We discuss the phenomenology of a pair of degenerate GeV-scale Heavy Neutral Leptons within the Left-Right Symmetric Model (LRSM) framework, with the third fermion serving as a dark matter candidate. We highlight the potential of the recently approved SHiP experiment to test the existence of a light dark matter species, and signatures of lepton number violation as a possible experimental probe of the model in various experiments. Our findings include concrete predictions for the effective right-handed couplings <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26339_Article_IEq1.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mfenced close=")" open="("> <msubsup> <mi>V</mi> <mi>e</mi> <mi>R</mi> </msubsup> </mfenced> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$ {\left({V}_e^R\right)}^2 $</EquationSource> </InlineEquation> : <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26339_Article_IEq2.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mfenced close=")" open="("> <msubsup> <mi>V</mi> <mi>μ</mi> <mi>R</mi> </msubsup> </mfenced> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$ {\left({V}_{\mu}^R\right)}^2 $</EquationSource> </InlineEquation> : <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26339_Article_IEq3.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mfenced close=")" open="("> <msubsup> <mi>V</mi> <mi>τ</mi> <mi>R</mi> </msubsup> </mfenced> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$ {\left({V}_{\tau}^R\right)}^2 $</EquationSource> </InlineEquation> = 0.16 : 0.47 : 0.38 (normal neutrino hierarchy), 0.489 : 0.22 : 0.30 (inverted hierarchy) of the degenerate HNL pair, and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26339_Article_IEq1.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mfenced close=")" open="("> <msubsup> <mi>V</mi> <mi>e</mi> <mi>R</mi> </msubsup> </mfenced> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$ {\left({V}_e^R\right)}^2 $</EquationSource> </InlineEquation> : <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26339_Article_IEq2.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mfenced close=")" open="("> <msubsup> <mi>V</mi> <mi>μ</mi> <mi>R</mi> </msubsup> </mfenced> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$ {\left({V}_{\mu}^R\right)}^2 $</EquationSource> </InlineEquation> : <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26339_Article_IEq3.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mfenced close=")" open="("> <msubsup> <mi>V</mi> <mi>τ</mi> <mi>R</mi> </msubsup> </mfenced> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$ {\left({V}_{\tau}^R\right)}^2 $</EquationSource> </InlineEquation> = 0.68 : 0.07 : 0.24 (normal), 0.02 : 0.57 : 0.41 for the dark matter candidate.

Quasi-degenerate heavy neutral leptons in the left-right symmetric model

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2025年6月4日

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Oleksii Mikulenko

摘要

We discuss the phenomenology of a pair of degenerate GeV-scale Heavy Neutral Leptons within the Left-Right Symmetric Model (LRSM) framework, with the third fermion serving as a dark matter candidate. We highlight the potential of the recently approved SHiP experiment to test the existence of a light dark matter species, and signatures of lepton number violation as a possible experimental probe of the model in various experiments. Our findings include concrete predictions for the effective right-handed couplings ${(V_{e}^{R})}^{2}$ $ {\left({V}_e^R\right)}^2 $ : ${(V_{μ}^{R})}^{2}$ $ {\left({V}_{\mu}^R\right)}^2 $ : ${(V_{τ}^{R})}^{2}$ $ {\left({V}_{\tau}^R\right)}^2 $ = 0.16 : 0.47 : 0.38 (normal neutrino hierarchy), 0.489 : 0.22 : 0.30 (inverted hierarchy) of the degenerate HNL pair, and ${(V_{e}^{R})}^{2}$ $ {\left({V}_e^R\right)}^2 $ : ${(V_{μ}^{R})}^{2}$ $ {\left({V}_{\mu}^R\right)}^2 $ : ${(V_{τ}^{R})}^{2}$ $ {\left({V}_{\tau}^R\right)}^2 $ = 0.68 : 0.07 : 0.24 (normal), 0.02 : 0.57 : 0.41 for the dark matter candidate.