  Particle emission, in addition to gravitational radiation from cosmic string
loops, affects the resulting loop distribution and hence the corresponding
observational consequences of cosmic strings. Here we focus on two models in
which loops of length $\ell$ are produced from the infinite string network with
a given power-law. For both models we find that, due to particle production,
the Stochastic Gravitational Wave Background (SGWB) is cut off outside the
region of parameter space probed by any current or planned GW experiment.
Therefore the present constraints from the LIGO-Virgo-Kagra (LVK) collaboration
still hold. However for one of these models, if a fraction $\gtrsim O(10^{-3})$
of these particles cascades into $\gamma$-rays, and if the gravitational
backreaction scale follows the Polchinski-Rocha model, then the string tension
is tightly constrained from below by measurements of the Diffuse $\gamma$-Ray
Background, and from above by the SGWB. With reasonable assumptions, the joint
constraint on the string tension set by these two possible observables reduces
the available parameter space of this cosmic string model to a narrow band.
Future upgrades to LVK will either rule out this model or detect strings.
