aainstitutetext: Instituto de Física Corpuscular, CSIC-Universitat de
València,
Catedrático José Beltrán 2, E-46980, Paterna, Spain

# Emerging jet probes of strongly interacting dark sectors

Juliana Carrasco a Jose Zurita<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

A strongly interacting dark sector can give rise to a class of signatures
dubbed dark showers, where in analogy to the strong sector in the Standard
Model, the dark sector undergoes its own showering and hadronization, before
decaying into Standard Model final states. When the typical decay lengths of
the dark sector mesons are larger than a few centimeters (and no larger than a
few meters) they give rise to the striking signature of emerging jets,
characterized by a large multiplicity of displaced vertices.

In this article we consider the general reinterpretation of the CMS search for
emerging jets plus prompt jets into arbitrary new physics scenarios giving
rise to emerging jets. More concretely, we consider the cases where the SM
Higgs mediates between the dark sector and the SM, for several benchmark decay
scenarios. Our procedure is validated employing the same model than the CMS
emerging jet search. We find that emerging jets can be the leading probe in
regions of parameter space, in particular when considering the so-called
_gluon portal_ and _dark photon portal_ decay benchmarks. With the current
16.1 fb-1 of luminosity this search can exclude down to ${\cal O}(20)\%$
exotic branching ratio of the SM Higgs, but a naive extrapolation to the 139
fb-1 luminosity employed in the current model-independent, indirect bound of
16 % would probe exotic branching ratios into dark quarks down to below 10 %.
Further extrapolating these results to the HL-LHC, we find that one can pin
down exotic branching ratio values of 1%, which is below the HL-LHC
expectations of 2.5$-$4 %. We make our recasting code publicly available, as
part of the LLP Recasting Repository.

††preprint:  IFIC 23-24

##  1 Introduction

Extensions of the Standard Model with a strongly coupled, non-Abelian dark
sector have received considerable attention in the recent years. The
phenomenological possibilities are varied, due the large number of parameters,
such as the gauge group dimension (number of dark colors), the matter field
content (number of dark flavors), the mass hierarchies in the dark sector, and
the coupling strengths between the dark sector and the Standard model, as well
as the internal dark sector couplings. Considering a collider operating at a
center of mass energy $\sqrt{s}$, the subclass of models which confine at a
scale $\Lambda_{D}$, and where the dark sector masses
$m_{D}\lesssim\Lambda_{D}<<\sqrt{s}$ give rise to a class of signatures
generically dubbed _dark showers_ , in analogy to the familiar parton shower
in the strong sector of the Standard Model, see Albouy:2022cin  for a
comprehensive review of the current phenomenological, experimental and
theoretical status. Dark showers give rise to uncommon, exotic collider
objects, such as trackless jets Daci:2015hca , emerging jets Schwaller:2015gea
, semi-visible jets Cohen:2015toa  and SUEPs Knapen:2016hky . An experimental
program aiming at dark shower signatures at the LHC is already underway
CMS:2018bvr ; CMS:2021rwb ; CMS:2021dzg ; ATLAS:2023swa .

It is customary Alimena:2019zri  to dissect the collider phenomenology of dark
showers into three pieces: i) _production_ , ii) _showering_ (which actually
includes hadronization) and iii) _decay_. The production part consists of the
parton-level production of dark quarks (customarily through $2\to 2$
processes), the showering phase includes both the emission of dark gluons and
dark quarks and the formation of bound states (dark hadrons), akin to the
known behaviour of the strong sector of the Standard model. Indeed, the
showering process yields a distinctive signal, as, unlike in normal searches
for new phenomena, one is not targeting one or two new particles, but in
principle many of them. Hence, the large multiplicity inherent to the dark
parton showering is what makes them stand out from other Beyond Standard Model
(BSM) searches. The decay modes of these dark hadrons (including SM particles
such as leptons, quarks, gluons, or potentially not decaying at all
contributing to the overall dark matter abundance) combined with the lifetime
spectra of these dark hadrons span a large number of phenomenologically
distinct scenarios. Decay benchmarks to guide the experimental exploration
have been recently put forward in Knapen:2021eip ; Knapen:2022afb .

If the dark sector contains some particles that are long-lived (another
research direction that has received considerable attention in the recent
past, see e.g. Alimena:2019zri ; Lee:2018pag ; Knapen:2022afb  for reviews),
with lifetimes in the few mm to few meters, which decay into SM particles,
they give rise to _emerging jets_ (EJ). In this work we present a simple and
flexible reinterpretation of the CMS search for emerging jets CMS:2018bvr
seizing all publicly available information. We validate our procedure by
reproducing the CMS results for their benchmark model, proposed in
Schwaller:2015gea . The software developed for the reinterpretation procedure
has been uploaded to the LLP Recasting Repository LLPrepo , which we expect to
be useful for those interested in a straightforward reinterpretation of this
study. We later apply our procedure to the concrete case of exotic Higgs
decays, namely we obtain bounds on the branching ratio of the SM-like 125 GeV
Higgs boson into a pair of dark quarks. We also show that the bounds arising
from the reinterpretation of the emerging jet search, albeit not designed to
target this scenario, can nonetheless provide leading constraints in large
portions of the parameter space.

This article is organized as follows. In section 2 we briefly review the
phenomenology of emerging jets and the t-channel models from Schwaller:2015gea
which give rise to them. In section 3, we show our validation of the CMS
emerging jet search. In section 4 we apply our recasting procedure to a series
of BSM decay benchmarks devised in Knapen:2021eip . We reserve section 5 for
conclusions. Technical details about the validation of the CMS Emerging Jet is
described in Appendix A.

##  2 Emerging jet phenomenology

When considering a strongly interacting dark sector, the known behaviour of
QCD provides a guidance for the relevant phenomenological features of the
model. A QCD-like sector with gauge group $SU(N_{C_{D}})$ and $N_{f_{D}}$
degenerate Dirac fermions (dark quarks, $q_{D}$) would then exhibit asymptotic
freedom, and confine at a scale $\Lambda_{D}$, where
$m_{q_{D}}\lesssim\Lambda_{D}$. When these particles are _produced_ at a
collider with a center-of-mass energy $\sqrt{s}\lesssim 30\Lambda_{D}$111If
$\Lambda_{D}$ would be closer to the available energy $\sqrt{s}$, then the
dark quarks have limited phase space to shower. The formed dark mesons can
then be probed by searches for resonant bound states see e.g Kribs:2018ilo ;
Hochberg:2015vrg ; Butterworth:2021jto ., the dark quarks _hadronize_ into
dark hadrons ($\pi_{D}$, $\rho_{D}$, $\omega_{D}$, …) which are clustered into
collimated dark jets. The resulting signatures will then depend on the dark
hadron _decay_ , more specifically on the lifetime spectrum $c\tau_{D}$, but
the main underlying theme is that the shower process can lead to a large
multiplicity of objects, while in traditional searches only one or two new
particles are targeted.

Following Alimena:2019zri , the dark shower can be decomposed into the three
parts described above: production, hadronization (in the dark sector) and dark
hadron decays. For the production at a collider, is necessary to connect the
Standard Model to the dark sector, which is done through a _portal_. For
emerging jets, the focus of this work, the model proposed in Bai:2013xga ;
Schwaller:2015gea  employs a a bi-fundamental scalar $X$ (namely, charged
under both QCD and the dark sector) which interacts with a SM down-type quark
and a dark quark via the following Lagrangian

${\cal L}\supset-\kappa_{ij}\bar{q}_{R\,i}q_{D_{j}}X\,\,.$ (1)

While in principle $\kappa$ is a $3\times N_{C_{D}}$ matrix, we consider here
the case where there is one single universal coupling to the right-handed down
type quark, to avoid bounds from flavour physics (FCNCs, neutral meson-mixing,
rare decays). In this model, $X$ is pair produced with a sizable rate through
gauge interactions, and the subsequent $X\to d_{R}~{}q_{D}$ decay (which
happens with 100 % branching ratio) leads us to expect two light jets and two
emerging jets. Since the mediator particle $X$ appears in t-channel exchanges,
the model of equation 1 is colloquially referred to as a _t-channel_ model.

In this paper we will also study the production via an s-channel SM Higgs
boson $h$, which falls in the category of exotic Higgs decays Curtin:2013fra ;
Cepeda:2021rql . Measurements of the Standard Model Higgs properties set
Br($h\to{\rm exotic}<0.16)$ at 95 % C.L. from both ATLAS ATLAS:2021vrm  and
CMS CMS:2022dwd  with a total integrated luminosity of 139 and 138 fb-1
respectively. These bounds are not completely model independent, as they
assume that the Higgs boson couples to the electroweak gauge bosons with a
strength equal or less to the SM one, which can be violated in certain BSM
scenarios. The combination of ATLAS and CMS with 3000 fb-1 is expected to set
a limit of 2.5%, under the assumption that the current systematic
uncertainties would be halved Cepeda:2019klc , or 4% with the current
systematic uncertainties deBlas:2019rxi . This leaves ample room for the $h\to
q_{D}q_{D}$ to occur with sizable rates. We note that the identification of a
resonant, long-lived $q_{D}q_{D}$ topology using Machine Learning techniques
has been recently studied in reference Lu:2023gjk  for the SM Higgs and in
reference Bardhan:2023mia  for a TeV scale Z’.

The showering and hadronization in the dark sector is conducted through the
Hidden Valley module Carloni:2010tw ; Carloni:2011kk  within Pythia8
Sjostrand:2014zea . The non-perturbative nature of the dark QCD-like theories
prevents from consistently connecting UV and IR parameters based on a
perturbative approach, and hence it is customary to consider a dark sector
consisting of spin-1 dark vector mesons $\rho_{D}$, and of spin-0 pseudoscalar
dark pions, $\pi_{D}$. As the $\pi_{D}$ arise from a breaking of a chiral dark
symmetry, they are parametrically lighter than the other mesons in the theory,
which decay into dark pions if kinematically allowed. Hence, the phenomenology
is dictated by the dark pion properties, in particular their lifetime
$c\tau_{\pi_{D}}$. We distinguish three possible regimes depending on the dark
pion lifetime. If the dark pions decay promptly ($c\tau_{\pi_{D}}\lesssim 1$
mm), they end up giving multi-jet signals222If some dark hadrons would remain
stable, one would have an invisible component within a jet, giving rise to
semi-visible jets Cohen:2015toa . . If, on the contrary, the dark pions are
stable in the detector ($c\tau_{\pi_{D}}\gtrsim 1$ m) then they appear as
missing energy, and can be targeted by the suite of missing energy signatures
that are customarily searches in the dark matter program at the LHC
Boveia:2018yeb . For $c\tau_{\pi_{D}}\in[0.001-1]$ m, the dark pions decay
inside the detector volume with different decay lengths, depending on their
boost and on the fact that their actual decay position is sampled from an
exponential distribution.

