Decoherence, Perturbations and Symmetry in Lindblad Dynamics -- Implications for Diffractive Dissociation

Abstract

We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schr\"{o}dinger and von Neumann equations to a dephasing Lindblad framework. This work develops further the odd-symmetric formulation involving dual temporal conditions from general dynamical considerations to specific tools of quantum mechanics. Applying the resulting scaling relations to published single- and double-diffractive data in $pp$ and $p\bar{p}$ collisions (ISR, UA4, UA5, CDF, D0, ALICE, and E710), we show that single-diffraction cross sections are well described by a three-parameter fit with a relative RMS deviation of $\sim 4\%$, substantially improving upon conventional approximations that neglect decoherence. The extracted decoherence factor is consistently $\phi \approx 0.89$, in agreement across SD, DD, and E710-based (direct) estimates, and is naturally interpreted as $\phi =1$ for CP-invariant dephasing but $\phi <1$ for CPT-invariant dephasing, favouring the latter.