#  Light-Front Holography Model of the EMC Effect

Dmitriy N. Kim and Gerald A. Miller  Department of Physics, University of
Washington, Seattle, WA 98195-1560, USA

###### Abstract

A new two-component model of the EMC effect based on Light-Front Holographic
QCD (LFHQCD) is presented. The model suggests the EMC effect is the result of
the nuclear potential breaking SU(6) symmetry. The model separates the
$F_{2}^{A}$ nuclear structure function into two parts: a free contribution,
involving the addition of proton and neutron structure functions weighted by
the number of protons and neutrons respectively, and a nuclear/medium modified
contribution that involves nucleus independent universal function. Further,
the model displays a correlation between the size of the EMC effect and the
SRC pair density, $a_{2}$ \- extracted from kinematic plateaus at around $x>1$
in inclusive quasi-elastic (QE) scattering.

##  I Introduction

Deep inelastic lepton-nucleus scattering experiments, involving squares of
four momentum transfers ($Q^{2}$) between 10 and hundreds of GeV2, have shown
that nuclear structure functions (per nucleon) are different than that of free
nucleons. This phenomenon is known as the EMC effect, named after the European
Muon Collaboration where it was first observed; see e.g. the review Hen  _et
al._ (2017) and the original work Aubert  _et al._ (1983); Gomez  _et al._
(1994). This was a shocking result as it was assumed that deep inelastic
scattering (DIS) off a nucleus $A$ was the same as scattering off $A$
nucleons. This experimental observation taught us quark interactions in nuclei
are important, and that parton distribution functions (PDFs) depend on the
nuclear environment.

The EMC effect is not large, of order 10-15%, but is of fundamental interest
because it involves the influence of nuclear properties on scales that resolve
the nucleon size. However, scales larger than the nucleon size are relevant
because modifications of nucleon structure must be caused by interactions with
nearby nucleons. Indeed, after the nucleon size, the next largest length is
the inter-nucleon separation length, $d$; this is the scale associated with
short range correlations (SRCs) between nucleons. Therefore, the EMC effect is
naturally connected with short range correlations between nucleons. On the
other hand, the inter-nucleon separation is not much smaller than that of the
nuclear size. This means that effects involving the entire nucleus cannot be
disregarded. Such effects are known as mean-field effects in which each
nucleon moves in the mean field provided by other nucleons. Thus, an
explanation of the EMC effect should involve physics at all three length
scales Miller (2020).

The contents of this paper is as follows: In Sec. II, we will discuss the role
of virtuality in motivating the use of quark degrees of freedom, as well as
aid us in identifying the dominant interactions in the EMC effect. In Sec. III
we will present a two-component model of the nucleon that will guide our
intuition throughout this paper. Furthermore, this model of the nucleon will
give us a relationship between virtuality and the nuclear potential. In Sec.
IV we will present our construction of a new model of the EMC effect using
holographic QCD. We will first summarize results from Sufian  _et al._ (2017);
de Teramond  _et al._ (2018), giving a framework in obtaining free nucleon
Parton Distribution Functions (PDFs) from free nucleon form factors. Then, we
will introduce the effects of a nuclear medium, allowing one to obtain the
modified nucleon PDFs. In Sec. V we will present the model’s expressions for
the EMC ratios show the model’s results for the EMC ratios for a variety of
nuclei. Sec. VI will present an argument that will identify the dominant
interaction in the EMC effect, mean field or SRC. Lastly, Sec. VII will
provide a check of the change in the electric charge radius of a nucleon
inside a nucleus. Our concluding remarks are given in Sec. VIII

##  II Virtuality - a small-distance scale

Bound nucleons of four momentum $p$ do not obey the standard Einstein
relation: $p_{\mu}p^{\mu}=p^{2}=M^{2}$, and are thus said to be off their mass
shell. By examining the intermediate nucleons in nucleon-nucleon scattering,
we can gain insight into why bound nucleons do not obey Einstein’s relation.
In the Blankenbecler-Sugar Blankenbecler and Sugar (1966) and Thompson
reductions Thompson (1970) of the Bethe-Salpeter equation Salpeter and Bethe
(1951), one nucleon emits a meson of zero energy and non-zero momentum, while
the other nucleon absorbs the meson. Since the momenta of the nucleons have
changed, but their energies have not, $p^{2}\neq M^{2}$, meaning the
intermediate nucleons are off their mass shell. In other reductions of the
Bethe-Salpeter equation Gross (1969), one nucleon is on the mass shell, and
the other is not. This means that the nuclear wave function, treated
relativistically, contains nucleons that are off their mass shell. Such
nucleons must undergo interactions before they can be observed, and are thus
denoted as virtual, with difference $p^{2}-M^{2}$ being proportional to the
virtuality, $\cal V$ Miller (2019). Experiments Egiyan  _et al._ (2003, 2006);
Fomin  _et al._ (2012) using leptonic probes at large values of Bjorken $x$
interrogate the virtuality of the bound nucleons. Plateaus, kinematically
corresponding to scattering by a pair of closely connected nucleons, have been
observed Fomin  _et al._ (2017) in this region.

For a nucleon to be so far off the mass shell, it needs to be interacting
strongly with another nearby nucleon. To see that, consider a configuration of
two bound nucleons initially at rest in the nucleus. This is a good
approximation for roughly 80% of the nuclear wave function. To acquire a large
virtuality, one nucleon must exchange a boson or bosons with four-momentum,
$\vec{P}$, comparable to that of the incident virtual photon. Such a bosonic
system can only travel a short distance $\Delta r$ between the nucleons with

$\Delta r\sim\frac{1}{|\vec{P}|}$ (1)

thus a highly virtual nucleon gets its virtuality from another nearby nucleon
which must be closely separated. High virtuality is a short-distance
phenomenon, and as such will help us determine whether an interaction is being
affected by SRCs.

Additionally, high virtuality serves as an intermediate step between using
nucleonic and quark degrees of freedom. To better understand this, consider a
virtual nucleon as a superposition of physical states that are eigenfunctions
of the QCD Hamiltonian. Virtual states with nucleon quantum numbers can be
expressed using the completeness of states of QCD,

$\displaystyle|N({\cal V})\rangle=\sum_{n=1}^{n_{\rm max}}c_{n}|N_{n}\rangle,$
(2)

in which the states $|N_{n}\rangle$ are resonances and also nucleon-multi-pion
states. Each of these states (with the total three-momentum of the state
$|N({\cal V})\rangle)$ has a detailed underlying structure in terms of quarks
and gluons. In exclusive reactions with not very large momentum transfer few
states are excited and one may use Eq. (2) to describe the physics. However,
for high energy inclusive reactions of experimental relevance one needs many
states. Because of the large number of states entering in Eq. (2) it is most
efficient to use quark degrees of freedom to understand DIS large values of
$Q^{2}$. Thus, the free nucleon can be regarded as a superposition of various
configurations or Fock states, each with a different quark-gluon structure.

##  III Two-Component Model of the Nucleon

As discussed in Sec. II, it is most efficient to use quark degrees of freedom
due to the large number of states entering Eq. (2). Motivated by the the QCD
physics of color transparency Frankfurt and Strikman (1985); Brodsky and de
Teramond (1988); Ralston and Pire (1988); Jennings and Miller (1993), we will
treat the infinite number of quark-gluon configurations of the nucleon as two
configurations: a large-sized, blob-like configuration (BLC), consisting of
complicated configurations of many quarks and gluons, and a small-sized,
point-like configuration (PLC) consisting of 3 quarks. The BLC can be thought
of as an object that is similar to a nucleon, and the PLC is meant to
represent a three-quark system of small size that is responsible for the
high-$x$ behavior of the distribution function; the smaller the number of
quarks, the more likely one can carry a large momentum fraction.

When placed in a nucleus, the blob-like configuration feels the usual nuclear
attraction and its energy decreases. The point-like-configuration feels far
less nuclear-attraction by virtue of color screening Frankfurt  _et al._
(1994), in which the effects of gluons emitted by small-sized configurations
are cancelled in low-momentum transfer processes. The nuclear attraction
increases the energy difference between the BLC and the PLC, therefore
reducing the PLC probability Frankfurt and Strikman (1985). Reducing the PLC
probability in the nucleus reduces the quark momenta, in qualitative agreement
with the EMC effect. Working out the consequences of the BLC-PLC model enables
the connection between the EMC effect and virtuality to be clarified.

