# Constraining the SMEFT with a differential cross section measurement of
$tWZ$ production at the HL-LHC.

James Keaveney<EMAIL_ADDRESS>University of Cape Town,
University Avenue, Cape Town, South Africa

###### Abstract

A prospective measurement of the differential cross section of $tWZ$
production with respect to the transverse momentum of the
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson using a general-purpose detector at the High-Luminosity Large Hadron
Collider (HL-LHC) is described. The response of a general-purpose detector at
the HL-LHC is simulated and used to estimate the uncertainties and covariances
of the differential cross section measurement. Constraints on the Standard
Model Effective Field Theory (SMEFT) enabled by the measurement are estimated.
A parametric model of the differential cross section in the SMEFT is
constructed and is used to determine the expected posterior probability
function of six SMEFT Wilson coefficients and the expected 95% Bayesian
credible intervals for each coefficient and pair of coefficients. The
intervals suggest that for all coefficients, the measurement will provide
competitive but weaker constraints than those derived from other HL-LHC
measurements involving top quarks and
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
bosons. However, as the measurement is simultaneously sensitive to to a unique
set of SMEFT coefficients, it will provide a useful input to a global SMEFT
analysis that considers many operators.

††preprint: APS/123-QED

##  I Introduction

The relevance of the top quark’s couplings to theories of new physics is well
documented [2, 3, 4, 1]. Given the lack of evidence of resonant production of
new particles in the Large Hadron Collider (LHC) data, attention has turned to
new physics scenarios in which new particles have masses around an energy
scale $\Lambda$ that is large with respect to the scales directly probed at
the LHC. The Standard Model Effective Field Theory (SMEFT) is a theoretical
framework that describes the effects of such heavy new particles on lower
energy observables. The SMEFT Lagrangian is obtained by extending the SM
Lagrangian with higher-order operators [12]. In the work presented here, only
the dominant, dimension-6 operators are considered with the contribution of
each operator to the Lagrangian scaled by a dimensionless Wilson coefficient
$c_{i}$ divided by $\Lambda^{2}$. If the scale of new physics is indeed large
with respect to the LHC energies, significant deviations of measurements of
$c_{i}$ from the SM expectation ($c_{i}=0$) may be the first evidence of new
physics. As the particle physics community prepares for the HL-LHC where
proton collision datasets of unprecedented size will be produced, it is
crucial to identify previously unexplored measurements that have the potential
to improve the precision at which $c_{i}$ can be determined. In this document,
the potential of a measurement of one such observable, the differential cross
section of $tWZ$ production, at a general-purpose detector is explored.

##  II Expectations for the $tWZ$ process at the HL-LHC

The $tWZ$ process refers to the electroweak production of a single top quark
in association with a
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson and a
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson. In 13 TeV proton collisions, $tWZ$ is predicted to have a SM cross
section of $\approx 107$ fb at NLO in QCD when an operational definition of
the $tWZ$ process is adopted [5]. The modelling of this process at NLO in QCD
has also been explored in [6] and the sensitivity of the inclusive $tWZ$ cross
section to the SMEFT coefficients has been quantified in [5, 7, 9]. As the
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson may be radiated from the initial-state bottom quark, the final-state top
quark, or the final-state
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson, the process already exhibits complex phenomenology at LO in the SM by
simultaneously embedding the
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$-$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$,
$\mathit{{b}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$-$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$,
and
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$-$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
electroweak couplings. Consequently, the $tWZ$ process is sensitive to
multiple SMEFT operators. These operators modify SM interaction vertices and
generate new vertices not present in the SM. Not all of the operators that
affect the $tWZ$ process involve the top quark field. Although the primary
goal of this work is to estimate potential constraints on SMEFT coefficients
related to top quark couplings, ignoring all other operators that affect the
$tWZ$ process could lead to an overestimation of the precision of the
constraints. Therefore the following set of operators are chosen on the basis
of them having a significant effect on either the overall rate or kinematics
of the $tWZ$ process. However the list is not exhaustive and investigation of
the expected complex interplay within a larger set of operators in an NLO
cross section calculation is left to future work. Similarly, interference
effects at NLO between the $tWZ$ and
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
processes may be important to a future analysis of $tWZ$ measurements at the
HL-LHC in the SMEFT. In this paper, the implementation of the SMEFT in the
SMEFTatNLO package [10] is adopted. The operator definitions in SMEFTatNLO are
provided explicitly in [11]. The definitions of first three of these
operators, taken from [11], are:

  * $\mathcal{O}^{(3)}_{\phi{}\mathit{{q}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}}~{}=~{}i(\phi^{\dagger}\overset{\text{\tiny$\bm{\leftrightarrow}$}}{D}_{\mu}\tau_{I}\phi)(\bar{Q}\gamma^{\mu}\tau^{I}Q)$

  * $\mathcal{O_{\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}}~{}=~{}i(\bar{Q}\tau^{\mu\nu}\tau_{I}t)\tilde{\phi}W^{I}_{\mu\nu}$+h.c.

  * $\mathcal{O}_{\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}G}=ig_{s}(\bar{Q}\tau^{\mu\nu}T_{A}t)\tilde{\phi}G^{A}_{\mu\nu}$ \+ h.c.

A linear combination of the effects of the operators
$\mathcal{O_{\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}}$
and
$\mathcal{O_{\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}B}}~{}=~{}i(\bar{Q}\tau^{\mu\nu}t)\tilde{\phi}B_{\mu\nu}$+h.c.
according to to the Weinberg angle is also considered leading to four
independent degrees of freedom in the SMEFT analysis.

The advantages of $tWZ$ measurements in constraining the SMEFT coefficients
are detailed in [9]. The effect of the SMEFT operators on the $tWZ$ process
show an energy dependence that is more pronounced than that of alternative
processes such as
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{q}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$.
Thus as more data is recorded and measurements of higher-energy phase space of
$tWZ$ become possible, constraints on SMEFT coefficients from $tWZ$ will
continue to improve after constraints from processes with weaker energy
dependence become saturated. This serves as particular motivation to assess
the potential of measuring $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ as a probe of
the high-energy phase space of $tWZ$.

Only two final-state topologies of the $tWZ$ process will be measurable with
reasonable precision at the HL-LHC. The first topology ($3\ell$) corresponds
to the case where the
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson decays to a pair of oppositely-charged electrons or muons and at least
one other electron or muon is produced from the decays of the
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
bosons. The second topology ($4\ell$) corresponds to the case where the
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson and both
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
bosons decay into electrons or muons.

The estimation of expected experimental uncertainties and inter-bin
covariances in the measurement of $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ at the
HL-LHC is now described. For all of the following studies, a proton-proton
centre-of-mass energy of 13 TeV and an integrated luminosity of 3000 fb-1 is
assumed. A set of Monte-Carlo simulation event samples corresponding to the SM
expectation for the signal and background processes were generated using
MadGraph5_aMC@NLO v2_6_7 for the matrix-element calculation and PYTHIA v8.306
for the parton shower and hadronisation modelling. For the $3\ell$ topology
the considered backgrounds are
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$,
the production of a
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
and
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson in association with at least two jets including b-jets
($\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{b}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{b}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}$),
and the production of the a single top quark in association with a
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson
($\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{q}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$).
For the $4\ell$ topology the considered backgrounds are
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$,
and the production of a pair of
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
bosons in association with at least two least two jets not including b-jets
($\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}jj$).
Other background processes are assumed to be negligible in the context of a
$tWZ$ cross section measurement.

The samples were processed with the DELPHES v3_5_0 framework [13] configured
to simulate the response of a general-purpose detector in the experimental
conditions of the HL-LHC. Two mutually-exclusive event selection schemes were
applied that target the two topologies while suppressing the respective
background processes. In Table 1, the common criteria applied to the _objects_
, i.e, electrons, muons and jets, reconstructed within each event and the two
sets of criteria to select events for the two topologies are detailed. In
Figures 1, and 2, the distributions of the transverse momentum of the
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson candidate reconstructed in each event for the two topologies
respectively are shown. The distributions are _stacked_ such that for each
figure the sum of the illustrated components corresponds to the total expected
distribution. In the case of the signal and
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
processes, the expected distributions are normalised according to the NLO QCD
cross sections. For the other background processes the LO QCD cross sections
are used.

