Proton Decay and Gauge Coupling Unification in an Extended SU(5) GUT with
45-Dimensional Higgs

Naoyuki Habaa,b, Keisuke Naganoa,c, Yasuhiro Shimizua,b
and Toshifumi Yamadad

aDepartment of Physics, Osaka Metropolitan University, Osaka 558-8585, Japan
bNambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),
Osaka Metropolitan University, Osaka 558-8585, Japan
cInstitute of Science and Engineering, Shimane University, Matsue 690-8504,
Japan
dInstitute for Mathematical Informatics, Meiji Gakuin University, Yokohama
244-8539, Japan

Abstract

We present a comprehensive study of an extended SU(5) grand unified theory
(GUT) that incorporates a 45-dimensional Higgs representation to address the
shortcomings of the minimal SU(5) GUT, such as the inability to generate
realistic fermion mass hierarchies and insufficient proton stability. By
considering a hierarchical mass spectrum for the scalar components of the
45-Higgs, we demonstrate that successful gauge coupling unification (GCU) can
be achieved. The color octet scalar, color triplet scalar, and color anti-
triplet scalar play crucial roles in realizing GCU when their masses are
significantly lighter than other components of the 45-Higgs. We focuses on the
proton decay channels mediated by the exchange of the color anti-triplet
scalar. Assuming that the 45-Higgs couples to all three generations of
fermions, we determine the 45-Higgs Yukawa couplings with which the observed
fermion mass matrices at low energies are realized. We calculate proton decay
rates using the Yukawa couplings obtained from renormalization group
evolutions and matching conditions at the GUT scale, thereby exploring the
dependence of proton decay rates on model parameters. We find that the
$p\to\nu\pi$ mode imposes the most stringent constraint on the mass of the
color anti-triplet scalar $M_{S_{1}}$. We also study the correlations between
the lower bounds on $M_{S_{1}}$ derived from different proton decay modes.

##  1 Introduction

The Standard Model (SM) of particle physics has been remarkably successful in
describing phenomena at currently accessible energy scales. However, it leaves
several fundamental unanswered questions, such as the origin of fermion masses
and mixings, the quantization of hypercharge, and the unification of the three
gauge interactions. Grand Unified Theories (GUTs) provide an appealing
framework to address these issues by embedding the SM gauge group into a
larger simple group [1]-[6].

One of the most studied GUT models is based on the SU(5) gauge group, which
allows the unified description of the strong and electroweak interactions [3].
Despite its elegance, the minimal SU(5) model faces several difficulties. It
predicts the same Yukawa couplings for down-type quarks and charged leptons at
the GUT scale, which contradict the observed mass relations. Furthermore, the
three gauge couplings do not precisely unify at a single high-energy scale in
non-supersymmetric models.

To overcome these limitations, extensions to the minimal SU(5) GUT have been
proposed. One of the promising approaches is inclusion of a special type of
Higgs field. If the Higgs field transforming as the 45-dimensional
representation is introduced, the 45-dimensional Higgs can generate separate
Yukawa matrices for quarks and leptons, potentially accommodating the observed
fermion mass hierarchies and mixing patterns [7]-[12]. Furthermore, the GCU
can achieved if we consider hierarchical mass spectrum for the components of
the 45 Higgs. In Ref. [13], we studied the GCU and proton decay via
45-dimensinal Higgs boson focused on the 45 Higgs coupling to the second
generation, to explain specific mass ratios like that of the strange quark and
muon through Georgi-Jarlskog-type mass matrices [12].

In this paper, we extend the analysis by considering an SU(5) GUT model where
the 45-representation Higgs field couples to all three generations of
fermions. The Yukawa couplings of the 45 Higgs are determined such that the
full structure of the observed fermion mass matrices, including hierarchies
and mixing angles, can be reproduced at low energies. To achieve successful
GCU and satisfy current experimental constraints on proton decay, we introduce
a hierarchical mass spectrum for the components of the ${45}_{H}$ Higgs
multiplet. By solving the renormalization group equations (RGEs) with various
mass hierarchies among the ${45}_{H}$ components, we identify viable parameter
regions that lead to precise unification of the gauge couplings while evading
stringent experimental bounds on proton decay. We focus on the case where the
three components of the 45-Higgs, which are the ($\overline{3}$,1), (3,3), and
(8,2) representations of the SM gauge group, are much lighter than the GUT
scale. We study proton decay mediated by the color anti-triplet Higgs
components and derived lower mass bounds on these components from the latest
experimental constraints, such as those set by the Super-Kamiokande
experiment. By analyzing the interplay among the Yukawa couplings, the mass
hierarchies of the ${45}_{H}$ Higgs components, and the RGE evolution of the
gauge couplings, we find that the $p\to\nu\pi$ mode imposes the most stringent
constraint on the color anti-triplet Higgs mass. We also study the
correlations among the lower bounds on the color anti-triplet Higgs mass
derived from different proton decay modes.

This paper is organized as follows. In Sect. 2, we review the SU(5) GUT with a
45 Higgs field. In Sect. 3, we discuss the GCU conditions assuming the
components of the 45 Higgs field have a hierarchical mass spectrum. In Sect.
4, we study the contribution of the colored Higgs component of the 45 Higgs
field to proton decay and identify the parameter region allowed by all the
experiments. Section 5 concludes the paper.

##  2 SU(5) GUT with 45 dimensional Higgs

In this section, we consider a non-SUSY SU(5) GUT with a $\bm{45}$ Higgs
boson. The fermions in the SM are embedded into the $\bm{\bar{5}}$ and
$\bm{10}$ representations of SU(5) as follows:

$\displaystyle\bm{\bar{5}}:\overline{\psi}^{a}_{i}=\begin{pmatrix}d_{Ri}^{Ca}&\epsilon_{\alpha\beta}\,(V_{DL})_{i}{}^{j}\,\ell_{Lj}^{\,\beta}\end{pmatrix},~{}~{}~{}~{}\bm{10}:\chi_{i\,ab}=\frac{1}{\sqrt{2}}\begin{pmatrix}\epsilon^{abc}\,(V_{QU})_{i}{}^{j}\,u^{C}_{Rj\,c}&q_{Li}^{\,\hat{a}\beta}\\\\[2.84526pt]
-q_{Li}^{\,b\alpha}&\epsilon^{\alpha\beta}\,(V_{QE})_{i}{}^{j}\,e_{Rj}^{\,c}\end{pmatrix}.$
(1)

Here, $a,b,c$ are SU(3) indices, $\alpha,\beta$ are SU(2) indices, and $i,j$
are generation indices. The unitary matrices $V_{DL}$, $V_{QU}$, and $V_{QE}$
are determined by imposing matching conditions between the GUT and SM fermion
sectors at the unification scale.

While the minimal SU(5) GUT incorporates Higgs transforming as the $\bm{24}$
and $\bm{5}$ representations, we extend this by introducing an additional
Higgs multiplet transforming as the $\bm{45}$ representation of SU(5), denoted
as ${45}_{H}$. The inclusion of ${45}_{H}$ allows for the generation of
realistic fermion mass patterns and mixings, which cannot be fully accounted
for by the minimal Higgs representations. The SU(5) invariant Yukawa
interactions can be written as:

$\displaystyle-\mathcal{L}_{Y}$
$\displaystyle=\frac{1}{8}\,(Y_{5}^{U})_{ij}\epsilon^{abcde}\,\chi_{i\,ab}\,\chi_{j\,cd}\,(5_{H})_{e}+(Y_{5}^{D})_{ij}\chi_{i\,ab}\,\overline{\psi}^{a}_{i}\,(5_{H}^{\dagger})^{b}$
$\displaystyle+\frac{1}{4}(Y_{45}^{U})_{ij}\epsilon^{abcde}\,\chi_{i\,ab}\,\chi_{i\,cf}\,({45}_{H})_{de}^{f}+\frac{1}{2}\,(Y_{45}^{D})_{ij}\chi_{i\,ab}\,\overline{\psi}^{c}_{j}({45}_{H}^{\dagger})_{ab}^{c}+\mathrm{h.c.}.$
(2)

Notice that ${45}_{H}$ are assumed to couple with all three generations of
fermions. By choosing these Yukawa coupling matrices, we can reproduce the
observed patterns of fermion masses and mixings. The 45 Higgs field, in
particular, plays a crucial role in generating realistic mass relations and
mixing angles that cannot be accounted for by the minimal Higgs
representations alone.

The ${5}_{H}$ and ${45}_{H}$ Higgs fields can be decomposed into their
components according to the SM representations as follows:

$\displaystyle{5}_{H}$ $\displaystyle=H^{(5)}(1,2)_{\frac{1}{2}}\oplus
S_{1}^{(5)*}(3,1)_{-\frac{1}{3}},$ (3) $\displaystyle{45}_{H}$
$\displaystyle=H^{(45)}(1,2)_{\frac{1}{2}}\oplus
S_{1}^{(45)*}(3,1)_{-\frac{1}{3}}\oplus S_{3}^{*}(3,3)_{-\frac{1}{3}}$
$\displaystyle\oplus\tilde{S}_{1}(\overline{3},1)_{\frac{4}{3}}\oplus
R_{2}^{*}(\overline{3},2)_{-\frac{7}{6}}\oplus
S_{6}^{*}(\overline{6},1)_{-\frac{1}{3}}\oplus S_{8}(8,2)_{\frac{1}{2}}.$ (4)

In order to achieve the GCU, we consider the mass hierarchy among the
components in the ${45}_{H}$ Higgs and assume that some components are much
lighter than the GUT scale.

