a a institutetext: Department of Physics, Faculty of Science and Technology,
Tokyo University of Science, Noda, Chiba 278-8510, Japanb b institutetext:
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan

# Composite Dark Matter with Forbidden Annihilation

Tomohiro Abe b Ryosuke Sato b and Takumu Yamanaka<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

A dark matter model based on QCD-like $SU(N_{c})$ gauge theory with
electroweakly interacting dark quarks is discussed. Assuming the dark quark
mass $m$ is smaller than the dynamical scale $\Lambda_{d}\sim 4\pi f_{d}$, the
main component of the dark matter is the lightest $G$-parity odd dark pion
associated with chiral symmetry breaking in the dark sector. We show that
nonzero dark quark mass induces the universal mass contribution to both
$G$-parity odd and even pions, and their masses tend to be degenerate. As a
result, dark pion annihilation into heavier $G$-parity even dark pion also
affects the dark matter relic abundance. Thus, our setup naturally
accommodates forbidden dark matter scenario and realizes heavy dark matter
whose mass is ${\cal O}(1$–$100)~{}{\rm TeV}$, which is different from
conventional electroweakly interacting dark matter such as minimal dark
matter. We also discuss CP-violation from $\theta$-term in the dark gauge
sector and find that the predicted size of electron electric dipole moment can
be as large as $\sim 10^{-32}~{}e~{}{\rm cm}$.

OU-HET-1219

##  1 Introduction

There is much evidence that almost a quarter of the energy in our current
universe consists of dark matter (DM) Planck:2018vyg . A new stable particle
in an extension of the Standard Model (SM) can be a candidate for DM, and the
thermal freeze-out scenario is one of the most attractive scenarios for the
production of particle DM in the early universe. In this scenario, the DM
interacts with the SM particles and couples with thermal plasma in the early
universe. Direct detection experiments can probe this interaction. There have
been extensive efforts for this search, and particularly the DM whose mass is
${\cal O}(1$–$100)~{}{\rm GeV}$ is severely constrained by direct detection
experiments such as LZ LZ:2022lsv  and XENONnT XENON:2023cxc .

A possible direction under this situation is to explore heavy DM whose mass is
${\cal O}(1$–$100)$ TeV, which is less constrained by the direct detection
experiments. The upper bound on the DM mass comes from the unitarity bound of
its annihilation cross section Griest:1989wd . Recently, there has been
significant progress on indirect detection experiments such as HAWC
HAWC:2019jvm , HESS HESS:2018cbt , MAGIC MAGIC:2022acl , and VERITAS
Acharyya:2023ptu , and those experiments started to be sensitive to the
annihilation of DM whose mass is above ${\cal O}(1)$ TeV. Furthermore, near-
future observations, CTA CTA:2020qlo , LHAASO LHAASO:2019qtb , and SWGO
Abreu:2019ahw  are expected to improve sensitivity on the DM annihilation
Rinchiuso:2020skh  (for a review, see, e.g., Boddy:2022knd .) Thus, we have a
chance to find such a heavy DM. In the thermal freeze-out scenario, heavier DM
requires a larger coupling to be consistent with the measured DM relic
abundance. One natural way to accommodate the large coupling is to assume that
DM is a composite particle from new strong dynamics.

In this paper, we discuss heavy composite particles as a DM candidate. For a
review, see refs. Kribs:2016cew ; Cacciapaglia:2020kgq ; Cline:2021itd . In
particular, we focus on a dark pion DM arising from chiral symmetry breaking
in a new QCD-like sector Bai:2010qg ; Buckley:2012ky ; Bhattacharya:2013kma ;
Hietanen:2013fya ; Bellazzini:2014yua ; Hochberg:2014dra ; Antipin:2014qva ;
Antipin:2015xia ; Mitridate:2017oky ; Redi:2018muu ; Dondi:2019olm ;
Contino:2020god . We assume dark quarks are charged under the electroweak
gauge symmetry, and the dark and SM sectors can communicate via electroweak
gauge interaction. Dark quark condensation provides the chiral symmetry
breaking and (pseudo) Nambu-Goldstone (NG) bosons, i.e., dark pions. The
lightest dark pion is stable because of $G$-parity and is a good candidate for
DM, as pointed out in ref. Bai:2010qg . We found that the mass term of the
dark quarks significantly affects the mass spectrum of the dark pions and
naturally accommodates the forbidden dark matter scenario DAgnolo:2015ujb .
Also, $\theta$-term in the dark $SU(N_{c})$ gauge sector induces CP-violating
interaction and electron electric dipole moment (EDM).

This paper is organized as follows. In section 2, we construct a chiral
Lagrangian of the dark pions and discuss their mass spectrum. We discuss the
DM relic abundance and the electron EDM in section LABEL:sec:phenomenology. In
section 4, we briefly discuss phenomenological aspects of direct detection
experiments, indirect detection experiments, collider experiments, and
gravitational wave (GW) observations. Section 5 is dedicated to presenting our
conclusions. In appendix A, we briefly show derivation of the Wess-Zumino-
Witten term.

##  2 Model

In this section, we describe a DM model based on a new QCD-like gauge theory.
Our model is an explicit example of models that were originally discussed in
ref. Bai:2010qg . We introduce an $SU(N_{c})$ gauge symmetry ($N_{c}\geq 3$)
and new Weyl fermions, $\psi$ and $\bar{\psi}$, as the dark quarks and dark
anti-quarks which are charged under the $SU(N_{c})$ and the SM gauge group,
$SU(3)_{c}\times SU(2)_{W}\times U(1)_{Y}$. The charge assignments are shown
in table 1. For a concrete discussion, in this paper, we introduce three
flavors of $\psi$ and $\bar{\psi}$, and they form triplets under the
$SU(2)_{W}$ gauge symmetry. We assume they are not charged under the
$SU(3)_{c}$ and $U(1)_{Y}$ gauge symmetry. The renormalizable Lagrangian is
given by

$\displaystyle\mathcal{L}=\mathcal{L}_{\text{SM}}$
$\displaystyle+\bar{\Psi}_{i}(i\not{D}-m)\Psi_{i}-\frac{1}{4}G_{\mu\nu}^{A}G^{A\mu\nu}+\frac{g_{d}^{2}\theta}{32\pi^{2}}G_{\mu\nu}^{A}\tilde{G}^{A\mu\nu},\quad\Psi_{i}\equiv\matrixquantity(\psi_{i}\\\
\bar{\psi}^{\dagger}_{i}),$ (1)

where $i=1,2,3$ is the flavor index, $m$ is the mass of the dark quarks, the
third term is the kinetic term of $SU(N_{c})$ gauge field, $g_{d}$ is the
gauge coupling of $SU(N_{c})$, and $\theta$ is the vacuum phase of $SU(N_{c})$
gauge sector. We take $-\pi<\theta\leq\pi$. Note that $\theta$ has a physical
effect if $m$ is nonzero. The $SU(N_{c})$ gauge interaction becomes strong at
low energy and confinement takes place at the dynamical scale $\Lambda_{d}$.
In this paper, we are interested in the case of the dark quark mass
$m\lesssim\Lambda_{d}$. The massless case has been discussed by the previous
literature including Bai:2010qg , and the other limit $m\gg\Lambda_{d}$ has
been discussed in ref. Mitridate:2017oky . For later purposes, we absorb the
CP-phase into the phase of the mass term by chiral phase rotation of the
$\Psi_{i}$ field:

