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Register a new userThe role of boundary conditions in quantum computations of scattering observables
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Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. This would give access to Minkowski-signature correlators, in contrast to the Euclidean calculations routinely performed at present. However, as with present-day calculations, quantum computation strategies still require the restriction to a finite system size, including a finite, usually periodic, spatial volume. In this work, we investigate the consequences of this in the extraction of hadronic and Compton-like scattering amplitudes. Using the framework presented in Phys. Rev. D101 014509 (2020), we quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty, even for volumes that are very large by the standards of present-day Euclidean calculations. We then present an improvement strategy, based in the fact that the finite volume has a reduced symmetry. This implies that kinematic points, which yield the same Lorentz invariants, may still be physically distinct in the finite-volume system. As we demonstrate, both numerically and analytically, averaging over such sets can significantly suppress the unwanted volume distortions and improve the extraction of the physical scattering amplitudes.
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We review the definition of hypergroups by Sunder, and we associate a hypergroup to a type III subfactor $Nsubset M$ of finite index, whose canonical endomorphism $gammainmathrm{End}(M)$ is multiplicity-free. It is realized by positive maps of $M$ that have $N$ as fixed points. If the depth is $>2$, this hypergroup is different from the hypergroup associated with the fusion algebra of $M$-$M$ bimodules that was Sunders original motivation to introduce hypergroups. We explain how the present hypergroup, associated with a suitable subfactor, controls the composition of transparent boundary conditions between two isomorphic quantum field theories, and that this generalizes to a hypergroupoid of boundary conditions between different quantum field theories sharing a common subtheory.
First-principles studies of strongly-interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with more precise theoretical determinations, e.g. for the anomalous magnetic moment of the muon and the CP-violating parameters in the decay of mesons. Quantifying the effects arising from enclosing QED in a finite volume remains a primary target of investigations. To this end, finite-volume corrections to hadron masses in the presence of QED have been carefully studied in recent years. This paper extends such studies to the self-energy of moving charged hadrons, both on and away from their mass shell. In particular, we present analytical results for leading finite-volume corrections to the self-energy of spin-0 and spin-$frac{1}{2}$ particles in the presence of QED on a periodic hypercubic lattice, once the spatial zero mode of the photon is removed, a framework that is called $mathrm{QED}_{mathrm{L}}$. By altering modes beyond the zero mode, an improvement scheme is introduced to eliminate the leading finite-volume corrections to masses, with potential applications to other hadronic quantities. Our analytical results are verified by a dedicated numerical study of a lattice scalar field theory coupled to $mathrm{QED}_{mathrm{L}}$. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of $mathrm{QED}_{mathrm{L}}$, a theory that is rendered non-local with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.
We report on a program to compute the electromagnetic form factors of mesons. We discuss the techniques used to compute the pion form factor and present results computed with domain wall valence fermions on MILC asqtad lattices, as well as with Wilson fermions on quenched lattices. The methods can easily be extended to rho-to-gamma-pi transition form factors.
We discuss methods to extract decay constants, meson masses and gluonic observables in the presence of open boundary conditions. The ensembles have been generated by the CLS effort and have 2+1 flavors of O(a)-improved Wilson fermions with a small twisted-mass term as proposed by Luscher and Palombi. We analyse the effect of the associated reweighting factors on the computation of different observables.
We propose a new method to evaluate the Lellouch-Luscher factor which relates the $Delta I=3/2$ $Ktopipi$ matrix elements computed on a finite lattice to the physical (infinite-volume) decay amplitudes. The method relies on the use of partially twisted boundary conditions, which allow the s-wave $pipi$ phase shift to be computed as an almost continuous function of the centre-of-mass relative momentum and hence for its derivative to be evaluated. We successfully demonstrate the feasibility of the technique in an exploratory computation.
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