Constructing a light QCD axion without <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:math> tuning

We consider axions lighter than what their QCD couplings might otherwise suggest. Starting with a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="double-struck">Z</a:mi><a:mi>N</a:mi></a:msub></a:math> axion, we introduce a small explicit <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi mathvariant="double-struck">Z</d:mi><d:mi>N</d:mi></d:msub></d:math> symmetry-breaking coupling between the Standard Model Higgs boson and a reheaton. This small explicit breaking allows us to populate a large portion of the light axion <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>m</g:mi><g:mi>a</g:mi></g:msub><g:mo>−</g:mo><g:msub><g:mi>f</g:mi><g:mi>a</g:mi></g:msub></g:math> plane, removes the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mn>1</i:mn><i:mo>/</i:mo><i:mi>N</i:mi></i:math> tuning in the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi mathvariant="double-struck">Z</k:mi><k:mi>N</k:mi></k:msub></k:math>-axion, and explains why only our sector was reheated. Because of finite temperature effects, axions of this sort undergo either “rigged” misalignment, where the axion misalignment angle is effectively <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>π</n:mi></n:math> regardless of its initial value, or “shuffled” misalignment, where the initial angle is effectively randomized.