$\displaystyle\Psi_{i}\to\exp\left(-\frac{i\theta}{6}\gamma^{5}\right)\Psi_{i}.$
(2)

Then, we obtain

$\displaystyle\mathcal{L}=\mathcal{L}_{\text{SM}}$
$\displaystyle+\bar{\Psi}_{i}\left[i\not{D}-m\exp\left(-\frac{i\theta}{3}\gamma^{5}\right)\right]\Psi_{i}-\frac{1}{4}G_{\mu\nu}^{A}G^{A\mu\nu}.$
(3)

Field | $SU(N_{c})$ | $SU(3)_{c}$ | $SU(2)_{W}$ | $U(1)_{Y}$
---|---|---|---|---
$\psi$ | $N_{c}$ | $\bm{1}$ | $\bm{3}$ | 0
$\bar{\psi}$ | $\bar{N_{c}}$ | $\bm{1}$ | $\bm{3}$ | 0
Table 1: The charge assignments of the dark quarks under $SU(N_{c})$ and the
SM gauge group, $SU(3)_{c}\times SU(2)_{W}\times U(1)_{Y}$.

###  2.1 Chiral Lagrangian

Let us discuss the chiral symmetry of the Lagrangian. The current Lagrangian
has an approximate $SU(3)_{L}\times SU(3)_{R}$ global symmetry. To be more
specific, $\psi_{i}$ and $\bar{\psi}^{\dagger}_{i}$ transform under this
global symmetry as

$\displaystyle\psi_{i}\to L_{ij}\psi_{j},\quad\bar{\psi}_{i}^{\dagger}\to
R_{ij}\bar{\psi}_{j}^{\dagger},$ (4)

where $L$ and $R$ are $3\times 3$ unitary matrices of the $SU(3)_{L}$ and
$SU(3)_{R}$ global transformations, respectively. The $SU(2)_{W}$ gauge
symmetry is embedded into the diagonal subgroup $SU(3)_{V}\subset
SU(3)_{L}\times SU(3)_{R}$, and the field transforms as

$\displaystyle\Psi_{j}\to[\exp(iT^{a}\theta^{a})]_{jk}\Psi_{k},$ (5)

where

The $SU(3)_{L}\times SU(3)_{R}$ symmetry is explicitly broken by the
$SU(2)_{W}$ gauge coupling and the dark quark mass $m$.

The $SU(N_{c})$ gauge interaction is asymptotically free, and confinement
occurs at the dynamical scale $\Lambda_{d}$. As in the case of the real QCD,
the dark quarks condense

$\displaystyle\langle{\bar{\psi}}\psi\rangle=-v_{d}^{3}\,\bm{1}.$ (6)

Then the approximate $SU(3)_{L}\times SU(3)_{R}$ global symmetry is
spontaneously broken into the diagonal subgroup $SU(3)_{V}$, in which the
$SU(2)_{W}$ gauge group is embedded. The low energy effective theory below the
dynamical scale $\Lambda_{d}$ is described by $3\times 3$ special unitary
matrix field $U$, which is transformed as $U\to LUR^{\dagger}$ under the
$SU(3)_{L}\times SU(3)_{R}$ transformation. The pion fields associated with
the chiral symmetry breaking are embedded into $U$. The dark quark mass matrix
$M\equiv\text{diag}(m,m,m)e^{i\theta/3}$ can be regarded as a spurion field
which is transformed as $M\to RML^{\dagger}$. Then we can construct ${\cal
O}(p^{2})$ chiral Lagrangian as

$\displaystyle\mathcal{L}_{2}$
$\displaystyle=\frac{f_{d}^{2}}{4}\Tr[D_{\mu}UD^{\mu}U^{\dagger}]-V(U),$ (7)
$\displaystyle V(U)$ $\displaystyle\equiv-v_{d}^{3}\Tr[MU+\mathrm{h.c.}],$ (8)

where $D_{\mu}U=\partial_{\mu}U-ig[W_{\mu},U]$, $g$ is the $SU(2)_{L}$ gauge
coupling, and  Figure 10: $\theta$-dependence in $\Omega_{\chi}h^{2}$ for
given $m\cos(\theta/3)$ and $f_{d}$. We take
$(m\cos(\theta/3),f_{d})=(0.1~{}{\rm TeV},~{}0.7~{}{\rm TeV})$ for the blue
curve, $(1~{}{\rm TeV},~{}2.3~{}{\rm TeV})$ for the orange curve, and
$(10^{-3}~{}{\rm TeV},~{}1.6~{}{\rm TeV})$ for the green curve.

Figure 11: _Left:_ $f_{d}$ and $d_{e}$ in $m\cos(\theta/3)$ \- $\theta$ plane.
Orange dash-dotted lines indicate the value of $f_{d}$ in the unit of TeV.
Black contours show the predicted value of the electron EDM. _Right:_
$m_{\chi}$ and $d_{e}$ in $m\cos(\theta/3)$ \- $\theta$ plane. Blue dashed
lines indicate the value of $m_{\chi}$ in the unit of TeV. The horizontal axis
is the real part of the dark quark mass $m\cos(\theta/3)$, and the vertical
axis is $\theta$. At each point, $f_{d}$ is chosen to achieve $\Omega_{\rm
DM}h^{2}=0.12$. Here we set the $\mathcal{O}(1)$ parameters in eq.
(LABEL:eq:baryon_annihilation) and (LABEL:eq:WeinbergOp_from_dark_sector) as
$c=1$ and $c_{\rm EDM}=1$, respectively. Red dashed lines indicate
$m/\Lambda_{d}=0.1$. In the red-filled region, we cannot trust our analysis
based on the chiral Lagrangian because of $m>\Lambda_{d}$.

In figure 11, we show the value of $f_{d}$ and the electron EDM in
$m\cos(\theta/3)$-$\theta$ plane. At each point in this plane, $f_{d}$ is
chosen to obtain $\Omega_{\rm DM}h^{2}=0.12$. We calculate the electron EDM by
using eqs. (LABEL:eq:WeinbergOp_from_dark_sector) and
(LABEL:eq:EDM_from_WeinbergOp) with $c_{\rm EDM}=1$. The maximal value of the
electron EDM in the parameter space is $\sim 10^{-32}~{}e~{}{\rm cm}$. The
value of the electron EDM in this model is below the current upper bound,
$|d_{e}|<4.1\times 10^{-30}e~{}{\rm cm}$ Roussy:2022cmp , and is out of the
reach of the ACME III experiment which will probe electron EDM at the level of
$0.3\times 10^{-30}e~{}{\rm cm}$ Doyle:2016edm . In order to probe the
parameter space, further improvements in the electron EDM experiments are
required.

