Beyond Plane Waves: Coherent Network Response to Collimated Gravitational-Wave Wavepackets

Abstract

We present a paraxial wavepacket model for collimated gravitational-wave bursts and derive the coherent response of detector networks to these structured signals. For current LIGO-Virgo baselines, analytic mismatch estimates and overlaps show that PWM waveforms are effectively indistinguishable from standard sine-Gaussian bursts, validating the plane-wave approximation. We then identify a regime relevant to third-generation networks in which finite transverse structure produces non-negligible geometric phase shifts. A toy event-level Monte Carlo compares a standard burst-search ranking with a paraxial wavepacket model-constrained statistic that penalizes geometric inconsistencies across detectors; in this controlled setup, the PWM prior yields a factor of $\sim3$-$4$ gain in detection efficiency at a fixed false-alarm rate, while maintaining performance on plane-wave-like signals.