CALT-TH-2016-036

DESY 16-101

Exploring the nearly degenerate stop region with sbottom decays

Haipeng An,a,111<EMAIL_ADDRESS>Jiayin Gu,b,c,222<EMAIL_ADDRESS>Lian-Tao
Wang$\,{}^{d,e,}$333<EMAIL_ADDRESS>
a Walter Burke Institute for Theoretical Physics,
California Institute of Technology, Pasadena, CA 91125.
b Center for Future High Energy Physics, Institute of High Energy Physics,
Chinese Academy of Sciences, Beijing 100049, China.
c DESY, Notkestraße 85, D-22607 Hamburg, Germany.
d Enrico Fermi Institute, University of Chicago, Chicago, IL 60637.
e Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL
60637.

###### Abstract

A light stop with mass almost degenerate with the lightest neutralino has
important connections with both naturalness and dark matter relic abundance.
This region is also very hard to probe at colliders. In this paper, we
demonstrate the potential of searching for such stop particles at the LHC from
sbottom decays, focusing on two channels with final states $2\ell+E^{\rm
miss}_{\rm T}~{}$and $1b1\ell+E^{\rm miss}_{\rm T}~{}$. We found that, if the
lightest sbottom has mass around or below 1 TeV and has a significant
branching ratio to decay to stop and $W$ ($\tilde{b}\to\tilde{t}\,W$), a stop
almost degenerate with neutralino can be excluded up to about 500–600 GeV at
the 13 TeV LHC with $300\,{\rm fb}^{-1}$ data. The searches we propose are
complementary to other SUSY searches at the LHC and could have the best
sensitivity to the stop-bino coannihilation region. Since they involve final
states which have already been used in LHC searches, a reinterpretation of the
search results already has sensitivity. Further optimization could deliver the
full potential of these channels.

###### Contents

  1. 1 Introduction
  2. 2 Search channels and backgrounds
  3. 3 Simulation procedure and event selection
    1. 3.1  $2\ell+E^{\rm miss}_{\rm T}$ channel
    2. 3.2 $1b1\ell+E^{\rm miss}_{\rm T}$ channel
  4. 4 Reach at the 13 TeV LHC
  5. 5 Conclusion

##  1 Introduction

A light stop is essential for the naturalness of supersymmetry (SUSY). The
stops have been extensively searched at the LHC. Traditional searches focus on
the direct production of a stop pair followed by each stop decaying to the top
quark and the lightest neutralino, $\tilde{t}\to t\,\chi$,111In this paper
$\tilde{t}$ and $\tilde{b}$ always denote the lighter mass eigenstates,
$\tilde{t}_{1}$ and $\tilde{b}_{1}$, unless specified otherwise. while the
lightest neutralino $\chi$ is the lightest superpartner (LSP). The signal of
these searches often includes large missing transverse momentum ($E^{\rm
miss}_{\rm T}$) from the LSP. The current LHC bound for R-parity conserving
SUSY models on stop mass is around $m_{\tilde{t}}\gtrsim 900\,$GeV, assuming
$\tilde{t}\to t\,\chi$ and a sufficiently large mass gap between
$m_{\tilde{t}}$ and $m_{\chi}$ [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11].222Stop may
also decay to the lightest neutralino via an intermediate chargino or heavier
neutralino, in which case the bounds on the stop mass is slightly weaker.

The stops can still be significantly lighter than this bound if they are
hiding in compressed regions $m_{\tilde{t}}\approx m_{t}+m_{\chi}$,
$m_{\tilde{t}}\approx m_{W}+m_{b}+m_{\chi}$ and $m_{\tilde{t}}\approx
m_{\chi}$, in which cases it is hard to discriminate the stop signal from
standard model (SM) backgrounds or the products of the stop decay is too soft
to be identified. Based on the stop-neutralino simplified model, searching
strategies have been proposed to search for stops in these regions [12, 13,
14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32,
33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51,
52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62]. 333See also Ref. [63] for a
recent analysis on the implication of a light stop sector.  In R-parity
conserving SUSY, the $m_{\tilde{t}}\approx m_{\chi}$ region is of special
interests if the neutralino $\chi$ is mainly composed by the bino $\tilde{B}$.
The reason is that the annihilation cross section of a pair of $\tilde{B}$ is
small due to the lack of gauge interaction. Therefore, for $\tilde{B}$ to be a
thermal dark matter candidate, a charged particle must be nearby to assist the
annihilation. This region is thus called stop-bino coannihilation region [64].
This region is also not very well constrained by dark matter direct detection
experiments [65]. According to the numerical simulation with micrOmegas4.2
[66], for sub-TeV bino-like dark matter, a mass difference
$m_{\tilde{t}_{1}}-m_{\chi}\approx 30\,$GeV is required to obtain the measured
relic abundance. In the simulations of this work, we fix this mass gap to be
30 GeV. The sensitivities of collider search discussed in this paper are
slightly better if the mass gap is smaller. In this compressed region, the
stop has two main decay channels, one is the flavor-conserving four-body decay
through off-shell top quark and W boson ($\tilde{t}\to bW^{*}\chi\to
bl\nu\chi/bjj\chi$) and the other is the flavor-changing two-body decay to a
charm quark ($\tilde{t}\to c\,\chi$). The decay rate of the flavor-changing
channel depends strongly on the flavor structure of the squark sector, whereas
the rate of the four-body channel depends only on the mixing angle between the
left and right handed stop. It turns out that with
$m_{\tilde{t}_{1}}-m_{\chi}=30$ GeV, the four-body channel alone makes the
stop decay promptly [47].

In this paper, we draw attention to a couple of additional useful search
channels using sbottom decays, to further probe this nearly degenerate region.
Naturalness prefers the second stop not to be too heavy. Due to the doublet
nature of the left handed quarks, the masses of the left handed sbottom is
connected to the mass of the left handed stop. The mixing between the left and
right handed stops usually makes the mass of the second stop heavier than the
left handed sbottom. To minimize the flavor violation induced by the squark
sector, the mixing between the left and right handed sbottoms is usually
assumed to be suppressed by the mass of the bottom quark. Therefore, we can
decouple the right handed sbottom in this work. Our search strategy relies on
a significant mass gap between the lightest stop and sbottom, which we obtain
by assuming $m_{\tilde{t}_{R}}$ is sufficiently smaller than
$m_{\tilde{t}_{L}}(=m_{\tilde{b}_{L}})$, and the lightest stop is mostly
right-handed. 444 A large mass gap could also be generated by a very large
stop $A$ term even if $m_{\tilde{t}_{R}}\approx m_{\tilde{t}_{L}}$, but with
such a large $A$ term also comes the risk of spontaneously breaking
$SU(3)_{\rm c}$. In this scenario, the decay $\tilde{b}\to\tilde{t}\,W$ would
dominate which makes our case even stronger.  To simplify the study we also
assume the winos and the Higgsinos are decoupled and the lightest neutralino
is pure bino. The spectrum of the SUSY particles is shown in Fig. 1. In this
simplified scenario, the lighter sbottom $\tilde{b}_{1}$ has two decay
channels

Figure 1: Spectrum of SUSY partners of the stop-bino coannihilation region.

