
focus on parliamentary debates, a salient research topic in both humanities
and social science disciplines, such as sociology, political science,
sociolinguistics, and history Skubic and Fišer, (2022). Our goal is to bring
more insight into the speeches of parliamentarians (MPs) of different
political leanings. First, by training machine learning models to predict if a
parliamentarian is left or right-leaning based on their speech. And then, by
using explainability techniques on the models, extract data and derive
knowledge on what actually differentiates left and right political speeches in
the parliament. To make things more politically relevant and methodologically
clear, we are focusing on the concerning topic of migrants and the European
migration crisis Barlai et al., (2017) where the left and right have evident
divergent stances: left-leaning parties showing consistent support to
immigrants from Asia and Africa throughout Europe, and right-leaning parties
showing moderate to strong opposition against immigration to Europe and their
country in particular van der Brug and Harteveld, (2021). We apply our
analysis to the Slovenian Parliament from 2014 to 2020. For data, we use the
open-access ParlaMint dataset Erjavec et al., (2022) which provides complete
parliamentary transcriptions for 17 countries, including Slovenia.

The paper is organized as follows. In Section 2., we briefly cover the related
work on using explainable AI in social sciences, as well as recent
applications of computational linguistics for parliamentary debates. In
Section 3. we provide a description of the ParlaMint SI dataset we are working
with, as well as the preprocessing steps required before training the models.
In Section 4. we dive into the training of the classical machine learning and
the modern language models. Finally, we discuss the results in Section 5. and
conclude in Section 6..

##  2\. Related Work

By the end of the 2010s and the beginning of 2020s, explainable AI has become
a topic that involved both computer and social scientists in discussions on
how to interpret and use the knowledge drawn from model explanations Miller,
(2019). Social scientists urge the importance of qualitative investigation
experts joining in XAI projects Johs et al., (2022). Yet, social qualitative
investigation done by non-experts is still very common. Combining qualitative
and quantitative approaches (mixed research) has a variety of hardships
Brannen, (2017), and researchers from both sides of the spectrum rarely have
insight into the benefits of combining knowledge with the opposite side. With
this work focusing on a specific social theme, we show an example of how XAI
research can be the initial step for a more thorough qualitative approach
Molina-Azorin, (2016).

Parliamentary discourse, although extensively researched in a qualitative
setting Ilie, (2015), is still underexplored in a quantitative manner. Naderi
and Hirst, (2015) use computational methods to analyze framing structures in
speeches of the Canadian Parliament. Greene and Cross, (2015) use dynamic
topic modeling to explore the evolution of the political agenda in the
European Parliament. Eskişar and Çöltekin, (2022) analyze the emotion
structure of speeches in the Turkish ParlaMint dataset.

Due to the European Migration crisis in 2015, researchers have been studying
the political stances of politicians Wallaschek, (2020), news media Krotofil
and Motak, (2018), and the effect of social media on the integration of
migrants Alencar, (2018). Computational techniques were also applied. For
example, Greussing and Boomgaarden, (2017) use techniques such as the bag-of-
words and principal component analysis to understand media framing on the
topic, while Heidenreich et al., (2019) apply topic modeling to observe the
dynamics of the migration narrative. In a more recent work by Skubic et al.,
(2022), the authors create mention networks for multiple parliaments on the
topic of migration and analyze the role of gender on speech influence.

