Chiral theory of nucleons and pions in the presence of an external gravitational field

H Alharazin,D Djukanovic,M V Polyakov,J Gegelia

doi:10.1103/physrevd.102.076023

Abstract

We extend the standard second order effective chiral Lagrangian of pions and nucleons by considering the coupling to an external gravitational field. As an application we calculate one-loop corrections to the one-nucleon matrix element of the energy-momentum tensor to fourth order in chiral counting, and next-to-leading order tree-level amplitude of the pion-production in an external gravitational field. We discuss the relation of the obtained results to experimentally measurable observables. Our expressions for the chiral corrections to the nucleon gravitational form factors differ from those in the literature. That might require to revisit the chiral extrapolation of the lattice data on the nucleon gravitational form factors obtained in the past.

Highlights

Three basic global mechanical properties of the nucleon can be obtained as a linear response of the effective action to the change of the spacetime metric.2 The mass, spin, and D-term correspond to the hadron gravitational form factors (GFFs) at zero momentum transfer [2,3]
In the current work we presented the effective chiral Lagrangian of pions and nucleons up to the second chiral order in the presence of external gravitational field
While the coefficients of these parametrizations can be expressed as linear combinations of the coupling constants of the effective Lagrangians of the corresponding chiral orders in the presence of an external gravitational field, derivation of these Lagrangians and the corresponding energy-momentum tensors is beyond the scope of this work

Summary

INTRODUCTION

Three basic global mechanical properties of the nucleon (mass, spin, and the D-term1) can be obtained as a linear response of the effective action to the change of the spacetime metric. The mass, spin, and D-term correspond to the hadron gravitational form factors (GFFs) at zero momentum transfer [2,3]. For systematic studies of hadronic processes induced by gravity in the low-energy domain one needs to derive the effective chiral Lagrangian (EChL) for nucleons and pions in curved space-time. To the EMT of pions and nucleons in Minkowski space-time and to GFFs of the nucleon as well as to hadronic processes induced by gravitational interaction. In this work we apply the derived EChL to: (i) manifestly Lorentz-invariant calculations of oneloop contributions to the nucleon gravitational form factors up to fourth order according to standard power counting rules. Our paper is organized as follows: In Sec. II we obtain the full second order EChL for pions and nucleons in curved space-time and the corresponding expression for EMT. The Appendixes contain definitions of loop integrals, explicit expressions of GFFs in the chiral limit, and the pion graviproduction amplitude

EFFECTIVE ACTION IN CURVED SPACE TIME AND THE ENERGY-MOMENTUM TENSOR

ONE LOOP CHIRAL CORRECTIONS TO NUCLEON GRAVITATIONAL FORM FACTORS

PION GRAVIPRODUCTION

SUMMARY