###  III.1 The Free Nucleon

The Hamiltonian for a free nucleon in the two-component model can be expressed
schematically by the matrix

$\displaystyle H_{0}=\left[\begin{array}[]{cc}E_{B}&V\\\
V&E_{P}\end{array}\right]$ (5)

where $P$ the PLC and $B$ represents BLC. We define the energy difference
between the PLC and the BLC to be $\Delta=E_{P}-E_{B}$. The hard-interaction
potential, $V$, connects the two components, causing the eigenstates of
$H_{0}$ to be $|N\rangle$ and $|X\rangle$ rather than $|B\rangle$ and
$|P\rangle$. The normalized eigenstates are given by

$|N\rangle=\frac{1}{\sqrt{1+\epsilon^{2}}}(|B\rangle+\epsilon|P\rangle),$ (6)

$|X\rangle=\frac{1}{\sqrt{1+\epsilon_{X}^{2}}}(|B\rangle+\epsilon_{X}|P\rangle).$
(7)

where

$\epsilon=\frac{-2V}{\Delta+\overline{\Delta}}\,,\,\,\,\,\,\,\,\
\epsilon_{X}=\frac{2V}{-\Delta+\overline{\Delta}}\,,\,\,\,\,\,\,\,\
\overline{\Delta}\equiv\sqrt{\Delta^{2}+4V^{2}}$ (8)

The notation $|X\rangle$ is used to denote the orthogonal excited state. For
later use, the probability of the PLC, $P_{PLC}$, for free nucleon is

$P_{PLC}=\frac{\epsilon^{2}}{1+\epsilon^{2}}.$ (9)

###  III.2 Medium effects

Now suppose the nucleon is bound to a nucleus. The nucleon feels an attractive
nuclear potential, here represented by $H_{1(n,p)}$, with

$\displaystyle H_{1(n,p)}=\left[\begin{array}[]{cc}U_{(n,p)}&0\\\
0&0\end{array}\right],$ (12)

to represent the idea that only the large-sized component of the nucleon feels
the influence of the nuclear attraction. Note that $U_{(n,p)}$ is dependent on
$A$ and $Z$. The treatment of the nuclear interaction, $U_{(n,p)}$, as a
number is clearly a simplification because the interaction necessarily varies
with the relevant kinematics.

The complete Hamiltonian $H=H_{0}+H_{1(n,p)}$ is:

$\displaystyle H=\left[\begin{array}[]{cc}E_{B}-|U_{(n,p)}|&V\\\
V&E_{P}\end{array}\right],$ (15)

in which the attractive nature of the nuclear binding potential is emphasized.
Then interactions with the nucleus increase the energy difference between the
bare BLC and PLC states and thereby decrease the PLC probability.

The medium-modified nucleon and its excited state, $|\tilde{N}\rangle$ and
$|\tilde{X}\rangle$, are now

$|\tilde{N}\rangle=\frac{1}{\sqrt{1+\tilde{\epsilon}^{2}}}(|B\rangle+\tilde{\epsilon}|P\rangle),$
(16)

$|\tilde{X}\rangle=\frac{1}{\sqrt{1+\tilde{\epsilon}_{X}^{2}}}(|B\rangle+\tilde{\epsilon}_{X}|P\rangle).$
(17)

The expression for $\tilde{\epsilon}$ can be obtained by making the
replacement: $\Delta\rightarrow\Delta+|U_{(n,p)}|$

$\tilde{\epsilon}={-2V\over\Delta+|U_{(n,p)}|+\sqrt{(\Delta+|U_{(n,p)}|)^{2}+4V^{2}}}$
(18)

Since $V$ is associated with the strong force, and $U_{(n,p)}$ to the nuclear
force, we can expand Eq. (18) to first order in $\frac{|U_{(n,p)}|}{\Delta}$,

$\tilde{\epsilon}_{(n,p)}\approx\epsilon(1-{|U_{(n,p)}|\over\overline{\Delta}})$
(19)

The probability of the modified PLC for the nucleon, $\tilde{P}_{PLC}(n,p)$,
is now

$\tilde{P}_{PLC}(n,p)={\tilde{\epsilon}_{(n,p)}^{2}\over
1+\tilde{\epsilon}_{(n,p)}^{2}}$ (20)

Replacing $\tilde{\epsilon}_{(n,p)}$ with Eq. (19), expanding to first order
in $\frac{|U_{(n,p)}|}{\overline{\Delta}}$, and solving for
$\tilde{r}_{(n,p)}$ we get

$\tilde{P}_{PLC}(n,p)={\epsilon^{2}\over
1+\epsilon^{2}}-\frac{2|U_{(n,p)}|\epsilon^{2}}{\overline{\Delta}(1+\epsilon^{2})^{2}}=P_{PLC}\left(1-\frac{2|U_{(n,p)}|}{\overline{\Delta}(1+\epsilon^{2})}\right)$
(21)

.

###  III.3 Connecting the Nuclear Potential to Virtuality

The next step is to relate $U_{(n,p)}$ to the virtuality which is done in Ref.
Ciofi degli Atti  _et al._ (2007). Suppose a photon interacts with a virtual
nucleon of four-momentum ${\bf P}_{\rm miss}$. The three-momentum ${\bf
P}_{\rm miss}$ opposes the $A-1$ recoil momentum ${\bf p}\equiv{\bf P}_{\rm
miss}=-{\bf P}_{A-1}$. The mass of the on-shell recoiling nucleus is given by
$M_{A-1}^{*}=M_{A}-M+E,$ where $E>0$ represents the excitation energy of the
spectator $A-1$ nucleus, and $M$ is the mass of the nucleon.

$\displaystyle M^{2}{\cal V}=P_{\rm miss}^{2}-M^{2}$ (22)
$\displaystyle=(M_{A}-\sqrt{(M_{A-1}^{*})^{2}+{\bf p}^{2}}\,\,)^{2}-{\bf
p}^{2}-M^{2}$ (23)

which reduces in the non-relativistic limit to

$\displaystyle M^{2}{\cal V}_{(n,p)}$ $\displaystyle\approx$
$\displaystyle-2M\left({{\bf p}^{2}\over 2M_{r}}+E_{(n,p)}\right),$ (24)

where the reduced mass $M_{r}=M(A-1)/A$. The virtuality, ${\cal V}(n,p)$, is
less than 0, and its magnitude increases with both the $A-1$ excitation energy
and the initial momentum of the struck nucleon.

Refs. Frankfurt and Strikman (1985); Ciofi degli Atti  _et al._ (2007)
obtained a relation between the potential $U_{(n,p)}$ and the virtuality
${\cal V}_{(n,p)}$ by using the extension of the Schroedinger equation to an
operator form:

$\displaystyle{{\bf p}^{2}\over 2M_{r}}+U_{(n,p)}=-E_{(n,p)},$ (25)

so that ${{\bf p}^{2}\over 2M_{r}}+E_{(n,p)}=-U_{(n,p)}=|U_{(n,p)}|$, we get

$\displaystyle{\cal V}_{(n,p)}={-2|U_{(n,p)}|\over M},$ (26)

thus directly connecting the nuclear potential and the virtuality.

##  IV Medium Modification in LFHQCD

We will now introduce a new model of the EMC effect using holographic QCD
nucleon form factors as a starting point Sufian  _et al._ (2017). The SU(6)
spin-flavor symmetric quark model is used in calculating the effective charges
of positive and negative helicity protons and neutrons. These effective
charges are used to obtain expressions for the nucleon form factors. In order
to extend this model to nuclei, the key idea is that the nuclear medium will
affect the probabilities of finding a spin up or down quark $q$ in a proton or
neutron, breaking SU(6) symmetry; thus, the effective charges are ultimately
modified as well. We will use intuition from the two-component model of the
nucleon to guide us in parameterizing the new modified effective charges.
Furthermore, connecting to arguments presented in Sec. II, the formalism of
LFHQCD presented in Ref. Sufian  _et al._ (2017) allows us to write valence
free and modified PDFs in terms of quark degrees of freedom.

###  IV.1 Free Nucleon PDFs from Holographic QCD

To summarize results in Sufian  _et al._ (2017), in LFHQCD the electromagnetic
form factor for an arbitrary twist-$\tau$ hadron is

$F_{\tau}(Q^{2})=\int\frac{dz}{z^{3}}V(Q^{2},z)\Phi_{\tau}^{2}$ (27)

$\Phi_{\tau}(z)=\sqrt{\frac{2}{\Gamma(\tau-1)}}\kappa^{\tau-1}z^{\tau}e^{\kappa^{2}z^{2}/2}$
(28)

where $V(Q^{2},z)$ is the bulk to boundary propogator, and $\Phi_{\tau}(z)$ is
the twist-$\tau$ hadronic wave function. The spin-nonflip elastic Dirac form
factor for a nucleon $N$, $F_{1}^{N}$, is given by

$F_{1}^{N}(Q^{2})=\sum_{\pm}g_{\pm}^{N}\int\frac{dz}{z^{4}}V(Q^{2},z)\Psi_{\pm}^{2}(z)$
(29)

with

$\begin{split}g_{+}^{N}=P_{N\uparrow}^{u}e_{u}+P_{N\uparrow}^{d}e_{d}\\\
g_{-}^{N}=P_{N\downarrow}^{u}e_{u}+P_{N\downarrow}^{d}e_{d},\end{split}$ (30)

where $g_{\pm}^{N}$ are the effective charges for a positive ($+$) or negative
($-$) chirality nucleon $N$, $P_{N(\uparrow,\downarrow)}^{q}$ is the
probability to find a spin up or down quark $q$ in a nucleon $N$, $e_{q}$ is
the charge of a quark $q$ in units of positron charge $e$, and $\Psi_{\pm}(z)$
are the wave functions corresponding to a positive ($+$) or negative ($-$)
chirality nucleon. Notably, $\Psi_{\pm}(z)$ have the following dependencies,

$\begin{split}\Psi_{+}(z)\sim
z^{\tau+\frac{1}{2}}e^{\kappa^{2}z^{2}/2}\,\,\,\,\,\\\ \Psi_{-}(z)\sim
z^{\tau+1+\frac{1}{2}}e^{\kappa^{2}z^{2}/2}.\end{split}$ (31)

