Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields

Abstract

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of m π ∼ 450 and 806 MeV in uniform, time-independent magnetic fields of strength jBj ∼ 10 19 -10 20 G to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems. DOI: 10.1103/PhysRevLett.116.112301 In most physical situations, external electromagnetic (EM) fields have only small effects on hadronic and nuclear systems, whose structure and dynamics are dominated by the internal strong interactions arising from quantum chromodynamics (QCD) and internal EM interactions. However, there are specific situations involving extremely large EM fields, created either naturally in astrophysical environments or in particle colliders, for which the effects of external fields are important. In magnetars, high magnetic field rotating neutron stars [1], surface magnetic fields are observed up to Oð10 14 Þ G (for reviews, see, e.g., Refs. [2,3]), and it is conjectured that interior magnetic fields reach up to Oð10 19 Þ G [4]. In heavy ion collisions, the currents produced by relativistic nuclei lead to large magnetic fields within the projectiles, particularly during (ultra-)peripheral collisions [5]. It is estimated that fields of Oð10 19 Þ G are experienced by the nuclei during the femtoseconds of the nuclear crossings [5]. Neither of these environments are easy to probe in a controlled way, and the detailed behavior of nuclei in such fields is an open question. As a step toward exploring nuclei in these extreme magnetic environments, we present the results of calculations of the effects of uniform, timeindependent magnetic fields on two-nucleon (as well as two-hyperon) systems performed with the underlying quark and gluon degrees of freedom. We find that such fields can potentially unbind the deuteron and significantly modify the nucleon-nucleon (NN) interactions in the 1 S 0 channel. At the unphysical quark masses where the calculations are performed, the scattering lengths in both the 3 S 1 -3 D 1 and 1 S 0 channels diverge at particular values of the field strength. Near these values, the low-energy dynamics of these systems will become unitary. The trends seen towards the physical values of the quark masses suggest that this feature may exist in nature in some of these systems. The prospect of such resonant behavior in nuclear systems is exciting and it will be important to incorporate this effect into models of magnetars and heavy ion collisions in which the relevant field strengths are probed.Before presenting the results of our calculations, it is interesting to consider phenomenological...

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