65 research outputs found
Consistency Checks for Two-Body Finite-Volume Matrix Elements. II. Perturbative Systems
Using the general formalism presented in [Phys. Rev. D 94, 013008 (2016); Phys. Rev. D 100, 034511 (2019)], we study the finite-volume effects for the 2 þ J → 2 matrix element of an external current coupled to a two-particle state of identical scalars with perturbative interactions. Working in a finite cubic volume with periodicity L, we derive a 1=L expansion of the matrix element through O(1=L5) and find that it is governed by two universal current-dependent parameters, the scalar charge and the threshold two particle form factor. We confirm the result through a numerical study of the general formalism and additionally through an independent perturbative calculation. We further demonstrate a consistency with the Feynman-Hellmann theorem, which can be used to relate the 1=L expansions of the ground-state energy and matrix element. The latter gives a simple insight into why the leading volume corrections to the matrix element have the same scaling as those in the energy, 1=L3, in contradiction to Phys. Rev. D 91, 074509 (2015), which found a 1=L2 contribution to the matrix element. We show here that such a term arises at intermediate stages in the perturbative calculation, but cancels in the final result
Partial-wave projection of the one-particle exchange in three-body scattering amplitudes
As the study of three-hadron physics from lattice QCD matures, it is
necessary to develop proper analysis tools in order to reliably study a variety
of phenomena, including resonance spectroscopy and nuclear structure.
Reconstructing the three-particle scattering amplitude requires solving
integral equations, which can be written in terms of data-constrained dynamical
functions and physical on-shell quantities. The driving term in these equations
is the so-called one-particle exchange, which leads to a kinematic divergence
for particles on-mass-shell. A vital component in defining three-particle
amplitudes with definite parity and total angular momentum, which are used in
spectroscopic studies, is to project the one-particle exchange into definite
partial waves. We present a general procedure to construct exact analytic
partial wave projections of the one-particle exchange contribution for any
system composed of three spinless hadrons. Our result allows one full control
over the analytic structure of the projection, which we explore for some
low-lying partial waves with applications to three pions.Comment: 73 pages, 17 figures, 4 appendices, ancillary Mathematica notebook at
https://github.com/ajackura/partial_wave_three_body_ope_noteboo
Amplitude analysis and the nature of the Zc(3900)
The microscopic nature of the XYZ states remains an unsettled topic. We show
how a thorough amplitude analysis of the data can help constraining models of
these states. Specifically, we consider the case of the Zc(3900) peak and
discuss possible scenarios of a QCD state, virtual state, or a kinematical
enhancement. We conclude that current data are not precise enough to
distinguish between these hypotheses, however, the method we propose, when
applied to the forthcoming high-statistics measurements should shed light on
the nature of these exotic enhancements.Comment: 14 pages, 10 figures, 3 tables. Version accepted for publication on
Phys.Lett.
Structure of Pion Photoproduction Amplitudes
We derive and apply the finite energy sum rules to pion photoproduction. We
evaluate the low energy part of the sum rules using several state-of-the-art
models. We show how the differences in the low energy side of the sum rules
might originate from different quantum number assignments of baryon resonances.
We interpret the observed features in the low energy side of the sum rules with
the expectation from Regge theory. Finally, we present a model, in terms of a
Regge-pole expansion, that matches the sum rules and the high-energy
observables.Comment: 19 pages, 15 figures and 4 table
Solving Relativistic Three-Body Integral Equations in the Presence of Bound States and Resonances
Three-body interactions play an important role throughout modern-day particle, nuclear, and hadronic physics; many experimentally observed reactions of interest for testing the Standard Model result in final states composed of three particles or more. Due to these issues, a full description of three-body interactions from Quantum Chromodynamics is required. The focus of this project was to extend previous results for a two-body subsystem with a bound state to include resonance channels. We first derived a novel single-variable observable, denoted as an intensity distribution, which is proportional to the probability density of the three-body scattering amplitude. We explored this distribution in the context of established results for a two-body subsystem with a bound state. We then developed a model two-body scattering amplitude with both a resonant and a bound state and examined the three-body scattering intensity distribution for this system. For each of these two-body scattering subsystem models, intensity distributions were computed, resulting in novel graphs of relevant scattering behavior.https://digitalcommons.odu.edu/reu2021_physics/1000/thumbnail.jp
On the and Photoproduction Beam Asymmetry at High Energies
We show that, in the Regge limit, beam asymmetries in and
photoproduction are sensitive to hidden strangeness components. Under
reasonable assumptions about the couplings we estimate the contribution of the
Regge pole, which is expected to be the dominant hidden strangeness
contribution. The ratio of the asymmetries in and production is
estimated to be close to unity in the forward region at the photon energy ~GeV, relevant for the upcoming
measurements at Jefferson Lab.Comment: 9 pages, 4 figure
Analyticity constraints for hadron amplitudes : going high to heal low energy issues
Analyticity constitutes a rigid constraint on hadron scattering amplitudes. This property is used to relate models in different energy regimes. Using meson photoproduction as a benchmark, we show how to test contemporary low-energy models directly against high-energy data. This method pinpoints deficiencies of the models and treads a path to further improvement. The implementation of this technique enables one to produce more stable and reliable partial waves for future use in hadron spectroscopy and new physics searches
On the Equivalence of Three-Particle Scattering Formalisms
In recent years, different on-shell scattering
formalisms have been proposed to be applied to both lattice QCD and infinite
volume scattering processes. We prove that the formulation in the infinite
volume presented by Hansen and Sharpe in Phys.~Rev.~D92, 114509 (2015) and
subsequently Brice\~no, Hansen, and Sharpe in Phys.~Rev.~D95, 074510 (2017) can
be recovered from the -matrix representation, derived on the basis of
-matrix unitarity, presented by Mai {\em et al.} in Eur.~Phys.~J.~A53, 177
(2017) and Jackura {\em et al.} in Eur.~Phys.~J.~C79, 56 (2019). Therefore,
both formalisms in the infinite volume are equivalent and the physical content
is identical. Additionally, the Faddeev equations are recovered in the
non-relativistic limit of both representations.Comment: 13 pages, 5 figure
Consistency Checks for Two-Body Finite-Volume Matrix Elements: Conserved Currents and Bound States
Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide nontrivial checks on the final results and also to explore limiting cases in which more straightforward predictions may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infmite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron\u27s scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state
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