OU-HEP-230701

Top squarks from the landscape at high luminosity LHC
Howard Baer1111Email<EMAIL_ADDRESS>, Vernon Barger2222Email:
<EMAIL_ADDRESS>Juhi Dutta1333Email<EMAIL_ADDRESS>
Dibyashree Sengupta3444Email<EMAIL_ADDRESS>and Kairui
Zhang2555Email<EMAIL_ADDRESS>
1Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma,
Norman, OK 73019, USA
2Department of Physics, University of Wisconsin, Madison, WI 53706 USA
3 INFN, Laboratori Nazionali di Frascati, Via E. Fermi 54, 00044 Frascati
(RM), Italy

Supersymmetric models with low electroweak finetuning are expected to be more
prevalent on the string landscape than finetuned models. We assume a fertile
patch of landscape vacua containing the minimal supersymmetric standard model
(MSSM) as low energy/weak scale effective field theory (LE-EFT). Then, a
statistical pull by the landscape to large soft terms is balanced by the
requirement of a derived value of the weak scale which is not too far from its
measured value in our universe. Such models are characterized by light
higgsinos in the few hundred GeV range whilst top squarks are in the 1-2.5 TeV
range with large trilinear soft terms which helps to push $m_{h}\sim 125$ GeV.
Other sparticles are generally beyond current LHC reach and the
$BR(b\rightarrow s\gamma)$ branching fraction is nearly equal to its SM value.
The light top-squarks decay comparably via $\tilde{t}_{1}\rightarrow
b\tilde{\chi}_{1}^{+}$ and $\tilde{t}_{1}\rightarrow t\tilde{\chi}_{1,2}^{0}$
yielding mixed final states of $b\bar{b}+\not\\!\\!\\!{E_{T}}$, $t\bar{b}/\
\bar{t}b+\not\\!\\!\\!{E_{T}}$ and $t\bar{t}+\not\\!\\!\\!{E_{T}}$. We
evaluate prospects for top squark discovery at high-luminosity (HL) LHC for
the well-motivated case of natural SUSY from the landscape. We find for HL-LHC
a $5\sigma$ reach out to $m_{\tilde{t}_{1}}\sim 1.7$ TeV and a 95% CL
exclusion reach to $m_{\tilde{t}_{1}}\sim 2$ TeV. These reaches cover most
(but not all) of the allowed stringy natural parameter space!

##  1 Introduction

The lightest supersymmetric (SUSY) partner of the top quark, the so-called
top-squark $\tilde{t}_{1}$, has for long been a lucrative target for
supersymmetry searches at hadron colliders. Early estimates of EENZ/BG[1, 2]
naturalness, using the measure $\Delta_{BG}\equiv
max_{i}|\frac{p_{i}}{m_{Z}^{2}}\frac{\partial m_{Z}^{2}}{\partial
p_{i}}|<\Delta_{BG}(max)$ (where the $p_{i}$ are taken as fundamental theory
parameters, usually assumed to be a set of high scale soft SUSY breaking
terms) found $m_{\tilde{t}_{1}}\lesssim 300-400$ GeV for
$\Delta_{BG}<10-30$[3]. Using an alternative measure $\delta
m_{h}^{2}/m_{h}^{2}<\Delta_{HS}$, it was expected that three third generation
squarks should all have mass $m_{\tilde{t}_{1,2},\tilde{b}_{1}}\lesssim 500$
GeV[4, 5, 6]. These theoretical naturalness computations may be compared to
recent limits from LHC searches where both ATLAS[7, 8] and CMS[9] find that
$m_{\tilde{t}_{1}}\gtrsim 1.2$ TeV from $pp$ collisions at $\sqrt{s}=13$ TeV
and with $\sim 139$ fb-1 of integrated luminosity. Taken at face value, this
confrontation between theory and experiment would indicate that the paradigm
of weak scale supersymmetry[10] is highly implausible as a route to physics
beyond the Standard Model (SM)[11].

One resolution to the supersymmetry naturalness conflict is that the early
theoretical naturalness calculations turned out to be large overestimates of
the actual finetuning[12, 13]. For the BG measure, it is emphasized in Ref.
[12, 14, 15, 13] that the fundamental theory parameters $p_{i}$ should not be
taken as a set of independent soft SUSY breaking terms, since in any more UV-
complete theory, these are all correlated. For example, in gravity-mediation
SUSY breaking models with a well-specified SUSY breaking sector, then the soft
terms are all computed as multiples of the gravitino mass $m_{3/2}$.111For
instance, in dilaton-dominated SUSY breaking, then $m_{0}=m_{3/2}$ with
$A_{0}=-m_{1/2}=\sqrt{3}m_{3/2}$[16]. Adopting independent soft terms as the
$p_{i}$ just parametrizes our ignorance of the SUSY breaking mechanism, but
can lead to overestimates of finetuning by up to three orders of
magnitude[13]. Alternatively, the $\Delta_{HS}$ measure attempts to tune
dependent quantities $m_{H_{u}}^{2}$ and $\delta m_{H_{u}}^{2}$ one against
the other, which again leads to up to three orders of magnitude overestimates
of finetuning[13]. If one instead adopts the more conservative electroweak
finetuning measure $\Delta_{EW}$[17, 18], then top-squark masses are allowed
up to several TeV at little cost to finetuning since their contributions to
the weak scale are suppressed by loop factors (for a recent review, see e.g.
Ref. [19]).

In most supersymmetric models of particle physics– even in the case of high
scale scalar mass universality– the lighter top squark $\tilde{t}_{1}$ is
expected to be the lightest of all the squarks. It thus presents a lucrative
target for supersymmetry discovery at hadron collider experiments such as the
CERN LHC. The lightness of the top squark, relative to other squarks, arises
from two reasons: 1\. the large top-quark Yukawa coupling $f_{t}$ acts to
drive top squark soft terms to lower values than other squarks (assuming an
initial degeneracy amongst all squark soft terms at the high scale) and 2\.
the large top Yukawa enhances the mixings amongst the top squarks, and large
mixing typically acts to further split the top squark eigenmasses, driving the
lighter one down and the heavier stop $\tilde{t}_{2}$ to larger values
(relative to the no mixing case).

A third effect arises from the string landscape picture[20, 21, 22]. In the
string landscape, where of order $10^{500}$ vacua solutions[23] arise from
compactification from 10 to 4 spacetime dimensions, then each vacuum solution
corresponds to a different set of $4-d$ low energy effective field theory law
of physics. The string landscape provides a natural setting for Weinberg’s
anthropic solution to the cosmological constant problem[24] in an eternally
inflating multiverse. If similar reasoning is applied to the origin of the
SUSY breaking scale, then it is expected that no particular value of the
(complex-valued) SUSY breaking $F$ terms or (real-valued) SUSY breaking
$D$-terms are favored over any other. In that case, then on rather general
grounds, the landscape is expected to statistically favor large soft terms via
a power law[25]

$f_{SUSY}\sim m_{soft}^{2n_{F}+n_{D}-1}$ (1)

where $f_{SUSY}$ encodes the expected statistical distribution of landscape
soft terms. Thus, even the textbook case of SUSY breaking via a single
$F$-term field would yield a linear draw to large soft terms.

Naively, one might expect such a distribution to favor high scale SUSY
breaking. However, the weak scale soft terms and SUSY-preserving $\mu$
parameter determine the magnitude of the weak scale via the scalar potential
minimization conditions under the radiative breaking of electroweak symmetry:

$m_{Z}^{PU2}=\frac{m_{H_{d}}^{2}+\Sigma_{d}^{d}-(m_{H_{u}}^{2}+\Sigma_{u}^{u})\tan^{2}\beta}{\tan^{2}\beta-1}-\mu_{PU}^{2}$
(2)

where the label $PU$ stands for parameter values in each separate pocket
universe within the greater multiverse. Here, following Weinberg, we assume a
so-called fertile patch of the multiverse wherein the low energy/weak scale
effective field theory (LE-EFT) consists of the MSSM (plus some additional
fields such as a PQ sector) but with variable soft terms and hence variable
values for the associated weak scale $m_{weak}^{PU}$. The value of
$m_{weak}^{PU}$ is typically $\neq m_{weak}^{OU}$, where $OU$ stands for a
quantity’s value in our universe. Agrawal et al. (ABDS)[26] have shown that
for complex nuclei– and hence atoms as we know them– to form in a PU, that the
value of $m_{weak}^{PU}$ must lie within the ABDS window, typically
$m_{weak}^{PU}\sim(0.5-5)m_{weak}^{OU}$ (the atomic principle). The ABDS
anthropic window thus vetoes vacua with improper electroweak symmetry breaking
(EWSB), such as solutions with no EWSB or charge or color breaking (CCB)
minima; it also excludes the vast majority of high scale SUSY solutions which
typically lead to $m_{weak}^{PU}$ far beyond the ABDS window. The string
landscape approach to soft SUSY breaking within the MSSM has led to some
success in that it statistically predicts a Higgs boson mass $m_{h}\simeq 125$
GeV whilst sparticles are typically well beyond current LHC search bounds[27].

Returning to top squarks, the large value of the top quark Yukawa coupling
enhances the radiative correction terms $\Sigma_{u}^{u}(\tilde{t}_{1,2})$ in
Eq. 2 relative to $\Sigma_{u}^{u}(\tilde{q}_{i})$ (where $\tilde{q}_{i}$
denotes squark masses of the first two generations. Thus, for independent soft
terms for each generation (as is generic in gravity mediation[28, 29, 16])
then the squark and slepton masses of the first two generations will get
pulled to much higher values, typically $m_{\tilde{q}_{i}}\sim 10-40$ TeV
(providing a mixed decoupling/quasi-degeneracy solution to the SUSY flavor and
CP problems[30]) whilst $m_{\tilde{t}_{1}}\sim 1-2.5$ TeV. As such, the string
landscape provides additional strong motivation for top-squark pair searches
at LHC as compared to other sparticle searches (although the search for light
higgsinos with $m(higgsino)\sim 100-400$ GeV is also especially lucrative[31,
32, 33, 34, 35, 36]).

In this paper, after a brief review of some previous relevant works in Subsec.
1.1, in Sec. 2 we will present landscape predictions for some of the relevant
properties of light top squarks as derived from string landscape predictions
with a simple $n=1$ power law draw to large soft terms. We will find that
while large stop mixing terms $m_{t}A_{t}$ are expected at the weak scale (and
indeed these help boost up the light Higgs mass to $m_{h}\sim 125$ GeV), the
lighter top squark $\tilde{t}_{1}$ is still typically mainly a right-top-
squark (assuming high scale degeneracy of left and right top squark soft terms
$m_{\tilde{t}_{L}}$ and $m_{\tilde{t}_{R}}$, as expected by intragenerational
degeneracy since the elements of each generation fill out the 16-dimensional
spinor-rep of $SO(10)$). Also, we will find that the branching fraction
$BR(b\rightarrow s\gamma)$ is expected to be very near its Standard Model (SM)
value (in agreement with data and in accord with the general expectation for
TeV-scale top-squarks). We will also determine the expected $\tilde{t}_{1}$
branching fractions which will determine the associated LHC search signatures.
In Sec. 3, we examine top-squark pair production rates and expected signal
channels which are expected for HL-LHC searches. In Sec. 4 we introduce a
natural top-squark benchmark point and associated model line. In Sec. 5, we
give cuts and $m_{T_{2}}$ distributions for each of the the three major signal
channels. By combining results, we present $5\sigma$ reach and 95%CL exclusion
limits versus $m_{\tilde{t}_{1}}$. In Sec. 6, we present a brief summary and
conclusions from our results.