The decay patterns of the dark pions can be quite varied. As mentioned before,
in reference Schwaller:2015gea  to avoid dealing with non-trivial bounds from
flavour processes, a 100 % decay rate to right-handed down quarks was assumed.
Yet, the possibilities for the decay are quite numerous, and in that light
reference Knapen:2021eip  proposed five decay benchmark models, dubbed _decay
portals_ , based on a minimal set of theoretical priors. These decay portals
describe how the pseudoscalar and vector dark mesons decay into Standard Model
particles 333In reference Knapen:2021eip  the pseudoscalar and vector mesons
are noted as $\tilde{\eta}$ and $\tilde{\omega}$. For a unified notation in
this paper, we replace them by $\pi_{D}$ and $\rho_{D}$, respectively. . If
$\pi_{D}$ decays into gluons (photons) through a dimension 5 operator we have
the gluon (photon) portal. If $\pi_{D}$ instead couples to the Standard Model
Higgs via the $H^{\dagger}H$ operator, then we have the Higgs portal, where
the decays to the SM quarks follow the Yukawa hierarchy of a SM-like Higgs
with $m_{H}=m_{\pi_{D}}$. The other two decay portals have the $\pi_{D}$
decaying either through its mixing with the photon (akin to the
$\gamma$-$\rho$ mixing in the Standard Model), or through the chiral anomaly
into a pair of dark photons $A^{{}^{\prime}}$, inspired by the
$\pi_{0}\to\gamma\gamma$ SM process. The corresponding Pythia configuration
cards for each of these portals can be generated through the public python
script DStool .

The number of free parameters in both our scenarios is still quite large, and
here we follow some additional choices made in the literature. Regarding the
t-channel EJ model, $N_{C_{D}}=3$ and $N_{f_{D}}=7$ are inspired by the study
of Bai:2013iqa , and the dark sector mass parameters are chosen in proportion
$\Lambda_{D}:m_{q_{D}}:m_{\rho_{D}}:m_{\pi_{\mathrm{D}}}$ being $2:2:4:1$.
This choice ensures that the vector meson always decays into two dark pions,
and was followed by the CMS collaboration in their emerging jets search
CMS:2018bvr  444The inclusion of a non-trivial flavour structure, where
$\Lambda_{D}>m_{q_{D}}$ is assumed, was studied in Renner:2018fhh .. The free
parameter for the analysis are then $m_{\mathrm{X}}$, $m_{\pi_{\mathrm{D}}}$
and $c\tau_{\pi_{\mathrm{D}}}$. Regarding the s-channel SM Higgs production
with its different decay portals we assume $N_{C_{D}}=3$ and $N_{f_{D}}=1$,
and $\Lambda_{D}:m_{q_{D}}:m_{\rho_{D}}:m_{\pi_{D}}$ is now $2.5:0.4:2.5:1$.
Since the mediator mass is known, the only free parameters of the model are
$m_{\pi_{\mathrm{D}}}$, $c\tau_{\pi_{\mathrm{D}}}$ and the exotic branching
ratio, $H\to q_{D}q_{D}$. We note that while in reference Knapen:2021eip  a
minimum proper lifetime as a function of the mass for each decay portal was
estimated from theoretical considerations, we prefer to remove those
prejudices and consider the three parameters as fully independent and
uncorrelated.

A few details about our simulations are in order. Within the Pythia Hidden
Valley module, we set the parameter HiddenValley:pTminFSR to 1.1 $\Lambda$,
and the probVector flag is set to 0.318, following the considerations
discussed in Appendix A of Knapen:2021eip . In section 3 we employ Pythia
version 8.212, used in the CMS study, as our aim is to reproduce the published
limits. For section 4 we employ instead Pythia 8.307, because (as explained in
Albouy:2022cin ) this version has corrected a previous flaw in the code, that
tended to overproduce hidden hadrons at very low $p_{T}$.

##  3 Validation of the CMS emerging jet search

In this section we discuss in detail the validation of the CMS search for
emerging jets using a total integrated luminosity of 16.1 fb-1 CMS:2018bvr .

The CMS collaboration targets the dark QCD model from Equation 1, via $pp\to
XX$ followed by $X\to q~{}q_{D}$. Hence naively one expect to find two
emerging jets and two SM jets. Events are selected by passing the $H_{T}>900$
GeV trigger, where $H_{T}$ is the scalar sum of the transverse momenta of all
hadronic jets in the event, clustered with $R=0.4$ using the anti-$k_{T}$
algorithm Cacciari:2008gp  applied to all tracks with $p_{T}>1$ GeV. These
events are required to have at least four jets within $|\eta|<2.0$, and they
undergo a further selection using kinematical variables to tag these jets as
“emerging” and to define signal regions (called sets in the CMS paper). The
explicit requirements are collected in Appendix A, together with the 95 % C.L.
limit to the number of signal events in each selection set, $S_{95}^{i}$.

The total number of signal events in each set can be computed as

$N_{S}^{i}(m_{\mathrm{X}},c\tau_{\pi_{\mathrm{D}}},m_{\pi_{\mathrm{D}}})=\sigma(pp\to
XX)\times({\rm BR(X\to q~{}q_{D}))^{2}}~{}\times
A_{i}(m_{\mathrm{X}},c\tau_{\pi_{\mathrm{D}}},m_{\pi_{\mathrm{D}}})\times{\cal
L}$ (2)

where ${\cal L}$ is the total integrated luminosity, $A_{i}$ is the acceptance
for the $i-$th set number 555In this article, we will use the terms
“efficiency” and “acceptance” interchangeably to denote the $A_{i}$ function.
and the production rate $\sigma(pp\to XX\to qq_{D}qq_{D})$ has been decomposed
into the pair production cross section for $X$ pairs (which proceeds through
gauge couplings and hence is independent of $m_{\pi_{\mathrm{D}}}$ and
$c\tau_{\pi_{\mathrm{D}}}$) times a branching ratio of $X\to qq_{D}$, which we
set to unity along this work 666We have explicitly verified that the narrow
width approximation is fulfilled in our model points, which allows us to
factorize the total rate into a cross section and a branching ratio.. To
benchmark the search, CMS considered the following parameters:

  * •

$m_{\mathrm{X}}$ [GeV]={400,600,800,1000,1250,1500,2000} .

  * •

$m_{\pi_{\mathrm{D}}}$ [GeV]={1,2,5,10} .

  * •

$c\tau_{\pi_{\mathrm{D}}}$ [mm]={1,2,5,25,45,60,100,150,225,300,500,1000}.

For the $m_{\pi_{\mathrm{D}}}=5$ GeV case, CMS has provided the acceptances
$A_{i}$ in the $c\tau_{\pi_{\mathrm{D}}}-m_{\mathrm{X}}$ plane, indicating
which of the seven selection numbers is the most sensitive one. In other
words, for each $c\tau_{\pi_{\mathrm{D}}}-m_{\mathrm{X}}$ point scanned, with
$m_{\pi_{\mathrm{D}}}=5$ GeV, only one of the possible seven $A_{i}$ functions
is given.

To validate the search, we proceed in three steps. First, we check that using
the provided $A_{i}$ efficiencies we can reproduce the published 95 % C.L
exclusion limits. In a second step, we check the degree of accuracy that we
obtain for the two published kinematic distributions for the emerging jet
tagging variables, and finally we show that we can reproduce with reasonable
accuracy the said efficiencies and exclusion limits. The last step is crucial
for our analysis, since this is what allows for reinterpretation, i.e.: derive
limits from a experimental search on a model that has not been targeted by the
experimental collaboration.

In what follows, we define “exclusion” by requiring that the ratio of our
predicted number of events from equation 2 over the excluded one,

$R_{\mathrm{95}}=\max_{i}\Biggl{\\{}\frac{N_{S}^{i}}{S_{95}^{i}}\Biggr{\\}}\,,$
(3)

is equal to unity, which is a common practice when performing
reinterpretations LHCReinterpretationForum:2020xtr .

###  3.1 Exclusion using published efficiencies

We start by comparing the published exclusion limit with those that can be
derived from using the $A_{i}$ map from CMS:2018bvr . We present our results
in figure 1, where the published CMS exclusion is shown as solid black. For
our results, we need to provide a production cross section for the $pp\to XX$
process. On one hand, we use the cross section reported during the run of
Pythia 8, which is a leading-order (LO) result in the strong QCD coupling
$\alpha_{S}$, shown in green. Second, we employ the cross sections used by CMS
from NLOcms  corresponding to down-type squark pair production, computed at
the next-to-leading order in perturbation theory, and including a next-to-
leading logarithmic correction from soft gluon resummation Borschensky:2014cia
, which is displayed in blue.

Figure 1:  Published signal exclusions from CMS (solid black) and those
obtained using the CMS acceptances and for $pp\to XX$ i) leading order cross
section in green and ii) NLO cross section in blue.

We conclude that the provided $A_{i}$ values are self-consistent, and we also
verify that the limits were derived using NLO cross sections.

###  3.2 Kinematic distributions

As a second step of our validation, we will employ the published kinematic
distributions. To tag the jets passing the selection as _emerging_ , the
following track-based variables CMS:2017poa  are considered:

  * •

$\langle IP_{\mathrm{2D}}\rangle$: the median of the unsigned transverse
impact parameter.

  * •

$PU_{\mathrm{dz}}$: distance between the $z$ position of the primary vertex
(PV), $z_{\mathrm{PV}}$ and the $z$ position of the track at its closest
approach to the PV.

  * •

$D_{\mathrm{N}}$: the 3-D distance between the track and the primary vertex,
weighted by the inverse resolution,

$D_{\mathrm{N}}^{2}=\Bigl{(}\frac{z_{\mathrm{PV}}-z_{\mathrm{trk}}}{0.01~{}{\rm
cm}}\Bigr{)}^{2}+\Bigl{(}\frac{r_{\mathrm{trk}}-r_{\mathrm{PV}}}{\sigma_{r}}\Bigr{)}^{2}\,.$
(4)

  * •

$\alpha_{\mathrm{3}D}$ : the ratio between the scalar $p_{T}$ sum of all
tracks with $D_{N}<$ (certain value), normalized by the scalar $p_{T}$ sum of
all tracks, hence $0\leq\alpha_{\mathrm{3}D}\leq 1$.

We illustrate the $\langle IP_{\mathrm{2D}}\rangle$ variable in figure 2. From
the primary vertex located at $(z,r)=(0,0)$ we consider that only a SM jet
(which tags the vertex) and a long-lived dark pion emerge. The dark pion
decays at $(z_{tr},r_{tr})$ into three tracks $1,2,3$, which for illustration
purposes we consider as giving rise to only one jet. The track trajectories
meet at the decay vertex: the tracks are drawn in black, and their
prolongations in grey. We indicate with $d_{i}$ the closest distance between
the $i-$th track and the primary vertex, hence the $r$($z$) component gives
the transverse (longitudinal) impact parameter. In the figure, the median of
the $(d_{i})_{r}$ corresponds to $(d_{2})_{r}$, hence the jet originating from
the dark pion has $\langle IP_{\mathrm{2D}}\rangle=|(d_{2})_{r}|$.

