Self-energy of Heavy Quark

We demonstrate that to calculate the self-energy of a heavy quark in the heavy quark limit (or the heavy fermion limit in what is called the Baryon Chiral Perturbation Theory), the use of standard dimensional regularization provides only the quantum limit: opposite to the heavy quark (or classical) limit that one wishes to obtain. We thus devised a standard ultraviolet/infrared regularization procedure in calculating the one- and two-loop contributions to the heavy quark self-energy in this limit. Then the one-loop result is shown to provide the standard classical Coulomb self-energy of a static colour source that is linearly proportional to the untraviolet cutoff $Λ$. All the two-loop contributions are found to be proportional to $Λ\ln(Λ/λ)$ where $λ$ is the infrared cutoff. Often only the contribution from the bubble (light quarks, gluon and ghost) insertion to the gluon propagator has been considered as the $O(α_s)$ correction to the Coulomb energy to this order. Our result shows that other contributions are of the same magnitude, thus have to be taken into account.

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