Development and Validation of a Fit to Extract Resonance Parameters of $\tau^-\to\pi^+\pi^-\pi^-\nu_\tau$ Decays at Belle~II

Sumitted to PubDB: 2026-07-13

Category: Master Thesis

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Principal Authors Godo Kurten, Miriam Weiskopf, Stefan Wallner, Stephan Paul, Hans-Günther Moser
Date 2026-07-06
Belle II Number BELLE2-MTHESIS-2026-053
Abstract In the quark-model picture the simplest strongly bound systems are light mesons, which are modeled as quark-antiquark pairs, where each quark is an up, down or strange quark. As modeling the properties of these light mesons requires approximate methods, experimental input is required to validate them. For some resonances, such as the $a_1(1260)$, this experimental input is not very precise. In order to contribute a precise measurement, we develop an analysis of $\tau^-\to\pi^+\pi^-\pi^-\nu_\tau$ decays at Belle~II to measure the masses and widths of $a_1$ and $\rho$-like mesons. These decays offer a clean environment, providing excellent conditions for precise measurements of resonances. In order to extract the resonance parameters, a partial-wave analysis is performed in a two-step approach. The first step disentangles the data into contributions of different partial waves that are identified by their quantum numbers, and measures their amplitudes as a function of the invariant mass of the $3\pi$ system $m_{3\pi}$. This step was already developed and tested in previous works. The second step models the $m_{3\pi}$ dependence of the partial waves explicitly, and extracts the masses and widths of the resonances in the partial waves. In this work we develop and validate this approach using simulated data. We find that the input model is recovered with small intrinsic analysis biases. For the $a_1(1260)$ the biases on mass and width are around \SI{3}{\MeVcc}. For the other resonances they are slightly larger. In all cases they remain smaller than the uncertainties currently quoted by the Particle Data Group (PDG). Furthermore, we investigate our sensitivity to the $a_1(1420)$ signal found by the COMPASS collaboration. This signal has an unclear origin, as the quark-model picture does not predict such a meson. One possible origin is the \TS. We determine the conditions under which we expect to differentiate between the hypothesis of a \TS and a genuine resonance as the source of the $a_1(1420)$ signal. Lastly, we investigate the possibility of a more elaborate model for the second step, in which a $K$-matrix approach is implemented. We test its validity on our pseudo-data samples and determine the limitations of this approach.
Institute MPP

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