##  3\. Data

Our choice of parliamentary transcriptions is the richly annotated ParlaMint
subset of the Slovenian Parliament. It covers all sessions of the National
Assembly from August 2014 to July 2020, with more than 20M words. In order to
prepare the data for training a political leaning model based on the
transcriptions, we first applied a few preprocessing steps according to the
metadata. First, we removed all guest and Chair speeches, leaving only regular
MPs. Next, used the party name data for each parliamentarian to extract the
main label (right or left) using Wikipedia’s "political position" English
metadata on the party. Far-right, right, and center-right are labeled as
right; far-left, left and center-left are labeled as left. Finally, we applied
speech selection according to the topic of our interest — migration. For this
purpose, we prepared a set of keywords directly connected to the migration
topic111The list of migration keywords was prepared in collaboration with
social scientists Andreja Vezovnik and Veronika Bajt. It contains 95 lemmas
with all their corresponding word forms prepared by Anka Supej.. The speech
selection is very straightforward. If any of our keywords appear in the
transcription (observed as lemmas), we select the speech. Table 1 shows a
general overview of the dataset magnitude, while Figure 1 shows a pie chart of
speech share selections from the set of keywords. The final dataset turned out
to be quite balanced between the two classes, with 1519 of the speeches
classified as “left”, and 1455 classified as right.

Dataset | #Parties | #Speakers (Left/Right) | #Speeches (Left/Right) | AWS | MSS
---|---|---|---|---|---
SI ParlaMint | 12 | 353 (114/48) | 75122 (70.6%/20.4%) | 1244.1 | 30.0
SI ParlaMint (MPs) | 12 | 166 (114/48) | 31151 (55.9%/40.9%) | 1210.5 | 125.5
SI Parlamint (MPs on migration) | 12 | 153 (105/48) | 2974 (51.1%/48.9%) | 854.7 | 12.0
Table 1: General statistics of the Slovenian ParlaMint dataset and two of its
subsets. AWS - Average words per speech. MSS - Median speeches per speaker.
Figure 1: Pie chart on the migration keywords.

##  4\. Models and Explainability

We followed two approaches to training machine learning models for text
classification. The first is a classical bag of words feature extraction
combined with a Linear SVM classifier Liu et al., (2010). The second approach
is using the state-of-the-art Transformer language models Vaswani et al.,
(2017). We applied several variations of both approaches, evaluated using
5-fold cross-validation, and compared the prediction accuracy. Finally, we
selected the best model for each approach and trained it on the full dataset
in order to apply explainability analysis.

For the classical approach, we trained a Linear SVM on three different bag-of-
words types: unigram; unigram and bigram; unigram, bigram, and trigram. As the
common practice, we used only lemmas which were already available in SI
ParlaMint. We used a well-refined stopwords list for the Slovenian language to
remove noise from the bag of words222https://github.com/stopwords-
iso/stopwords-sl, but we also used a minimum frequency of 5 appearances in the
whole dataset, and a maximum frequency of a word appearing in 35% of the
speeches which proved effective in removing the procedural parts of speeches
and improving the results. We optimized the model on each of the training
folds in a nested 5-fold cross-validation and we evaluated the optimized model
on the main testing folds, practically optimizing and evaluating five models
of the same kind, reporting the average and its 95% confidence interval.
Finally, using the hyperparameters of the best-performing model, we trained
one final model which we used for the explainability experiments.

Opposed to the common understanding of machine learning models, a Linear SVM
classifier is not a black box that cannot be explained in its calculations. It
creates a hyperplane that uses support vectors to maximize the distance
between the two predicted classes (in our case “left” and “right”). The
weights that represent the Linear SVM equation hyperplane are the vector
coordinates that are orthogonal to the hyperplane. So, their direction
indicates the predicted class. The absolute size of the coefficients in
relation to each other can then be used to determine feature importance for
the data separation task. For our task, the minimum (most negative) weight
coefficients correspond to words in the bag-of-words representation that led
the model to classify a speech as a “leftist”, while the maximum (most
positive) weight coefficients correspond to words that led it to classify a
speech as “right”. Using this explainability logic, we derived an
understanding of what makes the difference between a leftist and a rightist
ideology’s thought and word choice.