Figure 2:  Geometry of the considered variables. A SM jet and a dark pion
$\pi_{D}$ originates from $(r,z)=(0,0)$; the latter decays at
$(r_{tr},z_{tr})$ into three tracks. We illustrate here how the $\langle
IP_{\mathrm{2D}}\rangle$ variable is obtained from the transverse impact
parameter of the individual tracks. See main text for details.

Of the above variables, CMS presents results for $\langle
IP_{\mathrm{2D}}\rangle$ and $\alpha_{\mathrm{3}D}$, before the selection cuts
(which we describe below). Regarding the additional two variables, the
variable $D_{N}$ should be small for tracks originating from prompt particles,
and large for displaced tracks; while $PU_{\mathrm{dz}}$ is used for pile-up
rejection. We note that both $D_{N}$ and $PU_{\mathrm{dz}}$ enter in these
distributions through the definition of $\alpha_{\mathrm{3}D}$, which depends
on $D_{N}$. Since CMS has not made explicit the $D_{N}$ threshold employed in
their figure 3, we have considered the three values employed to define the
signal regions: 4, 10 and 20. Out of them, we have verified that the agreement
is maximized for $D_{N}=10$, and hence $D_{N}<10$ has been employed in the
shown $\alpha_{\mathrm{3}D}$ calculation shown below. As these last two
variables are defined at the track level instead of at the jets level, we
understand that kinematic distributions are not provided, which nonetheless
would have provided an additional validation check for the proper
reinterpretation of the search.

Two important effects ought to be included for a realistic attempt at the
reproduction of the CMS results: the tracking reconstruction efficiency
$\epsilon_{\rm trk}$ and the smearing of the impact parameters.

CMS reports the tracking efficiency dependence in terms of the $p_{T}$,
$\eta$, and transverse vertex position ($r$) of the track CMS:2014pgm . From
figure 8 of this article, one can see that above $p_{T}>1$ GeV one can
consider the tracking efficiency independent of $p_{T}$ and to a lesser
extent, of $\eta$. Regarding $r$, the efficiency diminishes with the
displacement distance, as can be seen from figure 12 of CMS:2014pgm , which is
obtained from a $t\bar{t}$ sample at $\sqrt{s}=7$ TeV. The figure shows the
cumulative efficiency for each of the iterations (0-5) of the tracking
algorithm. While this effect is less relevant for lifetimes of few
millimeters, it has an impact for the benchmark point with $c\tau_{D}=25$ mm
and for larger lifetimes.

Nonetheless, it is clear that since the tracking efficiency is a very
complicated function that can only be reliable obtained from having access to
the full detector simulation (and detector information) we will pursue four
different parametrizations for $\epsilon_{\rm trk}(r)$

  * •

Use the reported value of Iteration 5 from figure 12 of CMS:2014pgm .
[$It_{5}$]

  * •

Use the reported value of Iteration 4 from figure 12 of CMS:2014pgm .
[$It_{4}$]

  * •

Consider that tracks with at least one hit in the inner detector are
reconstructed with 100 % efficiency, and with 0 % if not: $\epsilon_{\rm
trk}(r)=\Theta(r-102~{}{\rm mm})$. [$R$].

  * •

Consider $\epsilon_{\rm trk}(r)=1$, to illustrate the typical deviation
obtained when no efficiency is considered. [$A$]

Regarding the impact parameter smearing, we note that for jets originating
from SM quarks, one can expect to have $\langle IP_{\mathrm{2D}}\rangle=0$, if
the majority of the tracks of the light jet are prompt. However, the value of
zero is obviously fictitious once the transverse impact parameter has been
smeared to account for reconstruction effects. While the smearing functions
have a non-trivial dependence with the $\eta$ and $p_{T}$ of the corresponding
track (the resolution $\sigma_{r}$, which we have taken from figures 14a and
15a of CMS:2014pgm ), the typical resolution would be of about 50 ${\rm\mu}$m,
and hence the $\langle IP_{\mathrm{2D}}\rangle$ variable would peak around
this value for SM light-quark jets.

Figure 3:  Comparison between the CMS published simulations and our Monte
Carlo setup, for $\langle IP_{\mathrm{2D}}\rangle$ (left) and
$\alpha_{\mathrm{3}D}$ (right) variables. For concreteness we only show the
results for the benchmark point of $m_{\mathrm{X}}=1$ TeV,
$m_{\pi_{\mathrm{D}}}=5$ GeV and $c\tau_{\pi_{\mathrm{D}}}=25$ mm, yet a
similar level of agreement between the CMS data and our simulation was found
for all benchmark points from CMS:2018bvr . We display results for the
tracking efficiency parametrizations $It_{5}$ (solid blue), $It_{4}$ (solid
orange), $R$ (solid green) and $A$ (dashed red). In the left panel, we include
as well the results for the QCD jets coming from the $X$ decays in dashed
purple.

We show our results for the $\langle IP_{\mathrm{2D}}\rangle$ and
$\alpha_{\mathrm{3}D}$ variables in Figure 3, where we present the results for
$A$ as dashed red, and for $It_{5}$, $It_{4}$ and $R$ in solid blue, orange
and green. From the left panel we see that the naive $A$ approach does not
describe the distribution as well as any of the other criteria, while the
three other curves fit the signal distribution with reasonable accuracy.
Moreover, we also see that the proper inclusion of the transverse impact
parameter smearing is necessary to explain the distribution of $\langle
IP_{\mathrm{2D}}\rangle$ for the QCD jets from the signal, which is displayed
as dashed purple.

From the right panel we see that the $\alpha_{\mathrm{3}D}$ distribution for
the signal does not change much with the different criteria $It_{5}$,
$It_{4}$, $R$ and $A$. Since on this variable one only applies a
$\alpha_{\mathrm{3}D}<0.25$ cut (see Appendix A) our attention is only in the
proper reproduction of the first bins, and the mismatch at the tails is not
relevant for us. Hence we delay the final judgement of which parametrization
of the tracking efficiency to use to the next step of our validation: to
reproduce the published $A_{i}$ efficiencies.

The analysis defined eight different jet identification criteria on the four
relevant variables to consider a jet as _emerging_. These criteria are
supplemented by the requirement to have a minimum of two EJs , or one EJ jet
with large transverse missing energy (MET), and by additional cuts on $H_{T}$
and on the $p_{T}$ of the four hardest jets. The combination of the EJ
criteria and the additional cuts define seven _selection sets_. The explicit
requirements are collected in Appendix A, together with the 95 % C.L. limit to
the number of signal events in each selection set, $S_{95}^{i}$.

###  3.3 Reproducing efficiencies and exclusion limits

If our interest would be to perform a reinterpretation of the emerging jets
results in the context of the _same_ model used by the collaboration (or one
with a similar topology) then we could employ the reported acceptances $A_{i}$
to derive the published limits, as we did in Section 3.1. We stress that our
goal is to perform a flexible reinterpretation of this search, namely to
employ it to derive limits on a model that the search has not considered.
Hence, what we need is to fully validate our pipeline to compute the
acceptance of the selection sets for the benchmark model used in the CMS
study. We show in Figure 4 the ratio of our computed acceptances over the
published CMS results in the left panels (the color bar indicate the $A_{i}$
value from CMS) and the obtained exclusion limits in the right panels, where
we have employed the $It_{5}$ (upper row), $It_{4}$ (middle row) and $R$
(lower row) parametrization of the tracking efficiencies. We can see that the
best agreement is obtained with the $R$ parametrization, while the other two
tend to overestimate the efficiencies. We see that we have agreement up to
20-30 % for large masses in the iteration $R$, which degrades for lower masses
and also extreme lifetime values, where the overall acceptances are
nonetheless at the per-mille level or lower. We also note that the $R$
parametrization also gives an acceptable exclusion limit, and hence we decide
to adopt it for the rest of the article. We note that with more examples
provided by CMS (or simply by providing the efficiencies in all signal
regions) one could attempt a more complex parametrization of the efficiency.

a

Figure 4:  Ratio of our $A_{i}$ over those reported by CMS, for
$m_{{\pi}_{D}}=5$ GeV (left panels) and 95 % exclusion limits (right panels)
in the $m_{X}-c\tau$ plane. The tracking efficiency parametrization $It_{5}$,
$It_{4}$ and $R$ have been used for the upper, middle and lower panels,
respectively. In the left panel the colored bar indicates the value of $A_{i}$
and the displayed indicates the ratio of our $A_{i}$ normalized to the CMS
one. In the right panel we show several exclusion limits: the CMS published
one (solid black), the one obtained using $A_{i}$ CMS efficiencies with NLO
predictions from figure 1 (dashed green), as well as those derived using our
$A_{i}$ with LO (dashed pink) and NLO (solid pink) cross sections. Both
$It_{4}$ and $It_{5}$ tend to overestimate the acceptance (hence the exclusion
limit), while the $R$ criteria reproduces better the exclusion curves. The
disagreement is larger for the regions of lower masses and/or large lifetime,
where the $A_{i}$ are below the per-mille level.

We consider hence this search as validated, and will proceed in the next
section to derive bounds on the parameter space of Exotic Higgs decays. Our
analysis code that allows us to derive the exclusions have been uploaded to
the LLP Recasting Repository LLPrepo , making it publicly available to
facilitate the reinterpretation of the emerging jets search for arbitrary
models. Further instructions and the relevant documentation to run the code
can be found in the Repository.

##  4 Reinterpretation for Higgs mediated dark showers

When the SM Higgs $h$ couples to the dark quarks the expected number of signal
events reads

$N_{S}^{i}(m_{\pi_{\mathrm{D}}},c\tau_{\pi_{\mathrm{D}}})=\sigma^{{\rm
proc}}_{\rm SM}\times{\rm BR}(h\to Q_{D}Q_{D})\times
A_{i}(m_{H},c\tau_{\pi_{\mathrm{D}}},m_{\pi_{\mathrm{D}}})\times{\cal L}\,,$
(5)

where now the only free physical parameters are the dark pion mass and its
lifetime, and the exotic Higgs branching ratio into dark quarks.

To further define our framework, we need to select a decay portal for our dark
mesons. We follow here the proposal of reference Knapen:2021eip  and we
consider the gluon, vector, Higgs and dark-photon portals.777It is obvious
that the photon portal, where $\pi_{D}\to\gamma\gamma$, does not pass the
emerging jet selection cuts. Hence this decay portal is not further considered
here. We have verified our implementation of these decay portal benchmarks by
reproducing the dark meson multiplicities from reference Knapen:2021eip .888We
are indebted to Simon Knapen for useful communication during the validation
phase. We start by analyzing the acceptance $A_{i}$ as a function of the dark
pion lifetime and masses, for the gluon decay portal, for all five considered
production Higgs mechanisms, which we show in figure 5. It is worth mentioning
here that we do expect the EJ search not to be optimal for Higgs decays into
dark quarks, as it originally targets two quarks and two dark quarks, while
the Higgs decay would only give at parton level two dark quarks. However,
since we are keeping the $\rho_{D}\to\pi_{D}\pi_{D}$ channel open, and since
there is additional radiation from the initial state gluons and from the decay
portals themselves, we do still obtain acceptances on the $10^{-4}$ range,
which can suffice to obtain an exclusion given that with 16.1 fb-1, ${\cal
O}(10^{6})$ Higgs bosons would be produced at the 13 TeV LHC via gluon-fusion.