###  1.1 A brief review of some previous relevant works

The first few papers on top-squark phenomenology focussed on the possibility
for $t\rightarrow\tilde{t}_{1}\tilde{\chi}_{i}^{0}$ decays which could disrupt
top-quark discovery signatures at the CERN S$p\bar{p}S$[37, 38] and Fermilab
Tevatron colliders[39]. Direct top-squark pair production at the Tevatron
within the framework of simplified models was already examined in Ref. [40]
shortly before the actual discovery of the top-quark. In Ref. [41], the
capability of LHC to measure the top-quark mixing angle $\theta_{t}$ was
examined: the strategy promoted was to as best as one can measure the various
top-squark branching fractions into different decay modes which depend on stop
mixing. In Ref. [42], the scenario of maximal stop mixing, which provides an
explanation for the rather high Higgs mass $m_{h}\simeq 125$ GeV, was examined
with a view towards resolving the apparent tension between naturalness and the
light Higgs mass. In Ref. [43], Graesser and Shelton examined top squark pair
production followed by mixed top-squark decay modes $\tilde{t}_{1}\rightarrow
b\tilde{\chi}_{1}^{+}$ with
$\tilde{t}_{1}^{*}\rightarrow\bar{t}\tilde{\chi}_{1}^{0}$ and suggested a new
search variable $t=$topness to aid in identifying top jets in the final state.
In Ref. [44], it is argued that conventional finetuning measures overestimated
the severeness of top-squark mass upper bounds and instead examined
implications of the $\Delta_{EW}$ measure for top-squark properties. Using
$\Delta_{EW}\lesssim 30$, then top squarks may range up to
$m_{\tilde{t}_{1}}\lesssim 3$ TeV provided there is a rather large weak scale
$A_{t}$ soft term mixing value which also elevates the Higgs mass
$m_{h}\rightarrow\sim 125$ GeV. Thus, there exists a significant portion of
natural SUSY parameter space that lies beyond ATLAS/CMS limits as displayed in
the $m_{\tilde{t}_{1}}$ vs. $m_{\tilde{\chi}_{1}^{0}}$ simplified model
parameter plane. In C. Han et al.[45], the authors recast various ATLAS/CMS
top squark search results into the $m_{\tilde{t}_{1}}$ vs.
$m_{\tilde{\chi}_{1}^{0}}$ top-squark search plane and compare against
naturalness using $\Delta_{EW}$. In Ref. [46], assuming
$\tilde{t}_{1}\rightarrow t\tilde{\chi}_{1}^{0}$ decay, Bai et al. impose a
very strong $\not\\!\\!\\!{E_{T}}$ cut against which two top jets merge. Cuts
on the resulting configuration boost signal over background by 40% over
conventional analyses.

In Ref. [47], the ATLAS Collaboration examined the reach of HL-LHC for top-
squark pair production followed by $\tilde{t}_{1}\rightarrow
t\tilde{\chi}_{1}^{0}$ in the top-squark search plane: for light
$m_{\tilde{\chi}_{1}^{0}}$, they find using LHC14 with 3000 fb-1 a $5\sigma$
reach to $m_{\tilde{t}_{1}}\sim 1.25$ TeV and a 95% CL exclusion to
$m_{\tilde{t}_{1}}\sim 1.7$ TeV. Similar results from CMS are shown in Ref.
[48].

##  2 Properties of top squarks from the landscape

###  2.1 Scan over landscape

In this Section, we wish to explore the predictions from the string landscape
for top squark properties. To this end, we will generate the distribution

$dN_{vac}=f_{SUSY}\cdot f_{EWSB}\cdot f_{cc}\cdot dm_{soft}$ (3)

where $dN_{vac}/dm_{soft}$ stands for the distribution of string vacua with
respect to the soft SUSY breaking parameters. We will assume a fertile patch
of the string landscape where the LE-EFT consists of the MSSM (possibly
augmented with a PQ sector which is only relevant for dark matter
considerations), but where in the string landscape the various soft terms

$m_{0}(1,2),\ m_{0}(3),\ m_{1/2},\ A_{0},\ \tan\beta,\ m_{A},\ \mu$ (4)

will scan independently[49]. (Note that while the soft terms would all be
correlated and hence dependent in our universe, as discussed earlier, they
should scan independently within the various pocket universes within the
greater multiverse.) The various independent soft terms scan as a power-law

$f_{SUSY}\sim m_{soft}^{2n_{F}+n_{D}-1}$ (5)

where $n_{F}$ is the number of hidden sector $F$-breaking fields (distributed
as complex numbers) and $n_{D}$ is the number of $D$-breaking fields
(distributed as real numbers). For simplicity, we will adopt the textbook case
$n_{F}=1$, a single $F$ breaking field, and $n_{D}=0$ so that $f_{SUSY}\sim
m_{soft}^{1}$, i.e. a linear statistical draw to large soft terms. We will
take the non-soft term $\tan\beta$ to scan uniformly and will fix the $\mu$
parameter to a natural value $\mu=200$ GeV. The cosmological constant
selection embedded in $f_{cc}$ does not impact the soft term selection as
emphasized by Douglas[25].

For the (anthropic) selection $f_{EWSB}$, we require the derived value of the
weak scale in each pocket universe to have 1. no charge or color breaking
minima (no CCB), 2. an appropriate breakdown of EW symmetry to $U(1)_{EM}$ and
3\. a derived value for the pocket universe lies within the ABDS window[26],
i.e. that $m_{weak}^{PU}\lesssim(0.5-5)m_{weak}^{OU}$. To be precise, in a
pocket universe with no finetuning, this corresponds to $\Delta_{EW}\lesssim
30$ since $m_{weak}^{PU}\sim m_{Z}\sqrt{\Delta_{EW}/2}$.

By combining the various effects in Eq. 3, we are able to obtain a measure of
what Douglas calls stringy naturalness[50, 51]. While stringy naturalness is
not measured by a number, we can measure it via a scan over SUSY model soft
terms in accord with Eq. 3. Here, we implement the $n\equiv 2n_{F}+n_{D}-1=1$
linear scan over the NUHM3[52] parameter space:

  * •

$m_{0}(1,2):0.1-45\ {\rm TeV}$,

  * •

$m_{0}(3):\ 0.1-10\ {\rm TeV}$,

  * •

$m_{1/2}:\ 0.5-3\ {\rm TeV}$,

  * •

$A_{0}:\ 0-(-20)\ {\rm TeV}$,

  * •

$\tan\beta:\ 3-60$ (uniform scan),

  * •

$m_{A}:\ 0.3-10\ {\rm TeV}$,

with $\mu$ fixed at a natural value of 200 GeV.222The SUSY conserving $\mu$
parameter arises from whatever solution to the SUSY $\mu$ problem is imposed.
For a review of twenty solutions to the SUSY $\mu$ problem, see Ref. [53]. For
each set of input parameters in the NUHM3 model, we use Isajet 7.88[54] to
compute the corresponding sparticle and Higgs boson masses and other
properties.

###  2.2 Top squark mass and mixing

Next, we wish to display properties of top squarks from probability
distributions reflecting stringy naturalness. After our landscape scan, we
display in Fig. 1 histograms of probability a) $dP/dm_{h}$ and b)
$dP/dm_{\tilde{t}_{1}}$. From frame a), we see that the stringy naturalness
prefers a light Higgs boson $h$ with mass between $120\ {\rm GeV}<m_{h}<126$
GeV with a peak at $m_{h}\sim 125$ GeV. This behavior arises due to maximizing
the soft terms that enter into the radiatively-corrected Higgs mass

$m_{h}^{2}\simeq
m_{Z}^{2}\cos^{2}2\beta+\frac{3g^{2}}{8\pi^{2}}\frac{m_{t}^{4}}{m_{W}^{2}}\left[\ln\frac{m_{\tilde{t}}^{2}}{m_{t}^{2}}+\frac{x_{t}^{2}}{m_{\tilde{t}}^{2}}\left(1-\frac{x_{t}^{2}}{12m_{\tilde{t}}^{2}}\right)\right]$
(6)

where $x_{t}=A_{t}-\mu\cot\beta$ and $m_{\tilde{t}}^{2}=m_{Q_{3}}m_{U_{3}}$ is
an effective stop mass which minimizes log corrections to the scalar potential
(here, $m_{Q_{3}}$ and $m_{U_{3}}$ are the third generation doublet and up-
squark soft terms and $A_{t}$ is the weak scale top-squark trilinear soft
term). For a given value of $m_{\tilde{t}}^{2}$, this expression gives a
maximal value for $m_{h}$ when $x_{t}^{max}=\sqrt{6}m_{\tilde{t}}$[55, 56,
57]. The pull on the $A_{0}$ term to large values (but not so large as to
enter CCB minima in the scalar potential) helps pull $m_{h}$ up into the $\sim
125$ GeV range.

In frame b), we show the probability distribution for $m_{\tilde{t}_{1}}$ from
the string landscape with an $n=1$ draw to large soft terms. While there is
just a small probability to have a top squark with mass below a TeV, the
distribution rises to a peak at $m_{\tilde{t}_{1}}\sim 1.5$ TeV followed by a
slow dropoff ending around $m_{\tilde{t}_{1}}\sim 2.5$ TeV. We also show the
present $m_{\tilde{t}_{1}}\gtrsim 1.2$ TeV limit from ATLAS/CMS searches. By
comparing, we see that LHC experiments are only beginning to probe the range
of top squark masses predicted by the landscape. The reach of LHC Run 3 and
HL-LHC should push into the peak probability region in the coming years,
making the search for light top-squarks of supersymmetry a highly motivated
priority.

Figure 1: a) Probability distribution for light Higgs mass $m_{h}$. b)
Probability distribution for lighter top squark mass $m_{\tilde{t}_{1}}$. We
assume statistical selection of soft terms from the string landscape with an
$n=1$ power-law draw to large soft terms.

In Fig. 2, we show the differential probability distribution
$dP/d(x_{t}/m_{\tilde{t}})$ where
$m_{\tilde{t}}\equiv\sqrt{m_{\tilde{t}_{1}}m_{\tilde{t}_{2}}}$. The vertical
dashed line denotes where $x_{t}=\sqrt{6}m_{\tilde{t}}$ which is where the
radiative corrections to the Higgs mass from top squarks are maximal. The
distribution peaks just below this point due to the landscape selection of
large trilinear soft terms $A_{t}$. This draw to large $A_{t}$, and hence
large $x_{t}$, helps to understand why the Higgs mass $m_{h}$ is pushed up to
$m_{h}\sim 125$ GeV in the string landscape.

