# Fifth forces from QCD axions scale differently

Martin Bauer  Guillaume Rostagni  Institute for Particle Physics
Phenomenology, Department of Physics
Durham University, Durham, DH1 3LE, United Kingdom

###### Abstract

We reexamine the low-energy potential for a macroscopic fifth force generated
from the exchange of two axions. The shift-symmetry of the linear axion
interactions leads to a potential falling off as $V(r)\sim 1/r^{5}$. We find
that in the case of the QCD axion higher-order terms in the Lagrangian break
the shift symmetry and lead to the dominant contribution to the potential
scaling as $V(r)\sim 1/r^{3}$. These terms are generated by the same physics
responsible for the axion mass and therefore the new contributions to the
potential induce a different force for external nucleons and leptons. We
demonstrate how this result affects the sensitivity of searches for new long-
range forces.

††preprint: IPPP/23/35

##  I Introduction

Fifth forces have been identified as potential probes for axions very early
Moody:1984ba . The early focus was on the exchange on spin-dependent
interactions, which are the consequence of the exchange of single light CP-odd
scalars. The leading contribution to a spin-independent long-range force
mediated by axions is generated by axion-pair exchange at one loop
Grifols:1994zz  and therefore similarly suppressed as the ’neutrino-force’
generated by the exchange of neutrino pairs Feinberg:1968zz ; Hsu:1992tg . The
potential corresponding to the exchange of a pair of neutrinos scales as
$V(r)\sim 1/r^{5}$, as does the potential generated by the exchange of pairs
of massless axions Grifols:1994zz ; Ferrer:1998ju . In contrast, the exchange
of pairs of pseudoscalars leads to a non-relativistic potential scaling as
$V(r)\sim 1/r^{3}$, whereas the potential for an axion-Higgs portal scales as
$V(r)\sim 1/r^{7}$ Ferrer:1998rw ; Bauer:2022rwf . The difference between the
potentials induced by pseudoscalars and axions is a consequence of the
manifest shift-symmetry that protects all linear axion interactions and have
been discussed already in the case of the pion in very early literature
Dyson:1948a ; Lepore:1952a ; Drell:1952a ; Drell:1953a .
In this letter we show that in the case of the QCD-axion the dominant
contribution to the potential is generated by the same physics responsible for
the axion mass and that these contributions generate a $V(r)\sim 1/r^{3}$
potential even though they are induced by higher-order operators in the
effective field theory (EFT) expansion in the axion decay constant. Since the
axion mass is generated by strong dynamics these additional contributions to
the low-energy potential only occur for external hadrons. Axion-induced forces
between leptons as well as between hadrons and leptons are substantially
weaker. This could allow to directly measure the contribution to the axion
mass from the chiral anomaly by comparing different searches for fifth forces.

There are several ways to search for the effects of a new, macroscopic force
including searches with Cavendish-type experiments Adelberger:2006dh ,
searches for new forces in atoms and molecules Safronova:2017xyt ,
measurements of the effective Casimir pressure Chiu:2010ybt ; Bezerra:2014dja
and experiments specifically designed to suppress the Casimir force
Chen:2014oda . We introduce the different contributions to axion interactions
at low energy in Section II, derive the potential for axions including the new
contributions from high-order operators in Section III, and demonstrate the
effect of the new contribution for the Casimir-less experiment Chen:2014oda
in Section IV.

##  II Two axion interactions

The Lagrangian for an axion interacting with fermions can be written in a form
that is explicitly shift invariant apart from the axion mass $m_{a}$,

$\displaystyle\mathcal{L}=\frac{1}{2}(\partial
a)^{2}-\frac{m_{a}^{2}}{2}a^{2}-\sum_{\psi}\frac{c_{\psi}}{2}\frac{\partial_{\mu}a}{f}\bar{\psi}\gamma_{5}\gamma^{\mu}\psi\,,$
(1)

up to linear order in the axion field over the axion decay constant. This
Lagrangian can be rewritten by using the divergence of the axial-vector
current

$\displaystyle\mathcal{L}$ $\displaystyle=\frac{1}{2}(\partial
a)^{2}-\frac{m_{a}^{2}}{2}a^{2}$
$\displaystyle\quad+\sum_{\psi}c_{\psi}im_{\psi}\frac{a}{f}\bar{\psi}\gamma_{5}\psi-
c_{\psi}\frac{\alpha
Q_{\psi}^{2}}{4\pi}\frac{a}{f}F_{\mu\nu}\tilde{F}^{\mu\nu},$ (2)

where we assume the fermions only carry electric charge, otherwise there would
be additional couplings to gauge bosons. Even though (1) and (II) are both
linear in $a/f$ they lead to contradicting results for processes with more
than one axion involved. The reason is that the divergence of the axial-vector
current or equivalently the equations of motion for the axion only capture
terms up to linear order in the fields. A consistent rescaling of the fermion
fields generates higher order terms in $a/f$ that precisely account for the
difference between results obtained from (1) and (II) (details are given in
Appendix A). The effects can be accounted for by modifying the anomaly
equation for the divergence of the axial-vector current

$\displaystyle\frac{c_{\psi}}{2}\frac{\partial_{\mu}a}{f}\bar{\psi}\gamma_{5}\gamma^{\mu}\psi$
$\displaystyle=-c_{\psi}im_{\psi}\frac{a}{f}\bar{\psi}\gamma_{5}\psi+c_{\psi}^{2}m_{\psi}\frac{a^{2}}{f^{2}}\bar{\psi}\psi$
$\displaystyle\quad+c_{\psi}\frac{\alpha
Q_{\psi}^{2}}{4\pi}\frac{a}{f}F_{\mu\nu}\tilde{F}^{\mu\nu}+\mathcal{O}\Big{(}\frac{a^{3}}{f^{3}}\Big{)}\,.$
(3)

To quadratic order in the axion fields the inclusion of the additional
operator in (II) restores the results obtained using the shift invariant
coupling. However the shift invariance in (1) is explicitly broken by the
presence of an axion mass. Treating $m_{a}^{2}$ as the only spurion that
breaks the shift invariance suggests the existence of higher order shift
symmetry breaking operators

$\displaystyle\mathcal{L}_{\text{ssb}}\ni\sum_{\psi}c_{m}\frac{m_{a}^{2}a^{2}}{f^{3}}\bar{\psi}\psi\,.$
(4)

These operators spoil the cancellation in (II). In general it is a
conservative assumption that the spurion is given by $m_{a}^{2}$, because the
source of shift symmetry breaking responsible for generating the axion mass
can induce higher-order operators that are less suppressed than (4). An
example of such an enhancement is the coupling of the QCD axion to nucleons.
The shift symmetry is broken by the presence of light quark masses and the QCD
confinement scale. Interactions between the QCD axion and nucleons are
therefore shift-invariant or suppressed by these spurions. At leading order
the operators of the two-flavor chiral Lagrangian coupling baryons to pions
and axions are

$\displaystyle\mathcal{L}^{(1)}=\bar{N}\left(i\not{D}-m_{N}+\frac{g_{A}}{2}\gamma^{\mu}\gamma^{5}u_{\mu}+g_{0}\gamma^{\mu}\gamma^{5}a_{\mu}^{(s)}\right)N\,.$
(5)

Couplings to the axion enter via the covariant derivative and the vielbeins
$u_{\mu}$ and $a_{\mu}^{(s)}$, which both contain the axion in an explicitly
shift-invariant way Vonk:2020zfh ; Bauer:2021mvw .

At second order there are four operators

$\displaystyle\mathcal{L}^{(2)}$
$\displaystyle=c_{1}\text{tr}[\chi_{+}]\bar{N}N-\frac{c_{2}}{4m^{2}}\text{tr}[u_{\mu}u_{\nu}](\bar{N}D^{\mu}D^{\nu}N+\text{h.c.})$
$\displaystyle+\frac{c_{3}}{2}\text{tr}[u_{\mu}u^{\mu}]\bar{N}N-\frac{c_{4}}{4}\bar{N}\gamma^{\mu}\gamma^{\nu}[u_{\mu},u_{\nu}]N\,.$
(6)

All operators in $\mathcal{L}^{(2)}$ are shift-invariant apart from the
operator with coefficient $c_{1}$, which contains a shift-symmetry breaking
interaction

$\displaystyle
c_{1}\text{tr}[\chi_{+}]\bar{N}N=c_{N}\frac{a^{2}}{f^{2}}\bar{N}N+\ldots$ (7)

The axion field enters via

$\displaystyle\\!\\!\chi_{+}$
$\displaystyle=2B_{0}\big{(}\xi^{\dagger}m_{q}(a)\xi^{\dagger}+\xi
m_{q}^{\dagger}(a)\xi\big{)}\,,$ (8) $\displaystyle\\!\\!m_{q}(a)$
$\displaystyle=e^{-i\kappa_{q}\frac{a}{2f}(2c_{GG}+c_{u}+c_{d})}m_{q}e^{-i\kappa_{q}\frac{a}{2f}(2c_{GG}+c_{u}+c_{d})}\\!,$
(9)

where $\xi=\exp(i/\sqrt{2}\,\Pi/f_{\pi})$ contains the pion fields, the quark
masses read $m_{q}=\text{diag}(m_{u},m_{d})$,
$\kappa_{q}=\text{diag}(\kappa_{u},\kappa_{d})$ are unphysical parameters
subject to the constraint $\kappa_{u}+\kappa_{d}=1$, and $c_{GG}$ denotes the
axion coupling to gluons

$\displaystyle\mathcal{L}\ni
c_{GG}\frac{\alpha_{s}}{4\pi}\frac{a}{f}G_{\mu\nu}\tilde{G}^{\mu\nu}\,.$ (10)

