Implications of Higgs mass for hidden sector SUSY breaking

Hidden sector supersymmetry (SUSY) breaking where charged hidden sector fields obtain SUSY breaking vacuum expectation values once seemed common in dynamical SUSY breaking (DSB). In such a case, scalars can obtain large masses but gauginos and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>A</a:mi></a:math>-terms gain loop-suppressed anomaly-mediated contributions which may be smaller by factors of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>16</c:mn><c:msup><c:mi>π</c:mi><c:mn>2</c:mn></c:msup><c:mo>∼</c:mo><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>160</c:mn></c:math>. This situation leads to models such as PeV or minisplit supersymmetry with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msub><e:mrow><e:mi>m</e:mi></e:mrow><e:mrow><e:mi>scalars</e:mi></e:mrow></e:msub><e:mo>∼</e:mo><e:mn>160</e:mn><e:msub><e:mrow><e:mi>m</e:mi></e:mrow><e:mrow><e:mi>gaugino</e:mi></e:mrow></e:msub></e:mrow></e:math>. In order to generate a light Higgs mass <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>m</g:mi><g:mi>h</g:mi></g:msub><g:mo>≃</g:mo><g:mn>125</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>GeV</g:mi></g:math>, the scalar mass terms are required in the 10–100 TeV range, leading to large, unnatural contributions to the weak scale. Alternatively, in gravity mediation with singlet hidden sector fields, then <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:msub><i:mrow><i:mi>m</i:mi></i:mrow><i:mrow><i:mi>scalars</i:mi></i:mrow></i:msub><i:mo>∼</i:mo><i:msub><i:mrow><i:mi>m</i:mi></i:mrow><i:mrow><i:mi>gauginos</i:mi></i:mrow></i:msub><i:mo>∼</i:mo><i:mi>A</i:mi></i:mrow></i:math>-terms and the large <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>A</k:mi></k:math>-terms lift <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>m</m:mi><m:mi>h</m:mi></m:msub><m:mo stretchy="false">→</m:mo><m:mn>125</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>GeV</m:mi></m:math> even for natural values of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>m</p:mi><p:msub><p:mover accent="true"><p:mi>t</p:mi><p:mo stretchy="false">˜</p:mo></p:mover><p:mn>1</p:mn></p:msub></p:msub><p:mo>∼</p:mo><p:mn>1</p:mn><p:mi>–</p:mi><p:mn>3</p:mn><p:mtext> </p:mtext><p:mtext> </p:mtext><p:mi>TeV</p:mi></p:math>. Requiring naturalness, which seems probabilistically preferred by the string landscape, then the measured Higgs mass seems to favor singlets in the hidden sector, which can be common in metastable and retrofitted DSB models.