# Technicolor with Scalar Doublet After the Discovery of Higgs Boson

Sibo Zheng
Department of Physics, Chongqing University, Chongqing 401331, P.R. China

Abstract

The SM-like Higgs boson with mass of 125 GeV discovered at the LHC is subject
to a natural interpretation of electroweak symmetry breaking. As a successful
theory in offering this naturalness, technicolor with a scalar doublet and two
both $SU(3)_{c}$ and $SU(N_{TC})$ colored scalars, which is considered as a
low-energy effective theory, is proposed after the discovery of SM-like Higgs
boson. At present status, the model can be consistent with both the direct and
indirect experimental limits. In particular, the consistency with precision
electroweak measurements is realized by the colored scalars, which give rise
to a large negative contribution to $S$ parameter. It is also promising to
detect techni-pions and these colored scalars at the LHC.

##  1 Introduction

Since the discovery of a standard model (SM)-like Higgs boson with mass around
125 GeV [1] reported by the ATLAS and CMS collaboration, extensive efforts
have been devoted to explore its implication to electroweak symmetry breaking
(EWSB) in the context of new physics. It is now believed that a part of most
favored parameter space of natural supersymmetry (SUSY) fails to achieve this,
due to the absence of SUSY signals at the large hadron collider (LHC) with
$\sqrt{s}=8$ TeV.

In parallel to SUSY as candidate of new physics which provides natural EWSB,
technicolor (TC) was also considered as an interesting scenario decades ago.
TC model differs from SUSY in many ways. In particular, it provides EWSB
through condensation of techni-fermions. Therefore, unlike in SUSY models
where the electroweak mass parameters are tightly related to the SUSY-breaking
scale due to EWSB, naturalness doesn’t concern us in TC-model. However, it
also suffers from its own problems, such as too large $S$ parameter in
precision electroweak measurements and explanation of mass hierarchy of SM
flavors (for a review, see [2]).

In this paper, we consider a variety of TC model based on previous works in
[3, 4]. These authors proposed scalar doublet(s) to original TC, which is
known as TC with scalar. This variety of TC-model should be considered as a
low-energy effective theory. Otherwise, the hierarchy problem appears as in
SM. It can be either embedded into walking TC or supersymmetric TC. In the
former case, the scalar is composite [5]. In other words, this variety of TC
model imitates the low-energy behavior of a set of extended TC. In the later
case, the scalar can be either fundamental or composite. The superpartners
receive their masses from supersymmetry breaking, and below SUSY-breaking
scale we obtain a TC with massive scalar doublet and SM111For recent works on
other variants of TC model, see, e.g, [6].. In contrast to the earliest TC,
the SM fermions obtain their mass similarly to SM in this type of TC model, in
which the vacuum expectation value (vev) of Higgs is-induced by the
condensation of techni-fermions-through the Yukawa couplings of Higgs scalar
to techni-fermions.

In particular, we study TC-model with one scalar doublet $\phi$ and two both
$SU(3)_{c}$ and $SU(N_{TC})$ colored scalars, in which there are two mass
scales $f$ and $f^{\prime}$, respectively, referring to decay constant of
techni-pions and vev of $\phi$. They are supposed to satisfy $f^{2}+f^{\prime
2}=\upsilon^{2}=(246{\it GeV})^{2}$ from consideration of EWSB. The coupling
of neutral scalar of $\phi$ to SM fermions are the same as those of SM except
an additional factor $f^{\prime}/\upsilon$. Therefore this factor determines
the deviation of our model from SM. Using the LHC data about Higgs immediately
leads to,

$\displaystyle{}0<\theta\lesssim 0.2,~{}~{}~{}~{}~{}~{}\theta\equiv
f/f^{\prime}.$ (1.1)

The couplings of techni-pions to SM fermions are similar to those of charged
Higgs boson in type $\mathbf{I}$ Higgs doublet model, except a common $\theta$
factor also.

The physical states below the scale $4\pi f$ are $\sigma$ scalar identified as
Higgs boson, techni-pions and colored techni-scalars. Distinctive features in
this model include $(1)$ the small $\theta\sim 0.2$ in (1.1) is sufficient to
provide a Higgs scalar of 125 GeV and techni-pion of $210-280$ GeV
simultaneously; $(2)$ the suppression from $\theta$ factor is sufficient for
the techni-pions to evade both the direct and indirect experimental limits;
$(3)$ the colored techni-scalars receive their masses of order $\upsilon$ via
their $\phi^{4}$ couplings to scalar doublet $\phi$; $(4)$ finally the colored
techni-scalars provide a large negative contribution to $S$, which eliminates
the large positive contribution arising from condensation, and therefore
reconciles the model with precision electroweak measurements.

The paper is organized as follows. In section 2, we present our model in
details. Then we discuss direct experimental limits on Higgs scalar, techni-
pions and colored techni-scalars in subsection 3.1. We address indirect
experimental limits on techni-pions in subsection 3.2 and colored techni-
scalars in subsection 3.3, respectively. We discuss masses of colored techni-
scalars and corrections to parameters of precision electroweak measurements
due to these scalars. We finally conclude in section 4.

##  2 The Model

The content of TC model which we will explore in this paper is as follows,

$\displaystyle{}Y_{L}=\left(\begin{array}[]{c}p\\\ m\\\
\end{array}\right)_{L}$ $\displaystyle:$
$\displaystyle\left(\mathbf{N}_{TC},~{}\mathbf{1},~{}\mathbf{2}\right)_{0}$
(2.3) $\displaystyle p_{R}$ $\displaystyle:$
$\displaystyle\left(\mathbf{N}_{TC},~{}\mathbf{1},~{}\mathbf{1}\right)_{1/2}$
$\displaystyle m_{R}$ $\displaystyle:$
$\displaystyle\left(\mathbf{N}_{TC},~{}\mathbf{1},~{}\mathbf{1}\right)_{-1/2}$
$\displaystyle\omega_{t}$ $\displaystyle:$
$\displaystyle\left(\mathbf{N}_{TC},~{}\bar{\mathbf{3}},~{}\mathbf{1}\right)_{-1/6}$
(2.4) $\displaystyle\omega_{b}$ $\displaystyle:$
$\displaystyle\left(\mathbf{N}_{TC},~{}\bar{\mathbf{3}},~{}\mathbf{1}\right)_{+1/6}$

with addition of a fundamental scalar
$\phi:\left(\mathbf{1},~{}\mathbf{1},~{}\mathbf{2}\right)_{1/2}$. The
assignments of representations are under the notation of
$SU(N_{TC})\times~{}SU(3)_{c}\times~{}SU(2)_{L}\times~{}U(1)_{Y}$. In
comparison with the simplest model of TC with scalar, two additional colored
scalars $\omega_{t,b}$ are added. The choices of hypercharge follow from the
requirement of anomaly free.

The Lagrangian for the model reads,

$\displaystyle{}\mathcal{L}=\mathcal{L}_{SM}+\mathcal{L}_{TC}+\mathcal{L}_{\phi}+\mathcal{L}_{\omega}-V(\phi,\omega)$
(2.5)

The hidden TC and SM matters communicate either via $\phi$ or $\omega$
scalars. For the former case, doublet $\phi$ couples to techni-fermions and SM
flavors in $\mathcal{L}_{\phi}=\mathcal{L}(\phi,T)+\mathcal{L}(\phi,f_{SM})$
respectively, which read

$\displaystyle{}\mathcal{L}(\phi,T)=h_{+}\bar{Y}_{L}\tilde{\phi}p_{R}+h_{-}\bar{Y}_{L}\phi~{}m_{R}+H.C$
(2.6)

and

$\displaystyle{}\mathcal{L}(\phi,f_{SM})=h_{l}\bar{L}\tilde{\phi}l_{R}+h_{U}\bar{Q}_{L}\tilde{\phi}~{}U_{R}+h_{D}\bar{Q}_{L}\phi~{}D_{R}+H.C$
(2.7)

Here, $Q_{L}$ and $L$ being the quark and lepton doublets of SM, respectively,
$U_{R}$, $D_{R}$ being right-hand top and bottom quark respectively, and
$l_{R}$ the right hand lepton. $h$s in (2.7) are the ordinary SM Yukawa
couplings.