After rotating into the mass eigenbasis and taking into account contributions
from pion mixing one can write the leading terms for the amplitude of axions
coupled to nucleons from (5) and (II) as

$\displaystyle\\!\\!\\!i\mathcal{A}(N(k^{\prime})\to
N(k)+a(q))=-\frac{g_{N}}{4f}\bar{u}_{N}(k^{\prime})\not{q}\gamma_{5}u_{N}(k),$
(11) $\displaystyle\\!\\!\\!i\mathcal{A}(N(k^{\prime})\to
N(k)+2a(q/2))=-\frac{c_{N}}{f^{2}}\bar{u}_{N}(k^{\prime})u_{N}(k),$ (12)

respectively. Here, the couplings are defined for protons and neutrons
$N=p,n$, as

$\displaystyle g_{p/n}$ $\displaystyle=g_{0}(c_{u}+c_{d}+2c_{GG})$
$\displaystyle\pm
g_{A}\frac{1}{1-\tau_{a}^{2}}\left(c_{u}-c_{d}+2c_{GG}\frac{m_{d}-m_{u}}{m_{u}+m_{d}}\right)\,,$
$\displaystyle c_{N}$
$\displaystyle=c_{1}\frac{m_{\pi}^{2}}{2}\frac{4c_{GG}^{2}(1-\tau_{a})^{2}+(c_{u}-c_{d})^{2}\tau_{a}^{2}}{(1-\tau_{a})^{2}}\,,$
(13)

where $\tau_{a}=m_{a}^{2}/m_{\pi}^{2}$. The iso-scalar and iso-vector coupling
constants are determined using lattice gauge theory Liang:2018pis ;
FlavourLatticeAveragingGroup:2019iem  $g_{0}=0.440(44)$ and experimentally
extracted from nucleon beta decay ParticleDataGroup:2020ssz
$g_{A}=1.2754(13)$, respectively. The low energy coefficients
$c_{1},c_{2},c_{3},c_{4}$ can be found in Alarcon:2012kn  and we use
$c_{1}=-1.26(14)$ GeV-1 here. The axion couplings to gluons and quarks in (II)
are to be evaluated at the QCD scale Chala:2020wvs ; Bauer:2020jbp .

Expanding $c_{N}$ in small axion masses and using the expression for the QCD
axion mass with $m_{u}=m_{d}$ one can write the coefficient in (4) as
$c_{m}=-8c_{1}f^{3}/f_{\pi}^{2}$, which corresponds to a substantial
enhancement compared with the naive assumption.

Since the axion has a potential, in principle any quadratic interaction can
also give rise to a linear spin-independent interaction _if_ the axion vacuum
expectation value doesn’t vanish. The Vafa-Witten theorem guarantees that
$\langle a\rangle=0$ in vacuum Vafa:1984xg , but in a high density environment
the potential is modified and $\langle a\rangle=a_{0}\neq 0$, leading to long-
range forces for large, dense objects such as neutron stars Hook:2017psm ;
Balkin:2020dsr . Linear interactions proportional to the theta angle are
strongly suppressed Chang:1985mu ; Haber:1987nx ; Mantry:2014eya . For the
remainder of this paper we focus on the spin-independent force induced by the
exchange of axion pairs. The importance of the shift-symmetry breaking
operator has been pointed out previously in the context of coherent axion-
nucleon scattering Fukuda:2021drn .

Figure 1: Diagrams contributing to the potential generated by two-axion
exchange from linear interactions $a)$ and $b)$, from linear and quadratic
interactions $c)$ and $d)$ and from purely quadratic interactions in $e)$.

##  III The axion force

In the following we will derive the potential for the spin-independent force
induced by the exchange of a pair of axions Grifols:1994zz ; Ferrer:1998rw ;
Ferrer:1998ue . We show explicitly that the contributions from the linear and
quadratic axion interactions in (II) cancel and that the shift-symmetry
breaking interaction induced by (7) spoils this cancellation and provides the
most important contribution to the potential. We obtain the non-relativistic
potential for the exchange of two axions can be obtained by taking the
discontinuities in the scattering amplitude in the non-relativistic limit and
perform the Fourier transform. Feynman diagrams for the two-axion exchange are
shown in Fig. 1. In the basis with derivative axion-interactions (1) only the
diagrams $a)$ and $b)$ contribute. We instead use the non-derivative basis for
which one needs to include diagrams $c)$, $d)$ and $e)$, taking into account
the quadratic axion coupling in (II) to obtain a consistent result. Operators
breaking the shift invariance generate additional contributions to $c),d)$ and
$e)$.

In the heavy fermion limit and retaining only terms odd in the momentum
exchanged $\sqrt{t}$ in the amplitudes111Terms even in $\sqrt{t}$ are
cancelled by the contribution from the iterated single-axion exchange
potential in the massless pseudoscalar limit Ferrer:1998ue , we assume this is
still the case for a massive pseudoscalar. we obtain the following spin-
independent contributions at next-to-leading order in $m_{a}$ for diagrams 1
$a)$ and $b)$

$\displaystyle V_{ab}$
$\displaystyle(r)=-\frac{c_{\psi_{1}}^{2}c_{\psi_{2}}^{2}}{64\pi^{3}f^{4}}m_{\psi_{1}}m_{\psi_{2}}\bigg{\\{}\frac{1}{r^{3}}x_{a}K_{1}(x_{a})$
$\displaystyle+\bigg{(}\frac{1}{m_{\psi_{1}}^{2}}+\frac{1}{m_{\psi_{2}}^{2}}-\frac{1}{2m_{\psi_{1}}m_{\psi_{2}}}\bigg{)}\frac{3}{r^{5}}$
$\displaystyle\quad\times\bigg{[}\left(x_{a}+\frac{x_{a}^{3}}{6}\right)K_{1}(x_{a})+\frac{x_{a}^{2}}{2}K_{0}(x_{a})\bigg{]}\bigg{\\}}$
(14)

in which we define the dimensionless variable $x_{a}=2m_{a}r$ and
$K_{0}(x_{a})$ and $K_{1}(x_{a})$ are modified Bessel functions of the second
kind. In the case of a pseudoscalar particles described by the linear coupling
in (II) the potential (III) would be the full potential and one recovers the
leading term

$V_{ab}(r)=-\frac{c_{\psi_{1}}^{2}c_{\psi_{2}}^{2}}{64\pi^{3}f^{4}}\frac{m_{\psi_{1}}m_{\psi_{2}}}{r^{3}}+O\left(\frac{m_{a}^{2}}{r^{3}},\frac{1}{r^{5}}\right)\,.$
(15)

The contributions from diagrams $c)$ and $d)$ are given by

$\displaystyle V_{c}(r)$
$\displaystyle=\frac{c_{\psi_{1}}^{2}c_{\psi_{2}}^{2}}{64\pi^{3}f^{4}}m_{\psi_{1}}m_{\psi_{2}}\bigg{\\{}\frac{1}{r^{3}}x_{a}K_{1}(x_{a})$
$\displaystyle+\frac{1}{m_{\psi_{2}}^{2}}\frac{3}{r^{5}}\bigg{[}\left(x_{a}+\frac{x_{a}^{3}}{6}\right)K_{1}(x_{a})+\frac{x_{a}^{2}}{2}K_{0}(x_{a})\bigg{]}\bigg{\\}}\,,$
$\displaystyle V_{d}(r)$ $\displaystyle=V_{c}(r)\quad\text{with}\quad
m_{\psi_{1}}\leftrightarrow m_{\psi_{2}}$ (16)

whereas diagram $e)$ gives

$V_{e}(r)=-\frac{c_{\psi_{1}}^{2}c_{\psi_{2}}^{2}}{64\pi^{3}f^{4}}m_{\psi_{1}}m_{\psi_{2}}\frac{1}{r^{3}}x_{a}K_{1}(x_{a})\,.$
(17)

In the sum of these contributions the terms proportional to $r^{-3}$ cancel
out and we are left with

$\displaystyle V(r)$ $\displaystyle=V_{ab}(r)+V_{c}(r)+V_{d}(r)+V_{e}(r)$ (18)
$\displaystyle=\frac{3c_{\psi_{1}}^{2}c_{\psi_{2}}^{2}}{128\pi^{3}f^{4}}\frac{1}{r^{5}}\bigg{[}\left(x_{a}+\frac{x_{a}^{3}}{6}\right)K_{1}(x_{a})+\frac{x_{a}^{2}}{2}K_{0}(x_{a})\bigg{]}$

Expanding this result around $x_{a}=0$ we recover the familiar $r^{-5}$
potential

$V(r)=\frac{3c_{\psi_{1}}^{2}c_{\psi_{2}}^{2}}{128\pi^{3}f^{4}}\left[\frac{1}{r^{5}}-\frac{1}{3}\frac{m_{a}^{2}}{r^{3}}+O(m_{a}^{4})\right]\,.$
(19)

In the case of axions with an explicit mass term the potential (18) is
proportional to $V(r)\sim 1/r^{5}$ up to terms suppressed by
$m_{a}^{2}<1/r^{2}$ as a result of the shift symmetry of the Lagrangian.
Additional contributions from shift-symmetry breaking operators (4) are
suppressed by $\sim 1/f^{6}$. However, in the case of the QCD axion there are
additional terms at the same order in $1/f^{4}$ induced by the quadratic
interaction terms (7) proportional to the shift-symmetry breaking spurion
responsible for the axion mass. Evaluated for a potential between two nucleons
$N_{1}$ and $N_{2}$ the additional diagrams generate the potential