$\displaystyle\tilde{b}_{1}$ $\displaystyle\rightarrow$ $\displaystyle
W+\tilde{t}_{1}\ ,$ $\displaystyle\tilde{b}_{1}$ $\displaystyle\rightarrow$
$\displaystyle b+\chi\ ,$ (1.1)

with decay rates

$\displaystyle\Gamma_{1}$ $\displaystyle\equiv$
$\displaystyle\Gamma_{\tilde{b}_{1}\rightarrow
W\,\tilde{t}_{1}}=\frac{g_{2}^{2}\sin^{2}\theta_{t}\cos^{2}\theta_{b}}{32\pi}\frac{[(m_{\tilde{b}}^{2}-(m_{\tilde{t}}+m_{W})^{2})(m_{\tilde{b}}^{2}-(m_{\tilde{t}}-m_{W})^{2})]^{3/2}}{m_{W}^{2}m_{\tilde{b}}^{3}}\
,$ $\displaystyle\Gamma_{2}$ $\displaystyle\equiv$
$\displaystyle\Gamma_{\tilde{b}_{1}\rightarrow
b\,\chi}~{}=\frac{g_{1}^{2}}{32\pi}\frac{(m_{\tilde{b}}^{2}-m_{\chi}^{2})^{2}}{m_{\tilde{b}}^{3}}4\left[\left(-\frac{1}{3}\right)^{2}\sin^{2}\theta_{b}+\left(\frac{1}{6}\right)^{2}\cos^{2}\theta_{b}\right]\
,$ (1.2)

where in calculating $\Gamma_{2}$ we neglect the mass of the bottom quark. The
stop and sbottom mixing angles are defined as

$\begin{pmatrix}\tilde{t}_{1}\\\
\tilde{t}_{2}\end{pmatrix}=\begin{pmatrix}\cos\theta_{t}&\sin\theta_{t}\\\
-\sin\theta_{t}&\cos\theta_{t}\end{pmatrix}\begin{pmatrix}\tilde{t}_{R}\\\
\tilde{t}_{L}\end{pmatrix}\,,\hskip 28.45274pt\begin{pmatrix}\tilde{b}_{1}\\\
\tilde{b}_{2}\end{pmatrix}=\begin{pmatrix}\cos\theta_{b}&\sin\theta_{b}\\\
-\sin\theta_{b}&\cos\theta_{b}\end{pmatrix}\begin{pmatrix}\tilde{b}_{L}\\\
\tilde{b}_{R}\end{pmatrix}\,.$ (1.3)

In the limit $m_{\tilde{b}}^{2}-m_{\tilde{t}}^{2}\gg m_{W}^{2}$, $\Gamma_{1}$
is seemingly enhanced by the factor $m_{\tilde{b}}^{2}/m_{W}^{2}$ due to the
longitudinal contribution. However, the stop mixing angle vanishes if the
electroweak symmetry is unbroken. Therefore, the stop mixing angle
$\theta_{t}$ is secretly proportional to $m_{W}$. In the limit $A_{t}v\ll
m_{\tilde{t}_{2}}^{2}\approx m_{\tilde{b}}^{2}$, we have

$\sin\theta_{t}\approx\frac{\sqrt{2}A_{t}m_{W}}{g_{2}m_{\tilde{b}}^{2}}\ ,$
(1.4)

where $A_{t}$ is the $A$ term for the stops. Assuming $A_{b}$ is suppressed by
$m_{b}$ for the sake of flavor physics constraints, we have
$\cos\theta_{b}\approx 1$. Therefore, $\Gamma_{1}$ and $\Gamma_{2}$ in Eq. (1)
can be simplified as

$\Gamma_{1}\approx\frac{A_{t}^{2}}{16\pi m_{\tilde{b}}}\
,\;\;\;\;\Gamma_{2}\approx\frac{\alpha_{\rm
em}m_{\tilde{b}}}{72\cos^{2}\theta_{W}}\ .$ (1.5)

The proportionality of $\Gamma_{1}$ to $A_{t}^{2}$ can also be inferred from
the goldstone equivalence theorem. The traditional sbottom search based on the
sbottom-neutralino simplified model assumes the sbottom decays 100% to $b$ and
the neutralino. However, as from Eq. (1.5) if $A_{t}$ is comparable to
$m_{\tilde{b}}$, $\Gamma_{1}/\Gamma_{2}$ can be as large as ${\cal O}(100)$.
This region is also favored by the Higgs mass. On the other hand, in some
specific SUSY breaking models (e.g. gauge mediation models) $A_{t}$ is one-
loop order suppressed compared to other soft SUSY breaking parameters. In this
case, $\Gamma_{1}\ll\Gamma_{2}$. Therefore, when searching for the signal from
sbottoms, it is important to consider both of the two decay channels.

We will focus on studying the potential of the sbottom decay channels shown in
(a) and (b) of Fig. 2. We apply relatively straightforward cuts to demonstrate
that these channels can lead to interesting reach with an integrated
luminosity of 300 fb-1 at the 13 TeV LHC. A more careful optimization of the
kinematical selection and more realistic simulation are needed to determine
the ultimate reach. This is beyond the scope of this paper. We also present
the reach in the more “conventional” sbottom search channel in shown in (c) of
Fig. 2 to illustrate the complementarity between these channels. We would like
to emphasize that even in the parameter region in which (c) has a better
reach, the new channels (a) and (b) studied in this paper is still useful in
the case of a discovery since they directly probe the presence of the stop.

The rest of this paper is organized as follows: In Section 2, we discuss the
main search channels and the corresponding backgrounds. In Section 3, we state
the selection cuts for each channel and show the results of a few case
studies. In Section 4, we show the exclusion regions in the parameter space of
the 13 TeV LHC with $300\,{\rm fb}^{-1}$ data and compare the reaches of
different channels. The conclusion is drawn in Section 5.