Figure 2: Probability distribution $dP/d(x_{t}/m_{\tilde{t}})$. The vertical
dashed line denotes where $x_{t}=\sqrt{6}m_{\tilde{t}}$ where the Higgs mass
radiative corrections becomes maximal. We assume statistical selection of soft
terms from the string landscape with an $n=1$ power-law draw to large soft
terms.

In Fig. 3, we plot dots of stringy naturalness in the $m_{\tilde{t}_{1}}$ vs.
$\cos\theta_{t}$ plane where the light top squark

$\tilde{t}_{1}=\cot\theta_{t}\tilde{t}_{L}-\sin\theta_{t}\tilde{t}_{R}$ (7)

in the notation of Ref. [10] and where $\theta_{t}$ is the top squark mixing
angle and $\tilde{t}_{L}$ and $\tilde{t}_{R}$ are the weak scale left- and
right-stop eigenstates. From the plot, we see that $\cos\theta_{t}\sim 0.1$
over the entire expected range of light top squark masses so that we expect
the light top-squark to be predominantly of $\tilde{t}_{R}$ variety in spite
of the expected large stop mixing. This is because, starting with common soft
top-squark masses at the high scale $m_{Q_{3}}=m_{U_{3}}=m_{D_{3}}\equiv
m_{0}(3)$, the renormalization group evolution suppresses the right top-squark
soft mass $m_{U_{3}}$ more than the left top squark soft mass $m_{Q_{3}}$.

Figure 3: Probability distribution for lighter top squark mass vs.
$\cos\theta_{t}$ where $\tilde{t}_{1}=\cos\theta_{t}\
\tilde{t}_{L}-\sin\theta_{t}\ \tilde{t}_{R}$. We assume statistical selection
of soft terms from the string landscape with an $n=1$ power-law draw to large
soft terms.

####  2.2.1 $b\rightarrow s\gamma$ branching fraction

A powerful virtual probe of top squark properties comes from the measured
value of the flavor-changing $b$ decay branching fraction $BR(b\rightarrow
s\gamma)$. In the SM, this process proceeds via a $tW$ loop while in 2HDMs
there is a comparable contribution from a $tH^{\pm}$ loop[58]. In the MSSM,
there are additional contributions from
$\tilde{t}_{i}\tilde{\chi}_{1,2}^{\pm}$ and even
$\tilde{q}\tilde{\chi}_{1,2}^{\pm}$ loops (the latter tend to decouple in our
picture since first/second generation squarks are drawn to
$m_{\tilde{q}_{i}}\sim 10-40$ TeV level (since their contributions to the weak
scale are suppressed by their tiny Yukawa couplings)). For top-squark and
chargino masses nearby to the weak scale, then the various stop loops tend to
dominate the contributions to the $C_{7}$ Wilson coefficient albeit with
either positive or negative contributions[59]. Nonetheless, one expects with
rather light top-squarks of a few hundred GeV that there would be large
measured deviations in the $BR(b\rightarrow s\gamma)$ compared to its SM
value. For top-squarks approaching the TeV scale, then these contributions
decouple and one expects the SUSY value for $BR(b\rightarrow s\gamma)$ to
nearly match the SM expectation. For our theory calculation, we adopt the NLO
evaluation which is included in Isajet[59, 60]. The Isajet value, which
doesn’t include 2-loop and nonperturbative effects, asymptotes to
$BR(b\rightarrow s\gamma)_{SM}^{Isajet}\sim 3.15\times 10^{-4}$. Thus, along
with the Isajet NLO perturbative estimate, we include a 2-loop and
nonperturbative contribution
$\delta\Gamma\equiv\delta\Gamma_{2-loop}+\delta\Gamma_{nonp}\simeq 0.25$ as
emphasized by Misiak[61].

The present measured average value from the HFLAV Collaboration[62] is given
as $BR(b\rightarrow s\gamma)=(3.49\pm 0.19)\times 10^{-4}$ which is dominated
by the Belle[63] and BaBar[64] measurements. The current SM theory estimate is
$BR(b\rightarrow s\gamma)_{SM}^{TH}=(3.36\pm 0.23)\times 10^{-4}$[61].

In Fig. 4, we plot points of stringy naturalness in the $m_{\tilde{t}_{1}}$
vs. $BR(b\rightarrow s\gamma)$ plane. The blue solid line and dashed bands
show the HFLAV value $\pm 2\sigma$. The theory values cluster around
$BR(b\rightarrow s\gamma)\sim 3.4\times 10^{-4}$ with some larger deviations
for lower $m_{\tilde{t}_{1}}\lesssim 1$ TeV. Thus, the measured
$BR(b\rightarrow s\gamma)$ branching fraction tends to support the scenario of
TeV-scale top-squarks as predicted by the string landscape and as expected
from the rather large value of the light Higgs mass $m_{h}\sim 125$ GeV.

Figure 4: Probability distribution for lighter top squark mass vs.
$BR(b\rightarrow s\gamma)$. We assume statistical selection of soft terms from
the string landscape with an $n=1$ power-law draw to large soft terms. The
horizontal lines show the PDG measured value $\pm 2\sigma$ error band while
the vertical dashed line shows the approximate LHC limit on
$m_{\tilde{t}_{1}}$ from simplified model analyses.

####  2.2.2 Top squark branching fractions

The top squark decay widths $\Gamma(\tilde{t}_{1}\rightarrow
t\tilde{\chi}_{i}^{0})$ ($i=1-4$) and $\Gamma(\tilde{t}_{1}\rightarrow
b\tilde{\chi}_{j}^{+}$) ($j=1-2$) are expected to be the dominant top-squark
decay modes and their formulae are listed in Ref. [10] as Equations B.39 and
B.43 respectively. The numerical values can be extracted from the Isajet[54]
code. The decay widths depend sensitively on the top-squark gauge couplings
and the top-quark Yukawa coupling along with the mixing angle $\theta_{t}$ and
the decay kinematics. In Fig. 5 we show the stringy natural values of
$BF(\tilde{t}_{1}\rightarrow b\tilde{\chi}_{1}^{+})$ vs. $m_{\tilde{t}_{1}}$.
From the plot, we see a rather uniform prediction vs. $m_{\tilde{t}_{1}}$ that
$BF(\tilde{t}_{1}\rightarrow b\tilde{\chi}_{1}^{+})$ occurs very close to the
50% level.

Figure 5: Probability distribution for lighter top squark mass vs.
$BF(\tilde{t}_{1}\rightarrow b\tilde{\chi}_{1}^{+})$. We assume statistical
selection of soft terms from the string landscape with an $n=1$ power-law draw
to large soft terms.

In Fig. 6, we show the prediction for $BF(\tilde{t}_{1}\rightarrow
t\tilde{\chi}_{1}^{0})$ vs. $m_{\tilde{t}_{1}}$. The result here is also
rather uniform in $m_{\tilde{t}_{1}}$: that $BF(\tilde{t}_{1}\rightarrow
t\tilde{\chi}_{1}^{0})\sim 20-25\%$. Likewise, in Fig. 7 we show the
$BF(\tilde{t}_{1}\rightarrow t\tilde{\chi}_{2}^{0})$. This branching fraction
also tends to occur at the 20-25% level with little variation vs.
$m_{\tilde{t}_{1}}$. Further branching fractions such as
$BF(\tilde{t}_{1}\rightarrow t\tilde{\chi}_{3}^{0})$ can occur at the several
percent level, while others such as $\tilde{t}_{1}\rightarrow
t\tilde{\chi}_{4}^{0}$ and $\tilde{t}_{1}\rightarrow b\tilde{\chi}_{2}^{+}$
tend to occur at the sub-percent level.

Figure 6: Probability distribution for lighter top squark mass vs.
$BF(\tilde{t}_{1}\rightarrow t\tilde{\chi}_{1}^{0})$. We assume statistical
selection of soft terms from the string landscape with an $n=1$ power-law draw
to large soft terms.  Figure 7: Probability distribution for lighter top
squark mass vs. $BF(\tilde{t}_{1}\rightarrow t\tilde{\chi}_{2}^{0})$. We
assume statistical selection of soft terms from the string landscape with an
$n=1$ power-law draw to large soft terms.

##  3 Production and decay of top squarks at LHC

For the benefit of the reader, we show in Fig. 8 the next-to-leading-order
(NLO) Prospino[65] prediction for top squark pair production at LHC with
$\sqrt{s}=14$ TeV collisions:
$\sigma(pp\rightarrow\tilde{t}_{1}\tilde{t}_{1}^{*}X)$ vs.
$m_{\tilde{t}_{1}}$. Starting just above the present LHC excluded region, with
$m_{\tilde{t}_{1}}=1.25$ TeV, we find
$\sigma(\tilde{t}_{1}\tilde{t}_{1}^{*})\sim 1$ fb, corresponding to 3000
signal events assuming the nominal HL-LHC integrated luminosity of 3 ab-1.
Even for $m_{\tilde{t}_{1}}$ as high as 2 TeV, we find
$\sigma(\tilde{t}_{1}\tilde{t}_{1}^{*})\sim 0.02$ fb, corresponding to 60
signal events at HL-LHC before cuts.

Figure 8: Plot of $\sigma(pp\rightarrow\tilde{t}_{1}\tilde{t}_{1}^{*}X)$ from
Prospino (NLO) versus $m_{\tilde{t}_{1}}$ for $pp$ collisions at $\sqrt{s}=14$
TeV.

The projected HL-LHC reach for top squark pair producton is usually presented
in terms of simplified models by the ATLAS and CMS collaborations where a
single top squark decay mode is assumed. We see from the previous subsection
that such analyses are not realistic from the point of view of the string
landscape and so we will examine the reach of LHC at HL-LHC using the several
predicted decay modes. This will give rise to mixed decay mode configurations
such as is shown in Fig. 9 where one $\tilde{t}_{1}\rightarrow
b\tilde{\chi}_{1}^{+}$ and the other $\tilde{t}_{1}\rightarrow
t\tilde{\chi}_{1}^{0}$. Thus, we expect three main signal channels:

  * •

$b\bar{b}+\not\\!\\!\\!{E_{T}}$,

  * •

$t\bar{t}+\not\\!\\!\\!{E_{T}}$ and

  * •

$t\bar{b}+\not\\!\\!\\!{E_{T}}$ (plus charge conjugate mode).

In addition, some subset of events will contain soft decay products from the
unstable higgsinos in the cascade decay. Of particular note is the ocassional
presence of
$\tilde{\chi}_{2}^{0}\rightarrow\tilde{\chi}_{1}^{0}\ell\bar{\ell}$ (with
$\ell=e$ or $\mu$) where
$m(\ell\bar{\ell})<m_{\tilde{\chi}_{2}^{0}}-m_{\tilde{\chi}_{1}^{0}}$.

Figure 9: Representative diagram for top squark pair production and decay at
LHC in natural SUSY.