$\displaystyle V_{\text{sp.}}(r)$
$\displaystyle=\frac{1}{64\pi^{3}f^{4}}\bigg{\\{}-c_{N_{1}}c_{N_{2}}\frac{1}{r^{3}}x_{a}K_{1}(x_{a})$
$\displaystyle+\frac{3}{4}\left[c_{N_{1}}g_{N_{2}}^{2}\frac{1}{m_{N_{2}}}+c_{N_{2}}g_{N_{1}}^{2}\frac{1}{m_{N_{1}}}\right]\frac{1}{r^{5}}$
$\displaystyle\quad\times\bigg{[}\left(x_{a}+\frac{x_{a}^{3}}{6}\right)K_{1}(x_{a})+\frac{x_{a}^{2}}{2}K_{0}(x_{a})\bigg{]}\bigg{\\}}\,$
$\displaystyle=-\frac{c_{N_{1}}c_{N_{2}}}{64\pi^{3}f^{4}}\frac{1}{r^{3}}+O\left(\frac{m_{a}^{2}}{r^{3}},\frac{1}{r^{5}}\right)\,,$
(20)

where $g_{N}$ and $c_{N}$ are defined in (II). The contributions from the
quadratic axion interaction induced by the spurion dominate over the
contribution from the interaction induced by shift-invariant operators even
though the latter appear at leading order in the EFT expansion. Note that this
is different from the corrections in the expansion (19) which are suppressed
by the axion mass, which in the case of the QCD axion scales as
$m_{a}^{2}\propto f_{\pi}^{4}/f^{2}$. While (18) results in a repulsive
potential, (III) can in principle have either sign, but is universally
attractive for a QCD axion only interacting with gluons. The effect of the
shift-symmetry breaking interaction -to leading order- doesn’t affect leptons,
because Feynman diagrams $c)$ and $d)$ in Fig. 1 don’t contribute to the
leading term in (III).

Figure 2: Limits on the axion-gluon couplings $c_{GG}/f$ obtained from the
Casimir-less experiment Chen:2014oda . The dashed blue contour corresponds to
the limit obtained using the pseudoscalar form of the potential (15), the
solid red contour corresponds to the axion potential without shift-symmetry
breaking terms (18), and the dotted purple line corresponds to the full axion
potential including the nucleon spurion term (III).

##  IV Fifth force constraints on QCD Axions

In the following we demonstrate the effect of the shift-symmetry breaking
interaction on the sensitivity of experiments searching for a fifth force. We
consider the simplest QCD axion model with a single coupling to gluons
described by the Wilson coefficient $c_{GG}$ keeping it’s mass $m_{a}$ a free
parameter. Bounds from atomic and molecular spectroscopy aren’t substantially
changed by the inclusion of the higher order operators (II) because the
leading effects only affect nucleon-nucleon interactions. We instead consider
experiments probing macroscopic, spin-independent forces such as the one
described in Chen:2014oda  in which the difference in the force between a
sphere and a plate of two different materials is probed, which minimises the
contribution from the Casimir effect. The accuracy in measuring this force (or
absence thereof) has been used in Klimchitskaya:2015zpa  to obtain the best
limits on the pseudoscalar-to-nucleon coupling in the meV–eV range for an
experiment of this type.
The corresponding differential force between a sphere of radius $R$ and a disk
with thickness $D$ with Au and Si coating placed at a distance $\ell$ from the
sphere reads

$\displaystyle\Delta F(\ell)$ $\displaystyle=2\pi
C_{s}\left[C_{\text{Au}}-C_{\text{Si}}\right]\\!\int_{\ell}^{2R+\ell}\\!\\!\\!\\!\\!\\!dz_{1}(R^{2}-(z_{1}-R-\ell)^{2})$
$\displaystyle\times\\!\frac{\partial}{\partial
z_{1}}\\!\int_{-D}^{0}\\!\\!dz_{2}\\!\int_{0}^{\infty}\\!\\!\rho
d\rho\,\mathcal{V}\big{(}\sqrt{\rho^{2}+(z_{1}-z_{2})^{2}}\big{)}\,,$ (21)

where we factor out the coupling constants such that
$V(r)=c_{\psi_{1}}^{2}c_{\psi_{2}}^{2}\mathcal{V}(r)$ in the case of the
potential derived from the derivative interaction (18) and
$V_{\text{sp}}(r)=c_{N_{1}}c_{N_{2}}\mathcal{V}_{\text{sp}}(r)$ for the
leading term of (III) and define the material-dependent prefactors in terms of
the axion couplings to nucleons (II)

$\displaystyle C_{X}$
$\displaystyle=\rho_{X}\left(\frac{g_{p}^{2}}{4}\frac{Z_{X}}{m_{X}}+\frac{g_{n}^{2}}{4}\frac{N_{X}}{m_{X}}\right)\quad\text{for}\quad\eqref{eq:fullpotential}\,,$
(22) $\displaystyle C_{X}$
$\displaystyle=\rho_{X}c_{N}\frac{A_{X}}{m_{X}}\quad\text{for}\quad\eqref{eq:potential_spur}\,,$
(23)

with density $\rho_{X}$, average number of protons and neutrons
$A_{X}=Z_{X}+N_{X}$ and mean masses $m_{X}$ of the disc and sphere atoms for a
material $X$. The calculation of (IV) is lengthy but straightforward following
Bezerra:2014dja ; Klimchitskaya:2015zpa ; Klimchitskaya:2021lak  and we give
the result in Appendix B. As expected the axion force derived from the shift-
symmetry breaking interactions $V_{\text{sp}}(r)$ grows with $\ell$ compared
to the force derived from derivative interactions as $\Delta
F_{\text{sp}}/\Delta F(\ell)\sim m_{\pi}^{2}\ell^{2}$.

The resulting bounds on $c_{GG}/f$ are shown as a function of the axion mass
in Fig. 2. The dashed blue line is the bound obtained by using the interaction
Lagrangian in (II). However, including the quadratic interaction terms as
shown in (II) changes the potential to the $1/r^{5}$ form in (18), resulting
in a substantially weaker bound compared to the previous potential as shown by
the position of the solid red line in the figure. The quadratic nucleon
spurion term in (7) generates the additional potential (III) proportional to
$1/r^{3}$ at leading order. Furthermore, the coupling of this term is not
suppressed by the axion mass unlike what one would expect from a spurion
breaking the axion shift symmetry. As a result this spurion term generates a
bound close to that obtained using the $1/r^{3}$ pseudoscalar potential; this
bound is shown by the dotted purple line in Fig. 2. Importantly, this
contribution to the low-energy potential is only relevant if the external
states are nucleons. As a result similar probes for fifth forces are only
sensitive to the leading term in the potential if they don’t depend on the
axion coupling to leptons. e.g. atomic or molecular spectroscopy
Karshenboim:2010ck ; Jaeckel:2010xx ; Salumbides:2013dua ; Salumbides:2013aga
; Salumbides:2015qwa ; Jones:2019qny  is only sensitive to the $1/r^{5}$
contribution to the potential, whereas measurements of cold neutron scattering
or bouncing Neutrons are sensitive to the dominant $1/r^{3}$ part of the
potential Frank:2003ms ; Nesvizhevsky:2007by ; Kamiya:2015eva ; Brax:2011hb ;
Brax:2013cfa . We’ll provide a more comprehensive discussion in a companion
paper.

##  V Conclusions

We identify the dominant contribution to the low-energy potential for the
macroscopic fifth force incuded by axion pair exchange for axions that -like
the QCD axion- interact with gluons and thus obtain part of their mass from
the chiral anomaly. This contribution arises from higher-order operators of
the axion Lagrangian that would be naively expected to produce subleading
effects. We show explicitly that these operators not only generate the most
important contribution to the low-energy potential but result in a scaling of
the non-relativistic potential $V(r)\sim 1/r^{3}$ as opposed to the leading
term $V(r)\sim 1/r^{5}$ expected from derivative interactions. Moreover, since
to the QCD axion mass is generated via strong dynamics, this new contribution
is only present for interactions between nucleons and so the nature of the
shift-symmetry breaking for an axion can be probed via the comparison of
different searches for fifth forces. We demonstrate the impact at the example
of a Casimir-less fifth-force experiment and find an improved sensitivity of
almost 5 orders of magnitude.

## Appendix A

The axion interaction with chiral fermions $\psi=\psi_{L}+\psi_{R}$ in the UV
theory can be derived from the Lagrangian

$\displaystyle\mathcal{L}_{\text{UV}}=\frac{1}{2}\bar{\psi}i\overset{\leftrightarrow}{\not{\partial}}\psi-y\bar{\psi}_{L}S\psi_{R}+h.c$
(24)

after the scalar$S$ developes a vacuum expectation value $f$ such that the
fermion mass is given by $m=yf$ and

$\displaystyle S=(f+s)\exp\Big{(}2i\frac{a}{f}\Big{)}$ (25)

with a scalar field $s$ and the Goldstone boson $a$. Ignoring interactions of
the scalar mode the Lagrangian reads

$\displaystyle\mathcal{L}=\frac{1}{2}\bar{\psi}i\not{\partial}\psi-m\bar{\psi}_{L}\exp\Big{(}2i\frac{a}{f}\Big{)}\psi_{R}+h.c$
(26)

For small $a/f$ one can expand the exponent and obtains interactions

$\displaystyle\mathcal{L}=\frac{1}{2}\bar{\psi}i\overset{\leftrightarrow}{\not{\partial}}\psi-m\left(2i\frac{a}{f}-2\frac{a^{2}}{f^{2}}+\mathcal{O}\left(\frac{a^{3}}{f^{3}}\right)\right)\bar{\psi}_{L}\psi_{R}+h.c$
(27)

