Octet baryons in large magnetic fields

Abstract

Magnetic properties of octet baryons are investigated within the framework of chiral perturbation theory. Utilizing a power counting for large magnetic fields, the Landau levels of charged mesons are treated exactly giving rise to baryon energies that depend nonanalytically on the strength of the magnetic field. In the small-field limit, baryon magnetic moments and polarizabilities emerge from the calculated energies. We argue that the magnetic polarizabilities of hyperons provide a testing ground for potentially large contributions from decuplet pole diagrams. In external magnetic fields, such contributions manifest themselves through decuplet-octet mixing, for which possible results are compared in a few scenarios. These scenarios can be tested with lattice QCD calculations of the octet baryon energies in magnetic fields.

Charged pion masses under strong magnetic fields in the NJL model

“…(86) one gets µ p > 0 and µ n < 0, as expected from phenomenology. In addition, the fact that the curves show negative slopes at B = 0 is consistent with the results fromChPT quoted in Ref [37]…”

“…Regarding the study of other hadrons, in the last few years some works have analyzed the effects of a magnetic field on baryon masses. This problem has been addressed in the context of ChPT [36,37], nonrelativistic quark models [38], extended linear sigma model [39], Walecka model [39,40], soliton models [41], Finite Energy QCD sum rules [42], and also lattice QCD [43]. It is worth noticing that these theoretical approaches lead to various different results for the behavior of nucleon masses.…”

Energy of a point-like neutron in an external electromagnetic field

“…It remains to treat the operator p 4 . Multiplying the form (46) for the operator p 2 by another factor p 2 from the left, one may discard the majority of the terms because they only contribute at orders that are dropped in the expansion pursued here. The remaining relevant terms are…”

“…( 44) with an extra p n applied from the left; i.e., the expression for p 2 obtained here, acting on a |v 2 = 0 state, differs from the one obtained when acting on a |v = 0 state, cf. (46), by the two additional terms in (63). For the discussion in the next section, it is useful to observe that these additional terms can also be cast as follows,…”

“…Chiral Effective Theory serves to connect such lattice data, which are obtained at heavier-than-physical pion masses on finite volumes, to the physical limit [4,[41][42][43]. In the case of magnetic fields, care must be taken to disentangle the mass shift from the Landau level structure [38][39][40]44], and effects beyond linear response may contaminate the analysis [45,46]. The subtleties involved in matching the background field calculations performed in Lattice QCD to the Effective Field Theory description of scattering amplitudes were examined in detail in [47,48].…”