Below the GUT scale, the $H^{(45)}(1,2)_{\frac{1}{2}}$ and
$S_{1}^{(45)}(3,1)_{-\frac{1}{3}}$ components mix with the
$H^{(5)}(1,2)_{\frac{1}{2}}$ and $S_{1}^{(5)}(3,1)_{-\frac{1}{3}}$,
respectively, depending on the parameters of the scalar potential. The mass
eigenstates resulting from these mixings are given as follows:

$\displaystyle\begin{pmatrix}H\\\
H^{\prime}\end{pmatrix}=\begin{pmatrix}c_{H}&e^{-i\delta_{H}}s_{H}\\\
-e^{i\delta_{H}}s_{H}&c_{H}\end{pmatrix}\begin{pmatrix}H^{(5)}\\\
H^{(45)}\end{pmatrix},\qquad\begin{pmatrix}H_{C}\\\
S_{1}\end{pmatrix}=\begin{pmatrix}c_{S}&e^{-i\delta_{S}}s_{S}\\\
-e^{i\delta_{S}}s_{S}&c_{S}\end{pmatrix}\begin{pmatrix}S_{1}^{(5)}\\\
S_{1}^{(45)}\end{pmatrix},$ (5)

where $c_{H}=\cos\theta_{H}$, $s_{H}=\sin\theta_{H}$, $c_{S}=\cos\theta_{S}$,
and $s_{S}=\sin\theta_{S}$. The SU(5) invariant Yukawa interactions in Eq.(2)
can be decomposed in terms of the component fields as follows [14]:

$\displaystyle-\mathcal{L}_{Y}$
$\displaystyle=(Y_{U})_{ij}\epsilon_{\alpha\beta}\,\bar{u}_{Rai}\,H^{\alpha}q^{a\beta}_{Lj}+(Y_{D})_{ij}\,\bar{d}_{Rai}\,H_{\alpha}^{*}\,q^{a\alpha}_{Lj}+(Y_{E})_{ij}\,\bar{e}_{Ri}\,H_{\alpha}^{*}\,\ell^{\,\alpha}_{Lj}$
$\displaystyle+(Y_{U}^{\prime})_{ij}\epsilon_{\alpha\beta}\,\bar{u}_{Rai}\,H^{\prime\alpha}q^{a\beta}_{Lj}+(Y_{D}^{\prime})_{ij}\,\bar{d}_{Rai}\,H_{\alpha}^{\prime*}\,q^{a\alpha}_{Lj}+(Y_{E}^{\prime})_{ij}\,\bar{e}_{Ri}\,H_{\alpha}^{\prime*}\,\ell^{\,\alpha}_{Lj}$
$\displaystyle+(Y_{C}^{QL})_{ij}\epsilon_{\alpha\beta}\,\bar{q}^{\,C\,a\alpha}_{Li}H_{C\,a}\,\ell_{Lj}^{\,\beta}+(Y_{C}^{UE})_{ij}\,\bar{u}_{R\,ai}\,H_{C}^{*a}e_{Rj}^{C}+(Y_{C}^{DU})_{ij}\epsilon^{abc}\bar{d}_{R\,ai}\,H_{C\,b}\,u_{R\,cj}^{C}$
$\displaystyle+\frac{(Y_{C}^{QQ})_{ij}}{2}\,\epsilon_{abc}\,\epsilon_{\alpha\beta}\,\bar{q}^{C\,a\,\alpha}_{Li}H_{C}^{*\,bq_{Lj}^{c}\,\beta}+\frac{(Y_{1}^{QQ})_{ij}}{2}\,\epsilon_{\hat{a}\hat{b}\hat{c}}\,\epsilon_{\alpha\beta}\,\bar{q}^{\,c\,\hat{a}\alpha}_{Li}S_{1}^{*\hat{b}}q_{Lj}^{\hat{c}\beta}$
$\displaystyle+(Y_{1}^{QL})_{ij}\epsilon_{\alpha\beta}\,\bar{q}^{\,c\,\hat{a}\alpha}_{Li}S_{1\hat{a}}\,\ell_{Lj}^{\,\beta}+(Y_{1}^{UE})_{ij}\,\bar{u}_{R\hat{a}i}\,S_{1}^{*\hat{a}}e_{Rj}^{c}+(Y_{1}^{DU})_{ij}\epsilon^{\hat{a}\hat{b}\hat{c}}\,\bar{d}_{R\hat{a}i}\,S_{1\hat{b}}\,u_{R\hat{c}j}^{c}$
$\displaystyle+(\tilde{Y}_{1}^{ED})_{ij}\,\bar{e}_{Ri}\,\tilde{S}_{1}^{*\hat{a}}d_{R\hat{a}j}^{\,c}+\frac{(\tilde{Y}_{1}^{UU})_{ij}}{2}\,\epsilon^{\hat{a}\hat{b}\hat{c}}\,\bar{u}_{R\hat{a}i}\,\tilde{S}_{1\hat{b}}\,u_{R\hat{c}j}^{c}+(Y_{2}^{UL})_{ij}\epsilon_{\alpha\beta}\,\bar{u}_{R\hat{a}i}\,R_{2}^{\,\hat{a}\alpha}\ell_{Lj}^{\,\beta}+(Y_{2}^{EQ})_{ij}\,\bar{e}_{Ri}\,R_{2\hat{a}\alpha}^{\,*}\,q_{Lj}^{\hat{a}\alpha}$
$\displaystyle+(Y_{3}^{QL})_{ij}\epsilon_{\alpha\beta}\,\bar{q}_{Li}^{\,c\,\hat{a}\gamma}(\sigma_{a})^{\alpha}{}_{\gamma}\,S_{3\hat{a}}^{a}\,\ell_{Lj}^{\,\beta}+\frac{(Y_{3}^{QQ})_{ij}}{2}\,\epsilon_{\hat{a}\hat{b}\hat{c}}\,\epsilon_{\alpha\beta}\,\bar{q}_{Li}^{c\,\hat{a}\alpha}(\sigma^{a})^{\beta}{}_{\gamma}\,S_{3}^{*a\hat{b}}q_{Lj}^{\hat{c}\,\gamma}$
$\displaystyle+(Y_{6}^{DU})_{ij}\,\bar{d}_{R\hat{a}i}\,(\eta^{A})^{\hat{a}\hat{b}}S_{6}^{A}\,u_{R\hat{b}j}^{c}+\frac{(Y_{6}^{QQ})_{ij}}{2}\,\epsilon_{\alpha\beta}\,\bar{q}_{Li}^{\,c\,\hat{a}\alpha}(\eta^{A})_{\hat{a}\hat{b}}\,S_{6}^{A*}\,q_{Lj}^{\hat{b}\beta}$
$\displaystyle+(Y_{8}^{UQ})_{ij}\epsilon_{\alpha\beta}\,\bar{u}_{R\hat{a}i}\,(\lambda^{A})^{\hat{a}}{}_{\hat{b}}\,S_{8}^{A\alpha}\,q_{Lj}^{\hat{b}\beta}+(Y_{8}^{DQ})_{ij}\,\bar{d}_{R\hat{a}i}\,(\lambda^{A})^{\hat{a}}{}_{\hat{b}}\,S_{8\alpha}^{A*}\,q_{Lj}^{\hat{b}\alpha}+\mathrm{h.c.}\,,$
(6)

Here the above Yukawa couplings are matched to the GUT Yukawa couplings at the
GUT scale as follows:

$\displaystyle Y_{U}=$
$\displaystyle-\frac{1}{2}\,V_{QU}^{T}\left(c_{H}\,Y_{5}^{U}+\sqrt{\frac{2}{3}}\,e^{i\delta_{H}}s_{H}\,Y_{45}^{U}\right)^{T},$
$\displaystyle Y_{U}^{\prime}=$
$\displaystyle\frac{1}{2}\,V_{QU}^{T}\left(e^{-i\delta_{H}}s_{H}\,Y_{5}^{U}-\sqrt{\frac{2}{3}}\,c_{H}\,Y_{45}^{U}\right)^{T},$
$\displaystyle Y_{D}=$
$\displaystyle-\frac{1}{\sqrt{2}}\left(c_{H}\,Y_{5}^{D}-\frac{1}{2\sqrt{6}}\,e^{-i\delta_{H}}s_{H}\,Y_{45}^{D}\right)^{T},$
$\displaystyle Y_{D}^{\prime}=$
$\displaystyle\frac{1}{\sqrt{2}}\left(e^{i\delta_{H}}s_{H}\,Y_{5}^{D}+\frac{1}{2\sqrt{6}}\,c_{H}\,Y_{45}^{D}\right)^{T},$
$\displaystyle Y_{E}=$
$\displaystyle-\frac{1}{\sqrt{2}}\,V_{QE}^{T}\left(c_{H}\,Y_{5}^{D}+\frac{\sqrt{3}}{2\sqrt{2}}\,e^{-i\delta_{H}}s_{H}\,Y_{45}^{D}\right)V_{DL}\,,$
$\displaystyle Y_{E}^{\prime}=$
$\displaystyle\frac{1}{\sqrt{2}}\,V_{QE}^{T}\left(e^{i\delta_{H}}s_{H}\,Y_{5}^{D}-\frac{\sqrt{3}}{2\sqrt{2}}\,c_{H}\,Y_{45}^{D}\right)V_{DL}\,,$
$\displaystyle Y_{C}^{QL}=$
$\displaystyle\frac{1}{\sqrt{2}}\left(c_{S}\,Y_{5}^{D}+\frac{1}{2\sqrt{2}}\,e^{i\delta_{S}}s_{S}\,Y_{45}^{D}\right)V_{DL}\,,$
$\displaystyle Y_{1}^{QL}=$
$\displaystyle\frac{1}{\sqrt{2}}\left(-e^{-i\delta_{S}}s_{S}\,Y_{5}^{D}+\frac{1}{2\sqrt{2}}\,c_{S}\,Y_{45}^{D}\right)V_{DL}\,,$
$\displaystyle Y_{C}^{UE}=$
$\displaystyle\frac{1}{2}\,V_{QU}^{\,T}\left(c_{S}\,Y_{5}^{U}-\sqrt{2}\,e^{-i\delta_{S}}s_{S}\,Y_{45}^{U}\right)V_{QE}\,,$
$\displaystyle Y_{1}^{UE}=$
$\displaystyle-\frac{1}{2}\,V_{QU}^{T}\left(e^{i\delta_{S}}s_{S}\,Y_{5}^{U}+\sqrt{2}\,c_{S}\,Y_{45}^{U}\right)V_{QE}\,,$
$\displaystyle Y_{C}^{DU}=$ $\displaystyle\
\frac{1}{\sqrt{2}}\left(-c_{S}\,Y_{5}^{D}+\frac{1}{2\sqrt{2}}\,e^{i\delta_{S}}s_{S}\,Y_{45}^{D}\right)^{T}V_{QU}\,,$
$\displaystyle Y_{1}^{DU}=$
$\displaystyle\frac{1}{\sqrt{2}}\left(e^{-i\delta_{S}}s_{S}\,Y_{5}^{D}+\frac{1}{2\sqrt{2}}\,c_{S}\,Y_{45}^{D}\right)^{T}V_{QU}\,,$
$\displaystyle Y_{C}^{QQ}=$ $\displaystyle\
\frac{1}{2}\,c_{S}\,Y_{5}^{U},~{}~{}Y_{1}^{QQ}=-\frac{1}{2}\,e^{i\delta_{S}}s_{S}\,Y_{5}^{U},$
$\displaystyle\tilde{Y}_{1}^{UU}=$
$\displaystyle\frac{1}{\sqrt{2}}\,V_{QU}^{\,T}\,Y_{45}^{U}\,V_{QU}\,,~{}~{}\tilde{Y}_{1}^{ED}=\frac{1}{2}\,V_{QE}^{T}\,Y_{45}^{D}\,,$
$\displaystyle Y_{2}^{EQ}=$
$\displaystyle\frac{1}{\sqrt{2}}\,V_{QE}^{T}\,Y_{45}^{U}\,,\qquad
Y_{2}^{UL}=\frac{1}{2}\,V_{QU}^{T}\,Y_{45}^{D}\,V_{DL}\,,$ $\displaystyle
Y_{3}^{QQ}=$
$\displaystyle\frac{1}{2}\,Y_{45}^{U}\,,~{}~{}~{}Y_{3}^{QL}=-\frac{1}{2\sqrt{2}}\,Y_{45}^{D}\,V_{DL}\,,$
$\displaystyle Y_{6}^{QQ}=$
$\displaystyle-\frac{1}{\sqrt{2}}\,Y_{45}^{U}\,,~{}~{}Y_{6}^{DU}=\frac{1}{2}\,(Y_{45}^{D})^{T}\,V_{QU}\,,$
$\displaystyle Y_{8}^{UQ}=$
$\displaystyle-\frac{1}{2}\,V_{QU}^{T}\,Y_{45}^{U}\,,~{}~{}Y_{8}^{DQ}=\frac{1}{2\sqrt{2}}\,(Y_{45}^{D})^{T}.$
(7)