The SU(6) symmetry approximation is used order to obtain
$P_{N(\uparrow,\downarrow)}^{q}$. Using this symmetry approximation, the
effective charges become

$g_{+}^{p}=1,\,\,\ g_{-}^{p}=0,\,\,\ g_{+}^{n}=-\frac{1}{3},\,\,\
g_{-}^{n}=\frac{1}{3}.$ (32)

Ref. Sufian  _et al._ (2017) next introduces a free parameter, $r$, that
multiplies the neutron effective charges, $g_{+}^{n}$ and $g_{-}^{n}$, in
order to properly match $F_{1}^{n}$ to existing experimental data. In this
paper, we will use $r=1.5$, as done in Ref. de Teramond  _et al._ (2018) and
further motivated by an argument using wave function normalization pri . The
effective charges now become

$g_{+}^{p}=1,\,\,\ g_{-}^{p}=0,\,\,\ g_{+}^{n}=-\frac{1}{2},\,\,\
g_{-}^{n}=\frac{1}{2}.$ (33)

In order to obtain expressions for the nucleon form factors, a simplified
model is introduced which only uses the leading twist-3 term in the nucleon
wave function. This leads to the following results for $F_{1}^{N}$,

$F_{1}^{p}(Q^{2})=F_{\tau=3}(Q^{2})$ (34)

$F_{1}^{n}(Q^{2})=-\frac{1}{2}F_{\tau=3}(Q^{2})+\frac{1}{2}F_{\tau=4}(Q^{2}).$
(35)

One can obtain the up ($u$) and down ($d$) valence PDFs of the free proton and
neutron by using a flavor decomposition of nucleon form factors Cates  _et
al._ (2011), and by writing the form factors for quark flavor $q$, $F^{q}$, in
terms of the valence GPD $H^{q}_{v}(x,t)$,

$F_{1}^{N}=\frac{2}{3}(F_{1}^{u})^{N}-\frac{1}{3}(F_{1}^{d})^{N},$ (36)

$F_{1}^{N}=\frac{2}{3}(F_{1}^{u})^{N}-\frac{1}{3}(F_{1}^{d})^{N}\xrightarrow[\text{Symmetry}]{\text{Isospin}}(F_{1}^{u})^{p}=2F_{1}^{p}+F_{1}^{n},\,\,\
(F_{1}^{d})^{p}=F_{1}^{p}+2F_{1}^{n},$ (37)

$(F^{q}_{1})^{N}=\int_{0}^{1}dx\,H^{q}_{v}(x,t)=\int_{0}^{1}dx\,q_{v}^{N}(x)e^{tf(x)},$
(38)

where $(F_{1}^{q})^{N}$ is the $F_{1}$ flavor form factor for quark $q$ in
nucleon $N$, $q_{v}^{N}(x)$ is the valence PDF for quark flavor $q$ in nucleon
$N$, and $f(x)$ is the profile function de Teramond  _et al._ (2018).

Furthermore, Ref. de Teramond and Brodsky (2010) recast Eq. (27) in terms of
an Euler Beta Function and determined what the PDF is for
$(F^{q}_{1})^{N}=F_{\tau}$. The corresponding PDF for $F_{\tau}$, referred to
as $q_{\tau}(x)$, is normalized to unity and is given by,

$\displaystyle
q_{\tau}(x)=\frac{\Gamma\left(\tau-\frac{1}{2}\right)}{\sqrt{\pi}\Gamma(\tau-1)}\big{(}1-w(x)\big{)}^{\tau-2}\,w(x)^{-{\frac{1}{2}}}\,w^{\prime}(x),$
(39)

with

$\displaystyle w(x)=x^{1-x}e^{-a(1-x)^{2}}$ (40)

where the flavor-independent parameter $a=0.531\pm 0.037$. Using Eqs. (34, 35,
37, 38) one can obtain the valence $u$ and $d$ proton quark distributions at
the matching scale between LFHQCD and pQCD, $\mu_{0}=1.06\pm 0.15$ GeV de
Teramond  _et al._ (2018).

$\displaystyle u_{v}^{p}(x)={3\over 2}q_{3}(x)+{1\over 2}q_{4}(x)$
$\displaystyle d_{v}^{p}(x)=q_{4}(x),$ (41)

One can obtain the neutron valence PDFs through isospin symmetry.

From now on, we will drop the subscript $v$ and it is implied that all PDFs
presented in this paper are valence. Also, notice that the above PDFs are
expressed as a superposition of twist-$\tau$ PDFs, our quark degrees of
freedom. The square of the proton and neutron wave functions are characterized
by,

$\Psi_{p}^{2}\sim u^{p}+d^{p}=\frac{3}{2}q_{3}(x)+\frac{3}{2}q_{4}(x)$ (42)

$\Psi_{n}^{2}\sim u^{n}+d^{n}=\frac{3}{2}q_{3}(x)+\frac{3}{2}q_{4}(x)$ (43)

Tying back to the two-component model, the elastic form factors in the LFHQCD
model fall asymptotically as $1/Q^{2\tau}$, and the slope of form factors as
$Q^{2}=0$ is proportional to $\tau$. These features mean that an increase in
the value of $\tau$ corresponds to an increase in effective size. Furthermore,
Ref. de Teramond  _et al._ (2018) notes that $\tau$ refers to the number of
constituents in a given Fock component of the hadron. Therefore, the function
$q_{3}$ is naturally associated with the a three quark PLC system and $q_{4}$
with the BLC. This association is also consistent with the discussion
regarding the PLC dominating at high-$x$ as can be seen by analyzing
$f(x)=q_{3}/q_{4}$ (Fig. 1).

Figure 1: A plot of $f(x)=q_{3}/q_{4}$, as a function of $x$. Notice that
$f(x)$ increases with increasing $x$, displaying the PLC dominance at
high-$x$.

Lastly, normalizing Eqs. (42, 43), the probability of the PLC, $P_{PLC}$, for
both nucleons is equal to 1/2. Using Eq. (9), we find that $\epsilon=-1$.

###  IV.2 Modified Nucleon PDFs From Holographic QCD

In order to introduce the effects of a nuclear medium we must identify terms
in which the medium would modify: these terms are the probabilities that go
into calculating the effective charges, $P_{N(\uparrow\downarrow)}^{q}$, and
the nucleon wave functions, $\Psi_{\pm}(z)$. To obtain the nucleon wave
functions, one must solve the effective single-variable light-front
Schrödinger Equation (SE) de Teramond and Brodsky (2010). The SE involves an
effective potential that encompasses the confining interaction terms in the
QCD Lagrangian, i.e. the potential due to the strong force. On the other hand,
the nuclear medium can be thought of as the potential due to the nuclear
force. As a result, the modification to the effective potential due to a
nuclear medium is small; the same is true for $P_{N(\uparrow\downarrow)}^{q}$
by similar reasoning. In this study, we will only consider the consequences of
nuclear mediums breaking SU(6) symmetry - i.e. modifying
$P_{N(\uparrow\downarrow)}^{q}$.

Motivated by np dominance in SRCs, we expect the nuclear potential to depend
on whether one introduces a proton or neutron into the nucleus. For example,
we expect the proton to feel a stronger attraction to a nucleus if there is an
abundance of neutrons and vice versa. We apply medium effects by introducing
two free parameters (which both depend on mass and atomic numbers $A$ and $Z$
respectively), $\delta r_{p}(A,Z)$ and $\delta r_{n}(A,Z)$. With these two
phenomenological parameters, we parameterize the effective charges in Eq. (33)
as

$\tilde{g}_{+}^{p}=1-\delta r_{p}(A,Z),\,\,\ \tilde{g}_{-}^{p}=\delta
r_{p}(A,Z),\,\,\ \tilde{g}_{+}^{n}=-\frac{1}{2}-\delta r_{n}(A,Z),\,\,\
\tilde{g}_{-}^{n}=\frac{1}{2}+\delta r_{n}(A,Z).$ (44)

The $A$ and $Z$ dependencies in $\delta r_{p}$ and $\delta r_{p}$ are dropped
from now on and are implied. The signs in front of $\delta r_{p}$ and $\delta
r_{n}$ are motivated by the suppression of the PLC from the two-component
model. We will soon see that the above parameterization leads to a suppression
of the PLC, $q_{3}(x)$. Notice that if there is no nuclear medium, $\delta
r_{p}$ = $\delta r_{n}$ = $0$, and the free nucleon effective charges are
regained.

