Bringing the Peccei-Quinn mechanism down to Earth

It is conventionally assumed that the physics underlying the Peccei-Quinn (PQ) mechanism for addressing the strong <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> problem is at very high energies, orders of magnitude above the weak scale. However, this may not be the case in general and the associated PQ boson <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>ϕ</c:mi></c:math>, besides the signature state, i.e., the ultralight axion <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>a</e:mi></e:math>, may emerge well below the weak scale. We consider this possibility and examine some of the conditions for its viability. The example model proposed here may also provide the requisite Standard Model Higgs mass parameter, without invoking new scalars above the giga-electron-volt (GeV) scale. The corresponding parameter space can maintain against quantum corrections. This scenario, depending on the choice of parameters, can potentially be constrained by flavor data. We point out that the current mild excess in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>B</g:mi><g:mo>+</g:mo></g:msup><g:mo stretchy="false">→</g:mo><g:msup><g:mi>K</g:mi><g:mo>+</g:mo></g:msup><g:mi>ν</g:mi><g:mover accent="true"><g:mi>ν</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math>, reported by the Belle II experiment, could in principle be explained in this setup as <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mi>B</l:mi><l:mo>+</l:mo></l:msup><l:mo stretchy="false">→</l:mo><l:msup><l:mi>K</l:mi><l:mo>+</l:mo></l:msup><l:mi>ϕ</l:mi></l:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>B</o:mi><o:mo>+</o:mo></o:msup><o:mo stretchy="false">→</o:mo><o:msup><o:mi>K</o:mi><o:mo>+</o:mo></o:msup><o:mi>a</o:mi></o:math>, with both <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>ϕ</r:mi></r:math> and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>a</t:mi></t:math> escaping the detector as missing energy. For a sufficiently heavy PQ boson, in the GeV regime (as the preferred explanation of the Belle II excess), one can separate these two contributions, due to the difference in <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mi>K</v:mi><v:mo>+</v:mo></v:msup></v:math> momenta. In this case, the axion may also affect lighter meson, e.g., kaon, decays while <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>ϕ</x:mi></x:math> would not be a kinematically allowed final state. Published by the American Physical Society 2024