Three-point energy correlators in hadronic Higgs boson decays

We present the analytic calculation of the leading-order three-point energy correlator (EEEC) in hadronic Higgs decays, including both the gluon-initiated channel <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>H</a:mi><a:mo stretchy="false">→</a:mo><a:mi>g</a:mi><a:mi>g</a:mi><a:mo>+</a:mo><a:mi>X</a:mi></a:math> and quark-initiated channel <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>H</d:mi><d:mo stretchy="false">→</d:mo><d:mi>q</d:mi><d:mover accent="true"><d:mi>q</d:mi><d:mo stretchy="false">¯</d:mo></d:mover><d:mo>+</d:mo><d:mi>X</d:mi></d:math>. The phase-space integration is evaluated directly using Mandelstam variables <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>s</i:mi><i:mrow><i:mi>i</i:mi><i:mi>j</i:mi></i:mrow></i:msub><i:mo>=</i:mo><i:mo stretchy="false">(</i:mo><i:msub><i:mi>p</i:mi><i:mi>i</i:mi></i:msub><i:mo>+</i:mo><i:msub><i:mi>p</i:mi><i:mi>j</i:mi></i:msub><i:msup><i:mo stretchy="false">)</i:mo><i:mn>2</i:mn></i:msup></i:math>, and the appearing square roots can be rationalized by either conformal ratios or celestial coordinate variables. Throughout the calculation, we observe the same transcendental function space as in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="script">N</m:mi><m:mo>=</m:mo><m:mn>4</m:mn></m:math> super–Yang-Mills theory and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msup><p:mi>e</p:mi><p:mo>+</p:mo></p:msup><p:msup><p:mi>e</p:mi><p:mo>−</p:mo></p:msup><p:mo stretchy="false">→</p:mo><p:mtext>hadrons</p:mtext></p:math>. Different infrared limits are also explored using the full analytic result, offering the fixed-order data for EEEC factorization and resummation. Given its nontrivial shape dependence, the EEEC presents an excellent opportunity to explore the dynamics of gluon jets originating from the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>H</s:mi><s:mo stretchy="false">→</s:mo><s:mi>g</s:mi><s:mi>g</s:mi></s:math> decay channel at future lepton colliders.