##  4 Signals

In this section, we briefly comment on possible signals to probe the current
DM model. The phenomenology of $SU(2)_{W}$ triplet real scalar DM has been
discussed in, e.g., refs. Cirelli:2005uq ; Araki:2011hm ; Abe:2014gua ;
Chiang:2020rcv ; Arakawa:2021vih ; Katayose:2021mew . Some aspects of the dark
pion DM $\chi$ are similar to the elementary scalar DM case. However, the
current DM model has richer signals from other composite particles and strong
dynamics of the dark sector.

###  4.1 Direct detection

The direct detection experiments can probe scattering between the DM and
nucleons, and it is sensitive to scattering amplitude between the DM and
quark/gluon. The leading contribution comes from one-loop diagrams for
scattering with quarks and two-loop diagrams for scattering with gluons. Thus,
spin-independent cross section $\sigma_{\rm SI}$ for scattering between
$SU(2)_{W}$ triplet scalar $\chi$ and nucleons is suppressed by the loop
factor. We are interested in the case with the DM mass to be $\gtrsim{\cal
O}(1)~{}{\rm TeV}$ and $\sigma_{\rm SI}$ should be almost independent on the
DM mass and its spin as shown in ref. Chen:2023bwg . Note that one-loop
radiative correction induces a coupling between $\chi$ and the SM Higgs as
${\cal L}\ni-\lambda_{\chi H}|\chi|^{2}|H|^{2}$ with $\lambda_{\chi
H}\sim\alpha_{W}^{2}$. However, contribution to the spin-independent cross
section $\sigma_{\rm SI}$ from this $\lambda_{\chi H}$ coupling is suppressed
by $m_{W}/m_{\chi}$ Katayose:2021mew ; Chen:2023bwg  compared to diagram
without the Higgs propagator and its effect is small. Ref. Hisano:2015rsa
shows $\sigma_{\rm SI}\simeq 2\times 10^{-47}~{}{\rm cm}^{2}$ for wino DM with
QCD NLO corrections. We expect $\chi$ should have a similar value of
$\sigma_{\rm SI}$ and it is much below the current constraints by LZ
LZ:2022lsv  and XENONnT XENON:2023cxc . However, for $m_{\chi}\lesssim
4~{}{\rm TeV}$, $\sigma_{\rm SI}$ is still above the neutrino floor
OHare:2021utq , and we could have a chance to detect DM in the direct
detection experiment in the future.

###  4.2 Indirect detection

The indirect detection experiments are one of the most promising ways to probe
the current model. By assuming wino-like annihilation, the region with
$m_{\chi}\lesssim 20~{}{\rm TeV}$ already started to be partly constrained by
HESS HESS:2018cbt  and MAGIC MAGIC:2022acl  though these constraints suffer
from the uncertainty of the density profile of our galaxy. In the analysis of
indirect detection of $SU(2)_{W}$ charged DM, the Sommerfeld effect
significantly changes its annihilation cross section Hisano:2002fk ;
Hisano:2003ec ; Hisano:2004ds  because of the large mass hierarchy between
$\chi$ and electroweak gauge bosons. Also, the Sommerfeld effect has an impact
on the calculation of the relic abundance of the MDM Cirelli:2007xd , and we
expect a parameter to give the observed relic abundance in the current model
to be affected by ${\cal O}(1)$ factor compared to our analysis presented in
section LABEL:sec:phenomenology, which used tree-level annihilation cross
section. Compared to the MDM case, our model is more involved because the
final state particle $\pi$ in a forbidden channel is also charged under
$SU(2)_{W}$. We left a comprehensive analysis including the Sommerfeld effect
for future study AbeSatoYamanakaSommerfeld .

###  4.3 Collider experiments

The particles in the dark sector of the current model are heavier than
$1~{}{\rm TeV}$, and they have only electroweak gauge interaction with the SM
particles. Thus, it is difficult to probe these particles in the LHC
experiment. However, it is interesting to discuss the possibility of probing
this model at a future high energy collider such as the 100 TeV $pp$ collider.
Since the DM $\chi$ has $SU(2)_{W}$ charge, it can be pair-produced via
electroweak interaction, such as $W^{+*}\to\chi^{0}\chi^{+}$. At 100 TeV $pp$
collider, $m_{\chi}={\cal O}(1)~{}{\rm TeV}$ region could be probed depending
on pileup scenario Chiang:2020rcv . In addition to $\chi$, $G$-parity even
$\pi$ would be an interesting target in future collider experiments. $\pi$ can
be produced from, e.g., $V^{*}\to\pi V^{\prime}~{}(V,V^{\prime}=\gamma,W,Z)$
via WZW interaction term, and $\rho^{*}\to\pi\pi$ where $\rho$ is spin-1
resonance in the dark sector Kilic:2009mi ; Draper:2018tmh . $\pi$ can decay
into a pair of photons and these production channels result in a multi-photon
channel. So we expect that $\pi$ provides a clean channel and this would be an
interesting target in the collider experiments. Since 100 TeV $pp$ collider
can have sensitivity on $Z^{\prime}$ with a mass of $\sim 40~{}{\rm TeV}$
fcchh , we naively expect $m_{\rho}={\cal O}(10)~{}{\rm TeV}$ can be probed by
such a future collider but a detailed study is required to have a prospect on
that.

###  4.4 Gravitational waves

Since the current model has the confining QCD-like sector, our universe
experienced the chiral phase transition and the confinement-deconfinement
phase transition in the early stage. If either (or both) of these phase
transitions is the first order, the GW can be produced, and it could be
detected in a near future observation Schwaller:2015tja ; Antipin:2015xia ;
Kahara:2012yr ; Kang:2021epo ; Reichert:2021cvs ; Morgante:2022zvc . Although
it is quite tough to study the details of the phase transition because of the
strong dynamics, some parameter space of QCD-like theory supports first-order
phase transitions. See, e.g., ref. Bernhardt:2023hpr  and references therein
for recent development and situation. By assuming the electroweak interaction
has little impact on the phase transition, the property of the phase
transition is determined by $N_{c}$, $N_{f}$, and the dark quark mass $m$.

According to a treatment in Caprini:2015zlo ; Caprini:2019egz , the GW signal
from the first order phase transition is parametrized by (dimensionless)
latent heat $\alpha$, (dimensionless) inverse time of duration of the phase
transition $\tilde{\beta}$, and the bubble wall velocity $v_{w}$. The sound
wave after bubble collision is considered to be the main source of GW and its
peak frequency and amplitude of the GW signal from phase transitions are
estimated as Hindmarsh:2015qta ; Caprini:2015zlo

$\displaystyle f_{\rm peak}$ $\displaystyle\sim 1.9\times 10^{1}~{}{\rm
Hz}\times\left(\frac{\tilde{\beta}}{10^{5}}\right)\left(\frac{1}{v_{w}}\right)\left(\frac{T}{1~{}{\rm
TeV}}\right)\left(\frac{g_{*}}{100}\right)^{1/6},$ (59)
$\displaystyle\Omega_{\rm GW,peak}h^{2}$ $\displaystyle\sim 2.65\times
10^{-16}\times\left(\frac{\tilde{\beta}}{10^{5}}\right)^{-1}\left(\frac{\kappa^{2}}{10^{-5}}\right)\left(\frac{\alpha}{1+\alpha}\right)^{2}\left(\frac{g_{*}}{100}\right)^{-1/3}\left(\frac{g_{*,{\rm
dark}}}{g_{*,{\rm dark}}+g_{*,{\rm SM}}}\right)^{2}.$ (60)

We can see that smaller $\tilde{\beta}$ is preferred to have a sizable GW
signal.

