# The HAYSTAC Axion Search Analysis Procedure

## TL;DR

This paper details the analysis procedure of the HAYSTAC experiment, introducing innovations like optimal filtering and maximum likelihood methods to set limits on axion-photon coupling for dark matter axions above 20 μeV.

## Contribution

It presents new analysis techniques including optimal filtering and a maximum likelihood approach for combining spectra, improving the sensitivity of axion searches.

## Key findings

- First limits on axion-photon coupling above 20 μeV from HAYSTAC
- Introduction of optimal filtering for power spectra
- Development of a maximum likelihood combination method

## Abstract

We describe in detail the analysis procedure used to derive the first limits from the Haloscope at Yale Sensitive to Axion CDM (HAYSTAC), a microwave cavity search for cold dark matter (CDM) axions with masses above $20\ \mu\text{eV}$. We have introduced several significant innovations to the axion search analysis pioneered by the Axion Dark Matter eXperiment (ADMX), including optimal filtering of the individual power spectra that constitute the axion search dataset and a consistent maximum likelihood procedure for combining and rebinning these spectra. These innovations enable us to obtain the axion-photon coupling $|g_\gamma|$ excluded at any desired confidence level directly from the statistics of the combined data.