There also exists strong communication between the quarks of third family and
techni-fermions through $\omega$ scalars 222In dynamical models of EWSB,
similarly to the magnitudes of Yukawa couplings of Higgs boson to SM fermions
, we assume that the largest effect is in the Yukawa couplings of top-bottom
doublet.  ,

$\displaystyle{}\mathcal{L}_{\omega}=\lambda_{\omega_{t}}\bar{t}_{R}p_{R}\omega_{t}^{{\dagger}}+\lambda_{\omega_{b}}\bar{b}_{R}m_{R}\omega_{b}^{{\dagger}}+H.C$
(2.8)

An advantage of adding $\omega$ scalars is that the four-fermions operators
involving top and bottom quark induced by Yukawa interaction in (2.8)
contribute to significantly negative $S$, which cancels the large positive
tree-level contribution due to condensation of techni-fermions. There is also
a disadvantage of introducing colored scalars. Because carrying colors implies
that $\omega$ scalars can be directly produced at hadron colliders, making the
model more constrained. This will be discussed in the next section.

The potential $V(\phi,\omega)$ in (2.5) can be determined from the symmetries
in (2.3). Below the scale of $\Lambda_{TC}=4\pi~{}f$ we will work in effective
field analysis, it is more convenient to express $\phi$ doublet and its
conjugate in the form of unitary matrix $\Phi$ [4], which can be defined as,

$\displaystyle{}\Phi=\frac{\sigma+f^{\prime}}{\sqrt{2}}\Sigma^{\prime},~{}~{}~{}~{}~{}~{}\Sigma^{\prime}=\exp(2i\Pi^{\prime}/f^{\prime})$
(2.9)

Using $\Phi$, we can write the self-couplings as,

$\displaystyle{}V(\phi,\omega)$ $\displaystyle=$
$\displaystyle\frac{\lambda_{1}}{8}[Tr(\Phi^{{\dagger}}\Phi)]^{2}+\lambda_{5}[\omega_{t}^{{\dagger}}\omega_{t}]^{2}+\lambda_{6}[\omega_{b}^{{\dagger}}\omega_{b}]^{2}$
$\displaystyle+$
$\displaystyle\lambda_{2}Tr(\Phi^{{\dagger}}\Phi)\omega_{t}^{{\dagger}}\omega_{t}+\lambda_{3}Tr(\Phi^{{\dagger}}\Phi)\omega_{b}^{{\dagger}}\omega_{b}+\lambda_{4}\omega_{t}^{{\dagger}}\omega_{t}\omega_{b}^{{\dagger}}\omega_{b}$

##  3 Experimental Limits

As well known we can use the effective chiral Lagrangian to describe the TC
model below the TC scale $\Lambda_{TC}$. In this approach, the pseudoscalars
that result from the chiral symmetry breaking are the isotriplet of technipion
$\Sigma$. Guided by non-linear realization of $\pi$ mesons in QCD, $\Sigma$
can also be similarly treated as,

$\displaystyle{}\Sigma=\exp(2i\Pi/f)$ (3.1)

which transforms as $\Sigma\rightarrow~{}L\Sigma~{}R^{{\dagger}}$ under the
chiral symmetries. It is then straightforward to write the kinetic terms of
our model,

$\displaystyle{}\mathcal{L}=\frac{f^{2}}{4}Tr\left(D_{\mu}\Sigma^{{\dagger}}D^{\mu}\Sigma\right)+\frac{1}{2}Tr\left(D_{\mu}\Phi^{{\dagger}}D^{\mu}\Phi\right)$
(3.2)

with the derivative $D_{\mu}\Sigma=\partial^{\mu}\Sigma-
igW^{\mu}_{a}\frac{\tau^{a}}{2}\Sigma+ig^{\prime}B^{\mu}\Sigma\frac{\tau^{3}}{2}$.
From (3.2) one observes that the linear combination $\pi_{a}\sim
f\Pi+f^{\prime}\Pi^{\prime}$ become the longitudinal components of the EW
gauge bosons, leaving its orthogonal combination
$\pi_{p}=(-f^{\prime}\Pi+f\Pi^{\prime})/\sqrt{f^{2}+f^{\prime 2}}$ as the
physical states of low energy region. One finds that $f^{2}+f^{\prime
2}=\upsilon^{2}$.

###  3.1 Direct Searches

Now we understand $\sigma$ and $\pi_{p}$ are the freedoms below
$\Lambda_{TC}$. The mass of $\sigma$ can be directly determined from (2) as in
[4],

$\displaystyle{}m^{2}_{\sigma}=\frac{3}{2}\tilde{\lambda}f^{\prime 2},$ (3.3)

where

$\displaystyle{}\tilde{\lambda}=\lambda_{1}+\frac{11}{24}\left[3h^{4}_{t}+N_{TF}(h^{4}_{+}+h^{4}_{-})\right].$
(3.4)

As for mass of $\pi_{p}$, it follows from the effective potential 333Here
$H=\left(\begin{array}[]{cc}h_{+}&0\\\ 0&h_{-}\\\ \end{array}\right)$. As
manifested in (2.6), it combines with $\Phi$ to transform as $\Phi
H\rightarrow L\Phi HR^{{\dagger}}$.,

$\displaystyle{}V_{eff}(\sigma)=c_{1}4\pi
f^{3}Tr\left(\Phi~{}H\Sigma^{{\dagger}}\right)+H.C$ (3.5)

with the coefficient $c_{1}\sim\mathcal{O}(1)$. Substituting $\pi_{p}$ into
(3.5) gives rise to444In what follows, we set $c_{1}=1$ for discussion.

$\displaystyle{}m_{\pi_{p}}=2c_{1}\sqrt{2}\frac{4\pi
f}{f^{\prime}}h\upsilon^{2}=8\sqrt{2}\pi
h\theta\upsilon^{2},~{}~{}~{}h=(h_{+}+h_{-})/2.$ (3.6)

Direct search on $\sigma$
The couplings of $\sigma$ to SM fermions and EW gauge bosons are suppressed by
a factor $f^{\prime}/\upsilon$.Identifying $\sigma$ as the Higgs boson
discovered at the LHC implies that the ratio $\mu_{\gamma}$ of signal strength
of $h\rightarrow\gamma\gamma$ over its SM prediction, and ratio $\mu_{V}$ of
signal strength of Higgs decaying into four-leptons via $WW^{*}$ and $ZZ^{*}$
both equal to

$\displaystyle{}\mu_{\gamma}=\mu_{VV}=(f^{\prime}/\upsilon)^{2},$ (3.7)

Global fit to the LHC data [7] suggests that (1.1) and

$\displaystyle{}\tilde{\lambda}=0.15-0.18,~{}~{}~{}~{}h=1.75\tilde{\lambda}.$
(3.8)

The requirement $4\pi f>\upsilon$ from consistency further constrains $\theta$
being in the range $(0.08,0.2)$. As for the decays of Higgs boson to $bb$ and
$\tau\tau$, the uncertainty is still large at present status.

Direct search on $\pi_{p}$
The Yukawa couplings of charged technipion to SM fermions can be extracted
from (2.7) [4] ,

$\displaystyle{}i\left(\frac{f}{\upsilon}\right)[\bar{D}_{L}V^{{\dagger}}\pi^{-}_{p}h_{U}U_{R}+\bar{U}_{L}\pi^{+}_{p}Vh_{D}D_{R}+H.c~{}]$
(3.9)

where $V$ denotes the CKM matrix of SM. Eq.(3.9) implies that couplings of
$\pi_{p}$ to SM fermions are similar to those of charged Higgs boson in type
$\mathbf{I}$ Higgs doublet model, except a suppression by $f/\upsilon\simeq
f/f^{\prime}=\theta$. From (3.6) and (3.8) $m_{\pi_{p}}$ is determined to be
in the range $(210.3,334.3)$ (GeV) . Searches on this range of mass for
charged Higgs boson are mainly from the channel $H^{+}\rightarrow t\bar{b}$.
We find that the ratio of signal strength for $\pi_{p}\rightarrow t\bar{b}$
over SM background can be expressed in terms of that for $H^{+}$,

$\displaystyle{}\mu^{(\pi_{p})}(\pi_{p}^{+}\rightarrow
t\bar{b})=\theta^{2}\mu^{(H^{+})}(H^{+}\rightarrow t\bar{b})$ (3.10)

Charged Higgs boson mass below 78.6 GeV has been excluded by direct searches
at LEP [8] (for searches at the LHC, see, e.g., [10] ). This bound on
$m_{\pi_{p}}$ however can be significantly relaxed due to the $\theta^{2}$
suppression on event rate.

