Naturalness (physics)
Encyclopedia
Naturalness is the property that all parameters (that are pure numbers) appearing in a theory take values of order 1 (that is, 2.34 rather than 234000). The requirement that satisfactory theories should be "natural" in this sense is a current of thought initiated around the 1960s in particle physics, and is an aesthetic criterion not always compatible with Occam's razor
, since many instances of "natural" theories have more parameters than "fine-tuned" theories such as the Standard Model.
In particle physics
, the assumption of naturalness means that, unless a more detailed explanation exists, all conceivable terms in the effective action
that preserve the required symmetries should appear in this effective action with natural coefficients.
Natural coefficients have the form
where
is the dimension of the operator, 
is the cutoff scale - an energy or length scale, the scale at which the effective field theory breaks down. The power of the cutoff is determined by dimensional analysis
. The remaining dimensionless ratio
should be a "random" number not much smaller than one, at the scale where the effective theory breaks down. Further renormalization group
running can reduce the value of c at an energy scale E, but by a small factor proportional to the
.
However, three parameters in the effective action of the standard model we know seem to have far smaller coefficients than required by naturalness. Each of these coincidences require an explanation of some sort. The three parameters are:
In addition, the coupling of the electron to the Higgs, the mass of the electron, is abnormally small, and to a lesser extent, the masses of the light quarks.
In models with large extra dimension
s, the assumption of naturalness is violated for operators which multiply field operators that create objects which are at localized at different positions in the extra dimensions.
Occam's razor
Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...
, since many instances of "natural" theories have more parameters than "fine-tuned" theories such as the Standard Model.
In particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, the assumption of naturalness means that, unless a more detailed explanation exists, all conceivable terms in the effective action
Effective action
In quantum field theory, the effective action is a modified expression for the action, which takes into account quantum-mechanical corrections, in the following sense:...
that preserve the required symmetries should appear in this effective action with natural coefficients.
Natural coefficients have the form
where
is the dimension of the operator, is the cutoff scale - an energy or length scale, the scale at which the effective field theory breaks down. The power of the cutoff is determined by dimensional analysisDimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...
. The remaining dimensionless ratio
should be a "random" number not much smaller than one, at the scale where the effective theory breaks down. Further renormalization groupRenormalization group
In theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...
running can reduce the value of c at an energy scale E, but by a small factor proportional to the
.However, three parameters in the effective action of the standard model we know seem to have far smaller coefficients than required by naturalness. Each of these coincidences require an explanation of some sort. The three parameters are:
- the strong theta angle: see strong CP problem
- the HiggsHiggs bosonThe Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
mass: see hierarchy problemHierarchy problemIn theoretical physics, a hierarchy problem occurs when the fundamental parameters of some Lagrangian are vastly different than the parameters measured by experiment. This can happen because measured parameters are related to the fundamental parameters by a prescription known as renormalization... - the cosmological constantCosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
: see cosmological constant problem
In addition, the coupling of the electron to the Higgs, the mass of the electron, is abnormally small, and to a lesser extent, the masses of the light quarks.
In models with large extra dimension
Large extra dimension
In particle physics, models with universal extra dimensions propose that there are one or more additional dimensions beyond the three spatial dimensions and one temporal dimension that are observed...
s, the assumption of naturalness is violated for operators which multiply field operators that create objects which are at localized at different positions in the extra dimensions.
Further reading
- Is "naturalness" unnatural? Invited talk presented at SUSY06: 14th International Conference On Supersymmetry And The Unification Of Fundamental Interactions 6/12/2006—6/17/2006