Abstract
We compute the neutral pion mass dependence on a magnetic field in the weak field approximation at one-loop order. The calculation is carried out within the linear sigma model coupled to quarks and using Schwinger's proper-time representation for the charged particle propagators. We find that the neutral pion mass decreases with the field strength provided the boson self-coupling magnetic field corrections are also included. The calculation should be regarded as the setting of the trend for the neutral pion mass as the magnetic field is turned on.
Highlights
Magnetic fields are involved in the properties of a large variety of physical systems including heavy-ion collisions [1,2], the interior of compact astrophysical objects [3,4,5] and even the early universe [6,7,8]
The calculation is carried out within the linear sigma model coupled to quarks and using Schwinger’s proper-time representation for the charged particle propagators
We find that the neutral pion mass decreases with the field strength provided the boson self-coupling magnetic field corrections are included
Summary
Magnetic fields are involved in the properties of a large variety of physical systems including heavy-ion collisions [1,2], the interior of compact astrophysical objects [3,4,5] and even the early universe [6,7,8]. It has been estimated that the magnetic field strength jeBj in peripheral heavy-ion collisions reaches values equivalent to a few times the pion mass squared, both at RHIC and at the LHC [9] The effects of such magnetic fields cannot be overlooked in a complete description of these systems and its understanding contributes, at a fundamental level, to a better characterization of the properties of QCD matter [10,11,12,13,14,15,16,17,18]. We leave for the appendices the explicit calculations of the various quantities involved
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