Figure 5: Maximum acceptance shown as a function of $c\tau_{\pi_{\mathrm{D}}}$
(left) and $m_{\pi_{\mathrm{D}}}$ (right) in the Gluon Portal decay Benchmark
for the Higgs production through Gluon Fusion (GF, solid), associated
production with a Z,W boson (ZH: dot-dashed, WH: dotted), Vector Boson Fusion
(VBF, dashed) and associated production with a $t\bar{t}$ pair (dashed with
dots).

From the figure we can see that the dependence in $c\tau_{\pi_{\mathrm{D}}}$
is non trivial, obtaining a maximum around 10 mm, while for
$m_{\pi_{\mathrm{D}}}$ the dependence is quite flat, except for the heavier
masses of 20-30 GeV: those dark pions obtain a reduced boost from the Higgs
compared to lighter ones. It is intriguing to see that, owing to the
additional radiation, the $ttH$ production has a higher acceptance, about an
order of magnitude larger than gluon fusion, and about a factor of five larger
than associated production with a vector boson. We note that vector fusion has
the lowest acceptance, and this is due to the fact that the additional
radiation in VBF goes in the forward direction, while the EJ analysis focuses
on central jets. We stress that while we only show the gluon portal decay
benchmark here, all the other portal decay models show an analogous behaviour.

The picture changes slightly once the production cross sections for each
mechanism is considered, which is shown in figure 6. Here we multiply the
maximum acceptance with the production cross section for each mechanism, and
the total luminosity of the emerging jet search (16.1 fb-1). Hence the y-axis
directly displays the expected number of events for each production mode. We
have added here the overall number of events obtained by summing over all
possible production modes, in a dashed-brown line. We see now, that owing to
the larger cross section of the GF mechanism (two orders of magnitude over
$ttH$, factors of 15-25 for the modes involving gauge bosons), the overall
number of events, $A\sigma{\cal L}$, is larger by an order of magnitude
compared to the other modes. We also see that the impact of including all
decay modes instead of only gluon fusion amounts to about 20 % of the total
number of events. In view of our findings we will focus from now on only on
the dependence of our results with the lifetime for a $m_{\pi_{\mathrm{D}}}=5$
GeV mass, and we will also include all Higgs production modes in our study.

Figure 6: Maximum acceptance times production cross section times the total
integrated luminosity of the EJ search (16.1 fb-1) shown as a function of
$c\tau_{\pi_{\mathrm{D}}}$ (left) and $m_{\pi_{\mathrm{D}}}$ (right) in the
Gluon Portal decay Benchmark for the Higgs production through Gluon Fusion
(GF, solid), associated production with a Z,W boson (ZH: dot-dashed, WH:
dotted), Vector Boson Fusion (VBF, dashed) and associated production with a
$t\bar{t}$ pair (dashed with dots).

We study now the sensitivity for the different decay portals considered in ref
Knapen:2021eip . To that end we present in figure 7 the efficiencies as a
function of the dark pion lifetime, for $m_{\pi_{\mathrm{D}}}=$ 5 GeV. In
order to obtain reliable estimates for these acceptances, we have simulated
$10^{7}$ Monte Carlo events per parameter space point.

Figure 7: Acceptance for the different decay portals, for the gluon fusion
production mode. We see that the gluon and dark photon portal have similar
efficiencies, which are higher than those from the Higgs and vector portal,
the latter pair also having similar efficiencies for the displayed mass. The
acceptancres peak at a lifetime of about 10 mm.

Of the possible decay portals, we then find that the sensitivity is larger
(and similar) for the dark photon and gluon portals, and lower (and similar)
for the vector and Higgs portals. We then will select in what follows the
gluon (G) and Higgs (H) decay portals, as they correspond to the extreme
values for the efficiencies for the four portal scenarios considered. These
two decay portals correspond to the following operators

$\pi_{D}G^{\mu\nu}\tilde{G}_{\mu\nu}\qquad{\rm(G)},\qquad\pi_{D}H^{\dagger}H\qquad{\rm(H)}\,.$
(6)

In the gluon portal one expects a showered enriched with SM hadrons produced
from the produced gluons, while in the Higgs portal the decays would follow a
Yukawa-like structure, and one can expect a shower enriched with heavy flavour
quarks.

Using the acceptance from figure 7, we show in figure 8 the excluded exotic
Higgs branching ratio as a function of the lifetime, for a dark pion mass of 5
GeV. The solid line is using the existing dataset from the EJ search (16.1
fb-1). For comparison we show the ATLAS limit of 0.21, which was obtained with
a 8 times larger dataset (139 fb-1), shown in red dashed. For a fair
comparison we rescale our EJ limit to this luminosity (dashed lines), assuming
that the uncertainty is dominated by the statistical error, which given the
event counts in the different signal regions, and the reported systematic
errors, is a good approximation. We also include constraints from prompt
searches using CheckMATE2 for prompt Dercks:2016npn  and long-lived searches
Desai:2021jsa , shown in dashed grey (green) for the gluon (Higgs) portal.
These constraints come from prompt searches including missing energy from
ATLAS, more concretely from ATLAS:2019lng ; ATLAS-CONF-2020-048 , using 139
fb-1 of data: as the lifetime of the dark pions become large, many of them
appear as missing transverse energy. We note that our benchmark choice for
$m_{\pi_{\mathrm{D}}}=5$ GeV correspond to a challenging phase space due to
the softness of the decay products, otherwise it is clear that for heavier
dark pion masses constraints from other searches would apply. One prominent
example would be the $Zh$ production, with $h$ decaying through light scalars
or pseudoscalars into displaced jets ATLAS:2021jig ; CMS:2021yhb , which
report meaningful bounds on the exotic branching fraction for pseudoscalar
masses as light as 15 GeV. Finally, we include an estimation of the HL-LHC,
for both the BSM Higgs branching ratio (taken from Cepeda:2019klc ) and for
the statistic dominated approximation of the EJ search. It is worth stressing
that the HL-LHC run would not be similar to the current LHC setup in terms of
capabilities to deal with long-lived particles (cite some HL-LHC
expectations), significantly improving in many aspects, hence these limits
must be considered with a grain of salt (also the statistical dominance of the
study might not be fully justified).

Figure 8: 95 % C.L limits on ${\rm BR}(h\to q_{D}q_{D})$ obtained by
reinterpreting the CMS emerging jet search, for the gluon portal and the Higgs
portal as a function of $c\tau_{\pi_{\mathrm{D}}}$ with
$m_{\pi_{\mathrm{D}}}=5$ GeV (left) and as a function of
$m_{\pi_{\mathrm{D}}}$ with $c\tau_{\pi_{\mathrm{D}}}=25$ mm (right). The
solid lines use the existing data, with a luminosity of 16.1 fb-1, which
correspond to the dataset of the current emerging jet search. The bounds from
existing prompt searches, obtained with CheckMATE2 Dercks:2016npn  are shown
as a hatched grey (green) region for the Higgs (gluon) portal. The dashed
lines correspond to 139 fb -1, the luminosity used on the current model-
independent exclusions on undetected (also called “BSM”) Higgs branching
ratios from ATLAS and CMS, while the dotted lines correspond to the projection
to 3000 fb -1, which we compare with the HL-LHC reach of the BSM Higgs
branching ratios, shown with a red band that encapsulates the different
assumptions on the systematic uncertainties (see main text for details).

From the figure we see that the EJ search can obtain better bounds than the
model-independent BSM branching fraction, for lifetimes in the 5-60 (7-50) GeV
when using the combined production (gluon fusion production) for the Higgs
portal decay benchmark. For the sake of illustration we will describe now the
bounds on this model, but the behaviour would be similar for other decay
portals. Prompt searches with missing energy can constrain large lifetimes
($c\tau\gtrsim 400$ mm). For clarity reasons we have refrained from showing
HL-LHC extrapolations from CheckMATE, but they would only be more sensitive
than the BSM Higgs study for lifetimes in the 300-700 mm range, with the exact
value depending on the final HL-LHC limit. Nonetheless, the phenomenological
picture is similar to the one with the current dataset: for low lifetimes the
BSM Higgs limit dominates, in an intermediate regime the EJ reinterpretation
takes over, and for longer lifetimes the BSM Higgs searches become more
sensitive, with missing energy searches becoming relevant for long-lifetimes.
As stressed before, exotic Higgs decays are not a target of the EJ analysis,
and hence it would be interesting to consider the use of emerging jet taggers
in other production modes. We leave this option for future work.

##  5 Conclusions and Outlook

In this work we have performed detailed studies focused on the
reinterpretation of the CMS emerging jet search. This signature belongs to the
class of signatures that are collectively dubbed as “dark showers”, which stem
from having a strongly-interacting dark (secluded) sector. In this dark sector
new matter (and gauge) fields are added, which are assumed to hadronize, like
in the SM strong sector. In particular, emerging jets correspond to the case
where the dark sector mesons are have macroscopically appreciable decay
lenghts, which make these final states also fall in the class of exotic
phenomena dubbed “long-lived particles” (LLPs).

Our reinterpretation procedure has been validated by carefully following the
CMS study. We have obtained good agreement with the published distributions on
the $\langle IP_{\mathrm{2D}}\rangle$ and $\alpha_{\mathrm{3}D}$ variables,
and also reproduced the publicly available efficiencies for the benchmark
model employed in the search. We have reproduced the published exclusion
limits through two different routes, one by employing directly the CMS
published efficiencies and another one by computing the efficiencies ourselves
through our own Monte-Carlo simulation. Here there is a large uncertainty in
the exact parametrization of the tracking efficiency. We have attempted a few
different parametrizations, and employed the one that, while possibly over-
simplified, can reproduce the published efficiencies (and exclusion limits)
with a reasonable accuracy.

We would like to stress that while the relevant information of the CMS study
was publicly available and clearly explained, getting in contact with the
authors of the experimental study was nonetheless needed in order to
comprehend a few crucial details. Their response has been instrumental to
understand details concerning the track efficiency and the impact parameter
smearing used in the study. Since it would be desirable that a
reinterpretation of an experimental study can be done without this contact (as
it can happen that the main authors of a given analysis might not be always
part of the collaboration), we also took the opportunity to comment in the
text for which aspects a clarification was needed, and which additional
material would have helped us to carry our the reinterpretation.