If we take the basis where the up-type quarks and the charged leptons are
their mass eigenstates, the GUT Yukawa matrices $Y_{5}^{U}$, $Y_{45}^{U}$,
$Y_{5}^{D}$, and $Y_{45}^{D}$ can be written as follows:

$\displaystyle Y_{5}^{U}$
$\displaystyle=-\frac{1}{c_{H}}\left(\,V_{QU}^{*}\,\hat{Y}_{U}+\hat{Y}_{U}\,V_{QU}^{\dagger}\right)\,,$
$\displaystyle Y_{45}^{U}$
$\displaystyle=\frac{\sqrt{3}}{\sqrt{2}\,e^{i\delta_{H}}s_{H}}\left(\,V_{QU}^{*}\,\hat{Y}_{U}-\hat{Y}_{U}\,V_{QU}^{\dagger}\right)\,,$
$\displaystyle Y_{5}^{D}$
$\displaystyle=-\frac{1}{2\sqrt{2}\,c_{H}}\left(3\,V_{\text{CKM}}^{*}\,\hat{Y}_{D}+V_{QE}^{*}\,\hat{Y}_{E}\,V_{DL}^{\dagger}\right)\,,$
$\displaystyle Y_{45}^{D}$
$\displaystyle=\frac{\sqrt{3}}{e^{-i\delta_{H}}s_{H}}\left(V_{\text{CKM}}^{*}\,\hat{Y}_{D}-V_{QE}^{*}\,\hat{Y}_{E}\,V_{DL}^{\dagger}\right)\,,$
(8)

where $\hat{Y}_{U}$, $\hat{Y}_{D}$, and $\hat{Y}_{E}$ represent diagonal
matrices in the mass basis and $V_{\text{CKM}}$ is the Cabbibo-Kobayashi-
Maskawa matrix, which are determined by the observed fermion masses and mixing
angles. On the other hand, the unitary matrices, $V_{QE}$, $V_{QU}$, $V_{DL}$,
cannot be determined solely from low-energy experiments. These matrices
represent the rotations required to diagonalize the quark-Higgs and lepton-
Higgs Yukawa couplings in the SU(5) GUT framework and are important for the
proton decay analysis.

##  3 Gauge Coupling Unification

In this section we briefly review the result of GCU in SU(5) GUT with 45-Higgs
discussed in Ref. [13]. By solving the renormalization group equations (RGEs)
at 1-loop, the running gauge coupling constants at an energy scale $Q$ can be
expressed as follows:

$\displaystyle\alpha_{i}^{-1}(M_{Z})=\alpha_{i}^{-1}(Q)-\frac{\beta_{i}}{2\pi}\log\left(\frac{M_{Z}}{Q}\right).$
(9)

Here $M_{Z}$ is the $Z$ boson mass and $\beta_{i}$’s represent the beta
functions of the three gauge coupling constants. Assuming the hierarchical
mass spectrum for the $45$ Higgs, the solutions are given as follows:

$\displaystyle\alpha_{1}^{-1}(M_{Z})=\alpha_{1}^{-1}(\Lambda)-\frac{1}{2\pi}\biggl{[}$
$\displaystyle\frac{41}{10}\log\frac{M_{Z}}{\Lambda}+\frac{1}{15}\log\frac{M_{H_{C}}}{\Lambda}-\frac{35}{2}\log\frac{M_{XY}}{\Lambda}+\frac{1}{10}\log\frac{M_{H^{(45)}}}{\Lambda}$
$\displaystyle+\frac{1}{15}\log\frac{M_{S_{1}^{(45)}}}{\Lambda}+\frac{1}{5}\log\frac{M_{S_{3}}}{\Lambda}+\frac{16}{15}\log\frac{M_{\tilde{S}_{1}}}{\Lambda}$
$\displaystyle+\frac{49}{30}\log\frac{M_{R_{2}}}{\Lambda}+\frac{2}{15}\log\frac{M_{S_{6}}}{\Lambda}+\frac{4}{5}\log\frac{M_{S_{8}}}{\Lambda}\biggr{]}-\frac{5}{12\pi},$
(10)
$\displaystyle\alpha_{2}^{-1}(M_{Z})=\alpha_{2}^{-1}(\Lambda)-\frac{1}{2\pi}\biggl{[}$
$\displaystyle-\frac{19}{6}\log\frac{M_{Z}}{\Lambda}-\frac{21}{2}\log\frac{M_{XY}}{\Lambda}+\frac{1}{3}\log\frac{M_{\Sigma}}{\Lambda}+\frac{1}{6}\log\frac{M_{S_{1}^{(45)}}}{\Lambda}$
$\displaystyle+2\log\frac{M_{S_{3}}}{\Lambda}+\frac{1}{2}\log\frac{M_{R_{2}}}{\Lambda}+\frac{4}{3}\log\frac{M_{S_{8}}}{\Lambda}\biggr{]}-\frac{5}{12\pi},$
(11)
$\displaystyle\alpha_{3}^{-1}(M_{Z})=\alpha_{3}^{-1}(\Lambda)-\frac{1}{2\pi}\biggl{[}$
$\displaystyle-7\log\frac{M_{Z}}{\Lambda}-\frac{1}{6}\log\frac{M_{H_{C}}}{\Lambda}-7\log\frac{M_{XY}}{\Lambda}-\frac{1}{2}\log\frac{M_{\Sigma}}{\Lambda}$
$\displaystyle+\frac{1}{6}\log\frac{M_{S_{1}^{(45)}}}{\Lambda}+\frac{1}{2}\log\frac{M_{S_{3}}}{\Lambda}+\frac{1}{6}\log\frac{M_{\tilde{S}_{1}}}{\Lambda}$
$\displaystyle+\frac{1}{3}\log\frac{M_{R_{2}}}{\Lambda}+\frac{5}{6}\log\frac{M_{S_{6}}}{\Lambda}+2\log\frac{M_{S_{8}}}{\Lambda}\biggr{]}-\frac{5}{12\pi},$
(12)

where $M_{XY}$, $M_{\Sigma}$ are the the messes of the $X$ gauge boson,
24-Higgs boson, respectively. If the GCU are achieved at $\Lambda$, the
following conditions are satisfied.

$\displaystyle\alpha_{1}(\Lambda)=\alpha_{2}(\Lambda)=\alpha_{3}(\Lambda),$
(13)

From the Eqs.(10)-(12) we can obtain the following equations.

$\displaystyle\alpha_{2}^{-1}(M_{Z})-3\alpha_{2}^{-1}(M_{Z})+2\alpha_{3}^{-1}(M_{Z})=-\frac{1}{2\pi}\biggl{[}$
$\displaystyle\frac{2}{5}\log\frac{M_{H_{C}}}{M_{Z}}-\frac{2}{5}\log\frac{M_{H^{(45)}}}{\Lambda}+\frac{2}{5}\log\frac{M(\overline{3},1)}{\Lambda}$
$\displaystyle-\frac{24}{5}\log\frac{M_{S_{3}}}{\Lambda}+\frac{7}{5}\log\frac{M_{\tilde{S}_{1}}}{\Lambda}+\frac{4}{5}\log\frac{M_{R_{2}}}{\Lambda}$
$\displaystyle+\frac{9}{5}\log\frac{M_{S_{6}}}{\Lambda}+\frac{4}{5}\log\frac{M_{S_{8}}}{\Lambda}\biggr{]}$
(14)
$\displaystyle-5\alpha_{2}^{-1}(M_{Z})+3\alpha_{2}^{-1}(M_{Z})+2\alpha_{3}^{-1}(M_{Z})=-\frac{1}{2\pi}\biggl{[}$
$\displaystyle-42\log\frac{M_{XY}}{M_{Z}}-2\log\frac{M_{\Sigma}}{M_{Z}}+6\log\frac{M_{S_{3}}}{\Lambda}$
$\displaystyle-5\log\frac{M_{\tilde{S}_{1}}}{\Lambda}-6\log\frac{M_{R_{2}}}{\Lambda}+\log\frac{M_{S_{6}}}{\Lambda}$
$\displaystyle+4\log\frac{M_{S_{8}}}{\Lambda}\biggr{]}.$ (15)

In Ref. [13], it has been shown that at least two light components of
45-Higggs are required in order to satisfy the GCU conditions. For the case of
two light components, we found that proton decay via the two light components
does not occur. For the three light components case where the components
(3,1), (3,3), and (8,2) are light, the (3,1) component, i.e. $S_{1}$, induces
proton decay and so we can constrain the model from the proton decay bounds.
To achieve GCU we consider the mass hierarchy where $S_{8}$, $S_{3}$, $S_{1}$
are lighter than the other components of $45$-Higgs. For example, it has been
demonstrated that GCU can be realized for the following scalar components
masses:

$\displaystyle M_{S_{8}}=3\times 10^{4}\mathrm{GeV},\quad M_{S_{3}}=5\times
10^{7}\mathrm{GeV},\quad M_{S_{1}}=1.8\times 10^{12}~{}\mathrm{GeV}.$ (16)

With this mass hierarchy, the GCU is achieved, and in this case the masses of
the GUT gauge bosons and the other scalar particles are $6.5\times
10^{15}~{}\mathrm{GeV}$. Furthermore, it has been shown that GCU can be
achieved in a wider region of the hierarchical mass spectrum where $S_{8}$,
$S_{3}$, and $S_{1}$ are lighter than the other components of $45$-Higgs.

