Unnuclear physics

Abstract

We investigate a nonrelativistic version of Georgi's "unparticle physics." We define the unnucleus as a field in a nonrelativistic conformal field theory. Such a field is characterized by a mass and a conformal dimension. We then consider the formal problem of scatterings to a final state consisting of a particle and an unnucleus and show that the differential cross section, as a function of the recoil energy received by the particle, has a power-law singularity near the maximal recoil energy, where the power is determined by the conformal dimension of the unnucleus. We argue that unlike the relativistic unparticle, which remains a hypothetical object, the unnucleus is realized, to a good approximation, in nuclear reactions involving emission of a few neutrons, when the energy of the final-state neutrons in their center-of-mass frame lies in the range between about 0.1 MeV and 5 MeV. Combining this observation with the known universal properties of fermions at unitarity in a harmonic trap, we predict a power-law behavior of an inclusive cross section in this kinematic regime. We compare our predictions with previous effective field theory and model calculations of the 6 He(p, pα)2n, 3 H(π − , γ)3n, and 3 H(µ − , ν µ )3n reactions and find excellent agreement.

General Freeze-in and Freeze-out

“…As in the relativistic unparticle case the phase space of non-relativistic initial particles is determined by conformal invariance, see [32] for a recent discussion in the context of nuclear physics.…”

“…In order to derive an explicit formula for the (imaginary part of the) amplitude more details about the theory have to be known. If the interaction can be parametrized in the form of effective operators as in [32], suppressed by some UV scale, the discussion would be in principle similar to the previous section. The 2-point function of scalar operators of NR CFTs is fixed to be,…”

From Nuclear to Unnuclear Physics

“…This phenomenon is well known in statistical mechanics, where in the vicinity of a second order phase transition the correlation length diverges, and fluctuations occur on all length scales. Correlation functions, for example the probability that a local density fluctuation in a fluid is correlated with a similar fluctuation separated by a spatial distance x, decay as a fractional 1 An essential feature of nuclear physics is the large separation of scales between the small binding energy of nuclei, typically a few MeV, and the large rest mass energy of the nucleon, about 940 MeV. An effective theory that exploits this separation of scales, constructed by Steven Weinberg in 1990 [3], treats nucleons as point-like nonrelativistic spin 1/2 particles.…”

“…Nuclear physics studies the stability, structure, and reactions of atomic nuclei, as well as the phase structure and properties of dense, strongly interacting matter. While nuclear reactions are exceedingly complicated, remarkably Hammer and Son [1] have discovered a low energy regime -which they call unnuclear physics -where certain nuclear reactions obey simple scaling rules, related to a new, emergent scaling symmetry of the nuclear force.…”

Interpretation of neutral charm mesons near threshold as unparticles

“…Hammer and Son recently pointed out that unparticles can also arise in nonrelativistic physics [8]. The nonrelativistic conformal symmetry group (also called the Schrödinger group) on 3+1-dimensional Galilean spacetime is a 13-dimensional group that includes the Galilean group and scale transformations as subgroups.…”