Est-ce bien naturel de demander à une théorie physique d'être ... naturelle ?

Rubrique dévissage 

Vous avez dit naturel ?

Le billet précédent exposait deux critiques de la pertinence du concept de naturalité pour l'élaboration de théories physiques plus fondamentales. Celui-ci évoquera au contraire quelques éléments d'une argumentation très précise en faveur de ce concept par James D. Wells, un physicien qui a beaucoup réfléchi sur cette question récemment. Commençons par le début avec une définition qui distingue deux aspects du concept de naturalité :

Formulating the question of whether Naturalness is a useful concept suffers from imprecision if we do not define the term explicitly, yet broadly enough to capture all its needed usage. Let us begin with what we call Absolute Naturalness. A theory has Absolute Naturalness if all dimensionless parameters and the ratio of any dimensionful parameters have explanation in terms of O(1) parameters. A parameter possesses Absolute Naturalness with respect to the rest of the theory if it can be explained by O(1) parameters. There can be difference of opinion about the precise range of values O(1) implies, but when it is helpful to think precisely about the value let us say O(1), or its inverse, can be as low as 10⁻³. An example of a parameter that is Absolutely Natural is Λ_QCD in quantum chromodynamics. Λ_QCD∼1GeV is Natural in this sense despite it being eighteen orders of magnitude smaller than the Planck scale (M_Pl∼10¹⁸GeV) because it can be explained by an O(1) parameter (strong coupling constant) near M_Pl, which upon renormalization group flow to the infrared diverges at E∼Λ_QCD. [...]

There is another notion of Naturalness that has been articulated from at least the early 1980’s, which is called Technical Naturalness, or sometimes ‘t Hooft Naturalness (‘t Hooft 1980). A theory has Technical Naturalness even if some parameters are small, if an enhanced symmetry develops when the small parameter is taken to zero. For example, a very light fermion mass is Technically Natural since an enhanced chiral symmetry emergences when the mass is taken to zero. In quantum field theory this protects the small parameter from any large quantum correction, and the small value is technically stable.

James D. Wells, The Utility of Naturalness, and how its Application to Quantum Electrodynamics envisages the Standard Model and Higgs Boson, 15/05/13

Mais c'est bien naturel !
On poursuit ici avec une illustration de l'efficacité du concept de naturalité au sens technique du terme tirée d'un exemple historiquement reconnu.

Assuming Naturalness as a law of nature imposes very strong constraints on model building. In the case of the Higgs boson, it leads not only to ideas like supersymmetry, which protects the Higgs boson from having a large mass, but the devotion one has to strict Naturalness leads to radically different hypothesized superpartner spectra.

In the past, Technical Naturalness has been used to understand experimental results that have already been measured. [...]

For example, the masses of the pions, proton and neutron are understood well from symmetries and Technical Naturalness. We know from asymptotic freedom of quantum chromodynamics (QCD) that the perturbative gauge coupling in the ultraviolet flows to strong value at the low scale and confinement happens at Λ_QCD∼1 GeV. This gives the characteristic scale of the hadrons in the theory, and the proton and neutron obtain mass approximately equal to this scale. However, the pion masses are much lower, and can be understood as the Goldstone bosons of SU(2)_L×SU(2)_R → SU(2)_V flavor symmetry breaking. The mass is exactly zero when there are no explicit quark masses in the theory, and this “hierarchy” is very well understood. Furthermore, few are distressed that the proton mass mp ∼ 1 GeV is much less than the Planck mass M_Pl∼10¹⁹ GeV = (G_N)^-1/2. The reason is as stated earlier: an O(1) number, namely the QCD gauge coupling, is an input at some high scale that through renormalization group flow generates an exponentially suppressed scale through dimensional transmutation. This is not concerning because no very big or very small numbers were needed as input. In other words, there is an explanatory theory that possesses Absolute Naturalness.

id. 

(Aurait-on pu) aller au delà de l'électrodynamique quantique en cherchant à expliquer pourquoi la masse de l'électron est naturellement faible ?

Voilà maintenant une présentation plus audacieuse du pouvoir heuristique de la naturalité à travers une réflexion épistémologique originale sur l'électrodynamique quantique vue dans le cadre plus général du Modèle Standard.

I will outline a series of Realistic Intellectual Leaps (RILs) that I think would be achieved in short order, and were ripe to do so at the time, if only researchers were committed to Naturalness and were unwaveringly tenacious at trying to explain the smallness of the electron mass. [...] the argument here is not reliant on historical analysis, but of conceptual inevitabilities once Naturalness is declared a primary goal. [...] Let us begin with the first RIL that would set it all in motion.

RIL #1: The value of m_e is closer to zero than it is to M_Fermi.

On the surface this may look like a strange statement, but we hear such statements frequently in many different contexts, and they have been part of physics discussions time immemorial. From the earliest days of Newtonian mechanics when considering orbits of “massless” planets, to present day collider physics where b quark is “massless” in comparison to the characteristic energies of the collisions, researchers have realized that for all practical purposes objects sometimes have a mass “closer to zero” than the other characteristic scales or masses of the problem. [...] Inspection of the Quantum Electro-Dynamics (QED) lagrangian tells us immediately that the problem is the existence of the gauge-invariant and Lorentz invariant operator . This mass operator is dimension three and so to round out the dimensions to four one needs a massive coupling, which Absolute Naturalness demands should be similar to M_Fermi. A reasonable starting path is to somehow recast the theory to make ψψ not an invariant, in the spirit of recognizing that m_e is “closer to zero than it is to M_Fermi.” If adherence to Absolute Naturalness is our primary concern, no ugliness or complexity should stop us from finding a way to banish this offending operator ψψ . In time it would be inevitable that theorists would recognize that there is something special about that operator compared to others. This leads to the next RIL.

RIL #2: The representation structure of the Lorentz group allows us to write QED in two-component spinors, which is seen to demonstrate a qualitatively unique feature to the mass operator.

We see that the mass term mixes the right and left handed components of the spinor, whereas the kinetic term and gauge interactions do not. [...]Thus, there is a qualitative difference in the Lorentz structure of the mass term compared to the kinetic and gauge potential interaction terms. Now that we have established this unique Lorentz structure of the mass term, the next leap is to recognize that the ψψ term can now be banished.  

RIL #3: The electron mass can be forbidden by assigning ψ_L different properties than ψ_R, thereby disallowing  ψ^†_Lψ_R + ψ^†_Rψ_L as an invariant of the theory.  

The first thought would be to give ψ_L and ψ_R different electric charge, but that violates experiment badly since there are not two different electric charges to be seen. The electric charge for both we must keep at -1, but we can assign different charges for each under a new symmetry G. [...] 

The principle of Naturalness cannot be derived from first principles, and its invocation in science is more of a product of intuition against the likelihood of large numbers conspiring together to give small numbers than it is on rigorous deduction. Nevertheless, the concept bears fruit and is satisfied with respect to our QED example here and other examples to be found in the literature. It remains to be seen if the hard pursuit of Naturalness for the Higgs boson sector has correctly predicted new physics, yet to be seen, that is near the Higgs boson mass scale.

 id.