Magnetic Corrections to $\pi$-$\pi$ Scattering Lengths in the Linear Sigma Model

Abstract

In this article we consider the magnetic corrections to $\pi$-$\pi$ scattering lengths in the frame of the linear sigma model. For this we consider all the one loop corrections in the s, t and u channels, associate to the insertion of a Schwinger propagator for charged pions, working in the region of small values of the magnetic field. Our calculation relies on an appropriate expansion for the propagator. It turns out that the leading scattering length, $l=0$ in the S-channel, increases for an increasing value of the magnetic field, in the isospin $I=2$ case whereas the opposite effect is found for the $I=0$ case. The isospin symmetry is valid because the insertion of the magnetic field occurs through the absolute value of the electric charges. The channel $I=1$ does not receive any corrections. These results, for the channels $I=0$ and $I=2$ are opposite with respect to the thermal corrections found previously in the literature.

arXiv comment6 pages. arXiv admin note: text overlap with arXiv:0801.2176; new references were added; to appear in Phys. Rev. D

References in corpus (16)

• Experimental evidence for a light and broad scalar resonance in $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decay
• The three-flavor chiral phase structure in hot and dense QCD matter
• Study of the $D_s^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decay and measurement of $f_0$ masses and widths
• Existence of the critical endpoint in the vector meson extended linear sigma model
• Effective potential at finite temperature in a constant magnetic field I: Ring diagrams in a scalar theory
• The critical surface of the SU(3)_L x SU(3)_R chiral quark model at non-zero baryon density
• Determination of $\pi \pi$ scattering lengths from measurement of ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Influence of the isospin and hypercharge chemical potentials on the location of the CEP in the mu_B-T phase diagram of the SU(3)_L x SU(3)_R chiral quark model
• Extracting $\pi \pi$ $S$-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions
• Quark deconfinement and gluon condensate in a weak magnetic field
• The linear sigma model at a finite isospin chemical potential
• Chiral-symmetry restoration in the linear sigma model at nonzero temperature and baryon density
• Magnetic Field Effect on Charged Scalar Pair Creation at Finite Temperature
• Thermal Behaviour of $\pi -\pi$ Scattering Lengths in the Nambu--Jona-Lasinio model
• Thermomagnetic correlation lengths of strongly interacting matter in the Nambu--Jona-Lasinio model
• Thermal Corrections to $\pi$-$\pi$ Scattering Lengths in the Linear Sigma Model

Cited by in corpus (7)

• Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field
• Renormalons in a scalar self interacting theory: thermal, thermomagnetic and thermoelectric corrections for all values of temperature
• A new perspective for the magnetic corrections to $\pi$-$\pi$ Scattering Lengths in the Linear Sigma Model
• Magnetic renormalons in a scalar self interacting $\lambda {\varphi }^4$ theory
• Thermomagnetic renormalons in a scalar self-interacting $\lambda {\varphi }^4$ theory
• Thermo-magnetic corrections to $\pi$-$\pi$ Scattering Lengths in the Linear Sigma Model
• Magneto-Thomson and transverse Thomson effects in an interacting hadron gas in the presence of an external magnetic field