In
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
, the pole mass of an elementary particle is the limiting value of the
rest mass
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...
of a particle, as the energy scale of measurement increases.
[Teresa Barillari]
''Top-quark and top-quark pole mass measurements with the ATLAS detector''
arXiv, 2017
Running mass
In quantum field theory, quantities like
coupling constant
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two ...
and
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
"run" with the
energy scale
In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot aff ...
of
high energy physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and b ...
. The running mass of a fermion or massive boson depends on the energy scale at which the observation occurs, in a way described by a
renormalization group equation (RGE) and calculated by a renormalization scheme such as the
on-shell scheme or the
minimal subtraction scheme
In quantum field theory, the minimal subtraction scheme, or MS scheme, is a particular renormalization scheme used to absorb the infinities that arise in perturbative calculations beyond leading order, introduced independently by Gerard 't Hooft ...
. The running mass refers to a
Lagrangian
Lagrangian may refer to:
Mathematics
* Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier
** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...
parameter whose value changes with the energy scale at which the renormalization scheme is applied. A calculation, typically done by a computerized algorithm intractable by paper calculations, relates the running mass to the pole mass. The algorithm typically relies on a perturbative calculation of the
self energy
In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy \Sigma, and represents the contribution to the particle's energy, or Effective mass (solid-state physics), effecti ...
.
Propagator pole
A loop in a
Feynman diagram
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduc ...
requires an integral over a continuum of possible energies and momenta. In general, the integrals of products of
Feynman propagator
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. In ...
s diverge at propagator poles, and the divergences must be removed by renormalization. The process of renormalization might be thought of as a theory of cancellations of virtual particle paths, thus revealing the "bare" or renormalized physics, such as the pole mass.
See also
*
Bare mass
In quantum field theory, specifically the theory of renormalization, the bare mass of an elementary particle is the limit of its mass as the scale of distance approaches zero or, equivalently, as the energy of a particle collision approaches infin ...
*
Landau pole
In physics, the Landau pole (or the Moscow zero, or the Landau ghost) is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite. Such a possibility was pointed out by the ph ...
References
Quantum field theory
Renormalization group
{{quantum-stub