Right-handed neutrino production from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>Z</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> interactions in forward search experiments

We study two general <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> extensions of the Standard Model (SM) those generate tiny neutrino masses via the seesaw mechanism after general <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:mo stretchy="false">)</e:mo> </e:math> breaking. These models predict a new neutral gauge boson ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>Z</i:mi> <i:mo>′</i:mo> </i:msup> </i:math> ) and right-handed neutrinos (RHNs), the latter introduced for anomaly cancellation and neutrino mass generation. In both scenarios, left- and right-handed fermions couple differently to the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi>Z</k:mi> <k:mo>′</k:mo> </k:msup> </k:math> , and RHNs mix with light neutrinos, enabling variety of decay modes. Focusing on the high-luminosity LHC (HL-LHC) and the future FASER2 experiment, we explore RHN pair production from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>Z</m:mi> <m:mo>′</m:mo> </m:msup> </m:math> decays in two cases; (i) long-lived <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msup> <o:mi>Z</o:mi> <o:mo>′</o:mo> </o:msup> </o:math> decays to visible modes and long-lived RHNs, and (ii) short-lived <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msup> <q:mi>Z</q:mi> <q:mo>′</q:mo> </q:msup> </q:math> decays to long-lived RHNs, which further decay visibly inside FASER2. We estimate projected limits on the general <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>U</s:mi> <s:mo stretchy="false">(</s:mo> <s:mn>1</s:mn> <s:mo stretchy="false">)</s:mo> </s:math> gauge coupling, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msup> <w:mi>Z</w:mi> <w:mo>′</w:mo> </w:msup> </w:math> mass, RHN mass, and light-heavy neutrino mixing for various <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>U</y:mi> <y:mo stretchy="false">(</y:mo> <y:mn>1</y:mn> <y:mo stretchy="false">)</y:mo> </y:math> charge assignments, and compare them with current experimental bounds.