Correlators of heavy-light quark currents in HQET: Perturbative contribution up to 4 loops and beyond

TL;DR

This paper computes the perturbative contributions to heavy-light quark current correlators in HQET up to four loops, including large-$eta_0$ limit analysis, revealing insights into renormalon poles and the limitations of naive nonabelianization.

Contribution

It provides the first four-loop calculation of heavy-light current correlators in HQET and examines the large-$eta_0$ limit, highlighting the challenges of naive nonabelianization.

Findings

Perturbative contributions calculated up to 4 loops.

Large-$eta_0$ limit analysis with all-order $n_f$ terms.

Naive nonabelianization performs poorly for these correlators.

Abstract

The perturbative contribution to the correlator of two HQET heavy-light currents expanded in light-quark masses up to quadratic terms is calculated up to 4 loops. The leading large-$\beta_0$ limit is also considered, so that terms with the highest degrees of $n_f$ are calculated to all orders in $\alpha_s$. Borel images of coefficient functions in this limit contain renormalon poles. Naive nonabelianization works surprisingly poorly for the coefficient functions considered here.