Leading Bounds on Micrometer to Picometer Fifth Forces from Neutron Star Cooling

The equivalence principle and the inverse-square law of gravity could be violated at short distances ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msup> <a:mrow> <a:mn>10</a:mn> </a:mrow> <a:mrow> <a:mo>−</a:mo> <a:mn>6</a:mn> </a:mrow> </a:msup> <a:mi>–</a:mi> <a:msup> <a:mrow> <a:mn>10</a:mn> </a:mrow> <a:mrow> <a:mo>−</a:mo> <a:mn>12</a:mn> </a:mrow> </a:msup> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi mathvariant="normal">m</a:mi> </a:mrow> </a:math> ) by scalars sporting a coupling <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi>g</d:mi> <d:mi>N</d:mi> </d:msub> </d:math> to nucleons and mass <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mi>eV</f:mi> <f:mo>≲</f:mo> <f:msub> <f:mrow> <f:mi>m</f:mi> </f:mrow> <f:mrow> <f:mi>ϕ</f:mi> </f:mrow> </f:msub> <f:mo>≲</f:mo> <f:mi>MeV</f:mi> </f:mrow> </f:math> . We show for the first time that stringent bounds on the existence of these scalars can be derived from the observed cooling of nearby isolated neutron stars (NSs). Although NSs can only be used to set limits comparable to the classic supernova (SN) 1987A cooling bound in the case of pseudoscalars such as the QCD axion, the shallow temperature dependence of the scalar emissivity results in a huge enhancement in the effect of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>ϕ</h:mi> </h:math> on the cooling of cold NSs. As we do not find evidence of exotic energy losses, we can exclude couplings down to <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:msub> <j:mrow> <j:mi>g</j:mi> </j:mrow> <j:mrow> <j:mi>N</j:mi> </j:mrow> </j:msub> <j:mo>≲</j:mo> <j:mn>5</j:mn> <j:mo>×</j:mo> <j:msup> <j:mrow> <j:mn>10</j:mn> </j:mrow> <j:mrow> <j:mo>−</j:mo> <j:mn>14</j:mn> </j:mrow> </j:msup> </j:mrow> </j:math> . Our new bound supersedes all existing limits on scalars across 6 orders of magnitude in <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msub> <l:mi>m</l:mi> <l:mi>ϕ</l:mi> </l:msub> </l:math> . These conclusions also extend to Higgs-portal models, for which the bound on the scalar-Higgs mixing angle is <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mrow> <n:mi>sin</n:mi> <n:mi>θ</n:mi> <n:mo>≲</n:mo> <n:mn>6</n:mn> <n:mo>×</n:mo> <n:msup> <n:mrow> <n:mn>10</n:mn> </n:mrow> <n:mrow> <n:mo>−</n:mo> <n:mn>11</n:mn> </n:mrow> </n:msup> </n:mrow> </n:math> .