##  4 A stringy natural top squark benchmark point

In the following Section, we will examine top squark pair production at LHC14
for the following Benchmark Point (BM) which is typical of stringy natural
models. The BM point comes from the NUHM2 model[52] with parameters as listed
in the Table 1. It is a natural SUSY benchmark point since $\Delta_{EW}=22$,
even though the lightest top squark lies at $m_{\tilde{t}_{1}}\sim 1.7$ TeV
and $m_{\tilde{g}}\sim 2.8$ TeV. The spectra is generated using the Isasugra
code[66] from Isajet[54]. We can also expand this natural SUSY BM point into a
natural SUSY Model Line by simply varying the $A_{0}$ parameter which results
in variation of $m_{\tilde{t}_{1}}:800-2200$ GeV while hardly changing $m_{h}$
or other sparticle masses.

parameter | stringy natural BM point
---|---
$m_{0}$ | 5 TeV
$m_{1/2}$ | 1.2 TeV
$A_{0}$ | -8 TeV
$\tan\beta$ | 10
$\mu$ | 250 GeV
$m_{A}$ | 2 TeV
$m_{\tilde{g}}$ | 2830 GeV
$m_{\tilde{u}_{L}}$ | 5440 GeV
$m_{\tilde{u}_{R}}$ | 5561 GeV
$m_{\tilde{e}_{R}}$ | 4822 GeV
$m_{\tilde{t}_{1}}$ | 1714 GeV
$m_{\tilde{t}_{2}}$ | 3915 GeV
$m_{\tilde{b}_{1}}$ | 3949 GeV
$m_{\tilde{b}_{2}}$ | 5287 GeV
$m_{\tilde{\tau}_{1}}$ | 4746 GeV
$m_{\tilde{\tau}_{2}}$ | 5110 GeV
$m_{\tilde{\nu}_{\tau}}$ | 5107 GeV
$m_{\tilde{\chi}_{1}^{\pm}}$ | 261.7 GeV
$m_{\tilde{\chi}_{2}^{\pm}}$ | 1020.6 GeV
$m_{\tilde{\chi}_{1}^{0}}$ | 248.1 GeV
$m_{\tilde{\chi}_{2}^{0}}$ | 259.2 GeV
$m_{\tilde{\chi}_{3}^{0}}$ | 541.0 GeV
$m_{\tilde{\chi}_{4}^{0}}$ | 1033.9 GeV
$m_{h}$ | 124.7 GeV
$\Omega_{\tilde{\chi}_{1}}^{std}h^{2}$ | 0.016
$BR(b\rightarrow s\gamma)\times 10^{4}$ | $3.1$
$BR(B_{s}\rightarrow\mu^{+}\mu^{-})\times 10^{9}$ | $3.8$
$\sigma^{SI}(\tilde{\chi}_{1}^{0},p)$ (pb) | $2.2\times 10^{-9}$
$\sigma^{SD}(\tilde{\chi}_{1}^{0},p)$ (pb) | $2.9\times 10^{-5}$
$\langle\sigma v\rangle|_{v\rightarrow 0}$ (cm3/sec) | $1.3\times 10^{-25}$
$\Delta_{\rm EW}$ | 22
Table 1: Input parameters (TeV) and masses (GeV) for the stringy natural SUSY
benchmark point from the NUHM2 model with $m_{t}=173.2$ GeV using Isajet 7.88
[54].

##  5 Reach of LHC for natural top squarks

We next examine the reach of HL-LHC ($\sqrt{s}=14$ TeV with 3000 fb-1) for the
top squarks of stringy natural SUSY. To proceed, we generate a SUSY Les
Houches Accord (SLHA) file[67] for our natural SUSY BM point and feed this
into Pythia[68] which is used for signal and the $2\rightarrow 2$ background
(BG) processes. For the $2\rightarrow 3$ BG processes, we use Madgraph[69]
coupled to Pythia. The SM BGs considered are: $t\bar{t}$, $b\bar{b}Z$,
$t\bar{t}Z$, $t\bar{t}W$, $b\bar{b}W$ and single-top production. We adopt the
toy detector simulation Delphes[70].

The baseline reconstructed objects are as follows.

Baseline small radius(SR) jet:

  1. 1.

Found by anti-$k_{t}$ jet finder algorithm with $p_{T}(min)=25$ GeV and
$R=0.4$ and

  2. 2.

$|\eta(j)|<4.5$.

Isolated lepton:

  1. 1.

$|\eta(\mu)|<2.5$ for muon, $|\eta(e)|<2.47$ for electron,

  2. 2.

$p_{T}(\mu)>25$ GeV for muon, $p_{T}(e)>20$ GeV for electron.

Large radius(LR) jet:

  1. 1.

Found by Cambridge/Aachen finder algorithm with $p_{T}(min)=400$ GeV with
$R=1.5$.

For signal objects, we also require signal b-jets:

  1. 1.

satisfy the baseline SR jet requirement above.

  2. 2.

$|\eta(b)|<2.4$ and

  3. 3.

tagged by Delphes as $b$-jet.

The signal top candidate is reconstructed with either of the following
criteria:

  * •

The fat jet $J$ is tagged by the HEPTopTagger2[71, 72] as a top. In such case,
the top 4-vector reconstructed by the tagger is used for further kinematics
calculations, or

  * •

The fat jet $J$ has a trimmed mass $115\ {\rm GeV}<m_{J}<225$ GeV and has at
least 1 $b$-jet within the cone radius of the fat jet $(\Delta R(J,b)<1.5$).
In such a case, the trimmed 4-vector of the fat jet is used for further
kinematics calculations.

The events then are separated into three channels:
$t\bar{t}+\not\\!\\!\\!{E_{T}}$, $tb+\not\\!\\!\\!{E_{T}}$, and
$b\bar{b}+\not\\!\\!\\!{E_{T}}$. The workflow to determine each channel is as
follows:

  * •

If there are at least 2 tops being tagged by the HEPTopTagger2, the two tops
with the hardest $p_{T}$ are chosen as signals, and this channel is labeled as
$t\bar{t}+\not\\!\\!\\!{E_{T}}$.

  * •

Otherwise, if the HEPTopTagger2 tags 1 top, and the trimming method tags at
least one other, this channel is labeled again as
$t\bar{t}+\not\\!\\!\\!{E_{T}}$. The top tagged by the HEPTopTagger2, and the
hardest fat jet found by the trimming method are chosen as signals.

  * •

Otherwise, if the HEPTopTagger2 fails to tag any tops, but the trimming method
found at least two, this channel is also labeled as
$t\bar{t}+\not\\!\\!\\!{E_{T}}$. The two tops with the hardest $p_{T}$ are
chosen as signals.

  * •

Otherwise, if there is exactly 1 top tagged by either HEPTopTagger2 or the
trimming method, then look for extra $b$-jet candidates. The $b$-jet
candidates must satisfy signal $b$-jet requirement listed above. The $b$-jet
candidate needs to be well separated with the 3 subjets of the reconstructed
top (Both HEPTopTagger2 and the trimming algorithm can provide the subjet
4-vectors): $\Delta R(subjet,b)>0.4$. If there are $b$-jets satisfying these
requirements, the $b$ candidate that minimizes the vector sum of
$\not\\!\\!\\!{E_{T}}+p_{T}(t)+p_{T}(b)$ is chosen as the signal. This channel
is labeled as $tb+\not\\!\\!\\!{E_{T}}$.

  * •

Otherwise, if the event fails any of the above selection requirements but has
at least two $b$ jets satisfied the signal $b$-jet requirement, this channel
is labeled as $b\bar{b}+\not\\!\\!\\!{E_{T}}$. The pair of $b$-jets that
minimize the vector sum of $\not\\!\\!\\!{E_{T}}+p_{T}(b_{1})+p_{T}(b_{2})$
are chosen as signals. The harder of the two is labeled as $b_{1}$, and the
other is $b_{2}$ in the following.

###  5.1 $b\bar{b}+\not\\!\\!\\!{E_{T}}$

We first examine the $b\bar{b}+\not\\!\\!\\!{E_{T}}$ channel. After examining
various distributions, we require the following.

  * •

$\not\\!\\!\\!{E_{T}}>800$ GeV,

  * •

$|\eta(b_{1})|<2.0$,

  * •

$p_{T}(b_{1})>200$ GeV,

  * •

$H_{T}>1500$ GeV,

  * •

$min[m_{T}(b_{1},\not\\!\\!\\!{E_{T}}),m_{T}(b_{2},\not\\!\\!\\!{E_{T}})]>175$
GeV,

  * •

$min(\Delta\phi(b,\not\\!\\!\\!{E_{T}}))>20^{\circ}$, where $b$ loops over all
$b$-jets in the event.

After these cuts, we construct the $m_{T_{2}}$ distribution[73] and plot the
resultant distribution in Fig. 10. The strategy becomes clear: look for a high
$m_{T_{2}}$ deviation from expected background at the higher $m_{T_{2}}$
values where we expect $m_{T_{2}}$ to be bounded from above by
$m_{\tilde{t}_{1}}$. In the plot, we show signal histograms for five different
values of $m_{\tilde{t}_{1}}$ along with leading backgrounds. While BG does
indeed dominate at low $m_{T_{2}}$, a signal emerges from BG at higher values.
If there are sufficient number of signal events above BG, then a signal can be
claimed.

Figure 10: Distribution in $m_{T2}$ from top-squark pair production at LHC14
in the $b\bar{b}+\not\\!\\!\\!{E_{T}}$ channel along with dominant SM
backgrounds after cuts listed in the text.

###  5.2 $tb+\not\\!\\!\\!{E_{T}}$

After examining various distributions, for the $tb+\not\\!\\!\\!{E_{T}}$
channel we require

  * •

$\not\\!\\!\\!{E_{T}}>400$ GeV,

  * •

$H_{T}>1400$ GeV,

  * •

$L_{T}>1800$ GeV (defined as the scalar sum of
$p_{T}(t)+p_{T}(b)+\not\\!\\!\\!{E_{T}}$), where $t$ and $b$ here are the
signal top and $b$-jet.

  * •

$min[m_{T}(t,\not\\!\\!\\!{E_{T}}),m_{T}(b,\not\\!\\!\\!{E_{T}})]>175$ GeV,

  * •

$min(\Delta\phi(b,\not\\!\\!\\!{E_{T}}))>40^{\circ}$, where $b$ loops over all
$b$-jets in the event.

  * •

$min(\Delta\phi(J,\not\\!\\!\\!{E_{T}}))>30^{\circ}$, where $J$ loops over all
fat jets in the event, no matter whether they’ve been tagged as top or not.

The resultant $m_{T_{2}}$ distribution is shown in Fig. 11 where again we
expect the signal distribution to be bounded from above by $m_{\tilde{t}_{1}}$
whilst BG is a continuum. The five signal histograms do indeed emerge from BG
at high $m_{T_{2}}$ although not necessarily at an observable rate. The
largest BG at high $m_{T_{2}}$ is from $t\bar{t}Z$ production.

Figure 11: Distribution in $m_{T2}$ from top-squark pair production at LHC14
in the $tb+\not\\!\\!\\!{E_{T}}$ channel along with dominant SM backgrounds
after cuts listed in the text.

