Investigating generalized minimal supergravity in the MSSM through the long-lived bino NLSP at the HL-LHC

The axino, the supersymmetric partner of the axion, is a well-motivated warm/hot dark/cold matter candidate and provides a natural solution to the relic density problem for the binolike neutralino if it is the lightest supersymmetric particle (LSP). With the generalized minimal supergravity, we study such kind of the viable parameter space where the binolike neutralino is the next-to-LSP (NLSP) and the axino is the LSP. In addition, we consider a scenario where the bino is a long-lived NLSP with the lifetime varying from <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>6</a:mn></a:mrow></a:msup></a:math> to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mn>10</c:mn><c:mrow><c:mo>−</c:mo><c:mn>4</c:mn></c:mrow></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi mathvariant="normal">s</c:mi></c:math> and then propose a new signal searching scheme involving one displaced photon together with the large missing transverse momentum at the HL-LHC. The binolike lightest neutralino lies under or around 100 GeV and is produced as a decay product of the right-handed sleptons. The relevant axion coupling <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>f</f:mi><f:mi>a</f:mi></f:msub></f:math> can be probed up to <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="script">O</h:mi><h:mo stretchy="false">(</h:mo><h:msup><h:mn>10</h:mn><h:mn>9</h:mn></h:msup><h:mo stretchy="false">)</h:mo><h:mtext> </h:mtext><h:mtext> </h:mtext><h:mi>GeV</h:mi></h:math> at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mn>2</m:mn><m:mi>σ</m:mi></m:mrow></m:math> level for the right-handed slepton mass under 800 GeV.