scholarly journals Two-particle scattering from finite-volume quantization conditions using the plane wave basis

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Lu Meng ◽  
E. Epelbaum
Keyword(s):  
Plane Wave ◽  
Partial Wave ◽  
Finite Volume ◽  
Single Channel ◽  
Pion Mass ◽  
Phase Shifts ◽  
Effective Field ◽  
P Wave ◽  
Range Interaction ◽  
Pion Scattering

Abstract We propose an alternative approach to Lüscher’s formula for extracting two-body scattering phase shifts from finite volume spectra with no reliance on the partial wave expansion. We use an effective-field-theory-based Hamiltonian method in the plane wave basis and decompose the corresponding matrix elements of operators into irreducible representations of the relevant point groups. The proposed approach allows one to benefit from the knowledge of the long-range interaction and avoids complications from partial wave mixing in a finite volume. We consider spin-singlet channels in the two-nucleon system and pion-pion scattering in the ρ-meson channel in the rest and moving frames to illustrate the method for non-relativistic and relativistic systems, respectively. For the two-nucleon system, the long-range interaction due to the one-pion exchange is found to make the single-channel Lüscher formula unreliable at the physical pion mass. For S-wave dominated states, the single-channel Lüscher method suffers from significant finite-volume artifacts for a L = 3 fm box, but it works well for boxes with L > 5 fm. However, for P-wave dominated states, significant partial wave mixing effects prevent the application of the single-channel Lüscher formula regardless of the box size (except for the near-threshold region). Using a toy model to generate synthetic data for finite-volume energies, we show that our effective-field-theory-based approach in the plane wave basis is capable of a reliable extraction of the phase shifts. For pion-pion scattering, we employ a phenomenological model to fit lattice QCD results at the physical pion mass. The extracted P-wave phase shifts are found to be in a good agreement with the experimental results.

scholarly journals Multi-hadron spectroscopy in a large physical volume

2018 ◽  
Vol 175 ◽  
pp. 05026 ◽  
Author(s):  
John Bulava ◽  
Ben Hörz ◽  
Colin Morningstar
Keyword(s):  
Finite Volume ◽  
Scattering Amplitude ◽  
Pion Mass ◽  
Spatial Extent ◽  
Good Precision ◽  
Hadron Spectroscopy ◽  
Pion Scattering ◽  
Physical Pion ◽  
Physical Volume ◽  
Treat All

We demonstrate the effcacy of the stochastic LapH method to treat all-toall quark propagation on a Nf = 2 + 1 CLS ensemble with large linear spatial extent L = 5:5 fm, allowing us to obtain the benchmark elastic isovector p-wave pion-pion scattering amplitude to good precision already on a relatively small number of gauge configurations. These results hold promise for multi-hadron spectroscopy at close-to-physical pion mass with exponential finite-volume effects under control.

scholarly journals Finite-volume and thermal effects in the leading-HVP contribution to muonic (g − 2)

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
M. T. Hansen ◽  
A. Patella
Keyword(s):  
Finite Volume ◽  
Thermal Effects ◽  
Pion Mass ◽  
Percent Level ◽  
Effective Field ◽  
Drop Out ◽  
Effective Theory ◽  
Electromagnetic Current ◽  
Point Function ◽  
Good Convergence

