VOLUME PHY, NUMBER 3903
PHYSICAL REVIEW LETTERS
14 NOVEMBER 2003
Quantum Chromodynamical Explanation of the Strong Nuclear Force
Jakub Cieniak, #2587463
Physics Department, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario, Canada K1N 6N5
(Received 14 November 2003)
The Strong Nuclear Force was proposed to explain the unintuitive attraction between
protons and neutrons within an atomic nucleus, despite the relatively immense repulsion
of the electromagnetic force overshadowing the attraction between the particles due to
gravitation. It is responsible for binding quarks, the building blocks of sub-atomic
particles like protons and neutrons, via a process governed by Quantum Chromodynamics
involving the exchange of colour-charged particles called gluons. Particles constituting
bound pairs of quarks, called mesons, are exchanged between the sub-atomic particles at
short distances to hold protons and neutrons together within the nucleus. These processes
will be explained in this paper in detail and different theories on the origin of the force
will be examined, including an explanation using the Gravitational Field Theory
proposing that the Strong Nuclear Force is nothing more than the Force of Gravity. The
properties of quarks and gluons will also be examined to aid in the explanation of the
interactions between them that create the Strong Nuclear Force.
PACS number(s): 12.38.Mh, 24.85.+p, 12.39.Ki, 13.60.Hb
The reason atoms heavier than
Hydrogen exist, despite the relatively
large repulsive Coulomb force between
protons at such close proximity as within
the nucleus of an atom, is a residual
effect of the Strong Nuclear Force, or
Strong Interaction [1] between the
fundamental building blocks of protons,
neutrons and other hadrons: quarks.
Quarks, at present, are considered the
fundamental particles in physics along
with leptons (electrons, muons, taus,
neutrinos and their respective antiparticles) (see Figure 1) as it cannot be
determined of what, if anything, these
particles are composed. Leptons,
however, lack colour-charge and hence
do not participate in Strong Interaction,
which is defined by the exchange of
colour-charge carriers called gluons as
explained by the Theory of Quantum
Chromodynamics (QCD) [2]. QCD
explains the interactions necessary to
keep particles, like nucleons within an
atom, from breaking apart into their
constituents, the quarks, and provides an
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explanation for the ability of protons to
overcome the repulsive forces between
them when part of an atomic nucleus.
There are six different types, or
flavours, of quarks as shown in Figure 1
and some of their properties are
described in Table I. Quarks will
combine [1]: in pairs (e.g. gluons, pions,
kaons) to form bosonic hadrons, or
mesons (see Table II); in triplets (e.g.
protons, neutrons) to form Fermionic
hadrons, or baryons (see Table III); and
even quintets (e.g. the recently
Figure 1. The Fundamental Particles
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VOLUME PHY, NUMBER 3903
PHYSICAL REVIEW LETTERS
14 NOVEMBER 2003
discovered Θ+ baryon [3]). (Bosons are
carrier particles of interactions with
integer units of quantum angular
momentum, or spin, and Fermions have
odd half units of spin and obey the Pauli
Exclusion
Principle.)
These
combinations are governed by a property
of the quarks called the colour-charge.
A quark can possess one of three
colours, for example red, green and blue.
Antiquarks possess the corresponding
anti-colours. (These colours are merely a
means of describing a characteristic of
the quarks and are in no way related to
any visual aspect of the quarks.) Similar
to electric charge, like colours repel and
unlike colours attract; a quark of a
certain colour will feel an especially
strong attraction to an antiquark of the
corresponding anti-colour. Observable
particles can only exist if their net colour
is neutral: a combination of a colour
with its anti-colour (creating a meson);
or a combination of each of the three
colours or each of the three anti-colours
(creating a baryon). Within a baryon or
meson (each a subset of particles called
hadrons), interactions between quarks
[2] occur by exchanging particles called
gluons carrying one colour charge and
one anti-colour charge. As per QCD, the
net change in colour-charge for such an
interaction must be zero; that is, colourcharge is conserved. For example, a
green quark interacts with a blue quark
within a baryon by emitting a gluon
carrying green and anti-blue colourcharges; this leaves the formerly green
quark with a blue colour-charge and
converts the blue quark into a green one.