Using our validated pipeline, we have focused on the exploration of a SM Higgs
boson decaying into two dark quarks (fermions charged solely under the new
strong sector, akin to the SM quarks). To that extent, we have considered the
inclusive production of the Standard Model Higgs from gluon fusion, Higgs-
strahlung, vector-boson-fusion and associated production with a $t\bar{t}$
pair, and analyzed four decay benchmark portal models proposed in
Knapen:2021eip , which are dubbed gluon, dark photon, Higgs and vector
portals. We have found that, while the efficiencies for the Higgs production
rank in the 10-3:-5 range, owing to the large production cross section we can
obtain meaningful bounds in the relevant parameter space, which are
competitive with the current exclusion on _undetected_ Higgs branching ratio
of 16 %, set by the ATLAS and CMS collaborations. We have checked, with the
help of CheckMATE, that the existing prompt searches can bring meaningful
bounds only for the large lifetime regime,
$c\tau_{\pi_{\mathrm{D}}}\gtrsim{\cal O}(100{\rm mm})$. We have also
considered the existing HL-LHC extrapolations for the _undetected_ Higgs
branching ratio, and compared them with a similar naive extrapolation of the
emerging jet search sensitivity (relying only on statistical uncertainties
being present). Yet, it is expected that the HL-LHC will have a number of
improvements to detect long-lived particles, which could render the final
projections better than our naive extrapolations.

As a byproduct of our analysis, we have made publicly available our Pythia 8
analysis code in the LLP Recating Repository LLPrepo , which can be used to
compute the experimental acceptance (and the exclusion limits) with arbitrary
BSM models, provided they are implemented in Pythia8.

We would like to stress that the exotic Higgs decay exclusion from
ATLAS:2019nkf  is an indirect bound, based on a global fit to the observed
Higgs properties. Hence, if a signal is detected, its characterization would
require an independent study. In contrast, if the emerging jet search starts
seeing an excess, one can already infer that a new long-lived object is being
produced from a Higgs boson decay, information that is crucial for the proper
characterization of a putative BSM signal.

We end by noting that the EJ requirements of having four hard jets do not
precisely target the exotic decays of a SM Higgs boson. In spite of the
analysis not being optimal, we see that we can exclude exotic branching ratio
of 30 % in the gluon and dark photon decay portals, which can go down to the
percent level for HL-LHC. Therefore, it might be worthwhile to explore EJ
searches that focus on dark quark decays from a SM Higgs boson (or from a new
scalar), which could have higher sensitivity than the model independent search
for undetected Higgs branching ratios.

### Acknowledgements

We would like to thank Juliette Alimena, Nishita Desai, Alberto Escalante del
Valle, Simon Knapen, Emmanuel Francois Perez and Pedro Schawaller for useful
discussions, and Baibhab Pattnaik for a careful reading of the manuscript. We
are indebted to the authors of the CMS emerging jet analysis: Alberto Belloni,
Yi-Mu Chen, Sarah Eno and Long Wang for their patience to answer our questions
about technical details in their study. JC and JZ are supported by the
Generalitat Valenciana (Spain) through the plan GenT program
(CIDEGENT/2019/068), by the Spanish Government (Agencia Estatal de
Investigación) and ERDF funds from European Commission
(MCIN/AEI/10.13039/501100011033, Grant No. PID2020-114473GB-I00).

##  Appendix A CMS emerging jets

In this Appendix we include additional material from our CMS validation
described in 3.

The CMS collaboration employs four variables to identify emerging jets in both
signal and background regions, which have been defined in section 3.2. For the
six signal regions, the specific requirements on each of these variables are
shown in Table 1.

Group |  $PU_{\mathrm{dz}}$ > … cm |  $D_{\mathrm{N}}$ < … |  $\langle IP_{\mathrm{2D}}\rangle$ > … cm |  $\alpha_{\mathrm{3}D}$ < …
---|---|---|---|---
EMJ-1 | 2.5 | 4 | 0.05 | 0.25
EMJ-2 | 4.0 | 4 | 0.10 | 0.25
EMJ-3 | 4.0 | 20 | 0.25 | 0.25
EMJ-4 | 2.5 | 4 | 0.10 | 0.25
EMJ-5 | 2.5 | 20 | 0.05 | 0.25
EMJ-6 | 2.5 | 10 | 0.05 | 0.25
Table 1: CMS requirements to tag a given jet as “emerging”. The variables are
defined in the main text.

Based on these requirements, CMS further defines signal regions (called “sets”
in the CMS paper), where a given EMJ criteria is accompanied by a set of cuts
on the jets, requiring either two emerging jets, or one emerging jet plus
large missing transverse energy. The event yield excluded in each signal
region at the 95 % C.L. by CMS is shown in the rightmost column, $S_{95}$.

Set # | $H_{T}$ | $p_{T}(1)$ | $p_{T}(2)$ | $p_{T}(3)$ | $p_{T}(4)$ | $p_{T}^{\rm miss}$ | $n_{\mathrm{E}MJ}>=$ | EMJ group | $S_{95}$
---|---|---|---|---|---|---|---|---|---
1 | 900 | 225 | 100 | 100 | 100 | 0 | 2 | 1 | 36.7
2 | 900 | 225 | 100 | 100 | 100 | 0 | 2 | 2 | 14.6
3 | 900 | 225 | 100 | 100 | 100 | 200 | 1 | 3 | 15.6
4 | 1100 | 275 | 250 | 150 | 150 | 0 | 2 | 1 | 15.1
5 | 1000 | 250 | 150 | 100 | 100 | 0 | 2 | 4 | 35.3
6 | 1000 | 250 | 150 | 100 | 100 | 0 | 2 | 5 | 20.7
7 | 1200 | 300 | 250 | 200 | 150 | 0 | 2 | 6 | 5.61
Table 2: Signal regions defined in the Emerging Jet study by CMS. The $S_{95}$
column indicates the 95 % C.L on the expected amount of signal events, which
we employ for limit setting.

The information from these tables has been included in the companion code
uploaded to the LLP Recasting Repository LLPrepo . We have also collected
there the details on the different tracking efficiency parametrization
employed in this work.

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It is a pleasure to thank the two anonymous referees for their feedback, which
greatly improved the content and clarity of the paper.

A.Y.Q.H. would like to thank Eliot Quataert, Dong Lai, Jim Cordes, and Sterl
Phinney for discussions on the physical origin of and and its flares; Shami
Chatterjee and Dillon Dong for advice on VLA calibration and imaging; Brad
Cenko for assistance with Swift observations; Murray Brightman and Brad Cenko
for assistance with Chandra data reduction; Kimberly Ward-Duong, Kate
Follette, Sarah Betti, Jada Louison, Jingyi Zhang, Raffaella Margutti, and
Ryan Chornock for assistance with Keck target-of-opportunity (ToO)
observations; Ilsang Yoon for advice on ALMA calibration and imaging; and Adam
Miller for discussions about optical time-series analysis. P. C. would like to
thank Yuri Beletsky for his assistance in remote observations with the
Magellan telescope. S. Schulze acknowledges support from the G.R.E.A.T.
research environment, funded by Vetenskapsrådet, the Swedish Research Council,
project number 2016-06012. VSD, ULTRASPEC, and ULTRACAM are funded by the UK’s
Science and Technology Facilities Council (STFC), grant ST/V000853/1. S.J.S.
acknowledges funding from STFC grants ST/T000198/1 and ST/S006109/1. This work
was funded by ANID, Millennium Science Initiative, ICN12_009. We thank Lulin
staff H.-Y. Hsiao, C.-S. Lin, W.-J. Hou, H.-C. Lin, and J.-K. Guo for
observations and data management. M.W.C. acknowledges support from the U.S.
National Science Foundation (NSF) with grants PHY-2010970 and OAC-2117997.
L.G., C.P.G, and T.E.M.B. acknowledge financial support from the Spanish
Ministerio de Ciencia e Innovación (MCIN), the Agencia Estatal de
Investigación (AEI) 10.13039/501100011033, the European Social Fund (ESF)
“Investing in your future,” the European Union Next Generation EU/PRTR funds,
the Horizon 2020 Research and Innovation Programme of the European Union, and
by the Secretary of Universities and Research (Government of Catalonia), under
the PID2020-115253GA-I00 HOSTFLOWS project, the 2019 Ramón y Cajal program
RYC2019-027683-I, the 2021 Juan de la Cierva program FJC2021-047124-I, the
Marie Skłodowska-Curie and the Beatriu de Pinós 2021 BP 00168 programme, and
from Centro Superior de Investigaciones Científicas (CSIC) under the PIE
project 20215AT016, and the program Unidad de Excelencia María de Maeztu
CEX2020-001058-M. A.G.-Y.’s research is supported by the EU via ERC grant
725161, the ISF GW excellence center, an IMOS space infrastructure grant, a
GIF grant, as well as the André Deloro Institute for Advanced Research in
Space and Optics, The Helen Kimmel Center for Planetary Science, the
Schwartz/Reisman Collaborative Science Program, and the Norman E. Alexander
Family M Foundation ULTRASAT Data Center Fund, Minerva and Yeda-Sela; A.G.-Y.
is the incumbent of the The Arlyn Imberman Professorial Chair. Nayana A.J.
would like to acknowledge DST-INSPIRE Faculty Fellowship (IFA20-PH-259) for
supporting this research C.C.N. is grateful for funding from the Ministry of
Science and Technology (Taiwan) under contract 109-2112-M-008-014-MY3. M.N. is
supported by the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreement No. 948381)
and by funding from the UK Space Agency. E.O.O. acknowledges grants from the
ISF, IMOS, and BSF. F.O. acknowledges support from MIUR, PRIN 2017 (grant
20179ZF5KS) “The new frontier of the Multi-Messenger Astrophysics: follow-up
of electromagnetic transient counterparts of gravitational wave sources.” D.P.
is grateful to the LAST Observatory staff. M.P. is supported by a research
grant (19054) from VILLUM FONDEN. A.V.F.’s group at U.C. Berkeley received
financial support from the Christopher R. Redlich Fund, Gary and Cynthia
Bengier, Alan Eustace, Sanford Robertson, Clark and Sharon Winslow, Briggs and
Kathleen Wood, and many other donors. The work of D.S. was carried out in the
framework of the basic funding program of the Ioffe Institute No.
0040-2019-0025.

Based in part on observations obtained with the Samuel Oschin Telescope
48-inch and the 60-inch Telescope at Palomar Observatory as part of the Zwicky
Transient Facility project. ZTF is supported by NSF grants AST-1440341 and
AST-2034437 and a collaboration including current partners Caltech, IPAC, the
Weizmann Institute of Science, the Oskar Klein Center at Stockholm University,
the University of Maryland, Deutsches Elektronen-Synchrotron and Humboldt
University, the TANGO Consortium of Taiwan, the University of Wisconsin at
Milwaukee, Trinity College Dublin, Lawrence Livermore National Laboratories,
IN2P3, University of Warwick, Ruhr University Bochum, Northwestern University
and former partners the University of Washington, Los Alamos National
Laboratories, and Lawrence Berkeley National Laboratories. Operations are
conducted by COO, IPAC, and UW. The ZTF forced-photometry service was funded
under Heising-Simons Foundation grant #12540303 (PI: M. Graham).

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
made possible through contributions by the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society
and its participating institutes, the Max Planck Institute for Astronomy,
Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
Garching, The Johns Hopkins University, Durham University, the University of
Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration (NASA)
under grant NNX08AR22G issued through the Planetary Science Division of the
NASA Science Mission Directorate, NSF grant AST-1238877, the University of
Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory,
and the Gordon and Betty Moore Foundation.

