Novel Corrections to the Momentum Sum Rule for Nuclear Structure Functions

TL;DR

This paper investigates novel interference effects in deep inelastic scattering on nuclei at low Bjorken x, revealing mechanisms that affect shadowing and anti-shadowing phenomena and challenge traditional sum rule extractions.

Contribution

It introduces a new quantum interference mechanism affecting nuclear structure functions and demonstrates its implications for the validity of sum rules in nuclear DIS analyses.

Findings

Interference between one-step and two-step scattering processes influences shadowing.

Standard sum rules cannot be directly applied to nuclear structure functions.

Numerical predictions align with neutrino and charged-lepton scattering data.

Abstract

We address novel features of deep inelastic lepton scattering on nuclei at small Bjorken variable $x_{Bj}$. In this regime the lepton-nuclear cross section involves the interference between the standard lepton-quark scattering amplitude for the deep inelastic scattering (DIS) process on a single nucleon and a two-step process where diffractive scattering on a first nucleon combines with the amplitude for DIS on a second nucleon. The phases associated with the $t$-channel exchanges to the diffractive amplitude can produce either a destructive or constructive quantum-mechanical interference of the one-step and two-step amplitudes. This provides a mechanism regulating the respective amounts of shadowing suppression and anti-shadowing enhancement at low $x_{Bj}$. Furthermore, the standard leading-twist operator product and handbag diagram analyses of the forward virtual Compton amplitude on the nucleus are inapplicable, barring a conventional probabilistic interpretation. A main observable consequence is the impossibility of extracting momentum and spin sum rules from nuclear structure functions. We present numerical predictions supporting this picture and test them against DIS neutrino-nucleus and charged-lepton-nucleus scattering data.