In ref. Pasechnik:2023hwv , the phase transition in QCD-like theories is
explored by employing the Polyakov-loop improved linear sigma model as an
effective theory and found that $\tilde{\beta}$ could be as small as ${\cal
O}(10^{3})$ when the mass of the sigma meson is small otherwise
$\tilde{\beta}\sim 10^{4}$ – $10^{5}$ (see also ref. Reichert:2021cvs ). If
this is the case, BBO Crowder:2005nr ; Corbin:2005ny ; Harry:2006fi  and
DECIGO Seto:2001qf ; Kawamura:2006up ; Yagi:2011wg ; Isoyama:2018rjb  are
reachable $\Omega_{\rm GW}h^{2}\sim{\cal O}(10^{-17})$ at $f\sim{\cal O}(0.1)$
Hz, and we could have a chance to detect the GW. This feature of relatively
small $\tilde{\beta}$ is shared with scenarios with a light dilaton
Witten:1980ez ; Antipin:2012sm ; Hambye:2013dgv ; Sannino:2015wka ;
Ellis:2020awk ; Chishtie:2020tze ; Baldes:2021aph ; Sagunski:2023ynd . For
given $N_{c}$, there exists a range of $N_{f}$ in which the QCD-like theories
have a non-trivial IR fixed point. We can expect that a light dilaton appears
if $N_{f}$ becomes close to this conformal window and we could have a
detectable GW signal. In addition to this, the dark quark mass $m$ gives non-
trivial effects on the dynamics of the phase transition (See, e.g., figure 1
in ref. Bernhardt:2023hpr ). To summarize, whether we can detect the GW
signals from composite DM models or not is highly non-trivial, and a dedicated
study is required to have a conclusive answer.

##  5 Conclusion

We have discussed a model of composite DM based on a new QCD-like sector with
$SU(N_{c})$ gauge symmetry. For concreteness of numerical analysis, we have
focused on the case where $N_{c}=3$ and three flavors of dark quarks
identified as an $SU(2)_{W}$ triplet with $Y=0$. The dark sector is confined
and its chiral symmetry is spontaneously broken. $G$-parity odd dark pion
$\chi$ and even dark pion $\pi$ arise from this symmetry breaking, and the
lightest component of $\chi$ and the lightest dark baryon $B$ are candidates
of the DM.

The renormalizable Lagrangian allows the mass term of the dark quark and the
$\theta$-term in the dark sector, and we have discussed their impact on DM
physics by utilizing the chiral Lagrangian. In the massless dark quark limit,
the electroweak radiative correction induces the mass splitting between $\chi$
and $\pi$ and their mass ratio is fixed to be $m_{\pi}/m_{\chi}=\sqrt{3}$.
Thus, $\pi$ hardly affects the freeze-out process of $\chi$ and the relic
abundance of $\chi$ is determined by their annihilation into the SM gauge
bosons as the MDM scenario. On the other hand, nonzero dark quark mass induces
the universal mass contribution to both $\chi$ and $\pi$ and their masses tend
to be degenerate. We have found, for $m\gtrsim 0.1~{}{\rm TeV}$, $\pi$ also
affects the relic abundance of $\chi$ via the forbidden annihilation channel
$\chi\chi\to\pi\pi$ and the mass of $\chi$ to give $\Omega_{\rm DM}h^{2}=0.12$
becomes larger than the mass of the MDM scenario. Thus, the current model
naturally accommodates the forbidden dark matter scenario, and we found our
setup realizes the DM mass with ${\cal O}(1$–$100)~{}{\rm TeV}$. The
$\theta$-term in the dark sector has CP-violating effect, and the current
model predicts the electron EDM as $\sim 10^{-32}~{}e~{}{\rm cm}$ as a maximal
value. This value is much below the current constraints but it can be a good
benchmark point for future electron EDM experiments.

The current model has a simple structure but it provides a rich phenomenology
as we have discussed in section 4. Although the DM mass is larger than $\sim
1~{}{\rm TeV}$, The near future progress in indirect detection experiments
will increase the chance of observing the annihilation of the DM in our
galaxy. Detailed discussion requires careful study of the Sommerfeld effect
and we leave it for future study. In addition, we could test this model at the
future 100 TeV $pp$ collider, direct detection experiments, and GW
observations. In closing, we comment that our analysis can be easily extended
to more generic models. Confining gauge interaction can be, for example,
$SO(N_{c})$ or $Sp(2N_{c})$ gauge interaction. We can also take other SM
charge assignments on the dark quarks. In addition to this, a flavor singlet
pseudoscalar $\eta^{\prime}$ can also play a role of $G$-parity even pions in
large $N_{c}$ limit. $\eta^{\prime}$ can be interpreted as an NG boson from
$U(1)_{A}$ breaking. Although it obtains mass from the chiral anomaly, this
contribution is suppressed by $1/N_{c}$ Veneziano:1979ec ; Witten:1979vv , and
the mass splitting between $\eta^{\prime}$ and pions is suppressed in large
$N_{c}$ limit.

## Acknowledgements

The authors thank Kohei Fujikura, Kunio Kaneta, and Satoshi Shirai for useful
comments and discussions. We draw Feynman diagrams using TikZ-Feynhand
Dohse:2018vqo  and TikZ-Feynman Ellis:2016jkw . The work is supported in part
by JSPS KAKENHI Grant Numbers 21K03549 (T.A.), 23K03415 (R.S.), and 24H02244
(R.S.).

##  Appendix A Wess-Zumino-Witten term

In this appendix, we discuss the Wess-Zumino-Witten term. For details, see,
e.g., section VII-5 of ref. Donoghue:2022wrw . Here we consider a QCD-like
$SU(N_{f})$ gauge theory with $N_{f}$ flavors of quarks. Let us write
$U=\exp(2i\varphi)$, and $\ell_{\mu}$ and $r_{\mu}$ are external currents
which couples to left-handed and right-handed fermions, respectively.
$\varphi$, $\ell_{\mu}$, and $r_{\mu}$ are $N_{f}\times N_{f}$ matrix fields.
Then, the Wess-Zumino-Witten term is given as