In the next section, we focus on the proton decay mediated by the exchange of
$S_{1}$. The proton decay widths and their dependence on the model parameters,
such as the Yukawa couplings and the mass of $S_{1}$, will be investigated in
detail.

##  4 Proton decay

When the $S_{1}$, $S_{3}$, and $S_{8}$ components of the 45-Higgs are
significantly lighter than the GUT scale, the proton decay can be induced via
the $S_{1}$ and $S_{3}$ exchange diagrams. As discussed in Ref. [13], the
proton decay mediated by the $S_{3}$ exchange imposes stringent constraints
due to the presence of two Yukawa couplings, $Y^{QQ}_{3}$ and $Y^{QL}_{3}$,
which govern the interaction between the $S_{3}$ component and the quarks and
leptons. These Yukawa couplings directly contribute to the proton decay
amplitudes. The current experimental limits from proton decay searches,
specifically the bound on the process $p\to e^{+}\pi$, constrain the product
of these Yukawa couplings as follows:

$\displaystyle|(Y_{3}^{QQ})_{12}(Y_{3}^{QL})_{11}|<10^{-17}S_{H},$ (17)

for $m_{S_{3}}=5\times 10^{7}$ GeV. By invoking the matching conditions
between the GUT and SM Yukawa couplings, as given in Eqs. (7), the above bound
can be translated into a constraint on the GUT Yukawa coupling associated with
the 45-Higgs:

$\displaystyle|(Y^{U}_{45})_{12}|<10^{-12}S_{H}.$ (18)

To suppress the proton decay rate mediated by the $S_{3}$ component and
satisfy the experimental constraints, we adopt the assumption that the GUT
Yukawa coupling $Y^{U}_{45}$ is forbidden at the GUT scale, following the
approach in Ref. [14]. Even with this assumption, it is possible to reproduce
realistic fermion masses and mixings within the framework of the extended GUT
model. We focus our analysis on the proton decay process mediated by the
exchange of the $S_{1}$ component. The partial decay widths for these
processes are calculated using the effective Lagrangian and taking into
account the relevant hadronic matrix elements and form factors as follows
[15]:

$\displaystyle\Gamma(p\to\mu^{+}K^{0})$
$\displaystyle=\frac{1}{64\pi}\left(1-\frac{m_{K}^{2}}{m_{p}^{2}}\right)^{2}\frac{m_{p}}{f^{2}}\left\\{(1+D-F)^{2}\alpha_{H}^{2}A_{RL}^{2}\frac{|\delta^{L}_{2112}|^{2}}{M_{S_{1}}^{4}}+(1-D+F)^{2}\beta_{H}^{2}A_{RL}^{2}\frac{|\delta^{R}_{2112}|^{2}}{M_{S_{1}}^{4}}\right\\},$
(19) $\displaystyle\Gamma(p\to\mu^{+}\pi^{0})$
$\displaystyle=\frac{1}{64\pi}\left(1-\frac{m_{\pi}^{2}}{m_{p}^{2}}\right)^{2}\frac{m_{p}}{f^{2}}\
\frac{1}{2}(1+D+F)^{2}\left\\{\alpha_{H}^{2}A_{RL}^{2}\frac{|\delta^{L}_{1112}|^{2}}{M_{S_{1}}^{4}}+\beta_{H}^{2}A_{RL}^{2}\frac{|\delta^{R}_{1112}|^{2}}{M_{S_{1}}^{4}}\right\\},$
(20) $\displaystyle\Gamma(p\to e^{+}K^{0})$
$\displaystyle=\frac{1}{64\pi}\left(1-\frac{m_{K}^{2}}{m_{p}^{2}}\right)^{2}\frac{m_{p}}{f^{2}}\left\\{(1+D-F)^{2}\alpha_{H}^{2}A_{RL}^{2}\frac{|\delta^{L}_{2111}|^{2}}{M_{S_{1}}^{4}}+(1-D+F)^{2}\beta_{H}^{2}A_{RL}^{2}\frac{|\delta^{R}_{2111}|^{2}}{M_{S_{1}}^{4}}\right\\},$
(21) $\displaystyle\Gamma(p\to e^{+}\pi^{0})$
$\displaystyle=\frac{1}{64\pi}\left(1-\frac{m_{\pi}^{2}}{m_{p}^{2}}\right)^{2}\frac{m_{p}}{f^{2}}\
\frac{1}{2}(1+D+F)^{2}\left\\{\alpha_{H}^{2}A_{RL}^{2}\frac{|\delta^{L}_{1111}|^{2}}{M_{S_{1}}^{4}}+\beta_{H}^{2}A_{RL}^{2}\frac{|\delta^{R}_{1111}|^{2}}{M_{S_{1}}^{4}}\right\\},$
(22) $\displaystyle\Gamma(p\to\bar{\nu}K^{+})$
$\displaystyle=\frac{1}{64\pi}\left(1-\frac{m_{K}^{2}}{m_{p}^{2}}\right)^{2}\frac{m_{p}}{f^{2}}\
\alpha_{H}^{2}A_{RL}^{2}\frac{1}{M_{S_{1}}^{4}}\left|\delta^{L}_{2111}\frac{2D}{3}+\delta^{L}_{1122}\left(1+\frac{D}{3}+F\right)\right|^{2},$
(23) $\displaystyle\Gamma(p\to\bar{\nu}\pi^{+})$
$\displaystyle=\frac{1}{64\pi}\left(1-\frac{m_{\pi}^{2}}{m_{p}^{2}}\right)^{2}\frac{m_{p}}{f^{2}}\
(1+D+F)^{2}\alpha_{H}^{2}A_{RL}^{2}\frac{|\delta^{L}_{1111}|^{2}}{M_{S_{1}}^{4}},$
(24)

where $m_{p},m_{K},m_{\pi}$ respectively denote the masses of proton, kaon,
pion, $f$ denotes the pion decay constant, $D,F$ are parameters of the baryon
chiral Lagrangian, $\alpha_{H}$ is the hadronic form factor, $A_{RL}$ accounts
for renormalization group evolutions of the dimension-six operators. For
$m_{p},m_{K},m_{\pi}$, we use the values in Particle Data Group [23]. We have
$D=0.80$, $F=0.46$, $f=0.093$ GeV. The hadronic form factor $\alpha_{H}$,
which accounts for the non-perturbative strong interaction effects, is
evaluated at the energy scale of 2 GeV using the result from Ref. [3], where
$\alpha_{H}(2~{}{\rm GeV})=-\beta_{H}(2~{}{\rm GeV})=-0.0144$ GeV [17]. This
form factor plays a crucial role in capturing the non-perturbative dynamics of
the proton decay process. Furthermore, the RGE of the dimension-six operators
contributing to proton decay is taken into account through the factor
$A_{RL}$. This factor is calculated by solving the one-loop RGE for the
effective coupling of the proton decay operator, yielding a value of
$A_{RL}=2.6$.

The mixing parameters $\delta^{L,R}_{ijkl}$, which encode the Yukawa couplings
of the fermions, are defined as follows:

$\displaystyle\delta^{L}_{ijkl}=(Y_{1}^{DU})_{ij}(Y^{QL}_{1})_{kl},$
$\displaystyle\delta^{R}_{ijkl}=(Y_{1}^{DU})_{ij}(Y^{UE}_{1})_{kl}.$ (25)

where $Y_{1}^{DU}$, $Y^{QL}$, $Y^{UE}_{1}$ are the Yukawa coupling matrices in
the mass basis. These mixing parameters are evaluated at the energy scale
$M_{S_{1}}$ by solving the corresponding RGEs.