Alternatively one can rescale the fermion fields

$\displaystyle\psi_{L}\to\exp\left(i\frac{a}{f}\right)\psi_{L},\quad\psi_{R}\to\exp\left(-i\frac{a}{f}\right)\psi_{R}\,,$
(28)

and find instead the explicitly shift invariant Lagrangian

$\displaystyle\mathcal{L}=\frac{1}{2}\bar{\psi}i\overset{\leftrightarrow}{\not{\partial}}\psi-\frac{\partial_{\mu}a}{f}\bar{\psi}\gamma_{5}\gamma^{\mu}\psi-m\bar{\psi}_{L}\psi_{R}+h.c$
(29)

This leads to a non-relativistic potential scaling like $1/r^{5}$. Often this
interaction term is rewritten using the equation of motion of the fermion
fields

$\displaystyle\mathcal{L}$
$\displaystyle=\frac{1}{2}\bar{\psi}i\overset{\leftrightarrow}{\not{\partial}}\psi-\frac{a}{f}\Big{(}\bar{\psi}\gamma_{5}\overset{\rightarrow}{\not{\partial}}\psi+\bar{\psi}\gamma_{5}\overset{\leftarrow}{\not{\partial}}\psi\Big{)}-m\bar{\psi}_{L}\psi_{R}+h.c$
$\displaystyle=\frac{1}{2}\bar{\psi}i\overset{\leftrightarrow}{\not{\partial}}\psi+2im\frac{a}{f}\bar{\psi}\gamma_{5}\psi-m\bar{\psi}_{L}\psi_{R}+h.c$
(30)

This form of the Lagrangian leads to different Feynman rules and for example
the non-relativistic potential from two axion exchange has a $1/r^{3}$
dependence, because higher-order terms aren’t captured by the naive
application of the equations of motion. Instead, we rescale the fermion fields
with field dependent factors that are linear in the axion field $L,R\propto a$
and factors that are quadratic in the axion fields $N,S\propto a^{2}$ such
that

$\displaystyle\psi_{L}+L\psi_{L}+N\psi_{L}\,,$ (31)
$\displaystyle\psi_{R}+R\psi_{R}+S\psi_{R}\,.$ (32)

We then find to linear order in $a$:

$\displaystyle\mathcal{L}(a)$
$\displaystyle=\frac{1}{2}\big{(}L+L^{\dagger}\big{)}\bar{\psi}_{L}i\overset{\leftrightarrow}{\not{\partial}}\psi_{L}+\frac{1}{2}(\partial_{\mu}L-\partial_{\mu}L^{\dagger})\bar{\psi}_{L}i\gamma^{\mu}\psi_{L}$
$\displaystyle+\frac{1}{2}\big{(}R+R^{\dagger}\big{)}\bar{\psi}_{R}i\overset{\leftrightarrow}{\not{\partial}}\psi_{R}+\frac{1}{2}(\partial_{\mu}R-\partial_{\mu}R^{\dagger})\bar{\psi}_{R}i\gamma^{\mu}\psi_{R}$
$\displaystyle-\frac{a}{f}\left(\bar{\psi}\gamma_{5}\overset{\rightarrow}{\not{\partial}}\psi+\bar{\psi}\gamma_{5}\overset{\leftarrow}{\not{\partial}}\psi\right)$
$\displaystyle-m(L^{\dagger}+R)\bar{\psi}_{L}\psi_{R}-m(L+R^{\dagger})\bar{\psi}_{R}\psi_{L}\,.$
(33)

Applying the equations of motions for the axion is equivalent to the choice
$L=ia/f$ and $R=-ia/f$. For this choice the first term vanishes and the terms
in line 2 and 3 in (A) cancel and the remaining term reads

$\displaystyle\mathcal{L}(a)=2mi\frac{a}{f}\psi\gamma_{5}\psi\,,$ (34)

in agreement with (A). Now we consistently shift the terms quadratic in $a$
and find

$\displaystyle\mathcal{L}(a^{2})$
$\displaystyle=\frac{1}{2}\big{(}LL^{\dagger}+N+N^{\dagger}\big{)}\bar{\psi}_{L}i\overset{\leftrightarrow}{\not{\partial}}\psi_{L}$
$\displaystyle+\frac{1}{2}(L^{\dagger}\partial_{\mu}L-L\partial_{\mu}L^{\dagger}+\partial_{\mu}N-\partial_{\mu}N^{\dagger})\bar{\psi}_{L}i\gamma^{\mu}\psi_{L}$
$\displaystyle+\frac{1}{2}\big{(}RR^{\dagger}+S+S^{\dagger}\big{)}\bar{\psi}_{R}i\overset{\leftrightarrow}{\not{\partial}}\psi_{R}$
$\displaystyle+\frac{1}{2}(R^{\dagger}\partial_{\mu}R-R\partial_{\mu}R^{\dagger}+\partial_{\mu}S-\partial_{\mu}S^{\dagger})\bar{\psi}_{R}i\gamma^{\mu}\psi_{R}$
$\displaystyle+\frac{a}{f}\bigg{[}(L+L^{\dagger})\Big{(}\bar{\psi}_{L}\overset{\rightarrow}{\not{\partial}}\psi_{L}+\bar{\psi}_{L}\overset{\leftarrow}{\not{\partial}}\psi_{L}\Big{)}$
$\displaystyle+(\partial_{\mu}L+\partial_{\mu}L^{\dagger})\bar{\psi}_{L}\gamma^{\mu}\psi_{L}$
(35)
$\displaystyle-(R+R^{\dagger})\Big{(}\bar{\psi}_{R}\overset{\rightarrow}{\not{\partial}}\psi_{R}+\bar{\psi}_{R}\overset{\leftarrow}{\not{\partial}}\psi_{R}\Big{)}$
$\displaystyle-(\partial_{\mu}R+\partial_{\mu}R^{\dagger})\bar{\psi}_{R}\gamma^{\mu}\psi_{R}\Big{]}$
$\displaystyle-m(LR^{\dagger}+N^{\dagger}+S)\bar{\psi}_{R}\psi_{L}-m(LR^{\dagger}+S^{\dagger}+N)\bar{\psi}_{R}\psi_{L}\,.$

Choosing $N$ and $S$ to be real eliminates every term apart from the first,
third and last line. Setting

$\displaystyle
2N=2S=-L^{\dagger}L=-R^{\dagger}R=-\frac{1}{2}\frac{a^{2}}{f^{2}}$ (36)

cancels the terms with derivative interactions and yields

$\displaystyle\mathcal{L}(a^{2})=2m\frac{a^{2}}{f^{2}}\bar{\psi}\psi\,.$ (37)

Including this operator in the calculation of the non-relativistic potential
cancels terms that scale as $1/r^{3}$ and reproduces the $1/r^{5}$ potential
obtained from the explicitly scale invariant form (29).

## Appendix B

Integrating (IV) for the potential (18) and (III) yields respectively

$\displaystyle\Delta F(\ell)$ $\displaystyle=\frac{3}{64\pi
m_{a}}\frac{1}{f^{4}}|C_{\text{Au}}-C_{\text{Si}}|$ (38)
$\displaystyle\times\int_{1}^{\infty}\mathrm{d}u\frac{\sqrt{u^{2}-1}}{u^{3}}\sum_{l}C_{l}\Psi(m_{a}u)\,,$
$\displaystyle\Delta F_{\text{sp}}(\ell)$ $\displaystyle=\frac{1}{32\pi
m_{a}}\frac{1}{f^{4}}|C_{\text{Au}}-C_{\text{Si}}|\int_{1}^{\infty}\mathrm{d}u$
(39)
$\displaystyle\times\frac{\sqrt{u^{2}-1}}{u^{3}}e^{-2m_{a}u\ell}\left(1-e^{-2m_{a}uD}\right)X(m_{a}u)$

where $\ell$ is the separation between the sphere and the surface of the disc
with thickness $D$. The coefficients $C_{\text{X}}$ are given by (22) and
(23), respectively, and the function $X(x)$ is given by eq (11) in
Klimchitskaya:2015zpa . The experiment measured the differential force between
either Au or Si sectors of a rotating disc.

The sphere is made of sapphire (sa.) coated with Au and Cr, and the sum in (B)
is

$\displaystyle\sum_{l}C_{l}\Psi(x)$
$\displaystyle=C_{\text{Au}}\Psi\left(x;R,r\right)$
$\displaystyle+\left(C_{\text{Cr}}-C_{\text{Au}}\right)\Psi\left(x;R-d_{\text{Au}},r+d_{\text{Au}}\right)$
$\displaystyle+\left(C_{\text{sa.}}-C_{\text{Cr}}\right)$
$\displaystyle\times\Psi\left(x;R-d_{\text{Au}}-d_{\text{Cr}},r+d_{\text{Au}}+d_{\text{Cr}}\right)$
(40)

with $R$ the radius of the sphere, $d_{\text{Au}}$ and $d_{\text{Cr}}$ the
thicknesses of the gold and chrome coatings, and the function

$\displaystyle\Psi(x;R_{l},r_{l})$
$\displaystyle=8x^{4}\int_{r_{l}}^{2R_{l}+r_{l}}\mathrm{d}z\
\left[R_{l}^{2}-(R_{l}+r_{l}-z)^{2}\right]$
$\displaystyle\times\Bigg{\\{}-\frac{e^{-2xz}}{2xz}\left(1-\frac{z}{D+z}e^{-2xD}\right)$
$\displaystyle+\text{Ei}\left[-2x(D+z)\right]-\text{Ei}\left[-2xz\right]\Bigg{\\}}\,,$
(41)

where Ei$(x)$ is the exponential integral function.

