# Magnetic moments of octet baryons with deformed Uq(su(3)) flavor symmetry

## TL;DR

This paper explores how a q-deformation of flavor symmetry affects octet baryon magnetic moments, finding an optimal deformation parameter that improves agreement with experimental data and allows quark mass estimation.

## Contribution

It introduces a quantum group Uq(su(3)) as a flavor symmetry to model baryon magnetic moments, revealing the impact of deformation parameter q on theoretical predictions.

## Key findings

- Deformation parameter q=1.774 minimizes the least square error.
- Approximate 10% improvement over the undeformed case.
- Quark masses for up and down quarks estimated at 331 MeV and 305 MeV.

## Abstract

The effect of a q-deformation of flavor symmetry on octet baryon magnetic moments is investigated by taking the quantum group Uq(su(3)) as a flavor symmetry and calculating expressions for the magnetic moments of the octet baryons. Using the experimental values for the magnetic moments of the proton, neutron, and Lambda baryons as input, the magnetic moments of the up, down, and strange quarks, and by extension those of the remaining octet baryons, depend on the value of the deformation parameter q. Plotting the least square error as a function of q we find the undeformed value q=1 is a local maximum. Nearby are a relative minimum (at q=0.610) and an absolute minimum (at q=1.774). The value q=1.774 gives an approximately 10% decrease in the least square error compared to the undeformed case. For this value of q the quark masses of the up and down quarks are calculated to be 331 MeV and 305 MeV respectively.