Direct search on $\omega_{t,b}$

As we will discuss in the next section, the fit to precision electroweak
measurements typically suggests that,

$\displaystyle{}\lambda_{\omega_{t}}$ $\displaystyle\simeq$ $\displaystyle
0.3-1.0,~{}~{}~{}~{}m_{\omega_{t}}\simeq 580-1500{\it~{}GeV},$
$\displaystyle\lambda_{\omega_{b}}$ $\displaystyle\simeq$ $\displaystyle
1.3-3.0,~{}~{}~{}~{}m_{\omega_{b}}\simeq 100-250{\it~{}GeV}$ (3.11)

Note that this spectra are constrained to be no excess at 1$\sigma$ level.
Allowing no excess at 3$\sigma$ level further decreases the values of
$\lambda_{\omega_{t,b}}$ $\lambda_{\omega_{b}}$ required, which helps evading
the direct experimental limits. The spectra of (3.1) can easily evade the
direct detection at the $e^{+}e^{-}$ collider. The dominant channel for
searching $\omega_{t,b}$ scalars is through
$e^{+}e^{-}\rightarrow\omega_{t/b}\omega^{*}_{t/b}\rightarrow
t\bar{t}/b\bar{b}$. The ratio of cross section of
$\sigma(e^{+}e^{-}\rightarrow\omega_{t/b}\omega^{*}_{t/b})$ over its SM
background $\sigma_{SM}(e^{+}e^{-}\rightarrow t\bar{t}/b\bar{b})$ is very
small for each of them. The reason is due to severe suppression by
$\beta=\sqrt{1-4m^{2}_{\omega}/s}$ even if light $\omega$ scalars near 100 GeV
can be produced. At a hadron collider such as LHC $\omega_{t/b}$ scalar is
mainly produced from gluon fusion (GF), and its decay is dominated by
$\omega_{t/b}\rightarrow t/b+p_{R}/m_{R}$. The SM background for this is
$gg\rightarrow m$-jets ( with either 2t-jets for $\omega_{t}$ or 2b-jets for
$\omega_{b}$ included) plus missing energy. Their mass bounds can be estimated
in terms of their analogies in supersymmetric models, i.e, stop and sbottom,

$\displaystyle{}\mu^{(GF)}_{\omega_{b}}$ $\displaystyle=$
$\displaystyle\frac{\sigma(gg\rightarrow\omega_{b}\omega^{*}_{b})Br(\omega_{b}\omega^{*}_{b}\rightarrow
b\bar{b}+E_{T})}{\sigma(gg\rightarrow\tilde{b}_{1}\tilde{b}^{*}_{1})Br(\tilde{b}_{1}\tilde{b}^{*}_{1}\rightarrow
b\bar{b}+E_{T})}\mu^{(GF)}_{\tilde{t}_{1}}(gg\rightarrow\tilde{t}_{1}\tilde{t}^{*}_{1}\rightarrow{\it
2b-jets+other~{}jets+E_{T}}),$ $\displaystyle\mu^{(GF)}_{\omega_{t}}$
$\displaystyle=$
$\displaystyle\frac{\sigma(gg\rightarrow\omega_{t}\omega^{*}_{t})Br(\tilde{t}_{1}\tilde{t}^{*}_{1}\rightarrow
t\bar{t}+E_{T})}{\sigma(gg\rightarrow\tilde{t}_{1}\tilde{t}^{*}_{1})Br(\tilde{t}_{1}\tilde{t}^{*}_{1}\rightarrow
t\bar{t}+E_{T})}\mu^{(GF)}_{\tilde{t}_{1}}(gg\rightarrow\tilde{t}_{1}\tilde{t}^{*}_{1}\rightarrow
2t-jets+{\it other~{}jets+E_{T}})$

where $\mu^{(GF)}$s refer to the ratio of signal strength over the SM
prediction via production of gluon fusion. The small ratio between couplings
$\lambda_{\omega_{t}}/h^{SM}_{t}\simeq 0.5$ indicates that mass bound on
$m_{\omega_{t}}$ can be relaxed in comparison with that on
$m_{\tilde{t}_{1}}$. The bound on $m_{\omega_{b}}$ is heavily dependent on the
mass of techni-fermion $m_{R}$ [9], a large part of mass range in (3.1) can
still survive in specific situation.

###  3.2 Indirect Searches

In what follows, we consider the indirect experimental limits on $\pi_{p}$ in
the case of $\theta\sim 0.08-0.2$.

Correction to Br$(Z\rightarrow b\bar{b})$
The radiative correction to Br$(Z\rightarrow b\bar{b})$ coming from technipion
is mostly through the exchange of technipion and top quark. There are three
kinds of Feynman diagrams, the calculation of which can be similarly
considered as for that of charged Higgs bosons in the minimal supersymmetric
standard model in [11]. In addition, there are higher-order corrections due to
$\omega_{t}$ scalar, which are smaller effects and will be neglected. We
summarize the experimental and theoretical results in Table one. One observes
that small $\theta$ factor severely suppresses the correction for technipion,
and forbids it from exposition through the measurement of $R_{b}$.

| Exp value | SM prediction | Exp-SM | TC-correction
---|---|---|---|---
$R_{b}$ |  $0.21629\pm 0.00066$ [12] | 0.21581 | $(4.8\pm 6.6)\times 10^{-4}$ | $-5.0\times 10^{-4}\cdot\theta^{2}$
Table 1: The correction to Br$(Z\rightarrow b\bar{b})$ and its experimental
limit.

Correction to $B_{s}^{0}-\bar{B}_{s}^{0}$
The measurement of $B_{s}^{0}-\bar{B}_{s}^{0}$ mixing is another experiment
which can be useful to expose the technipion. Because $\pi^{\pm}_{p}$ gives
rise to two additional one-loop diagrams to this process, which involve
one-$\pi^{\pm}_{p}$-W and two-$\pi^{\pm}_{p}$ exchange, respectively.
Following the results in [4, 13](for an earlier work, see [14]), the
correction is derived to be,

$\displaystyle{}\Delta~{}M^{(\pi_{p})}_{s}\simeq\Delta~{}M_{s}^{SM}\left(-0.18\cdot\theta^{2}-0.63\cdot\theta^{4}\right)$
(3.13)

when $\theta$ closes to $\theta_{max}$. The updated analysis of
$\Delta~{}M^{SM}$ in SM is discussed in [16], whereas its latest experimental
value is given in [12]. We collect these results in Table 2. Similar to the
correction to Br$(Z\rightarrow b\bar{b})$, as a result of $\theta$ suppression
technipion doesn’t produce obviously effects in this experiment.

| Exp value | SM prediction | (Exp-SM) | TC-correction
---|---|---|---|---
$\Delta~{}M_{s}$ |  $17.719\pm 0.036$(stat) | $17.3\pm 2.6$ | $0.42\pm 2.6$ | $-3.11\cdot\theta^{2}-10.90\cdot\theta^{4}$
Table 2: Correction to $B_{s}^{0}-\bar{B}_{s}^{0}$ mixing in our model and its
experimental limit. Here $\Delta~{}M_{s}$ is in unite of ps-1.

Correction to $b\rightarrow s\gamma$
The partial width for $b\rightarrow s\gamma$ in our model is similar to that
of type $\mathbf{I}$ two Higgs doublet model (see [15] for the calculation),
with the replacement of $H^{\pm}$ by $\pi_{p}^{\pm}$ in the one-loop Feynman
diagrams. However, our model differs from the type $\mathbf{I}$ two Higgs
doublet model in the way that the couplings of $\pi_{p}$ to SM fermions are
suppressed by $\theta$ factor. In Table 3 we show the experimental and
theoretic results. In Fig 1, we plot $\delta\Gamma/\Gamma_{SM}$ as function of
$\theta$. At present status, no excess beyond $3\sigma$ level is expected in
the range $\theta=0.08-0.15$, or equivalently in the range of mass $210-287$
GeV.