With Eq. (44), Eqs. (34, 35) now become

$\tilde{F}_{1}^{p}(Q^{2})=(1-\delta r_{p})F_{\tau=3}(Q^{2})+\delta
r_{p}F_{\tau=4}(Q^{2}),$ (45)

$\tilde{F}_{1}^{n}(Q^{2})=-\left(\frac{1}{2}+\delta
r_{n}\right)F_{\tau=3}(Q^{2})+\left(\frac{1}{2}+\delta
r_{n}\right)F_{\tau=4}(Q^{2}).$ (46)

Care must be taken in obtaining the modified nucleon $u$ and $d$ valence PDFs.
For $N\neq Z$, one cannot use Eq. (37) as the nuclear medium modifies protons
and neutrons differently. However, one can use Eq. (37) for $N=Z$. We can thus
obtain the expressions of modified nucleon valence PDFs for $N=Z$ and use
their forms to intuit expressions for what the valence PDFs should be for
arbitrary $N$ and $Z$. This process gives us the following medium modified
proton valence PDFs,

$\tilde{u}^{p}=\left(\frac{3}{2}-3\delta
r_{p}\right)q_{3}(x)+\left(\frac{1}{2}+3\delta r_{p}\right)q_{4}(x)$ (47)

$\tilde{d}^{p}=\left(-3\delta r_{p}\right)q_{3}(x)+\left(1+3\delta
r_{p}\right)q_{4}(x)$ (48)

and the following modified neutron valence PDFs.

$\tilde{u}^{n}=\left(-3\delta r_{n}\right)q_{3}(x)+\left(1+3\delta
r_{n}\right)q_{4}(x)$ (49)

$\tilde{d}^{n}=\left(\frac{3}{2}-3\delta
r_{n}\right)q_{3}(x)+\left(\frac{1}{2}+3\delta r_{n}\right)q_{4}(x)$ (50)

One can check that the above expressions for the modified PDFs, using Eqs.
(36, 38), give Eqs. (45, 46). Again, notice that the above modified PDFs are
expressed as a superposition quark degrees of freedom, $q_{\tau}$. Further,
notice that we have a suppression of the PLC contribution to the above
modified nucleon valence PDFs.

It is important to note that Eqs. (47, 48, 49, 50) are not quantities
constrained by data, the quantites that experimental DIS data constrains are
the nuclear PDFs, $f^{A}$. Motivated by Ref. Kovarik  _et al._ (2016), we will
define the nuclear PDFs as

$f^{A}=Z\tilde{f}^{p}+N\tilde{f}^{n},$ (51)

Where $f$ denotes the quark flavor, $Z$ is the atomic number, $N$ is the
number of neutrons, and $\tilde{f}^{p}$ ($\tilde{f}^{n}$) is the modified
proton (neutron) PDF in nucleus $A$.

Lastly, the square of the modified proton and neutron wave functions are
characterized by,

$\tilde{\Psi}_{p}^{2}\sim\tilde{u}^{p}+\tilde{d}^{p}=\left(\frac{3}{2}-6\delta
r_{p}\right)q_{3}(x)+\left(\frac{3}{2}+6\delta r_{p}\right)q_{4}(x)$ (52)

$\tilde{\Psi}_{n}^{2}\sim\tilde{u}^{n}+\tilde{d}^{n}=\left(\frac{3}{2}-6\delta
r_{n}\right)q_{3}(x)+\left(\frac{3}{2}+6\delta r_{n}\right)q_{4}(x)$ (53)

where even though we ignored the effects of the nuclear medium on
$\Psi^{\pm}$, the wave functions still get modified due to modifications in
the effective charges. Normalizing Eqs. (52, 53), we find that the modified
PLC probability is

$\tilde{P}_{PLC}=\frac{1}{2}-2\delta r_{p}.$ (54)

Using Eq. (21) and noting that $P_{PLC}=1/2$, which leads to $\epsilon=1$, we
get a relationship between $\delta r_{(n,p)}$ and the nuclear potential,

$\tilde{P}_{PLC}=\frac{1}{2}-2\delta
r_{p}=\frac{1}{2}\left(1-\frac{|U_{(n,p)}|}{\overline{\Delta}}\right),$ (55)

$\delta r_{(n,p)}=\frac{1}{4}\frac{|U_{(n,p)}|}{\overline{\Delta}}.$ (56)

Lastly, using Eq. (26) we can obtain a relationship between $\delta r_{(n,p)}$
and virtuality

$\delta
r_{(n,p)}=\frac{1}{4}\frac{|U_{(n,p)}|}{\overline{\Delta}}=-\frac{M}{8}\frac{{\cal
V}_{(n,p)}}{\overline{\Delta}}.$ (57)

##  V EMC Ratios

Rewriting the modified proton valence PDFs in Eqs. (47, 48),

$\tilde{u}^{p}=u^{p}+3\delta r_{p}(q_{4}-q_{3})$ (58)

$\tilde{d}^{p}=d^{p}+3\delta r_{p}(q_{4}-q_{3}),$ (59)

and vice versa for the modified neutron PDFs. The modified DIS structure
function for the proton is,

$\frac{\tilde{F}_{2}^{p}}{x}=\frac{4}{9}\tilde{u}^{p}+\frac{1}{9}\tilde{d}^{p}$
(60)

$\frac{\tilde{F}_{2}^{p}}{x}=\frac{F_{2}^{p}}{x}+\frac{5}{3}\delta
r_{p}(q_{4}-q_{3})$ (61)

The modified DIS structure function for the neutron is obtained the same way:

$\frac{\tilde{F}_{2}^{n}}{x}=\frac{F_{2}^{n}}{x}+\frac{5}{3}\delta
r_{n}(q_{4}-q_{3}).$ (62)

Thus, the $F_{2}$ DIS structure function for a nucleus of mass number A, with
Z protons and N neutrons, is

$F_{2}^{A}=Z\tilde{F}_{2}^{p}+N\tilde{F}_{2}^{n}=\frac{4}{9}xu^{A}+\frac{1}{9}xd^{A},$
(63)

$F_{2}^{A}=ZF_{2}^{p}+NF_{2}^{n}+\frac{5x}{3}(q_{4}-q_{3})(Z\delta
r_{p}+N\delta r_{n}).$ (64)

The EMC ratio for deuterium is thus,

$\frac{F_{2}^{d}}{F_{2}^{p}+F_{2}^{n}}=1+4\,\delta
r(^{2}H)\left(\frac{1-f(x)}{1+f(x)}\right),$ (65)

where $\delta r(^{2}H)$ is the value of $\delta r_{p}$ and $\delta r_{n}$ for
deuterium. Lastly, the EMC ratio, relative to deuterium, for a nucleus of mass
and atomic numbers A and Z is

$\frac{2}{A}\frac{F_{2}^{A}}{F_{2}^{d}}=\frac{2}{A}\frac{ZF_{2}^{p}+NF_{2}^{n}+\frac{5x}{3}(Z\delta
r_{p}+N\delta r_{n})(q_{4}-q_{3})}{F_{2}^{p}+F_{2}^{n}+\frac{10x}{3}\delta
r(^{2}H)(q_{4}-q_{3})}.$ (66)

###  V.1 Fitting

We determined $\delta r_{p}$ and $\delta r_{p}$ for a variety of nuclei by
performing a $\chi^{2}$ minimization procedure.

$\chi^{2}=\sum_{exp}\sum_{i}\frac{(f(x_{i})-y_{i}*\eta_{exp})^{2}}{\sigma_{i^{2}}}$
(67)

We have a sum over experiments because we have data from different experiments
for the same EMC ratio measurement. It is implied that the sum over $i$ is for
the given experiment that is being summed over. $f(x_{i})$ is the model’s
prediction for the EMC effect evaluated at Bjorken $x_{i}$, $y_{i}$ is the
experimental EMC effect data measured at Bjorken $x_{i}$, $\sigma_{i}$ is the
uncertainty in the measurement of the EMC effect at Bjorken $x_{i}$, and
$\eta_{exp}$ is the normalization factor that multiplies every data point in a
given experiment. The inclusion of $\eta_{exp}$ is to further optimize the
fitting of our model to experimental data. Most experiments include a
normalization uncertainty, meaning that all measured data points can be
multiplied by a constant that is within the normalization uncertainty. In
addition to $\delta r_{p}$ and $\delta r_{p}$, $\eta_{exp}$ is also used as a
fitting parameter with its fitting bounds being the normalization uncertainty
for the given experiment being summed over.

Furthermore, uncertainties in $\delta r_{p}$ and $\delta r_{n}$ due to
uncertainties outside of fitting, e.g. uncertainties in experimental data,
were obtained through Monte Carlo error propagation. The uncertainties due to
fitting were accounted for by adding them to the Monte Carlo uncertainties in
quadrature, and then taking the square root.

The fitting procedure done in this paper goes as follows: we first fit the
deuterium EMC ratio data in order to obtain $\delta r(^{2}H)$. Using this
value of $\delta r(^{2}H)$, we then fit the rest of the EMC ratio data we had.
For the case with ${}^{3}He/^{2}H$ and ${}^{3}He/^{3}H$, we performed a
simultaneous fitting in order to obtain $\delta r_{p}$ and $\delta r_{n}$
values for ${}^{3}He$ and ${}^{3}H$.

###  V.2 Results

For the figures in this section, the published data from SLAC was obtained
from Ref. Gomez  _et al._ (1994), JLab from Refs. Seely  _et al._ (2009);
Arrington  _et al._ (2021), CLAS from Ref. Schmookler  _et al._ (2019),
MARATHON from Ref. Abrams  _et al._ (2022), and BONuS from Ref. Griffioen  _et
al._ (2015). Furthermore, we removed all isoscalar corrections in all
experimental data used in this paper.