$\displaystyle{\cal L}_{\rm WZW}$
$\displaystyle=-\frac{N_{c}}{4\pi^{2}}\epsilon^{\mu\nu\rho\sigma}\int_{0}^{1}d\tau{\rm
tr}\Biggl{[}\varphi\biggl{(}\frac{1}{4}\bar{v}_{\mu\nu}\bar{v}_{\rho\sigma}+\frac{1}{12}\bar{a}_{\mu\nu}\bar{a}_{\rho\sigma}$
$\displaystyle\qquad\qquad\qquad\qquad-\frac{2i}{3}\bar{a}_{\mu}\bar{a}_{\nu}\bar{v}_{\rho\sigma}-\frac{2i}{3}\bar{a}_{\mu}\bar{v}_{\nu\rho}\bar{a}_{\sigma}-\frac{2i}{3}\bar{v}_{\mu\nu}\bar{a}_{\rho}\bar{a}_{\sigma}-\frac{8}{3}\bar{a}_{\mu}\bar{a}_{\nu}\bar{a}_{\rho}\bar{a}_{\sigma}\biggr{)}\Biggr{]},$
(61)

where

$\displaystyle\xi_{\tau}$ $\displaystyle\equiv\exp(i\tau\varphi),$ (62)
$\displaystyle\bar{\ell}_{\mu}$
$\displaystyle\equiv\xi_{\tau}^{\dagger}\ell_{\mu}\xi_{\tau}-i\xi_{\tau}^{\dagger}\partial_{\mu}\xi_{\tau},\quad\bar{\ell}_{\mu\nu}\equiv\xi^{\dagger}_{\tau}(\partial_{\mu}\ell_{\nu}-\partial_{\mu}\ell_{\nu}+i[\ell_{\mu},\ell_{\nu}])\xi_{\tau},$
(63) $\displaystyle\bar{r}_{\mu}$
$\displaystyle\equiv\xi_{\tau}r_{\mu}\xi_{\tau}^{\dagger}-i\xi_{\tau}\partial_{\mu}\xi_{\tau}^{\dagger},\quad\bar{r}_{\mu\nu}\equiv\xi_{\tau}(\partial_{\mu}r_{\nu}-\partial_{\mu}r_{\nu}+i[r_{\mu},r_{\nu}])\xi_{\tau}^{\dagger},$
(64) $\displaystyle\bar{v}_{\mu}$
$\displaystyle\equiv\frac{1}{2}\bar{\ell}_{\mu}+\frac{1}{2}\bar{r}_{\mu},\quad\bar{v}_{\mu\nu}\equiv\frac{1}{2}\bar{\ell}_{\mu\nu}+\frac{1}{2}\bar{r}_{\mu\nu},$
(65) $\displaystyle\bar{a}_{\mu}$
$\displaystyle\equiv\frac{1}{2}\bar{\ell}_{\mu}-\frac{1}{2}\bar{r}_{\mu},\quad\bar{a}_{\mu\nu}\equiv\frac{1}{2}\bar{\ell}_{\mu\nu}-\frac{1}{2}\bar{r}_{\mu\nu}.$
(66)

Let us apply this generic expression to the model described in section 2.
Then, we identify

$\displaystyle\varphi\to\frac{1}{\sqrt{2}f_{d}}(\Pi_{3}+\Pi_{5}),\quad\ell_{\mu}\to
W_{\mu},\quad r_{\mu}\to W_{\mu}.$ (67)

Here $W_{\mu}$ is the matrix form of the $SU(2)_{W}$ gauge field defined in
eq. (LABEL:eq:Wmu_matrix). Then, we can rewrite $\bar{a}_{\mu}$,
$\bar{v}_{\mu\nu}$, and $\bar{a}_{\mu\nu}$ by using $W_{\mu}$ as

$\displaystyle\bar{a}_{\mu}$
$\displaystyle=\frac{1}{2}\xi_{\tau}^{\dagger}W_{\mu}\xi_{\tau}-\frac{1}{2}\xi_{\tau}W_{\mu}\xi_{\tau}^{\dagger}-i\xi_{\tau}^{\dagger}\partial_{\mu}\xi_{\tau}+i\xi_{\tau}\partial_{\mu}\xi_{\tau}^{\dagger},$
(68) $\displaystyle\bar{v}_{\mu\nu}$
$\displaystyle=\frac{1}{2}\xi_{\tau}^{\dagger}W_{\mu\nu}\xi_{\tau}+\frac{1}{2}\xi_{\tau}W_{\mu\nu}\xi_{\tau}^{\dagger},$
(69) $\displaystyle\bar{a}_{\mu\nu}$
$\displaystyle=\frac{1}{2}\xi_{\tau}^{\dagger}W_{\mu\nu}\xi_{\tau}-\frac{1}{2}\xi_{\tau}W_{\mu\nu}\xi_{\tau}^{\dagger}.$
(70)

Under the $G$-parity transformation defined in eqs.
(LABEL:eq:gparity_elementary) and (LABEL:eq:gparity), $\varphi$ and
$\xi_{\tau}$ transform as

$\displaystyle\varphi\to\varphi^{T},\quad\xi_{\tau}\to\xi_{\tau}^{T}.$ (71)

Since $W_{\mu}$ is invariant under the $G$-parity transformation, we obtain
the transformation law of $\bar{a}_{\mu}$, $\bar{v}_{\mu\nu}$, and
$\bar{a}_{\mu\nu}$ given in eqs. (68)–(70) as

$\displaystyle\bar{a}_{\mu}\to\bar{a}_{\mu}^{T},\quad\bar{v}_{\mu\nu}\to-\bar{v}_{\mu\nu}^{T},\quad\bar{a}_{\mu\nu}\to\bar{a}_{\mu\nu}^{T}.$
(72)

Thus, ${\cal L}_{\rm WZW}$ given in eq. (61) is invariant under this
transformation.

At the leading order of the pion fields, we can approximate as
$\bar{\ell}_{\mu}\simeq\tau\partial_{\mu}\varphi$ and
$\bar{r}_{\mu}\simeq-\tau\partial_{\mu}\varphi$. Then, we obtain

$\displaystyle\bar{a}_{\mu}\simeq\tau\partial_{\mu}\varphi,\quad\bar{v}_{\mu\nu}\simeq
W_{\mu\nu},\quad\bar{a}_{\mu\nu}\simeq 0.$ (73)

By plugging those expressions into eq. (61), we obtain eq. (LABEL:eq:wzw).

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# Rethinking Large Language Models
in Mental Health Applications

Shaoxiong Ji  Tianlin Zhang  Kailai Yang  Sophia Ananiadou  Erik Cambria

###### Abstract

Large Language Models (LLMs) have become valuable assets in mental health,
showing promise in both classification tasks and counseling applications. This
paper offers a perspective on using LLMs in mental health applications. It
discusses the instability of generative models for prediction and the
potential for generating hallucinatory outputs, underscoring the need for
ongoing audits and evaluations to maintain their reliability and
dependability. The paper also distinguishes between the often interchangeable
terms “explainability” and “interpretability”, advocating for developing
inherently interpretable methods instead of relying on potentially
hallucinated self-explanations generated by LLMs. Despite the advancements in
LLMs, human counselors’ empathetic understanding, nuanced interpretation, and
contextual awareness remain irreplaceable in the sensitive and complex realm
of mental health counseling. The use of LLMs should be approached with a
judicious and considerate mindset, viewing them as tools that complement human
expertise rather than seeking to replace it.