##  2 Search channels and backgrounds

(a)

(b)

(c)

Figure 2: Three ways for a sbottom pair to decay for the scenario studied in
this paper: (a) symmetric decay of $\tilde{b}\to\tilde{t}\,W$, (b) asymmetric
decay, and (c) symmetric decay of $\tilde{b}\to b\,\chi$.

With two decay channels $\tilde{b}\to\tilde{t}\,W$ and $\tilde{b}\to b\,\chi$,
a pair of sbottoms produced at the LHC has three ways to decay, as shown in
Fig. 2. The symmetric decay chain of $\tilde{b}\to b\,\chi$ in Fig. 2(c) has
already been searched at the LHC in the channel with final states $2b+E^{\rm
miss}_{\rm T}~{}$under the assumption of $100\%$ branching ratio (BR), and
sbottom with mass up to 800 GeV are excluded for $m_{\chi}\lesssim 360\,$GeV
[67]. With a smaller branching ratio, the reach of this channel is
significantly weaker. Here our main interest is in the decay chains that
involves the stop, namely, the symmetric decay chain in Fig. 2(a) and the
asymmetric decay chain in Fig. 2(b). As such, we will focus on two channels,
one with final states of two opposite sign leptons and $E^{\rm miss}_{\rm T}$
($2\ell+E^{\rm miss}_{\rm T}$), and the other with one hard b-jet, one lepton
and $E^{\rm miss}_{\rm T}$ ($1b1\ell+E^{\rm miss}_{\rm T}$). These two
channels are studied in details in Section 3, while in Section 4 we compare
their reaches together with the one of the $2b+E^{\rm miss}_{\rm T}~{}$channel
for different sbottom branching ratios.

The $2\ell+E^{\rm miss}_{\rm T}~{}$channel is designed to pick up the the
symmetric decay chain in Fig. 2(a) with both $W$s decaying leptonically, and
should be the optimal search channel if the decay $\tilde{b}\to\tilde{t}\,W$
dominates. This channel has been searched at the LHC for the searches of
sleptons and electroweakinos [68, 69], for which the main background is top
quark pair production ($t\bar{t}$ ) and diboson ($WW/WZ/ZZ$). We also found
the $t\bar{t}Z$ events to have a significant contribution to the SM
backgrounds after imposing our selection cuts.

The $1b1\ell+E^{\rm miss}_{\rm T}~{}$channel is designed for the asymmetric
decay chain in Fig. 2(b), but could also pick up some events from the
symmetric decay chain in Fig. 2(a) with one $W$ decaying hadronically, if the
event happens to have a hard b-jet. This channel is similar to the direct
search of stop pair in the semileptonic channel [6, 7, 11], where the main
backgrounds include $t\bar{t}$, $tW$, $W+\,$jets, diboson and $ttZ$. We expect
this channel to be useful if the branching ratios of
$\tilde{b}\to\tilde{t}\,W$ and $\tilde{b}\to b\,\chi$ are comparable.

In principle, one could also search in the channel with final states of one
lepton, $E^{\rm miss}_{\rm T}$ and one or two hard jets with no b-jets
($1\ell+\rm{jets}+E^{\rm miss}_{\rm T}$), which could come from either Fig.
2(a) with one $W$ decaying hadronically or Fig. 2(b) if the b-jet is not
tagged. While this channel could contain significant amount of signal events,
the backgrounds are also large and more complicated. In this paper, we focus
on the simpler leptonic channels as an initial assessment of the potential of
these new decay channels.

##  3 Simulation procedure and event selection

For both signal and backgrounds, the events are generated at parton level
using Madgraph5 [70], followed by parton showering with PYTHIA6.4 [71]. The
detector simulation is performed with Delphes [72] in which the b-tagging
efficiency is from Ref. [73]. In particular, the b-tagging efficiency is
within 60%–70% for $p_{T}$ in the range 50–300 GeV, while the mis-tag rate is
below 15% for a charm jet and below 0.5% for a light jet with $p_{T}<400$ GeV.
We use the above procedure to generate the events of sbottom pair production
and then rescale the cross section to the values from the NLO+NLL calculation
in Ref. [74, 75]. 555 Jet matching is not performed for signal events as
scanning the parameter space with jet matching requires a huge amount of
computing power. Since for signal events the hard b-jets and charged leptons
are from the decay of the sbottoms, we do not expect the behavior of ISR jets
to have a strong effect on the behavior of the signal. We have also checked
with specific signal benchmark points that this is indeed the case.  For
$t\bar{t}$, single top and $W,Z$+jets events, the MLM matching procedure is
also employed. For $t\bar{t}$ events, the total cross section is scaled to the
NNLO+NNLL result given in Ref. [76, 77]. For single top (including $tW$)
events, the total cross section is scaled to the NLO results in Ref. [78]. For
diboson events, the total cross section is scaled to the NLO result in Ref.
[79]. For $t\bar{t}Z$ events, we scale the cross section to the central value
of the recent measurement in Ref. [80].

We present the details of our collider study in this section, including the
selection cuts for each channel and the results of a few case studies. The
signal samples listed Table 1 are used for the case studies. Signal S1 & S2
has ${\rm BR}(\tilde{b}\to\tilde{t}\,W)=0.9$ and are ideal for the
$2\ell+E^{\rm miss}_{\rm T}~{}$channel, while S3 & S4 has ${\rm
BR}(\tilde{b}\to\tilde{t}\,W)=0.5$ which is better covered by the
$1b1\ell+E^{\rm miss}_{\rm T}~{}$channel. For S1 & S3, we assume the stop only
decays to charm and neutralino, $\tilde{t}\to c\,\chi$; for S2 & S4, we assume
that the stop only goes through the 4-body decay, $\tilde{t}\to bW^{*}\chi\to
bl\nu\chi/bjj\chi$. The mass spectra in Table 1 are chosen to roughly
correspond to the “best reach” of the two channels, which are shown later in
Section 4.

signal | $\sigma{\rm[pb]}$ | $m_{\tilde{b}}{\rm[GeV]}$ | $m_{\tilde{t}}{\rm[GeV]}$ | $m_{\chi}{\rm[GeV]}$ | BR($\tilde{b}\to\tilde{t}\,W$) |  $\tilde{t}$ decay
---|---|---|---|---|---|---
S1 | 0.00615 | 1000 | 600 | 570 | 0.9 | $c\,\chi$
S2 | 0.00615 | 1000 | 600 | 570 | 0.9 | $bl\nu\chi/bjj\chi$
S3 | 0.0129 | 900 | 500 | 470 | 0.5 | $c\,\chi$
S4 | 0.0129 | 900 | 500 | 470 | 0.5 | $bl\nu\chi/bjj\chi$
Table 1: Signal samples used for the case studies in the $2\ell+E^{\rm
miss}_{\rm T}~{}$channel (S1 & S2) and the $1b1\ell+E^{\rm miss}_{\rm
T}~{}$channel (S3 & S4).