Abstract The leading finite-volume and thermal effects, arising in numerical lattice QCD calculations of $$ {a}_{\mu}^{\mathrm{HVP},\mathrm{LO}}\equiv {\left(g-2\right)}_{\mu}^{\mathrm{HVP},\mathrm{LO}}/2 $$ a μ HVP , LO ≡ g − 2 μ HVP , LO / 2 , are determined to all orders with respect to the interactions of a generic, relativistic effective field theory of pions. In contrast to earlier work [1] based in the finite-volume Hamiltonian, the results presented here are derived by formally summing all Feynman diagrams contributing to the Euclidean electromagnetic-current two-point function, with any number of internal pion loops and interaction vertices. As was already found in ref. [1], the leading finite-volume corrections to $$ {a}_{\mu}^{\mathrm{HVP},\mathrm{LO}} $$ a μ HVP , LO scale as exp[−mL] where m is the pion mass and L is the length of the three periodic spatial directions. In this work we additionally control the two sub-leading exponentials, scaling as exp[−$$ \sqrt{2} $$ 2 mL] and exp[−$$ \sqrt{3} $$ 3 mL]. As with the leading term, the coefficient of these is given by the forward Compton amplitude of the pion, meaning that all details of the effective theory drop out of the final result. Thermal effects are additionally considered, and found to be sub-percent-level for typical lattice calculations. All finite-volume corrections are presented both for $$ {a}_{\mu}^{\mathrm{HVP},\mathrm{LO}} $$ a μ HVP , LO and for each time slice of the two-point function, with the latter expected to be particularly useful in correcting small to intermediate current separations, for which the series of exponentials exhibits good convergence.

scholarly journals On the three-particle analog of the Lellouch-Lüscher formula

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Fabian Müller ◽  
Akaki Rusetsky
Keyword(s):  
Field Theory ◽  
Finite Volume ◽  
Effective Field Theory ◽  
Effective Field ◽  
Infinite Volume ◽  
Leading Order ◽  
Particle Decay ◽  
Particle Decays

Abstract Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

scholarly journals Distributed acoustic sensing as a tool for exploration and monitoring: a proof-of-concept

2021 ◽  
Author(s):  
Nicola Piana Agostinetti ◽  
Alberto Villa ◽  
Gilberto Saccorotti
Keyword(s):  
High Resolution ◽  
Plane Wave ◽  
Geothermal Field ◽  
P Wave ◽  
Apparent Velocity ◽  
Near Surface ◽  
Acoustic Sensing ◽  
Geothermal Activity ◽  
Distributed Acoustic Sensing ◽  
Microseismic Event

Abstract. We use PoroTOMO experimental data to compare the performance of Distributed Acoustic Sensing (DAS) and geophone data in executing standard exploration and monitoring activities. The PoroTOMO experiment consists of two "seismic systems": (a) a 8.6 km long optical fibre cable deployed across the Brady geothermal field and covering an area of 1.5 x 0.5 km with 100 m long segments, and (b) an array of 238 co-located geophones with an average spacing of 60 m. The PoroTOMO experiment recorded continuous seismic data between March 10th and March 25th 2016. During such period, a ML 4.3 regional event occurred in the southwest, about 150 km away from the geothermal field, together with several microseismic local events related to the geothermal activity. The seismic waves generated from such seismic events have been used as input data in this study. For the exploration tasks, we compare the propagation of the ML 4.3 event across the geothermal field in both seismic systems in term of relative time-delay, for a number of configurations and segments. Defined the propagation, we analyse and compare the amplitude and the signal-to-noise ratio (SNR) of the P-wave in the two systems at high resolution. For testing the potential in monitoring local seismicity, we first perform an analysis of the geophone data for locating a microseismic event, based on expert opinion. Then, we a adopt different workflow for the automatic location of the same microseismic event using DAS data. For testing the potential in monitoring distant event, data from the regional earthquake are used for retrieving both the propagation direction and apparent velocity of the wavefield, using a standard plane-wave-fitting approach. Our results indicate that: (1) at a local scale, the seismic P-waves propagation and their characteristics (i.e. SNR and amplitude) along a single cable segment are robustly consistent with recordings from co-located geophones (delay-times δt ∼ 0.3 over 400 m for both seismic systems) ; (2) the interpretation of seismic wave propagation across multiple separated segments is less clear, due to the heavy contamination of scattering sources and local velocity heterogeneities; nonetheless, results from the plane-wave fitting still indicate the possibility for a consistent detection and location of the event; (3) at high-resolution (10 m), large amplitude variations along the fibre cable seem to robustly correlate with near surface geology; (4) automatic monitoring of microseismicity can be performed with DAS recordings with results comparable to manual analysis of geophone recordings (i.e. maximum horizontal error on event location around 70 m for both geophones and DAS data) ; and (5) DAS data pre-conditioning (e.g., temporal sub-sampling and channel-stacking) and dedicated processing techniques are strictly necessary for making any real-time monitoring procedure feasible and trustable.