###  5.3 $t\bar{t}+\not\\!\\!\\!{E_{T}}$

Next, we examine various distributions for signal and BG in the
$t\bar{t}+\not\\!\\!\\!{E_{T}}$ signal channel. We then require the following:

  * •

$\not\\!\\!\\!{E_{T}}>300$ GeV,

  * •

$H_{T}>1400$ GeV,

  * •

$min[m_{T}(t_{1},\not\\!\\!\\!{E_{T}}),m_{T}(t_{2},\not\\!\\!\\!{E_{T}})]>175$
GeV,

  * •

$min(\Delta\phi(b,\not\\!\\!\\!{E_{T}}))>40^{\circ}$, where $b$ loops over all
$b$-jets in the event.

  * •

$min(\Delta\phi(J,\not\\!\\!\\!{E_{T}}))>30^{\circ}$, where $J$ loops over all
fat jets in the event, no matter whether they’ve been tagged as top or not.

The subsequent $m_{T_{2}}$ distribution is plotted in Fig. 12. The signal
distributions emerge from SM BG at high $m_{T_{2}}$ but at more marginal rates
than the other channels due to the lower efficiency to tag top-jets.

Figure 12: Distribution in $m_{T2}$ from top-squark pair production at LHC14
in the $t\bar{t}+\not\\!\\!\\!{E_{T}}$ channel along with dominant SM
backgrounds after cuts listed in the text.

###  5.4 Cumulative reach of HL-LHC for top squark pair production in natSUSY

Using the analysis cuts for the various signal channels discussed above, we
can now create reach plots to show the HL-LHC discovery sensitivity versus
$m_{\tilde{t}_{1}}$ along our natural SUSY model line. We use the $5\sigma$
level to claim discovery of a top-squark and assume the true distribution one
observes experimentally corresponds to signal-plus-background. We then test
this against the background-only distribution in order to see if the
background-only hypothesis can be rejected at the $5\sigma$ level.
Specifically, we use the binned $m_{T_{2}}$ distributions (bin width of 100
GeV) from each signal channel as displayed above to obtain the
discovery/exclusion limits.

In the case of the exclusion line, the upper limits for exclusion of a signal
are set at 95% CL; one assumes the true distribution one observes in
experiment corresponds to background-only. The limits are then computed using
a modified frequentist $CL_{s}$ method[74] where the profile likelihood ratio
is the test statistic. For both the exclusion and discovery plots, the
asymptotic approximation for obtaining the median significance is
employed[75]. For both discovery and exclusion estimates, we combine results
from all three top-squark signal channels: $t\bar{t}+\not\\!\\!\\!{E_{T}}$,
$b\bar{b}+\not\\!\\!\\!{E_{T}}$ and $tb+\not\\!\\!\\!{E_{T}}$.

In Fig. 13a), we show the $5\sigma$ discovery cross section as the dashed line
along with 1- and 2-$\sigma$ error bands. We show the corresponding natural
SUSY model line as blue dots. We see that HL-LHC with 3000 fb-1 fb of
integrated luminosity can discover natural SUSY top-squarks out to
$m_{\tilde{t}_{1}}\sim 1700$ GeV. In Fig. 13b), we plot the HL-LHC 95%
exclusion reach. In this case, the exclusion reach extends out to
$m_{\tilde{t}_{1}}\sim 2000$ GeV. By comparing these results with expectations
from stringy naturalness in Fig. 1b), we see that HL-LHC can cover the bulk of
stringy natural parameter space, although a tail of probability does extend
past $m_{\tilde{t}_{1}}\sim 2$ TeV.

Figure 13: Expected 5$\sigma$ discovery limit and expected 95$\%$ CL exclusion
limit on top-squark pair production cross section vs. $m_{\tilde{t}_{1}}$ from
a natural SUSY model line at HL-LHC with $\sqrt{s}=14$ TeV and 3000 fb-1 of
integrated luminosity.

##  6 Conclusions

In this paper we have examined what sort of values of top squark masses and
other properties are expected from the string landscape where a power-law draw
to large soft terms is expected, but where the derived value of the weak scale
must lie within the ABDS window in order to allow for complex nuclei (and
hence atoms) in each anthropically-allowed pocket universe. Under this stringy
naturalness requirement, we find $m_{\tilde{t}_{1}}\sim 1-2.5$ TeV with large
mixing. These results are in accord with measurements of $BR(b\rightarrow
s\gamma)$ which are suggestive of TeV-scale top-squarks so that SUSY
contributions to this decay rate decouple. The large mixing helps boost
$m_{h}\rightarrow 125$ GeV while minimizing the top squark contributions to
the weak scale $\Sigma_{u}^{u}(\tilde{t}_{1,2})$.

In spite of the large mixing, the lighter top-squark is mainly a right-squark,
but decays at $\tilde{t}_{1}\rightarrow b\tilde{\chi}_{1}^{+}$ at $\sim 50\%$
and $\tilde{t}_{1}\rightarrow t\tilde{\chi}_{1,2}^{0}$ at $\sim 25\%$ each.
Thus, we expect top-squark pair production at LHC Run 3 and HL-LHC to lead to
mixed final states of $b\bar{b}+\not\\!\\!\\!{E_{T}}$,
$t\bar{t}+\not\\!\\!\\!{E_{T}}$ and $tb+\not\\!\\!\\!{E_{T}}$. We evaluated
some optimized cuts for each of these channels, and then expect the top-squark
pair production to be revealed as an enhancement in the $m_{T_{2}}$
distribution at high values of $m_{T_{2}}$. We combined the reaches in these
three channels to find that HL-LHC operating at $\sqrt{s}=14$ TeV with 3000
fb-1 of integrated luminosity should have a $5\sigma$ discovery reach to
$m_{\tilde{t}_{1}}\sim 1.7$ TeV and a 95% CL exclusion reach to about
$m_{\tilde{t}_{1}}\sim 2$ TeV. Now our HL-LHC reach results can be added to
Fig. 1b) as a final summary frame: Fig. 14.

Figure 14: Probability distribution for lighter top squark mass
$m_{\tilde{t}_{1}}$ with an $n=1$ power-law draw to large soft terms. We also
show the present reach on $m_{\tilde{t}_{1}}$ from LHC Run 2, and the expected
HL-LHC $5\sigma$ and 95% CL reach in the figure.

These HL-LHC reach limits will cover most (but not all) of the expected
stringy natural parameter space from SUSY on the landscape!

Acknowledgements:

This material is based upon work supported by the U.S. Department of Energy,
Office of Science, Office of High Energy Physics under Award Number DE-
SC-0009956 and DE-SC-0017647.

