Rare Higgs boson decay into a photon and a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> </mml:math> boson in radiatively driven natural supersymmetry

In this article, we study the rare decay process in which a Higgs boson decays into a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Z</a:mi> </a:math> boson and a photon. In the first part of the paper, we analyze the Standard Model (SM) contributions to the corresponding decay width, including the full leading-order result, two-loop <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>O</c:mi> <c:mo stretchy="false">(</c:mo> <c:msub> <c:mi>α</c:mi> <c:mi>s</c:mi> </c:msub> <c:mo stretchy="false">)</c:mo> </c:math> QCD corrections, and the recently reported two-loop <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>O</g:mi> <g:mo stretchy="false">(</g:mo> <g:mi>α</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> electroweak corrections, evaluated under four different <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>α</k:mi> </k:math> renormalization schemes. The dependence on the Higgs boson mass is studied within the experimentally allowed range reported by the LHC. In the considered schemes, a non-negligible variation of about 4% is found when the mass is varied within its current experimental uncertainty. In the second part of the paper, we analyze the leading-order contributions to the same process within the minimal supersymmetric Standard Model (MSSM). The spectrum of soft SUSY-breaking parameters and SUSY particle masses at the electroweak scale, which enter the computation of the one-loop amplitudes contributing to the decay width, is obtained by evolving the grand unified theory (GUT)-scale parameters of a radiatively driven natural supersymmetry (RNS) model with nonuniversal Higgs boson masses. Variations of the RNS parameters can enhance the average SM prediction by up to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mo>∼</m:mo> <m:mn>20</m:mn> <m:mo>%</m:mo> </m:math> , reaching a value of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mo>∼</o:mo> <o:mn>7.5</o:mn> <o:mtext> </o:mtext> <o:mtext> </o:mtext> <o:mi>keV</o:mi> </o:math> , while still satisfying the Higgs boson mass constraint. However, this comes at the cost of allowing a moderately large fine-tuning parameter, with values exceeding 100, thereby placing the model outside its most natural parameter region. The predicted decay width in the RNS scenario is closer to the recent ATLAS RUN <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mrow> <q:mn>2</q:mn> <q:mo>+</q:mo> <q:mn>3</q:mn> </q:mrow> </q:math> combined measurement than the average SM expectation.