Nuclear forces in the chiral limit

Abstract

We investigate the behaviour of the nuclear forces as a function of the light quark masses (or, equivalently, pion mass) in the framework of chiral effective field theory at next-to-leading order. The nucleon-nucleon force is described in terms of one and two-pion exchange and local short distance operators, which depend explicitly and implicitly on the quark masses. The pion propagator becomes Coulomb-like in the chiral limit and thus one has significant scattering in all partial waves. The pion-nucleon coupling depends implicitly on the quark masses and we find that it becomes stronger in the chiral limit. There is a further quark mass dependence in the S-wave fournucleon couplings, which can be estimated by means of dimensional analysis. We find that nuclear physics in the chiral limit becomes natural. There are no new bound states, the deuteron binding energy is B We also discuss the extrapolation to larger pion masses pertinent for the extraction of these quantities from lattice simulations.

Partially quenched nucleon-nucleon scattering

“…Given the unknown D 2 coefficients that encode the shortdistance quark-mass dependence in the S-wave channels one may question the motivation for an improved, partially-quenched simulation of the NN scattering lengths with pion masses within the NN EFT, since such simulation will, at best, simply determine the D 2 operators. It has recently been shown [23,32,49] that to leading order in the NN EFT, and assuming perfect knowledge of the single-nucleon sector, the D 2 operators determine the quark-mass dependence of the deuteron and, more generally, of dinucleon binding. Since small changes in m q can in principle lead to drastic changes in the positions of nuclear energy levels, much attention has been given to light-element abundances predicted by big-bang nucleonsynthesis and to the abundance of isotopes produced by the Oklo "natural reactor" in the hope that these abundances can be used to constrain high-energy physics [50].…”

Cosmology and the standard model

“…However, it is arguable [15,16] that the dinucleon remains unbound even in the chiral limit, in contradiction to the choice made above. But, it will turn out that in what follows we will not consider any region of parameter space where, given the parameters we have chosen, the diproton is bound, so that for us the issue is moot.…”

“…Even for the smallest universe that we shall consider, with radius 100 microns, there is good separation (a factor [10][11][12][13][14][15][16][17][18][19][20] between the electroweak scale and the strong interaction scale. Heavy quarks, electroweak gauge bosons, Higgs particles, etc.…”

“…What is important in our application is the value of (m π /m p ) for which the deuteron becomes unbound, as well as the value of (m π /m p ) for which the diproton and/or dineutron might become bound. We choose here an estimate which lies in the midrange of what is generally considered [15,16], and has the sign dictated by naive intuition; as one approaches the chiral limit, the binding energies increase. Our choices are as follows:…”

Chiral perturbation theory for electroweak reactions on deuterium

“…Calculations have shown that the NN phase shifts can be understood, and deuteron bound-state static properties reliably computed, with NN potentials derived from χPT [7,8,9,10,11]. This is now a sophisticated enterprise, with N 3 LO [O(P 4 )] potentials recently having been obtained [11,12,13]. These potentials can reproduce NN data with an accuracy which rivals that of "high-quality" NN potentials, at least for T lab < 200 MeV.…”