###  3.1  $2\ell+E^{\rm miss}_{\rm T}$ channel

Selection cuts: For an event to pass the cut, we require it to have $E^{\rm
miss}_{\rm T}>150\,$GeV and contain exactly 2 leptons with opposite charge. We
require the scalar sum of the $p_{T}$ of the two leptons to be larger than
$200\,$GeV. We also apply a b-veto by requiring the event to have no b-jet
with $p_{T}>50\,$GeV. The requirement on $p_{T}$ of b-jets could prevent one
from removing signal events with soft b-jets from stop decays. We require the
invariant mass of the lepton pair ($m_{ll}$) to be larger than $20\,$GeV to
remove potential backgrounds from low mass resonances. If the two leptons have
the same flavor, we further require their invariant mass to be at least 20 GeV
away from the $Z$ boson mass. A stringent cut around the $Z$ resonance helps
remove the $ZZ$ background with $ZZ\to\ell^{+}\ell^{-}\nu\bar{\nu}$, which
cannot be efficiently removed by the $M_{\rm T2}$ variable [81, 82] due to the
different event topology. In order to remove events with a large $E^{\rm
miss}_{\rm T}$ coming from mis-measurements of jet energy, we require that the
azumithal angle between the missing transverse momentum and any jet with
$p_{T}>50\,$GeV to satisfy $|\phi_{\rm MET}-\phi_{j}|>0.2$. Finally, we
require the $M_{\rm T2}$ of the lepton pair to be larger than $150\,$GeV.

Figure 3: Distributions of $E^{\rm miss}_{\rm T}$ (top left), $\sum p^{l}_{T}$
(top right) and $M_{\rm T2}$ (bottom) of the $2\ell+E^{\rm miss}_{\rm
T}~{}$channel for signal sample S1 and the major backgrounds. $\sum p^{l}_{T}$
is the scalar sum of the $p_{T}$ of the two leptons. To illustrate the
usefulness of the variables, the cuts {$\sum p^{l}_{T}>200\,$GeV , $M_{\rm
T2}>150\,$GeV} are removed. The number of events correspond to $300\,{\rm
fb}^{-1}$ at the 13 TeV LHC.

The distributions of $E^{\rm miss}_{\rm T}$, $\sum p^{l}_{T}$ (scalar sum of
the $p_{T}$ of the two leptons) and $M_{\rm T2}$ are shown in Fig. 3 for
signal S1, S2 and the major backgrounds. In Fig. 3 one could clearly see the
endpoint feature of the $M_{\rm T2}$ distribution of the $t\bar{t}$,
$WW/WZ/ZZ$ and $tW$ backgrounds. 666Note that most $ZZ$ background are removed
by the lepton invariant mass cut. If this cut is not imposed, a significant
amount of $ZZ$ background will have $M_{\rm T2}\gtrsim m_{W}$.  A cut on
$M_{\rm T2}$ with a value much larger than the $W$ mass is very efficient at
removing these backgrounds. On the other hand, the $t\bar{t}Z$ background has
additional neutrinos and does not have the endpoint feature. While it has a
much smaller cross section, after the $M_{\rm T2}$ cut we found it to be
comparable with other major backgrounds. The numbers of signals and
backgrounds after the selection cuts and the corresponding $s/\sqrt{b}$ for
$300\,{\rm fb}^{-1}$ data are shown in Table 2. Comparing the results of S1
and S2, one could see that the decay channel of the light stop has a rather
small impact on the reach, due to the high jet and lepton threshold we choose
to use.

| # of events ($300\,{\rm fb}^{-1}$) | $s/\sqrt{b}$
---|---|---
S1 | 13 | 2.0
S2 | 12 | 2.0
$t\bar{t}$ | 11 |
$WW/WZ/ZZ$ | 15 |
$t\bar{t}Z$ | 8.4 |
$tW$ | 5.1 |
total SM | 40 |
Table 2:  Number of events of signal and backgrounds and the corresponding
$s/\sqrt{b}$ after all of the selection cuts for the $2\ell+E^{\rm miss}_{\rm
T}~{}$channel with $300\,{\rm fb}^{-1}$ data. The details of signal samples S1
& S2 are listed in Table 1. All the generated backgrounds are included in the
row “total SM.”

###  3.2 $1b1\ell+E^{\rm miss}_{\rm T}$ channel

Selection cuts: We require the event to have $E^{\rm miss}_{\rm T}>350\,$GeV
and contain exactly one lepton, one b-jet with $p_{T}>150\,$GeV and no
additional b-jet with $p_{T}>50\,$GeV. To remove events with large $E^{\rm
miss}_{\rm T}$ due to mis-measurements of jet energy, we require $|\phi_{\rm
MET}-\phi_{j}|>0.3$ for any jet with $p_{T}>100\,$GeV. We require the
transverse mass of the lepton $M_{T}>200\,$GeV in order to remove backgrounds
of which the dominate source of missing energy is from the leptonically
decaying $W$ (e.g. semileptonic $t\bar{t}$). Finally, we require the variable
$M^{W}_{\rm T2}$ reconstructed from the event to be at least 200 GeV. An event
is also kept if it does not contain any additional jet for $M^{W}_{\rm T2}$ to
be constructed.

The variable $M^{W}_{\rm T2}$, proposed in Ref [83], is constructed for
dileptonic $t\bar{t}$ background with one lepton not reconstructed, and has
been shown to be useful in suppressing this type of background [9, 7].777Other
variables have also been proposed for suppressing this background, such as
$am_{\rm T2}$ [84] and topness [85]. As their performances are somewhat
similar, for simplicity we only use $M^{W}_{\rm T2}$ in this paper. The
calculation of $M^{W}_{\rm T2}$ requires one to identify the two b-jets and to
know which one is on the same side as the visible lepton. In practice, one
does not have this knowledge and would usually calculate the $M^{W}_{\rm T2}$
for different possible combinations and output the minimum value from these
combinations. Here we assume the other b-jet is among the three leading non-b-
tagged jets. We then choose the combination which minimizes $M^{W}_{\rm T2}$.

