Standard Model tests with smeared experiment and theory

TL;DR

This paper proposes a novel approach to Standard Model tests using smeared experimental and theoretical data, enabling more reliable lattice QCD predictions for processes involving hadronic states, despite current smearing limitations.

Contribution

It introduces a method of smearing both experimental and theoretical results to facilitate model-independent lattice QCD predictions for hadronic processes.

Findings

Demonstrates the feasibility of using finite-width smearing for Standard Model tests.

Provides concrete examples with meson decay and rare semileptonic decay.

Addresses challenges in achieving small smearing widths in lattice simulations.

Abstract

For Standard Model processes in which on-shell intermediate hadronic states contribute - including inclusive semileptonic decays and long-distance effects in rare exclusive decays such as $D\to \pi \ell\ell$ and $B\to K^{(\ast)}\ell\ell$ - spectral-reconstruction techniques provide a promising route to model-independent lattice QCD predictions for use in phenomenological predictions. The central ingredient is the computation of the energy-smeared spectral density. Following the continuum and infinite-volume limits, the physical amplitude is recovered as the limit of vanishing smearing width. However, achieving sufficiently small smearing for a controlled extrapolation remains a significant challenge for current lattice simulations. In this paper, we therefore propose Standard Model tests, in which both experimental results and theory predictions are smeared with finite width, similar to what has previously been done in the literature for experimental and lattice $R$-ratio data in the context of the muon $(g-2)_\mu$. As concrete examples, we discuss the cases of inclusive meson decay and long-distance contributions to rare semileptonic meson decay.