This work has made use of data from the Asteroid Terrestrial-impact Last Alert
System (ATLAS) project. The Asteroid Terrestrial-impact Last Alert System
(ATLAS) project is primarily funded to search for near-Earth objects (NEOs)
through NASA grants NN12AR55G, 80NSSC18K0284, and 80NSSC18K1575; byproducts of
the NEO search include images and catalogues from the survey area. This work
was partially funded by Kepler/K2 grant J1944/80NSSC19K0112 and HST GO-15889,
and STFC grants ST/T000198/1 and ST/S006109/1. The ATLAS science products have
been made possible through the contributions of the University of Hawaii
Institute for Astronomy, the Queen’s University Belfast, the Space Telescope
Science Institute (STScI), the South African Astronomical Observatory, and The
Millennium Institute of Astrophysics (MAS), Chile.

The Liverpool Telescope is operated on the island of La Palma by Liverpool
John Moores University in the Spanish Observatorio del Roque de los Muchachos
of the Instituto de Astrofisica de Canarias with financial support from the UK
Science and Technology Facilities Council. Based in part on observations made
with ULTRASPEC at the Thai National Observatory, which is operated by the
National Astronomical Research Institute of Thailand (Public Organization).
Based in part on observations obtained with the Spectral Energy Distribution
Machine on the Kitt Peak 84-inch telescope (SEDM-KP). The SEDM-KP team thanks
the NSF and the National Optical-Infrared Astronomy Research Laboratory for
making the Kitt Peak 2.1 m telescope available. SEDM-KP is supported by the
Heising Simons Foundation under grant 2021-2612 titled “The SEDM Kitt Peak
Project,” and a collaboration including current partners Caltech, University
of Minnesota, the University of Maryland, Northwestern University, and STScI.

This work made use of data from the GROWTH-India Telescope (GIT) set up by the
Indian Institute of Astrophysics (IIA) and the Indian Institute of Technology
Bombay (IITB). It is located at the Indian Astronomical Observatory (Hanle),
operated by IIA. We acknowledge funding by the IITB alumni batch of 1994,
which partially supports operations of the telescope. Telescope technical
details are available online.[1] We thank the staff of IAO, Hanle and CREST,
Hosakote, that made these obervations possible. The facilities at IAO and
CREST are operated by the Indian Institute of Astrophysics, Bangalore. This
paper includes data gathered with the 6.5 m Magellan Telescopes located at Las
Campanas Observatory, Chile. Based on observations made with the Nordic
Optical Telescope, owned in collaboration by the University of Turku and
Aarhus University, and operated jointly by Aarhus University, the University
of Turku, and the University of Oslo, representing Denmark, Finland, and
Norway (respectively), the University of Iceland, and Stockholm University at
the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto
de Astrofisica de Canarias. This publication has made use of data collected at
Lulin Observatory, partly supported by MoST grant 108-2112-M-008-001. Based
partially on observations collected at the European Organisation for
Astronomical Research in the Southern Hemisphere, Chile, as part of ePESSTO+
(the advanced Public ESO Spectroscopic Survey for Transient Objects Survey).
ePESSTO+ observations were obtained under ESO program 108.220C (PI: Inserra).

Some of the data presented herein were obtained at the W. M. Keck Observatory,
which is operated as a scientific partnership among the California Institute
of Technology, the University of California, and NASA. The Observatory was
made possible by the generous financial support of the W. M. Keck Foundation.
The authors wish to recognise and acknowledge the very significant cultural
role and reverence that the summit of Maunakea has always had within the
indigenous Hawaiian community. We are most fortunate to have the opportunity
to conduct observations from this mountain.

GMRT is run by the National Centre for Radio Astrophysics of the Tata
Institute of Fundamental Research

The Submillimeter Array is a joint project between the Smithsonian
Astrophysical Observatory and the Academia Sinica Institute of Astronomy and
Astrophysics and is funded by the Smithsonian Institution and the Academia
Sinica. This paper makes use of the following ALMA data:
ADS/JAO.ALMA#2022.A.00010.T. ALMA is a partnership of ESO (representing its
member states), NSF (USA), and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO,
and NAOJ. The National Radio Astronomy Observatory is a facility of the NSF
operated under cooperative agreement by Associated Universities, Inc. Based in
part on observations carried out with the IRAM Interferometer NOEMA. IRAM is
supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain).

This work made use of data supplied by the UK Swift Science Data Centre at the
University of Leicester. The scientific results reported in this article are
based in part on observations made by the Chandra X-ray Observatory. This
research has made use of software provided by the Chandra X-ray Center (CXC)
in the application packages CIAO and Sherpa.

All authors reviewed the manuscript and contributed to the source
interpretation. A.Y.Q.H. identified the source; coordinated the follow-up
observations; performed radio, X-ray, and some optical data analysis;
performed the source analysis and modeling; and wrote the majority of the
manuscript. D.A.P. performed the optical image subtraction and photometry, and
contributed significantly to the follow-up campaign, the source analysis, and
the manuscript. P.C. observed the source with Magellan and LAST, made the
first flare identification, and assisted with follow-up observations and X-ray
data analysis. S.S. performed the host-galaxy analysis, assisted with Swift
data analysis, and performed follow-up observations with the NOT. V.D.
provided follow-up observations with ULTRACAM and ULTRASPEC. H.K., V.S., A.S.,
and V.B. performed follow-up observations and image reduction with the GIT and
the HCT. M.B. performed NOEMA follow-up observations and data reduction.
S.J.S. provided ATLAS and Pan-STARRS photometry. J.P.A., C.P.G., L.G., M.G.,
C.I., T.E.M., F.O., M.P., P.J.P, P.W., Y.W., and D.Y. are ePESSTO+ builders.
A.G.C. and S.B. are GIT builders. S.A. and S. P. enabled NARIT/TNT
observations. E.B., R.B., M.C., A.D., M.G., A.M., B.R., R.R., and A.W. are ZTF
builders. S.B., D.P., E.S., and N.S. are LAST builders. T.B. M.F., H.G., E.M.,
M.N., K.S., and S.S. assisted with Pan-STARRS data analysis. T.G.B., J.C.,
C.F., J.F., S.R.K., M.M.K., V.K., and M.S. assisted with Keck follow-up
observations. N.A.J. and P.C. performed uGMRT follow-up observations and data
analysis. T.-W.C., W.-P.C., C.-C.N., Y.-C.P., and S.Y. assisted with Lulin
observations and data reduction. K.K.D. observed with the P200. A.V.F.
assisted with Keck follow-up observations and thoroughly reviewed the
manuscript. A.G.-Y. assisted with LAST follow-up observations. K.H. assisted
with LT follow-up observations. T.M. contributed to Pan-STARRS and ePESSTO+
data analysis. E.O.O. assisted with LAST follow-up observations and performed
LAST data reduction and photometry. C.M.B.O. contributed to the source
analysis. G.P. performed SMA follow-up observations and data analysis. A.R.
performed CHIMERA observations and data reduction. R.R. created the SEDM2
robotic observing software. Y.S. performed KP84 observations. J.S. assisted
with NOT follow-up observations. D.S. performed the GRB search. Y.Y. helped
write the transient scanning code and assisted with X-ray observations.

The authors declare no competing interests.

Correspondence and requests for materials should be addressed to Anna Y. Q. Ho
(email: annayqho@cornell.edu).

The reduced optical photometric data of and are provided in Supplementary
Table 1 and Supplementary Table 2. Spectroscopy of AT2022tsd will be made
available via the WISeREP public database. Facilities that make all their data
available in public archives, either promptly or after a proprietary period,
include the VLA, the Liverpool Telescope, the W. M. Keck Observatory, the
Palomar 48-inch/ZTF, the Neil Gehrels Swift Observatory, _Chandra_ , and ALMA.
Additionally, all of the data required to reproduce the figures is available
in a public Github repository (see “Code Availability”).

The code and data used to perform the calculations and produce the figures for
this paper are available in a public Github
repository.gggwww.github.com/annayqho/AT2022tsd

Extended Data Figure 1: Optical spectra of and obtained with Keck/LRIS.
Spectra are binned using 3Å bins. Regions with identified narrow host-galaxy
emission lines, used to measure the best-fit redshift of $z=0.2564\pm 0.0003$,
are marked. Regions used to search for $z=0$ emission lines, as would be
expected from a foreground Galactic transient, are also marked.

a

b

Extended Data Figure 2: X-ray (0.3–10 keV) light curve of and . a Full light
curve with best-fit power law of $\alpha=-1.81\pm 0.13$, where $f_{\nu}\propto
t^{\alpha}$. Upper limits (3$\sigma$) are shown with open circles. b
Individual Chandra observations binned in time with 500 s bins. Diamonds show
an optical ($i$-band) flare detected with LRIS during one of the Chandra
observations. Error bars are 1$\sigma$ confidence intervals.

a

b

Extended Data Figure 3: Radio data of and . a Selected radio light curves and
SEDs from the VLA (15–45 GHz), NOEMA (77–207 GHz), and ALMA ($350$ GHz). Open
circles mark 5$\sigma$ upper limits, and dashed lines connect upper limits to
detections. Vertical shaded regions mark epochs of rest-frame radio SEDs.
Inset shows SED from late-time observations with the GMRT and VLA. Solid line
marks the $f_{\nu}\propto\nu^{5/2}$ power law expected from synchrotron self-
absorption, and dotted line marks the shallower $f_{\nu}\propto\nu^{1}$. b
Peak frequency ($\nu_{p}$) at a fixed time post-explosion ($\Delta t$) vs.
peak luminosity of extragalactic radio transients. Error bars are 1$\sigma$
confidence intervals. See Methods section 12 for additional details and data
sources.

Extended Data Figure 4: Collage of and flares, corrected for Milky Way
extinction. For ULTRASPEC, ULTRACAM, and KP84, open points are $<5\sigma$ and
filled points are $\geq 5\sigma$. The insets of the ULTRASPEC and ULTRACAM
light curves show 3 min and 1 min running averages, respectively. Error bars
are 1$\sigma$ confidence intervals. The cadence of the ULTRASPEC, ULTRACAM,
and KP84 light curves are 30 s, 20 s, and 120 s respectively, and the filled
points are  Extended Data Figure 5: Lomb-Scargle periodogram of the ULTRASPEC
flares. Each panel shows the periodogram for the flare itself, for a region of
the light curve with no significant detections (“noise”), and for the full
light curve (“all”). Horizontal dashed lines mark the power expected for a
false-alarm peak (with false-alarm probability 2.5%) under the assumption that
there is no periodicity present in the data, using a bootstrap simulation. The
only peaks higher than this threshold are from the cadence of the observation
(30 s, and an alias at half that value), from the overall flare width, and
from the duration of the observation. Extended Data Figure 6: Lomb-Scargle
periodogram of X-ray observations. Periodogram was constructed using the first
four epochs of Chandra X-ray data. The horizontal line shows the power
expected for a false-alarm peak (with false-alarm probability 2.5%) under the
assumption that there is no periodicity present in the data, using a bootstrap
simulation. The observed peaks arise from the 500 s sampling and aliases
(marked with vertical dotted lines). Extended Data Figure 7: The stellar mass
and star-formation rate (SFR) of and ’s host galaxy. For reference we show the
stellar mass and star-formation rate of other transient host galaxies[161],
including core-collapse supernovae[161], long-duration $\gamma$-ray
bursts[161], and luminous fast blue optical transients[28, 12, 11, 10, 7].
Error bars are 1$\sigma$ confidence intervals.