Figure 4: Distributions of $E^{\rm miss}_{\rm T}$ (top left), $p^{b}_{T}$ (top
right), $M_{\rm T}$ (bottom left) and $M_{\rm T2}$ (bottom right) of the
$1b1\ell+E^{\rm miss}_{\rm T}~{}$channel for signal sample S3 and the major
backgrounds. To illustrate the usefulness of the variables, the cuts {$E^{\rm
miss}_{\rm T}>350\,$GeV, $p^{b}_{T}>150\,$GeV, $M_{\rm T}>200\,$GeV,
$M^{W}_{\rm T2}>200\,$GeV} are replaced by looser cuts {$E^{\rm miss}_{\rm
T}>200\,$GeV, $p^{b}_{T}>50\,$GeV, $M_{\rm T}>150\,$GeV, $M^{W}_{\rm
T2}>0\,$GeV}. For the $M^{W}_{\rm T2}$ distribution, events for which
$M^{W}_{\rm T2}$ cannot be constructed below 1 TeV are stacked on the last
bin. The number of events correspond to $300\,{\rm fb}^{-1}$ at the 13 TeV
LHC.

The distributions of $E^{\rm miss}_{\rm T}$, $p^{b}_{T}$, $M_{\rm T}$ and
$M^{W}_{\rm T2}$ are shown in Fig. 4 for signal S1 and the major backgrounds.
For the $M^{W}_{\rm T2}$ distribution, events for which $M^{W}_{\rm T2}>1$ TeV
are stacked on the last bin. The usefulness of $M^{W}_{\rm T2}$ can be seen in
Fig. 4, as the number of background events, in particular for $t\bar{t}$,
falls sharply with $M^{W}_{\rm T2}$ above the top mass. The numbers of signals
and backgrounds after the selection cuts and the corresponding $s/\sqrt{b}$
for $300\,{\rm fb}^{-1}$ data are shown in Table 3. For the $1b1\ell+E^{\rm
miss}_{\rm T}~{}$channel, the reach is also not very sensitive to the decay
channel of stop.

| # of events ($300\,{\rm fb}^{-1}$) | $s/\sqrt{b}$
---|---|---
S3 | 35 | 1.8
S4 | 43 | 2.2
$t\bar{t}$ | 207 |
$W+\,$jets | 84 |
$tW$ | 43 |
$WW/WZ/ZZ$ | 28 |
$t\bar{t}Z$ | 26 |
total SM | 389 |
Table 3:  Number of events of signal and backgrounds and the corresponding
$s/\sqrt{b}$ after all of the selection cuts for the $1b1\ell+E^{\rm
miss}_{\rm T}~{}$channel with $300\,{\rm fb}^{-1}$ data. The details of signal
samples S3 & S4 are listed in Table 1. All the generated backgrounds are
included in the row “total SM.”

##  4 Reach at the 13 TeV LHC

We scan over the signal parameter space to determine the reach of the
$2\ell+E^{\rm miss}_{\rm T}~{}$and $1b1\ell+E^{\rm miss}_{\rm T}~{}$channels
at the 13 TeV LHC, assuming an integrated luminosity of $300\,{\rm fb}^{-1}$.
For comparison, we also include the results of the conventional search channel
of the sbottom, $2b+E^{\rm miss}_{\rm T}~{}$, which has the best reach if
the dominant decay of sbottom is $\tilde{b}\to b\,\chi$. To estimate the reach
of the $2b+E^{\rm miss}_{\rm T}~{}$channel, we adopt the cuts in Ref. [67] for
signal region SRA450, which has the best reach if the mass gap between sbottom
and neutralino is large. We have checked that the total number of backgrounds
after the selection cuts, if normalized to $3.2\,{\rm fb}^{-1}$, is in good
agreement with Ref. [67]. We use the asymptotic formula for the significance
in Ref. [86] (also adopted by Ref. [55, 56]),

$\sigma=\sqrt{2\left[(s+b)\log{(1+s/b)}-s\right]}\,,$ (4.1)

which reduces to the usual $s/\sqrt{b}$ in the limit $b\gg s$. While the
optimal values of the selection cuts depend on the signal spectrum, for
simplicity we fix the cuts as in Section 3. In particular, for the
$2\ell+E^{\rm miss}_{\rm T}~{}$channel the cuts we choose are relatively
conservative to maintain a sufficiently large simulated signal sample. A more
sophisticated optimization method could further improve the reach of the
searches.

Figure 5: Expected $2\,\sigma$ limits (left) and $5\,\sigma$ reaches (right)
in the $(m_{\tilde{b}},~{}{\rm BR}(\tilde{b}\to\tilde{t}\,W))$ plane from the
13 TeV LHC with $300\,{\rm fb}^{-1}$ data, assuming
$m_{\tilde{b}}-m_{\tilde{t}}=400$ GeV and $m_{\tilde{t}}-m_{\chi}=30$ GeV. The
red, blue and green contours indicate the regions excluded by the
$2\ell+E^{\rm miss}_{\rm T}~{}$, $1b1\ell+E^{\rm miss}_{\rm T}~{}$and
$2b+E^{\rm miss}_{\rm T}~{}$channels, respectively. The solid (dashed) curves
corresponds to the stop decay $\tilde{t}\to c\,\chi$ ($\tilde{t}\to
bW^{*}\chi\to bl\nu\chi/bjj\chi$) with $100\%$ BR. The contours are obtained
by scanning the $(m_{\tilde{b}},~{}{\rm BR}(\tilde{b}\to\tilde{t}\,W))$ plane
with a grid spacing of (20 GeV, 0.05) and fitting the points to a
2-dimensional polynomial.