## References

  * [1] J. R. Ellis, K. Enqvist, D. V. Nanopoulos, F. Zwirner, Observables in Low-Energy Superstring Models, Mod. Phys. Lett. A 1 (1986) 57.  doi:10.1142/S0217732386000105.
  * [2] R. Barbieri, G. F. Giudice, Upper Bounds on Supersymmetric Particle Masses, Nucl. Phys. B 306 (1988) 63–76.  doi:10.1016/0550-3213(88)90171-X.
  * [3] S. Dimopoulos, G. F. Giudice, Naturalness constraints in supersymmetric theories with nonuniversal soft terms, Phys. Lett. B 357 (1995) 573–578.  arXiv:hep-ph/9507282, doi:10.1016/0370-2693(95)00961-J.
  * [4] R. Kitano, Y. Nomura, Supersymmetry, naturalness, and signatures at the LHC, Phys. Rev. D 73 (2006) 095004.  arXiv:hep-ph/0602096, doi:10.1103/PhysRevD.73.095004.
  * [5] M. Papucci, J. T. Ruderman, A. Weiler, Natural SUSY Endures, JHEP 09 (2012) 035\.  arXiv:1110.6926, doi:10.1007/JHEP09(2012)035.
  * [6] C. Brust, A. Katz, S. Lawrence, R. Sundrum, SUSY, the Third Generation and the LHC, JHEP 03 (2012) 103.  arXiv:1110.6670, doi:10.1007/JHEP03(2012)103.
  * [7] G. Aad, et al., Search for a scalar partner of the top quark in the all-hadronic $t{\bar{t}}$ plus missing transverse momentum final state at $\sqrt{s}=13$ TeV with the ATLAS detector, Eur. Phys. J. C 80 (8) (2020) 737\.  arXiv:2004.14060, doi:10.1140/epjc/s10052-020-8102-8.
  * [8] G. Aad, et al., Search for new phenomena with top quark pairs in final states with one lepton, jets, and missing transverse momentum in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector, JHEP 04 (2021) 174.  arXiv:2012.03799, doi:10.1007/JHEP04(2021)174.
  * [9] A. M. Sirunyan, et al., Search for top squark production in fully-hadronic final states in proton-proton collisions at $\sqrt{s}=$ 13 TeV, Phys. Rev. D 104 (5) (2021) 052001.  arXiv:2103.01290, doi:10.1103/PhysRevD.104.052001.
  * [10] H. Baer, X. Tata, Weak scale supersymmetry: From superfields to scattering events, Cambridge University Press, 2006.
  * [11] M. Dine, Naturalness Under Stress, Ann. Rev. Nucl. Part. Sci. 65 (2015) 43–62.  arXiv:1501.01035, doi:10.1146/annurev-nucl-102014-022053.
  * [12] H. Baer, V. Barger, D. Mickelson, How conventional measures overestimate electroweak fine-tuning in supersymmetric theory, Phys. Rev. D 88 (9) (2013) 095013\.  arXiv:1309.2984, doi:10.1103/PhysRevD.88.095013.
  * [13] H. Baer, V. Barger, D. Martinez, S. Salam, On practical naturalness and its implications for weak scale supersymmetryarXiv:2305.16125.
  * [14] A. Mustafayev, X. Tata, Supersymmetry, Naturalness, and Light Higgsinos, Indian J. Phys. 88 (2014) 991–1004.  arXiv:1404.1386, doi:10.1007/s12648-014-0504-8.
  * [15] H. Baer, V. Barger, D. Mickelson, M. Padeffke-Kirkland, SUSY models under siege: LHC constraints and electroweak fine-tuning, Phys. Rev. D 89 (11) (2014) 115019.  arXiv:1404.2277, doi:10.1103/PhysRevD.89.115019.
  * [16] A. Brignole, L. E. Ibanez, C. Munoz, Towards a theory of soft terms for the supersymmetric Standard Model, Nucl. Phys. B 422 (1994) 125–171, [Erratum: Nucl.Phys.B 436, 747–748 (1995)].  arXiv:hep-ph/9308271, doi:10.1016/0550-3213(94)00068-9.
  * [17] H. Baer, V. Barger, P. Huang, A. Mustafayev, X. Tata, Radiative natural SUSY with a 125 GeV Higgs boson, Phys. Rev. Lett. 109 (2012) 161802.  arXiv:1207.3343, doi:10.1103/PhysRevLett.109.161802.
  * [18] H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev, X. Tata, Radiative natural supersymmetry: Reconciling electroweak fine-tuning and the Higgs boson mass, Phys. Rev. D 87 (11) (2013) 115028.  arXiv:1212.2655, doi:10.1103/PhysRevD.87.115028.
  * [19] H. Baer, V. Barger, S. Salam, D. Sengupta, K. Sinha, Status of weak scale supersymmetry after LHC Run 2 and ton-scale noble liquid WIMP searches, Eur. Phys. J. ST 229 (21) (2020) 3085–3141.  arXiv:2002.03013, doi:10.1140/epjst/e2020-000020-x.
  * [20] R. Bousso, J. Polchinski, The string theory landscape, Sci. Am. 291 (2004) 60–69.  doi:10.1038/scientificamerican0904-78.
  * [21] L. Susskind, The Anthropic landscape of string theory (2003) 247–266arXiv:hep-th/0302219.
  * [22] M. R. Douglas, S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733–796.  arXiv:hep-th/0610102, doi:10.1103/RevModPhys.79.733.
  * [23] S. Ashok, M. R. Douglas, Counting flux vacua, JHEP 01 (2004) 060.  arXiv:hep-th/0307049, doi:10.1088/1126-6708/2004/01/060.
  * [24] S. Weinberg, Anthropic Bound on the Cosmological Constant, Phys. Rev. Lett. 59 (1987) 2607.  doi:10.1103/PhysRevLett.59.2607.
  * [25] M. R. Douglas, Statistical analysis of the supersymmetry breaking scalearXiv:hep-th/0405279.
  * [26] V. Agrawal, S. M. Barr, J. F. Donoghue, D. Seckel, Viable range of the mass scale of the standard model, Phys. Rev. D 57 (1998) 5480–5492.  arXiv:hep-ph/9707380, doi:10.1103/PhysRevD.57.5480.
  * [27] H. Baer, V. Barger, H. Serce, K. Sinha, Higgs and superparticle mass predictions from the landscape, JHEP 03 (2018) 002.  arXiv:1712.01399, doi:10.1007/JHEP03(2018)002.
  * [28] S. K. Soni, H. A. Weldon, Analysis of the Supersymmetry Breaking Induced by N=1 Supergravity Theories, Phys. Lett. B 126 (1983) 215–219.  doi:10.1016/0370-2693(83)90593-2.
  * [29] V. S. Kaplunovsky, J. Louis, Model independent analysis of soft terms in effective supergravity and in string theory, Phys. Lett. B 306 (1993) 269–275.  arXiv:hep-th/9303040, doi:10.1016/0370-2693(93)90078-V.
  * [30] H. Baer, V. Barger, D. Sengupta, Landscape solution to the SUSY flavor and CP problems, Phys. Rev. Res. 1 (3) (2019) 033179.  arXiv:1910.00090, doi:10.1103/PhysRevResearch.1.033179.
  * [31] H. Baer, V. Barger, P. Huang, Hidden SUSY at the LHC: the light higgsino-world scenario and the role of a lepton collider, JHEP 11 (2011) 031.  arXiv:1107.5581, doi:10.1007/JHEP11(2011)031.
  * [32] Z. Han, G. D. Kribs, A. Martin, A. Menon, Hunting quasidegenerate Higgsinos, Phys. Rev. D 89 (7) (2014) 075007.  arXiv:1401.1235, doi:10.1103/PhysRevD.89.075007.
  * [33] H. Baer, A. Mustafayev, X. Tata, Monojet plus soft dilepton signal from light higgsino pair production at LHC14, Phys. Rev. D 90 (11) (2014) 115007.  arXiv:1409.7058, doi:10.1103/PhysRevD.90.115007.
  * [34] C. Han, D. Kim, S. Munir, M. Park, Accessing the core of naturalness, nearly degenerate higgsinos, at the LHC, JHEP 04 (2015) 132.  arXiv:1502.03734, doi:10.1007/JHEP04(2015)132.
  * [35] H. Baer, V. Barger, S. Salam, D. Sengupta, X. Tata, The LHC higgsino discovery plane for present and future SUSY searches, Phys. Lett. B 810 (2020) 135777.  arXiv:2007.09252, doi:10.1016/j.physletb.2020.135777.
  * [36] H. Baer, V. Barger, D. Sengupta, X. Tata, New angular and other cuts to improve the Higgsino signal at the LHC, Phys. Rev. D 105 (9) (2022) 095017.  arXiv:2109.14030, doi:10.1103/PhysRevD.105.095017.
  * [37] I. I. Y. Bigi, S. Rudaz, SEARCH FOR SCALAR SUPERPARTNERS OF THE TOP QUARK, Phys. Lett. B 153 (1985) 335–340.  doi:10.1016/0370-2693(85)90560-X.
  * [38] H. Baer, X. Tata, Implications of the T Quark Signal for Stop Squarks and Charged Higgs Bosons, Phys. Lett. B 167 (1986) 241–247.  doi:10.1016/0370-2693(86)90607-6.
  * [39] H. Baer, M. Drees, R. Godbole, J. F. Gunion, X. Tata, Phenomenology of light top squarks at the Fermilab Tevatron, Phys. Rev. D 44 (1991) 725–740.  doi:10.1103/PhysRevD.44.725.
  * [40] H. Baer, J. Sender, X. Tata, The Search for top squarks at the Fermilab Tevatron Collider, Phys. Rev. D 50 (1994) 4517–4528.  arXiv:hep-ph/9404342, doi:10.1103/PhysRevD.50.4517.
  * [41] K. Rolbiecki, J. Tattersall, G. Moortgat-Pick, Towards Measuring the Stop Mixing Angle at the LHC, Eur. Phys. J. C 71 (2011) 1517.  arXiv:0909.3196, doi:10.1140/epjc/s10052-010-1517-x.
  * [42] F. Brummer, S. Kraml, S. Kulkarni, Anatomy of maximal stop mixing in the MSSM, JHEP 08 (2012) 089.  arXiv:1204.5977, doi:10.1007/JHEP08(2012)089.
  * [43] M. L. Graesser, J. Shelton, Hunting Mixed Top Squark Decays, Phys. Rev. Lett. 111 (12) (2013) 121802.  arXiv:1212.4495, doi:10.1103/PhysRevLett.111.121802.
  * [44] H. Baer, V. Barger, N. Nagata, M. Savoy, Phenomenological profile of top squarks from natural supersymmetry at the LHC, Phys. Rev. D 95 (5) (2017) 055012, [Addendum: Phys.Rev.D 103, 059902 (2021)].  arXiv:1611.08511, doi:10.1103/PhysRevD.95.055012.
  * [45] C. Han, J. Ren, L. Wu, J. M. Yang, M. Zhang, Top-squark in natural SUSY under current LHC run-2 data, Eur. Phys. J. C 77 (2) (2017) 93.  arXiv:1609.02361, doi:10.1140/epjc/s10052-017-4662-7.
  * [46] Y. Bai, J. Berger, J. Osborne, B. A. Stefanek, Search for Heavy Stops with Merged Top-Jets, Phys. Rev. D 96 (9) (2017) 095035.  arXiv:1611.05046, doi:10.1103/PhysRevD.96.095035.
  * [47] ATLAS sensitivity to top squark pair production at the HL-LHC, ATL-PHYS-PUB-2018-021 (2018).
  * [48] X. Cid Vidal, et al., Report from Working Group 3: Beyond the Standard Model physics at the HL-LHC and HE-LHC, CERN Yellow Rep. Monogr. 7 (2019) 585–865.  arXiv:1812.07831, doi:10.23731/CYRM-2019-007.585.
  * [49] H. Baer, V. Barger, S. Salam, D. Sengupta, String landscape guide to soft SUSY breaking terms, Phys. Rev. D 102 (7) (2020) 075012.  arXiv:2005.13577, doi:10.1103/PhysRevD.102.075012.
  * [50] M. R. Douglas, The String landscape and low energy supersymmetry, 2012, pp. 261–288.  arXiv:1204.6626, doi:10.1142/9789814412551_0012.
  * [51] H. Baer, V. Barger, S. Salam, Naturalness versus stringy naturalness (with implications for collider and dark matter searches), Phys. Rev. Research. 1 (2019) 023001.  arXiv:1906.07741, doi:10.1103/PhysRevResearch.1.023001.
  * [52] H. Baer, A. Mustafayev, S. Profumo, A. Belyaev, X. Tata, Direct, indirect and collider detection of neutralino dark matter in SUSY models with non-universal Higgs masses, JHEP 07 (2005) 065.  arXiv:hep-ph/0504001, doi:10.1088/1126-6708/2005/07/065.
  * [53] K. J. Bae, H. Baer, V. Barger, D. Sengupta, Revisiting the SUSY $\mu$ problem and its solutions in the LHC era, Phys. Rev. D 99 (11) (2019) 115027.  arXiv:1902.10748, doi:10.1103/PhysRevD.99.115027.
  * [54] F. E. Paige, S. D. Protopopescu, H. Baer, X. Tata, ISAJET 7.69: A Monte Carlo event generator for pp, anti-p p, and e+e- reactionsarXiv:hep-ph/0312045.
  * [55] M. Carena, H. E. Haber, Higgs Boson Theory and Phenomenology, Prog. Part. Nucl. Phys. 50 (2003) 63–152.  arXiv:hep-ph/0208209, doi:10.1016/S0146-6410(02)00177-1.
  * [56] H. Baer, V. Barger, A. Mustafayev, Implications of a 125 GeV Higgs scalar for LHC SUSY and neutralino dark matter searches, Phys. Rev. D 85 (2012) 075010.  arXiv:1112.3017, doi:10.1103/PhysRevD.85.075010.
  * [57] V. Barger, P. Huang, M. Ishida, W.-Y. Keung, Scalar-Top Masses from SUSY Loops with 125 GeV mh and Precise Mw, Phys. Lett. B 718 (2013) 1024–1030.  arXiv:1206.1777, doi:10.1016/j.physletb.2012.11.049.
  * [58] V. D. Barger, J. L. Hewett, R. J. N. Phillips, New Constraints on the Charged Higgs Sector in Two Higgs Doublet Models, Phys. Rev. D 41 (1990) 3421–3441.  doi:10.1103/PhysRevD.41.3421.
  * [59] H. Baer, M. Brhlik, QCD improved b —$>$ s gamma constraints on the minimal supergravity model, Phys. Rev. D 55 (1997) 3201–3208.  arXiv:hep-ph/9610224, doi:10.1103/PhysRevD.55.3201.
  * [60] H. Baer, M. Brhlik, D. Castano, X. Tata, b —$>$ s gamma constraints on the minimal supergravity model with large tan Beta, Phys. Rev. D 58 (1998) 015007.  arXiv:hep-ph/9712305, doi:10.1103/PhysRevD.58.015007.
  * [61] M. Misiak, Radiative Decays of the $B$ Meson: a Progress Report, Acta Phys. Polon. B 49 (2018) 1291–1300.  doi:10.5506/APhysPolB.49.1291.
  * [62] Y. Amhis, et al., Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of 2021arXiv:2206.07501.
  * [63] A. Limosani, et al., Measurement of Inclusive Radiative B-meson Decays with a Photon Energy Threshold of 1.7-GeV, Phys. Rev. Lett. 103 (2009) 241801.  arXiv:0907.1384, doi:10.1103/PhysRevLett.103.241801.
  * [64] J. P. Lees, et al., Precision Measurement of the $B\rightarrow X_{s}\gamma$ Photon Energy Spectrum, Branching Fraction, and Direct CP Asymmetry $A_{CP}(B\rightarrow X_{s+d}\gamma)$, Phys. Rev. Lett. 109 (2012) 191801.  arXiv:1207.2690, doi:10.1103/PhysRevLett.109.191801.
  * [65] W. Beenakker, R. Hopker, M. Spira, PROSPINO: A Program for the production of supersymmetric particles in next-to-leading order QCDarXiv:hep-ph/9611232.
  * [66] H. Baer, C.-H. Chen, R. B. Munroe, F. E. Paige, X. Tata, Multichannel search for minimal supergravity at $p\bar{p}$ and $e^{+}e^{-}$ colliders, Phys. Rev. D 51 (1995) 1046–1050.  arXiv:hep-ph/9408265, doi:10.1103/PhysRevD.51.1046.
  * [67] P. Z. Skands, et al., SUSY Les Houches accord: Interfacing SUSY spectrum calculators, decay packages, and event generators, JHEP 07 (2004) 036.  arXiv:hep-ph/0311123, doi:10.1088/1126-6708/2004/07/036.
  * [68] T. Sjostrand, S. Mrenna, P. Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026.  arXiv:hep-ph/0603175, doi:10.1088/1126-6708/2006/05/026.
  * [69] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, MadGraph 5 : Going Beyond, JHEP 06 (2011) 128.  arXiv:1106.0522, doi:10.1007/JHEP06(2011)128.
  * [70] J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaître, A. Mertens, M. Selvaggi, DELPHES 3, A modular framework for fast simulation of a generic collider experiment, JHEP 02 (2014) 057.  arXiv:1307.6346, doi:10.1007/JHEP02(2014)057.
  * [71] C. Anders, C. Bernaciak, G. Kasieczka, T. Plehn, T. Schell, Benchmarking an even better top tagger algorithm, Phys. Rev. D 89 (7) (2014) 074047.  arXiv:1312.1504, doi:10.1103/PhysRevD.89.074047.
  * [72] T. Plehn, M. Spannowsky, M. Takeuchi, How to Improve Top Tagging, Phys. Rev. D 85 (2012) 034029.  arXiv:1111.5034, doi:10.1103/PhysRevD.85.034029.
  * [73] A. Barr, C. Lester, P. Stephens, m(T2): The Truth behind the glamour, J. Phys. G 29 (2003) 2343–2363.  arXiv:hep-ph/0304226, doi:10.1088/0954-3899/29/10/304.
  * [74] A. L. Read, Presentation of search results: the ${CL_{s}}$ technique, J. Phys. G 28 (2002) 2693.  doi:10.1088/0954-3899/28/10/313.
  * [75] G. Cowan, K. Cranmer, E. Gross, O. Vitells, Asymptotic formulae for likelihood-based tests of new physics, Eur.Phys. J. C 71.  arXiv:1007.1727, doi:10.1140/epjc/s10052-011-1554-0.


