Pair creation and decay of a massive particle near and far away from a cosmic string.

Abstract

We study the total transition probabilities of the tree-level processes of the pair creation and decay of a massive particle for real Klein-Gordon fields in the spacetime of an infinite straight static cosmic string. Basing the discussion on cylindrical modes characterized by an approximate radius of closest approach ${\mathit{r}}_{\mathrm{min}}$, it is possible to approximately localize the non-Minkowskian processes to cylindrical effective interaction regions around the cosmic string. A physical understanding of the space dependence of the transition probabilities is obtained on the basis of analytic expressions for different energy domains referring to regions close to and far away from the string. For pair creation the Compton wavelength ${\ensuremath{\lambda}}_{\mathit{C}}$ of the created particles proves to be a crucial length scale. For ${\mathit{r}}_{\mathrm{min}}$\ensuremath{\ll}${\ensuremath{\lambda}}_{\mathit{C}}$ the creation probability is insensitive to a variation of ${\mathit{r}}_{\mathrm{min}}$. For large ${\mathit{r}}_{\mathrm{min}}$ it falls off at least exponentially with ${\mathit{r}}_{\mathrm{min}}$. This agrees with an alternative ``integrated'' approach to localization: the cross section around the cosmic string is proportional to the Compton wavelength ${\ensuremath{\lambda}}_{\mathit{C}}$. The decay of the massive particle on the other hand contains processes allowed in Minkowski spacetime and leads to another type of local behavior.