<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>eff</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> at CMB challenges <mml:math xmlns:mml="htt

The relativistic degrees of freedom (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>N</a:mi><a:mi>eff</a:mi></a:msub></a:math>) is one of the crucial cosmological parameters. The precise measurement of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>N</c:mi><c:mi>eff</c:mi></c:msub></c:math> at the time of cosmic microwave background formation, by Planck 2018 can be used to understand the new fundamental interactions, in particular involving light mediators. Presence of any new particle with sufficient energy density and sizeable interactions with Standard Model particles at the temperature around <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo>∼</e:mo><e:mi>MeV</e:mi></e:math> can significantly alter the neutrino decoupling and hence <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>N</g:mi><g:mi>eff</g:mi></g:msub></g:math>. Thus the bound on <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>N</i:mi><i:mi>eff</i:mi></i:msub></i:math> can place stringent constraints on various beyond Standard Model paradigms involving light particles. <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><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>X</k:mi></k:msub></k:mrow></k:math> models are among such scenarios and are widely studied in several aspects. In this work, we consider several popular <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>U</o:mi><o:mo stretchy="false">(</o:mo><o:mn>1</o:mn><o:msub><o:mo stretchy="false">)</o:mo><o:mi>X</o:mi></o:msub></o:math> models with light <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>Z</s:mi><s:mo>′</s:mo></s:msup></s:math> boson like <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>, <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:msub><y:mo stretchy="false">)</y:mo><y:mrow><y:mi>B</y:mi><y:mo>−</y:mo><y:mn>3</y:mn><y:msub><y:mi>L</y:mi><y:mi>i</y:mi></y:msub></y:mrow></y:msub></y:math>, <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>U</cb:mi><cb:mo stretchy="false">(</cb:mo><cb:mn>1</cb:mn><cb:msub><cb:mo stretchy="false">)</cb:mo><cb:mrow><cb:msub><cb:mi>B</cb:mi><cb:mi>i</cb:mi></cb:msub><cb:mo>−</cb:mo><cb:mn>3</cb:mn><cb:msub><cb:mi>L</cb:mi><cb:mi>j</cb:mi></cb:msub></cb:mrow></cb:msub></cb:math>, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>U</gb:mi><gb:mo stretchy="false">(</gb:mo><gb:mn>1</gb:mn><gb:msub><gb:mo stretchy="false">)</gb:mo><gb:mrow><gb:msub><gb:mi>L</gb:mi><gb:mi>i</gb:mi></gb:msub><gb:mo>−</gb:mo><gb:msub><gb:mi>L</gb:mi><gb:mi>j</gb:mi></gb:msub></gb:mrow></gb:msub></gb:math>; <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mrow><kb:mrow><kb:mi>i</kb:mi></kb:mrow><kb:mo>,</kb:mo><kb:mrow><kb:mi>j</kb:mi><kb:mo>=</kb:mo><kb:mn>1</kb:mn></kb:mrow><kb:mo>,</kb:mo><kb:mn>2</kb:mn><kb:mo>,</kb:mo><kb:mn>3</kb:mn></kb:mrow></kb:math> being the flavor indices and study their impact on <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi>N</mb:mi><mb:mi>eff</mb:mi></mb:msub></mb:math>. We also examine the constraints from ground based experiments like Xenon1T, Borexino, trident, etc. Our analysis shows that for light mass <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi>M</ob:mi><ob:msup><ob:mi>Z</ob:mi><ob:mo>′</ob:mo></ob:msup></ob:msub><ob:mo>≲</ob:mo><ob:mi mathvariant="script">O</ob:mi><ob:mo stretchy="false">(</ob:mo><ob:mi>MeV</ob:mi><ob:mo stretchy="false">)</ob:mo></ob:math> the <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:msub><tb:mi>N</tb:mi><tb:mi>eff</tb:mi></tb:msub></tb:math> provides the most stringent constraints on the <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:msup><vb:mi>Z</vb:mi><vb:mo>′</vb:mo></vb:msup></vb:math> mass and coupling, far exceeding the existing constraints from other experiments. Published by the American Physical Society 2024