# [Call for Papers] The 2nd BabyLM Challenge: Sample-efficient pretraining
on a developmentally plausible corpus
https://babylm.github.io/

Leshem Choshen
IBM Research, MIT Ryan Cotterell
ETH Zürich Michael Y. Hu
NYU Tal Linzen
NYU Aaron Mueller
Northeastern University Candace Ross
Meta AI Alex Warstadt
ETH Zürich Ethan Wilcox
ETH Zürich Adina Williams
Meta AI Chengxu Zhuang
MIT

###### Abstract

After last year’s successful BabyLM Challenge, the competition will be hosted
again in 2024/2025. The overarching goals of the challenge remain the same;
however, some of the competition rules will be different. The big changes for
this year’s competition are as follows: First, we replace the loose track with
a _paper track_ , which allows (for example) non-model-based submissions,
novel cognitively-inspired benchmarks, or analysis techniques. Second, we are
relaxing the rules around pretraining data, and will now _allow participants
to construct their own datasets_ provided they stay within the 100M-word or
10M-word budget. Third, we introduce a _multimodal vision-and-language track_
, and will release a corpus of 50% text-only and 50% image–text multimodal
data as a starting point for LM model training. The purpose of this CfP is to
provide rules for this year’s challenge, explain these rule changes and their
rationale in greater detail, give a timeline of this year’s competition, and
provide answers to frequently asked questions from last year’s challenge.

##  1 The BabyLM Challenge

After last year’s successful BabyLM Challenge, the competition will be hosted
again in 2024/2025. The overarching goals of the challenge remain the same,
however, some of the competition rules will be different. The purpose of this
CFP is to provide a timeline of this year’s competition, explain the rule
changes and their rationale, and provide answers to frequently asked questions
from last year’s challenge.

As before, the goal of the BabyLM shared task is to incentivize researchers
interested in pretraining and/or cognitive modeling to focus their efforts on
optimizing pretraining given data limitations inspired by human development.
Additionally, we hope to democratize research on pertaining by drawing
attention to open problems that can be addressed on a university budget.
Please see the previous call for paper (Warstadt et al., 2023a) or the
introduction to last year’s proceedings (Warstadt et al., 2023b) for a deeper
discussion of the rationale behind the challenge.

This year’s version of the BabyLM challenge will remain the same in terms of
goals, but with a few key differences, which we list below:

  * •

To encourage contributions that are related to the goals of the challenge, but
do not involve direct competition entries, we are introducing a paper-only
track. Paper track submissions could include things like novel cognitively-
inspired evaluation metrics or in-depth analyses of one particular BabyLM
model.

  * •

Last year, all competition entrants were required to pre-train on a fixed
corpus, meaning that submissions could not investigate the impact of data
quality on pretraining. This year we will relax this requirement. While we
will still provide language-only and multi-modal (see below) datasets of 100M
and 10M words, participants are free to construct their own datasets, provided
that they stay within the 100M or 10M word budget. Participants will be asked
to provide a datasheet for any datasets they construct themselves.

  * •

Human language learning is inherently multi-modal. To encourage more multi-
modal submissions, we are replacing last year’s loose track with a vision-
language track. For this track, we will release a corpus of 50% text-only and
50% image–text multimodal data.

##  2 Key Dates

  * •

March 30 2024: Training data released

  * •

April 30 2024: Evaluation pipeline released

  * •

September 13 2024: Results due

  * •

September 20 2024: Papers due

  * •

October 8 2024: Peer review begins

  * •

October 30 2024: Peer review ends, acceptances and leaderboard released

  * •

December 9-15, 2024: Presentations at NeurIPS (pending acceptance)

Dataset | Description | # Words (multimodal track) | # Words (strict track) | # Images
---|---|---|---|---
Localized Narratives Pont-Tuset et al. (2020a) | Image Caption | 27M | – | 0.6M
Conceptual Captions 3M Sharma et al. (2018a) | Image Caption | 23M | – | 2.3M
CHILDES (MacWhinney, 2000) | Child-directed speech | 15M | 29M | –
British National Corpus (BNC), dialogue portion | Dialogue | 4M | 8M | –
Project Gutenberg (children’s stories) (Gerlach and Font-Clos, 2018) | Written English | 13M | 26M | –
OpenSubtitles (Lison and Tiedemann, 2016) | Movie subtitles | 10M | 20M | –
Simple English Wikipedia | Written Simple English | 7M | 15M | –
Switchboard Dialog Act Corpus (Stolcke et al., 2000) | Dialogue |  $<$1M | 1M | –
_Total_ | – | 100M | 100M | 2.9M

Table 1: Datasets for the multimodal and strict tracks of the 2nd BabyLM
Challenge. Word counts are approximate and subject to slight changes.

##  3 Participation Rules: Tracks

The second BabyLM Challenge includes three tracks: Strict, Strict-small, and
Vision and Paper.

The Strict and Strict-small tracks require that submissions be trained on 100M
words or less (in Strict) and 10M words or less (in Strict-small). These
tracks no longer require that participants use the fixed dataset from last
year’s challenge, although we will still provide an updated version of this
dataset for participants interested in using it. See Section 4 for details on
the updated version of this language-only dataset. Models in these tracks will
be evaluated on language-only evaluation tasks.

In the Vision track, participants will train multi-modal image-text models.
Participants can use whatever training procedure they wish, as long as models
can provide (pseudo) log-likelihoods to strings of text, conditioned on an
image. Participants are free to use whatever data they wish, as long as the
dataset is within a 100M word budget. To facilitate easier participation in
this track, we will release a suggested multimodal dataset that consists of
50% text-only and 50% paired image–text data. Submissions to this track will
be evaluated on language-only tasks, as well as multi-modal tasks.

In the Paper track, participants are invited to submit a paper on a topic
relevant to cognitive modeling with language models and scaled-down
pertaining. Some submissions we have in mind include novel cognitively-
inspired evaluation metrics or an in-depth analysis of one particular BabyLM
model. Submissions to this track are welcome to include a BabyLM model, and to
report its scores, however, evaluation task scores will not necessarily
determine the best-paper awardee from this track.

##  4 Participation Rules: Provided Dataset

For this year, we update the dataset from the text-only dataset from the
previous year and provide a novel multi-modal vision/text dataset for the
Vision track. Note that, as long as participants stay under the 100M or 10M
word budget, they are free to create their own datasets instead of using the
ones provided. Data for both the multimodal and text-only datasets can be
downloaded from https://osf.io/ad7qg/

For the text-only dataset updates, we replace the QED portion of the previous
dataset with data from CHILDES. This was done because, on further inspection,
it was found that the QED dataset was of poorer quality than hoped for.
CHILDES now comprises a larger portion of the new dataset, but the relative
proportions of the rest of the data sources remain the same. Please see the
previous year’s CFP for more details about these data sources (Warstadt et
al., 2023a)

In addition, we provide a novel image–text dataset to facilitate easier
participation in the Visionrack. This dataset includes two components: First,
we provide 50M words of text-only data, which is downsampled from the 100M
corpus (that is, we preserve the relative distribution from the different data
sources). Second, we provide paired text–image data that includes 50M words of
text. This dataset is drawn from two sources: 27M words from the Localized
Narratives (Pont-Tuset et al., 2020b) and 23M words from the conceptual
captions 3M dataset (Sharma et al., 2018b). For the Localized Narratives
dataset, our challenge uses the text captions and the images from the MS-COCO
Lin et al. (2014) and Open Images Kuznetsova et al. (2020) subset in this
dataset. For the CC3M dataset, we used the image-caption pairs whose images
were still valid in January 2024. In the OSF directory at the above link, we
provide scripts to download the images. We will provide visual embeddings of
these images computed from a visual encoder pretrained using DINOv2 Oquab et
al. (2023), one of the SOTA unsupervised learning algorithms. In addition to
the text-image data, we provide half of the 100 million words from the text-
only dataset as a text-only portion of this dataset. We take the first half of
every corpus within the text-only corpora mentioned above. Table 1 gives an
overview of the datasets used.

