DOI: 10.5281/zenodo.7620202
title: DFSZ Axions and Where to Find Them

description: Supplemental datasets for the paper DFSZ Axions and Where to Find Them by Johannes Diehl and Emmanouil Koutsangelas. <strong>prior-countmaps.zip </strong> Contains anomaly ratio countmaps for the four cases described in the paper in Tab. IV in human readable .txt format. If you are interested only in out of the box prior distributions usable for Bayesian axion analysis, look here! All files have two columns: Numerical value of all unique anomaly ratios and corresponding normalized probability. Files: DFSZ.txt: Results from this work, [2302.04667]. Contains DFSZ models with up to nine Higgs doublets, extrapolating beyond DFSZ₇, assuming equal probability for all numbers of Higgs doublets. KSVZ.txt: Results from [2107.12378]. Contains complete set of preferred KSVZ models, assuming equal probability for all numbers of additional quarks. Combined.txt: KSVZ and DFSZ cases combined, assuming equal probability for a DFSZ axion as for a KSVZ axion. N+DW=1.txt: KSVZ and DFSZ cases combined assuming equal probability for a DFSZ axion as for a KSVZ axion, only considering models with domain wall number of one. <strong>AxionBands.txt</strong> Contains the data included in Tab. IV in the paper with detailed description of the underlying assumptions. <strong>complete_models.zip </strong> Contains three equivalent .h5 and .txt files with all solutions for the number of Higgs doublets \(n_D\) mentioned in the respective titles, including all Higgs charges and the LSE that was solved. The columns in the textfiles are: model string consists of number of Higgs fields and indicators which Higgs are meant to be equal (i.e. u1_u1_u1 means that the Higgs field H_u1 couples to all of the up-type quarks and therefore χHu1, χHu2 and χHu3 obviously also have to be equal, because they are actually the charge of the same particle) model multiplicity indicates 'how often' a model is realized. Completely analogous models like u1_u2_u1 and u1_u1_u3 (i.e. two up-type quarks couple to the same Higgs, one to another) are only calculated once. Since there are three options for this specific case, but e.g. for all up-type quarks coupling to the same Higgs there's only one options, this difference in probability between the two models is accounted for by our parameter 'model multiplicity'. terms multiplicity indicates differences in the probability of the specific terms1-9 arising due to a specific potential. This can be ignored if potentials leading to the same solutions for Higgs charges are deemed equivalent. The difference in probability comes from multiple (quadrilinear) potential terms possibly leading to the same equation (e.g. (Hu1 Hu2') (Hu2 Hd1) leads to the same equation as (Hu1 Hl1) (Hl1' Hd1). Anomaly Ratio is E/N electromagnetic anomaly E color anomaly N χHi: Charge of the Higgs particle coupling to the quark i. If i=s, charge of the Higgs singlet, always set =1 (without loss of generality for calculating the Anomaly Ratio). eqi: Equation number i. At least nD equations are needed to fix all nD Higgs charges. The nomenclature e.g. u1 is here simplified for χHu1. Together all equations give the matrix that is calculated to obtain solutions for the charges. <strong>multiplicity_as_defined_in_paper.zip</strong> Contains anomaly ratio countmaps in two folders, distinguishing the cases of all models and models specifically with \(N_\mathrm{DW} = 1\). There are separate files for each \(n_D\) in .jld2 format, which can be read via the corresponding code on GitHub. For \(n_D = 8\) and \(n_D=9\) results are biased samples of the full distribution. Instead of these datasets an extrapolation estimate based on results for lower \(n_D\) was used. all_Ndw: 7 files, naming: Number of Higgs doublets+"EoNs_full_nomulti"+"_sample"+".jld2". "sample" is used when only biased samples could be obtained. "nomulti" refers to choosing every solution for the charges to occur only once in accordance with the procedure outlined in the paper. Ndw=1: 4 files, similar naming with "NDW1" added to distinguish them from files in first folder. Below \(n_D = 4\) no solutions with \(N_\mathrm{DW} = 1\) exist, above \(n_D = 7\) computation was prohibitive. <strong>minimal_potentials.zip</strong> Similarly contains anomaly ratio countmaps, but under the assumption that all minimal potentials are separate theories (i.e. not connecting potentials leading to the same charges to one model. This interpretation is rejected in the paper, the data provided should only be used for purpose of making a comparison and estimating the influence of varying theory assumptions. 7 files, sampling starts already at \(n_D = 7\), but is unbiased under these assumptions.
description: v1.1 implements slight changes in the treatment of KSVZ results to make them better comparable to DFSZ results