[Paper Review] Decays of $ au ightarrow ho(770) ( ho'(1450)) u_ au$ and $ au ightarrow K^{*}(892) (K^{*'}(1410)) u_ au$ in the extended Nambu - Jona- Lasinio model

A. I. Ahmadov, Yu. L. Kalinovsky+1 more|arXiv (Cornell University)|Jun 8, 2015

Quantum Chromodynamics and Particle Interactions17 references5 citations

TL;DR

This study investigates the decay widths of tau lepton decays into vector mesons—specifically $\tau \to \rho(770)\,\rho'(1450)\,\mu_\tau$ and $\tau \to K^*(892)\,K^{*'}(1410)\,\mu_\tau$—within the extended Nambu-Jona-Lasinio model using quark one-loop calculations. The model successfully reproduces the $\tau \to K^*(892)\,K^{*'}(1410)\,\mu_\tau$ decay widths in agreement with experimental data, while also providing theoretical estimates for the $\rho(770)$ and $\rho'(1450)$ decay channels.

ABSTRACT

In the extended Nambu - Jona - Lasinio model the decay widths $ au ightarrow ho(770) ( ho'(1450)) u_ au$ and $ au ightarrow K^{*}(892) (K^{*'}(1410)) u_ au$ are studied in the quark one -loop approximation. Our estimations of the decay widths $ au ightarrow K^{*}(892) (K^{*'}(1410)) u_ au$ are in satisfactory agreement with experimantal data. In the paper, the decay widths $ au ightarrow ho(770) ( ho'(1450)) u_ au$ are also calculated.

Motivation & Objective

• To theoretically evaluate the decay widths of $\tau \to \rho(770)\,\rho'(1450)\,\mu_\tau$ and $\tau \to K^*(892)\,K^{*'}(1410)\,\mu_\tau$ within a quantum field theory framework.
• To test the predictive power of the extended Nambu-Jona-Lasinio model in describing hadronic tau decays involving light vector mesons.
• To assess the consistency of the model's predictions with experimental measurements, particularly for the $K^*$-channel decays.
• To extend the applicability of the quark one-loop approximation in the context of strong and electroweak interactions in the tau decay sector.

Proposed method

• The extended Nambu-Jona-Lasinio model is employed as an effective field theory to describe low-energy QCD dynamics.
• Quark one-loop diagrams are calculated to compute the decay amplitudes for $\tau \to \text{vector meson} \times \mu_\tau$ processes.
• The model incorporates explicit vector meson degrees of freedom through the introduction of auxiliary fields or resonant couplings.
• Chiral symmetry and its spontaneous breaking are dynamically realized via the model's Lagrangian structure.
• The decay widths are derived from the imaginary parts of the relevant self-energy diagrams in the one-loop approximation.
• Theoretical predictions are compared with available experimental data, particularly for the $K^*(892)$ and $K^{*'}(1410)$ final states.

Experimental results

Research questions

• RQ1 How well does the extended Nambu-Jona-Lasinio model reproduce the measured decay width of $\tau \to K^*(892)\,\mu_\tau$?
• RQ2 What are the predicted decay widths for $\tau \to \rho(770)\,\mu_\tau$ and $\tau \to \rho'(1450)\,\mu_\tau$ within this model?
• RQ3 To what extent does the quark one-loop approximation in the extended NJL model capture the dynamics of hadronic tau decays?
• RQ4 How do the model's predictions for the $K^{*'}(1410)$ channel compare with experimental observations?

Key findings

• The theoretical prediction for the decay width of $\tau \to K^*(892)\,\mu_\tau$ is in satisfactory agreement with experimental data.
• The model also provides a theoretical estimate for the decay width of $\tau \to K^{*'}(1410)\,\mu_\tau$, consistent with the framework's expectations.
• The calculated decay width for $\tau \to \rho(770)\,\mu_\tau$ is obtained within the same theoretical framework.
• The decay width for $\tau \to \rho'(1450)\,\mu_\tau$ is also computed, extending the model's predictive reach to higher-mass vector states.