Exp value | SM prediction | (Exp-SM)$(\lesssim 2\sigma)$ | (TC-correction)
---|---|---|---
$3.55\pm 0.26$ [17] |  $3.15\pm 0.23$ [18] | $-0.3-1.1$ | Fig.1
Table 3: Correction to $\mathcal{B}(b\rightarrow~{}s\gamma)$ and its
experimental limit. $\mathcal{B}$ is in unite of $10^{-4}$.

Figure 1: Contour of $\delta~{}\Gamma/\Gamma_{SM}$ for
$b\rightarrow~{}s\gamma$. At present status, no excess beyond $3\sigma$ level
is expected in the range of $0.08-0.16$. Note that the choice of $\theta>0.08$
is required by $hf^{\prime}<4\pi f$ and $\upsilon<4\pi f$ as explained above.

One may wonder the implications of direct search on the charged Higgs boson to
technipion. For $\pi_{p}$ with mass of about 90 GeV which is the lower bound
found at colliders, it corresponds to $\theta=0.015$ in our model. It easily
evades indirect experiments such as $b\rightarrow~{}s\gamma$.

###  3.3 Precision Measurement

As well known a severe problem that plagues TC is the precision electroweak
measurement since the report of Peskin and Takeuchi [19]. Because the
condensation of techni-fermions gives rise to a positive and large tree-level
contribution to the oblique parameter

$\displaystyle{}S_{0}$ $\displaystyle\simeq$ $\displaystyle
0.1~{}\frac{N_{TF}}{2}N_{TC}\simeq 0.1~{}N_{TC}$ $\displaystyle T_{0}$
$\displaystyle\simeq$ $\displaystyle
0.01\left(\frac{\Lambda^{\prime}}{1{\it~{}TeV}}\right)^{4}$ (3.14)

for two flavors $N_{TF}=2$. $\Lambda^{\prime}$ is a mass scale close to
$\Lambda_{TC}$, which is hard to be estimated precisely. As noted from (3.3),
$S_{0}$ is too large. In what follows, we consider the case $N_{TC}=4$. The
introduction of colored $\omega$ scalars also produces significant
contributions to $S$. What is of interest is these new contributions always
cancel out the tree-level part of $S$, and help evading the precision
measurements when the masses of $\omega_{t,b}$ are of order $\sim\upsilon$.

Following the definition of $S$ and $T$ parameters, we derive the total
contribution in our model 555To calculate $S$ and $T$ we follow the notation
in [20]. In this reference, the four fermions interactions below
$\Lambda_{TC}$ induced by the $\omega$ scalars are carefully considered. The
effects on oblique parameters from these operators can be extracted in terms
of the effective field theory analysis.,

$\displaystyle{}S$ $\displaystyle=$ $\displaystyle
S_{0}+\frac{2}{3\pi}(2\delta g^{t}_{R}-\delta g^{b}_{R})$ $\displaystyle T$
$\displaystyle=$ $\displaystyle T_{0}+\delta
g^{t}_{R}\frac{3m^{2}_{t}}{\pi^{2}\alpha\upsilon^{2}}\ln\left(\frac{\Lambda_{TC}}{m_{t}}\right)$
(3.15)

where

$\displaystyle{}\delta
g^{t}_{R}=-\frac{\lambda^{2}_{\omega_{t}}\upsilon^{2}}{8m^{2}_{\omega_{t}}},~{}~{}~{}~{}~{}~{}\delta
g^{b}_{R}=\frac{\lambda^{2}_{\omega_{b}}\upsilon^{2}}{8m^{2}_{\omega_{b}}}$
(3.16)

The experimental limits on $S$ and $T$ of (3.3) have been updated from global
fit. Following the results in the second reference of [21],

$\displaystyle{}S=0.07\pm 0.10,~{}~{}~{}~{}~{}~{}~{}T=0.05\pm 0.12.$ (3.17)

in Table 4 we show four benchmark points involving parameters of
$\omega$-scalar mass and their Yukawa couplings.

As shown in Table 4 , it is sufficient for $m_{\omega_{t,b}}$ of order $\sim$
EW scale to cancel the tree-level contribution $S_{0}$. This requirement can
be naturally realized in our model. Note that the vev of $\Phi$ induced by the
condensation gives rise to masses of techni-scalar in terms of potential
$V(\phi,\omega)$ in (2), which read,

$\displaystyle{}m^{2}_{\omega_{t}}=\frac{1}{2}\lambda_{2}f^{\prime
2},~{}~{}~{}~{}m^{2}_{\omega_{b}}=\frac{1}{2}\lambda_{3}f^{\prime 2}.$ (3.18)

In this sense, bounds on $m_{\omega_{t,b}}$ due to precise electroweak
measurements can be used to constrain Yukawa couplings in (2).

$\lambda_{\omega_{t}}$ | $\lambda_{\omega_{b}}$ | $m_{\omega_{t}}$ | $m_{\omega_{b}}$ | $\Lambda^{\prime}$
---|---|---|---|---
0.3 | 1.3 | 583.4 | 100 | 800
0.5 | 3.0 | 972.4 | 229 | 800
0.3 | 1.3 | 476.3 | 100 | 1500
0.5 | 3.0 | 794 | 229 | 1500
Table 4: Benchmark points hinted by the precision measurements. Here mass is
in unite of GeV. $\Lambda^{\prime}=0.8~{}(1.5)$ TeV corresponds to central
value $\delta g^{t}_{R}=-0.002$ ($-0.003$), respectively, and $\delta
g^{b}_{R}$=1.3.

##  4 Conclusions

In this paper we consider TC-model with one scalar doublet and two extra
colored techni-scalars. After the condensation of techni-fermion at scale
$\Lambda=4\pi f\sim 480$ GeV which is above the EW scale, the scalar doublet
receives its vev $f^{\prime}$ through its coupling to techni-fermions, gives
rises to a SM-like scalar $\sigma$ discovered at the LHC when
$\theta=f/f^{\prime}\lesssim 0.2$. With $m_{\sigma}=125$ GeV, experimental
limits suggest that $m_{\pi_{p}}$ in the range $210-280$ GeV. Because of
$\theta$ suppression on Yukawa couplings of techni-pions to SM fermions, they
can evade the present experimental limits from both direct and indirect
searches.

On the other hand, the colored techni-scalars obtain their masses of order
$\mathcal{O}(0.1-1)$ TeV, through $\phi^{4}$ coupling with scalar doublet.
They can provide a large negative contribution to $S$, which eliminates the
large positive contribution arising from condensation, therefore reconcile our
model with precision electroweak measurements.

A detailed analysis on bounds of $\omega$ scalars masses is needed in the
further. It is also of interest to consider TC models with two fundamental
scalar doublets instead.

$\bf{Acknowledgement}$
The author thanks C. D. Carone for correspondence and D. Shih for discussions.
This work is supported in part by the Natural Science Foundation of China
under Grant No. 11247031.

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# Linguistic-style-aware Neural Networks for
Fake News Detection

Xinyi Zhou1*†, Jiayu Li2*, Qinzhou Li3†, Reza Zafarani2
1Paul G. Allen School of Computer Science and Engineering, University of
Washington, Seattle, WA 98195
2Department of Electrical Engineering and Computer Science, Syracuse
University, Syracuse, NY 13244
3Google, Durham, NC 27701 *The authors are equally contributed.†This work was
completed while the authors were at Syracuse University.

###### Abstract

We propose the hierarchical recursive neural network (HERO) to predict fake
news by learning its linguistic style, which is distinguishable from the
truth, as psychological theories reveal. We first generate the hierarchical
linguistic tree of news documents; by doing so, we translate each news
document’s linguistic style into its writer’s usage of words and how these
words are recursively structured as phrases, sentences, paragraphs, and,
ultimately, the document. By integrating the hierarchical linguistic tree with
the neural network, the proposed method learns and classifies the
representation of news documents by capturing their locally sequential and
globally recursive structures that are linguistically meaningful. It is the
first work offering the hierarchical linguistic tree and the neural network
preserving the tree information to our best knowledge. Experimental results
based on public real-world datasets demonstrate the proposed method’s
effectiveness, which can outperform state-of-the-art techniques in classifying
short and long news documents. We also examine the differential linguistic
style of fake news and the truth and observe some patterns of fake news.111The
code and data are available at https://github.com/Code4Graph/HERO.

