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# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Direct lattice calculation of inclusive hadronic tau decay rates

Aug 9, 2022, 7:00 PM
1h
Poster Presentation Weak Decays and Matrix Elements

### Speaker

Antonio Evangelista

### Description

Inclusive hadronic $\tau$ decays are particularly interesting from the phenomenological since they give access to $V_{ud}$ and $V_{us}$. A long-standing issue is the tension between the $V_{us}$ determinations coming from leptonic and semileptonic kaon decays and the ones obtained from inclusive hadronic $\tau$ decays. To date (as far as we know) the problem has been addressed indirectly by using sum-rule techniques and non-perturbative lattice inputs complemented with perturbative calculations. In this talk we discuss how a recent method for the extraction of smeared spectral densities from euclidean lattice correlators can profitably be used to obtain a direct lattice calculation of inclusive hadronic $\tau$ decay rates. No perturbative inputs are used in our approach as the decay rate is extracted directly from euclidean correlators with two insertions of the relevant hadronic weak current. We also present preliminary numerical results obtained by applying our method to the correlators produced by ETMC with $N_f=2+1+1$ dynamical flavours at $a=0.08\,\mathrm{fm}$ and physical pion masses.

### Primary authors

Antonio Evangelista Francesco Sanfilippo (INFN, Sezione Roma Tre) Giuseppe Gagliardi (INFN Sezione di Roma Tre) Nazario Tantalo (University and INFN of Rome Tor Vergata) Roberto Frezzotti (University and INFN of Roma Tor Vergata) Silvano Simula (INFN, Sezione Roma Tre) Vittorio Lubicz (Dipartimento di Fisica, Università Roma Tre and INFN, Sezione di Roma Tre)