Abstract
We determine the light meson spectrum in QCD in the presence of background magnetic fields using quenched Wilson fermions. Our continuum extrapolated results indicate a monotonous reduction of the connected neutral pion mass as the magnetic field grows. The vector meson mass is found to remain nonzero, a finding relevant for the conjectured $\rho$-meson condensation at strong magnetic fields. The continuum extrapolation was facilitated by adding a novel magnetic field-dependent improvement term to the additive quark mass renormalization. Without this term, sizable lattice artifacts that would deceptively indicate an unphysical rise of the connected neutral pion mass for strong magnetic fields are present. We also investigate the impact of these lattice artifacts on further observables like magnetic polarizabilities and discuss the magnetic field-induced mixing between $\rho$-mesons and pions. We also derive Ward-Takashi identities for QCD+QED both in the continuum formulation and for (order $a$-improved) Wilson fermions.
Highlights
Background magnetic fields have a decisive impact on the physics of quarks and gluons and offer a wide range of applications
The results indicate that gρþ is close to the free-case value g 1⁄4 2, which is in qualitative agreement with previous lattice computations [68,69,70] and findings in chiral perturbation theory [71]
It has been found that the polarizability becomes negative for physical quark masses, which disagrees with expectations from chiral perturbation theory [72,73,74]
Summary
Background magnetic fields have a decisive impact on the physics of quarks and gluons and offer a wide range of applications. Pions are expected to be dominant in this respect It is well known from chiral perturbation theory [13] that charged and neutral pions respond oppositely to the magnetic field B 1⁄4 jBj. While lattice results employing staggered [9] and quenched unimproved Wilson [14] quarks agree that the charged pion mass mπÆ is increased by the presence of a magnetic field, there is a discrepancy in the literature about mπ0ðBÞ for intermediate magnetic fields. [21] and discuss the improvement of scaling toward the continuum limit via the B-dependent additive mass renormalization in more detail Performing this improvement reveals that the neutral pion mass monotonously decreases as B grows and, resolves the existing disagreement between the quenched Wilson and overlap formulations. Three Appendixes contain our results in the free case (Appendix A), the derivation of Ward-Takahashi identities for nonzero electromagnetic fields (Appendix B), and a perturbative check of the B-independence of the multiplicative mass renormalization constant in QCD (Appendix C)
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