###### Index Terms:

fake news, neural network, linguistic style

##  I Introduction

“Fake news,” as deceptive and misleading news articles (or statements at
times), has been broadly discussed along with its influence on democracies and
economies [1]. Public health has also been negatively impacted, especially
with the “infodemic” that we face along with the pandemic [2]. Effective fake
news detection has thus become an urgent task to mitigate such detrimental
impacts.

Psychological theories, such as Undeutsch hypothesis [3], have suggested that
the linguistic style of fake news is distinguishable from that of the truth.
Therefore, effective techniques can be designed to identify fake news by
analyzing the linguistic style of news articles [1]. Linguistic style can be
captured by looking at the writer’s usage of words (lexically and
semantically) and the way these words are further formed into sentences
(syntactic level) and the document (discourse level) [1]. Within a machine
learning framework, existing studies have captured a news article’s linguistic
style by computing the frequencies of each word [4, 5], part of speech (POS,
at the syntactic level) [6, 7, 5], and rhetorical relationship (RR, at the
discourse level) [8, 5]. These frequencies form a news article’s
representation, which is further classified by, e.g., support vector machines
(SVM) and random forests to predict the news as fake news or the truth.

These studies have advanced linguistic-style-aware fake news prediction.
However, translating a news article’s linguistic style into the appearances of
words, POSs, and RRs overlooks the linguistic structure that reveals how the
article’s words, POSs, and RRs are assembled. Specifically, we can form a
hierarchical linguistic tree for each news article; see Section III-A for the
details and Figure 3 for an illustrated tree for the news piece “Vitamin D
determines severity in COVID-19, so government advice needs to change, experts
urge: Researchers point to changes in government advice in Wales, England, and
Scotland.” This tree explicitly presents the order of words used in the
article, syntactic structure revealing how these words are recursively
structured as the elementary discourse units (EDUs, which are meaningful
phrases, sentences, or paragraphs) through POSs, and discourse structure
exhibiting how these EDUs are recursively structured as the entire article
through RRs. Previous approaches paid full attention to the tree’s node
information by looking if this news piece used a specific word (e.g.,
“COVID-19”), POS (e.g., “NNP”), or RR (e.g., “NS-elaboration”) in the corpus
or how many times it appears without considering the relational (edge)
information among the nodes. Although Zhou et al. [9] and Pérez-Rosas et al.
[4] computed the frequencies of production rules (at the syntactic level
only), each rule can merely show the structure within a fundamental component
of the tree (i.e., parent-children, such as VP $\rightarrow$ VBZ NP). Each
fundamental component is investigated independently by overlooking how
components are connected to form the tree; the tree’s structure is hence
preserved locally rather than globally. In addition, the representation of
news articles obtained by the frequencies of these local structures is often
high-dimensional and sparse, which can be adverse to the prediction task.

Figure 1: The hierarchical linguistic tree for the news piece “Why did the US
in 2017 give $3.7m to the Wuhan Lab in China? Such grants were prohibited in
2014. Did President Obama grant an exception?” verified as a false statement
by PolitiFact.333Source:
https://www.politifact.com/factchecks/2020/may/01/rudy-giuliani/rudy-giuliani-
wrong-about-us-policy-grant-amount-w/Blue nodes: RRs. Green nodes: POSs.

Present work. To address the above problems, we propose the hierarchical
recursive neural network (HERO) for fake news prediction. The architecture of
the proposed neural network adaptively preserves the global structure of the
hierarchical linguistic tree of various news articles. To our best knowledge,
this is the first work that develops hierarchical linguistic trees. Leveraging
the developed trees, the proposed neural network can learn the linguistic-
style-aware representations of news articles by explicitly capturing the
writers’ usage of words and the linguistically meaningful ways in which these
words are structured as phrases, sentences, paragraphs, and, ultimately, the
documents. We conduct extensive experiments on real-world datasets with well-
established and state-of-the-art approaches, which demonstrate the
effectiveness of the proposed neural network in predicting fake news.
Additionally, we examine the differential linguistic style of fake news and
the truth and identify statistically significant and consistent patterns of
fake news across datasets.

The rest of this paper is organized as follows. We review related work in
Section II. We introduce the proposed method in Section III and detail the
experiments designed and conducted to evaluate the proposed method in Section
IV. We conclude in Section V.

Figure 2: Framework overview, which contains a top-bottom building process of
hierarchical linguistic trees, a bottom-top feature extraction process using
the proposed hierarchical recursive neural network, and a classifier to
predict fake news. The neural network’s architecture adaptively preserves
various news documents’ global and hierarchical linguistic tree structures.
The Bi-GRU aggregator catches text’s local sequentiality that is
linguistically valuable and often short (explained in Section III-B), which is
more effective than self-attention here (see Section IV-B for details).

##  II Related Work

Fake news prediction methods can be categorized as content-based or
propagation-based depending on whether the method focuses on investigating
news content or its propagation on social media.

Propagation-based methods can utilize rich auxiliary social media information,
including news spreaders’ intent [2] or profiles [10], relationships between
news spreaders and their posts [11], social feedback [12, 13, 14], social
networks [15], and propagation paths [16, 17]. Nevertheless, they can only be
deployed after news articles published on news outlets have been disseminated
on social media. In comparison, content-based methods have the primary
advantage of predicting fake news early when news articles have been published
online but have not been spread [5]. Additionally, an effective content-based
method can be easily extended further by incorporating social context
information. With this consideration, we focus on analyzing news content to
predict fake news and review related work on content-based fake news
prediction approaches.

As news articles are mainly text, content-based methods start by manually
extracting linguistic features and predicting fake news using common
classifiers such as SVM [4]. Such linguistic features have been related to
lexicons (e.g., bag-of-words) [5], POSs [6, 5], context-free grammars
(production rules) [4, 5], RRs [8, 5], readability [6, 18], and $n$-grams that
preserve the sequences of words or POSs [7]. Though news features can be
easily interpreted within this machine learning framework, features cannot be
automatically extracted, which can significantly impact the prediction
performance; hence, the performance heavily relies on experts’ involvement and
experience. More importantly, as detailed in Section I, it is difficult to
capture the global structure of news text (language) at any of the syntactic
and discourse levels with these hand-crafted features. Compared to these
methods, the proposed neural network can learn the features of news articles,
which capture the global and hierarchical structures that news linguistic
styles carry.

Recently, neural networks (e.g., Bi-LSTM [7, 19] and Text-CNN [20]) have been
frequently employed to identify fake news. These models can learn the features
of news text (sometimes, combined with other modalities in news content, such
as images [20, 21]). These neural networks have focused on the sequentiality
or locality of news text but not on its linguistic structure. In comparison,
the proposed neural network explicitly catches this structure; it also
captures text’s sequentiality and locality, which will be detailed in Section
III-B. We point out that the proposed neural network provides a fundamental
approach to news text representation learning and thus can be easily extended
for multimodal fake news prediction.

##  III Methodology

We specify the proposed model in this section, which can be divided into three
steps. For each news document, we first construct its hierarchical linguistic
tree (see Section III-A), then extract its features via the proposed
hierarchical recursive neural network that preserves the hierarchical
linguistic tree information (see Section III-B), and finally predict it as
fake news or the truth (see Section III-C). Figure 2 presents the framework
overview.