The figures indicate that the $tWZ$ signal is small compared to the
backgrounds. Hence the total uncertainties on the measurement of
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ will be dominated by the uncertainties on
the background contributions. In a recent CMS paper[14], the differential
cross sections of the
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{q}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
process and background contributions were estimated via a maximum-likelihood
fit. With this technique the uncertainty on the background contribution is
largely determined by the statistical uncertainties on the background
contributions and additional modelling and instrumental uncertainties.
Assuming that such a technique will be applied to the measurement of
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$, the total expected uncertainty on the
measurement is estimated as the quadrature sum of the statistical uncertainty
on the total background and a 10% systematic uncertainty on the measured cross
section to account for additional modelling effects. However there is
significant potential for further reduction of the background contributions
and hence greater precision on the $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$
measurement. The
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{b}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{b}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}$
and
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{q}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
backgrounds in the $3\ell$ topology could be reduced via the reconstruction
and selection of hadronically-decaying
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
bosons from dijet systems that are a feature of the signal process but will
not be present in the
$\mathit{{W}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{b}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{b}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}$
process when the ($3\ell$) topology is selected. Due to the fundamental
similarity between the $tWZ$ and
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
processes, suppression of the of
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
background is more difficult. However multivariate techniques can exploit
subtle differences in the kinematics of the $tWZ$ and
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
processes associated with the differing number of resonant top quarks. This
approach has been successfully employed in the measurement of the differential
cross sections of the
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{q}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
process in [14]. The development of multivariate algorithms depends crucially
on precise and calibrated simulation of the detector response and is thus not
attempted here in this exploratory study.

The statistical uncertainties within each bin depend on the binning scheme.
Increasing the number of bins will yield greater sensitivity to the SMEFT
coefficients as the shape of the distributions is measured in greater detail.
Furthermore the number of coefficients that can be independently constrained
by a single absolute differential cross section is limited by the number of
bins. Conversely, statistical uncertainties in each bin increase as the number
of bins increases, degrading the constraints on the SMEFT coefficients. A
binning scheme that consisting of four equal-width bins between 0 and 300 GeV
that aims to balance these concerns is adopted.

Differential cross sections are typically measured after an unfolding
procedure in which the resolution effects of the detector response are
accounted for. The unfolding procedure introduces statistical correlations
between the measured values of $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ in the bins
of the unfolded differential cross section due to migrations of events across
bin boundaries. These migrations are modelled with a migration matrix that
encodes the probabilities of events in a given bin at unfolded level being
observed in each bin at detector level. Similarly, sources of systematic
uncertainty that cause correlated effects in multiple bins introduce
additional inter-bin correlations. The uncertainties on a measurement of the
unfolded $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ are estimated by combining the
expected detector-level distributions in the two topologies and unfolding the
combined distributions using the ROOUNFOLD package [18] in which the Iterative
Bayesian unfolding algorithm [8] is applied. The number of iterations for this
algorithm was set to 4 as this was found to produce good agreement between the
true and unfolded $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ distributions. The
robustness of the unfolding setup in the presence of SMEFT signals was
verified by applying an multiplicative factor to
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ at detector- and truth-levels that depended
linearly on $p^{Z}_{T}$ and varied from 1.0 in the first bin to 1.5 in the
last bin and applying the unfolding that was developed with the SM $tWZ$
prediction. The agreement between unfolded and true
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ distributions remained excellent in the
presence of this signal. The binning of the unfolded distribution is chosen to
match that of the detector-level distributions. The migration matrix is
estimated by comparing the simulated sample of $tWZ$ events at detector- and
generator-levels. In the upper panel of Figure 3, the SM prediction for
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ in the chosen binning scheme is shown. The
estimated total uncertainty on after the application of the unfolding process
is shown by the blue band. The estimated systematic uncertainty is shown by
the gold band. The central panel of the figure shows the same two
uncertainties expressed as percentages of the SM expectation. As none of the
suggested kinematic reconstruction or multivariate techniques have been
applied, these estimates of the uncertainties may be considered conservative.

Table 1: The criteria applied to objects and events for the two topologies are
shown. Where the object criterion for the two topologies differ, the criterion
applied in the $4\ell$ topology is shown in brackets. Objects
---
Object type | Criteria
$\ell$ |  $p_{T}$ $>$ 15 (10) GeV, iso $<$ 0.1, $|\eta|<4$
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$ candidate |  $60<m_{\ell,\bar{\ell}}<120$ GeV
jet |  $p_{T}$ $>$ 30 (20) GeV, $|\eta|<4.5$
Events
Topology | Criteria
$3\ell$ |  $N_{\ell}=3$, $N_{Z}=1$, $N_{jet}\geq 3$, $N_{btag}\geq 1$
$4\ell$ |  $N_{\ell}=4$, $N_{Z}=1$, $N_{jet}\geq 1$, $N_{btag}\geq 1$
Figure 1: The expected distributions of $p^{Z}_{T}$ for the signal and
background processes after the application of the $3\ell$ selection at the HL-
LHC are shown. Figure 2: The expected distributions of $p^{Z}_{T}$ for the
signal and background processes after the application of the $4\ell$ selection
at the HL-LHC are shown. Figure 3: The prediction for
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ at 13 TeV calculated in the SM with
MadGraph5_aMC@NLO at LO in QCD but normalised according to the NLO cross
section is shown in the upper panel. The expected total and systematic
uncertainties of a measurement of this distribution at the HL-LHC are shown by
the blue and gold bands respectively. The central panel shows the
uncertainties expressed as percentages of the central values of the
prediction. The lower panel shows the differences between the SM prediction
and a set of SMEFT predictions corresponding to each coefficient set to a
value of $c_{i}=1.0$ TeV-1 with all other coefficients set to 0 TeV-1. The
differences are expressed as percentages of the SM prediction.

##  III Differential cross sections in the SMEFT

If the SMEFT Lagrangian contains $n$ dimension-6 operators $c_{i}$ and the
number of such operators in each Feynman diagram is limited to one, any cross
section in the SMEFT can be expressed as a 2nd order multivariate polynomial
in $c_{i}$:

$\sigma(c_{i})=\sigma_{SM}+\sum^{i=n}_{i=1}\frac{c_{i}}{\Lambda^{2}}\beta_{i}+\sum^{j=n}_{j=1}\sum^{i=n}_{i=1}\frac{c_{i}c_{j}}{\Lambda^{4}}\beta_{ij}$

In this expression, $\sigma(c_{i})$ is the cross section in the SMEFT, written
explicitly as a function of the $n$ SMEFT coefficients and $\sigma_{SM}$ is
the SM cross section. The $\frac{c_{i}}{\Lambda^{2}}\beta_{i}$ terms represent
the contributions from the product of the SM amplitude and the amplitudes of
diagrams containing a dimension-6 vertex. The group of terms
$\frac{c_{i}c_{j}}{\Lambda^{4}}\beta_{ij}$ represent the $n^{2}$ contributions
from the products of amplitudes of diagrams containing a vertex from the
$i^{th}$ operator with the amplitudes of diagrams containing a vertex from the
$j^{th}$ operator and thus includes the contributions from the squares of the
amplitudes of diagrams containing a vertex from the $i^{th}$ operator. As
$\frac{c_{i}c_{j}}{\Lambda^{4}}\beta_{ij}=\frac{c_{j}c_{i}}{\Lambda^{4}}\beta_{ji}$,
only $(\frac{(n)(n+1)}{2})$ independent contributions are present in the
$\sum^{j=n}_{j=1}\sum^{i=n}_{i=1}\frac{c_{i}c_{j}}{\Lambda^{4}}\beta_{ij}$
term. The terms $\sigma_{SM}$, $\beta_{i,1}$ and $\beta_{i,j}$, are specific
to the process and represent the $b$ unknowns of the polynomial where
$b=1+n+(\frac{(n)(n+1)}{2})$. Thus for $n$ operators, $b$ is the $(n+1)^{th}$
triangular number. If the $\sigma$ and $\beta$ terms are vectors with elements
corresponding to the contributions to the differential cross section within
each bin, then the polynomial represents a parametric model of a differential
cross section.

