The Goldstone theorem mandates that a spontaneous symmetry breaking entails the emergence of gap(mass)less excitations. In the case where a rotational invariance of a system of spin magnetic moments is broken by an antiferromagnetic order, these are well-known transverse spin waves. The interaction of such Goldstone magnons with the Higgs amplitude mode of the order parameter is usually discarded, even though glimpses of Higgs physics have recently been reported in a quantum magnet, a topological insulator, and ferroelectric and disordered superconductor systems. The Goldstone-Higgs interactions could be expected to grow in importance near a quantum critical point (QCP), where the symmetry-breaking order is weak, and its amplitude fluctuations are significant. Here we report an electron spin resonance (ESR) study of a nearly one-dimensional spin-1/2 chain system, Sr$_2$CuO$_3$, which presents exactly such a case. The ESR spectra at $T > T_N$, in the disordered Luttinger-spin-liquid phase with unconfined spinons reveal ideal Heisenberg-chain behavior with only very small, field-independent linewidth, $sim 1/T$. In the ordered state, below $T_N$, we identify antiferromagnetic resonance (AFMR) modes, which are well described by pseudo-Goldstone magnons in the model of a collinear biaxial antiferromagnet with two gaps, $Delta_1 = 23.0$ GHz and $Delta_2 = 13.3$ GHz. Additionally, we observe a major resonant response of special nature, which we attribute to magnon interaction with the Higgs amplitude mode in a weakly ordered antiferromagnet. Its unusual field dependence indicates the presence of a quantum phase transition at $mu_0 H simeq 9.4$ T.
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