The net colour-charge is conserved as
the process results in one green and one
blue quark, just as before the interaction.
In a meson composed of a red quark and
an anti-red antiquark, for example, the
red quark can turn into a green quark by
emitting a gluon carrying red and antigreen colour-charges that the anti-red
antiquark will absorb turning it into an
anti-green antiquark. Again, colourcharge is conserved as a colour-neutral
meson is obtained. The flavour of a
quark is one characteristic that can never
be changed by an exchange of gluons
between two quarks.
This interaction between quarks in a
hadron is very similar to the interaction
known as the Strong Nuclear Force, or
what is called the Residual Strong
Interaction. This force is responsible for
keeping protons and neutrons together
within an atomic nucleus; the minor
difference between the two forces is the
Table II. Some Bosonic Hadrons (Mesons) [1]
Table III. Some Fermionic Hadrons (Baryons) [1]
Table I. The Different Flavours of Quarks [1]
Flavour
up (u)
down (d)
strange (s)
charm (c)
bottom (b)
top (t)
Mass
(Gev/c2)
0.004
0.008
0.15
1.5
4.7
176
Electronic
Charge
+2/3
-1/3
-1/3
+2/3
-1/3
+2/3
Quark Electronic Mass
Name
Content Charge (GeV/c2) Spin
pion, π+
ud+1
0.140
0
+
kaon, K
su
-1
0.494
0
rho, ρ+
ud+1
0.770
1
eta-c, ηc
cc0
2.979
0
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Quark Electronic Mass
Name
Content Charge (GeV/c2) Spin
proton, p
uud
+1
0.938 1/2
neutron, n udd
0
0.940 1/2
lambda, Λ uds
0
1.116 1/2
omega, Ω- sss
-1
1.672 3/2
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VOLUME PHY, NUMBER 3903
PHYSICAL REVIEW LETTERS
Figure 2. Multi-Jet Hadronic Event [1] showing
Three Distinct Localized Hadronic Jets
scale. The participants of the Strong
Nuclear Force are the composite
particles of quarks, the nucleons. The
force between the nucleons is created by
the exchange of particles carrying
colour-charges, like the exchange of
gluons between quarks. These particles
are in fact the mesons, e.g. pions, kaons.
If the nucleons are close enough that
their boundaries actually overlap, the
Strong Interaction can occur between
quarks of different hadrons.
One major difference between the
strong nuclear force and the other
fundamental forces of nature is that the
force between two interacting quarks
increases with increasing separation
distance between the quarks. Additional
energy is needed to increase the force,
and if the quarks are separated far
enough, there is enough energy to create
new quarks that will group with the
separating ones, thereby creating more
hadrons. This phenomenon, also known
as confinement, is the reason for not
being able to observe quarks directly, on
their own, outside of a hadron.
Conversely, when quarks are very close
to each other, it is presumed that the
force between them becomes nonexistent, thereby making the quarks
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14 NOVEMBER 2003
‘free’ particles. This condition is known
as asymptotic freedom. However, recent
experiments at CERN [4] have brought
about a notion of a quark-gluon plasma
(QGP) phase consisting of quarks and
gluons that are essentially ‘free’ particles
not confined to the structure of a hadron.
The plasma is formed from hot, dense
nuclear matter that is subjected to
relativistic collisions. Tests still need to
be performed to analyze the new matter
phase and confirm that it is indeed
composed of these fundamental particles
in the ‘free’ state.
High-energy hadronic collisions are
also studied to examine particular effects
of the confinement phenomenon of QCD
called Multi-Jet Hadronic Events [1].