In Fig. 5, we show the expected exclusion regions for the three channels in
the $(m_{\tilde{b}},~{}{\rm BR}(\tilde{b}\to\tilde{t}\,W))$ plane, assuming
$m_{\tilde{b}}-m_{\tilde{t}}=400$ GeV and $m_{\tilde{t}}-m_{\chi}=30$ GeV. On
the left panel, the red, blue and green contours indicate the 2-sigma limits
of the $2\ell+E^{\rm miss}_{\rm T}~{}$, $1b1\ell+E^{\rm miss}_{\rm T}~{}$and
$2b+E^{\rm miss}_{\rm T}~{}$channels, respectively, and the corresponding
shaded regions are excluded at 95% confidence level (CL). On the right panel,
the 5-sigma reaches are shown instead. The contours are obtained by scanning
the $(m_{\tilde{b}},~{}{\rm BR}(\tilde{b}\to\tilde{t}\,W))$ plane with a grid
spacing of (20 GeV, 0.05). A fit to a 2-dimensional polynomial was performed
to reduce the unphysical fluctuations due to the statistical uncertainties of
the simulations. We also checked manually that the fitted curves are in good
agreement with the grid of data points. For the solid curves, we assume the
stop only decays to charm and neutralino, $\tilde{t}\to c\,\chi$; for the
dashed curves, we assume that the stop only goes through the 4-body decay,
$\tilde{t}\to bW^{*}\chi\to bl\nu\chi/bjj\chi$. As we expected, the stop decay
channel has a small impact on the reach. The complementarity of different
channels is well demonstrated in Fig. 5. The $2\ell+E^{\rm miss}_{\rm
T}~{}$($2b+E^{\rm miss}_{\rm T}~{}$) channel has the best reach if the decay
$\tilde{b}\to\tilde{t}\,W$ ($\tilde{b}\to b\,\chi$) is dominant, and the
$1b1\ell+E^{\rm miss}_{\rm T}~{}$channel has a better reach if the branching
ratio of the two decay channels are comparable. We also found that the
$2b+E^{\rm miss}_{\rm T}~{}$channel has rather good reaches, comparable to the
reach of the $1b1\ell+E^{\rm miss}_{\rm T}~{}$channel even for ${\rm
BR}(\tilde{b}\to\tilde{t}\,W)\sim 0.5$. Nevertheless, the $1b1\ell+E^{\rm
miss}_{\rm T}~{}$channel could still significantly improve the overall
significance (of all channels combined) and impose constraints on the stop
mass.

Figure 6: Expected $2\,\sigma$ limits (left) and $5\,\sigma$ reaches (right)
in the $(m_{\tilde{b}},~{}m_{\tilde{b}}-m_{\tilde{t}})$ plane from the 13 TeV
LHC with $300\,{\rm fb}^{-1}$ data, assuming $m_{\tilde{t}}-m_{\chi}=30$ GeV.
The top (bottom) panel assumes ${\rm
BR}(\tilde{b}\to\tilde{t}\,W)=0.9~{}(0.5)$. The red, blue and green contours
indicate the regions excluded by the $2\ell+E^{\rm miss}_{\rm T}~{}$,
$1b1\ell+E^{\rm miss}_{\rm T}~{}$and $2b+E^{\rm miss}_{\rm T}~{}$channels,
respectively. The solid (dashed) curves corresponds to the stop decay
$\tilde{t}\to c\,\chi$ ($\tilde{t}\to bW^{*}\chi\to bl\nu\chi/bjj\chi$) with
$100\%$ BR. The dotted diagonal lines correspond to constant values of
$m_{\tilde{t}}$. The contours are obtained by scanning the
$(m_{\tilde{b}},~{}m_{\tilde{b}}-m_{\tilde{t}})$ plane with a grid spacing of
(20 GeV, 30 GeV) and fitting the points to a 2-dimensional polynomial.

To determine the bounds on masses of sbottom and stop, we also show the
2-sigma limits and 5-sigma reaches in the
$(m_{\tilde{b}},~{}m_{\tilde{b}}-m_{\tilde{t}})$ plane in Fig. 6 for ${\rm
BR}(\tilde{b}\to\tilde{t}\,W)=0.9$ (top panel) and $0.5$ (bottom panel),
assuming $m_{\tilde{t}}-m_{\chi}=30$ GeV. Similar to Fig. 5, the contours are
obtained by scanning the $(m_{\tilde{b}},~{}m_{\tilde{b}}-m_{\tilde{t}})$
plane with a grid spacing of (20 GeV, 30 GeV) and fitting the points to a
2-dimensional polynomial. A few benchmarks of stop masses are also shown,
which correspond to diagonal lines in the
$(m_{\tilde{b}},~{}m_{\tilde{b}}-m_{\tilde{t}})$ plane. For ${\rm
BR}(\tilde{b}\to\tilde{t}\,W)=0.9$, it is clear that the $2\ell+E^{\rm
miss}_{\rm T}~{}$channel has the best reach, and stop masses up to $\sim
600\,$GeV can be excluded for $m_{\tilde{b}}\lesssim 1\,$TeV. For ${\rm
BR}(\tilde{b}\to\tilde{t}\,W)=0.5$, the $1b1\ell+E^{\rm miss}_{\rm T}~{}$and
$2b+E^{\rm miss}_{\rm T}~{}$channels have comparable reaches, with the
$1b1\ell+E^{\rm miss}_{\rm T}~{}$($2b+E^{\rm miss}_{\rm T}~{}$) channel
having better constraints on $m_{\tilde{t}}$ in the regions with smaller
(larger) $m_{\tilde{b}}$. However, it should be noted that the $2b+E^{\rm
miss}_{\rm T}~{}$channel does not direct constrain $m_{\tilde{t}}$, and the
exclusion region shown in Fig. 6 is based on the assumption
$m_{\tilde{t}}-m_{\chi}=30$ GeV. For the $1b1\ell+E^{\rm miss}_{\rm
T}~{}$channel, stop masses up to $\sim 500\,$GeV can be excluded for
$m_{\tilde{b}}\lesssim 900\,$GeV. It should also be noted that in obtaining
the constraints we have assumed a sufficient mass gap between the sbottom and
the stop. If the mass gap is small, the search strategy can be drastically
different, in particular in the region $m_{\tilde{b}}-m_{\tilde{t}}\lesssim
m_{W}$. Further studies are required to determine the collider reach in this
region.

Comparing to the reach of the direct stop search, the recent results from the
ATLAS mono-jet search has excluded stop masses below 323 GeV with $3.2\,{\rm
fb}^{-1}$ data at $\sqrt{s}=13\,$TeV, assuming $m_{\tilde{t}}-m_{\chi}\approx
5\,$GeV [59]. This already surpasses the constraints from the 8 TeV run [25,
26]. CMS conducted a search with $2.3\,{\rm fb}^{-1}$ data at
$\sqrt{s}=13\,$TeV using the $\alpha_{\rm T}$ variable which can exclude stop
masses up to 400 GeV assuming $m_{\tilde{t}}-m_{\chi}\approx 10\,$GeV [60]. In
both searches, the bounds on stop mass are also significantly weaker for
slightly larger values of $m_{\tilde{t}}-m_{\chi}$. In Ref. [35], it is
estimated that the high luminosity LHC with $3000\,{\rm fb}^{-1}$ data at
$\sqrt{s}=14\,$TeV is required for the bounds on stop mass from mono-jet
search to reach $\sim 500$ GeV, assuming the stop is in the coannihilation
region. While the constraints from mono-jet searches do not rely on the
properties of sbottom and are hence more robust, the search with sbottom
decays could potentially have a much better reach. The two searches are also
complementary; if a significant excess is found in the $2\ell+E^{\rm
miss}_{\rm T}~{}$or $1b1\ell+E^{\rm miss}_{\rm T}~{}$channel, one may also
expect a mild excess in the mono-jet search if the excess comes from a light
stop in the coannihiliation region.

