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

TL;DR

This paper systematically computes one-loop mass corrections for higher-spin states in Type II string theory, addressing IR divergences and analyzing mass shifts up to level 10, with implications for state mixing and random matrix behavior.

Contribution

It provides a closed-form expression for one-loop mass corrections of higher-spin states, regularizes IR divergences, and explores the behavior of mass shifts up to level 10 in Type II string theory.

Findings

Mass corrections computed up to level 10.

IR divergences regularized using $i\varepsilon$-prescription.

Speculation on mixing and random matrix behavior of mass matrix.

Abstract

We start 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.