Q -balls in K -field theory

We study the existence and stability of Q-balls in noncanonical scalar field theories, K(|φ|2,X), where φ 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+XK,XX>0 are necessary but not sufficient conditions. The perturbations define a strongly hyperbolic system if (K,X-2φ′2K,XX)(K,X+2ω2φ2K,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.