To numerically calculate the proton decay rates, we follow a systematic
procedure. First, we solve the RGEs for the SM Yukawa couplings, evolving them
from the electroweak scale up to the GUT scale, $\Lambda=6.5\times
10^{15}~{}\mathrm{GeV}$. This GUT scale is determined by the reference values
of the scalar masses given in Eq. (16), which lead to successful GCU. For the
input parameters at the electroweak scale, we use the values listed in Table 1
[23]. By solving the RGEs, we obtain the values of the Yukawa coupling
matrices $Y_{U}$, $Y_{D}$, and $Y_{E}$ at the GUT scale. From these Yukawa
coupling matrices at the GUT scale, we can calculate the GUT-scale Yukawa
couplings $Y^{U}_{5}$, $Y^{D}_{5}$, $Y^{U}_{45}$, and $Y^{D}_{45}$ using the
matching equations in Eq. (8). Importantly, we assume that the Yukawa coupling
$Y^{U}_{45}$ vanishes at the GUT scale, following the assumption made in the
previous discussion. This assumption implies that the unitary matrix $V_{QE}$
should be the identity matrix to satisfy the matching conditions. For the
other unitary matrices, $V_{QU}$ and $V_{DL}$, we assume that they are random
unitary matrices whose elements are distributed according to the Haar measure
as in Ref. [24], because their specific forms are not directly constrained by
low-energy observables. We also assume that $\delta_{H}$ and $\theta_{H}$ are
random values. Once the GUT-scale Yukawa couplings are determined, we can
obtain the Yukawa couplings for the light scalar components of the 45-Higgs,
namely $S_{8}$, $S_{3}$, and $S_{1}$, from the matching conditions in Eqs.
(7). With these boundary conditions at the GUT scale, we solve the RGEs for
the Yukawa couplings, including the contributions from the light scalar
components of $45_{H}$, evolving them from the GUT scale down to the mass
scale of $S_{1}$. Using the Yukawa couplings at the $M_{S_{1}}$ scale, we can
calculate the partial decay widths for various proton decay modes, such as
$p\rightarrow\mu^{+}K^{0}$ and $p\rightarrow\mu^{+}\pi^{0}$, using the
formulae given in Eqs. (19)-(24). These partial decay widths depend on the
Yukawa couplings, the scalar masses, and other input parameters related to the
hadronic matrix elements and form factors. If we further evolve these Yukawa
couplings from the $M_{S_{1}}$ scale down to the electroweak scale using the
RGEs, the resulting Yukawa coupling matrices $Y_{U}$, $Y_{D}$, and $Y_{E}$
would differ from their initial input values at the electroweak scale. This
discrepancy arises because we first evolved the Yukawa couplings using the SM
RGEs from the electroweak scale to the GUT scale, and then introduced
additional contributions from the scalar components of $45_{H}$ when evolving
from the GUT scale to the $M_{S_{1}}$ scale. While this discrepancy exists, it
is not expected to significantly affect the estimation of the proton decay
rates, which primarily depend on the Yukawa couplings at the $M_{S_{1}}$
scale. For simplicity and to avoid unnecessary complications, we neglect this
discrepancy and focus on the Yukawa couplings at the $M_{S_{1}}$ scale when
calculating the proton decay rates.

Table 1: The Yukawa coupling constants for the up-type quarks, down-type quarks, charged leptons and the Wolfenstein parameters of the CKM matrix at the $M_{Z}$ scale [23]. $y_{u}$ | $y_{c}$ | $y_{t}$ | $y_{d}$ | $y_{s}$ | $y_{b}$ | $y_{e}$ | $y_{\mu}$ | $y_{\tau}$
---|---|---|---|---|---|---|---|---
$7.05\times 10^{-6}$ | 0.00363 | 0.955 | $1.54\times 10^{-5}$ | 0.000306 | 0.0163 | $2.79\times 10^{-6}$ | 0.000590 | 0.0100
$\lambda$ | $A$ | $\overline{\rho}$ | $\overline{\eta}$ |  |  |  |  |
0.225 | 0.826 | 0.159 | 0.352 |  |  |  |  |
Table 2: Experimental constraints on the life times of various proton decay modes by Super-KamioKande [18][19][20][21][22]. Decay mode | $p\rightarrow\mu^{+}K^{0}$ | $p\rightarrow\mu^{+}\pi^{0}$ | $p\rightarrow e^{+}K^{0}$ | $p\rightarrow e^{+}\pi^{0}$ | $p\rightarrow\overline{\nu}K^{+}$ | $p\rightarrow\overline{\nu}\pi^{+}$
---|---|---|---|---|---|---
90% C.L. (years) | $3.6\times 10^{33}$ | $1.6\times 10^{34}$ | $1.0\times 10^{33}$ | $2.4\times 10^{34}$ | $5.9\times 10^{33}$ | $3.9\times 10^{32}$

In Fig. 1, we present the probability distributions for the lower bounds on
the mass $M_{S_{1}}$ derived from the experimental constraints on various
proton decay modes, which are listed in Table 2. Our analysis reveals that the
$p\rightarrow\nu\pi$ mode yields the lowest peak position for the $M_{S_{1}}$
lower bound, around $3\times 10^{11}$ GeV. On the other hand, The
$p\rightarrow\mu\pi$ mode exhibits the highest peak position for the
$M_{S_{1}}$ lower bound, approximately $3\times 10^{12}$ GeV. We found that
the $p\rightarrow\nu\pi$ mode imposes the most stringent constraint on
$M_{S_{1}}$.

In Fig. 2, we present correlations among the lower bounds on the mass
$M_{S_{1}}$ derived from the experimental constraints on various proton decay
modes. We observe that the data points in the plot between $p\to\nu\pi$ and
$p\to\mu K$ modes exhibit some scatter. This scatter can be attributed to the
different contributions to the decay widths of these two modes. The decay
width for the $p\to\nu\pi$ mode is primarily determined by the term
$|\delta^{L}|^{2}$, which represents the contribution from the left-handed
mixing parameters $\delta^{L}_{ijkl}$. On the other hand, the decay width for
the $p\to\mu K$ mode receives contributions from both $|\delta^{L}|^{2}$ and
$|\delta^{R}|^{2}$ terms. The $|\delta^{R}|^{2}$ term represents the
contribution from the right-handed mixing parameters $\delta^{R}_{ijkl}$. The
presence of both $|\delta^{L}|^{2}$ and $|\delta^{R}|^{2}$ contributions in
the $p\to\mu K$ decay width leads to a larger spread in the values of the
lower bound on $M_{S_{1}}$ compared to the $p\to\nu\pi$ mode, which depends
only on $|\delta^{L}|^{2}$. This difference in the dependence on the mixing
parameters results in the observed scatter between the data points in the
plot. These plots demonstrate the importance of properly constraining these
parameters using experimental data from different proton decay channels to
obtain robust bounds on the mass scale $M_{S_{1}}$.

Fig. 1: The probability distributions for the lower bound on the mass scale
$M_{S_{1}}$ derived from the experimental constraints on various proton decay
modes.

Fig. 2: The correlations between the lower bounds on $M_{S_{1}}$ derived from
various proton decay modes.

##  5 Summary

In this paper, we have studied proton decay in an extended SU(5) grand unified
theory that incorporates a 45-dimensional Higgs representation. Our analysis
demonstrates that the inclusion of $45$-Higgs provides a rich framework for
addressing some of the shortcomings of the minimal SU(5) GUT, such as the
inability to generate realistic fermion mass hierarchies and the lack of
sufficient proton stability.

We have shown that successful gauge coupling unification can be achieved in
this extended model by considering a hierarchical mass spectrum for the scalar
components of $\Phi_{45}$. The color octet scalar ($S_{8}$), color triplet
scalar ($S_{3}$), and color anti-triplet scalar ($S_{1}$) play a crucial role
in realizing GCU when their masses are significantly lighter than the other
components of $\Phi_{45}$. Furthermore, we have identified a wider region of
the parameter space where GCU can be maintained, providing greater flexibility
in accommodating experimental constraints.

Our proton decay analysis focused on the channels mediated by the exchange of
the color anti-triplet scalar $S_{1}$. By calculating the proton decay rates
using the Yukawa couplings obtained from renormalization group evolution and
matching conditions at the GUT scale, we have explored the dependence of the
decay rates on the model parameters. We found that the $p\to\nu\pi$ mode
imposes the most stringent constraint on $M_{S_{1}}$. The correlations between
the lower bounds on the $S_{1}$ mass scale derived from different proton decay
modes, particularly the $p\to\nu\pi$ and $p\to\mu K$ channels, reveal the
intricacies of the model’s parameter space.

The scatter observed in the correlation plot between the $p\to\nu\pi$ and
$p\to\mu K$ modes highlights the sensitivity of the proton decay rates to the
Yukawa couplings and mixing parameters of the model. This underscores the
importance of precisely measuring these parameters and using experimental data
from various proton decay channels to place robust constraints on $M_{S_{1}}$.

## Acknowledgments

This work is partially supported by Scientific Grants by the Ministry of
Education, Culture, Sports, Science and Technology of Japan, No. 21H00076 (NH)
and No. 19K147101 (TY).

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#  Text2Event: Controllable Sequence-to-Structure Generation
for End-to-end Event Extraction

Yaojie Lu1,3, Hongyu Lin1, Jin Xu4,, Xianpei Han1,2,11footnotemark: 1, Jialong
Tang1,3,
Annan Li1,3, Le Sun1,2, Meng Liao4, Shaoyi Chen4
1Chinese Information Processing Laboratory 2State Key Laboratory of Computer
Science
Institute of Software, Chinese Academy of Sciences, Beijing, China
3University of Chinese Academy of Sciences, Beijing, China
4Data Quality Team, WeChat, Tencent Inc., China
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>Corresponding authors.

###### Abstract

Event extraction is challenging due to the complex structure of event records
and the semantic gap between text and event. Traditional methods usually
extract event records by decomposing the complex structure prediction task
into multiple subtasks. In this paper, we propose Text2Event, a sequence-to-
structure generation paradigm that can directly extract events from the text
in an end-to-end manner. Specifically, we design a sequence-to-structure
network for unified event extraction, a constrained decoding algorithm for
event knowledge injection during inference, and a curriculum learning
algorithm for efficient model learning. Experimental results show that, by
uniformly modeling all tasks in a single model and universally predicting
different labels, our method can achieve competitive performance using only
record-level annotations in both supervised learning and transfer learning
settings.

##  1 Introduction

Event extraction is an essential task for natural language understanding,
aiming to transform the text into event records (Doddington et al., 2004; Ahn,
2006). For example, in Figure 1, mapping “The man returned to Los Angeles from
Mexico following his capture Tuesday by bounty hunters.” into two event
records {Type: Transport, Trigger: returned, Arg1 Role: Artifact, Arg1: The
man, Arg2 Role: Destination, Arg2: Los Angeles, … } and {Type: Arrest-Jail,
Trigger: capture, Arg1 Role: Person, Arg1: The man, Arg2 Role: Agent, Arg2:
bounty hunters, … }.

