## Author(s)

Auclair, Pierre, Leyde, Konstantin, Steer, Danièle A.## Abstract

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 ℓ 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 ≳𝒪(10$^{-3}$) of these particles cascades into γ-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 γ-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.

## Figures

Schematic trajectories of non self-intersecting loops in the $(\tau,\ell)$ phase space (orange). The blue region corresponds to the production of loops, that is the green line is $\gbr t$, and the blue one is $\gamma_\infty t$. These delimit the $\Theta$-function shown in the loop production function of \cref{eq: def polchinski rocha production}. There are three distinct possibilities for the ordering of $\tstar$, $\tau_0$ and $\tbr$, which appear in the boundaries of \cref{eq: final result n}. This depends on whether the loop had length $\ell_0$ before (\textit{top left}), during (\textit{top right}) or after (\textit{bottom}) loop production.

Schematic trajectories of non self-intersecting loops in the $(\tau,\ell)$ phase space (orange). The blue region corresponds to the production of loops, that is the green line is $\gbr t$, and the blue one is $\gamma_\infty t$. These delimit the $\Theta$-function shown in the loop production function of \cref{eq: def polchinski rocha production}. There are three distinct possibilities for the ordering of $\tstar$, $\tau_0$ and $\tbr$, which appear in the boundaries of \cref{eq: final result n}. This depends on whether the loop had length $\ell_0$ before (\textit{top left}), during (\textit{top right}) or after (\textit{bottom}) loop production.

Schematic trajectories of non self-intersecting loops in the $(\tau,\ell)$ phase space (orange). The blue region corresponds to the production of loops, that is the green line is $\gbr t$, and the blue one is $\gamma_\infty t$. These delimit the $\Theta$-function shown in the loop production function of \cref{eq: def polchinski rocha production}. There are three distinct possibilities for the ordering of $\tstar$, $\tau_0$ and $\tbr$, which appear in the boundaries of \cref{eq: final result n}. This depends on whether the loop had length $\ell_0$ before (\textit{top left}), during (\textit{top right}) or after (\textit{bottom}) loop production.

Loop number density for model A with kinks (left panel) and with cusps (right panel) for $G\mu = 10^{-13}$. Solid colored lines show the density for redshifts, from top to bottom $z = 10^6, 10^7, 10^8, 10^9, 10^{10}, 10^{11}, 10^{12}, 10^{13}, 10^{14}$ and $ 10^{15}$. The dashed dark line shows the scaling distribution when one assumes that all the energy goes into gravitational waves.

Loop number density for model A with kinks (left panel) and with cusps (right panel) for $G\mu = 10^{-13}$. Solid colored lines show the density for redshifts, from top to bottom $z = 10^6, 10^7, 10^8, 10^9, 10^{10}, 10^{11}, 10^{12}, 10^{13}, 10^{14}$ and $ 10^{15}$. The dashed dark line shows the scaling distribution when one assumes that all the energy goes into gravitational waves.

Loop number density for model B with kinks (left panel) and with cusps (right panel) for $G\mu = 10^{-13}$. Solid colored lines show the density for redshifts, from top to bottom $z = 10^6, 10^7, 10^8, 10^9, 10^{10}, 10^{11}, 10^{12}, 10^{13}, 10^{14}$ and $ 10^{15}$. The dashed dark line shows the scaling distribution when one assumes that all the energy goes into gravitational waves.

Loop number density for model B with kinks (left panel) and with cusps (right panel) for $G\mu = 10^{-13}$. Solid colored lines show the density for redshifts, from top to bottom $z = 10^6, 10^7, 10^8, 10^9, 10^{10}, 10^{11}, 10^{12}, 10^{13}, 10^{14}$ and $ 10^{15}$. The dashed dark line shows the scaling distribution when one assumes that all the energy goes into gravitational waves.

Stochastic background of gravitational waves for different $G\mu$. Top panel: Model A, lower panel: Model B. Solid line assume that cusps on the loops emit particles ($n = 1/2$). Dashed lines assume that all the emitted energy goes into gravitational waves.

Stochastic background of gravitational waves for different $G\mu$. Top panel: Model A, lower panel: Model B. Solid line assume that cusps on the loops emit particles ($n = 1/2$). Dashed lines assume that all the emitted energy goes into gravitational waves.

Diffuse $\gamma$-ray background in the presence of only cusps (blue) and only kinks (green) for $f_\mathrm{eff} = 1$ (solid lines) and $f_\mathrm{eff} = 10^{-3}$ (dashed lines). Left panel: Model A, right panel: Model B.

Diffuse $\gamma$-ray background in the presence of only cusps (blue) and only kinks (green) for $f_\mathrm{eff} = 1$ (solid lines) and $f_\mathrm{eff} = 10^{-3}$ (dashed lines). Left panel: Model A, right panel: Model B.

Left panel: One of the two cusps for a loop with $\alpha=3/4$ and an artificial width in the rest frame of the loop. The tip of the cusp goes at the speed of light in the direction of $\vb{\dot{X}}_0$. Right panel: a slice of the cusp along the plane parallel to $\vec{X}_0^{\prime\prime}$. The two branches of the cusp are separated by a distance $x_m$. The ellipses of the two branches are tilted with angle $\theta$.

Left panel: One of the two cusps for a loop with $\alpha=3/4$ and an artificial width in the rest frame of the loop. The tip of the cusp goes at the speed of light in the direction of $\vb{\dot{X}}_0$. Right panel: a slice of the cusp along the plane parallel to $\vec{X}_0^{\prime\prime}$. The two branches of the cusp are separated by a distance $x_m$. The ellipses of the two branches are tilted with angle $\theta$.

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