One-loop mass corrections and decay widths of Type II heavy string states

Abstract

We approach a systematic investigation of the one-loop mass corrections to (super-)string massive higher-spin states. While the imaginary part of the relevant amplitudes are finite, being related to the width of the decay of the states into two lower-mass states at tree level, the real part is generally IR-divergent and needs regularization and renormalization. We mostly focus on states of the first Regge trajectory in the NS-NS sector of Type-II string theories. We explicitly derive a closed-form expression for the integral over the insertion point, relying on properties of elliptic functions and lattice sums. We then regularize the IR divergent integral over the modular parameter of the torus, applying the $i\varepsilon$-prescription in string theory. As a result we compute the desired mass corrections up to level $N = 10$ and analyze their behavior at increasing $N$. Finally, we speculate on the existence of mixing among lower-spin states and conjecture that the one-loop mass matrix be governed by some random matrix theory.