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# Constructing Cross-lingual Consumer Health Vocabulary with Word-Embedding
from Comparable User Generated Content*
*Note: This manuscript has been accepted to the IEEE International Conference on Healthcare Informatics (IEEE ICHI 2024).

Chia-Hsuan Chang  College of Computing and Informatics
Drexel University
Philadelphia, USA
Email<EMAIL_ADDRESS>Lei Wang  College of Computing and
Informatics
Drexel University
Philadelphia, USA
Email<EMAIL_ADDRESS>Christopher C. Yang  College of Computing and
Informatics
Drexel University
Philadelphia, USA
Email<EMAIL_ADDRESS>
###### Abstract

The online health community (OHC) is the primary channel for laypeople to
share health information. To analyze the health consumer-generated content
(HCGC) from the OHCs, identifying the colloquial medical expressions used by
laypeople is a critical challenge. The open-access and collaborative consumer
health vocabulary (OAC CHV) is the controlled vocabulary for addressing such a
challenge. Nevertheless, OAC CHV is only available in English, limiting its
applicability to other languages. This research proposes a cross-lingual
automatic term recognition framework for extending the English CHV into a
cross-lingual one. Our framework requires an English HCGC corpus and a non-
English (i.e., Chinese in this study) HCGC corpus as inputs. Two monolingual
word vector spaces are determined using the skip-gram algorithm so that each
space encodes common word associations from laypeople within a language. Based
on the isometry assumption, the framework aligns two monolingual spaces into a
bilingual word vector space, where we employ cosine similarity as a metric for
identifying semantically similar words across languages. The experimental
results demonstrate that our framework outperforms the other two large
language models in identifying CHV across languages. Our framework only
requires raw HCGC corpora and a limited size of medical translations, reducing
human efforts in compiling cross-lingual CHV.

##  I Introduction

The increasing popularity of social media has facilitated discussion between
Internet users and encourages us to share information and experiences. Such
development contributes to the emergence of online health communities (OHCs).
It stimulates a new channel for exchanging healthcare knowledge, including
personal experiences of diseases, reflections on medicines, and communications
between physicians and patients [1, 2]. OHCs possess a wide variety of health
consumer-generated content (HCGC). Analyzing HCGC helps study a wide range of
research questions, such as the doctors-patients interaction [3, 4, 5] and
health information search behavior [6]. HCGC also serves as a valuable
resource for extracting consumer health vocabulary [7, 8, 9, 10, 11, 12, 13,
14], identifying authoritative health answers [15], and facilitating many
consumer-oriented applications such as language simplification system [16].

However, analyzing HCGC is challenging because the vocabulary used by
consumers is very different from that used in the medical literature and
electronic health records. For example, consumers tend to use colloquial
expressions like watery stool rather than professional jargon such as diarrhea
for describing their bowel suffering. The open-access and collaborative
consumer health vocabulary (OAC CHV) [17, 7] is compiled to address this
language gap. Compared with other professional-oriented vocabularies organized
in the Metathesaurus of Unified Medical Language System (UMLS), OAC CHV
intends to capture the medical expressions used by consumers, who are usually
laypeople.

###  I-A Motivations

We have two motivations for driving this study. The first is the
underdevelopment of automatic term recognition (ATR) methods for identifying
CHV across languages. In order to recognize the expression evolution and
enrich the original OAC CHV [17], several studies propose various monolingual
ATR methods such as applying string patterns [7, 18, 10, 12], co-occurrence
analysis [9], machine learning models [7, 11], and word embedding techniques
[13, 14]. Unfortunately, most studies expand English vocabulary and rely on
language-specific features that barely apply to other languages. Besides, most
cross-lingual ATR methods rely on costly resources, such as parallel corpus
[19] and manual annotations [20, 21, 22, 23, 24], which are labor-intensive to
build up.

The second motivation is that the lack of cross-lingual CHV prevents the
development of consumer-oriented healthcare applications for non-English
languages. Although English dominates the health information on the Internet,
only 379 million people, which represent 4.9% of the world population, are
English native speakers. Considering the initiative proposed by the World
Health Organization, “Bridging the Language Divide in
Health111http://dx.doi.org/10.2471/BLT.15.020615”, there is still a large
population of laypeople using their native languages to share and search for
health information. Nowadays, language is a primary barrier for laypeople to
search relevant health information on the Internet [25, 26].

###  I-B Research Objectives & Contributions

This study aims at proposing a cross-lingual ATR framework that helps extend
the English CHV into other languages. The framework starts with collecting
HCGC corpora of two different languages. With the corpora, the framework
adopts word2vec techniques [27] on each monolingual corpus to learn the word
associations used by laypeople. To identify similar medical concepts across
languages, we align monolingual word spaces into a cross-lingual word space
[28, 29] using a small size of medical concept translations. The contributions
of this study are as follows.

  1. 1.

Compared with previous cross-lingual ATR frameworks, we propose a resource-
efficient framework to identify CHV across languages, which only requires a
small set of medical entity translations and the HCGC corpus of each language.

  2. 2.

Compared with advanced large language models (LLMs), the cross-lingual word
space induced by our framework outperforms two state-of-the-art LLMs (i.e.,
GPT-3.5-Turbo and Cohere Rerank) in identifying CHV across languages, showing
an economic benefit of using our framework.

  3. 3.

We design a retrieval mechanism, dynamic threshold, to retrieve more quality
CHV translations based on our cross-lingual word space.

The rest of the paper is structured as follows: Section II reviews related
works in monolingual ATR methods and cross-lingual ATR methods. Section III
illustrates our proposed cross-lingual ATR framework, and Section IV describes
the experimental settings, metrics, and results. We then discuss implications,
limitations, and future directions in Section V. Finally, we draw a conclusion
in Section VI.

##  II Literature Review

We review previous ATR techniques for expanding the medical vocabulary and
categorize them into Monolingual ATR and Cross-lingual ATR. In the following,
we discuss the limitations and inspirations of these studies.

###  II-A Monolingual ATR

Previous studies on monolingual ATR relied on lexical patterns. Zeng et al.
[7] utilized MedlinePlus query logs for ATR, employing three components:
identifying string candidates, expert collaboration for noise reduction, and
estimating each remaining candidate’s score (i.e., termhood) using nested
string patterns [30]. Doing-Harris & Zeng-Treitler [8] adopted a similar
approach on the collected HCGC from PatientLikeMe.com for ATR. Vydiswaran et
al. [10] proposed string rule mapping (e.g., also called, also known as, and
also referred to as) to extract synonyms from health-related Wikipedia pages.
Likewise, Hou et al. [12] used string patterns, e.g., 又稱 (as known as) to
identify consumer-used disease terms from a Chinese online health forum.
Instead of using ad-hoc lexical patterns, Jiang and Yang [9] modified the tf-
idf technique and applied it on MedHelp threads for extracting frequent co-
occurring lay terms. He et al. [11] used clustering with combined lexical,
syntactic, and contextual features and extracted potential term candidates
from Yahoo Know! Q&As. Gu et al. [13] and Ibrahim et al. [14] proposed word
embedding techniques and identified semantically-similar terms from collected
health corpora.

Most previous monolingual ATR methods required string patterns and lexical
features that were only applicable to English, which causes difficulty in
generalizing to other languages. Even though co-occurrence calculation and
word embedding determination are language-agnostic techniques, a clearer way
to apply them across languages is needed.

###  II-B Cross-lingual ATR

Marko et al. [31] and Campillos-Llanos [32] depended on morpho-syntactic
features for linking potential translation and synonyms across languages.
However, the morphological pattern only worked for cognate languages, such as
Indo-European languages, that shared linguistic connections. Lu et al. [19]
created a parallel corpus, which utilized both Web anchor texts and search
result pages. They then used the parallel corpus to identify high-quality
English–Chinese medical term pairs. On the other hand, Chapman et al. [20] and
Alfano et al. [21] recruited a group of translators to translate English CHV
into other languages. Rahimi et al. [22] relied on aliases across languages on
the Wikidata to link UMLS concepts. Both parallel corpus preparation and
manual translation process took much work to scale and had coverage concerns.

As morphological patterns hardly worked for non-cognate languages. Moreover,
previous cross-lingual ATR methods relied on expensive resources, such as
parallel corpus and many manual annotations. In this study, we leveraged the
space alignment technique [28] for aligning the word contextual information
across languages, which was applicable across any language pairs [29] and only
required very few manual supervisions.

##  III The Cross-lingual ATR Framework

Fig. 1 illustrates our cross-lingual ATR framework for expanding CHV across
languages. Our framework consists of four main modules. With collected health
Q&A corpora, the first pre-processing module employs existing NLP toolkits to
clean the raw texts and transforms them into processed contents. Subsequently,
using a word embedding technique, the word semantic space learning module
determines the word vector space of each language from collected corpora. To
compare words in a language-agnostic way, the space alignment module pairs up
the spaces across languages utilizing a set of bilingual medical translation
pairs as anchors in the spaces. Given the bilingual word space, the last term
candidate expansion module requires a set of seed words, e.g., OAC CHV [17],
to expand their synonyms for eliciting the bilingual CHV. In the following
subsections, we present the data collection and detail each module of our
cross-lingual ATR framework.

Figure 1: Our framework for bilingual medical term expansion

###  III-A Data Collection

We collected the healthcare Q&A corpus from OHCs, the platforms for laypeople
to exchange health-related information, where people tend to use colloquial
expressions rather than professional jargon. Hence, we can exploit the usage
of health vocabulary from such HCGCs on the OHCs.