For language models, we used two types: the multilingual BERT and the
SloBERTa. The multilingual BERT Devlin et al., (2018) was trained in 104
languages and is one of the first successful language models which serves as
an appropriate baseline for fine-tuning the model to any kind of textual task.
SloBERTa Ulčar and Robnik-Šikonja, (2021) uses the BERT architecture and it is
monolingual, meaning it is trained purely on Slovenian data, making it more
suitable for tasks where the model is applied specifically to Slovenian text,
as is ours. Both pre-trained models were fine-tuned on the raw SI ParlaMint
transcriptions using 30 epochs. The Learning rate of the BERT model was 5e-6,
for the SloBERTa was 6e-6. As in the SVM case, we optimized the number of
epochs and the learning rate using 5-fold nested cross-validation. For
preprocessing, we used the standard respective tokenizers of BERT and
SloBERTa. As both models are limited to 512 tokens, we applied an automatic
truncation, using the first 512 words in each speech for training and
predicting. Both models are limited to a maximum of 512 tokens, and speeches
above that limit were truncated.

For explaining the deep learning models, we used a technique introduced
Lundberg and Lee, (2017) called by SHAP. It is a powerful technique that uses
classic equations from cooperative game theory to compute explanations of
model predictions. Shapley values are feature importance values derived when a
model is trained on all feature subset combinations, mathematically
calculating the importance of each. Calculating Shapley values in this manner
is computationally expensive, so what SHAP manages to do is derive these
values by sampling approximations. Reading the SHAP results is very similar to
reading the explainability analysis of the Linear SVM: more negative values
refer to words leading the model to classify a speech as “leftist” and more
positive values refer to the “rightist” words. There are two ways of
presenting the token importance using Shapley values: its total Shapley in the
entire dataset or its maximum/minimum recorded value. The issue with the first
technique is that it prioritizes common words such as stopwords and should be
generally avoided. We use the second technique, as it leads to more sensible
results. A third variation of normalizing the Shapley sum according to the
number of occurrences is also an option, yet we leave out this experimentation
and plan it as our further work.

##  5\. Results and Discussion

Table 2 shows the results of classifying speeches on the topic of migration as
“leftist” or “rightist”, depending on the political affiliation of the speaker
in the Slovenian Parliament. The classical Tf-idf approach using unigrams,
bigrams and trigrams showed the best results, with around 91% accuracy. From
the language models, the SloBERTa outperformed BERT yet with only 87%
accuracy. One reason behind the worse performance of the language models could
be its inability to operate on very long sequences, as more than 60% of the
speeches in our dataset contain more than 512 tokens (maximum sequence for
BERT).

Model | Accuracy
---|---
Random Baseline | 0.511
Tf-Idf + Lin. SVM (1-grams) | $0.866\pm 0.01$
Tf-Idf + Lin. SVM (1, 2-grams) | $0.903\pm 0.01$
Tf-Idf + Lin. SVM (1, 2, 3-grams) | $0.913\pm 0.02$
Multilingual BERT | $0.819\pm 0.01$
SloBERTa | $0.877\pm 0.03$
Table 2: Classification scores on predicting political leanings based on
speech transcriptions. Figure 2: SVM feature importance. The left (red) side
contains phrases that have the highest significance for the model predicting a
speech as “leftist”. The same explanation is for the right (blue) side for the
“rightist” speeches. Phrases marked with * refer to party names.

The models showed that predicting parliamentary political leaning from speech
transcriptions is possible. Since statistical models can differentiate
“leftist” and “rightist” speeches, we investigated if their explanation
through feature importance makes sense from a political linguistics
perspective. Figures 2 and 3 show the results of the feature importance
analysis. Here, we can notice some obvious similarities and differences
between the classical and the language model approach. The first difference is
that the SVM feature importance can catch not only tokens (words) but also
bigrams and trigrams, which can be useful for a better linguistic context.
Since it uses lowercase lemmas, it mitigates duplicates in different word
forms, yet it can potentially lead to ambiguities. The most important
difference is that the SVM feature importances are the general values for the
whole dataset, while the Shapley values are detected maximums for a particular
comment, which does not mean that these words have the same negative (leftist)
or positive (rightist) effect for all samples.

