Z′ mediated right-handed neutrinos from meson decays at the FASER

We investigate the pair production of right-handed neutrinos mediated by a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>Z</a:mi><a:mo>′</a:mo></a:msup></a:math> mainly from the meson decays at the FASER detector of the HL-LHC. The <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>Z</c:mi><c:mo>′</c:mo></c:msup></c:math> can be the additional gauge boson in either the <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:msub><e:mo stretchy="false">)</e:mo><e:mrow><e:mi>B</e:mi><e:mo>−</e:mo><e:mi>L</e:mi></e:mrow></e:msub></e:math> or sterile <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>ν</i:mi></i:math>-specific <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>U</k:mi><k:mo stretchy="false">(</k:mo><k:mn>1</k:mn><k:msub><k:mo stretchy="false">)</k:mo><k:mi>s</k:mi></k:msub></k:math> model. Taking the gauge coupling or the kinetic mixing at the current limits, we analyze the sensitivity to the masses of the heavy neutrinos, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>M</o:mi><o:mi>N</o:mi></o:msub></o:math>, and active-sterile mixing, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mo stretchy="false">|</q:mo><q:msub><q:mi>V</q:mi><q:mrow><q:mi>l</q:mi><q:mi>N</q:mi></q:mrow></q:msub><q:msup><q:mo stretchy="false">|</q:mo><q:mn>2</q:mn></q:msup></q:math>, of FASER2. In a background-free scenario, for the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>U</u:mi><u:mo stretchy="false">(</u:mo><u:mn>1</u:mn><u:msub><u:mo stretchy="false">)</u:mo><u:mrow><u:mi>B</u:mi><u:mo>−</u:mo><u:mi>L</u:mi></u:mrow></u:msub></u:math> case, FASER2 is able to probe <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mo stretchy="false">|</y:mo><y:msub><y:mi>V</y:mi><y:mrow><y:mi>l</y:mi><y:mi>N</y:mi></y:mrow></y:msub><y:msup><y:mo stretchy="false">|</y:mo><y:mn>2</y:mn></y:msup><y:mo>≈</y:mo><y:msup><y:mn>10</y:mn><y:mrow><y:mo>−</y:mo><y:mn>8</y:mn></y:mrow></y:msup></y:math> when <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>M</cb:mi><cb:mi>N</cb:mi></cb:msub><cb:mo>∼</cb:mo><cb:mn>0.3</cb:mn><cb:mtext> </cb:mtext><cb:mtext> </cb:mtext><cb:mi>GeV</cb:mi></cb:math>, which is comparable to the current limits from the beam dump experiments. When comes to the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>U</eb:mi><eb:mo stretchy="false">(</eb:mo><eb:mn>1</eb:mn><eb:msub><eb:mo stretchy="false">)</eb:mo><eb:mi>s</eb:mi></eb:msub></eb:math> model, FASER2 can probe <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mo stretchy="false">|</ib:mo><ib:msub><ib:mi>V</ib:mi><ib:mrow><ib:mi>l</ib:mi><ib:mi>N</ib:mi></ib:mrow></ib:msub><ib:msup><ib:mo stretchy="false">|</ib:mo><ib:mn>2</ib:mn></ib:msup><ib:mo>≈</ib:mo><ib:msup><ib:mn>10</ib:mn><ib:mrow><ib:mo>−</ib:mo><ib:mn>10</ib:mn></ib:mrow></ib:msup></ib:math>, which is better than the current limits for at least one magnitude, in all three flavors. A proposed long-lived particle detector, FACET, is also studied, but no significant difference from FASER2 is derived.