Probing a left-right symmetric model from a displaced shower at the CMS muon system

We study the potential collider discovery for right-handed neutrinos (RHNs) in the minimal left-right symmetric model (LRSM). In this model, the RHNs can be either produced from the right-handed gauge boson <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>W</a:mi><a:mi>R</a:mi><a:mo>±</a:mo></a:msubsup></a:math>, or the scalar triplet <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="normal">Δ</c:mi></c:math> decays. The RHNs can subsequently decay via the heavy <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msubsup><f:mi>W</f:mi><f:mi>R</f:mi><f:mo>±</f:mo></f:msubsup></f:math>, making them potentially long-lived. In looking for such long-lived RHNs, a search for displaced shower at the CMS muon system is reinterpreted for either the processes, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>p</h:mi><h:mi>p</h:mi><h:mo stretchy="false">→</h:mo><h:msubsup><h:mi>W</h:mi><h:mi>R</h:mi><h:mo>±</h:mo></h:msubsup><h:mo stretchy="false">→</h:mo><h:msup><h:mo>ℓ</h:mo><h:mo>±</h:mo></h:msup><h:mi>N</h:mi></h:math> or <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>p</l:mi><l:mi>p</l:mi><l:mo stretchy="false">→</l:mo><l:mi mathvariant="normal">Δ</l:mi><l:mo stretchy="false">→</l:mo><l:mi>N</l:mi><l:mi>N</l:mi></l:math>. From the former process, we exclude <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>M</q:mi><q:msub><q:mi>W</q:mi><q:mi>R</q:mi></q:msub></q:msub><q:mo>≲</q:mo><q:mn>3.6</q:mn><q:mtext> </q:mtext><q:mtext> </q:mtext><q:mi>TeV</q:mi></q:math> using current CMS data, or <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo>≲</s:mo><s:mn>8.0</s:mn><s:mtext> </s:mtext><s:mtext> </s:mtext><s:mi>TeV</s:mi></s:math> at the future HL-LHC. For the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>p</u:mi><u:mi>p</u:mi><u:mo stretchy="false">→</u:mo><u:mi mathvariant="normal">Δ</u:mi><u:mo stretchy="false">→</u:mo><u:mi>N</u:mi><u:mi>N</u:mi></u:math> process, HL-LHC is able to probe much larger parameter space as long as the proper decay length of the RHNs, <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mrow><z:mn>0.01</z:mn><z:mtext> </z:mtext><z:mtext> </z:mtext><z:mi mathvariant="normal">m</z:mi><z:mo stretchy="false">≲</z:mo><z:msub><z:mi>L</z:mi><z:mn>0</z:mn></z:msub><z:mo>≲</z:mo><z:mn>1</z:mn><z:mtext> </z:mtext><z:mtext> </z:mtext><z:mi mathvariant="normal">m</z:mi></z:mrow></z:math>. This implies that the displaced shower searches are able to explore the parameter space of the LRSM which have not been excluded yet.