Event extraction is challenging due to the complex structure of event records
and the semantic gap between text and event. First, an event record contains
event type, trigger, and arguments, which form a table-like structure. And
different event types have different structures. For example, in Figure 1,
Transport and Arrest-Jail have entirely different structures. Second, an event
can be expressed using very different utterances, such as diversified trigger
words and heterogeneous syntactic structures. For example, both “the
dismission of the man” and “the man departed his job” express the same event
record {Type: End-Position, Arg1 Role: PERSON, Arg1: the man}.

Figure 1:  The framework of Text2Event. Here, Text2Event takes raw text as
input and generates a Transport event and an Arrest-Jail event.

Currently, most event extraction methods employ the decomposition strategy
(Chen et al., 2015; Nguyen and Nguyen, 2019; Wadden et al., 2019; Zhang et
al., 2019b; Du and Cardie, 2020; Li et al., 2020; Paolini et al., 2021), i.e.,
decomposing the prediction of complex event structures into multiple separated
subtasks (mostly including entity recognition, trigger detection, argument
classification), and then compose the components of different subtasks for
predicting the whole event structure (e.g., pipeline modeling, joint modeling
or joint inference). The main drawbacks of these decomposition-based methods
are: (1) They need massive and fine-grained annotations for different
subtasks, often resulting in the data inefficiency problem. For example, they
need different fine-grained annotations for Transport trigger detection, for
Person entity recognition, for Transport.Artifact argument classification,
etc. (2) It is very challenging to design the optimal composition architecture
of different subtasks manually. For instance, the pipeline models often lead
to error propagation. And the joint models need to heuristically predefine the
information sharing and decision dependence between trigger detection,
argument classification, and entity recognition, often resulting in suboptimal
and inflexible architectures.

In this paper, we propose a sequence-to-structure generation paradigm for
event extraction – Text2Event, which can directly extract events from the text
in an end-to-end manner. Specifically, instead of decomposing event structure
prediction into different subtasks and predicting labels, we uniformly model
the whole event extraction process in a neural network-based sequence-to-
structure architecture, and all triggers, arguments, and their labels are
universally generated as natural language words. For example, we generate a
subsequence “Attack fire” for trigger extraction, where both “Attack” and
“fire” are treated as natural language words. Compared with previous methods,
our method is more data-efficient: it can be learned using only coarse
parallel text-record annotations, i.e., pairs of $\langle$sentence, event
records$\rangle$, rather than fine-grained token-level annotations. Besides,
the uniform architecture makes it easy to model, learn and exploit the
interactions between different underlying predictions, and the knowledge can
be seamlessly shared and transferred between different components.

Furthermore, we design two algorithms for effective sequence-to-structure
event extraction. First, we propose a constrained decoding algorithm, which
can guide the generation process using event schemas. In this way, the event
knowledge can be injected and exploited during inference on-the-fly. Second,
we design a curriculum learning algorithm, which starts with current pre-
trained language models (PLMs), then trains them on simple event substructure
generation tasks such as trigger generation and independent argument
generation, finally trains the model on the full event structure generation
task.

We conducted experiments111Our source codes are openly available at
https://github.com/luyaojie/text2event on ACE and ERE datasets, and the
results verified the effectiveness of Text2Event in both supervised learning
and transfer learning settings. In summary, the contributions are as follows:

  1. 1.

We propose a new paradigm for event extraction -– sequence-to-structure
generation, which can directly extract events from the text in an end-to-end
manner. By uniformly modeling all tasks in a single model and universally
predicting different labels, our method is effective, data-efficient, and easy
to implement.

  2. 2.

We design an effective sequence-to-structure architecture, which is enhanced
with a constrained decoding algorithm for event knowledge injection during
inference and a curriculum learning algorithm for efficient model learning.

  3. 3.

Many information extraction tasks can be formulated as structure prediction
tasks. Our sequence-to-structure method can motivate the learning of other
information extraction models.

##  2 Text2Event: End-to-end Event Extraction as Controllable Generation

Given the token sequence $x=x_{1},...,x_{|x|}$ of the input text, Text2Event
directly generate the event structures $E=e_{1},...,e_{|E|}$ via an encoder-
decoder architecture. For example, in Figure 1, Text2Event take the raw text
as input and output two event records including {Type: Transport, Trigger:
returned, Arg1 Role: Artifact, Arg1: The man, …} and {Type: Arrest-Jail,
Trigger: capture, …, Arg2 Role: Agent, Arg2: bounty hunters, …}.

For end-to-end event extraction, Text2Event first encodes input text, then
generates the linearized structure using the constrained decoding algorithm.
In the following, we first introduce how to reformulate event extraction as
structure generation via structure linearization, then describe the sequence-
to-structure model and the constrained decoding algorithm.

(a) Record format.

(b) Tree format.

((Transport returned

(Artifact The man)

(Destination Los Angeles)

(Origin Mexico))

(Arrest-Jail capture

(Person The man)

(Time Tuesday)

(Agent bounty hunters))

(c) Linearized format.

Figure 2:  Examples of three event representations. The  red solid line
indicates the event-role relation; the  blue dotted line indicates the label-
span relation where the head is a label and the tail is a text span. For
example, “Transport-returned” is a label-span relation edge, which head is
“Transport” and tail is “returned”.

###  2.1 Event Extraction as Structure Generation

This section describes how to linearize event structure so that events can be
generated in an end-to-end manner. Specifically, the linearized event
representations should: (1) be able to express multiple event records in a
text as one expression; (2) be easy to reversibly converted to event records
in a deterministic way; (3) be similar to the token sequence of general text
generation tasks so that text generation models can be leveraged and
transferred easily.

Concretely, the process of converting from record format to linearized format
is shown in Figure 2. We first convert event records (Figure 2(a)) into a
labeled tree (Figure 2(b)) by: 1) first labeling the root of the tree with the
type of event (Root - Transport, Root - Arrest-Jail), 2) then connecting
multiple event argument role types with event types (Transport - Artifact,
Transport - Origin, etc.), and 3) finally linking the text spans from the raw
text to the corresponding nodes as leaves (Transport - returned, Transport -
Origin - Mexico, Transport - Artifact - The man, etc.). Given the converted
event tree, we linearize it into a token sequence (Figure 2(c)) via depth-
first traversal (Vinyals et al., 2015), where “(” and “)” are structure
indicators used to represent the semantic structure of linear expressions. The
traversal order of the same depth is the order in which the text spans appear
in the text, e.g., first “return” then “capture” in Figure 2(b). Noted that
each linearized form has a virtual root – Root. For a sentence that contains
multiple event records, each event links to Root directly. For a sentence that
doesn’t express any event, its tree format will be linearized as “()”.

###  2.2 Sequence-to-Structure Network

Based on the above linearization strategy, Text2Event generates the event
structure via a transformer-based encoder-decoder architecture (Vaswani et
al., 2017). Given the token sequence $x=x_{1},...,x_{|x|}$ as input,
Text2Event outputs the linearized event representation $y=y_{1},...,y_{|y|}$.
To this end, Text2Event first computes the hidden vector representation
$\mathbf{H}=\mathbf{h}_{1},...,\mathbf{h}_{|x|}$ of the input via a multi-
layer transformer encoder:

$\mathbf{H}=\text{Encoder}(x_{1},...,x_{|x|})$ (1)

where each layer of $\text{Encoder}(\cdot)$ is a transformer block with the
multi-head attention mechanism.

After the input token sequence is encoded, the decoder predicts the output
structure token-by-token with the sequential input tokens’ hidden vectors. At
the step $i$ of generation, the self-attention decoder predicts the $i$-th
token $y_{i}$ in the linearized form and decoder state $\mathbf{h}^{d}_{i}$
as:

$y_{i},\mathbf{h}^{d}_{i}=\text{Decoder}([\mathbf{H};\mathbf{h}^{d}_{1},...,\mathbf{h}^{d}_{i-1}],y_{i-1})$
(2)

where each layer of $\text{Decoder}(\cdot)$ is a transformer block that
contains self-attention with decoder state $\mathbf{h}^{d}_{i}$ and cross-
attention with encoder state $\mathbf{H}$.

The generated output structured sequence starts from the start token
“$\langle$bos$\rangle$” and ends with the end token “$\langle$eos$\rangle$”.
The conditional probability of the whole output sequence $p(y|x)$ is
progressively combined by the probability of each step $p(y_{i}|y_{<i},x)$:

$p(y|x)=\prod_{i}^{|y|}p(y_{i}|y_{<i},x)$ (3)

where $y_{<i}=y_{1}...y_{i-1}$, and $p(y_{i}|y_{<i},x)$ is the probability
over the target vocabulary $\mathcal{V}$ normalized by softmax($\cdot$) .

Because all tokens in linearized event representations are also natural
language words, we adopt the pre-trained language model T5 Raffel et al.
(2020) as our transformer-based encoder-decoder architecture. In this way, the
general text generation knowledge can be directly reused.

###  2.3 Constrained Decoding

Given the hidden sequence $\mathbf{H}$, the sequence-to-structure network
needs to generate the linearized event representations token-by-token. One
straightforward solution is to use a greedy decoding algorithm, which selects
the token with the highest predicted probability $p(y_{i}|y_{<i},x)$ at each
decoding step $i$. Unfortunately, this greedy decoding algorithm cannot
guarantee the generation of valid event structures. In other words, it could
end up with invalid event types, mismatch of argument-type, and incomplete
structure. Furthermore, the greedy decoding algorithm ignores the useful event
schema knowledge, which can be used to guide the decoding effectively. For
example, we can constrain the model to only generate event type tokens in the
type position.

To exploit the event schema knowledge, we propose to employ a trie-based
constrained decoding algorithm (Chen et al., 2020a; Cao et al., 2021) for
event generation. During constrained decoding, the event schema knowledge is
injected as the prompt of the decoder and ensures the generation of valid
event structures.

Concretely, unlike the greedy decoding algorithm that selects the token from
the whole target vocabulary $\mathcal{V}$ at each step, our trie-based
constrained decoding method dynamically chooses and prunes a candidate
vocabulary $\mathcal{V^{\prime}}$ based on the current generated state. A
complete linearized form decoding process can be represented by executing a
trie tree search, as shown in Figure 3(a). Specifically, each generation step
of Text2Event has three kinds of candidate vocabulary $\mathcal{V^{\prime}}$:

  * •

Event schema: label names of event types
${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{T}}$
and argument roles
${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{R}}$;

  * •

Mention strings: event trigger word and argument mention
${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathcal{S}}$,
which is the text span in the raw input;

  * •

Structure indicator: “(” and “)” which are used to combine event schemas and
mention strings.