Figure 3: Maximum and minimum Shapley values for the SloBERTa model.
Left/right (red/blue) side shows the words that had the highest signal in
predicting a “leftist/rightist” speech.

Both model interpretations show that right-wing parliamentarians’ motif is to
mention the country name (Slovenia) and its forms. The SVM interpretation also
reveals that the rightists emphasize their party names. Regarding migration,
their motif is to focus on the illegal aspect of the migration, with the SVM
models catching the phrase “illegal migrant” as something that almost
exclusively right-wing politicians use. The leftists tend to use the word
“begunec” (angl. refugee) instead of “migrant”, as the meaning behind the
former refers to someone who is fleeing. They tend to use words such as
“united” and “debate” and they often times refer to their party opponents by
the party abbreviations instead of the full name. One interesting case is that
the SVM manages to recognize the leftists emphasizing the word “grims”. Grims
is the surname of the right-wing politician Branko Grims who is strongly
against immigrants in Slovenia and Europe and was the most active politician
in the parliament on the topic.

Although much more can be drawn from the feature importance, this is where our
analysis stops. The model interpretability through the list of words that had
the most meaningful impact on the classification opens up a great possibility
for further qualitative work. Researchers studying political linguistics could
observe the usages of these lists and find patterns in the connotation of the
words used. They could confirm or debunk ideological concepts used by the
different sides of the political spectrum. Or, they could analyze if these
words and phrases actually contain the primary message of a sentence or if
their role is more on the stylistic side of political speeches.

##  6\. Conclusion

Explaining the decision-making of machine learning models (known as XAI) can
be a great tool in interdisciplinary research. When the goal is not just to
classify, but to understand patterns that appear across classification groups,
XAI can complement qualitative research.

In this work, we used XAI to bridge the gap between computational and
political linguistics. We developed classical machine learning as well as deep
learning language models that can classify parliamentary speeches as “leftist”
and “rightist” for the topic of migration. We applied our approach to the
Slovenian parliament using the ParlaMint dataset with data from 2014 to 2020.
With both approaches showing great predictive success, we applied methods
(such as calculating the Shapley values) that can explain the decisions of our
models and show which words and phrases differentiate “leftist” from
“rightist” speeches and vice versa. While left-leaning parliamentarians use
concepts such as “unity” and “debate”, the right-leaning parliamentarians put
more emphasis on the national symbols (mentioning Slovenia) and their party
names.

We leave an opening for further work in multiple directions. One is the
improvement of the interpretability methods for models that work with text.
Different feature importance techniques could be applied and a comparative
study could help us understand the strengths and weaknesses of the methods.
Another direction is exploring the ways the model explanations can be used in
interdisciplinary research. How to use the words that give the most value to
models’ predictions in a qualitative continuation of the work. Or, how to
understand and communicate model flaws with experts from the social sciences
in order to improve them.

### Acknowledgements

The work was supported by the Slovenian Research Agency research projects and
programmes P6-0436: Digital Humanities: resources, tools and methods
(2022–2027), P6-0280: Economic, Social and Environmental History of Slovenia
(2022–2027), P2-0103: Knowledge Technologies (2022–2027), J6-2581: Computer-
assisted multilingual news discourse analysis with contextual embeddings
(2020-2023) and J5-3102: Hate speech in contemporary conceptualizations of
nationalism, racism, gender and migration (2021-2024), as well as the DARIAH-
SI research infrastructure (2022-2027). We also acknowledge the financial
support from the RobaCOFI project, which has indirectly received funding from
the European Union’s Horizon 2020 research and innovation action programme via
the AI4Media Open Call #1 issued and executed under the AI4Media project
(Grant Agreement no. 951911). We also thank Andreja Vezovnik and Veronika Bajt
for their help in preparing the migration keywords.

### Code

The source code is publicly available at:
github.com/boevkoski/xaicl_parliaments

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