Lattice calculation of the R-ratio smeared with Gaussian kernels
A. De Santis*, C. Alexandrou, S. Bacchio, P. Dimopoulos, J. Finkenrath, R. Frezzotti, G. Gagliardi, M. Garofalo, K. Hadjiyiannakou, B. Kostrzewa, K. Jansen, V. Lubicz, M. Petschlies, F. Sanfilippo, S. Simula, N. Tantalo, C. Urbach and U. Wenger
January 25, 2023
April 06, 2023
The ratio $R(E)$ of the cross-sections for $e^+e^-\to$ hadrons and $e^+e^-\to \mu^+\mu^-$ is a valuable energy-dependent probe of the hadronic sector of the Standard Model. Moreover, the experimental measurements of $R(E)$ are the inputs of the dispersive calculations of the leading hadronic vacuum polarization contribution to the muon $g-2$ and these are in significant tension with direct lattice calculations and with the muon $g-2$ experiment. In this talk we discuss the results of our first-principles lattice study of $R(E)$. By using a recently proposed method for extracting smeared spectral densities from Euclidean lattice correlators, we have calculated $R(E)$ convoluted with Gaussian kernels of different widths $\sigma$ and central energies up to $2.5$ GeV. Our theoretical results have been compared with the KNT19  compilation of experimental results smeared with the same Gaussian kernels and a tension (about three standard deviations) has been observed for $\sigma\sim 600$ MeV and central energies around the $\rho$-resonance peak.
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