Some Thoughts on (the Incompleteness of) the (Double) Differential Event Rates for Elastic WIMP-Nucleus Scattering in (Directional) Direct Dark Matter Detection Physics

TL;DR

This paper critically examines the commonly used formulas for differential event rates in elastic WIMP-nucleus scattering, highlighting overlooked issues and discussing their implications for directional dark matter detection.

Contribution

It provides a detailed critique of existing expressions for event rates, revealing their incompleteness and proposing considerations for more accurate modeling in dark matter detection.

Findings

Identifies gaps in current differential rate formulas

Demonstrates the impact of these issues on detection analysis

Suggests improvements for theoretical modeling

Abstract

In this paper, we revisit the expressions for the (double) differential event rates for elastic WIMP-nucleus scattering and discuss some unusual thoughts on (the incompleteness of) the uses of these expressions in (directional) direct Dark Matter detection physics. Several not-frequently mentioned (but important) issues will be argued and demonstrated in detail.