$\langle$bos$\rangle$()$\langle$eos$\rangle$(${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{T}}$${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathcal{S}}$))$\langle$eos$\rangle$(${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{R}}$${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathcal{S}}$)(…)…

(a) The trie of event structure.

(b) The trie of event type
${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{T}}$.

Figure 3:  The prefix tree (trie) of the constrained decoding algorithm for
controllable structure generation.
${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{T}}$
and
${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{R}}$
indicate the label name of event type and argument role.
${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathcal{S}}$
indicates the text span in the raw text, which is the event trigger or
argument mention of the extracted event.

The decoding starts from the root “$\langle$bos$\rangle$” and ends at the
terminator “$\langle$eos$\rangle$”. At the generation step $i$, the candidate
vocabulary $\mathcal{V}^{\prime}$ is the children nodes of the last generated
node. For instance, at the generation step with the generated string
“$\langle$bos$\rangle$ (”, the candidate vocabulary $\mathcal{V}^{\prime}$ is
{“(”, “)”} in Figure 3(a). When generating the event type name
${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{T}}$,
argument role name
${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\mathcal{R}}$
and text span
${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\mathcal{S}}$,
the decoding process can be considered as executing search on a subtree of the
trie tree. For example, in Figure 3(b), the candidate vocabulary
$\mathcal{V}^{\prime}$ for “( Transfer” is {“Ownership”, “Money”}.

Finally, the decoder’s output will be transformed to event records and used as
final extraction results.

##  3 Learning

This section describes how to learn the Text2Event neural network in an end-
to-end manner. Our method can be learned using only the coarse parallel text-
record annotations, i.e., pairs of $\langle$sentence, event records$\rangle$,
with no need for fine-grained token-level annotation used in traditional
methods. Given a training dataset
$\mathcal{D}=\\{(x_{1},y_{1}),...(x_{|\mathcal{D}|},y_{|\mathcal{D}|})\\}$
where each instance is a $\langle$sentence, event records$\rangle$ pair, the
learning objective is the negative log-likelihood function as:

$\mathcal{L}=-\sum_{(x,y)\in\mathcal{D}}\log p(y|x,\mathbf{\theta})$ (4)

where $\mathbf{\theta}$ is model parameters.

Unfortunately, unlike general text-to-text generation models, the learning of
sequence-to-structure generation models is more challenging: 1) There is an
output gap between the event generation model and the text-to-text generation
model. Compared with natural word sequences, the linearized event structure
contains many non-semantic indicators such as “(” and “)”, and they don’t
follow the syntax constraints of natural language sentences. 2) The non-
semantic indicators “(” and “)” appear very frequently but contain little
semantic information, which will mislead the learning process.

To address the above challenges, we employ a curriculum learning (Bengio et
al., 2009; Xu et al., 2020) strategy. Specifically, we first train PLMs using
simple event substructure generation tasks so that they would not overfit in
non-semantic indicators; then we train the model on the full event structure
generation task.

#### Substructure Learning.

Because event representations often have complex structures and their token
sequences are different from natural language word sequences, it is
challenging to train them with the full sequence generation task directly.
Therefore, we first train Text2Event on simple event substructures.

Specifically, we learn our model by starting from generating only “(label,
span)” substructures, including “(type, trigger words)” and “(role, argument
words)” substructures. For example, we will extract substructure tasks in
Figure 2(c) in this stage as: (Transport returned) (Artifact The man) (Arrest-
Jail capture), etc. We construct a $\langle$sentence, substructures$\rangle$
pair for each extracted substructures, then train our model using the loss in
equation 4.

#### Full Structure Learning.

After the substructure learning stage, we further train our model for the full
structure generation task using the loss in equation 4. We found the
curriculum learning strategy uses data annotation more efficiently and makes
the learning process more smooth.

##  4 Experiments

This section evaluates the proposed Text2Event model by conducting experiments
in both supervised learning and transfer learning settings.

###  4.1 Experimental Settings

#### Datasets.

We conducted experiments on the event extraction benchmark – ACE2005 (Walker
et al., 2006), which has 599 English annotated documents and 33 event types.
We used the same split and preprocessing step as the previous work (Zhang et
al., 2019b; Wadden et al., 2019; Du and Cardie, 2020), and we denote it as
ACE05-EN.

In addition to ACE05-EN, we also conducted experiments on two other
benchmarks: ACE05-EN+ and ERE-EN, using the same split and preprocessing step
in the previous work (Lin et al., 2020). Compared to ACE05-EN, ACE05-EN+ and
ERE-EN further consider pronoun roles and multi-token event triggers. ERE-EN
contains 38 event categories and 458 documents.

Statistics of all datasets are shown in Table 1.

For evaluation, we used the same criteria in previous work (Zhang et al.,
2019b; Wadden et al., 2019; Lin et al., 2020). Since Text2Event is a text
generation model, we reconstructed the offset of predicted trigger mentions by
finding the matched utterance in the input sequence one by one. For argument
mentions, we found the nearest matched utterance to the predicted trigger
mention as the predicted offset.

Dataset | Split | #Sents | #Events | #Roles
---|---|---|---|---
ACE05-EN | Train | 17,172 | 4,202 | 4,859
Dev | 923 | 450 | 605
Test | 832 | 403 | 576
ACE05-EN+ | Train | 19,216 | 4,419 | 6,607
Dev | 901 | 468 | 759
Test | 676 | 424 | 689
ERE-EN | Train | 14,736 | 6,208 | 8,924
Dev | 1,209 | 525 | 730
Test | 1,163 | 551 | 822

Table 1: Dataset statistics.

#### Baselines.

Currently, event extraction supervision can be conducted at two different
levels: 1) Token-level annotation, which labels each token in a sentence with
event labels, e.g., “The/O dismission/B-End-Position of/O ..”; 2) Parallel
text-record annotation, which only gives $\langle$sentence, event$\rangle$
pairs but without expensive token-level annotations, e.g., $\langle$The
dismission of …, {Type: End-Position, Trigger: dismission, …}$\rangle$.
Furthermore, some previous works also leverage golden entity annotation for
model training, which marks all entity mentions with their golden types, to
facilitate event extraction. Introducing more supervision knowledge will
benefit the event extraction but is more label-intensive. The proposed
Text2Event only uses parallel text-record annotation, which makes it more
practical in a real-world application.

Models | Trig-C | Arg-C | PLM
---|---|---|---
P | R | F1 | P | R | F1
Models using Token Annotation + Entity Annotation
Joint3EE (Nguyen and Nguyen, 2019) | 68.0 | 71.8 | 69.8 | 52.1 | 52.1 | 52.1 | -
DYGIE++ (Wadden et al., 2019) | - | - | 69.7 | - | - | 48.8 | BERT-large
GAIL (Zhang et al., 2019b) | 74.8 | 69.4 | 72.0 | 61.6 | 45.7 | 52.4 | ELMo
OneIE${}_{\text{w/o Global}}$ (Lin et al., 2020) | - | - | 73.5 | - | - | 53.9 | BERT-large
OneIE (Lin et al., 2020) | - | - | 74.7 | - | - | 56.8 | BERT-large
Models using Token Annotation
EEQA (Du and Cardie, 2020) | 71.1 | 73.7 | 72.4 | 56.8 | 50.2 | 53.3 | 2$\times$BERT-base
MQAEE (Li et al., 2020) | - | - | 71.7 | - | - | 53.4 | 3$\times$BERT-large
Generation-based Baselines using Token Annotation
TANL (Paolini et al., 2021) | - | - | 68.4 | - | - | 47.6 | T5-base
Multi-Task TANL (Paolini et al., 2021) | - | - | 68.5 | - | - | 48.5 | T5-base
Our Model using Parallel Text-Record Annotation
Text2Event | 67.5 | 71.2 | 69.2 | 46.7 | 53.4 | 49.8 | T5-base
Text2Event | 69.6 | 74.4 | 71.9 | 52.5 | 55.2 | 53.8 | T5-large
Table 2: Experiment results on ACE05-EN. Trig-C indicates trigger
identification and classification. Arg-C indicates argument identification and
classification. PLM represents the pre-trained language models used by each
model.

To verify Text2Event, we compare our method with the following groups of
baselines:

1\. Baselines using token annotation: TANL is the SOTA sequence generation-
based method that models event extraction as a trigger-argument pipeline
manner (Paolini et al., 2021); Multi-task TANL extends TANL by transferring
structure knowledge from other tasks; EEQA (Du and Cardie, 2020) and MQAEE (Li
et al., 2020) are QA-based models which use machine reading comprehension
model for trigger detection and argument extraction.

2\. Baselines using both token annotation and entity annotation: Joint3EE is a
joint entity, trigger, argument extraction model based on the shared hidden
representations (Nguyen and Nguyen, 2019); DYGIE++ is a BERT-based model which
captures both within-sentence and cross-sentence context (Wadden et al.,
2019); GAIL is an inverse reinforcement learning-based joint entity and event
extraction model (Zhang et al., 2019b); OneIE is an end-to-end IE system which
employs global feature and beam search to extract globally optimal event
structures (Lin et al., 2020).

#### Implementations.

We optimized our model using label smoothing (Szegedy et al., 2016; Müller et
al., 2019) and AdamW (Loshchilov and Hutter, 2019) with learning rate=5e-5 for
T5-large, 1e-4 for T5-base. For curriculum learning, the epoch of substructure
learning is 5, and full structure learning is 30. We conducted each experiment
on a single NVIDIA GeForce RTX 3090 24GB. Due to GPU memory limitation, we
used different batch sizes for different models: 8 for T5-large and 16 for
T5-base; and truncated the max length of raw text to 256 and linearized form
to 128 during training. We added the task name as the prefix for the T5
default setup.