##  5 Conclusion

A light stop with mass almost degenerate with the lightest neutralino is an
appealing SUSY scenario. It could evade the bounds of traditional stop
searches and hence reduce the tension between naturalness and the current LHC
results, while also having interesting implications for bino dark matter. In
this paper, we propose a novel way of probing such stop particles by searching
for it from sbottom decays, under the assumptions that the sbottom is not too
heavy and has a significant branching ratio of decaying into a stop and a $W$
boson ($\tilde{b}\to\tilde{t}\,W$). Such assumptions are favored by
naturalness and Higgs mass considerations. In this scenario, the constraints
on the masses of stop and sbottom from the traditional searches are weak. We
show that a dedicated search for a sbottom pair with one or both sbottom
decaying to stop and $W$ at the 13 TeV LHC could impose strong constraint on
this scenario, hence making it the optimal search channel. Assuming
$m_{\tilde{t}}-m_{\chi}\approx 30\,$GeV, if the decay
$\tilde{b}\to\tilde{t}\,W$ is dominant, the channel with final states
$2\ell+E^{\rm miss}_{\rm T}~{}$has the best reach, and can exclude stop masses
up to $\sim 600\,$GeV with $300\,{\rm fb}^{-1}$ data if the sbottom is below 1
TeV; if the sbottom decays to either $\tilde{t}\,W$ or $b\,\chi$ with
comparable branching ratios, the channel with final states $1b1\ell+E^{\rm
miss}_{\rm T}~{}$has a better reach and could exclude the stop with mass up to
$\sim 500\,$GeV with $300\,{\rm fb}^{-1}$ data if the sbottom is below 900
GeV. While the results rely on the properties of the sbottom, the reaches are
potentially much better than the one from direct searches of stop with mono-
jet + $E^{\rm miss}_{\rm T}$ final states, which could only reach up to $\sim
500\,$GeV with $3000\,{\rm fb}^{-1}$ data at $\sqrt{s}=14\,$TeV. The
traditional search channel of sbottom with final states $2b+E^{\rm miss}_{\rm
T}$ is also complementary to the ones we propose. Together, these searches can
cover a wide range of model parameter space and provide valuable information
on the status of SUSY.

There are other interesting scenarios not explored in this paper but may worth
further investigation. It is possible that the chargino or second neutralino
are lighter than the sbottom, making its decay more complicated [87]. In this
case, searching for the asymmetric decay chains with one sbottom decaying to
$\tilde{t}\,W$, the other decaying to $t\chi^{\pm}$ or $b\chi_{2}$ could be
useful. For larger values of the stop-neutralino mass gap, the stop decay
products become more visible and it might be useful to look at channels with
multiple b-jets or multiple leptons [56], or try to tag the charm quark from
stop decay [23, 24, 25]. On the other hand, if the mass gap is smaller, the
stop decay could exhibit displaced vertex, which can help reduce SM background
in both the mono-jet search and the search with sbottom decays. It is also
complementary to search for the lighter stop from the decays of the heavier
stop [88, 89, 90].

Our study serves as a proof of concept. A search carried out by the LHC
experimental groups is desired to fully determine the reach of the proposed
channels. Since the $2\ell+E^{\rm miss}_{\rm T}~{}$channel has been used to
search for sleptons and electroweakinos, and the conventional search of stop
in the semileptonic channel is very similar to the $1b1\ell+E^{\rm miss}_{\rm
T}~{}$channel we studied, reinterpretation of those search results can already
lead to interesting reach. At the same time, optimizing the searches with
these new channels in mind is needed to realize their full potential. While
the current data is still not very constraining, in the future it is
straightforward to interpret the results of conventional searches in these two
channels in terms of constraints on the scenario studied in this paper. If
deviations from the SM is observed, it is non-trivial to discriminate
different new physics scenarios that leads to similar signals, and the
comparisons between different search channels are important.

### Acknowledgments

We would like to thank Zhen Liu for useful discussions. HA is supported by the
Walter Burke Institute at Caltech and by DOE Grant de-sc0011632. JG is
supported by the International Postdoctoral Exchange Fellowship Program
between the Office of the National Administrative Committee of Postdoctoral
Researchers of China (ONACPR) and DESY. JG would also like to express a
special thanks to the Mainz Institute for Theoretical Physics (MITP) for its
hospitality and support. LTW is supported by DOE grant DE-SC0013642.

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# SemEval-2024 Task 8: Weighted Layer Averaging RoBERTa for Black-Box Machine-
Generated Text Detection

Ayan Datta†
IIIT Hyderabad
ayan.datta
@research.iiit.ac.in
&Aryan Chandramania†
IIIT Hyderabad
aryan.chandramania
@research.iiit.ac.in
Radhika Mamidi
IIIT Hyderabad
<EMAIL_ADDRESS>
###### Abstract

This document contains the details of the authors’ submission to the
proceedings of SemEval 2024’s Task 8: Multigenerator, Multidomain, and
Multilingual Black-Box Machine-Generated Text Detection Subtask A
(monolingual) and B. Detection of machine-generated text is becoming an
increasingly important task, with the advent of large language models (LLMs).
In this document, we lay out the techniques utilized for performing the same,
along with the results obtained.

$\dagger$$\dagger$footnotetext: These authors contributed equally to this
work.

##  1 Introduction

Language modeling is a foundational task in NLP, and encompasses learning of
all the features that make up language. Different levels of linguistic
information are stored in language models’ (LM) hidden states. This may
include syntax, morphological features, phrasing, and so on. Our aim is to
leverage this encoded information to help us discern machine-generated text.

The advent of large language models (LLMs) has transformed the digital
landscape, and this has also led to the proliferation of machine-generated
text in spaces spanning from legal proceedings, to articles, to school
submissions. With this, there has been a consequential rise in the need to be
able to distinguish between machine- and human-generated text across domains.
Just as important is the need to be able to identify the generators for text
that has been flagged as being generated by machines.

