Phenomenological constraints on Higgs reheating

In many models of inflation, reheating is realized through a coupling between the inflaton and the Higgs boson. Often, the mass of the inflaton is of order <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mn>10</a:mn> <a:mn>13</a:mn> </a:msup> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi>GeV</a:mi> </a:math> determined by the amplitude of the scalar fluctuation spectrum. However, in models where the inflaton potential is of the form <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>V</c:mi> <c:mo>∼</c:mo> <c:msup> <c:mi>ϕ</c:mi> <c:mi>k</c:mi> </c:msup> </c:math> about its minimum, the inflaton is massless for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>k</e:mi> <e:mo>≥</e:mo> <e:mn>4</e:mn> </e:math> unless a bare mass term, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mfrac> <g:mn>1</g:mn> <g:mn>2</g:mn> </g:mfrac> <g:msubsup> <g:mi>m</g:mi> <g:mi>ϕ</g:mi> <g:mn>2</g:mn> </g:msubsup> <g:msup> <g:mi>ϕ</g:mi> <g:mn>2</g:mn> </g:msup> </g:math> , is present. In this case, the inflaton mass may be of order the electroweak scale and may be subject to existing collider constraints. In particular, we investigate the constraints on the inflaton mass and reheating temperature <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>T</i:mi> <i:mrow> <i:mi>rh</i:mi> </i:mrow> </i:msub> </i:math> arising from the decay of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>ϕ</k:mi> </k:math> into <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi mathvariant="script">H</m:mi> </m:math> through an interaction term <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>μ</p:mi> <p:mi>ϕ</p:mi> <p:mo stretchy="false">|</p:mo> <p:mi mathvariant="script">H</p:mi> <p:msup> <p:mo stretchy="false">|</p:mo> <p:mn>2</p:mn> </p:msup> </p:math> . We perform a renormalization group analysis to determine the relative values of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>μ</u:mi> </u:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>m</w:mi> <w:mi>ϕ</w:mi> </w:msub> </w:math> such that the Higgs potential remains stable (and perturbative) at high energy. Taking into account the running of the Higgs quartic self-coupling and the experimental constraints from the LHC via the iggsools public code, we find that <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mn>3.4</y:mn> <y:mo>×</y:mo> <y:msup> <y:mn>10</y:mn> <y:mn>6</y:mn> </y:msup> <y:mtext> </y:mtext> <y:mtext> </y:mtext> <y:mrow> <y:mi>GeV</y:mi> </y:mrow> <y:mo>≲</y:mo> <y:msub> <y:mi>T</y:mi> <y:mrow> <y:mi>rh</y:mi> </y:mrow> </y:msub> <y:mo>≲</y:mo> <y:mn>3.9</y:mn> <y:mo>×</y:mo> <y:msup> <y:mn>10</y:mn> <y:mn>12</y:mn> </y:msup> <y:mtext> </y:mtext> <y:mtext> </y:mtext> <y:mi>GeV</y:mi> </y:math> with a corresponding constraint on the inflaton bare mass <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mn>260</ab:mn> <ab:mtext> </ab:mtext> <ab:mtext> </ab:mtext> <ab:mi>GeV</ab:mi> <ab:mo>≲</ab:mo> <ab:msub> <ab:mi>m</ab:mi> <ab:mi>ϕ</ab:mi> </ab:msub> <ab:mo>≲</ab:mo> <ab:mn>3.8</ab:mn> <ab:mo>×</ab:mo> <ab:msup> <ab:mn>10</ab:mn> <ab:mn>10</ab:mn> </ab:msup> <ab:mtext> </ab:mtext> <ab:mtext> </ab:mtext> <ab:mi>GeV</ab:mi> </ab:math> . The dependencies between <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>T</cb:mi> <cb:mrow> <cb:mi>rh</cb:mi> </cb:mrow> </cb:msub> </cb:math> and the inflaton bare mass <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>m</eb:mi> <eb:mi>ϕ</eb:mi> </eb:msub> </eb:math> as well as between <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>μ</gb:mi> </gb:math> and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msub> <ib:mi>m</ib:mi> <ib:mi>ϕ</ib:mi> </ib:msub> </ib:math> are provided.