The determination of the range of values for the mass of an up quark, or any other fundamental particle, is primarily based on experimental measurements and theoretical calculations within the framework of particle physics.
Experimental measurements: Scientists use a variety of experimental techniques to probe the properties of particles, including quarks. For determining the mass of a quark, experiments typically involve colliding particles at high energies and studying the resulting particle interactions. By analyzing the patterns and energies of the particles produced in these collisions, scientists can extract information about the masses of the quarks involved.
One of the key experimental tools used for such measurements is particle accelerators like the Large Hadron Collider (LHC). These accelerators can produce collisions with sufficiently high energies to create and study quarks directly or indirectly. By measuring the energies and momenta of the particles produced in these collisions, scientists can infer the masses of the quarks involved.
Theoretical calculations: In addition to experimental measurements, theoretical calculations based on quantum field theory, specifically quantum chromodynamics (QCD), are used to study the properties of quarks. QCD is the theory that describes the strong nuclear force and the interactions of quarks and gluons.
Through theoretical calculations, physicists can analyze the behavior of quarks within the framework of QCD and make predictions about their masses. These calculations involve complex mathematical equations and computational techniques. However, due to the inherent complexities of QCD, precise calculations of quark masses from first principles are challenging. Therefore, calculations often rely on approximations and numerical simulations using supercomputers.
Combining experimental measurements with theoretical calculations: To determine the range of values for the mass of an up quark, experimental measurements and theoretical calculations are combined. Experimental data provide constraints on the possible values, and theoretical calculations refine the understanding of the underlying physics and help interpret the experimental results.
It's worth noting that determining precise masses for quarks is inherently challenging due to their confinement within particles and the complexities of the strong force. Quark masses are typically reported as ranges or uncertainties to account for the limitations in the measurements and calculations. These ranges are continually refined as experimental techniques improve and theoretical understanding advances.