Analytic description of monodromy oscillons

We develop precise analytic description of oscillons - long-lived quasiperiodic field lumps - in scalar field theories with nearly quadratic potentials, e.g. the monodromy potential. Such oscillons are essentially nonperturbative due to large amplitudes, and they achieve extreme longevities. Our method is based on a consistent expansion in the anharmonicity of the potential at strong fields, which is made accurate by introducing a field-dependent "running mass." At every order, we compute effective action for the oscillon profile and other parameters. Comparison with explicit numerical simulations in (3+1)-dimensional monodromy model shows that our method is significantly more precise than other analytic approaches.