Abstract
We study the two-point correlation functions under an influence of the constant homogeneous magnetic field. In addition to the correlators of scalar, pseudoscalar, vector and axial-vector fermionic currents, we calculate the non-diagonal one including the tensor and pseudoscalar currents. The tensor current is a fermionic part of the Pauli Lagrangian relevant for the electromagnetic interaction of fermions through the anomalous magnetic moment. Its contribution to the photon polarization operator is briefly discussed.
Highlights
The Standard Model — the gauge theory based on the S U(3)C⊗S U(2)L⊗U(1)Y group — is intensively testing for its consistency and no significant experimental deviations from theoretical predictions have been found yet [1]
To get a good agreement with experimental data at the Large Hadron Collider (LHC), production cross-sections should be known in the Next-to-Leading Order (NLO) and some of them even in the Next-to-Next-to-Leading Order (NNLO)
We present the propagator of a charged fermion in the constant homogeneous magnetic field in the Fock-Schwinger representation, show some selected results for the two-point correlation functions and conclude with a discussion of further applications of the formalism considered
Summary
The Standard Model — the gauge theory based on the S U(3)C⊗S U(2)L⊗U(1)Y group — is intensively testing for its consistency and no significant experimental deviations from theoretical predictions have been found yet [1]. In a difference to LHC, electron-positron colliders allow to get detail information about the photon propagation from the energy scan in the electron-positron annihilation process e−e+ → hadrons In this case, one needs to know the photon polarization function (see, for example, [2, 3]): 3Q2 Π(Q2) = i d4 x ei(qx) 0|T jμ(x) jμ(0) |0 ,. For more complicated physical systems like astrophysical objects and the early Universe or in heavy-ion collisions one needs to take into account effects of an external medium Note that such a medium can significantly modify a wave-function and dispersion properties of a charged fermion and, as a consequence, change substantially the quantum field of the photon. We present the propagator of a charged fermion in the constant homogeneous magnetic field in the Fock-Schwinger representation, show some selected results for the two-point correlation functions and conclude with a discussion of further applications of the formalism considered
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