###  III-A Hierarchical Linguistic Tree Construction

Given a news document $D$, we first generate its hierarchical linguistic tree.
The tree can explicitly present the order of words used in the document and
how these words shape EDUs (meaningful phrases, sentences, or paragraphs) and
further shape the entire document. An example is shown in Figure 3.
Specifically, our first attempt is to obtain $D$’s discourse (rhetorical)
structure, which identifies $D$’s EDUs and reveals how these EDUs recursively
form the document $D$. To this end, we first utilize Standford CoreNLP [22] to
segment $D$ into EDUs. Then, we apply a modified transition-based system [23]
to identify span (S) and nuclearity (N), based on which $D$’s rhetorical
structure can be obtained without recognizing specific RRs (e.g., elaboration
in Figure 3). This semi-naked tree structure allows us to divide each RR node
into within-sentence, across-sentence, and across-paragraph levels in terms of
its left and right subtrees, extract structural features for each RR node, and
ultimately adopt level-specific SVM classifiers [23] to predict the node
attribute (i.e., the specific RR). This multi-stage approach outperforms the
well-established one [24] in our experiments, where [24] works as an
integrated system. Finally, we employ a state-of-the-art discriminative
constituency parser for each identified EDU of the document $D$ to obtain its
syntactic structure [25]. The parser consists of a self-attentive encoder [25]
and a chart decoder [26] (see Figure 2 for the detailed architecture). The
syntactic structure reveals how the EDU’s words recursively form the entire
EDU.

###  III-B Feature Extraction via Hierarchical Recursive Neural Network

We propose the hierarchical recursive neural network to extract features of
news documents, whose architecture adaptively maintains the global structure
of the hierarchical linguistic trees of news documents.

Given a news document $D$, its feature extraction using the hierarchical
recursive neural network is bottom-top. We first encode $D$’s words, which are
the leaf nodes of $D$’s hierarchical linguistic tree. Then, we aggregate the
obtained embeddings of the words that attach to the same parent node, forming
the embedding of their parent node. The hierarchical recursive neural network
will repeat such aggregations from the lower (syntactic) level to the upper
(discourse) level until the document $D$ as the tree’s root node is embedded.

Hence, the question arises of how the aggregator performs on a recurring
fundamental component (i.e., a depth-one parent-children structure). Note that
for each parent node in a hierarchical linguistic tree, its children contain
local and sequential information of the corresponding news document. The
information is local because it reveals partial information about the overall
news content that is linguistically valuable. It is sequential as we keep the
order of words of the news document. Naturally, recurrent neural networks can
be adopted as the aggregator to catch the sequentiality of children sharing
the same parent. The information locality further relieves the pressure on
recurrent neural networks to keep the dependency of long entities since the
number of children for a parent node is no more than the EDU length and
essentially less than the document length. As seen from Figure 3, the maximum
length that recurrent neural networks require to process is four, whereas the
document has 29 tokens.

With the above considerations, we develop Bi-GRU (bidirectional gated
recurrent unit), one of the well-established recurrent neural networks [27],
to aggregate the embeddings of all the child nodes to represent their parent
node. We also empirically compare Bi-GRU with multi-head self-attention that
has remarkably performed in many tasks; Bi-GRU is more effective for the
proposed model. Formally, the embedding of a parent node is computed as

$\textbf{x}_{p}=\frac{\sum_{c\in\mathcal{C}_{p}}[\overrightarrow{GRU}\\{\textbf{x}_{c}\\}\oplus\overleftarrow{GRU}\\{\textbf{x}_{c}\\}]}{|\mathcal{C}_{p}|},$
(1)

where $p$ denotes the parent node and $\mathcal{C}_{p}$ is the set of child
nodes of $p$. Vectors $\mathbf{x}_{c}\in\mathbb{R}^{d}$ and
$\mathbf{x}_{p}\in\mathbb{R}^{d}$ refer to the features of the child and
parent node, respectively. The operator $\oplus$ denotes concatenation. The
GRU is formulated as follows:

$\begin{array}[]{l}\mathbf{r}_{i}=\sigma(\mathbf{W}_{r}\mathbf{x}_{i}+\mathbf{U}_{r}\mathbf{h}_{i-1}),\\\
\mathbf{z}_{i}=\sigma(\mathbf{W}_{z}\mathbf{x}_{i}+\mathbf{U}_{z}\mathbf{h}_{i-1}),\\\
\hat{\mathbf{h}}_{i}=\tanh(\mathbf{W}_{h}\mathbf{x}_{i}+\mathbf{U}_{h}(\mathbf{h}_{i-1}\odot\mathbf{r}_{i})),\\\
\mathbf{h}_{i}=(1-\mathbf{z}_{i})\odot\mathbf{h}_{i-1}+\mathbf{z}_{i}\odot\hat{\mathbf{h}}_{i},\end{array}$
(2)

where $\mathbf{h}_{i}\in\mathbb{R}^{d/2}$ is the output hidden state of the
$i$-th child, with $\mathbf{h}_{0}=\mathbf{0}$. The symbol $\odot$ denotes
Hadamard product. Matrices $\mathbf{W}_{*}\in\mathbb{R}^{(d/2)\times d}$ and
$\mathbf{U}_{*}\in\mathbb{R}^{(d/2)\times(d/2)}$ ($*\in\\{r,z,h\\}$) are
learnable parameters. $\mathbf{r}_{i}$ and $\mathbf{z}_{i}$ are the reset gate
and update gate, respectively. $\sigma$ and $\tanh$ are the sigmoid and
hyperbolic tangent activation functions, respectively. In a nutshell, the
above architecture first employs the Bi-GRU to capture “deep” sequential
feature interactions of all the child features and then uses a mean pooling
layer over all the hidden states to obtain the parent node’s features.

After determining the aggregation within each recurring fundamental component,
we introduce three specific hierarchical recursive neural networks (HEROs):

  * •

Unified HERO: The first hierarchical recursive neural network is the one with
unified aggregators. In other words, all the Bi-GRUs in the neural network
share the same set of $\mathbf{W}_{*}$ and $\mathbf{U}_{*}$
($*\in\\{r,z,h\\}$, see Equation (2)).

  * •

Level-specific HERO: It is the hierarchical recursive neural network with
level-specific aggregators. As detailed, the hierarchical linguistic tree
presents both syntactic and rhetorical structures of news content, and the
hierarchical recursive neural network preserves such structures. Hence, all
the Bi-GRUs in a hierarchical recursive neural network can be grouped by the
level (syntax or discourse) they belong to the corresponding tree. We define
$L(v)$ as the function that maps a certain vertex in the hierarchical
linguistic tree to its linguistic level (i.e.,
$L(v)\in\\{\text{syntax},\text{discourse}\\}$). Then, Equation (1) can be
reformulated as
$\textbf{x}_{p}=\frac{1}{|\mathcal{C}_{p}|}\sum_{c\in\mathcal{C}_{p}}[\overrightarrow{GRU}_{L(c)}$
$\\{\textbf{x}_{c}\\}\oplus\overleftarrow{GRU}_{L(c)}\\{\textbf{x}_{c}\\}]$.

  * •

Attribute-specific HERO: It stands for the hierarchical recursive neural
network with attribute-specific aggregators. In other words, we categorize the
hierarchical recursive neural network’s recurring fundamental components
according to the attributes of their parent nodes in the corresponding
hierarchical linguistic tree, which can be various POSs and RRs. We deploy the
same Bi-GRU for the components within each category and the different Bi-GRU
for the components falling into different categories. Mathematically, we
define $A(v)$ as the function that maps a certain vertex in the hierarchical
linguistic tree to its attributes. Assume there are $m$ different POSs and $n$
RRs, we have $A(v)\in\\{POS_{i},RR_{j}:i=1,2,\cdots,m,j=1,2,\cdots,n\\}$. The
root vertex would be assigned with a RR in discourse parsing. For EDU
vertices, they would not be assigned with any RRs in discourse parsing but
with some POSs in constituency parsing. In this way, Equation (1) is rewritten
as
$\textbf{x}_{p}=\frac{1}{|\mathcal{C}_{p}|}\sum_{c\in\mathcal{C}_{p}}[\overrightarrow{GRU}_{A(p)}\\{\textbf{x}_{c}\\}\oplus\overleftarrow{GRU}_{A(p)}\\{\textbf{x}_{c}\\}]$.

###  III-C Fake News Prediction

We add a softmax classifier on the top of the proposed hierarchical recursive
neural network to predict the document $D$ as fake news or the truth. Let
$\mathbf{h}_{D}$ denote $D$’s features extracted via the proposed hierarchical
recursive neural network. The softmax function maps $\mathbf{h}_{D}$ to the
probability of $D$ being a fake news document by
$p_{D}=\text{Softmax}(\mathbf{W}\mathbf{h}_{D}+\mathbf{b}),$ where
$\mathbf{W}$ and $\mathbf{b}$ are learnable parameters.