##  1 Introduction

Mental health is important and has been studied by natural language processing
(NLP) using text (e.g., social posts and doctor-patient conversations) as the
data sources, leading to the development of automatic methods for various
applications, including early detection of mental disorders [Zhang et al.,
2022] and mental health counseling [Althoff et al., 2016]. Researchers have
employed techniques, ranging from traditional feature engineering to automatic
feature learning, such as convolutional neural networks, recurrent neural
networks, and transformer networks, for mental illness detection and
classification [Zhang et al., 2022]. Recent advances utilize pretrained
language models (PLMs). PLMs trained with the masked language modeling
objective have become popular for training classification models in this
domain. Domain-specific continual pre-training has also undergone intensive
development to acquire domain knowledge with representative discriminative
models including PsychBERT [Vajre et al., 2021], MentalBERT [Ji et al., 2022],
PHS-BERT [Naseem et al., 2022], and MentalLongformer [Ji et al., 2023]. A
recent shift as in Figure 1 has occurred towards prompt learning, where
generative large language models (LLMs) such as SmileChat [Qiu et al., 2023a],
Psy-LLM [Lai et al., 2023], Mental-LLM [Xu et al., 2023], MentalLLaMA [Yang et
al., 2023b], ChatCounselor [Liu et al., 2023a], and MindWatch [Bhaumik et al.,
2023], are used to generate predictions or counseling based on input prompts
related to mental health conditions. This shift signifies a growing interest
in leveraging generative LLMs and prompt learning for mental health-related
tasks. However, one question looms large: is this a mere hype? This paper
delves into the recent developments and concerns surrounding the use of LLMs
for early prediction of mental health conditions, generating explanations for
mental health conditions, and generating responses in mental health
counseling.

Figure 1: A paradigm shift in NLP for mental health applications from masked
language models such as BERT to generative language models such as GPT and
LLaMA. Images of BERT, GPT, LLaMA are generated by Midjourney AI Art
Generator.

The landscape of large language models has undergone substantial
transformation in recent years. Current LLMs boast hundreds of billions of
parameters, a stark contrast to the relatively modest sizes seen in the early
2010s, typically ranging from millions to tens of millions of parameters.
Notably, models such as BERT, with 110 million parameters, and GPT-2, with 1.5
billion parameters, which were once considered large, now fall into the
category of medium-sized language models by standards at the time of writing.
It is important to note that the size of language models is not the only
factor determining their performance. Other factors, such as model
architecture, training data, and fine-tuning, also play significant roles in
their capabilities. This growth in model size reflects the ongoing evolution
of AI language models. This paper focuses on the recent use of generative LLMs
in mental health applications. For the purpose of this paper, the term “LLMs”
refers to generative models trained with the causal language modeling
objective, often called next-word prediction in a simpler term.

Our paper offers perspectives on rethinking large language models in the
context of mental healthcare. When using generation to predict mental health
conditions based on a prompt and post, it is worth noting that the generation-
as-prediction process can exhibit instability and unpredictability, even with
minor changes to the input prompt. We discuss empirical results related to
this instability and explore theoretical studies on meta-optimization that may
underlie this unpredictability. Consequently, we advocate carefully auditing
generative LLMs when they are used to predict mental health conditions.

When employing LLMs for mental health prediction, a significant concern
revolves around the interpretability of the generated output or the so-called
explanations. LLMs often operate as black-box neural networks, making it
challenging to discern how they arrive at their conclusions. Therefore, it is
essential to emphasize that claims of interpretable mental health analysis
should not be taken at face value but substantiated with rigorous proof and
verification. One fundamental concern when using LLMs for mental health
prediction is that the generated explanations may not necessarily imply true
interpretability.

In the context of early prediction of mental disorders, providing explanations
for mental health conditions, and counseling for mental health-related
queries, LLMs have the potential to produce incorrect information akin to
hallucinations. This risk underscores the necessity for further research to
assess the reliability and accuracy of these models. Developing safeguards and
validation mechanisms is essential to minimize the potential for
misinformation in mental health applications. Notably, some LLMs, like LLaMA
and BLOOM, have explicitly stated that their use in high-stakes settings is
either out of scope or prohibited. This underscores the recognition within the
AI community of the ethical and practical concerns surrounding the application
of LLMs in situations where human well-being and mental health are at stake.

In conclusion, these limitations and guidelines should serve as a reminder
that LLMs are not universally suitable for all mental health applications and
should be used judiciously with a full understanding of their strengths and
limitations.

##  2 Early Prediction Through LLMs’ Generation

Social media platforms have become a rich data source for studying and
potentially detecting mental health issues [Pavalanathan and De Choudhury,
2015, Harrigian et al., 2021, Zhang et al., 2022]. Early detection of mental
health concerns on social media involves using models to identify signs and
patterns that may indicate emotional distress, mental health issues, or
potential crises. The emergent prompt-based learning follows the steps of
pretraining, prompting, and predicting. For example, an LLM, such as GPT-3
[Brown et al., 2020] and its successors, generates the predicted mental
disorder label given a prompt and a social post as the input. The generation-
as-prediction paradigm has many advantages in many NLP tasks. In the mental
health analysis, an early evaluation on ChatGPT [Amin et al., 2023] and other
LLMs [Yang et al., 2023a] indicate LLMs are good generalist models but not as
good as specialized discriminative classification models trained specifically
for downstream tasks. Recently, Mental-LLM [Xu et al., 2023] and MentalLLaMA
[Yang et al., 2023b] show that instructional fine-tuning can improve the
prediction performance. However, finetuning generative large models with
billions of model parameters still did not outperform discriminative models
with millions of parameters.

### Instablity of Generation-as-Prediction

The dynamic nature of generative models means that small alterations in the
input prompt can lead to significantly different outputs. In the context of
mental health prediction, this unpredictability poses a serious concern. A
minor modification in the wording or framing of a prompt could yield varying
and potentially incorrect assessments of an individual’s mental health
condition. For example, Yang et al. [2023a] reported that the model’s
performance is highly sensitive to variations in adjectives describing
condition severity while mentioning that few-shot learning could be a possible
way to mitigate it. Specifically, altering the adjectives of severity from
any, some to very severe can result in fluctuations in predictive accuracy
without a discernible pattern. This instability underscores the necessity of
thorough audits of the model’s performance and response to different inputs.

### From the View of Meta Optimization

Some recent research in machine learning has provided insights into the in-
context learning behavior of LLMs. For example, Dai et al. [2023] suggested
that LLMs perform implicit gradient descent at inference time. There are some
similar views, such as the concept of learning in-context through gradient
descent [Von Oswald et al., 2023] and the mechanism of causal language
modeling through meta-learning [Wu and Varshney, 2023]. Meta optimization
seems a quite reasonable explanation for the “learning” process of LLMs’
generation given a prompt. However, there is no definitive consensus on this
matter. For example, Min et al. [2022] showed that ground truth demonstrations
are not required for in-context learning, raising the question of whether LLMs
might rely on a form of hard memorization. The debate continues, and a
conclusive answer remains elusive. In the context of unpredictable prediction
of LLMs’ generation, the optimization process, when viewed as a form of meta-
optimization, can appear arbitrary without a certain optimization objective,
especially when prompted with free-form inputs as illustrated in Figure 2. In
the case study conducted by Yang et al. [2023a], the adjectives of severity
affect the inference time optimization. This underscores the challenges in
adapting LLMs to complex human mental states and the nuances present in self-
reported mental health posts. Overall, the nature of LLMs’ in-context learning
and the design of prompts remain subjects of ongoing research and debate,
given the unique characteristics and challenges posed by LLMs in their
generation of text.