In this paper, we describe our methodology and attempts to create a system
that can perform the task effectively.

##  2 System Overview

We have used RoBERTa-base for all experiments in the scope of this paper. The
baseline set by the task organizers is reported to have been from a finetuned
RoBERTa model. RoBERTa has the same architecture as BERT, but uses a byte-
level BPE as a tokenizer and uses a different pretraining scheme and has
become a SOTA model since its release [Liu et al., 2019].

###  2.1 Weighted Layer Averaging

The standard fine-tuning setup uses the [CLS] Representation of the last layer
of RoBERTa. It has been shown that different layers of BERT-like models
capture different levels of linguistic information [Rogers et al., 2020]. We
believe that using just the last layer representation may discard some of the
syntactic and lexical information, which could be crucial for the task of
detecting machine generated text. We use the weighted sum of all the token
representations, where each layer is assigned a corresponding weight, trained
along with the downstream task, similar to ElMo [Peters et al., 2018].

###  2.2 Parameter Efficient Tuning with AdaLoRa

Model | Accuracy
---|---
`Ours` | `0.7535`
`Baseline` | `0.8846`
Table 1:  Results for Subtask A as computed by the organizers  Model | Accuracy
---|---
`Ours` | `0.7387`
`Baseline` | `0.7460`
Table 2:  Results for Subtask B as computed by the organizers  Dataset | Precision | Recall | Accuracy | F1 Score
---|---|---|---|---
`Our Dev` | `0.9841` | `0.9949` | `0.9900` | `0.9895`
`Official Dev` | `0.9744` | `0.9444` | `0.9598` | `0.9592`
`Official Test` | `0.6823` | `0.9942` | `0.7538` | `0.8092`
Table 3:  Results for Subtask A as computed by us  Dataset | Precision${}_{\text{Micro}}$ | Recall${}_{\text{Micro}}$ | Accuracy | F1 Score${}_{\text{Micro}}$
---|---|---|---|---
`Our Dev` | `0.979` | `0.979` | `0.979` | `0.979`
`Official Dev` | `0.9783` | `0.9783` | `0.9783` | `0.9783`
`Official Test` | `0.7398` | `0.7398` | `0.7398` | `0.7398`
Table 4:  Results for Subtask B as computed by us

A full continual finetune of RoBERTa (and LLMs, in general) with all the
weights being updated is known to potentially lead to catastrophic forgetting
[Ramasesh et al., 2022], which may cause the model to become unable to
generalize, with the pretraining being, for all intents and purposes, in vain.

It has also been shown that common pre-trained models have a very low
intrinsic dimension; in other words, there exists a low dimension
reparameterization that is as effective for fine-tuning as the full parameter
space [Aghajanyan et al., 2020]. This implies that full continual finetuning –
being potentially harmful as well as unnecessary – can be replaced with a
better, more parameter efficient method, which grants us more freedom with
regards to model and data sizes.

Low-rank Adapters (LoRA) [Hu et al., 2021] were designed with this in mind.
LoRA freezes the pretrained model weights and injects trainable rank
decomposition matrices into each layer of the Transformer architecture,
greatly reducing the number of trainable parameters for downstream tasks. They
also offer an improvement over unfreezing just the last few layers by
attaching to every layer in the model, which allows them to modify information
flow at every step, starting from the source.

For our task, we made use of Adaptive LoRA (AdaLoRA) [Zhang et al., 2023],
which adjusts the matrices based on parameters learned during training, i.e.
the ranks of the adapters themselves are learned. Our hope is that by doing
this, we prevent unnecessarily large adapters where there is not much to do,
and conversely provide the flexibility to have larger matrices to handle
greater amounts of information change.

##  3 Data

Data for the task was provided by the organizers. It is an extension of the M4
Dataset [Wang et al., 2023]. The name stands for multi-generator, multi-
domain, and multi-lingual corpus for machine-generated text detection. As the
name suggests, the dataset has been created with text from different
generators spanning multiple domains. The data for subtask A and B follow the
same format, consisting of source (such as Wikipedia), model (such as Dolly),
label (such as Human), and the text to be classified. The data for subtask C
contains text with a combination of human- and machine-generated text, and a
label indicating the word index at which the split occurs.

For our experiments, we resplit the training and dev datasets and split them
uniformly across generators and domains in an 80-20 split‘. Our split of the
dev set is bigger than the official dev set, to get a better estimate of our
model’s performance.

##  4 Experimental Setup

We use RoBERTa’s tokenizer and trained our models for Subtask A (monolingual)
(Binary Classification) and Subtask B (Multi-Class Classification) on the
resplit train data and use the resplit evaluation data for early stopping. Our
Hyperparameter Configuration has been specified in Appendix A.

##  5 Results

Our model while doing really well on our evaluation set, falls short on the
test set scoring around 13 percentage points lower than the baseline for
subtask A and around 1 percentage point lower than the baseline for subtask B.
This could be attributed to the model not being as good in generalising to
unseen domains and generators. We hypothesize more hyperparameter tuning,
better aggregation of the token representations than averaging by utilizing
models like LSTMs [Hochreiter and Schmidhuber, 1997], may help the model
better generalise to unseen domains and generators by being able to capture
more complex features and patterns. The submission scores as computed by the
task organizers have been reported in Tables 1 and 2. Scores on our
Validation, the official validation and the official test set as computed by
us have been reported in Tables 3 and 4.

##  6 Conclusion

We have demonstrated that linguistic information encoded in the various layers
of large language models such as RoBERTa can be used to effectively
demonstrate if a text is machine-generated or not, across different domains
and generators.

## References

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##  Appendix A Hyperparameters

Hyperparameter | Value
---|---
`Learning Rate` | `5e-4`
`Batch Size` | `8`
`Weight Decay` | `5e-5`
`Warmup Ratio` | `0.1`
`init_r` | `12`
`target_r` | `8`
`lora_alpha` | `200`
`lora_dropout` | `0.4`
Table 5:  Hyperparameters for Subtask A (Monolingual)  Hyperparameter | Value
---|---
`Learning Rate` | `5e-4`
`Batch Size` | `8`
`Weight Decay` | `5e-5`
`Warmup Ratio` | `0.01`
`init_r` | `12`
`target_r` | `8`
`lora_alpha` | `200`
`lora_dropout` | `0.4`
Table 6:  Hyperparameters for Subtask B