An exact solution for the unknowns of the polynomial can be found by making a
minimum number of theoretical calculations for $\sigma_{SMEFT}$ at distinct
points in $c_{i}$ space and forming a system of linear equations in an
approach known as _morphing_ [16, 17]. An alternative approach based on
Bayesian reasoning is presented in [19]. In general, Monte-Carlo based
theoretical predictions carry significant statistical uncertainties,
especially in regions of phase space with small cross sections. Furthermore,
in SMEFT calculations involving multiple operators, one or more of the
unknowns may be extremely small relative to the others at all of the points in
$c_{i}$ space used to construct the system of linear equations. Hence these
relatively small unknowns can be imprecisely determined by the exact solution
to the linear system. When contributions associated to these unknowns become
large in other regions of the SMEFT coefficient space, inaccuracies in the
predictions of the morphing model can arise. The approach pursued here, termed
_regression morphing_ , alleviates this issue. Instead of producing an exact
solution of a system of linear equations, the unknowns are determined by
minimising the sum of squared differences $S$ between $p$ theoretical
predictions for the differential cross section at randomly distributed points
in the SMEFT coefficient space and the corresponding predictions of the
regression morphing model. For a model derived from $p$ predictions, each with
$q$ bins, $S$ is defined as

$S(\vec{\beta})=\sum^{i=p}_{i=1}\sum^{j=q}_{j=1}(d\sigma_{i,j}-{x(\vec{\beta})_{i,j}})^{2}$

where $S$ is written explicitly as a function of a vector of the model’s
unknowns $\vec{\beta}$, $d\sigma_{i,j}$ is the differential cross section in
the $j^{th}$ bin of the $i^{th}$ theoretical prediction and
$x(\vec{\beta})_{i,j}$ is the corresponding prediction of the model. The
regression morphing model can be made arbitrarily accurate in any region of
the SMEFT coefficient space by including a sufficient number of predictions
when minimising $S$.

##  IV Constraining SMEFT coefficients

To construct a regression morphing model for
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ at the HL-LHC, 270 _training_ predictions
for $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ 13 TeV proton collisions were generated
at random points in the $c_{i}$ space. The predictions were produced with the
SMEFTatNLO [10] package implemented in the MadGraph5_aMC@NLO Monte Carlo
generator version v2_6_7 [20] at LO in QCD and in fixed-order mode. Although
fixed-order predictions lack the parton shower and hadronisation modelling
usually important to the modelling of hadron collider observables, the speed
of generation and lack of a need to process large MC event samples makes them
invaluable in the construction of regression morphing models and are
sufficient to demonstrate the sensitivity of
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ to the SMEFT coefficients. Similarly, the
usage of NLO predictions would yield more precise estimates of
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ and expected constraints on the $c_{i}$.
However, NLO predictions would require either the application of a diagram
removal scheme to suppress components of the $tWZ$ calculation that overlap
with the
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
process or a calculation that fully accounts for overlapping components and
associated interference effects. Such a theoretical treatment is left to
future work.

To validate the model, 30 _test_ predictions, statistically independent from
the training predictions, were generated at random points in the SMEFT
coefficient space and compared to the corresponding predictions of the model.
The binned residuals between the test predictions and model predictions
expressed as percentages of the test predictions are Gaussian-distributed with
a mean of -0.0005 % and standard deviation of 0.0089 %, demonstrating that the
inaccuracies in the regression morphing model model are negligible. The
posterior probability density function $p(c_{i}|x,\Sigma)$ is used to derive
constraints on the four SMEFT coefficients where $c_{i}$ are the SMEFT
coefficients, $x$ are expected measured values of
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ in the SM scenario, and $\Sigma$ is the
estimated covariance matrix of $x$ given the previously stated assumptions on
uncertainties and correlations.

Figure 4: An array of the marginalised posterior probability density functions
is shown. The 1-D functions for each of the SMEFT coefficients are placed
along the grid diagonal. For each 1-D function, the median $c_{i}$ value is
indicated with the difference between this value and the limits of the 95%
credible intervals given by the superscripts and subscripts and also by the
vertical dashed lines. The 95% credible intervals are also represented by the
blue bars in the panel on the top right after they have been shifted such that
the best-fit values equal 0. The 2-D functions for each pair of coefficients
are shown in the other grid spaces. The white regions on the 2-D functions are
CIs constructed to coincide with the 1-D CIs.

The expected data are assumed to be Gaussian-distributed hence the log-
likelihood is approximated as a $\chi^{2}$ function accounting for the inter-
bin correlations of the data introduced by the _unfolding_ process used to
correct for detector resolution effects. This leads to the final expression
for $p(c_{i}|x,\Sigma)$:

$p(c_{i}|x,\Sigma)=p(c_{i})(-0.5)(d(c_{i},x)^{T}\Sigma^{-1}d(c_{i},x))$

where $p(c_{i})$ is the prior probability of the SMEFT coefficients,
$d(\frac{c_{i}}{\Lambda^{2}},x)$ is a column vector of the residuals between
the regression morphing model and expected data for the coefficient values
$\frac{c_{i}}{\Lambda^{2}}$, $d(\frac{c_{i}}{\Lambda^{2}},x)^{T}$ is the
transpose of $d(\frac{c_{i}}{\Lambda^{2}},x)$, and $\Sigma^{-1}$ is the
inverse of the covariance matrix of the expected data. This expression ignores
the constant factor present in the canonical definition of the posterior
probability which has no effect on the constraints. The prior probability is
chosen to be constant as a function of all SMEFT coefficients within an
allowed region that is much larger than the expected 95% credible intervals
(CI) of the posterior function and zero elsewhere. The central values of the
expected data are chosen the match the prediction of the model in the SM
($c_{i}=0$) hypothesis. A numerical estimation of $p(c_{i}|x,\Sigma)$ is
produced using the emcee package [21] that implements a Markov Chain Monte
Carlo algorithm. The constraint on a given single SMEFT coefficient is defined
as the 95% CI of the 1-D pdf obtained by marginalising $p(c_{i}|x,\Sigma)$
over the other coefficients centered around 0. In order to verify the validity
of the SMEFT in the energy regime of a differential cross section it has been
suggested to compare results with and without the highest energy bin included
[15]. Thus the analysis is also performed after the removal of the last bin of
the $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ distribution and hence the last row and
column of the covariance matrix. The difference in results between these two
setups is small indicating that the sensitivity of the
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ measurement is not dominated by the last
bin and checks of the validity of the SMEFT model in this energy regime will
be possible in an analysis using real HL-LHC data.

In Figure 4, the 1- and 2-D marginalised posterior functions are shown in a
grid arrangement. The marginalisations of $p(c_{i}|x,\Sigma)$ are performed
with the corner package [22]. The median values of the posterior function and
the positive and negative distances to the edges of the CI are shown in text
above each 1-D pdf. The edges of 95% CI centered around the median for the
each of the six 1-D function are illustrated by vertical dashed lines. The
blue lines indicate the SM expectation ($c_{i}$). The white regions on the 2-D
distributions are CIs constructed as to coincide with the 1-D CIs. The SM
expectations for the $c_{i}$ are indicated by intersections of the blue lines.
An additional plot with the final constraints and those produced with the last
bin omitted is provided in the upper-right corner of the figure. The
sensitivity of $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ to all six coefficients is
apparent by the finite widths of the CI. Correlations between the values of
$c_{t\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}}$
and $c_{tW}$ are apparent in the shape of the corresponding 2-D functions.
These correlations could be mitigated by utilising an alternative differential
distribution or by including measurements of other processes such as
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
and
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$$\mathit{{q}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
that are sensitive to subsets of these operators.

In Figure 5, the constraints are shown alongside frequentist 95% confidence
intervals on subsets of these four coefficients reported a set of five other
analyses for the purposes of broad comparison. The set comprises an analysis
of an array of top quark measurements using LHC data with the SMEFiT framework
[23], a similar SMEFT analysis focusing top quark data from the LHC performed
by the IFIT collaboration [24], constraints from a measurement of the
differential cross section at 13 TeV from the CMS experiment [25], expected
constraints from a measurement of the inclusive
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
cross section at the HL-LHC by the CMS experiment [26] and an estimation of
the constraints obtainable from a future measurement of the
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
cross section at the HL-LHC in the channel where the
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson decays to a pair of neutrinos [27]. Due to the LO modelling of the $tWZ$
signal, the approximations made to derive expected uncertainties and
covariances of the $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ measurement, and the
different statistical definitions of the constraints, quantitative comparison
of the constraints is difficult. However it is apparent that the constraint on
$c_{tZ}$ derived from the measurement of $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$
will be competitive with those already obtained from global analyses of LHC
data using the SMEFiT framework [23]. The constraints on $c_{tZ}$
$\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ are significantly weaker than derived from
measurements of the
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
process. However it is not clear that this difference will remain when the
many four-quark operators that affect the
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
process but not the $tWZ$ process are considered. While the constraints on the
other $c_{i}$ appear significantly weaker than those from other measurements,
the large number of operators affecting $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$
suggests that this observable will be useful in improving constraints in
analysis simultaneously utilising large sets of top quark measurements.