###  4.2 Results in Supervised Learning Setting

Table 2 presents the performance of all baselines and Text2Event on ACE05-EN.
And Table 3 shows the performance of SOTA and Text2Event on ACE05-EN+ and ERE-
EN. We can see that:

1) By uniformly modeling all tasks in a single model and predicting labels
universally, Text2Event can achieve competitive performance with weaker
supervision and simpler architecture. Our method, only using the weak parallel
text-record annotations, surpasses most of the baselines using token and
entity annotations and achieves competitive performance with SOTA.
Furthermore, using the simple encoder-decoder architecture, Text2Event
outperforms most of the counterparts with complicated architectures.

2) By directly generating event structure from the text, Text2Event can
significantly outperform sequence generation-based methods. Our method
improves Arg-C F1 by 4.6% and 2.7% over the SOTA generation baseline and its
extended multi-task TANL. Compared with sequence generation, structure
generation can be effectively guided using event schema knowledge during
inference, and there is no need to generate irrelevant information.

3) By uniformly modeling and sharing information between different tasks and
labels, the sequence-to-structure framework can achieve robust performance.
From Table 2 and Table 3, we can see that the performance of OneIE decreases
on the harder dataset ACE05-EN+, which has more pronoun roles and multi-token
triggers. By contrast, the performance of Text2Event remains nearly the same
on ACE05-EN. We believe this may be because the proposed sequence-to-structure
model is a universal model that doesn’t specialize in labels and can better
share information between different labels.

Datasets | Trig-C | Arg-C
---|---|---
P | R | F1 | P | R | F1
SOTA (Token + Entity Annotation)
ACE05-EN+ | - | - | 72.8 | - | - | 54.8
ERE-EN∗ | 56.9 | 58.7 | 57.8 | 51.9 | 47.8 | 49.8
Text2Event (Parallel Text-Record Annotation)
ACE05-EN+ | 71.2 | 72.5 | 71.8 | 54.0 | 54.8 | 54.4
ERE-EN | 59.2 | 59.6 | 59.4 | 49.4 | 47.2 | 48.3

Table 3:  Experiment results on ACE05-EN+ and ERE-EN. SOTA indicates the
state-of-the-art system – OneIE. * The result of SOTA for ERE-EN is reproduced
by the official release code because of the slightly different dataset
statistic result on ERE-EN.

###  4.3 Results in Transfer Learning Setting

Text2Event is a universal model, therefore can facilitate the knowledge
transfer between different labels. To verify the transfer ability of
Text2Event, we conducted experiments in the transfer learning setting, and the
results are shown in Table 4. Specifically, we first randomly split the
sentences which length larger than 8 in ACE05-EN+ into two equal-sized subsets
src and tgt: src only retains the annotations of the top 10 frequent event
types, and tgt only retains the annotations of the remaining 23 event types.
For both src and tgt, we use 80% of the dataset for model training and 20% for
evaluation. For transfer learning, We first pre-trained an event extraction
model on the src dataset, then fine-tuned the pre-trained model for extracting
the new event types in tgt. From Table 4, we can see that:

Settings | Trig-C | Arg-C
---|---|---
P | R | F1 | P | R | F1
OneIE (Token + Entity Annotation)
Non-transfer | 78.1 | 62.3 | 69.3 | 50.9 | 37.9 | 43.5
Transfer | 78.9 | 61.7 | 69.2 | 57.1 | 40.0 | 47.0
Gain |  |  | -0.1 |  |  | +3.5
EEQA (Token Annotation)
Non-transfer | 69.9 | 67.3 | 68.6 | 36.5 | 37.4 | 36.9
Transfer | 79.5 | 61.7 | 69.5 | 33.9 | 41.2 | 37.2
Gain |  |  | +0.9 |  |  | +0.3
Text2Event (Parallel Text-Record Annotation)
Non-transfer | 79.4 | 61.1 | 69.0 | 58.4 | 40.9 | 48.0
Transfer | 82.1 | 65.3 | 72.7 | 58.8 | 45.4 | 51.2
Gain |  |  | +3.7 |  |  | +3.2

Table 4:  Experiment results on the $tgt$ subset of ACE05-EN+ in the transfer
learning setting.

1) Data-efficient Text2Event can make better use of supervision signals. Even
training on $tgt$ from scratch, the proposed method also outperforms strong
baselines. We believe that this may because baselines using token and entity
annotation require massive fine-grained data for model learning. Different
from baselines, Text2Event uniformly models all subtasks, thus the knowledge
can be seamlessly transferred, which is more data-efficient.

2) Text2Event can effectively transfer knowledge between different labels.
Compared with the non-transfer setting, which is directly trained on $tgt$
training set, the transfer setting of Text2Event can achieve significant F1
improvements of 3.7 and 3.2 on Trig-C and Arg-C, respectively. By contrast,
the other two baselines cannot obtain significant F1 improvements of both
Trig-C and Arg-C via transfer learning. Note that the information of entity
annotation is shared across src and tgt. As a result, OneIE can leverage such
information to better argument prediction even with worse trigger prediction.
However, even without using entity annotation, the proposed method can still
achieve a similar improvement in the transfer learning setting. This is
because the labels are provided universally in Text2Event, so the parameters
are not label-specific.

###  4.4 Detailed Analysis

This section analyzes the effects of event schema knowledge, constrained
decoding, and curriculum learning algorithm in Text2Event. We designed four
ablated variants based on T5-base:

  * •

“Text2Event” is the base model that is directly trained with the full
structure learning.

  * •

“+ CL” indicates training Text2Event with the proposed curriculum learning
algorithm.

  * •

“w/o CD” discards the constrained decoding during inference and generates
event structures as an unconstrained generation model.

  * •

“w/o ES” replaces the names of event types and roles with meaningless symbols,
which is used to verify the effect of event schema knowledge.

Trig-C F1 | 1% | 5% | 25% | 100%
---|---|---|---|---
Text2Event \+ CL | 24.6 | 52.8 | 65.5 | 71.4
Text2Event | 17.9 | 52.1 | 65.0 | 69.6
w/o CD | 13.2 | 46.8 | 64.3 | 68.6
w/o ES | 0.0 | 24.3 | 31.6 | 55.5
Arg-C F1 | 1% | 5% | 25% | 100%
Text2Event \+ CL | 8.6 | 33.6 | 44.0 | 53.3
Text2Event | 3.7 | 30.9 | 44.7 | 52.6
w/o CD | 2.3 | 27.3 | 44.4 | 52.3
w/o ES | 0.0 | 7.0 | 8.2 | 28.9

Table 5:  Experiment results of variants trained with different-sized training
set on the development set of ACE05-EN.

Table 5 shows the results on the development set of ACE05-EN using different
training data sizes. We can see that: 1) Constrained decoding can effectively
guide the generation with event schemas, especially in low-resource settings.
Comparing to “w/o CD”, constrained decoding improves the performance of
Text2Event, especially in low-resource scenarios, e.g., using 1%, 5% training
set. 2) Curriculum learning is useful for model learning. Substructure
learning improves 4.7% Trig-C F1 and 5.8% Arg-C F1 on average. 3) It is
crucial to encode and generate event labels as words, rather than meaningless
symbols. Because by encoding labels as natural language words, our method can
effectively transfer knowledge from pre-trained language models.

##  5 Related Work

Our work is a synthesis of two research directions: event extraction and
structure prediction via neural generation model.

Event extraction has received widespread attention in recent years, and
mainstream methods usually use different strategies to obtain a complete event
structure. These methods can be divided into: 1) pipeline classification (Ahn,
2006; Ji and Grishman, 2008; Liao and Grishman, 2010; Hong et al., 2011, 2018;
Huang and Riloff, 2012; Chen et al., 2015; Sha et al., 2016; Lin et al., 2018;
Yang et al., 2019; Wang et al., 2019; Ma et al., 2020; Zhang et al., 2020c),
2) multi-task joint models (McClosky et al., 2011; Li et al., 2013, 2014; Yang
and Mitchell, 2016; Nguyen et al., 2016; Liu et al., 2018; Zhang et al.,
2019a; Zheng et al., 2019), 3) semantic structure grounding (Huang et al.,
2016, 2018; Zhang et al., 2020a), and 4) question-answering (Chen et al.,
2020b; Du and Cardie, 2020; Li et al., 2020; Liu et al., 2020).

Compared with previous methods, we model all subtasks of event extraction in a
uniform sequence-to-structure framework, which leads to better decision
interactions and information sharing. The neural encoder-decoder generation
architecture (Sutskever et al., 2014; Bahdanau et al., 2015) has shown its
strong structure prediction ability and has been widely used in many NLP
tasks, such as machine translation (Kalchbrenner and Blunsom, 2013), semantic
parsing (Dong and Lapata, 2016; Song et al., 2020), entity extraction
(Straková et al., 2019), relation extraction (Zeng et al., 2018; Zhang et al.,
2020b), and aspect term extraction (Ma et al., 2019). Like Text2Event in this
paper, TANL (Paolini et al., 2021) and GRIT (Du et al., 2021) also employ
neural generation models for event extraction, but they focus on sequence
generation, rather than structure generation. Different from previous works
that extract text span via labeling Straková et al. (2019) or copy/pointer
mechanism Zeng et al. (2018); Du et al. (2021), Text2Event directly generate
event schemas and text spans to form event records via constrained decoding
(Cao et al., 2021; Chen et al., 2020a), which allows Text2Event to handle
various event types and transfer to new types easily.

##  6 Conclusions

In this paper, we propose Text2Event, a sequence-to-structure generation
paradigm for event extraction. Text2Event directly learns from parallel text-
record annotation and uniformly models all subtasks of event extraction in a
sequence-to-structure framework. Concretely, we propose an effective sequence-
to-structure network for event extraction, which is further enhanced by a
constrained decoding algorithm for event knowledge injection during inference
and a curriculum learning algorithm for efficient model learning. Experimental
results in supervised learning and transfer learning settings show that
Text2Event can achieve competitive performance with the previous SOTA using
only coarse text-record annotation.

For future work, we plan to adapt our method to other information extraction
tasks, such as N-ary relation extraction.

## Acknowledgments

We sincerely thank the reviewers for their insightful comments and valuable
suggestions. This work is supported by the National Natural Science Foundation
of China under Grants no. U1936207 and 61772505, Beijing Academy of Artiﬁcial
Intelligence (BAAI2019QN0502), and in part by the Youth Innovation Promotion
Association CAS(2018141).

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