MedHelp is a popular English OHC consisting of various communities for
consumers to discuss diseases. We extracted 520,659 discussion threads from
106 different communities in MedHelp. To gather Chinese contents, we collected
three Chinese healthcare Q&A websites, including
eDoctor222http://taiwanedoctor.mohw.gov.tw/, MED-NET333https://expert.med-
net.com/index\\#/index, and
Kingnet444https://www.kingnet.com.tw/knNew/inquiry/outpatient.html, to
retrieve 259,709 inquires and their responses, where most questions are
answered by doctors and solved by one response. Table I presents descriptive
statistics of two corpora, in which the English corpus has more textual
content (meaured by characters) than the Chinese one.

TABLE I: Descriptive statistics of our collected corpora.

| No. of Documents | No. of Sentences | Avg. Content Length
---|---|---|---
English Corpus | 520,659 | 15.82M | 754.11
Chinese Corpus | 259,709 | 0.70M | 177.70

###  III-B Pre-processing

After collecting the corpora, we processed our textual data using existing NLP
toolkits. For English, we applied sciSpacy [33], a package for biomedical text
processing, for word tokenization and medical concepts extraction by
consulting Metathesaurus of UMLS [34]. Regarding pre-processing Chinese texts,
we employed jieba555https://github.com/fxsjy/jieba for word tokenization. Due
to the lack of a reliable medical name entity recognition tool in the Chinese
language, we collected 7,824 Chinese medical entities from the healthcare
category of BaiduBaike666https://baike.baidu.com/wikitag/taglist?tagId=76625,
and 11,604 Chinese medical entities from Wikipedia. The two Chinese entity
sets were combined as our custom dictionary for entity extraction. To prevent
breaking multiword expressions with high co-occurrences into separate words,
we utilized the phrases identification method [27] to connect them. We
filtered out the noises, including stop words, special symbols, and
punctuations for both languages.

###  III-C Determining Monolingual Word Vector Space

In the second module, we leverage the word embedding technique to determine
the word vector space of each language. The word vector space helps us compare
semantic similarities between words. One of the powerful word embedding
algorithms is Skip-gram [27], known for preserving the word semantics and
capable of encoding each word into a continuous vector representation. By
utilizing Skip-gram, we determined two word vector spaces
$V^{en}\in\mathbb{R}^{|W^{en}|\times d}$ and
$V^{zh}\in\mathbb{R}^{|W^{zh}|\times d}$ for English and Chinese healthcare
Q&A corpus, respectively. Note that $W^{en}(W^{zh})$ is the set of words
appearing in the English (Chinese) corpus, and $d$ is the size of hidden
dimensions representing each word. Moreover, we normalize every word vector by
applying $l2$-norm, where $V^{l}_{i}$ is a vector of word $i$ in language $l$.
With the normalization, we obtain two $d$-dimensional spheres, each for one
language.

###  III-D Aligning the Spaces of Different Languages

With the contextual information of words determined from the word semantic
space learning module, the word spaces were determined independently,
resulting in unaligned word dimensions between languages. We aligned consumer
health vocabularies of different languages in the space alignment module. To
facilitate the alignment procedure, we assumed the space structures were
topologically similar, also called isometric in previous studies, across
languages [28, 29]. This assumption allowed us to use a linear transformation
matrix $L\in\mathbb{R}^{d\times d}$ for aligning one source word space into
one target word space. In our setting, we treated the Chinese word space
$V^{zh}$ as source word space and applied $L$ on it to align with the target
word space – English word space $V^{en}$.

Determining $L$ required a set of translation pairs $P\subseteq W^{en}\times
W^{zh}$ as anchor points between the two word spaces. We leveraged Wikipedia
as our knowledge source to identify quality $P$ for our two health-oriented
word spaces. Because of collective intelligence and multilingualism, Wikipedia
possesses numerous health entities compiled into several languages. The title
of each page is usually the name of an entity. Hence, we followed the data
collection strategy proposed in [10] to collect a bilingual title list of
health-related pages from Wikipedia. In detail, we adopted the MediaWiki
Action API to traverse the category hierarchy organized in Wikipedia and drill
down subcategories for health category with a depth of five layers. We then
recorded the English title of each relevant page and its Chinese title as one
translation pair by querying the langlink property in MediaWiki Action API.
For instance, using “Diarrhea” as a query, we find its corresponding Chinese
title “腹瀉” (Diarrhea) 777The retrieved result can be verified by using
https://en.wikipedia.org/w/api.php?action=query&titles=Diarrhea&prop=langlinks&lllang=zh&format=json..

After compiling $P$, to optimize $L$, each title pair were represented as a
vector pair by consulting $V^{en}$ and $V^{zh}$, which resulted into two
subspaces: $V^{en}_{\dagger}\in\mathbb{R}^{|P|\times d}$ and
$V^{zh}_{\dagger}\in\mathbb{R}^{|P|\times d}$. The objective of $L$ aims at
minimizing the following equation:

$\mathop{\arg\min}_{L}\|{V^{zh}_{\dagger}}L-V^{en}_{\dagger}\|^{F}\text{ s.t.
}L^{T}L=I,$ (1)

where the orthogonal constraint of $L$ keeps the density between words in
$V^{zh}_{\dagger}$ invariant after transforming. Solving $L$ is hereby an
orthogonal Procrustes problem which has a analytical solution [29] using
singular value decomposition (SVD):

$L=UV,\text{with
}U{\Sigma}V^{T}=SVD(({V^{zh}_{\dagger}})^{T}V^{en}_{\dagger}).$ (2)

To better illustrate the alignment procedure, we provide an example in Fig. 2,
where the red items with the same number in Fig. 2a and 2b represent anchor
pairs in the $P$. The goal of $L$ is to transform $V^{zh}$ to align each
anchor pair using the $V^{en}$ as a standard reference. When $L$ is
determined, the bilingual word space is derived as Eq. 3.

$V^{bi}=(V^{zh}\cdot L)\cup V^{en},$ (3)

where $V^{bi}\in\mathbb{R}^{|W^{bi}|\times d}$ and $W^{bi}=W^{en}+W^{zh}$.

(a) $V^{zh}$

(b) $V^{en}$

(c) $V^{bi}$

Figure 2: The illustration of the spaces alignment

The alignment module not only aligned anchor word pairs in $P$ (red items in
Fig. 2) but also indirectly aligned non-anchor words (i.e., those words are
not in $P$) across languages. Fig. 2c explains three possible alignment cases
between non-anchor words across languages.

  1. 1.

Case 1: Non-anchor words close to the anchors. Even though only anchors
involve in determining $L$, we could expect to find more synonyms after
transformation due to the similar representations encoded in neighbors of
anchors. For example, given diarrhea and nausea as queries, we not only can
find their corresponding anchors 腹瀉 (diarrhea) and 噁心 (nausea), but also 拉肚子
(liquid bowel movements) as well as 想吐 (want to vomit), respectively.

  2. 2.

Case 2: Non-anchor words distributed similarly across languages. As we
transform the whole source space into the target space, the words with similar
meanings will match up by $L$ due to the assumption of topological similarity
between spaces. For example, even if we do not provide insomnia or its
neighborhoods as anchors, we still could find its Chinese synonym 失眠  (cannot
sleep). This is because similar word concepts are distributed closely across
languages after aligning.

  3. 3.

Case 3: Non-anchor words that bias at a particular language space. As shown in
Table I, the size of corpus is significantly different between languages.
Besides, some diseases, drugs, or other medical entities may differ between
languages, which causes some areas to be monolingual in the resultant
bilingual word space. In this situation, given an English word, its Chinese
neighbors have significantly greater distances than the ones in the previous
two cases.

###  III-E Word Expansion by Querying the Spaces

Given the bilingual word space, the words should be language-agnostic; hence,
we can compute semantic closeness between any two words using the cosine
similarity: $\text{cos}(V^{bi}_{i},V^{bi}_{j})$, where $i,j\in W^{bi}$ and
$V^{bi}_{i}$ is the word vector of word $i$. Given a set of seed words $Q$ of
a language as queries, we can search for their synonym candidates across
languages using the bilingual word space. In this study, seed words could be
either English or Chinese, so we have two query directions: (1) EN
$\rightarrow$ ZH, and (2) ZH $\rightarrow$ EN. For each seed word $q\in Q$, we
find the nearest words as candidates. To ensure the expansion quality, we only
kept the candidate $r$ whose similarity with the query beyond a threshold
($\delta$): $\text{cos}(q,r)>=\delta$.

Dynamic Threshold. Instead of using only one $\delta$ to filter out noisy
synonym candidates, we also consider using different thresholds for different
queries. This is because we observe that it is not easy to find an appropriate
$\delta$ for all queries. Take Table II as an example, we could set $0.64$ as
$\delta$ to filter out the noisy candidates of “高血壓” (hypertension), but this
$\delta$ is too strict for “雞眼” (wart). On the other hand, if we lower the
$\delta$ for “雞眼” (wart), the $\delta$ is adversely too vague for “高血壓”
(hypertension). The three cases can explain this phenomenon resulting from the
space alignment module. Some queries are distributed equally across languages
because they belong to case 1 or 2. In contrast, some queries are biased
toward a language that makes them far away from their synonyms of the other
language.

