Axion dark matter and additional BSM aspects in an extended 2HDM setup

We illustrate and discuss the phenomenology of a model featuring a two-Higgs doublet sector augmented by two <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math> singlet scalars. The gauge symmetry group is extended as well with a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:msub><e:mo stretchy="false">)</e:mo><e:mrow><e:msub><e:mi>L</e:mi><e:mi>μ</e:mi></e:msub><e:mo>−</e:mo><e:msub><e:mi>L</e:mi><e:mi>τ</e:mi></e:msub></e:mrow></e:msub></e:math> component whose spontaneous breaking leads to the gauge boson which has an important effect in the muon (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>g</i:mi><i:mo>−</i:mo><i:mn>2</i:mn></i:math>). A global PQ symmetry is introduced upon its breaking; we have the axion particle which is also dark matter (DM) in our work. In particular, we have focused on type-X and type-II 2HDM models and found out that (<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>g</k:mi><k:mo>−</k:mo><k:mn>2</k:mn></k:math>) cannot be explained only by the scalar sector for type-II 2HDM mainly due to stringent constraint from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>b</m:mi><m:mo stretchy="false">→</m:mo><m:mi>s</m:mi><m:mi>γ</m:mi></m:math> resulted in <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>M</p:mi><p:msup><p:mi>H</p:mi><p:mo>±</p:mo></p:msup></p:msub><p:mo>></p:mo><p:mn>800</p:mn><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>GeV</p:mi></p:math>. For type-II 2HDM, we can have axion coupling with the gluons which generates the axion potential and possible explanation for the strong <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>C</r:mi><r:mi>P</r:mi></r:math> problem. The proposed model accommodates neutrino masses via the type-I seesaw mechanism with an upper bound on the right-handed neutrino mass 1 GeV (1 TeV) for type-II (type-X) 2HDM due to the presence of Planck scale suppressed operators. Moreover, we also have additional scalars which affect the oblique parameters and hence the W-boson mass which leads us to explain the W-boson mass observed at the CDF-II detector. The most stringent constraints on the masses and quartic couplings come from the perturbativity and potential bound from the below conditions which leads to fine-tuning among the parameters in part of the parameter space. Finally, we discuss the possible detection prospects of the axion DM and the additional gauge boson.