The construction and validation of the regression morphing model as well as
interfaces to emcee and corner is provided by _d_ EFT, a python package
available on GitHub111The _d_ EFT codebase is available under a GNU GENERAL
PUBLIC LICENSE at _d_ EFT on GitHub..

Figure 5: The expected 1-D 95% CI on the four SMEFT coefficients produced in
this work are shown by the blue bars. Frequentist 95% confidence intervals on
subsets of these coefficients reported elsewhere are shown for broad
comparison [23, 24, 25, 26, 27].

##  V Conclusion and outlook

An analysis of the effects of a set of four dimension-6 operators in the SMEFT
on the differential cross section of $tWZ$ production with respect to the
transverse momentum of the
$\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}$
boson is presented. Estimates of the uncertainties and covariances of the a
measurement based on LHC data are used to estimate the expected constraints on
the SMEFT coefficients. A method termed regression morphing is used to
construct a parametric model of $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ as a
function of the SMEFT coefficients.

A numerical approximation of the expected posterior probability function is
derived. Constraints on the coefficients are defined as 95% credible intervals
determined by marginalising the posterior probability function. In the case of
$c^{(3)}_{\phi{}\mathit{{q}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}}$,
the constraint is comparable or stronger than those derived from arrays of LHC
measurements [23, 24] and is comparable to expected constraints from
measurements of the inclusive
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
cross section at the HL-LHC and the differential
$\mathit{{t}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}\mathit{{\mkern
4.0mu\overline{\mkern-4.0mu{t}}}{}_{\mspace{-2.0mu}\scriptstyle{}}^{\mspace{0.0mu}\scriptstyle{}}}{}\mathit{{Z}{}_{\mspace{-3.0mu}\scriptstyle{}}^{\mspace{-1.0mu}\scriptstyle{}}}{}$
cross section at the LHC [23, 24, 25, 26, 27].

The measurement will also constrain the other coefficients to a lesser degree
than other HL-LHC measurements and LHC measurements considered. Hence we
conclude that measurements of $\frac{d\sigma_{tWZ}}{dp^{Z}_{T}}$ at the HL-LHC
will be an important input to a global analysis of SMEFT coefficients with the
potential to increase the discovery potential for new physics in the top quark
sector in the HL-LHC data.

###### Acknowledgements.

The author would like to acknowledge the usage of the High Performance
Computing cluster at the University of Cape Town and to thank Ilaria Brivio
and Stephen Farry for much useful feedback.

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# Bandgap manipulation of hBN by alloying with aluminum: absorption properties
of hexagonal BAlN

Jakub Iwański<EMAIL_ADDRESS>Mateusz Tokarczyk  Aleksandra K.
Dąbrowska
Jan Pawłowski  Piotr Tatarczak  Johannes Binder  Andrzej Wysmołek  Faculty of
Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland

###### Abstract

The versatile range of applications for two-dimensional (2D) materials has
encouraged scientists to further engineer the properties of these materials.
This is often accomplished by stacking layered materials into more complex van
der Waals heterostructures. A much less popular but technologically promising
approach is the alloying of 2D materials with different element compositions.
In this work, we demonstrate a first step in manipulating the hBN bandgap in
terms of its width and indirect/direct character of the optical transitions.
We present a set of aluminum alloyed hexagonal boron nitride (hBAlN) samples
that were grown by metal organic vapor phase epitaxy (MOVPE) on 2-inch
sapphire substrates with different aluminum concentration. Importantly, the
obtained samples revealed a sp2-bonded crystal structure. Optical absorption
experiments disclosed two strong peaks in the excitonic spectral range with
absorption coefficient $\alpha\sim 10^{6}$ cm-1. Their energies correspond
very well with the energies of indirect and direct bandgap transitions in hBN.
However, they are slightly redshifted. This observation is in agreement with
predictions that alloying with Al leads to a decrease of the bandgap energy.
The observation of two absorption peaks can be explained in terms of mixing
electronic states in the K and M conduction band valleys, which leads to a
significant enhancement of the absorption coefficient for indirect
transitions.

BAlN alloy, hBN, epitaxy, MOVPE, bandgap manipulation, excitonic absorption

##  I INTRODUCTION

The initial research on graphene has motivated researchers to explore the
properties of other atomically thin layered materials (2D materials) and their
stacks, sometimes referred to as NanoLego structures [1, 2, 3, 4]. This is
typically accomplished by stacking different layers together into into van der
Waals heterostructures [5, 6]. Combining these materials using epitaxial
growth provides the additional opportunity to scale-up such structures or to
create new ones by growing materials as alloys with appropriate composition
[7, 8]. In the case of hexagonal boron nitride (hBN), the natural choice is
alloying hBN with aluminum and gallium, since they are in the same group of
the periodic table as boron. Research on the novel hB1-x-yAlxGayN material
(where $x$ and $y$ stand for Al and Ga concentration in the alloy
respectively) is interesting in terms of exploration of new physical phenomena
as well as form a technological point of view. hBN with its, unusual for
III-N, strong sp2 covalent bonds in plane and weak van der Waals bonds out of
plane exhibits extraordinary properties [9]. One of the intriguing facts is
that inspite of the indirect character of the bandgap, hBN shows a
photoluminescence (PL) emission intensity of the band-edge transition as
strong as for direct semiconductors [10]. Thus, the possibility of tuning the
hBN bandgap using Al opens up further prospects for applications in hBN-based
quantum wells and optoelectronic devices. The same scheme could be used for
hBN alloying with Ga. Tunable hBAlN, hBGaN or hBAlGaN alloys could become
promising candidates for building blocks of efficient light sources in the
deep UV spectral range (DUV, 200-280 nm, 4.4-6.2 eV). Such candidates are of
high importance, since nowadays the efficiency of semiconductor light sources
operating in DUV is very limited ($\sim$10% for 270-280 nm and $\sim$3% for
250 nm) [11]. This spectral range is crucial, for example for the disinfection
and sterilization of air, water and surfaces [12, 13].

However, before hBN-based quantum structures and DUV light sources can be
realized, more fundamental questions must be answered. Firstly, it is still
unclear how to tune the hBN bandgap energy. This knowledge would be of great
importance for designing hBN-based quantum wells that would trap carriers and
enhance emission from the structure. Moreover, it would be very beneficial for
further improvement if one could change the nature of the hBN bandgap from
indirect to direct [14, 15].

In this work, we present results for boron nitride layers grown by metal
organic vapor phase epitaxy (MOVPE) that were alloyed with aluminum. We
obtained materials that preserve a sp2-bonded crystal structure. The produced
hB1-xAlxN layers with aluminum concentration $x$ up to a few percent exhibit
strong absorption for two energies that coincide with energies of indirect and
direct bandgap in hBN. Our approach that uses MOVPE to grow this novel
material provides a perspective for further development of the hBAlN alloy
composition control in terms of doping for conductivity, manipulation of the
bandgap, and commercial up-scaling.