TABLE II: The results of two queries:
“高血壓” (hypertension) and “雞眼” (wart)

Query | Candidate | $cos(q,r)$ | Query | Candidate | $cos(q,r)$
---|---|---|---|---|---
高血壓 | hypertension | 0.81 | 雞眼 | wart | 0.58
htn | 0.74 | plantar_wart | 0.55
high_bp | 0.73 | callus | 0.54
hbp | 0.72 | splinter | 0.54
high_blood_pressure | 0.72 | ganglion_cyst | 0.53
hypertention | 0.65 | skin_tag | 0.52
hypertensive | 0.64 | ingrown_toenail | 0.52
high_cholesterol | 0.62 | bunion | 0.51
hyperlipidemia | 0.61 | athlete_foot | 0.51
blood_pressure_problem | 0.61 | hard_skin | 0.50

Our dynamic threshold mechanism is based on modularity. Modularity is a metric
to evaluate the bias level of a query in a specific language in the bilingual
word vector space. The lower modularity of a query means more words of the
other language surrounding that query. The higher modularity of a query
instead means that the query has more words of the same language as its
neighbors. To measure the modularity, we refer to the previous work [35] and
design our calculation for approximating the modularity score in the Algorithm
1. Given a query $q$, Line 1 and Line 2 collect top-$K$ English and Chinese
nearest neighbors as two sets of words $G^{en}$ and $G^{zh}$, respectively.
Line 3 and Line 4 are then used to calculate an average score of cosine
similarity $\eta^{en}(\eta^{zh})$ for $G^{en}(G^{zh})$. As Line 5, the
modularity is the difference between $\eta^{en}$ and $\eta^{zh}$. Therefore,
the lower modularity of a query indicates that its nearest neighbors of the
other language are close. In other words, when a query with lower modularity,
the more possibilities the query is either in case 1 or case 2. Otherwise,
when a query with higher modularity, it will possibly be case 3.

Algorithm 1 The algorithm for calculating modularity

0: bilingual word space $V^{bi}$, a query $q$, number of neighbors $K$

1: $G^{en}$ = top-$K$ similar English words of $q$

2: $G^{zh}$ = top-$K$ similar Chinese words of $q$

3: $\eta^{en}=\mathbb{E}_{r\sim G^{en}}[\text{cos}(q,r)]$

4: $\eta^{zh}=\mathbb{E}_{r\sim G^{zh}}[\text{cos}(q,r)]$

5: return $m=|\eta^{en}-\eta^{zh}|$

To dynamically set different $\delta$ for queries, we applied Algorithm 1 on
each seed word $q$. After sorting the seed words ascendingly with respect to
their modularity scores, we grouped $Q$ into $N$ subsets of equal size based
on quantiles $\\{Q_{i}\\}^{N}_{i=1}$, in which $Q_{1}$ contains the queries
with the lowest modularity. As a result, we searched the best $\delta$ of each
subset with regard to a determined metric (e.g., F1-score).

##  IV Evaluation

###  IV-A Experiment Setups

Parameter Settings. We determined the word vector space of each language by
feeding all texts from English and Chinese healthcare Q&A corpus. We employed
the word2vec module from
gensim888https://radimrehurek.com/gensim/models/word2vec.html, which
implements the Skip-gram algorithm [27]. All parameters of the Skip-gram were
default values. The size of vocabulary for English and Chinese word space are
54,061 and 17,882, respectively. We used 719 bilingual title pairs from
Wikipedia to enable the process of space alignment. Note that we collected
11,604 pairs in total, yet we dropped a pair if either English or Chinese
title in a pair did not exist in our word spaces. In our further evaluations,
we demonstrated effective performances even with a small proportion of words
as anchors.

Test Set Preparation. We evaluated our proposed framework by testing the query
performance of frequently used medical entities selected from our collected
healthcare Q&A corpora. Only five divisions (community groups in MedHelp),
including General-Health, Women-Health, Dermatology, Ear-Nose-Throat, and
Neurology, were involved in the further evaluations because these divisions
were the most popular topics in our corpora. To generate English test queries,
we calculated the frequency of each term that was selected from the OAC CHV
[17] and only retained terms that belonged to two semantic types: Sign or
Symptom [T184] and Disease or Syndrome [T047]999Both T184 and T047 were the
semantic types defined in the Semantic Network of UMLS.. After filtering out
the general terms (i.e., terms appearing in all divisions), we picked the top
10 frequent words as queries from each division, resulting in 50 English
queries. On the other hand, we sorted every word by its frequency within each
division in the Chinese Q&A corpus to select Chinese queries. We filtered out
the words that did not represent a sign, symptom, disease, or syndrome. After
that, we picked each division’s top 10 frequent words as queries from the
remaining words. As a result, we had 50 Chinese queries. Subsequently, we
manually scrutinized the top 100 nearest neighbors of each Chinese and English
query to make the ground truth. The labeling strategy was as follows: If a
neighbor word has the same semantic meaning as the query, it will be labeled
as a relevant item, otherwise a non-relevant item. Three annotators were
responsible for the labeling procedure. All annotators had research
experiences in health informatics and are Chinese-English bilingual speakers.
The inter-rater agreement was measured using Cohen’s kappa coefficient
($\kappa$) and reached $0.83$. All conflict annotations were resolved by
majority rule.

Two Experiments. We conducted two experiments and reported the results in the
following subsections. The first experiment compared the quality of bilingual
health word embedding induced by our proposed framework with other existing
language models for identifying CHV across languages. The second experiment
evaluated the sensitivity of the parameters of our proposed framework, mainly
focused on parameters for retrieval, including similarity threshold $\delta$
and dynamic threshold mechanism.

###  IV-B Experiment 1: Model Comparison

Performance Metrics. We used mean reciprocal rank (MRR) as the metric for
evaluating the retrieval performances of different systems. For each query
$q_{i}$, we identified the rank of its first relevant result $rank_{i}$. As
such, given a set of queries and ranks $Qr=\\{q_{i}:rank_{i},1\leq
i\leq|Qr|\\}$, MRR is the average of reciprocal ranks for $Qr$, calculated as
follows:

$MRR=\frac{1}{|Qr|}\sum^{|Qr|}_{i=1}\frac{1}{rank_{i}}$ (4)

When the system places the relevant item in the first place, its MRR will be
$1$. In our case, high MRR means relevant translations are identified earlier,
which prevents people from reading through many irrelevant translations.
Reversely, if a system hardly identifies relevant items or places those items
in the latter positions, the MRR will be close to 0.

Competitive Models. We compared our induced bilingual health word embedding
with (1) OpenAI’s GPT-3.5-Turbo and (2) Cohere’s Rerank. Both models were
easily accessed by their official APIs and were the most common and accessible
resources for most NLP tasks.

  1. 1.

GPT-3.5-Turbo 101010We have considered BioGPT, health-specific GPT; however,
it is pre-trained only using English corpora., it is pre-trained using a
significant amount of web data; it should learn about health vocabulary usage
from the online health communities of different languages. It also performs
well on various NLP tasks, including translation task [36].

  2. 2.

Rerank 111111We have considered OpenAI’s embedding API, but the official
document does not suggest the usage beyond English., it is supported by
rerank-multilingual-v2.0, an LLM pre-trained using a set of multilingual
corpora. Its ability on cross-lingual information retrieval has been
demonstrated [37].

To test GPT-3.5-Turbo, we designed a prompt (see Fig. 3) which provides GPT a
query term and its list of translations. As we have annotated all 100 nearest
translations for each query, we randomly shuffled all of them and asked GPT to
sort the order of translations by their relevance to the query. This task was
to test whether GPT could identify the semantic translation (i.e., the
translation that shares the same meaning as the query) and give it a good rank
(i.e., 1 is the best). The task mimicked how we used the induced bilingual
health word space to search translations for each query term. To test Rerank,
we called Cohere’s rerank API 121212https://docs.cohere.com/reference/rerank-1
and set the query and documents field as testing query and list of
translations, respectively.

Figure 3: The prompt template for asking GPT-3.5-Turbo to rerank the
translations by relevance.

Results. Table III reports the MRR performance for each model, in which EN
$\rightarrow$ ZH means that we used English queries to find Chinese synonym
candidates (i.e., Chinese translations), and ZH $\rightarrow$ EN was the
reverse query direction. All three models outperformed the random baseline,
indicating that all of them could suggest relevant translations for a given
query. The bilingual health word embedding induced by our system reached the
best MRR performance. That is, relevant translations retrieved by our system
could be ranked high (supported in Fig. 4). To check the statistical
significance, we employed the Wilcoxon signed-rank test to test the difference
between the returned list of ranks across models. The results suggested that
our framework significantly, $p<0.01$ marked by $\text{}^{***}$, prevailed
over the other two models. Our results conformed to the finding reported in
[38] that large language models may perform worse than health domain-specific
models with significantly smaller parameters. As a result, our framework was
more reproducible and adopted by others because it only required relatively
small corpora and a few bilingual anchors. Besides, our induced bilingual word
embedding was more economically efficient, i.e., free from the need for GPU
and efficient query time achieved by computing cosine similarity between two
words rather than computing across layers of transformers.