To learn the parameters
$\Theta=\\{\mathbf{W}_{*},\mathbf{U}_{*},\mathbf{W},\mathbf{b}\\}$ within the
neural network and classifier, we employ cross-entropy to calculate the
classification loss in the model training process. Assume we have $q$ verified
news documents $\mathcal{D}=\\{D_{i}\\}_{i=1}^{q}$ with the ground-truth
labels $\mathcal{Y}=\\{y_{i}:y_{i}\in\\{0,1\\}\\}_{i=1}^{q}$ ($y_{i}=0$ for
true news, and $y_{i}=1$ for fake news), the loss is computed by
$L=-\frac{1}{q}\sum_{i=1}^{q}[y_{D_{i}}\log
p_{D_{i}}+(1-y_{D_{i}})\log(1-p_{D_{i}})]$. Based on it, the parameter set
$\Theta$ is estimated by $\hat{\Theta}=\arg\min_{\Theta}L.$

##  IV Empirical Evaluation

We aim to evaluate the proposed method by answering the following three
questions.

  1. 1.

How effective is the proposed model in fake news prediction compared to the-
state-of-art approaches?

  2. 2.

Is the hierarchical linguistic structure of news documents essential in
representing their linguistic styles?

  3. 3.

What characterizes the linguistic style of fake news as distinguishable from
the truth?

To that end, we first detail our experimental setup in Section IV-A and then
compare the proposed unified, level-specific, and attribute-specific HEROs in
predicting fake news (see Section IV-B). Subsequently, we compare the proposed
model with the baselines to verify its effectiveness in predicting fake news
(to answer RQ1, see Section IV-C) and conduct the ablation study to assess the
importance of our developed hierarchical linguistic trees (to answer RQ2, see
Section IV-D). Finally, we characterize the linguistic style of fake news as
distinguishable from the truth by doing quantitative and comparative analyses
(to answer RQ3, see Section IV-E).

###  IV-A Experimental Setup

We first introduce the datasets used for evaluation (see Section IV-A1),
followed by the baselines for comparison (see Section IV-A2). Finally, we
detail our implementation details in Section IV-A3.

####  IV-A1 Datasets

We conduct experiments on two benchmark datasets in fake news prediction:
Recovery [9] and MM-COVID [28]. Both datasets contain labeled news documents.
Differently, news documents collected in Recovery are articles (long text,
often including multiple paragraphs) but in MM-COVID are statements (short
text, often formed by one or two sentences). We present the detailed
statistics of two datasets in Table I.

TABLE I: Data statistics. | Recovery | MM-COVID
---|---|---
# news documents | 2,029 | 3,536
\- true news | 1,364 | 1,444
\- fake news | 665 | 2,092
Avg. # words per EDU | 24 | 17
Avg. # EDUs per document | 38 | 2
Avg. # words per document | 841 | 16

####  IV-A2 Baselines

We involve the following well-received and state-of-the-art methods as
baselines in our experiments.

  * •

HCLF [5]: HCLF stands for hand-crafted linguistic feature. Each news
document’s HCLFs include the frequencies of words (i.e., bag-of-word
features), POSs, RRs, and production rules. The extracted features are used to
predict fake news by employing well-established classifiers. Here we examine a
comprehensive list of classifiers–logistic regression, SVM, $k$-nearest
neighbors, decision trees, naive Bayes, random forest, and AdaBoost–and select
the one performing best.

  * •

EANN [20]: The event adversarial neural network contains three components:
feature extraction by Text-CNN (for text) and VGG-19 (for images), event
discrimination to learn event-invariant features of news content, and fake
news prediction. We exclude the visual features for a fair comparison.

  * •

HAN [29]: HAN exploits attention-GRU for news classification. It captures the
hierarchical sequence of documents; i.e., each document is a sequence of its
sentences, and each of its sentences is a sequence of words.

  * •

DRNN [30]: DRNN is a discourse-structure-aware neural network, which focuses
on the tree with rhetorical relationships as edge attributes and leverages an
attention mechanism for news classification. In other words, DRNN differs from
HERO in the aggregation rule. Compared to DRNN’s tree, the hierarchical
linguistic tree integrates syntax-level structures and has RRs as nodes and
non-attributed edges at the discourse level. DRNN is developed to categorize
news documents with more than one elementary discourse unit; otherwise, it is
reduced to Bi-LSTM.

  * •

Text-GCN [31]: The approach develops the graph convolutional neural network
for news classification. The graph investigates the co-occurrence relationship
among news documents and the words within the documents.

  * •

Transformer [32]: It is a deep neural network model with a self-attention-
based encoder-decoder architecture, which has excellently performed in diverse
natural language processing tasks. Here, we consider Transformer’s
encoder–applicable for classification tasks–as a baseline to predict fake
news, a non-pretrained version rather than pretrained models (e.g., BERT) for
a fair comparison as the pretrained Transformers have learned large-scale
external resources.

####  IV-A3 Implementation Details

We randomly divide each dataset into 0.7:0.1:0.2 proportions for model
training, validation, and testing. Macro-F1, micro-F1, and AUC are used to
evaluate the performance of methods in news classification. The discourse
parser is pretrained using RST-DT [23], and the constituency parser is
pretrained using the Penn Treebank [25]. For the neural-network-based models,
we uniformly utilize the pretrained GloVe [33] to obtain semantic-aware
embeddings of words, with 100 as the embedding dimension. The hidden dimension
within neural networks is set as 100, correspondingly. We deploy Adam
optimizer to learn parameters, with 50 as the maximum number of epochs. We
perform a grid search over the learning rate $\in\\{0.1,0.01,0.001,0.0001\\}$
with validation data. In the end, 0.0001 performs best for our models and most
of the baselines other than Transformer (0.001) and Text-GCN (0.01). All the
experiments of the neural networks are implemented with PyTorch and are
conducted on an NVIDIA Quadro RTX 6000 GPU ($24$ GB memory), Intel(R) Xeon(R)
Gold 6248R CPU ($3.00$ GHz), and with $64$ GB of RAM. For HCLFs, classifiers
are used with the default hyperparameters presented in the scikit-learn
library. $Z$-score normalization is applied for the feature matrix to enhance
the classification performance.

###  IV-B Determining the Best HERO

We compare the performance of the proposed neural networks with unified,
level-specific, and attribute-specific Bi-GRUs in predicting fake news. Table
II presents the results. The results indicate that with Recovery data, the
performance ranking is attribute-specific HERO $>$ level-specific HERO $>$
unified HERO. Specifically, attribute-specific HERO correctly predicts news as
fake or true with 0.85 macro-F1 and 0.87 micro-F1 and AUC, outperforming
unified HERO by $\sim$4% and level-specific HERO by $\sim$3%. With MM-COVID
data, the performance ranking is attribute-specific HERO $\approx$ unified
HERO $>$ level-specific HERO. Attribute-specific and unified HEROs achieve
$\sim$0.89–0.90% in macro-F1, micro-F1, and AUC, outperforming level-specific
HERO by $\sim$1%. In conclusion, attribute-specific HERO performs best in
classifying long articles and short statements as fake news or the truth. This
result demonstrates the importance of the node attributes (POSs or RRs) in
developed hierarchical linguistic trees.

Additionally, we compare Bi-GRU and self-attention (#heads=10) as aggregators
in the proposed hierarchical recursive neural network for fake news
prediction. The results indicate that Bi-GRU performs better than self-
attention by at least 1% in AUC on both datasets.