##  II METHODS

###  II.1 Samples

The samples used in these studies were grown using an Aixtron CCS 3$\times$2”
metal organic vapor phase epitaxy system. The growth was carried out on 2-inch
sapphire $c$-plane substrates with 0.3∘ off-cut. For the growth of layered
sp2-bonded hB1-xAlxN samples ammonia, triethylboron (TEB) and
trimethylaluminum (TMAl) were used as nitrogen, boron, and aluminum
precursors, respectively and hydrogen was used as a carrier gas. Note that we
used the hBAlN notation (with letter h) to highlight the importance of the
hexagonal hBN-like crystal structure of the obtained material. The precursors
were injected alternatively following the flow modulation epitaxy growth mode
[16]. The scheme of pulses in a single cycle was as follows: TEB-NH3-TMAl-NH3.
The growth temperature was kept at 1300 ∘C. The temperature value was obtained
with an in situ multipoint optical pyrometer (ARGUS). NH3 and TEB flows were
fixed for all samples (V/III ratio for TEB-NH3 pulses was $\sim 15000$). The
TMAl/III ratio (III = TEB + TMAl) in the process varied for the samples:
$S_{0.02}$ (ratio 0.02), $S_{0.04}$ (ratio 0.04), $S_{0.07}$ (ratio 0.07),
$S_{0.13}$ (ratio 0.13). Such a ratio (TMAl/III) gives an insight into
relation between B and Al source in a gas phase during the process and very
initial predictions of the material composition $x$. To obtain the lowest
ratio, the duration of consecutive pulses of TMAl and NH3 was reduced by half.
This step was enforced by the minimal precursor flow limitation in our system.
The number of pulsing cycles was chosen in such a way that all samples were
grown 60 minutes.

###  II.2 Experimental details

The crystal structure of the samples was examined with a Panalytical X’Pert
diffractometer with standard CuKα x-ray source. The x-ray light beam was
formed by an x-ray mirror for Bragg-Brentano optics. Infrared reflectance
spectra were collected with a Thermo Scientific Nicolet Continuum Infrared
Microscope equipped with a 32x Schwarzschild infinity corrected objective (NA
0.65). All samples of $7\times 10$ mm were measured with a perpendicular
incident beam on five $70\times 70$ $\mu$m areas placed in the center and four
corners of the sample. Spectra were collected in the range of 650-4000 cm-1
with a resolution of 0.482 cm-1. The surface morphology was examined by
scanning electron microscopy (SEM) using a FEI Helios NanoLab 600 system.
Absorption spectra were measured using a Varian Cary 5000 UV-vis-NIR
spectrophotometer in dual-beam mode with nitrogen purging. The spectral
bandwidth was set to 1 nm.

Although our samples are very homogeneous on the wafer scale [17, 18], we
decided to measure each of the samples taken from the exact same area on the
wafer.

##  III RESULTS

###  III.1 x-ray diffraction

In figure 1a) we present x-ray diffraction $2\theta/\omega$ scans collected
for all the studied samples. The peaks at $\sim 20.5^{\circ}$, $\sim
40^{\circ}$ and $\sim 41.75^{\circ}$ correspond to the 0003 and 0006 planes of
Al2O3. In figures 1b), c) we present a zoom on the peaks at $\sim 26^{\circ}$
and $\sim 36^{\circ}$ that come from the reflection of the 0002 planes in
sp2-BAlN and sp3-AlN. The parameters of the Gaussian curve fit performed on
the data concerning hBAlN are included in table 1. Note that the 0002 BAlN
peak related to sample $S_{0.02}$ is asymmetric, so we fitted two Gaussian
curves yielding two different components of the peak. The components originate
from turbostratic (tBAlN, lower angles) and hexagonal (hBAlN, higher angles)
phases of sp2-bonded BAlN [17, 19]. In the further analysis we will focus only
on the hexagonal phase. In table 1 we do not observe significant changes in
the peak position $2\theta_{B}$ and the full width at half maximum (FWHM) for
the hBAlN peak. This implies that the $c$ lattice constant is comparable for
all the samples ($\sim 3.41$ Å) as well as the thickness of the crystal. The
only monotonous trend can be found in the amplitude of the hBAlN peak. This
means that the misorientation of the 0002 crystal planes is enlarged when
increasing the TMAl flow.

Figure 1:  X-ray diffraction $2\theta/\omega$ scans of the studied samples: a) scan in a broad $2\theta$ range, b) zoom on the peak related to hBAlN and c) zoom on the peak related to AlN. Table 1:  Parameters of the Gaussian curve fit to 0002 BAlN XRD peak. Sample | amplitude (cps) | 2$\theta_{B}$ (deg) | FWHM (deg)
---|---|---|---
$S_{0.02}$ | 7.0(6) | 25.84(1) | 0.51(4)
28.2(5) | 26.187(9) | 1.28(1)
$S_{0.04}$ | 18.5(2) | 26.136(6) | 1.29(1)
$S_{0.07}$ | 15.0(2) | 26.078(7) | 1.31(2)
$S_{0.13}$ | 11.4(2) | 26.122(8) | 1.36(2)

The signal associated to AlN consists of a very broad peak, which is alike for
all the samples and a narrower component that changes its intensity. In fact,
these two components have different origins. The broad component comes from an
unintentional thin ($\sim$2 nm) AlN layer that is created on the hBAlN-
sapphire interface during the initial growth stage. This kind of layer is
characteristic for MOVPE-grown hBN [19, 20]. However, in accordance with the
enhancement of the sharp component with an increase in TMAl, we can deduce the
formation of AlN crystals in our samples. These crystals do not seem to
influence the crystal structure of hBAlN as we do not observe any correlation
between the intensity of the sharp peak at $\sim 36^{\circ}$ and the values of
$2\theta_{B}$ and FWHM in table 1 which are related to BAlN.

###  III.2 Fourier-transform infrared spectroscopy

Figure 2:  Fourier-transform infrared reflectance spectrum for the $S_{0.02}$
sample with the lowest TMAl flow (black dots). The red line is the fitted
curve. The inset shows a zoom on the peak of the $E_{1u}$ vibrational mode,
which is strong evidence for a sp2 crystal structure for all hBAlN samples.
The black dots represent the experimental data and the lines are the fitted
curves: red for $S_{0.02}$, green for $S_{0.04}$, blue for $S_{0.07}$, yellow
for $S_{0.13}$.

In figure 2 we present exemplary infrared reflectance spectra obtained for the
studied samples. The peak observed about 1368 cm-1 is related to the $E_{1u}$
vibrational mode characteristic for hBN [21]. The observation of this peak
provides direct evidence that our samples are sp2 bonded. The high reflectance
below 1000 cm-1 comes from the sapphire substrate. Barely visible small and
sharp peaks about 1550 cm-1, 2300 cm-1 and 3500 cm-1 correspond to transitions
in the atmospheric gases present during the experiment.

To make the FTIR results quantitative, we implemented a spectra analysis
method, as described in the Ref. [22]. In this method, it is assumed that the
material is composed of harmonic oscillators with self-energy $\omega$ and
damping parameter $\gamma$. It makes use of the Dynamic Dielectric Function
(DDF) of the materials in the structure (boron nitride and sapphire in this
case). The substantial advantage of this method is the possibility of
characterizing the grown layer itself. The self-energy of the oscillator
$\omega_{BAlN}$ (phonon energy, peak position), its damping parameter
$\gamma_{BAlN}$ (peak broadening) and layer thickness provide information
about strain, homogeneity and growth rate. In table 2 we present the best fit
parameters obtained as an average of 5 points measured for each sample.

Table 2:  Averages of the best fit parameters of the FTIR spectra obtained for the studied samples. Sample |  $\omega_{BAlN}$ (cm-1) |  $\gamma_{BAlN}$ (cm-1) |  $d_{BAlN}$ (nm)
---|---|---|---
$S_{0.02}$ | 1368.94(5) | 24.5(1) | 18.6(5)
$S_{0.04}$ | 1368.03(3) | 22.1(2) | 9.1(4)
$S_{0.07}$ | 1368.7(2) | 26.5(6) | 9.8(3)
$S_{0.13}$ | 1369.3(2) | 30.1(5) | 10.1(3)

The fitted parameters are monotonous for the samples $S_{0.04}$, $S_{0.07}$
and $S_{0.13}$. The increase in TMAl flow leads to an increase in phonon
energy and peak broadening, which suggest the introduction of an inhomogeneous
compressive strain within the layer. The changes of $\omega_{BAlN}$
($\sim$0.63 cm-1 for the following samples) and $\gamma_{BAlN}$ ($\sim$4 cm-1
for the following samples) are significant in terms of FTIR measurements.
Remarkably different is the trend for the layer thickness. The 4-time increase
in amount of TMAl (samples $S_{0.04}$ and $S_{0.13}$) resulted in a layer that
is only 1 nm thicker, which is equivalent to the increase of the growth rate
by less than 0.02 nm/min.

