# Inclusive hadronic decay rate of the tau lepton from lattice QCD

#### Inclusive hadronic decay rate of the tau lepton from lattice QCD

- Event time: 1:00pm until 3:00pm
- Event date: 15th November 2023
- Speaker: Giuseppe Gagliardi (UniversitĂ Roma Tre)
- Location: Higgs Centre Seminar Room, Room 4305, James Clerk Maxwell Building (JCMB) (James Clerk Maxwell Building (JCMB)) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

Title:

Inclusive hadronic decay rate of the tau lepton from lattice QCD

Abstract:

The inclusive hadronic decays of the $\tau$ are of great interest, as they provide an alternative way of determining the CKM matrix elements

$V_{\rm ud}$ and $V_{\rm us}$. However, a direct lattice QCD calculation of the corresponding inclusive hadronic decay rates is hindered by the

need of performing a numerical inverse Laplace transform of an Euclidean correlation function, a notoriously ill-posed problem. In this seminar, I will discuss a novel approach that effectively bypasses the inverse Laplace transform problem, and that allowsÂ to evaluate the inclusive decay rates in given flavour channels without relying on the operator-product expansion or perturbative QCD. The method is applied to the inclusive decay $\tau \to X_{\rm ud} \nu_{\tau}$, where $X_{\rm ud}$ represents any hadronic state with $\bar{u}d$ flavour quantum numbers. With all sources of systematic errors under control, except for isospin-breaking effects, we obtain a value for $|V_{ud}|$ with an accuracy of $0.4\%$, which is in agreement with the determination from superallowed nuclear beta decays. Finally, I will discuss the prospects for determining $|V_{\rm us}|$ from $\tau \to X_{\rm us} \nu_{\tau}$.

### About Particle Physics Theory seminars

The Particle Physics Theory seminar is a weekly series of talks reflecting the diverse interests of the group. Topics include analytic and numerical calculations based on the Standard Model of elementary particle physics, theories exploring new physics, as well as more formal developments in gauge theories and gravity..