Extended Data Table 1: Summary of targeted flare searches. The number of exposures $N_{\mathrm{exp}}$, the total observing time $T_{\mathrm{exp}}$, the typical depth per exposure, and the number of flares detected are listed. For reference, we include the Magellan/IMACS observation in which flaring was first noticed. Telescope | Filters | $N_{\mathrm{exp}}$ |  $T_{\mathrm{exp}}$ (min) | Depth (AB mag) | # Flares
---|---|---|---|---|---
Magellan/IMACS | $g$ | 4 | 12 | 24.2 | 1
LT/IO:O | $gr$ | 134 | 265 | 22.6 | 1
NOT/ALFOSC | $gr$ | 15 | 20 | 23.5 | 1
NTT/ULTRACAM | $giru$ | 1981 | 660 | 22.3 | 1
TNT/ULTRASPEC | $gr$ | 1045 | 519 | 22.0 | 3
KP84/SEDM2 | clear | 60 | 120 | 22.7 | 1
NTT/EFOSC | $gr$ | 30 | 47 | 23.7 | 1
GIT | clear | 59 | 295 | 21.1 | 0
HCT | $R$ | 55 | 275 | 22.4 | 0
SLT | $r$ | 28 | 140 | 99.0 | 0
LOT | $g$ | 27 | 135 | 99.0 | 0
KeckI/LRIS | $giu$ | 16 | 71 | 24.8 | 2
P200/CHIMERA | $gr$ | 420 | 350 | 21.3 | 0
LAST | $G_{p}$ | 646 | 9312 | 20.0 | 0

Extended Data Table 2: Summary of and flare properties. We include time of brightest detection ($t_{\mathrm{peak,obs}}$), time interval in which 90% of the flux was measured ($T_{90}$), peak luminosity ($\nu L_{\nu}$ in the specified band), and total energy radiated $E_{\mathrm{rad}}$. Flares are defined as $\geq 5\sigma$ detections, verified visually, with an MJD after 59856.4 ($\Delta t_{\mathrm{obs}}=27\,$d). In cases with flares observed in multiple filters, quantities are calculated using the first filter listed. Note that, with the exception of the ULTRASPEC and ULTRACAM sequences, observations did not capture the start and end of the flare. $t_{\mathrm{peak,obs}}$ (MJD) | Telescope | Band |  $T_{90,\mathrm{obs}}$ (min) |  $L_{\mathrm{peak,obs}}$ (erg s-1) |  $E_{\mathrm{rad}}$ (erg)
---|---|---|---|---|---
59856.4122 | P48/ZTF | $r$ | – | $>4\times 10^{43}$ | –
59857.3403 | P48/ZTF | $i$ | – | $>8\times 10^{43}$ | –
59871.4392 | Keck1/LRIS | $gi$ | $>20$ | $>1\times 10^{43}$ | $>2\times 10^{46}$
59899.3533 | PS1/GPC1 | $w$ | 40 | $2\times 10^{43}$ | $4\times 10^{46}$
59909.3598 | PS1/GPC1 | $w$ | $>50$ | $>2\times 10^{43}$ | $>6\times 10^{46}$
59928.1951 | Magellan/IMACS | $g$ | 16 | $6\times 10^{43}$ | $6\times 10^{46}$
59929.8585 | LT/IO:O | $g$ | 10 | $4\times 10^{43}$ | $2\times 10^{46}$
59932.6580 | TNT/ULTRASPEC | $r$ | 19 | $5\times 10^{43}$ | $6\times 10^{46}$
59933.0822 | NTT/ULTRACAM | $rgu$ | 12 | $8\times 10^{42}$ | $3\times 10^{45}$
59933.2858 | KP84/SEDM2 | clear | $>15$ | $2\times 10^{43}$ | $>2\times 10^{46}$
59933.7107 | TNT/ULTRASPEC | $g$ | 7 | $2\times 10^{43}$ | $8\times 10^{45}$
59933.7556 | TNT/ULTRASPEC | $g$ | 78 | $3\times 10^{43}$ | $1\times 10^{47}$
59936.0720 | NOT/ALFOSC | $g$ | $>15$ | $>8\times 10^{42}$ | $3\times 10^{45}$
59937.1105 | NTT/EFOSC | $g$ | $>8$ | $>6\times 10^{42}$ | $2\times 10^{45}$
59942.4238 | Keck1/LRIS | $iu$ | – | $>3\times 10^{42}$ | –

Extended Data Table 3:  and flare duty cycle for different apparent-magnitude thresholds. We consider the date range MJD 59,856.41–59,942.43 (from the first flare detection to the last flare detection). $N_{\mathrm{exp}}$ is the number of exposures brighter than the given magnitude threshold, $T_{\mathrm{exp}}$ is the total exposure time, $T_{\mathrm{on}}$ is the total time with a flare detected, and the bounds are 97.5% confidence intervals (see Methods section 4) on the duty cycle $T_{\mathrm{on}}/T_{\mathrm{exp}}$.  Threshold (AB Mag) | $N_{\mathrm{exp}}$ |  $T_{\mathrm{exp}}$ (Minutes) |  $T_{\mathrm{on}}$/$T_{\mathrm{exp}}$ | Bounds
---|---|---|---|---
21.0 | 1271 | 1142 | 0.02 | [0.001, 0.1]
22.5 | 68 | 155 | 0.1 | [0.01, 0.6]
24.0 | 13 | 65 | 0.5 | [0.03, 1]

Object | Band |  $L_{\mathrm{flare}}$ (erg s-1) | Amp. | Duration | Persistence
---|---|---|---|---|---
_Unknown_
AT2022tsd (this paper) | 500 nm |  $10^{43}$–$10^{44}$ | $\gtrsim 100\times$ | 10–80 min |  $\gtrsim 100$ d
GRB 070610 (BH? NS?) | 800 nm |  $10^{35}$? | $\gtrsim 100\times$ | 10 s–mins | 5 d
NGC 1313 X-2 (ULX) | 0.3–10 keV | $10^{40}$ | $\sim 10\times$ | 10 min | –
_Neutron Stars_
SGR in M81/M82 (GF Spike) | 20 keV–10 MeV | $1.8\times 10^{47}$ | $\sim 10^{11}\times$ | 0.5 s | –
SGR 1806-20 (GF Tail) | 20 keV–10 MeV | $1.3\times 10^{42}$ | $\sim 10^{7}\times$ | 8 min | –
Crab (nanoshot) | 8 GHz | $10^{34}$ | $>1000\times$ | 2 ns | –
_Stellar-mass black holes_
GRS 1915+105 (XRB) | 2.2 $\mu$m | $\gtrsim 10^{36}$ | $\lesssim 10\times$ | 10 min | –
GRB 080319B (GRB) | 500 nm | $10^{50}$ | $>10\times$ | 40 s | 60 s
_Supermassive black holes_
AT2019ehz (TDE) | 0.3–10 keV | $10^{44}$ | $>10\times$ | 10 d | 70 d
Sagittarius A* | 2.1 $\mu$m | $10^{34}$ | $\lesssim 10\times$ | 30 min | –
M87 | 350 GeV | $10^{42}$ | $\gtrsim 10\times$ | Few days | –
S5 1803+784 (blazar) | 600 nm | $10^{46}$ | $10\times$ |  $\gtrsim 1\,$month | –
GSN 069 (QPE) | 0.4–1 keV | $10^{43}$ | $\gtrsim 10\times$ | 1 hr | –
ASASSN-14ko (TDE?) | 200–500 nm |  $10^{43}$–$10^{44}$ | $>10\times$ | 10 d | –
Supplementary Information Table 1: Summary of large-amplitude ($\gtrsim
10\times$) flares from representative literature objects. See Methods section
14 for additional details and data sources.

