Naturalness (physics) - Introduction

Introduction

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:

1. the strong theta angle: see strong CP problem
2. the Higgs mass: see hierarchy problem
3. the cosmological constant: 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 dimensions, the assumption of naturalness is violated for operators which multiply field operators that create objects which are localized at different positions in the extra dimensions.