Figure 2: Deuterium EMC ratio comparisons between the LFHQCD model (red line)
and published experimental data (removed isoscalar corrections) obtained from
BONuS data (filled stars). The red bands display 1$\sigma$ uncertainties for
the LFHQCD EMC model. The number in parenthesis next to the experiment name in
the legend is the normalization factor that multiplies all the data points,
$\eta_{exp}$ in Eq. (67). Figure 3: EMC ratio comparisons between the LFHQCD
model (red line) and published experimental data (removed isoscalar
corrections) obtained from JLab (solid points) and MARATHON (solid triangles).
The red bands display 1$\sigma$ uncertainties for the LFHQCD EMC model. The
number in parenthesis next to the experiment name in the legend is the
normalization factor that multiplies all the data points, $\eta_{exp}$ in Eq.
(67). Figure 4: EMC ratio comparisons between the LFHQCD model (red line) and
published experimental data (removed isoscalar corrections) obtained from SLAC
(open boxes), JLab (solid points), and CLAS (crosses). The red bands display
1$\sigma$ uncertainties for the LFHQCD EMC model. The number in parenthesis
next to the experiment name in the legend is the normalization factor that
multiplies all the data points, $\eta_{exp}$ in Eq. (67). Figure 5: EMC ratio
comparisons between the LFHQCD model (red line) and published experimental
data (removed isoscalar corrections) obtained from SLAC (open boxes), JLab
(solid points), and CLAS (crosses). The red bands display 1$\sigma$
uncertainties for the LFHQCD EMC model. The number in parenthesis next to the
experiment name in the legend is the normalization factor that multiplies all
the data points, $\eta_{exp}$ in Eq. (67). Figure 6: EMC ratio comparisons
between the LFHQCD model (red line) and published experimental data (removed
isoscalar corrections) obtained from SLAC (open boxes), JLab (solid points),
and CLAS (crosses). The red bands display 1$\sigma$ uncertainties for the
LFHQCD EMC model. The number in parenthesis next to the experiment name in the
legend is the normalization factor that multiplies all the data points,
$\eta_{exp}$ in Eq. (67).

There are strong parallels in the expressions for $F_{2}^{A}$ in this model
and the SRC-based model in Ref. Schmookler  _et al._ (2019). Specifically,
both models have expressions for $F_{2}^{A}$ which involve ”free”,
$ZF_{2}^{p}+NF_{2}^{n}$, and medium modified contributions. Furthermore, in
both models, the medium modified contribution depends on two parameters that
capture the effects of a nuclear medium on the proton and neutron, multiplied
by a function that is nucleus independent (the approach of using a nuclear
independent universal function was also used in Ref. Alekhin  _et al._ (2022),
which controlled off shell correlations ). Motivated by this, we determined
the relationships between our $\delta r_{p}$ and $\delta r_{n}$ values and the
$a_{2}^{p}$ and $a_{2}^{n}$ values given in Ref. Schmookler  _et al._ (2019).

$a_{2}^{p}=\frac{1}{Z}\frac{\sigma_{A}(Q^{2},x)}{\sigma_{d}(Q^{2},x)}\Bigg{|}_{Q^{2}>1.5,\,\,1.5\,\,\leq\,\,x\,\,\leq
2}\,\,\,,\,\,\,\,\,\,a_{2}^{n}=\frac{1}{N}\frac{\sigma_{A}(Q^{2},x)}{\sigma_{d}(Q^{2},x)}\Bigg{|}_{Q^{2}>1.5,\,\,1.5\,\,\leq\,\,x\,\,\leq
2}$ (68)

$a_{2}^{p}=\frac{\delta r_{p}}{\delta
r(^{2}H)},\,\,\,\,\,\,\,\,a_{2}^{n}=\frac{\delta r_{n}}{\delta r(^{2}H)}$ (69)

Where $A$ is the atomic number, $Z$ is the number of neutrons, $\sigma_{A}$ is
the cross section of nucleus $A$, $\sigma_{d}$ is the cross section of
deuterium, and the evaluation of $Q^{2}$ is in units of GeV2. $a_{2}^{p}$ and
$a_{2}^{n}$ are the per-proton and per-neutron SRC scaling coefficients, which
are interpreted as the relative abundance of high-momentum nucleons in the
measured nucleus relative to deuterium; they take into account the kinematic
plateaus due to SRCs in inclusive QE scattering. With this parallel between
both models in mind, our results for $\delta r_{(p,n)}$ from fitting are
subject to the same relation between $a_{2}^{p}$ and $a_{2}^{n}$.

$\frac{a_{2}^{p}}{a_{2}^{n}}=\frac{\delta r_{p}}{\delta r_{n}}=\frac{N}{Z}$
(70)

Fig. 7 shows a comparison between the universal function in Ref. Schmookler
_et al._ (2019), parameterized in Ref. Segarra  _et al._ (2020), and the
LFHQCD EMC model. They both agree within uncertainty within $0.35<x<0.7$.

Figure 7: Comparison between Deuterium EMC ratio predicted by the LFHQCD Model (blue line) and by the universal function (orange line) parameterized in Segarra $\it{et}$ $\it{al.}$ 2020: Ref. Segarra  _et al._ (2020). The blue and orange shaded regions are the 1$\sigma$ uncertainty bands for the LFHQCD Model and universal function respectively. Nucleus | This Work | B. Schmookler $\it{et}$ $\it{al.}$ 2019 | O. Hen $\it{et}$ $\it{al.}$ 2012
---|---|---|---
|  $\delta r_{p}$ |  $\delta r_{n}$ |  $\delta r_{p}$ |  $\delta r_{n}$ |  $\delta r_{p}$ |  $\delta r_{n}$
2H |  0.010 $\pm$ 0.003 |  0.010 $\pm$ 0.003 |  |  |  |
3He |  0.031 $\pm$ 0.003 |  0.061 $\pm$ 0.006 |  |  |  0.016 $\pm$ 0.005 |  0.03 $\pm$ 0.01
3H |  0.032 $\pm$ 0.006 |  0.016 $\pm$ 0.003 |  |  |  |
4He |  0.040 $\pm$ 0.004 |  0.040 $\pm$ 0.004 |  |  |  0.04 $\pm$ 0.01 |  0.04 $\pm$ 0.01
9Be |  0.044 $\pm$ 0.004 |  0.035 $\pm$ 0.003 |  |  |  0.045 $\pm$ 0.014 |  0.036 $\pm$ 0.012
12C |  0.049 $\pm$ 0.003 |  0.049 $\pm$ 0.003 |  0.046 $\pm$ 0.015 |  0.046 $\pm$ 0.015 |  0.048 $\pm$ 0.016 |  0.048 $\pm$ 0.016
27Al |  0.057 $\pm$ 0.003 |  0.053 $\pm$ 0.003 |  0.051 $\pm$ 0.016 |  0.047 $\pm$ 0.015 |  |
56Fe |  0.074 $\pm$ 0.003 |  0.064 $\pm$ 0.003 |  0.053 $\pm$ 0.017 |  0.046 $\pm$ 0.015 |  |
63Cu |  0.052 $\pm$ 0.003 |  0.044 $\pm$ 0.003 |  |  |  0.058 $\pm$ 0.019 |  0.049 $\pm$ 0.016
197Au |  0.072 $\pm$ 0.004 |  0.048 $\pm$ 0.003 |  |  |  0.065 $\pm$ 0.021 |  0.044 $\pm$ 0.014
208Pb |  0.078 $\pm$ 0.005 |  0.051 $\pm$ 0.003 |  0.062 $\pm$ 0.020 |  0.041 $\pm$ 0.013 |  |
Table 1: The $\delta r_{p}$ and $\delta r_{n}$ medium modifications used in
this study and ones calculated from values in B. Schmookler $\it{et}$
$\it{al.}$ 2019: Ref. Schmookler  _et al._ (2019) and O. Hen $\it{et}$
$\it{al.}$ 2012: Ref. Hen  _et al._ (2012) using Eq. (69). The uncertainties
for $\delta r_{p}$ and $\delta r_{n}$ calculated from the references were
propagated using Eq. (69).  Figure 8: Plotted $\delta r_{p}$ values as a
function of mass number, A, from Table. I (B. Schmookler $\it{et}$ $\it{al.}$
2019: Ref. Schmookler  _et al._ (2019), O. Hen $\it{et}$ $\it{al.}$ 2012: Ref.
Hen  _et al._ (2012)).  Figure 9: Plotted $\delta r_{n}$ values as a function
of mass number, A, from Table. I (B. Schmookler $\it{et}$ $\it{al.}$ 2019:
Ref. Schmookler  _et al._ (2019), O. Hen $\it{et}$ $\it{al.}$ 2012: Ref. Hen
_et al._ (2012)).

##  VI Test for SRC Dominance

From Eq. 57, we see that $\delta r_{(n,p)}$ is proportional to the nuclear
potential $|U_{(n,p)}|$, which is also proportional to the virtually. We can
determine $|U_{(n,p)}|$ from our fitted $\delta r_{(p,n)}$ values by using Eq.
(56), and noting that the energy difference, $\overline{\Delta}$, between the
nucleon ground state, $|N\rangle$, and the first excited state, $|X\rangle$,
is approximately equal to the 500 MeV, the Roper Resonance. For $A\geq 4$,
$\delta r_{(p,n)}$ values range from 0.035 to 0.078, thus
$70\,\,\mbox{MeV}\leq|U_{(n,p)}|\leq 156\,\,\mbox{MeV}$. We decompose the
nuclear potential into mean field and SRC contributions,

$U_{(n,p)}=U_{mean}+U_{SRC}$ (71)

Using a value of 50 MeV for the absolute value of the mean field Lilley
(2009), obtained from the nuclear shell model, we find the model is consistent
with the intuition that high virtuality is due to SRCs; by ”high” virtuality,
we mean virtuality greater than the typical average virtuality due to the
nuclear mean field. The arguments presented here cannot be used for nuclei
with $A<4$, as the mean field is undetermined.