Supplementary Information Table 2: Host-galaxy photometry for and , not corrected for Milky Way extinction. Error bars are 1$\sigma$ confidence intervals. Survey | Filter | Brightness (AB mag)
---|---|---
PanSTARRS | $g$ | $21.32\pm 0.10$
PanSTARRS | $r$ | $20.59\pm 0.07$
PanSTARRS | $i$ | $20.67\pm 0.05$
PanSTARRS | $z$ | $20.87\pm 0.36$
PanSTARRS | $y$ | $20.14\pm 0.10$
Supplementary Information Figure 1: Best-fit host-galaxy properties of and . The observed host-galaxy photometry is shown as black data points, the observed host-galaxy spectrum is shown in grey, and the best-fit model is shown in blue. The shaded region indicates the region of the spectrum used in the prospector fit.  Supplementary Information Figure 2: SED of and at $\Delta t_{\mathrm{obs}}\approx 25\,$d post-discovery. X-ray data are shown with a photon index of $\Gamma=2.01$ across the Swift/XRT 0.3–10 keV bandpass. Lines mark power laws connecting the radio to submillimeter data (solid), and the millimeter to X-ray data (dashed). $t$ | $\Delta t$ | $t_{\mathrm{exp}}$ | Count Rate | $F_{X}$ | $L_{X}$
---|---|---|---|---|---
(UT) | (days) | (ks) | ($10^{-3}$ s-1) | ($10^{-14}$ erg s-1 cm-2) |  $(10^{43}$ erg s-1)
2022-10-04 09:17 | $22.65\pm 0.24$ | 3.64 | $10.43\pm 2.06$ | $53.17\pm 10.50$ | $11.43\pm 2.26$
2022-10-06 14:55 | $24.41\pm 0.22$ | 3.78 | $9.06\pm 1.85$ | $46.19\pm 9.44$ | $9.93\pm 2.03$
2022-10-08 02:17 | $25.65\pm 0.29$ | 2.47 | $8.46\pm 2.24$ | $43.14\pm 11.43$ | $9.28\pm 2.46$
2022-10-09 05:06 | $26.54\pm 0.29$ | 2.29 | $10.92\pm 2.91$ | $55.67\pm 14.84$ | $11.97\pm 3.19$
2022-10-10 09:47 | $27.31\pm 0.11$ | 2.37 | $5.07\pm 2.60$ | $25.85\pm 13.26$ | $5.56\pm 2.85$
2022-10-21 16:35 | $36.60\pm 0.42$ | 1.44 | $<11.89$ | $<60.63$ | $<13.04$
2022-10-24 09:25 | $38.57\pm 0.24$ | 1.04 | $<13.97$ | $<71.27$ | $<15.32$
2022-10-26 01:27 | $40.03\pm 0.37$ | 2.77 | $5.35\pm 1.88$ | $27.30\pm 9.56$ | $5.87\pm 2.06$
2022-11-06 01:21 | $48.65\pm 0.24$ | 4.39 | $1.86\pm 0.99$ | $9.50\pm 5.04$ | $2.04\pm 1.08$
2022-11-16 01:40 | $56.48\pm 0.11$ | 1.87 | $2.02\pm 1.57$ | $10.29\pm 8.01$ | $2.21\pm 1.72$
2022-11-17 07:44 | $57.61\pm 0.24$ | 1.96 | $3.60\pm 1.99$ | $18.38\pm 10.16$ | $3.95\pm 2.18$
2022-12-01 02:23 | $68.65\pm 0.32$ | 5.75 | $1.28\pm 0.78$ | $6.54\pm 3.99$ | $1.41\pm 0.86$
2022-12-15 00:09 | $79.78\pm 0.38$ | 2.97 | $<3.99$ | $<20.33$ | $<4.37$
2022-12-16 09:52 | $81.10\pm 0.58$ | 2.67 | $<4.50$ | $<22.97$ | $<4.94$
Supplementary Information Table 3: Swift XRT (0.3–10 keV) observations of and . The table includes epochs $\Delta t$ since discovery in the rest frame, exposure time $t_{\mathrm{exp}}$, flux $F_{X}$, and luminosity $L_{X}$. Error bars are 1$\sigma$ and upper limits are given as 3$\sigma$. $t_{\mathrm{start}}$ | $\Delta t$ | $t_{\mathrm{exp}}$ | $F_{X}$ | $L_{X}$
---|---|---|---|---
(UT) | (days) | (ks) | ($10^{-14}$ erg s-1 cm-2) |  $(10^{43}$ erg s-1)
2022-10-16 23:14 | 32.42 | 20 | $14.60^{+3.33}_{-3.22}$ | $3.14^{+0.72}_{-0.69}$
2022-10-27 21:54 | 41.13 | 20 | $10.46^{+2.78}_{-2.22}$ | $2.25^{+0.60}_{-0.48}$
2022-11-04 12:33 | 47.19 | 20 | $7.59^{+2.64}_{-2.40}$ | $1.63^{+0.57}_{-0.52}$
2022-11-22 05:26 | 61.27 | 20 | $9.17^{+3.14}_{-2.53}$ | $1.97^{+0.68}_{-0.54}$
2022-12-26 14:11 | 88.62 | 24 | $1.68^{+2.03}_{-0.92}$ | $0.36^{+0.44}_{-0.20}$
2022-12-29 07:06 | 90.77 | 16 | $2.48^{+4.98}_{-1.57}$ | $0.53^{+1.07}_{-0.34}$
2023-01-30 16:28 | 116.55 | 40 | $0.96^{+1.04}_{-0.51}$ | $0.21^{+0.22}_{-0.11}$
2023-07-11 03:37 | 244.09 | 16 | $0.66^{+0.54}_{-0.43}$ | $0.14^{+0.12}_{-0.09}$
2023-07-11 to 2023-07-16 | 244–248 | 40 | $0.38^{+0.15}_{-0.12}$ | $0.08^{+0.03}_{-0.03}$
Supplementary Information Table 4: Chandra X-ray Observatory 0.5–6 keV
observations of AT2022tsd. The table includes epochs $\Delta t$ since
discovery in the rest frame, exposure time $t_{\mathrm{exp}}$, flux $F_{X}$,
and luminosity $L_{X}$. Error bars are 1$\sigma$ confidence intervals. The
final row shows the stacked measurement from three observations conducted on
three different days.

Supplementary Information Table 5: Radio observations of AT2022tsd. Table includes epochs since discovery $\Delta t$ in the rest frame, observed frequency $\nu_{\mathrm{obs}}$, flux density $f_{\nu}$ of the source (if detected), and root-mean-square (RMS) of a region close to the source in the image. Start Date | $\Delta t$ | $\nu_{\mathrm{obs}}$ | $f_{\nu}$ | RMS | Telescope
---|---|---|---|---|---
(UT) | (days) | (GHz) | (mJy) | (mJy) |
2022-10-02 06:50:00 | 19.75 | 15.00 | $0.023$ | $0.004$ | VLA
2022-10-04 07:20:00 | 21.36 | 230.00 | – | $0.270$ | SMA
2022-10-04 22:07:00 | 21.85 | 77.26 | $0.283$ | $0.075$ | NOEMA
2022-10-04 22:07:00 | 21.85 | 92.74 | $0.245$ | $0.065$ | NOEMA
2022-10-10 08:02:00 | 26.16 | 45.00 | $0.127$ | $0.033$ | VLA
2022-10-10 08:02:00 | 26.16 | 22.00 | $0.038$ | $0.009$ | VLA
2022-10-10 08:02:00 | 26.16 | 15.00 | $0.031$ | $0.004$ | VLA
2022-10-10 08:02:00 | 26.16 | 33.00 | $0.086$ | $0.013$ | VLA
2022-10-10 21:16:00 | 26.59 | 134.76 | $0.212$ | $0.047$ | NOEMA
2022-10-10 21:16:00 | 26.59 | 150.24 | $0.232$ | $0.057$ | NOEMA
2022-10-11 00:45:00 | 26.71 | 77.26 | $0.239$ | $0.035$ | NOEMA
2022-10-11 00:45:00 | 26.71 | 92.74 | $0.284$ | $0.032$ | NOEMA
2022-10-11 02:53:00 | 26.78 | 207.26 | $0.574$ | $0.114$ | NOEMA
2022-10-11 02:53:00 | 26.78 | 222.74 | $0.551$ | $0.117$ | NOEMA
2022-10-12 02:50:00 | 27.57 | 77.26 | $0.298$ | $0.082$ | NOEMA
2022-10-12 02:50:00 | 27.57 | 92.74 | $0.316$ | $0.078$ | NOEMA
2022-10-13 23:24:00 | 29.05 | 77.26 | $0.170$ | $0.039$ | NOEMA
2022-10-13 23:24:00 | 29.05 | 92.74 | $0.179$ | $0.037$ | NOEMA
2022-10-14 02:04:00 | 29.14 | 134.76 | $0.277$ | $0.087$ | NOEMA
2022-10-14 02:04:00 | 29.14 | 150.24 | $0.411$ | $0.117$ | NOEMA
2022-10-19 04:29:00 | 33.20 | 350.50 | $0.313$ | $0.027$ | ALMA
2022-10-20 05:44:00 | 34.04 | 15.00 | $0.033$ | $0.004$ | VLA
2022-10-20 05:44:00 | 34.04 | 33.00 | $0.071$ | $0.010$ | VLA
2022-10-20 05:44:00 | 34.04 | 22.00 | $0.056$ | $0.007$ | VLA
2022-10-20 05:44:00 | 34.04 | 10.00 | $0.031$ | $0.004$ | VLA
2022-10-20 05:44:00 | 34.04 | 45.00 | $0.075$ | $0.021$ | VLA
2022-10-21 04:54:40 | 34.81 | 412.00 | $0.259$ | $0.038$ | ALMA
2022-10-22 03:52:39 | 35.57 | 242.00 | $0.300$ | $0.028$ | ALMA
2022-10-28 00:54:00 | 40.25 | 77.26 | $0.363$ | $0.113$ | NOEMA
2022-10-28 00:54:00 | 40.25 | 92.74 | $0.299$ | $0.093$ | NOEMA
2022-10-28 00:54:00 | 40.25 | 150.24 | $0.328$ | $0.037$ | NOEMA
2022-10-29 23:00:00 | 41.77 | 150.24 | $0.330$ | $0.040$ | NOEMA
2022-10-29 23:00:00 | 41.77 | 134.76 | $0.228$ | $0.028$ | NOEMA
2022-11-01 23:03:00 | 44.16 | 222.74 | $0.198$ | $0.052$ | NOEMA
2022-11-01 23:03:00 | 44.16 | 207.26 | $0.175$ | $0.048$ | NOEMA
2022-11-08 04:52:00 | 49.13 | 15.00 | $0.031$ | $0.004$ | VLA
2022-11-08 04:52:00 | 49.13 | 22.00 | $0.043$ | $0.006$ | VLA
2022-11-08 04:52:00 | 49.13 | 33.00 | $0.075$ | $0.008$ | VLA
2022-11-08 04:52:00 | 49.13 | 45.00 | $0.120$ | $0.015$ | VLA
2022-11-18 20:08:00 | 57.60 | 77.26 | $0.252$ | $0.039$ | NOEMA
2022-11-18 20:08:00 | 57.60 | 92.74 | $0.304$ | $0.030$ | NOEMA
2022-11-26 22:16:00 | 64.04 | 134.76 | $0.111$ | $0.030$ | NOEMA
2022-11-26 22:16:00 | 64.04 | 150.24 | $0.119$ | $0.032$ | NOEMA
2022-12-03 03:26:00 | 68.98 | 22.00 | $0.078$ | $0.007$ | VLA
2022-12-03 03:26:00 | 68.98 | 33.00 | $0.099$ | $0.009$ | VLA
2022-12-03 03:26:00 | 68.98 | 45.00 | $0.108$ | $0.018$ | VLA
2022-12-03 03:26:00 | 68.98 | 15.00 | $0.049$ | $0.004$ | VLA
2022-12-14 18:56:00 | 78.25 | 77.25 | $0.131$ | $0.028$ | NOEMA
2022-12-14 18:56:00 | 78.25 | 92.74 | $0.153$ | $0.024$ | NOEMA
2023-01-27 01:26:00 | 112.69 | 45.00 | – | $0.016$ | VLA
2023-01-27 01:26:00 | 112.69 | 33.00 | $0.052$ | $0.011$ | VLA
2023-01-27 01:26:00 | 112.69 | 15.00 | $0.048$ | $0.003$ | VLA
2023-01-27 01:26:00 | 112.69 | 22.00 | $0.048$ | $0.006$ | VLA
2023-03-04 12:14 | 141.70 | 1.27 | $0.140$ | $0.033$ | uGMRT
2023-03-05 12:14 | 142.50 | 0.65 | – | $0.195$ | uGMRT
2023-03-06 10:19 | 143.23 | 0.44 | – | $0.810$ | uGMRT
2023-03-23 13:19:00 | 156.86 | 77.25 | – | $0.045$ | NOEMA
2023-03-23 13:19:00 | 156.86 | 92.74 | – | $0.047$ | NOEMA
2023-03-31 08:10 | 163.06 | 1.37 | $0.131$ | $0.035$ | uGMRT
2023-04-01 10:05 | 163.92 | 0.65 | – | $0.165$ | uGMRT
2023-04-02 10:05 | 164.71 | 0.43 | – | $0.465$ | uGMRT
2023-04-05 23:00:00 | 167.53 | 6.00 | – | $0.009$ | VLA
2023-04-05 23:00:00 | 167.53 | 10.00 | $0.038$ | $0.009$ | VLA
2023-04-05 23:00:00 | 167.53 | 22.00 | – | $0.009$ | VLA
2023-04-05 23:00:00 | 167.53 | 3.00 | – | $0.018$ | VLA