The sample $S_{0.02}$ clearly stands out and does not follow the same trends.
The reason for this behavior is most likely due to the change of TMAl-NH3
pulse duration necessary to obtain a TMAl/III ratio equal to 0.02. This led to
a double increase in growth rate compared to the sample $S_{0.04}$. This
result is reasonable, since the TMAl/III ratio for $S_{0.02}$ was twice higher
than for $S_{0.04}$. At the same time the number of TEB pulses increased by
33%. So we find the competition between TEB-NH3 and TMAl-NH3 pulses to be more
important for the growth rate rather than the change in number of TEB pulses
in the growth process.

###  III.3 scanning electron microscopy

Figure 3:  Scanning electron microscopy images of the samples a) $S_{0.02}$,
b) $S_{0.04}$, c) $S_{0.07}$, d) $S_{0.13}$. The scale bar corresponds to 1
$\mu$m for each image.

The morphology of the studied samples is presented in figure 3. For each
sample, a characteristic wrinkle pattern is observed. The wrinkles are created
during cooling down the material after the growth process and are due to the
relaxation of strain caused by the difference in thermal expansion
coefficients of the layer and the substrate [22]. Because of the mechanism of
the wrinkle formation their presence is an evidence for the continuity of the
hBAlN epitaxial layer. The wrinkles are most pronounced for sample $S_{0.02}$,
which is due to a much larger thickness. The darker circular areas in the
images are bubbles with hydrogen inside. They are created during SEM imaging
and are the result of the radiolysis of interfacial water via electron
irradiation [23]. The size of crystalline objects on the surface of the layer
is correlated with the amount of TMAl present in the process. This observation
is in good agreement with the XRD results for which the AlN narrow diffraction
peak was observed for $S_{0.04}$, $S_{0.07}$ and $S_{0.13}$. This leads to the
conclusion that the observed crystals are related to sp3 bonded aluminum
nitride. More detailed atomic force microscopy and Raman spectroscopy studies
of these objects are presented in the Supplementary Materials.

###  III.4 UV-vis spectroscopy

To extract the absorption coefficient from the measured absorbance, we
subtracted the absorbance spectrum obtained for bare sapphire. To calculate
the absorption coefficient we used the thickness of the layer $d_{BAlN}$ taken
from table 2. The absorption coefficient spectra of the samples studied are
presented in figure 4. The spectrum for the reference epitaxial boron nitride
without aluminum sample was obtained in the same way. The reference sample was
grown analogously to the sample $S^{I}$ presented in the work in Ref. [17].
The absorption coefficient for all the samples is of order of $\alpha=2\times
10^{6}$ cm-1. This value is twice higher as compared to those previously
reported for boron nitride [9, 24, 25]. In contrast to the reference sample,
the samples with aluminum exhibit two well-resolved peaks. In previous studies
only peak shifting was observed, which was accompanied by a broadening due to
a decrease of sample quality [26]. In the case of our samples the two peak
energies are close to the dash-dotted navy and dashed green lines that are
positioned at energies corresponding to the indirect (5.955 eV [27]) and
direct (6.125 eV [28, 29]) band-edge transitions in boron nitride,
respectively. Depending on the TMAl flow, one can change the intensity of
those peaks and the intensity ratio between higher and lower energetic peaks.
However, this relationship does not correlate with the amount of TMAl in the
growth process.

Figure 4:  Absorption coefficient spectra of the samples studied. The solid
gray line is the spectrum collected for the reference boron nitride sample
without aluminum. It was multiplied by factor 0.45 for clarity. The reference
sample was grown in analogy to the $S^{I}$ from Ref. [17]. The uncertainty of
the results is of order of $0.5\times 10^{5}$ cm-1. Green dashed and dash-
dotted navy lines illustrate the energies of direct and indirect bandgaps in
boron nitride.

The lower energy peak, which is not observed for the reference sample, could
be thought to be the result of the crystaline objects presented in the SEM
images (figure 3). However, the peak intensity does not scale with the number
of objects on the layer’s surface. Secondly, as has been mentioned before, the
crystalities are identified as sp3 bonded AlN which is known to have a bandgap
energy of 6.2 eV [30]. Possible alloying of sp3 bonded wurtzite-AlN (wAlN)
with boron would, on the other hand, further increase the bandgap since
wurtzite-BN (wBN) is a wider bandgap semiconductor [14]. Consequently, the
signal coming from AlN should be observed in the absorption spectra for
higher, not lower energies when comparing to the peak of pure boron nitride.
However, we cannot provide conclusive information about the AlN-related
spectral component since this energy range is close to the limit of detection
for our spectrometer.

##  IV DISCUSSION

As presented in figure 1b) and table 1, the x-ray diffraction peak is observed
at angles lower than expected for the 0002 hBN plane (26.764∘ [31]). This
indicates a larger lattice constant in the $c$ direction. However, the peak
position does not change significantly between the samples, which is in
contrast to the results reported in Ref. [32] in which authors observed peak
position shifting towards higher angles with an increasing TMAl flow.
According to theoretical DFT calculations presented in Ref. [33], a decrease
in the $c$ lattice constant should be observed when hBN is alloyed with Al,
since hexagonal aluminum nitride has calculated a smaller $c$ lattice
constant. We conclude that since we do not have a perfect hexagonal phase the
main reason for the XRD peak position change in our samples is that it is
attributed to random twists of subsequent atomic layers, which make the
material more turbostratic. In this case we postulate that the peak position
variations related to the alloying with small amounts of Al are just a higher
order correction. This hypothesis seems to be confirmed by the fact that all
samples were grown under the same growth conditions. Another prominent feature
presented in figure 1c) is the peak at $\sim 36^{\circ}$, whose intensity
increases with the increase in TMAl flow. The value of the peak position is in
agreement with the XRD peak of 0002 AlN in the crystal structure of wurtzite
[34]. This indicates the creation of sp3 bonded wAlN crystals, which scale
with the amount of TMAl. This additional notable peak is a proof of the phase
separation of sp2 bonded hBAlN and sp3 bonded wAlN. The observation agrees
with SEM (figure 3), Raman spectroscopy and AFM (Supplementary Materials)
measurements. Indeed, the number and size of crystaline objects correlate with
the amount of TMAl, which provides strong evidence for the very limited
solubility of aluminum in the hexagonal boron nitride layer at the temperature
and pressure used in the growth process (1300 ∘C, 400 mbar). Consequently, the
experimental determination of the material composition is very difficult and
needs further studies. Standard composition-determination techniques such as
energy-dispersive x-ray spectroscopy (EDS), x-ray photoelectron spectroscopy
(XPS), secondary ion mass spectroscopy (SIMS) cannot be employed to correctly
determine the composition. Because the analyzed material is dielectric,
electron charging is significant and does not allow EDS to be measured in one
area for a longer period of time. Additionally, due to the electrons
penetration depth in EDS it is hard to differentiate signal for Al that comes
from the hBAlN layer and Al2O3 substrate. XPS and SIMS hardly distinguish Al
from the hBAlN layer and AlN crystalities on its surface.

Although AlN crystalines can be observed, the sp2-bonded, layered structure of
hBAlN is maintained, which is proved by FTIR measurement presented in figure
2. However, by introducing TMAl we modify the optical properties of the layer.
This can be seen as a shift of the phonon energy $\omega_{BAlN}$ towards
higher energies that suggests compressive stress in the structure as
demonstrated in Ref. [35]. Furthermore, the increase in TMAl is followed by a
broadening of the peak described by the parameter $\gamma_{BAlN}$, which
indicates a defect-related inhomogeneity of the strain within the layer.

