Naturalness (physics)

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.^[1]

Natural coefficients have the form

h = cΛ^{4 − d}

where d is the dimension of the operator, Λ 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 c 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 log(E / Λ).

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 at localized at different positions in the extra dimensions.^[2]

See also

• Fine tuning
• Large extra dimensions
• Split supersymmetry

References

1. ^ N. Seiberg (1993). "Naturalness versus supersymmetric non-renormalization theorems". Physics Letters B 318 (3): 469–475. arXiv:hep-ph/9309335. Bibcode 1993PhLB..318..469S. doi:10.1016/0370-2693(93)91541-T. 
2. ^ N. Arkani-Hamed, M. Schmaltz (2000). "Hierarchies without Symmetries from Extra Dimensions". Physical Review D 61 (3): 033005. arXiv:hep-ph/9903417. Bibcode 2000PhRvD..61c3005A. doi:10.1103/PhysRevD.61.033005. 

Further reading

• 't Hooft, G. (1980). "Naturalness, Chiral Symmetry and Spontaneous Chiral Symmetry Breaking". In 't Hooft, G.. Recent Developments in Gauge Theories. Plenum Press. ISBN 9780306404795. 
• 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