If not using our pre-fixed datasets, participants will be required to submit a
datasheet for their dataset (Gebru et al., 2021).

##  5 Participation Rules: Evaluation

As in the previous year, we will distribute a shared evaluation pipeline based
on Google Colab. For the Strict and Strict-small track, evaluation tasks will
be, largely, the same as the previous year. For the Vision track, we will
include an additional set of multimodal evaluation tasks. As before, our
evaluation code will be public, so that those who wish to use their own
computational resources instead of the Google Colab may do so. More details
about the evaluation pipeline and the set of tasks will be released
subsequently.

In response to comments from the previous year, this year’s evaluation
pipeline will use catwalk, which will make it easier to submit models that do
not conform to HuggingFace transformers library (although it will still be
easy to submit models if they _do_ conform to HuggingFace standards). All
models must be able to assign a (pseudo) log-likelihood to a string of text
and must be able to be fine-tuned to perform classification tasks. Models do
not need to be able to generate sequences. Submissions must include model
outputs for each of the core evaluations in a format that we specify in our
evaluation pipeline.

###  5.1 Baselines

We will release a series of baseline models. As opposed to last year’s
baselines, which were trained relatively naively, this year’s baseline will be
based on the winning submissions from last year. For the Strict and Strict-
small tracks, we will release the following baselines: GPT2 (decoder-only;
Radford et al., 2019), LTG-Bert (encoder-only; Samuel et al., 2023), and
Contextualizer (decoder-only; Xiao et al., 2023). For the Vision track, we
will release the GIT Wang et al. (2022) and Flamingo Alayrac et al. (2022)
baselines. These baselines are meant to encourage participants to innovate and
improve beyond existing models.

##  6 The Submission Process

###  6.1 Results submission

As with last year, submissions will be made using the Dynabench platform,
which is an online platform for dynamic data collection and model
benchmarking.111https://dynabench.org/

What you Need to Submit:

  * •

A link where we can download the model (any file-hosting service will do)

  * •

Model predictions for our evaluation pipeline

  * •

A datasheet for your dataset and a download link (if not using ours)

###  6.2 Paper submission

Submissions will be made through OpenReview. All submissions will be full
archival papers and can be up to eight pages in length. Formatting
requirements for submissions will be announced at a later date, once the
presentation venue has been finalized. As before, we do allow dual-submission,
however, we do not allow dual publication.

###  6.3 Review & Publication

BabyLM will hold its own review process. The acceptance criteria are based on
soundness: We plan only to reject submissions that make incorrect or
unjustified claims. Other feedback will be directed at the improvement of
submissions.

##  7 FAQs

#### Can papers be submitted to multiple tracks?

Yes. For example, a single paper can describe models that are submitted
separately to the Strict and Vision tracks.

#### Can I submit a paper about my work?

Yes, we require that all submissions be accompanied by a paper, which can be
up to eight pages in length (although it doesn’t have to be). Papers will be
published in an archival format. All papers can describe experiments and
analyses beyond the scope of the competition, and this type of non-competition
contribution is required for the Paper track.

#### Can I submit additional evaluation metrics?

Yes, you may submit additional evaluation metrics alongside a competition
model in the Strict, Strict-small, and Vision tracks. This type of
contribution is especially encouraged in the Paper track.

#### What training regimes are permitted?

Any kind of training objective/regime is permitted, as long as the data
restrictions are followed. If you use ancillary models, for example for
reranking or data augmentation, then the training data for these models is
counted towards your 100M word budget.

For evaluation purposes, we require that the model provides a function to
score a sequence of words without the need for additional fine-tuning.

#### Are there any limits on hyperparameters?

No. But please share at the end what you found so we can learn from your
efforts.

#### Are there any limits on the number of epochs?

No. We put no restrictions on the number of epochs, for several reasons:
First, from an engineering perspective, training LMs with SGD tends to require
multiple epochs at these scales to achieve peak performance. Second, from a
cognitive perspective, humans have a memory of linguistic experience and can
continue to access and learn from these memories. Third, we try not to make a
stand on implementations to allow the most freedom for innovation. Our
internal results suggest, however, that under regular circumstances, over-
training on more than a couple epochs give minor gains at most.

#### Can I use external tools?

Yes, but if they learned on language their tokens are counted towards the
100M. That means one can train on the same text both a tokenizer, a parser, an
LM etc. or on parts of the 100M, but the sum of all text seen by all training
can not surpass the amount of text allowed. This raises the questions of
synthetic data. It is allowed, under some restrictions. You may generate the
100M tokens in any legal way you like (yes, distilling or writing your own is
fair, if you figure what text facilitates learning it is interesting
regardless of how to gather such text), you may also train eventually on more
than 100M words by augmentation, however that only works in a closed system,
i.e., the augmentors training data counts toward the limit, so for example
training two LMs on half of the words, and then have them generate more words
and train a model on both the original data and the new one is legit (and it
was not tested in the previous competition, so even the example itself is
interesting).

#### I have different modalities that can help

If it is not linguistic data, prove it, last year’s submission did not gain
from non-linguistic grounding, but we encourage such scientific questions. If
it is linguistic in nature (e.g., audio), then the words should still count
towards the overall number of learnt words.

##  8 Organizing Committee

(Alphabetical by last name) Leshem Choshen, Ryan Cotterell, Michael Hu, Tal
Linzen, Aaron Muller, Candace Ross, Alex Warstadt, Ethan Wilcox, Adina
Williams, Chengzu Zhuang. Feel free to contact members of the organizing
committee at<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
## References

  * Alayrac et al. (2022) Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. 2022.  Flamingo: a visual language model for few-shot learning.  _Advances in neural information processing systems_ , 35:23716–23736.
  * Gebru et al. (2021) Timnit Gebru, Jamie Morgenstern, Briana Vecchione, Jennifer Wortman Vaughan, Hanna Wallach, Hal Daumé Iii, and Kate Crawford. 2021.  Datasheets for datasets.  _Communications of the ACM_ , 64(12):86–92.
  * Gerlach and Font-Clos (2018) Martin Gerlach and Francesc Font-Clos. 2018.  A standardized Project Gutenberg corpus for statistical analysis of natural language and quantitative linguistics.  _Computing Research Repository_ , arXiv:1812.08092.
  * Kuznetsova et al. (2020) Alina Kuznetsova, Hassan Rom, Neil Alldrin, Jasper Uijlings, Ivan Krasin, Jordi Pont-Tuset, Shahab Kamali, Stefan Popov, Matteo Malloci, Alexander Kolesnikov, et al. 2020.  The open images dataset v4: Unified image classification, object detection, and visual relationship detection at scale.  _International journal of computer vision_ , 128(7):1956–1981.
  * Lin et al. (2014) Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. 2014.  Microsoft coco: Common objects in context.  In _Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13_ , pages 740–755. Springer.
  * Lison and Tiedemann (2016) Pierre Lison and Jörg Tiedemann. 2016.  OpenSubtitles2016: Extracting large parallel corpora from movie and TV subtitles.  In _Proceedings of the Tenth International Conference on Language Resources and Evaluation (LREC’16)_ , pages 923–929, Portorož, Slovenia. European Language Resources Association (ELRA).
  * MacWhinney (2000) Brian MacWhinney. 2000.  _The CHILDES project: The database_ , volume 2.  Psychology Press.
  * Oquab et al. (2023) Maxime Oquab, Timothée Darcet, Théo Moutakanni, Huy Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel Haziza, Francisco Massa, Alaaeldin El-Nouby, et al. 2023.  Dinov2: Learning robust visual features without supervision.  _arXiv preprint arXiv:2304.07193_.
  * Pont-Tuset et al. (2020a) Jordi Pont-Tuset, Jasper Uijlings, Soravit Changpinyo, Radu Soricut, and Vittorio Ferrari. 2020a.  Connecting vision and language with localized narratives.  In _Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part V 16_ , pages 647–664. Springer.
  * Pont-Tuset et al. (2020b) Jordi Pont-Tuset, Jasper Uijlings, Soravit Changpinyo, Radu Soricut, and Vittorio Ferrari. 2020b.  Connecting vision and language with localized narratives.  In _Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part V 16_ , pages 647–664. Springer.
  * Radford et al. (2019) Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. 2019.  Language models are unsupervised multitask learners.  _OpenAI blog_ , 1(8):9.
  * Samuel et al. (2023) David Samuel, Andrey Kutuzov, Lilja Øvrelid, and Erik Velldal. 2023.  Trained on 100 million words and still in shape: Bert meets british national corpus.  _arXiv preprint arXiv:2303.09859_.
  * Sharma et al. (2018a) Piyush Sharma, Nan Ding, Sebastian Goodman, and Radu Soricut. 2018a.  Conceptual captions: A cleaned, hypernymed, image alt-text dataset for automatic image captioning.  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 2556–2565.
  * Sharma et al. (2018b) Piyush Sharma, Nan Ding, Sebastian Goodman, and Radu Soricut. 2018b.  Conceptual captions: A cleaned, hypernymed, image alt-text dataset for automatic image captioning.  In _Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 2556–2565.
  * Stolcke et al. (2000) Andreas Stolcke, Klaus Ries, Noah Coccaro, Elizabeth Shriberg, Rebecca Bates, Daniel Jurafsky, Paul Taylor, Rachel Martin, Marie Meteer, and Carol Van Ess-Dykema. 2000.  Dialogue act modeling for automatic tagging and recognition of conversational speech.  _Computational Linguistics_ , 26(3):339–371.
  * Wang et al. (2022) Jianfeng Wang, Zhengyuan Yang, Xiaowei Hu, Linjie Li, Kevin Lin, Zhe Gan, Zicheng Liu, Ce Liu, and Lijuan Wang. 2022.  Git: A generative image-to-text transformer for vision and language.  _arXiv preprint arXiv:2205.14100_.
  * Warstadt et al. (2023a) Alex Warstadt, Leshem Choshen, Aaron Mueller, Adina Williams, Ethan Wilcox, and Chengxu Zhuang. 2023a.  Call for papers–the babylm challenge: Sample-efficient pretraining on a developmentally plausible corpus.  _arXiv preprint arXiv:2301.11796_.
  * Warstadt et al. (2023b) Alex Warstadt, Aaron Mueller, Leshem Choshen, Ethan Wilcox, Chengxu Zhuang, Juan Ciro, Rafael Mosquera, Bhargavi Paranjabe, Adina Williams, Tal Linzen, et al. 2023b.  Findings of the babylm challenge: Sample-efficient pretraining on developmentally plausible corpora.  In _Proceedings of the BabyLM Challenge at the 27th Conference on Computational Natural Language Learning_ , pages 1–34.
  * Xiao et al. (2023) Chenghao Xiao, G Thomas Hudson, and Noura Al Moubayed. 2023.  Towards more human-like language models based on contextualizer pretraining strategy.  In _Proceedings of the BabyLM Challenge at the 27th Conference on Computational Natural Language Learning_ , pages 317–326.