##  VII Nucleon Charge Radius Check

Using our values of $\delta r_{(p,n)}$, we can determine the effects of medium
modifications to the charge radius. The modified electromagnetic Sachs form
factor is

$\tilde{G}_{EM}^{N}(Q^{2})=\tilde{F}_{1}^{N}(Q^{2})-\frac{Q^{2}}{2M^{2}}\tilde{F}_{2}^{N}(Q^{2}).$
(72)

Where $F_{1}^{N}$ is obtained from Eqs. (34, 35), $\tilde{F}_{1}^{N}$ is
obtained from Eqs. (45, 46), and $M$ is the nucleon mass which is
approximately 938 MeV for the proton and neutron. The elastic form factors
$F_{2}^{N}$ from LFHQCD are obtained from Ref. Sufian  _et al._ (2017),

$F_{2}^{p}=\chi_{p}[(1-\gamma_{p})F_{\tau=4}+\gamma_{p}F_{\tau=6}],$ (73)

$F_{2}^{n}=\chi_{n}[(1-\gamma_{n})F_{\tau=4}+\gamma_{n}F_{\tau=6}].$ (74)

Where $\chi_{p}=1.793$ is the proton anomalous moment, $\chi_{n}=-1.913$ is
the neutron anomalous moment, and $\gamma_{p}$ and $\gamma_{n}$ are the higher
Fock probabilities given as 0.27 and 0.38 respectively from Ref. Sufian  _et
al._ (2017). It is important to note that in our study, $F_{2}^{N}$ is not
modified by the nuclear medium because it’s expression does not involve
effective charges. The change in the charge radius is given by

$\sqrt{\frac{d\tilde{G}_{EM}^{N}(Q^{2})}{dQ^{2}}\Bigg{|}_{Q^{2}=0}\Bigg{/}\frac{dG_{EM}^{N}(Q^{2})}{dQ^{2}}\Bigg{|}_{Q^{2}=0}}$
(75)

Using the largest values for $\delta r_{p}$ and $\delta r_{n}$ from our fits,
we find that, in the sample of nuclei that we have studied, the greatest
increase in the proton and neutron charge radius is by 0.48% and 2.9%
respectively. These results are consistent with an upper limit on the charge
radius increase of 3.6% given in Ref. Mckeown (1986).

##  VIII Summary & Discussion

The results presented here provide a new model for the EMC effect using
LFHQCD, motivated by a two-component model of the nucleon. The model suggests
that the EMC effect is a result of the nuclear potential further breaking
SU(6) symmetry. The effects of a nuclear medium are applied through two free
parameters, $\delta r_{p}$ and $\delta r_{n}$, which modify the effective
charges of a proton and neutron with positive and negative chiralities. The
LFHQCD EMC model has strong parallels with the phenomenological model
presented in Ref. Schmookler  _et al._ (2019) in that the nuclear structure
functions have contributions from uncorrelated nucleons and correlated
nucleons in SRC pairs. As such, the model displays a connection with the
correlation between the EMC effect and the SRC pair density. This model leads
to good description of the EMC effect for a variety of nuclei, and gives
results regarding changes to the proton and neutron charge radii that are
consistent with Ref. Mckeown (1986). A further study into the medium
modification of nucleon wave functions would lead to a complete description of
nuclear modifications in LFHQCD, as well as provide the first corrections to
this model. Additionally a study into the nuclear potential’s $A$ and $Z$
dependence would provide useful insight into the analytic form of $\delta
r_{(n,p)}$. The degeneracy in the BLC and PLC due to $r$ = 3/2 leads to
$\Delta=0$, meaning that the PLC and BLC energy is degenerate, and is an
unresolved issue.

## Acknowledgements

D. N. Kim and G. A. Miller would like to thank Barak Schmookler, Or Hen, John
Arrington, Guy F. de Teramond, Stanley J. Brodsky, Andrew W. Denniston, and
Jackson Pybus for useful discussions. This work was supported by the U. S.
Department of Energy Office of Science, Office of Nuclear Physics under Award
Number DE-FG02-97ER-41014.

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# IXA/Cogcomp at SemEval-2023 Task 2: Context-enriched Multilingual Named
Entity Recognition using Knowledge Bases

Iker García-Ferrero  HiTZ Center - Ixa, University of the Basque Country
UPV/EHU  Jon Ander Campos  HiTZ Center - Ixa, University of the Basque Country
UPV/EHU  Oscar Sainz  HiTZ Center - Ixa, University of the Basque Country
UPV/EHU
Ander Salaberria  HiTZ Center - Ixa, University of the Basque Country UPV/EHU
Dan Roth  University of Pennsylvania

###### Abstract

Named Entity Recognition (NER) is a core natural language processing task in
which pre-trained language models have shown remarkable performance. However,
standard benchmarks like CoNLL 2003 Tjong Kim Sang and De Meulder (2003) do
not address many of the challenges that deployed NER systems face, such as
having to classify emerging or complex entities in a fine-grained way. In this
paper we present a novel NER cascade approach comprising three steps: first,
identifying candidate entities in the input sentence; second, linking the each
candidate to an existing knowledge base; third, predicting the fine-grained
category for each entity candidate. We empirically demonstrate the
significance of external knowledge bases in accurately classifying fine-
grained and emerging entities. Our system exhibits robust performance in the
MultiCoNER2 Fetahu et al. (2023b) shared task, even in the low-resource
language setting where we leverage knowledge bases of high-resource languages.

Figure 1: Illustration of our fine-grained named entity recognition system.

##  1 Introduction

The research on the Named Entity Recognition field has mainly focused on
recognizing entities from news corpora. Datasets like CoNLL 2003 Tjong Kim
Sang and De Meulder (2003) or OntoNotes Hovy et al. (2006) have been the
standard benchmarks for a long time. It is not difficult to find systems that
perform over 92% of F1 score on those datasets. However, it is known that
actual models perform pretty well on relatively easy entity types (such as
person names) but have been struggling to extract more complex entities Luken
et al. (2018); Hanselowski et al. (2018). Moreover, the evaluation setup
usually involves a large overlap on the entities from the train and test sets,
overestimating the systems performance. Removing such overlap resulted on a
large performance drop, consequently showing that models tend to memorize
rather than generalize to complex or unseen entities Meng et al. (2021);
Fetahu et al. (2022).

Motivated by these insights, recent works have developed new and more complex
datasets like MultiCoNER Malmasi et al. (2022a) or UFET Choi et al. (2018)
that involve complex entity mentions with higher granularity on the type
definition. To address these new challenges large language models (LLMs) are
commonly used, with the hope that after being trained on billions of tokens
the models become aware of the relevant entities. Despite the capacity of the
models to memorize information about each individual entity, they face a harsh
reality: the knowledge that a model can memorize is limited by the date on
which the model was pre-trained. So, new emerging entities can be difficult to
categorize for models trained years ago. Moreover, there are cases when it is
not possible to identify the fine-grained category of an entity just from the
context, and thus requires prior knowledge about the entity. For example:
George Bernard Shaw, Douglas Fairbanks, Mary Pickford and Margaret Thatcher
are some of the famous guests who stayed at the hotel.. From the previous
sentence, it is impossible to categorize George Bernard Shaw and Margaret
Thatcher as politicians neither Douglas Fairbanks and Mary Pickford as artist.
We hypothesize that a possible solution for this problem is to allow the
models access updated Knowledge Bases, and use the updated information to
infer the correct type of the entity of interest.

To overcome the mentioned challenges, in this work we present a NER approach
(see Figure 1) that (1) identifies possible entity candidates by analyzing the
input sentence structure, (2) links the candidate to an existing updated
knowledge base if possible, and (3) performs the fine-grained classification
using the input sentence plus the retrieved information from the KB about the
entity. The approach allowed us to perform fine-grained NER with updated world
knowledge when possible, and standard NER otherwise. Our code is publicly
available to facilitate the reproducibility of the results and its use in
future research111https://github.com/ikergarcia1996/Context-enriched-NER.

##  2 Related Work

Named Entity Recognition (NER) Grishman and Sundheim (1996) is a core natural
language processing task where the goal is to identify entities belonging to
predefined semantic types such as organizations, products and locations. Since
its inception, different approaches have been developed, from statistical
machine learning methods Zhou and Su (2002); Konkol and Konopík (2013); Agerri
et al. (2014) to the ones based on neural networks Strubell et al. (2017); Xia
et al. (2019) and the mix of both Huang et al. (2015); Chen et al. (2017).
Recently, the use of richer contextual embeddings computed via Transformer
models Vaswani et al. (2017); Devlin et al. (2018); He et al. (2020) have
considerably improved the state-of-the-art of the task. Nevertheless, these
models still have problems detecting and labelling unseen or complex entities
Augenstein et al. (2017); Meng et al. (2021).