Figure 2: An illustration of prompting from the view of meta update. The
change in the prompt might lead to suboptimal, possibly explaining the
unpredictable LLMs’ generation-as-prediction.

### Reliablity and Auditing

Generative language models provide a more flexible and accessible way through
API than the preceding pre-training and fine-tuning paradigm, largely due to
their rapid development. OpenAI’s ChatGPT, for example, stands as a prominent
model accessible via an API, facilitating the creation of generation-as-
prediction pipelines for a wide user base. At the time of writing, despite
their larger model size, LLMs utilized for generation-as-prediction still
exhibit lower predictive performance than previous models trained with task-
specific classification heads [Xu et al., 2023, Yang et al., 2023b].
Additional (instruction) fine-tuning mitigates this performance gap. The
significance of fine-tuning on diverse and representative datasets cannot be
overstated. Addressing biases in the training data and optimizing model
hyperparameters to achieve improved performance in mental health
classification tasks remain less explored, primarily due to the extensive
computing requirements for training large models and searching
hyperparameters. These factors collectively contribute to the responsible and
effective utilization of LLMs in mental health assessment. Furthermore, the
instability of LLMs’ generation-as-prediction remains a challenging problem.
The viewpoint of meta-optimization can probably potentially shed light on the
early prediction of mental disorder through LLMs’ generation, for example,
quantitatively evaluating the equivalent parameter contributions [Lan et al.,
2019] of prompts tailored for mental health applications. Besides, it is
crucial to establish auditing processes [Mökander et al., 2023] that assess
the model’s reliability, sensitivity to input variations, and potential biases
to ensure the responsible and accurate use of generative models in mental
health applications. Such audits can help identify and mitigate issues related
to unpredictability and instability, ultimately improving the model’s
suitability for assisting in mental health prediction and ensuring that its
outputs are consistent and dependable.

##  3 LLM-generated Explanation $\neq$ Interpretablity

While deep learning models are often considered opaque, recent research has
unveiled that these hidden representations can, to some extent, offer
explanations. For instance, there has been ongoing discussion regarding
whether attention mechanisms serve as explanations [Bibal et al., 2022], and
we acknowledge that there is no definitive consensus on this matter. In the
context of mental health applications, our stance aligns with the perspective
put forth in these publications regarding explainability. LLMs have the
ability of self-explanation to provide explanations for their responses or
generate text that clarifies the reasoning behind their answers, which is a
form of step-by-step reasoning as referred to chain-of-thought [Wei et al.,
2022]. However, such explanations can be unfaithful [Xu et al., 2023] and
require targeted efforts for improvements [Turpin et al., 2023]. Assessing the
robustness and faithfulness of LLM-generated explanations in the context of
mental health is crucial. LLMs may sometimes produce explanations that are
overly simplistic or misleading, potentially impacting the quality of mental
health interventions. It is essential to rigorously evaluate the explanations
generated by LLMs to ensure they align with established clinical knowledge and
guidelines. Besides, it is crucial to exercise caution and prudence when
making claims about the explainability and interpretability of LLMs-based
methods applied to mental health applications. LLMs’ generated explanations do
not imply LLMs for mental health analysis are inherently interpretable.
Research works must refrain from using “interpretability” and “explainability”
interchangeably to avoid misconceptions and ensure clarity in discussions
surrounding LLMs in mental health applications.

### Interpretability and Explanability

Interpretability and/or explainability are frequently employed in many mental
health publications [Joyce et al., 2023]. It is crucial to recognize the
distinct contrast between “interpretability”, which pertains to a model’s
inherent characteristics, and “explainability”, which refers to the methods
used to explain a model or make a model interpretable, while “explanations”
encompass the actual insights or justifications provided by the model to
facilitate users’ comprehension of its predictions [Rudin, 2019]. Despite
this, it is worth noting that some literature within the field of LLM uses
interpretability and explainability interchangeably, such as Zhao et al.
[2023]. Recent work such as Yang et al. [2023a] explores how LLMs generate
text to explain the prediction of mental disorders. It is important to
recognize that these explanations may lack interpretability. In other words,
LLMs may provide detailed explanations (putting aside the faithfulness aspect
for now), but these explanations may not be straightforward or easily
comprehensible to human users who seek to understand why the model generates
such textual explanations. It is crucial to understand that LLMs’
explanations, as post-hoc generated text, do not guarantee that the model will
be inherently interpretable. Users may need to exert additional effort or
engage in further processing to make sense (or nonsense) of these explanations
and render them readily digestible.

### Call for Interpretability

LLMs are getting more performant in many applications and improving in mental
health applications. While LLM-based methods are employed for mental health
analysis, the claim of interpretability should be considered cautiously. Our
intention is not to dismiss the value of ongoing research on self-explanation.
Instead, we aim to clarify definitions and claims, particularly within
critical applications like mental healthcare. One avenue of research in the
realm of LLM self-explanation involves engineering techniques or experimental
testing that explains the significance of the model’s representations and
draws intuitive conclusions about the performance of these generated
explanations or representations. In mental health, relying solely on the
model-generated explanation is insufficient. Human judgment and clinical
expertise should be integral in explaining and validating the results. When
explaining the causes behind mental disorders, it is crucial to verify the
accuracy and evidence-based nature of the explanations provided by LLMs.
Additionally, it is essential to carefully monitor and mitigate the potential
for LLMs to generate stigmatizing or harmful explanations. Interpretability is
a critical factor, especially in fields where decisions can profoundly affect
individuals’ well-being [Joyce et al., 2023]. More importantly, we call upon
the computational research community in the field of mental health to focus on
developing techniques that make these models more inherently interpretable,
rigorously define the knowledge being modeled or applied within the
mathematical theory, and adhere to proof or analysis that has been done
through conceptual representation capacity, generalization, and robustness of
neural networks in theory. The black-box nature of neural networks in LLMs
underscores the need for transparency and validation in mental health
applications, allowing clinicians and experts to trust and validate the
results. Although the trade-off between interpretability and accuracy is still
a matter of debate, the emphasis on interpretability can help ensure that LLMs
become valuable tools in mental health while mitigating the risks associated
with their black-box nature. The future trajectory in integrating LLMs into
mental health applications could be ensuring that the LLMs’ outputs align with
clinical perspectives in interpreting and validating the model’s prediction
and developing specialized tools tailored for mental health professionals to
comprehend the model. In this context, data-driven methods like LLMs serve as
a user interface to improve the overall usability of the mental health support
system and interpretable methods are used for certain aspects of decision-
making (Figure 3). An analogy is the well-established diagnostic tools like
the nine-item Patient Health Questionnaire (PHQ-9) for assessing depressive
symptoms [Kroenke et al., 2001]. Interpretable methods that foster an
understanding of their inner workings enable users, especially mental health
professionals, to grasp the rationale behind the model’s prediction.

Figure 3: LLMs serve as the user interface to facilitate service quality,
while interpretable models are critical for decision-making.

