Q-balls in K-field theory

We study the existence and stability of Q-balls in noncanonical scalar field theories, $K(\mathrm{\mid }\mathrm{\Phi }{\mathrm{\mid }}^2,X)$ where $\mathrm{\Phi }$ is the complex scalar field and $X$ is the kinetic term. We extend the Vakhitov-Kolokolov stability criterion to K-field theories. We derive the condition for the perturbations to have a well-posed Cauchy problem. We find that $K_{,X}>0$ and $K_{,X}+X{K}_{,XX}>0$ are necessary but not sufficient conditions. The perturbations define a strongly hyperbolic system if $(K_{,X}-2{\phi }^{\mathrm{\prime }2}{K}_{,XX})(K_{,X}+2{\omega }^2{\phi }^2{K}_{,XX})>0$. For all modifications studied, we found that perturbations propagate at a speed different from light. Generically, the noncanonical scalar field can lower the charge and energy of the Q-ball and therefore improves its stability.