論文の公開元へLattice study of the trace anomaly contribution to glueball mass using renormalized energy-momentum tensor
概要
It is a fundamental question: what is the origin of mass? For nucleon mass, which
has decisive contributions to the visible mass in the Universe, there are two known mechanisms to account for its emergence. One is the Higgs mechanism [1, 2, 3] that gives
mass to elementary particles and thus quarks acquire their mass called “current quark
mass” through this particular mechanism. However, in quark models, where the nucleon
is simply described as a composite particle of three quarks, the sum of three quark masses
explains only about 1% of the nucleon mass. It implies that most of the nucleon mass
is generated by another mechanism, the Nambu mechanism, where quarks in hadron acquire much heavier masses than the current quark masses for the light flavors (up, down
and strange) through the spontaneous and dynamical breaking of chiral symmetry as described in the Nambu-Jona-Lasinio (NJL) model [4, 5]. In this model, the “constituent
quark mass” is dynamically generated by quark-antiquark condensation and then accounts
for about 99% of the nucleon mass.
Although both mechanisms share a focus on the quark component of the nucleon,
Quantum Chromodynamics (QCD), which is the fundamental theory of strong interaction, describes that the nucleon is composed of both quarks and gluons. There should
be some contributions from gluons to the nucleon mass. In fact, there are experimental implications that about half of the momentum of nucleons is carried by gluons [6].
This indicates that a deeper understanding of gluon properties in hadrons provides further
understanding of mass generation for hadrons including the nucleon.
Let us consider how to evaluate the gluon contributions to the hadron masses from
the first-principle calculation of QCD. Since QCD is a non-Abelian gauge theory with
SU(3) gauge group, it has the characteristic property of asymptotic freedom due to the
gluon self-interaction. Therefore, the gauge coupling constant becomes smaller at higher
energy scale, while it stays large or strong in the low-energy region. Because of this
property, perturbative calculations are not applicable in the low-energy region. Therefore
a non-perturbative approach is required to study the low-energy physics of QCD. Lattice
QCD approach, which numerically evaluates the path integral of QCD in 4-dimensional
discretized Euclidean space-time, is the only method that allows us to treat QCD at low
energies.
In 1995, X. Ji proposed the interesting idea that the nucleon mass can be decomposed
in terms of contributions from gluons and quarks, based on the traceful and traceless parts
of the energy-momentum tensor (EMT) operator [7]. Since this idea can be applied to any
hadron state, lattice studies of the hadron mass decomposition have been recently carried
out for both mesons [8] and baryons [9]. According to Ref. [9] the trace anomaly contributions which include the quantum anomalies of both quark and gluon become dominant
on the nucleon mass in the chiral limit. However, further systematic studies are necessary
to solely measure the gluon contribution in the trace anomaly.
Here, it is worth recalling that since gluons carry color charges and then interact themselves, the existence of composite states consisting solely of gluons, called glueballs, is
one of the most important predictions of QCD. Since there is still no indisputable experimental evidence for their existence, lattice QCD plays an essential role to study the
physics of glueballs. ...