Many datasets Malmasi et al. (2022a); Fetahu et al. (2023a) and methods Choi
et al. (2018); Zhou et al. (2018); Mengge et al. (2020) have been developed as
a result of the difficulty to label complex entities. The MultiCoNER Malmasi
et al. (2022a) shared task focuses on detecting semantically ambiguous and
complex entities in low-context settings. Almost every participant of the task
used Transformer based models as their backbone model, XLM-RoBERTa Conneau et
al. (2020a) being the most popular. The best two models presented for the task
Wang et al. (2022); Chen et al. (2022) show that the use of external KBs, such
as Wikipedia and Wikidata, improve their results significantly. Meanwhile,
other best performing models Gan et al. (2022); Pu et al. (2022); Pais (2022)
take advantage of different data augmentation methods without relying on
external KBs. The gap between the performance of the first two methods was
less noticeable than the gap between the second best and the rest of
approaches, implying that exploiting external KBs during training and
inference is a promising research line. This difference was greater when more
complex entities have to be identified. However, the overall results showed
that recognizing complex or infrequent entities is still difficult Malmasi et
al. (2022b).

In this work we focus on the MultiCoNER2 Fetahu et al. (2023a) dataset, a
second version of MultiCoNER Malmasi et al. (2022b) with higher granularity
than its predecessor. Comparing to the state-of-the-art of the first
MultiCoNER task, our approach for this task also uses XLM-RoBERTa for entity
boundary detection and entity classification, but differs on how we retrieve
information from the external KBs. Instead of retrieving relevant text
passages to classify a given entity from a query sentence Wang et al. (2022),
or building a Gazetteer network from Wikidata entities and their derived
labels to further enrich token representations Chen et al. (2022), we directly
predict Wikidata IDs from entity candidates by integrating mGENRE De Cao et
al. (2022a) as our entity linking module. Previous models have already tried
to link entities with external KBs Tsai et al. (2016); Zhou et al. (2018);
Wang et al. (2021). However, mGENRE allows us to easily access both Wikidata
entity descriptors and Wikipedia articles to increase our candidate’s context
for entity classification.

##  3 System description

Our method implements three steps. First we identify entity candidates in the
input sentence. Then, we link the candidate to an existing knowledge base.
Finally, we predict the fine-grained category for each entity candidate.

###  3.1 Entity Boundary Detection

Figure 2: Entity Boundary Detection. We use a XLM-RoBERTa model to predict
named entity boundaries.

Given unlabelled text as input, we predict named entity boundaries by
analyzing the input sentence structure (Figure 2). We treat this task as a
sequence labelling task in which the model predicts if a given token is part
of an entity or not ("B-ENTITY", "I-ENTITY","O"). We use the multilingual XLM-
RoBERTa-large model Conneau et al. (2020b) with a token classification layer
(a linear layer) on top of each token representation. Our implementation is
based on the sequence labelling implementation of the Huggingface open-source
library Wolf et al. (2019). We evaluate the model in the development set at
the end of each epoch and then select the best performing checkpoint. We train
five independent models and then use majority vote as the ensembling strategy
at inference time.

###  3.2 Entity Linking and Information Retrieval

Figure 3: Entity Linking step. Given a sentence and the boundaries of a named
entity, we use mGENRE to predict the Wikidata ID that corresponds to the
entity

Given a sentence and the boundaries of a named entity between the sentence, we
aim to link the entity mention to its corresponding Wikidata/Wikipedia page
(Figure 3). To accomplish this task, we employ the mGENRE entity linking
system De Cao et al. (2021); De Cao et al. (2022b). mGENRE is a sequence-to-
sequence system for Multilingual Entity Linking, which can generate entity
names in over 100 languages from left to right, token-by-token in an
autoregressive manner, conditioned by the context. In order to ensure that
only valid entity identifiers are generated mGENRE employs a prefix tree
(trie) to enable constrained beam search. mGENRE predicts both, Wikipedia page
title that corresponds to the entity and the language in which the entity
mention is written, and subsequently both identifiers to the Wikidata ID. In
our work, we utilize the pre-trained mGENRE model provided by its authors. The
authors fine-tuned an mBART Liu et al. (2020); Lewis et al. (2020) model that
had been pre-trained on 125 languages using Wikipedia hyperlinks in 105
languages. For each entity, we use constrained beam search to predict the five
most probable Wikidata IDs for each predicted entity from the Entity Boundary
Detection step.

Figure 4: Information Retrieval step. Given a wikidata ID, we retrieve the
relevant information from the Wikidata and Wikipedia that can help us
determining the correct category of the entity.

As illustrated in Figure 4, we leverage the predicted Wikidata ID to obtain
the Wikidata description for the entity, as well as the contents of the
instance_off and occupation arguments. In the multilingual track, we also
retrieve the subclass_off argument. Due to time constraints, we were unable to
retrieve this argument in the other tracks. As Wikidata pages contain links to
their corresponding Wikipedia webpages, we also retrieve the Wikipedia
summary. These summaries are generally more detailed than the Wikidata
descriptions.

We initiate the retrieval process by querying the Wikidata ID with the highest
probability, as predicted by mGENRE. If the predicted ID corresponds to a page
that has been deleted, is empty, or is a list/disambiguation page, we discard
the ID and proceed to the next most probable predicted ID. We found that,
while Wikidata descriptions and arguments are mostly available in English for
the entities in MultiCoNER, this is not the case for other languages such as
Bangla or Farsi. Similarly, a large number of entities have a Wikipedia page
available in English but not in other languages. For this reason, we always
retrieve the Wikidata description and arguments, as well as the Wikipedia
summary, in English.

###  3.3 Entity Category Classifier

Figure 5: Given the boundaries of a named entity and the information retrieved
from Wikipedia/Wikidata, we use a XLM-RoBERTa model to predict the correct
category for the entity.

In our final step, we aim to classify the entity candidates into fine-grained
categories by combining all the knowledge we have. We create a text input by
concatenating the sentence where the entity is annotated with an HTML-style
markup, the wikidata description, a list of all retrieved arguments, and the
Wikipedia summary. We use the special token __SEP__ to delimit each piece of
information. If we fail to retrieve a Wikidata or Wikipedia page, we use the
text "No Wikidata/Wikipedia summary found," and the model predicts the
category solely based on the context of the entity.

We use the multilingual XLM-RoBERTa-large model Conneau et al. (2020b) with a
text classification layer (a linear layer) on top of the first token. We
implement this using the Huggingface open-source library’s text classification
implementation Wolf et al. (2019). During training, we generate the train and
development datasets using the gold entity boundaries. During inference, we
predict the categories for the entity boundaries computed in the entity
boundary detection step. We evaluate the model at the end of each epoch and
choose the model with the highest performance on the development set. We train
five independent models and merge the predictions at inference using majority
voting.

##  4 Experimental Setup and Dataset

We use the official MultiCoNER2 dataset Fetahu et al. (2023a) in all tracks to
train our entity boundary and entity classification models. To query external
knowledge, we utilize the MediaWiki API to retrieve data from the live version
of Wikipedia/Wikidata. MultiCoNER2 consists of two substacks, the monolingual
task with 12 monolingual datasets and a multilingual task that contains data
from all languages. For 7 languages (EN, ZH, IT, ES, FR, PT, SV) some
sentences were corrupted with noise, either on context tokens or entity
tokens. The results of the shared task are evaluated based on entity-level
macro F1 scores, where all label categories contribute equally to the final
score, regardless of the number of entities labeled with each category. The
dataset consists of 36 pre-defined fine-grained categories which are grouped
into 6 coarse-grained categories: Medical entities, Locations, Creative Works,
Groups, Persons and Products. A description of the hyper-parameters used,
dataset stats and hardware used in available in the Appendix.

##  5 Results

Team Name EN ES SV UK PT FR FA DE ZH HI BN IT MULTI AVG XLM-RoBERTa-large
59.85 62.60 65.76 65.67 61.09 62.98 57.17 62.86 51.89 68.06 65.97 65.17 69.12
62.93 NetEase - - - - - - - - 84.05 - - - - - USTC-NELSLIP 72.15 74.44 75.47
74.37 71.26 74.25 68.85 78.71 66.57 82.14 80.59 75.70 75.62 74.72 PAI 80.00
71.67 72.38 71.28 81.61 86.17 68.46 88.09 74.87 80.96 84.39 84.88 77.00 78.59
DAMO-NLP 85.53 89.78 89.57 89.02 85.97 89.59 87.93 84.97 75.98 78.56 81.60
89.79 84.48 85.59 Our System 72.82 73.81 76.54 75.25 72.28 74.52 69.49 80.35
64.86 79.56 78.95 74.67 78.17 74.71

Table 1: Our system macro-F1 score for all the tracks compared with our
baseline and the systems that achieved the best results.

Our team participated in all the 12 monolingual tracks and the multilingual
track. More than 35 team participated in the shared task. We achieved the 3rd
positions in four tracks. The shared task results computed by the organizers
are shown in Table 1. We first compare our system with an XLM-RoBERTa-large
Conneau et al. (2020b) baseline. For this baseline, we added a token
classification layer (linear layer) on top of each token representation of an
XLM-RoBERTa-large model and fine-tuned the model to directly predict the fine-
category for each token. The results were much lower than the ones achieved
with our system, which confirms our hypothesis that external knowledge is
needed to predict the entity categories.

