Inclusive reactions from finite Minkowski spacetime correlation functions

The need to determine scattering amplitudes of few-hadron systems for arbitrary kinematics expands a broad set of subfields of modern-day nuclear and hadronic physics. In this work, we expand upon previous explorations on the use of real-time methods, like quantum computing or tensor networks, to determine few-body scattering amplitudes. Such calculations must be performed in a finite Minkowski spacetime, where scattering amplitudes are not well defined. Our previous work presented a conjecture of a systematically improvable estimator for scattering amplitudes constructed from finite-volume correlation functions. Here we provide further evidence that the prescription works for larger kinematic regions than previously explored as well as a broader class of scattering amplitudes. Finally, we devise a new method for estimating the order of magnitude of the error associated with finite time separations needed for such calculations. In units of the lightest mass of the theory, we find that to constrain amplitudes using real-time methods within <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">O</a:mi><a:mo stretchy="false">(</a:mo><a:mn>10</a:mn><a:mo>%</a:mo><a:mo stretchy="false">)</a:mo></a:math>, the spacetime volumes must satisfy <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mi>m</f:mi><f:mi>L</f:mi><f:mo>∼</f:mo><f:mi mathvariant="script">O</f:mi><f:mo stretchy="false">(</f:mo><f:mn>10</f:mn><f:mi>–</f:mi><f:msup><f:mrow><f:mn>10</f:mn></f:mrow><f:mrow><f:mn>2</f:mn></f:mrow></f:msup><f:mo stretchy="false">)</f:mo></f:mrow></f:math>) and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>m</k:mi><k:mi>T</k:mi><k:mo>∼</k:mo><k:mi mathvariant="script">O</k:mi><k:mo stretchy="false">(</k:mo><k:mrow><k:msup><k:mrow><k:mn>10</k:mn></k:mrow><k:mrow><k:mn>2</k:mn></k:mrow></k:msup><k:mi>–</k:mi><k:mrow><k:msup><k:mrow><k:mn>10</k:mn></k:mrow><k:mrow><k:mn>4</k:mn></k:mrow></k:msup></k:mrow></k:mrow><k:mo stretchy="false">)</k:mo></k:mrow></k:math>. Published by the American Physical Society 2024