##  4 LLMs in Mental Health Counseling

Chatbots for mental health, such as Woebot, have been developed to provide
emotional support and aid in Cognitive Behavioral Therapy (CBT) through
conversation with people living in mental health conditions [Fitzpatrick et
al., 2017]. Sarkar et al. [2023] reviewed conversational agents for mental
health and emphasized clinical knowledge and clinical practice guidelines in
making them explainable and safe. Developments such as MindWatch [Bhaumik et
al., 2023] may play a role in monitoring such risks, but their use should be
guided by best practices and ethical considerations.

Here, we discuss whether LLM-generated text is good for counseling in recent
studies on empathy, user intention, emotion cause, and beyond. We expect
reinforcement learning from human feedback to enable helpful and harmless
generation, which could possibly enhance LLM-based mental health counseling.
LLM-generated text can have potential applications in counseling, especially
in psychological therapies like cognitive behavioral therapy (CBT). However,
it’s essential to approach this with caution. The recent development of LLMs
might assist in providing information or exercises but should not replace the
human element of counseling to offer personalized guidance and adapt
interventions to the individual’s unique needs, especially in sensitive mental
health contexts.

### Human Intent, Touch and Empathy

While LLMs can provide automated responses and information and process long
context [Liu et al., 2023b], the generation mainly relies on learned model
parameters from the pretraining corpus and the calculation of the likelihood
of the next word. They can be distracted by irrelevant context [Shi et al.,
2023] and may not fully understand the nuances of individual experiences,
especially when there is insufficient individual training data, making their
advice less tailored. These models lack the empathetic and contextual
understanding that human counselors possess, which are crucial in counseling,
especially in mental health contexts [Sharma et al., 2021]. LLMs are required
to have the human touch, empathy, and comprehension that human counselors can
provide to enable more effective counseling. Reinforcement learning is adopted
to facilitate empathic conversations [Sharma et al., 2021], generate
motivational and empathetic responses with long-term reward maximization [Saha
et al., 2022], and promote polite and empathetic counseling [Mishra et al.,
2023]. Reinforcement learning in combination with LLMs can enhance the
potential for a better dialogue system and reinforce counseling strategies in
mental health. Ji [2022] showcased that language models struggle to comprehend
user intentions and can inadvertently generate harmful or hateful content. In
such cases, it becomes essential to employ contextual intent understanding,
model the intention awareness [Cambria et al., 2023], and reason to identify
the root causes of mental conditions, which could be used to enable empathetic
conversational chatbot [Li et al., 2021], and generate responses with human-
consistent empathetic intents [Chen et al., 2022]. These strategies highlight
the importance of understanding why users turn to LLM-based counseling and
what they anticipate, offering insights for the design and deployment of these
systems and making them more humane and responsive.

### Promises and Caveats

The use of LLMs in mental health counseling brings both potential benefits and
perils. Chatbots engage in complex conversations with mental health consumers
but struggle to identify and respond effectively to signs of distress, and
consumers react negatively to unhelpful or risky chatbot responses [De Freitas
et al., 2022]. The responses of some publicly available LLM-based chatbots,
when presented with prompts of increasing depression severity and suicidality,
failed to recognize the risk progression appropriately [Heston, 2023].
Generative LLMs such as ChatGPT struggled to detect unsafe responses in mental
health support dialogues [Qiu et al., 2023b]. Cabrera et al. [2023] examined
ethical issues using chatbots for mental health, identifying 24 moral dilemmas
that cut across bioethical principles. LLMs as chatbots require regulation,
but the unreliability stops them from applying to the real world [Gilbert et
al., 2023]. ChatCounselor [Liu et al., 2023a] conducted supervised fine-tuning
of base LLMs on real-world conversations between consulting clients and
professional psychologists, although only evaluated the performance with GPT-4
without human grounds. Deploying LLM-based technology at scale for mental
health may pose risks of misuse and require careful development and ongoing
evaluation more systematically. [Li et al., 2023] studied an annotation
framework for understanding counselors’ strategies and client reactions.
Interacting with LLMs can provide insights into tailoring the use of these
models in mental health counseling and make LLMs more professional virtual
counselors, leading to the need for interactive language processing [Wang et
al., 2023]. Human preference data tailored for mental health scenarios can
also be used to train reinforcement learning models to enable helpful and
harmless dialogue agents [Bai et al., 2022]. LLM-based methods facilitate
psychological intervention and educational outreach for non-professionals [Fu
et al., 2023] and meanwhile posit some potential risks such as unreliable
generation [Gilbert et al., 2023] and weakness in assessment of risk
progression [Heston, 2023]. To ensure safe usage, more rigorous improvements
and tests are needed.

##  5 Conclusion

AI indeed has the potential to be a valuable tool for identifying and
supporting individuals who may be facing mental health challenges on social
media platforms. However, it is essential to acknowledge and address the
current challenges and concerns associated with its use. This paper discusses
the problems associated with large language models in mental health
applications and emphasizes the importance of conducting further research to
enhance the safety and reliability of LLM-based methods. While this study
raises concerns regarding their effectiveness and explainability, it is
essential to clarify that its intention is not to discredit the existing
efforts made in this field. Instead, the research works discussed in this
paper are regarded as essential steps toward exploring LLMs’ real-world
applications. Our perspectives on rethinking LLMs in mental health
applications aim to encourage the research community to reflect more deeply on
LLMs’ applicability, accountability, trustworthiness, and reliability [Cambria
et al., 2023].

Firstly, it is noteworthy to mention that the application of LLMs for
generative prediction in mental health has made significant progress, albeit
without achieving a breakthrough. Nevertheless, several crucial issues, such
as the instability in generated predictions and the performance of the
generation-as-prediction paradigm, continue to persist and remain unresolved.

Secondly, LLMs possess the capability to generate explanations during
generative predictions. This feature provides supplementary information to
support the predictions made by LLMs. However, it is important to note that
this does not necessarily imply that the model is inherently interpretable
when applied to mental health analysis.

Thirdly, LLMs have shown considerable promise in generating coherent and
fluent textual content. This quality makes them viable candidates for
automatic mental health counseling. Nonetheless, it is important to emphasize
the need for further research and development to ensure that the generated
content is genuinely helpful and harmless for safe and effective application
in mental health scenarios.

In conclusion, LLMs represent a promising frontier in mental health, but they
must be approached with caution and respect for ethical principles. Their role
should be one of support for human experts, emphasizing their unique abilities
in the field. Our perspectives serve an important but not exhaustive view of
applying LLMs in mental health. Notably, there are other important aspects and
considerations, such as cultural sensitivity, privacy, and data security.
Robustness, ethical guidelines, and careful monitoring are essential
components of deploying LLMs in the crucial task of addressing challenges in
computational methods for mental health.

## Ethical Considerations

Ethical considerations are undeniably pivotal in deploying LLMs in mental
health applications. Guaranteeing user safety, preserving privacy, and
mitigating biases in responses are critical aspects that demand careful
attention. This paper underscores the exclusive reliance on publicly available
publications for its research. Furthermore, it is essential to emphasize that
there is no engagement in efforts to identify or directly interact with the
individuals behind the social media posts. For research involving LLMs
engaging in interactions with human beings, it is important to adhere to the
user guidelines provided by the corresponding LLMs and to uphold the
principles of research ethics rigorously. This ensures that ethical standards
are maintained in all aspects of LLM-based research, especially in sensitive
contexts like mental health.

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