The most striking result that emerges from our work is the observation of an
additional low energy peak in the absorption spectra. The hBN conduction band
is known to consist of minima at the K and M points of the Brillouin zone that
are energetically close to each other [10]. They are responsible for direct
and indirect band transitions, respectively. As an indirect transition is a
three-particle (photon, electron, phonon) event, it has a much lower
probability to occur than a direct transition, which requires only two
particles (photon, electron). Consequently, the absorption coefficient related
to indirect transitions is usually 2-3 orders of magnitude lower as compared
to direct ones. However, in the case of our samples, we observe two peaks at
energies which coincide with the energies of direct and indirect transitions
in hBN (dash-dotted and dashed lines in figure 4). Furthermore, both have a
very high value of the absorption coefficient ($\alpha\sim 10^{6}$ cm-1)
typical for direct bandgap transitions. Notably that the lower-energy peak has
even lower energy than expected for the indirect transition in hBN. This
observation is in agreement with predictions about a decrease in bandgap
energy when hBN is alloyed with Al [36]. To understand the mechanism that
stands behind the observation of the two peaks in the absorption spectra, we
need to be aware of the role of aluminum in the crystal structure. Al
incorporation introduces short range disorder, which in turn would lead to the
mixing of states with large $k$-vectors. As presented in Ref. [10], conduction
and valence bands along KH and ML points in hBN are very flat and almost
parallel to each other. This feature leads to high oscillator strength and
consequently very efficient absorption. A disorder induced by Al incorporation
further modifies the band structures and the probability of electronic
transitions, i.e. oscillator strength. Consequently, other absorption channels
are enabled through the defect-related states. The modification of states
caused by Al-related defects allows us to observe highly effective absorption
for both energies. However, further increase of TMAl flow and limited
solubility of Al in hBN lead to a deterioration of optical quality of the
material which is observed in broadening of spectroscopic peaks in the spectra
(same for FTIR and UV-Vis).

##  V CONCLUSIONS

In this work, we have shown the results for MOVPE grown hB1-xAlxN layers with
TMAl/III ratio ranging from 0.02 to 0.13. X-ray diffraction and Fourier-
transform infrared spectroscopy measurements proved that the obtained material
maintained a sp2-bonded layered crystal structure, which is characteristic for
hBN. At this stage of the research, we are faced with a challenge of
insufficient information regarding the exact composition of the material, as
well as the presence of crystaline sp3-bonded AlN clusters on the surface of
the material. However, despite these obstacles, we managed to observe a
significant change in the layer properties. Most importantly, we have shown
two peaks of strong absorption ($\alpha\sim 10^{6}$ cm-1) typical for direct
excitonic transitions in hBN. The peak energies coincide with the energy of
the indirect and direct bandgap transition in hBN. This observation becomes
possible due to an activation of the absorption channels through defects
caused by Al incorporation. The presented results are of great importance to
understand how the boron nitride bandgap can effectively be manipulated in
terms of its indirect/direct nature and its width. Understanding these
processes is a key aspect for the fabrication of hBN-based structures for
efficient deep UV emission.

###### Acknowledgements.

This work was supported by the National Science Centre, Poland, under the
decisions 2019/33/B/ST5/02766, 2020/39/D/ST7/02811 and 2022/45/N/ST5/03396.

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# Segment Anything Meets Semantic Communication

Shehbaz Tariq, Brian Estadimas Arfeto, Chaoning Zhang, Hyundong Shin  This
work was supported by the National Research Foundation of Korea (NRF) grant
funded by the Korea government (MSIT) (NRF-2019R1A2C2007037,
NRF-2022R1A4A3033401) and by the MSIT (Ministry of Science and ICT), Korea,
under the ITRC (Information Technology Research Center) support program
(IITP-2023-2021-0-02046) supervised by the IITP (Institute for Information &
Communications Technology Planning & Evaluation). S. Tariq, B. E. Arfeto, C.
Zhang, and H. Shin are with the Department of Electronics and Information
Convergence Engineering, Kyung Hee University, 1732 Deogyeong-daero, Giheung-
gu, Yongin-si, Gyeonggi-do 17104 Korea (e-mail: hshin@khu.ac.kr).

###### Abstract

In light of the diminishing returns of traditional methods for enhancing
transmission rates, the domain of semantic communication presents promising
new frontiers. Focusing on image transmission, this paper explores the
application of foundation models, particularly the Segment Anything Model
(SAM) developed by Meta AI Research, to improve semantic communication. SAM is
a promptable image segmentation model that has gained attention for its
ability to perform zero-shot segmentation tasks without explicit training or
domain-specific knowledge. By employing SAM’s segmentation capability and
lightweight neural network architecture for semantic coding, we propose a
practical approach to semantic communication. We demonstrate that this
approach retains critical semantic features, achieving higher image
reconstruction quality and reducing communication overhead. This practical
solution eliminates the resource-intensive stage of training a segmentation
model and can be applied to any semantic coding architecture, paving the way
for real-world applications.

###### Index Terms:

segment anything, semantic communications, image transmission

##  I Introduction

As we approach Shannon’s limits, traditional methods to enhance transmission
rates, such as increasing power, expanding bandwidth, and adding antennas, are
becoming less effective due to spectrum limitations and high power consumption
[1]. Consequently, exploring the semantic domain has become crucial for
significantly improving communication efficiency. Semantic communication
allows the compact representation of the source information at a semantic
level to retain only the task-relevant information, which can then be used to
recover the source data[2] or perform some intelligent tasks [3], such as
classification, object detection, etc., more efficiently. The robustness of
semantic communication holds significant potential for various 6G applications
[4], such as the metaverse, mobile broadband, digital twins, and fully
autonomous driving, as shown in Fig 1. By ensuring reliability and efficiency,
semantic communication can contribute to building a strong foundation for 6G
systems[5]. These systems will support seamless interactions and data exchange
in the metaverse, optimize content delivery in mobile broadband, enable real-
time data exchange in digital twins, and facilitate precise control in fully
autonomous driving. Consequently, numerous studies have shown that deep
learning-based semantic communication outperforms traditional techniques[6, 7,
8].

However, a challenge persists: many current deep learning techniques require a
shared knowledge base, which makes them highly task-specific and restricts
their ability to generalize to downstream tasks. Building upon this, the
remarkable rise of foundational models [9, 10] (e.g., BERT and GPT) has been
compared to seminal discoveries like electricity and the internet for
humanity. These models, subjected to self-supervised learning [11] on a vast
array of multi-modal data, demonstrate the capacity to generalize downstream
tasks without explicit training using prompt engineering [12]. The foundation
models also significantly contribute to the development of generative AI
(AIGC) [13], like ChatGPT [14] and text-to-image [15], text-to-3D [16].
Inspired by these successes, we explore the application of the Segment
Anything Model (SAM) [17], a novel foundation model for computer vision
developed by Meta AI Research, for semantic communication.

SAM is a promptable image segmentation model that has gained significant
attention for its ability to perform zero-shot segmentation tasks without
finetuning[18]. This model allows for the segmentation of any image with just
a simple prompt, thereby eliminating the need for labor-intensive image
labeling and domain expertise. Moreover, it also gives the flexibility to send
only the necessary segments of an image, which reduces communication overhead
and enhances intelligent task achievability, such as object detection and
image classification across various domains [19, 20]. Building on the
remarkable generalization capability of SAM, we propose a new approach to
semantic communication for image transmission that requires image
segmentation, followed by a lightweight neural network architecture for joint
source and channel encoding and decoding that significantly reduces the
communication overhead and retains higher image quality. By taking advantage
of SAM’s segmentation, we demonstrate that our approach allows for preserving
meaningful semantic features, resulting in higher image reconstruction quality
as measured by the peak signal-to-noise ratio (PSNR) compared to the non-
segmentation-based approach. Moreover, by obviating the need for domain-
specific expertise and training a segmentation model, which is often the most
resource-intensive stage in the semantic communication pipeline, we can plug
the SAM into any semantic encoder, thus providing a pragmatic solution for
real-world applications, as shown in Fig 1.

Figure 1:  Depiction of the robustness, speed, and reliability underpinning 6G
Networks, highlighting the potential integration of a SAM-based Semantic
Communications model for diverse applications.

##  II Related Work

The pioneering work in semantic communication was the deep joint source-
channel coding for image transmission [21], which proposed directly mapping
image pixel values to channel inputs. This approach demonstrated improved PSNR
performance compared to conventional compression techniques such as JPEG and
JPEG2000 [22] under noisy channel conditions. Subsequently, an alternative
approach, the Wireless Image Transmission Transformer for Semantic
Communications (WITT) [2], was introduced, leveraging a different neural
network architecture based on transformers [23]. This approach, demonstrating
robustness, further enhanced the PSNR. Nevertheless, both of these
methodologies perform semantic encoding and decoding of the entire image,
potentially including irrelevant information.