We also compare our system with the performance of systems from others teams
that got the first position in any of the tracks. Our system was most
competitive in Hindi and Bangla, as well as the multilingual track. Hindi and
Bangla are by far the languages with the smallest Wikipedia’s, ranked 59th and
63rd by the number of articles
respectively.222https://meta.wikimedia.org/wiki/List_of_Wikipedias We
attribute this to our decision to retrieve the external knowledge from the
English Wikipedia/Wikidata for all the tracks. Because we predict a wikidata
ID, we are able to retrieve knowledge in any language in which it is
available. This enables our system to be used for low-resource languages for
which no large, up-to-date knowledge base is available, thanks to being able
to link the entities found to a knowledge base in high-resource languages. On
the other hand, our system is not as competitive in very high-resource
languages, such as English and Chinese.

###  5.1 Clean vs Noisy Performance

Track Clean Noisy EN 76.64 64.36 ES 77.65 66.09 SV 80.75 68.69 PT 76.00 65.54
FR 78.60 65.81 ZH 70.35 48.37 IT 78.16 67.66

Table 2: Our system macro-F1 score in the clean and noisy data from the test
sets as computed by the organizers

In seven languages (EN, ZH, IT, ES, FR, PT, SV), some sentences contained
noise, either on context tokens or entity tokens. Table 2 shows the results of
our system on the set of sentences that were not corrupted and the set of
corrupted sentences. We observed a significant drop in performance when noise
was introduced in the sentences, especially for the Chinese track. We believe
that this is because our entity linking step depends too much on the entity
itself and does not sufficiently take into account the context in which the
entity appears. Improving our system’s ability to consider contextual
information is something we need to work on.

###  5.2 Ablation Study

In this section, we evaluate the different steps in our system and check how
different design decisions affect performance.

#### How important is external knowledge to classify entities?

We aim to measure the importance of retrieving external knowledge for accurate
entity classification in the MultiCoNER dataset. To achieve this, we train our
text classification system on the training split and evaluate its performance
on the development data. We use the gold labeled entity spans for both splits.
We assess the relevance of external knowledge by varying the amount of
external knowledge used in the evaluation. Table 3 shows the results obtained
using different combinations of external knowledge, including using only the
entity in its context (no external knowledge). As we observed in Table 1, the
results without external knowledge are very poor. The most relevant external
knowledge is the content of the Wikidata arguments. However, as we provide
more external knowledge to the model, the performance improves. These results
also demonstrate that our system achieves remarkable results in classifying
entities into fine-grained categories when the correct entity spans are
provided, indicating that the entity boundary detection step hinders the
performance of our system. The entity classification confusion matrix for the
English development set is available in Appendix D.

Initial Context Wikidata Description Wikidata Arguments Wikipedia Summary EN
ZH 79 81 82 84 88 88 86 86 89 86 90 89

Table 3: Our system macro-F1 score in the development split when using gold
entity boundaries and different amount of external knowledge

#### Entity boundary detection performance

EN ZH Multi Entity Boundary Detection 90.05 90.49 90.52

Table 4: F1-score of the Entity Boundary Classification Step in the
development split

Our initial hypothesis was that external knowledge is required to accurately
classify entities into fine-grained categories. However, we also hypothesized
that detecting the boundaries of named entities does not require external
knowledge. For instance, it is possible to identify that a sequence of words
corresponds to the name of a person without needing to know anything about
that person. Table 4 shows the performance the entity boundary detection step
in the development dataset, which does not utilize any external knowledge. We
were able to identify a significant proportion of the entities in the dataset.
However, the results were lower than those of the entity classification step
in Table 3. This indicates that the entity boundary detection step is the
weakest point in our system. We believe that incorporating external knowledge
into this step would enhance the results.

##  6 Conclusion

We have developed a system that identifies potential entity candidates and
leverages external knowledge from an up-to-date knowledge base to classify
them into a set of predefined fine-grained categories, addressing the
challenges posed by temporal knowledge and unknown entities. Our results
demonstrate exceptional performance in classifying entities into fine-grained
categories, underscoring the need for external knowledge in accurately
classifying entities in the MultiCoNER dataset. However, our current entity
boundary detection step does not incorporate external knowledge, which we plan
to improve in the future.

Furthermore, our system exhibits promising results for low-resource languages
where a comprehensive Wikipedia is unavailable. By linking the identified
entities to a knowledge base in a high-resource language, it can be used to
process low-resource languages. In future work, we intend to integrate all the
steps and insights gained from our current system into a single end-to-end
model. Although each step performs well when evaluated independently, the
current pipeline multiplies errors at each step, which we aim to address in
the integrated model.

## Acknowledgements

This work has been partially supported by the HiTZ center and the Basque
Government (Research group funding IT-1805-22). We also acknowledge the
funding from the following projects: (i) DeepKnowledge (PID2021-127777OB-C21)
MCIN/AEI/10.13039/501100011033 and ERDF A way of making Europe; (ii) DeepR3
(TED2021-130295B-C31) by MCIN/AEI/10.13039/501100011033 and EU NextGeneration
programme EU/PRTR. (iii) IARPA BETTER Program contract No. 2019-19051600006
(ODNI, IARPA).

Iker García-Ferrero, Oscar Sainz and Ander Salaberria are supported by
doctoral grants from the Basque Government (PRE_2022_2_0208, RE_2022_2_0110
and PRE_2022_2_0219, respectively). Jon Ander Campos enjoys a doctoral grant
from the Spanish MECD (FPU18/01271).

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##  Appendix A Dataset details

Figure 6: MultiCoNER2 Taxonomy Figure 7: MultiCoNER2 label distribution
computed as the sum of the label count for every language and split

We use the MultiCoNER2 dataset in all our experiments Fetahu et al. (2023a).
The number of sentences for each language and dataset split is available in
Table 5. The dataset Taxonomy is visualized in Figure 6. The label
distribution is visualized in Figure 7.

##  Appendix B Hyper parameters

###  B.1 Entity Boundary Detection

We use the XLM-RoBERTa-large model in all our experiments. We train the model
for 8 epochs, with a batch size of 16, AdamW optimizer Loshchilov and Hutter
(2019) with 2e-5 learning rate. We use a max sequence size of 256 tokens,
larger sequences are truncated to the first 256 tokens. The rest of hyper
parameters are the default values for the sequence labelling implementation of
the Huggingface library
333https://github.com/huggingface/transformers/tree/main/examples/pytorch/token-
classification. As described in 3.1 we evaluate the model in the development
set at the end of each epoch and then select the best performing checkpoint.
We train five independent models and then use majority vote as the ensembling
strategy at inference time.

###  B.2 Entity Linking and Information Retrieval

We use the mGENRE implementation
444https://github.com/facebookresearch/GENRE/tree/main/examples_mgenre in the
fairseq library Ott et al. (2019). We use the prefix tree provided buy the
authors and marginalization. This constrains the model to only generate valid
identifiers. We retrieve data from Wikipedia using the pymediawiki
555https://github.com/barrust/mediawiki wrapper and parser for the MediaWiki
API. We use Wikidata client library for Python
666https://github.com/dahlia/wikidata to retrieve knowledge from Wikidata.

###  B.3 Entity Category Classifier

We use the XLM-RoBERTa-large model in all our experiments. We train the model
for 8 epochs, with a batch size of 16, AdamW optimizer Loshchilov and Hutter
(2019) with 2e-5 learning rate. We use a max sequence size of 256 tokens. The
rest of hyper parameters are the default values for the text classification
implementation of the Huggingface library
777https://github.com/huggingface/transformers/tree/main/examples/pytorch/text-
classification. As described in 3.3 we evaluate the model in the development
set at the end of each epoch and then select the best performing checkpoint.
We train five independent models and then use majority vote as the ensembling
strategy at inference time.

##  Appendix C Hardware used

We perform all our experiments using a single NVIDIA A100 GPU with 80GB
memory. The machine used has two AMD EPYC 7513 32-Core Processors and 512GB of
RAM. Although our system can also run on GPUs with 24GB of VRAM.

##  Appendix D Text Classification Confusion Matrix

We show the text classification confusion matrix (Figure 8) for the English
development test using the gold labelled spans to better understand which type
of entities are the most difficult ones to classify for our model. As we can
see in the matrix, the entities related to persons are the most ambiguous and
difficult to classify.

Figure 8: text classification confusion matrix for the English development
test using gold labelled spans

Lang Split Sentences BN train 9,708 dev 507 test 19,859 DE train 9,785 dev 512
test 20,145 EN train 16,778 dev 871 test 249,980 ES train 16,453 dev 854 test
246,900 FA train 16,321 dev 855 test 219,168 FR train 16,548 dev 857 test
249,786 HI train 9,632 dev 514 test 18,399 IT train 16,579 dev 858 test
247,881 PT train 16,469 dev 854 test 229,490 SV train 16,363 dev 856 test
231,190 UK train 16,429 dev 851 test 238,296 ZH train 9,759 dev 506 test
20,265 MULTI train 170,824 dev 8,895 test 358,668

Table 5: Number of sentences for each file in the dataset