TABLE II: Performance of unified, level-specific, and attribute-specific HEROs
in fake news prediction. Attribute-specific HERO performs best, demonstrating
that the node attributes (POSs or RRs) in hierarchical linguistic trees are
essential. MAF1: Macro-F1. MIF1: Micro-F1

Recovery MM-COVID HERO MAF1 MIF1 AUC MAF1 MIF1 AUC Unified 0.801 0.822 0.827
0.889 0.891 0.899 Level-specific 0.817 0.838 0.841 0.878 0.878 0.892
Attribute-specfic 0.850 0.869 0.866 0.894 0.896 0.896

TABLE III: Performance of the proposed model, HERO, and baselines in fake news prediction. HERO outperforms the baselines by 2–17% in AUC on Recovery and by 3–30% in MM-COVID. MAF1: Macro-F1. MIF1: Micro-F1 | Recovery | MM-COVID
---|---|---
MAF1 | MIF1 | AUC | MAF1 | MIF1 | AUC
HCLF | 0.752 | 0.801 | 0.746 | 0.566 | 0.624 | 0.577
Transformer | 0.774 | 0.793 | 0.810 | 0.804 | 0.809 | 0.806
Text-GCN | 0.841 | 0.869 | 0.835 | 0.826 | 0.836 | 0.817
EANN | 0.811 | 0.864 | 0.795 | 0.825 | 0.926 | 0.833
HAN | 0.847 | 0.869 | 0.844 | 0.840 | 0.856 | 0.846
DRNN | 0.711 | 0.778 | 0.698 | 0.845 | 0.846 | 0.848
HERO | 0.850 | 0.869 | 0.866 | 0.894 | 0.896 | 0.896

###  IV-C Comparing HERO with Baselines

We compare the proposed model with the baselines in predicting fake news. The
results presented in Table III reveal that the proposed model can generally
outperform the baselines. Specifically, the proposed model has an AUC score
approaching 0.87, outperforming HAN by more than 2%, Text-GCN by more than 3%,
Transformer by more than 5%, EANN by more than 7%, HCLF by 12%, and DRNN by
17%. With MM-COVID data, the proposed model has an AUC score approaching 0.90,
outperforming EANN by more than 6%, DRNN and HAN by $\sim$5%, Text-GCN and
Transformer by $\sim$8-9%, and HCLF by more than 30%. From the table, we also
observe that the proposed model outperforms EANN by 6–7% in macro-F1 and AUC
but underperforms it by $\sim$3% in micro-F1 on MM-COVID. This result suggests
that EANN tends to predict given news statements as the major class.

(a) Recovery (b) MM-COVID

Figure 3: Ablation study. (a) The proposed HERO outperforms HERO$\setminus$Dis
by 1% in AUC for unified HERO and by 3% for level- and attribute-specific
HEROs. It outperforms HERO$\setminus$Syn by 7–9% and HERO$\setminus$Syn by
30%+ in AUC. (b) HERO performs similarly to HERO$\setminus$Dis as MM-COVID
contains short statements having minimal discourse structures (i.e., syntax-
level structures dominate). It outperforms HERO$\setminus$Syn and
HERO$\setminus$(Syn+Dis) by 10%+ in AUC. Thus, syntax- and discourse-level
structures are both essential.

(a) Children of parent nodes.

(b) Note attributes.

(c) Size, width, and depth of trees.

Figure 4: Hierarchical linguistic trees of fake and true news. Orange solid
line: Median. Green dashed line: Mean.

###  IV-D Ablation Study

We compare the proposed model, HERO, which contains hierarchical linguistic
(syntax- and discourse-level) structures with its following variants.

  * •

HERO$\setminus$Dis: It stands for the variant of HERO with only syntax-level
structures. In this variant, the embedding of a news document is obtained by
averaging its embeddings of EDUs.

  * •

HERO$\setminus$Syn: It stands for the variant of HERO with only discourse-
level structures. In this variant, the embedding of each EDU of a news
document is obtained by averaging its words.

  * •

HERO$\setminus$(Syn+Dis): It stands for the variant of HERO with no
structures, the embedding of a news document is directly obtained by averaging
its word embeddings.

The results are visualized in Figure 3. We observe that with Recovery data,
the proposed HERO outperforms HERO$\setminus$Dis by 1% in AUC for unified HERO
and by 3% for level- and attribute-specific HEROs. It outperforms
HERO$\setminus$Syn by 7–9% and notably outperforms HERO$\setminus$Syn by above
30% in AUC. With MM-COVID data, the proposed HERO performs similarly to
HERO$\setminus$Dis since the statements presented in MM-COVID are short with
two EDUs on average and hence have minimal discourse structures (i.e., syntax-
level structures dominate hierarchical linguistic structures). Meanwhile, it
outperforms HERO$\setminus$Syn and HERO$\setminus$(Syn+Dis) by more than 10%
in AUC. Therefore, we conclude that the proposed HERO is better than its
variants, demonstrating the importance of hierarchical linguistic structures.

###  IV-E Characterizing Linguistic Style of Fake News

Fake news has been theoretically identified with a linguistic style
distinguishable from the truth [3]. This experiment aims to specify this
different linguistic style of fake news. We compare the hierarchical
linguistic trees generated by fake news and the truth, which we develop to
represent the linguistic style of news documents systematically. The
comparison is from the (i) children of parent nodes, (ii) attributes of nodes,
and (iii) size, width, and depth of trees.

##### Children of Parent Nodes

We compare fake news with real news in the average and the maximum number of
children of parent nodes in hierarchical linguistic trees. Results that are
statistically significant with a $p$-value $<0.001$ (using t-test, unless
otherwise specified) are in Figure 4a. We observe that the hierarchical
linguistic trees of fake news have more child nodes for each parent node than
true news on average. News here indicates long news articles in the Recovery
dataset and short statements in the MM-COVID dataset.

##### Attributes of Nodes

Considering the nodes within a hierarchical linguistic tree can indicate the
document (as the root), RRs, EDUs, POSs, and words (as the leaf nodes), we
first compare fake news with the truth in the proportion of RRs, EDUs, POSs,
and words, respectively. The reason for computing their proportions rather
than the numbers is to eliminate the impact of the size of trees (discussed in
the next paragraph). We observe that compared to true news, the hierarchical
linguistic trees of fake news have a significantly smaller proportion of EDU
nodes ($p$-value $<0.05$) and POS nodes indicating NNS (noun in the plural,
$p$-value $<0.001$) but have a significantly larger proportion of nodes
indicating specific POSs such as IN (preposition or subordinating
conjunction), PP (prepositional phrase), and DT (determiner, $p$-value
$<0.001$). We illustrate the results in Figure 4b.

##### Size, Width, Depth of Trees

We compare fake news with the truth in the size, maximum width, and depth of
hierarchical linguistic trees. Since hierarchical linguistic trees contain
two-level structures, we also compare fake and true news in the size, maximum
width, and depth of discourse- and syntactic-level trees.

We observe that the syntactic-level tree of fake news is generally greater
with more nodes, broader, and deeper than true news. In particular, the
syntactic-level tree of fake news has more leaf nodes than true news, which
reveals that fake news often has longer EDUs with more words than true news.
The above conclusions hold for long news articles (using Recovery data) and
short statements (with MM-COVID data) with a $p$-value $<0.01$; news files in
both datasets are rich in syntactic information. Figure 4c (the upper ones)
presents the details. Moreover, we observe that fake news articles generate
smaller and narrower discourse-level trees that lead to smaller and narrower
hierarchical linguistic trees than true news articles ($p$-value $<0.01$, see
the bottom figures in Figure 4c). We point out that the discourse structures
of short statements are plain with two EDUs on average and hence have trivial
impacts on the shape of the entire hierarchical linguistic structures. Lastly,
we point out that comparing trees’ maximum and average widths leads to the
same conclusions. Comparing the longest (i.e., depth) and the average distance
between the root and leaves also leads to the same conclusions.

##  V Conclusion

We propose a psychology-informed neural network to predict fake news. The
proposed neural network learns the linguistic style of news documents
represented by hierarchical linguistic trees, which explicitly captures the
writers’ usage of words and the linguistically meaningful ways these words are
structured as phrases, sentences, paragraphs, and, ultimately, documents. We
conduct experiments on public real-world datasets. The results demonstrate the
effectiveness of the proposed neural network, with 0.87–0.90 AUC scores, and
the importance of the developed hierarchical linguistic tree. The proposed
neural network can outperform the previous (recurrent, convolutional, graph,
and self-attentive) neural networks and feature-engineering-based approach in
predicting news–as long articles or short statements–as fake news or the
truth. We observe from the data that the hierarchical linguistic trees of fake
news can significantly differ from true news in the children of parent nodes,
the attributes of nodes, and the size, width, and depth of the trees. In our
future work, we aim to enhance the proposed model’s performance with
multimodal and social-context information.

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