To address this, a Semantic Segmentation-based Semantic Communication System
for image transmission [24] was proposed, which semantically segments the
image to distinguish between regions of interest (ROI) and regions of non-
interest (RONI) before encoding and decoding. This approach further improved
transmission accuracy over existing methods. However, the segmentation process
is the bottleneck, requiring expert labeling of the image into ROI and RONI,
followed by training [25]. Consequently, identifying ROI and RONI for specific
task achievability remains challenging. The outlined approach necessitates
training two distinct semantic encoders and decoders for each ROI, often
termed the foreground and for each RONI, or the background. While potentially
effective for a single ROI, this methodology presents scalability concerns
when confronted with images encompassing multiple ROIs. The complexity of
training individual models for each distinct region might become prohibitively
high, posing constraints on the applicability and efficacy of this system for
more intricate image analysis.

Therefore, we propose a pragmatic architecture in this paper that leverages
the zero-shot learning capability of Segment Anything (SAM) to generate masks
of the image given a prompt for the ROI. Prior works have also investigated
SAM under challenging scenarios like glass (transparent objects) and
adversarial attack [18, 26, 27, 28]. It has been found in [26] SAM is more
biased towards texture than shape. A complete survey on SAM is provided in
[18]. Our work is the first to combine semantic communication with SAM, which
eliminates the need for expert labeling and training on new data to get ROI.
As a promptable segmentation model, it also adds flexibility to generate
multiple masks. We show that SAM-based architecture eliminates the need to
train for segmentation and improves performance on benchmarks similar to those
in [24], thanks to its high-quality masks.

##  III System Model

Figure 2: SAM-based framework architecture for Semantic Communication.

In this section, SAM based semantic communication system is proposed for image
transmission. The system model is shown in Fig 2. It can be broken down into
three parts. The transmitter uses SAM to segment the image and extract the
semantic features of their structured representations from the generated masks
and then extracts their compressed semantic features; the channel is used to
simulate realistic noise; The receiver is used to reconstruct the original
image from the noisy, compressed features.

###  III-A Image Transmission

This process is separated into encoding, feature extraction, and decoding on
the sender side. The result that we get is masked objects along with the
background. We employ a systematic process to achieve accurate image
segmentation using SAM for semantic communication. SAM mainly consists of
three parts, a prompt encoder that takes in a prompt to segment a specific
region and a Vision transformer(ViT) based image encoder that takes in an RGB
image. The generated image embeddings are sent to a lightweight decoder with
the embedded prompt.

Image Encoding Let $s\in\mathbb{R}^{H\times W\times C}$ be an image, where
$H,W,$ and $C$ are the image height, width, and channel, respectively. The SAM
image encoder $S_{enc}$, a trained neural network specifically designed for
segmentation tasks, transforms the $s$ into embedding
$x_{e}\in\mathbb{R}^{H\times W\times C}$.

Prompt encoding Let $p_{i}$ be a $256$-dimensional vector that encodes the
$i$th prompt, which can be a point on the image, a box around an object, a
free-form text, or some shaded area over the object. SAM can also work in
“everything” mode by generating masks on almost every object on the image.

Mask decoder The embedding $x_{e}$ of the image $s$ and the input prompt
$p_{i}$ are then used to produce a mask $m_{i}$ with a lightweight decoder.
These masks effectively act as semantic representations of the original image,
providing a concise visual summary. By transmitting only the masks, we retain
the essential information necessary for accurate image reconstruction while
achieving a higher compression level, enabling more efficient data
transmission.

Joint source-channel coding (JSCC) We employ a Convolutional Neural Network
(CNN)-based architecture, comprised of an encoder $F_{enc}$ and a decoder
$F_{enc}$, dedicated solely to the source-channel coding of the masks. The
architecture of the model is illustrated in Fig 3. The semantic features,
denoted as $x_{s}$, are obtained by encoding the input $x_{in}$, which could
be either the input image, mask, or a batch of masks. Mathematically, this
process can be expressed as:

$x_{s}=F_{enc}(x_{in}),$ (1)

Figure 3: Semantic encoder and semantic decoder atchitectures.

A noteworthy feature of this architecture is its ability to compress the
transmitted signal size by $\mathbf{83.3\%}$, enabling more efficient
communication channel utilization. The achieved compression is quantifiable
via the compression ratio (CR), given by:

$CR=\frac{C_{o}\times H_{o}\times W_{o}}{C_{in}\times H_{in}\times W_{in}},$
(2)

where $C_{o},H_{o},W_{o}$ represent the output channels, height, and width
from the semantic encoder, respectively. Conversely, $C_{in},H_{in},W_{in}$
denote their corresponding values for the input image.

###  III-B Channel Layer

To establish a communication channel, we consider the presence of noise in the
environment. Although the real physical noise is more complex to model for
simplicity, we consider two common types of noise, additive white Gaussian
noise (AWGN) and Rayleigh fading (RF), that are more widely adopted in several
studies [29, 21, 2, 24]. AWGN represents random noise, while RF accounts for
signal attenuation due to multipath propagation.

Figure 4: Performance comparison of the image recovery of masked images and
original images under AWGN noise.

###  III-C Image Reconstruction Block

The noisy received signal $y\in\mathbb{R}^{H_{o}\times W_{o}\times C_{o}}$ is
subsequently input to the CNN decoder, which reconstructs the original image,
represented as $x_{in}^{\prime}\in\mathbb{R}^{H_{in}\times W_{in}\times
C_{in}}$. This process is formalized as:

$x_{in}^{\prime}=F_{dec}(y).$ (3)

This decoding operation assures accurate image reconstruction while
maintaining computational efficiency.

Figure 5: Performance comparison of the image recovery of masked images and
original images under RF noise.

##  IV Results and Discussion

In this paper, we use Pascal VOC as the dataset [30]. However, SAM’s zero-shot
learning advantage enables it to accurately segment and recognize objects
without any training or labeled examples, which means it is ready to use for
any image data. This versatility allows for efficient adaptation and effective
semantic communication in real-life applications. We train on images from the
dataset without any noise and then test them under noisy conditions. Table I
presents the hyperparameters used in this study.

TABLE I: Dataset and Hyperparameter Details Hyperparameters | Description
---|---
Number of Test Images | $60$
Image Resolution | $3\times 512\times 512$
Semantic Features | $128\times 32\times 32$
Compression Ratio | $\frac{1}{6}$
Epoch | $1500$
Learning Rate | $0.001$
Loss Function | MSE
Optimizer | Adam
Noise Channel | AWGN - RF
Desired SNR | $1-20$

We train the model without using SAM on the original images, then we plug SAM
and segment the images before feeding them to the network for training. We
then test the image reconstruction quality in two noisy cases, AWGN and RF
noise, for different SNR conditions, as shown in Fig 4 and fig 5, using masked
images for training improves the PSNR. In Fig 6, we show the reconstructed
images in both cases. From these results, we conclude that SAM-based
segmentation helps the model to capture more features in training and thus can
show more robustness to channel noise. The rationale for using SAM is its
ability to segment anything without being trained. It gives us more
flexibility to use this on real-life personalized datasets and only trains the
semantic coding models. In this paper, for brevity, we only show the
performance of the reconstruction capability of the proposed architecture.
However, using SAM has even more potential applications for a practical level
of communication to focus on the efficiency of task achievability, i.e., image
recognition. In such specific tasks, we do not need to send the whole image
but just the ROI, and SAM can achieve this in a zero-shot manner with a given
prompt. The masks are more robust to noise than sending the whole image,
potentially increasing task achievability.

|  |
---|---|---
|  |

(a) Original Image

(b) RF

(c) AWGN

(d) ROI from SAM

(e) RF

(f) AWGN

Figure 6: Visual comparison of the original image (a) and ROI (d), recovery
without the use of SAM (b and c), and recovery of masks employing SAM (e and
f).

##  V Conclusion and Future Work

In this paper, we study the influence of segmentation on the training of
semantic coding models. We presented a practical image segmentation method
using SAM, eliminating the need for expert data labeling. Instead, it requires
a simple prompt to segment ROI, reflecting the nature of a foundational model.
Our findings show improvement in image recovery performance post-exposure to a
noisy communication channel through this approach. While our focus in this
paper was limited to the impact of segmentation on image recovery in semantic
coding models, future research could extend this to investigate its role in
task achievability. Additionally, the burgeoning potential of the transformer
architecture, noted for its scalability and superior performance in computer
vision tasks, could be harnessed for further investigation.

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