Ultra-Planckian quark and gluon scattering in agravity

We investigate tree-level scattering processes involving quarks (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>q</a:mi></a:math>) and gluons (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>g</c:mi></c:math>) mediated by graviton exchange in the framework of agravity, a dimensionless and renormalizable theory of quadratic quantum gravity. Focusing on the ultra-Planckian regime, characterized by the Mandelstam variable <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>s</e:mi><e:mo>=</e:mo><e:mo stretchy="false">(</e:mo><e:msub><e:mi>p</e:mi><e:mn>1</e:mn></e:msub><e:mo>+</e:mo><e:msub><e:mi>p</e:mi><e:mn>2</e:mn></e:msub><e:msup><e:mo stretchy="false">)</e:mo><e:mn>2</e:mn></e:msup></e:math>, which corresponds to the total energy squared in the center-of-momentum frame, being much larger than any particle mass scale, we compute the squared amplitudes and analyze the differential cross sections for the processes <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>g</i:mi><i:mi>g</i:mi><i:mo stretchy="false">→</i:mo><i:mi>g</i:mi><i:mi>g</i:mi></i:math>, <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>g</l:mi><l:mi>g</l:mi><l:mo stretchy="false">→</l:mo><l:mi>q</l:mi><l:mover accent="true"><l:mi>q</l:mi><l:mo stretchy="false">¯</l:mo></l:mover></l:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>g</q:mi><q:mi>q</q:mi><q:mo stretchy="false">→</q:mo><q:mi>g</q:mi><q:mi>q</q:mi></q:math>, and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>q</t:mi><t:mi>q</t:mi><t:mo stretchy="false">→</t:mo><t:mi>q</t:mi><t:mi>q</t:mi></t:math>. We demonstrate that all amplitudes scale as <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>1</w:mn><w:mo>/</w:mo><w:mi>s</w:mi></w:math> at high energies, in agreement with expectations for a UV-complete theory of gravity. In addition, we explore the issue of unitarity in the presence of higher-derivative ghost modes by analyzing the positivity properties of the squared amplitudes. While IR divergences appear in the forward scattering of massless particles, we show that these are regularized by finite quark masses. Our findings support the viability of agravity as a perturbatively unitary and UV-complete extension of general relativity, capable of consistently describing gravitational interactions among elementary matter fields at trans-Planckian energies.