When hadrons collide with enough
energy such that their confined quarks
are forced to separate, the unconfined
quarks can sometimes radiate one last
gluon of high energy before new quarks
and antiquarks are formed to create
hadrons. This unconfined gluon will
result in the production of a stream, or
jet, of hadrons in order to decrease the
energy of the unmatched quarks and
antiquarks. This process can in fact
result in multiple localized jets as can be
seen in Figure 1. Many of these events
can be examined to determine the
average angle at which the jets occur
with respect to the axes perpendicular to
the axis of the collision of the hadrons.
Specifically, experiments are being
performed at CERN to study the
collisions between gold nuclei, for
example.
One property of the quarks that QCD
cannot explain is their mass. There is a
proposition that suggests a simple
mechanism called the Higgs mechanism
that accounts for the mass of the
fundamental particles. The proposal
involves the exchange of a particle
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VOLUME PHY, NUMBER 3903
PHYSICAL REVIEW LETTERS
called the Higgs boson as part of a new
fundamental force, the Higgs force. This
particle, however, has yet to be
discovered.
A completely different explanation
for the ability of protons to overcome the
Coulombic force repelling them from
each other within the nucleus of an atom
is proposed by Kenneth F. Wright.
Wright suggests [5] that it can be proven
using quantum mechanics, Newton’s
Law of Gravity and Einstein’s Theory of
General Relativity that the strong
nuclear force and the force of gravity are
actually the same force. To summarize,
Wright relates the energy of the force
produced by an electric field of a proton
with the energy of a photon and, using
the equation for the energy of a photon,
E = hc/λ, he associates a particular
wavelength with the proton’s electric
field. Wright likens the energy levels of
the protons within an atomic nucleus
with that of gamma- and X-rays as both
are on the order of MeV. Since the
wavelengths of gamma- and X-rays are
on the order of 10-13 to 10-12 meters, 10
to 1000 times greater than the diameters
of atomic nuclei, the nuclei are
‘invisible’ to the incoming rays. Wright
claims that this same analysis can be
related to the ‘wavelength’ of the electric
fields of protons and that at such small
distances as those within a nucleus, the
electrostatic repulsion force becomes
invisible to the protons. Consequently,
the force of gravity takes over as the
reigning force acting between the
nucleons when within the boundary of
the nucleus. One problem with this
hypothesis is that the energy state of a
proton confined to an atomic nucleus is
unrelated to the potential energy created
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14 NOVEMBER 2003
by the electric field acting between two
protons.
Consequently,
Wright
associates a static energy value for the
potential between the two interacting
protons when, in fact, the energy is
dependent on the distance between the
protons and increases as they approach
each other. Using Wright’s analogy, the
‘wavelength’ of the electrostatic force
field would decrease proportionally as
the two protons approached each other to
within nuclear distances; hence, the
electrostatic force would not vanish as
he suggests.
Quantum
chromodynamics
has
provided a sound theory that is gaining
more and more supporting evidence
from
experiments.
The
recent
developments in the Quark-Gluon
Plasma matter phase still leave questions
to be answered; fortunately, procedures
are underway at laboratories like CERN
that will hopefully shed some light on
this new discovery.
[1] Theory: SLAC Virtual Visitor Center,
www2.slac.standford.edu/vvc/theory.html
and webpages therein; last accessed 13
November 2003.
[2] Encyclopedia: Strong nuclear force, www.
nationmaster.com/encyclopedia/strongnuclear-force; last accessed 2 October 2003.
[3] B. Schwarzschild, Four Experiments Give
Evidence of an Exotic Baryon With Five
Quarks, www.physicstoday.org/vol-56/iss-9/
p19.html; last accessed 2 October 2003.
[4] S. Hamieh, J. Letessier, and J. Rafelski,
Phys. Rev. C 62, 064901 (2000).
[5] K. F. Wright, Nuclear Gravitation Field
Theory, Chapter VIII: Nuclear Gravitation
Field Theory Versus Accepted Strong
Nuclear
Force
Overcoming
Proton
Electrostatic Repulsion, www.gravitywarp
drive.com/NGFT_Chapter_8.htm;
last
accessed 13 November 2003.
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