8.8.2.1. Mass

Table of Contents

Meaning of Quark Mass

Mass is one of the basic properties used to describe a quark. It tells us how much inertia the quark has, and it also enters the energy of the particle through relativity. In particle physics, mass is usually given in energy units such as electron volts, especially megaelectron volts, MeV, or gigaelectron volts, GeV, using the relation $E = mc^2$.

For quarks, mass is more subtle than it is for ordinary everyday objects. Quarks are never observed in isolation because of confinement, so their masses are not measured by putting a single quark on a scale. Instead, quark masses are inferred from the behavior and properties of hadrons, the particles made from quarks.

Quark mass is not measured directly for a free quark, because free quarks are not observed. It is inferred indirectly from experiments and theory.

Units Used for Quark Mass

In high energy physics, it is common to write mass in units of $\text{eV}/c^2$, but very often physicists set $c = 1$, so mass is written simply in eV, MeV, or GeV. For example, instead of writing

$$m_u \approx 2.2 \,\text{MeV}/c^2,$$

physicists often write

$$m_u \approx 2.2 \,\text{MeV}.$$

This is a shorthand based on natural units.

Light and Heavy Quarks

The six quark flavors have very different masses. The up, down, and strange quarks are much lighter than the charm, bottom, and top quarks. This difference strongly affects the hadrons they can form and the energy scales involved in their interactions.

A useful approximate table is:

Quark	Symbol	Approximate mass
Up	$u$	$2.2\ \text{MeV}$
Down	$d$	$4.7\ \text{MeV}$
Strange	$s$	$96\ \text{MeV}$
Charm	$c$	$1.27\ \text{GeV}$
Bottom	$b$	$4.18\ \text{GeV}$
Top	$t$	$173\ \text{GeV}$

These values are approximate and depend somewhat on the exact definition used in theory.

The top quark is by far the heaviest quark. The up and down quarks are the lightest quarks and are the main constituents of ordinary matter.

Quark Mass and Hadron Mass

A very important beginner idea is that the mass of a hadron is not usually just the simple sum of the masses of its quarks. For example, a proton is made of two up quarks and one down quark, but

$$m_p \neq 2m_u + m_d$$

in any simple direct sense.

If we use approximate quark masses,

$$2m_u + m_d \approx 2(2.2) + 4.7 = 9.1\ \text{MeV},$$

but the proton mass is about

$$938\ \text{MeV}.$$

So most of the proton's mass does not come from the small masses of its quarks alone. A large part comes from the energy of quark motion and the strong interaction fields inside the proton.

This is one of the striking ideas of modern particle physics. Energy inside a bound system contributes to its total mass.

For hadrons such as the proton and neutron, most of the mass comes from strong interaction energy, not just from adding the quark masses.

Current Mass and Effective Mass Ideas

When physicists discuss quark mass, they may mean different things depending on context. A common idea is the quark's intrinsic or bare like mass parameter used in the theory, often called the current quark mass. In models of hadrons, one also encounters larger effective masses, sometimes called constituent quark masses, which include effects of the surrounding strong interaction environment.

For beginners, the key point is simple. A quark inside a hadron does not behave like an isolated little ball with a fixed easily measured mass. The strong interaction changes how mass appears in calculations and models.

A rough comparison is:

Type of mass idea	Meaning
Current quark mass	Fundamental mass parameter used in the underlying theory
Constituent quark mass	Effective mass used in simple hadron models

For example, in simple constituent models, an up or down quark may be assigned a mass of a few hundred MeV, much larger than its current mass of only a few MeV.

Why the Top Quark Is Special

The top quark is unusual because it is extremely heavy. Its mass is much larger than that of the other quarks. It also decays so quickly that it does not form ordinary hadrons in the same way lighter quarks do. This makes it a special case in particle physics.

Its very large mass means it plays an important role in testing theoretical ideas about how particles get mass.

Visual Comparison of Quark Masses

Rendering scientific sketch…

Approximate quark mass hierarchy

Mass and Energy

Because relativity connects mass and energy, a quark's mass contributes to the total energy of a system. For a particle at rest,

$$E_0 = mc^2.$$

For moving particles, the total energy is related to mass and momentum by

$$E^2 = p^2c^2 + m^2c^4.$$

In natural units, this becomes

$$E^2 = p^2 + m^2.$$

This relation is especially useful in particle physics, where quarks are produced and studied in high energy collisions.

In relativity, mass is one contribution to energy. For quarks inside hadrons, kinetic energy and strong interaction energy are also essential parts of the total mass of the hadron.

Summary

Quark mass is a fundamental property, but it is not as simple as the mass of a familiar macroscopic object. Quarks have very different masses depending on flavor, ranging from a few MeV for the lightest quarks to about $173\ \text{GeV}$ for the top quark. Because quarks are confined, their masses are inferred indirectly. Also, the mass of a hadron is not just the sum of the masses of its quarks, since much of it comes from the energy of the strong interaction inside the hadron.

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