Smeared spectral functions from lattice QCD: opportunities and challenges

Abstract

A broad class of physical observables can be expressed in terms of smeared spectral functions. Important examples include the hadronic vacuum polarization contribution to the muon $g-2$, hadronic $\tau$ decays, inclusive semileptonic $B$ and $D$ decays, and amplitudes for rare processes such as $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$. In recent years, a variety of methods have been proposed to reconstruct or constrain such spectral functions from Euclidean correlators and related inputs. However, the inverse problem is intrinsically ill-posed, making it difficult to obtain fully reliable, model-independent results with controlled uncertainties. In this contribution, I summarize recent developments, discuss the opportunities offered by smeared spectral observables, and highlight the main challenges that remain.

arXiv commentContribution to The 43rd International Symposium on Lattice Field Theory (Lattice 2026), July 26 to August 1, 2026, University of Maryland, College Park, USA