TABLE III: MRR performance comparison

| Our System | GPT-3.5-Turbo | Rerank | Random Baseline
---|---|---|---|---
ZH $\rightarrow$ EN | $0.825^{***}$ | $0.413$ | $0.322$ | $0.02$
EN $\rightarrow$ ZH | $0.664^{***}$ | $0.398$ | $0.337$ | $0.04$

(a) $\text{ZH}\rightarrow\text{EN}$

(b) $\text{EN}\rightarrow\text{ZH}$

Figure 4: The rank distributions of different systems

###  IV-C Experiment 2: Sensitivity Analysis

Performance Metrics. We used precision, recall, and $\text{F}_{1}$ to report
the query performance, and those metrics are defined as follows:

$\text{precision}=\frac{|\text{relevant items}\cup\text{retrieved
items}|}{|\text{retrieved items}|}$ (5)

$\text{recall}=\frac{|\text{relevant items}\cup\text{retrieved
items}|}{|\text{relevant items}|}$ (6)

$\text{F}_{1}=2\times\frac{\text{precision}\times\text{recall}}{\text{precision}+\text{recall}}$
(7)

Influence on Similarity Threshold. Fig. 5a and Fig. 5b showed the influence of
a similarity threshold $\delta$ to the precision, recall, and $\text{F}_{1}$.
Both query directions (EN $\rightarrow$ ZH and ZH $\rightarrow$ EN) had
consistent trends of three metrics with respect to the x-axis, $\delta$. With
the higher $\delta$, our methodology generated the more-precise synonym
candidates across languages, and the precision approached the peak when
$\delta=0.75$. On the other hand, the recall was at the peak as $\delta$
stayed low; however, the price was that loose criteria included too many noisy
candidates, resulting in undesirably low precision. For the task of
determining bilingual medical vocabulary, both precision and recall have the
same importance. Therefore, we could set 0.6 as $\delta$ for both query
directions to reach the best $\text{F}_{1}$. Comparing with the previous
studies on expanding vocabularies within the same languages [9, 11], our
$\text{F}_{1}$ performance was competent even in the more challenging
context—expanding vocabularies across languages. The ZH $\rightarrow$ EN had a
better performance than EN $\rightarrow$ ZH. We attributed this phenomenon to
the unbalanced size between corpora of different languages. Since the English
language has a three times larger vocabulary than the Chinese language, it is
more probable for a Chinese query to find its English synonyms.

(a) EN $\rightarrow$ ZH

(b) ZH $\rightarrow$ EN

Figure 5: Performance of precision, recall, and $F_{1}$ under different
$\delta$

Moreover, when we set $\delta$ at 0.6 (where $\text{F}_{1}$ performs the
best), the correct ratio 131313The correct ration is calculated by dividing
number of relevant items by number of retrieved items. of EN $\rightarrow$ ZH
and ZH $\rightarrow$ EN were 25.76%(59/229) and 33.26%(314/944), respectively.
That is, we could find one correct Chinese candidate among every 4 Chinese
candidates and one correct English candidate among every 3 English candidates.
This retrieval performance demonstrated that our methodology was effective for
vocabulary expansion and helped to avoid scanning ten thousand possible
candidates of each query.

Efficacy of Dynamic Threshold Mechanism. To show the necessity of applying the
dynamic setting of $\delta$, we ascendingly sorted the whole query set by the
modularity score. We then grouped it into four quarters, namely
$Q_{1},Q_{2},Q_{3}$, and $Q_{4}$, based on the quartile. Fig. 6a and Fig. 6b
showed the $F_{1}$ curve of each quarter, in which the queries in each quarter
reach the highest $F_{1}$ at different value of $\delta$. The curves of
$Q_{4}$ are central on smaller $\delta$ than ones of other quarters. Instead,
the curves of $Q_{1}$ tend to require higher $\delta$ to reach a peak of
$F_{1}$. These patterns imply the phenomenon provided in Table II that we
cannot use a single threshold for every query. Also, the modularity score is
the one potential factor to set the appropriate threshold. As a result, after
grouping queries concerning modularity score, the dynamic threshold mechanism
helped to adopt the threshold which reached the highest $F_{1}$ for each
quarter (e.g., in EN $\rightarrow$ ZH we set $0.5$ as $\delta$ for $Q_{4}$ and
$0.6$ for $Q_{1}$) to achieve better retrieval performance.

(a) EN $\rightarrow$ ZH

(b) ZH $\rightarrow$ EN

Figure 6: $F_{1}$ performance for different subsets of queries

To benchmark the performance of the dynamic threshold mechanism, we compared
it with the other two alternative query methods: $k$-NN and single threshold.
For $k$-NN, we searched its best performance of $k$ in a range from 5 to 50
with five as step size, and for single threshold, we searched its best
performance of $\delta$ in a range from 0.5 to 0.75 with 0.05 as a step size.
Table IV presented the performance of each method. After applying the dynamic
threshold mechanism, the total candidates retrieved in ZH $\rightarrow$ EN
direction shrank, yet the proportion of correct candidates increased, leading
to the better $\text{F}_{1}$. In EN $\rightarrow$ ZH, its $\text{F}_{1}$ also
rose, and it helped identify more correct candidates without compromising
correct ratios.

TABLE IV: Query performance between different methods

Query Direction | Query Method | #Retrieved Items | Correct Ratio | $F_{1}$
---|---|---|---|---
ZH $\rightarrow$ EN |  $k$-NN | 750 | 33.07% | 38.21%
Single Threshold | 944 | 33.26% | 42.09%
Dynamic Threshold | 716 | 40.84% | 44.31%
EN $\rightarrow$ ZH |  $k$-NN | 250 | 28.80% | 31.65%
Single Threshold | 229 | 25.76% | 27.19%
Dynamic Threshold | 427 | 25.29% | 33.13%

###  IV-D Qualitative Result

We provided the retrieved samples in Table V. When we took 拉肚子(diarrhea) as
the query, our approach helped identify not only the correct synonym–diarrhea
but also some common wrong-spelling alternatives used by laypeople such as
diarhea, diareah, diarreha, diarreah, diaherra, diahrrea, and diahrea. Even
though stomach_ache and stomach_cramp do not match the exact meaning of the
query, both terms have similar contents. Those misspelled and similar
contextual words may contribute to subsequent consumer-oriented health
applications such as information retrieval or query expansion [26]. On the
other hand, when we set diarrhea as the query, several Chinese synonyms (i.e.,
腹瀉(diarrhea), 水瀉(watery stools), 拉肚子(diarrhea), 拉水(watery stools),
瀉(diarrhea), 下痢(diarrhea), 腹泄(diarrhea), 瀉肚子(diarrhea)) were successfully
identified, including two words with similar contexts: 肚痛(abdominal pain) and
消化不良(indigestion). From the above two query examples, we found that laypeople
used different expressions to describe a symptom, and our framework can help
identify those expressions.

TABLE V: Retrieved samples of 拉肚子(diarrhea) and diarrhea

Query | Rank | Candidates | Query | Rank | Candidates
---|---|---|---|---|---
拉肚子(diarrhea) | 1 | diarhea | diarrhea | 1 | 腹瀉(diarrhea)
2 | diareah | 2 | 水瀉(watery stools)
3 | diarreha | 3 | 拉肚子(diarrhea)
4 | diarrhea | 4 | 拉水(watery stools)
5 | diarreah | 5 | 瀉(diarrhea)
6 | diaherra | 6 | 下痢(diarrhea)
7 | stomach_ache | 7 | 肚痛(abdominal pain)
8 | diahrrea | 8 | 腹泄(diarrhea)
9 | diahrea | 9 | 消化不良(indigestion)
10 | stomach_cramp | 10 | 瀉肚子(diarrhea)

##  V Discussion

###  V-A Practical Implications & Limitations

This study presents two implications for practitioners. First, the induced
non-English CHV connects to the existing English CHV thanks to the bilingual
word space. Such connections help the induced non-English medical terms
conform to the existing medical terminology, such as concept unique
identifiers (CUI) in UMLS. Therefore, it is possible to construct a language-
agnostic CHV for benefiting multilingual applications (e.g., analyzing code-
switching medical texts). Second, since the cross-lingual ATR learns word
association patterns from the collected HCGC, it helps capture the commonly
used medical expressions from laypeople, facilitating subsequent consumer-
oriented applications such as medical chatbots. The learned vocabulary also
helps translate professional medical terms into consumer-friendly terms [16]
(i.e., language simplification task), improving the communication between
patients and physicians.

There are two limitations to our proposed method. The first one is that the
technique we adopt for handling multiword expressions may not be effective for
infrequent expressions. We employ phrase identification [27] to capture the
frequent term co-occurrences as multiword expressions, such as “loose bowel
movements” and “blood pressure problem”. Therefore, some of the less frequent
multiword expressions may be ignored. The second one is that the unbalanced
size of corpora between languages could harm synonym retrieval performance.
For example, in our evaluation, the size of the Chinese corpus is
significantly less than one of the English corpus, so we find the query
direction EN $\rightarrow$ ZH has worse performance than that of ZH
$\rightarrow$ EN because of the limited potential synonym candidates in
Chinese.

###  V-B Future Directions

Our proposed method can be generalized to align word vector spaces of two more
languages to compare consumer-oriented expressions across multiple languages.
The framework can be used for exploring different vocabulary usage patterns in
different countries and generate a language-agnostic CHV for facilitating
cross-lingual medical information retrieval. Another direction is to develop a
query suggestion tool using our cross-lingual ATR framework. Using the
appropriate terms in the query is critical to consumer health search [25, 26].
Since every non-English native consumer may have different English literacy,
recommending common-used medical expressions as a query is potentially helpful
to most consumers for having results with better readability [39]. Lastly, our
framework may be extended to consider more guidances from the pre-defined
English medical terminology. Medical professionals have constructed several
medical terminologies, such as MedDRA, in a hierarchical structure defined by
the relationships between medical entities. Once that English human-crafted
knowledge can be propagated across different languages, it will benefit most
other languages.

##  VI Conclusion

To automatically expand English OAC CHV into other languages, we proposed a
cross-lingual ATR framework, capturing word semantics from HCGC within each
language using the word embedding technique. The words of different languages
will be aligned into a cross-lingual word space by referring to a few pairs of
medical word translations. The resultant cross-lingual word space effectively
retrieves similar health-related expressions across languages, such as
misspelling words and colloquial terms. Our framework prevents vocabulary
organizers from screening thousands of candidates to select appropriate
translations.

## Acknowledgment

This work was supported in part by the National Science Foundation under the
Grants IIS-1741306 and IIS-2235548, and by the Department of Defense under the
Grant DoD W91XWH-05-1-023. This material is based upon work supported by
(while serving at) the National Science Foundation. Any opinions, findings,
and conclusions or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of the National Science
Foundation.

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