scholarly journals Role of Spin in NN → NNπ

2016 ◽  
Vol 40 ◽  
pp. 1660061
Author(s):  
Vadim Baru
Keyword(s):  
Partial Wave ◽  
Pion Production ◽  
Low Energy ◽  
Partial Wave Analysis ◽  
P Wave ◽  
Wave Analysis ◽  
Theoretical Predictions

The recent measurements of the reactions [Formula: see text] and [Formula: see text] by the ANKE collaboration at COSY are analyzed with the focus on the p-wave pion production amplitudes. These amplitudes are known to provide an important connection between [Formula: see text] and other low-energy few-nucleon reactions. The results of the recent partial wave analysis of the ANKE data are discussed and compared with the theoretical predictions.

The phase-functions method and scalar amplitude of nucleon–nucleon scattering

2016 ◽  
Vol 25 (11) ◽  
pp. 1650088
Author(s):  
V. I. Zhaba
Keyword(s):  
Single Channel ◽  
Scattering Amplitude ◽  
Nucleon Nucleon ◽  
Phase Shifts ◽  
Computational Method ◽  
Nucleon Scattering ◽  
The Difference ◽  
Scalar Scattering ◽  
Scalar Amplitude ◽  
Phase Functions

A known phase-functions method (PFM) has been considered for calculation of a single-channel nucleon–nucleon scattering. The following partial waves of a nucleon–nucleon scattering have been considered using the phase shifts by PFM: 1S0-, 3P0-, 3P1-, 1D2-, 3F3-states for nn-scattering, 1S0-, 3P0-, 3P1-, 1D2-states for pp-scattering and 1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-states for np-scattering. The calculations have been carried out using phenomenological nucleon–nucleon Nijmegen group potentials (NijmI, NijmII, Nijm93 and Reid93) and Argonne v18 potential. The scalar scattering amplitude has been calculated using the obtained phase shifts. Our results are not much different from those obtained by using the known phase shifts published in other papers. The difference between calculations depending on a computational method of phase shifts makes: for real (imaginary) parts 0.14–4.36% (0.16–4.05%) for NijmI. 0.02–4.79% (0.08–3.88%) for NijmII. 0.01–5.49% (0.01–4.14%) for Reid93 and 0.01–5.11% (0.01–2.40%) for Argonne v18 potentials.

scholarly journals Partial-wave mixing in Hamiltonian effective field theory

2020 ◽  
Vol 101 (11) ◽  
Author(s):  
Yan Li ◽  
Jia-Jun Wu ◽  
Curtis D. Abell ◽  
Derek B. Leinweber ◽  
Anthony W. Thomas
Keyword(s):  
Field Theory ◽  
Partial Wave ◽  
Effective Field Theory ◽  
Effective Field ◽  
Wave Mixing

Green's function of the Lord–Shulman thermo-poroelasticity theory

2020 ◽  
Vol 221 (3) ◽  
pp. 1765-1776 ◽  
Author(s):  
Jia Wei ◽  
Li-Yun Fu ◽  
Zhi-Wei Wang ◽  
Jing Ba ◽  
José M Carcione
Keyword(s):  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Heterogeneous Media ◽  
Numerical Algorithms ◽  
Heat Diffusion ◽  
P Wave ◽  
Wave Analysis ◽  
S Wave ◽  
S Waves

SUMMARY The Lord–Shulman thermoelasticity theory combined with Biot equations of poroelasticity, describes wave dissipation due to fluid and heat flow. This theory avoids an unphysical behaviour of the thermoelastic waves present in the classical theory based on a parabolic heat equation, that is infinite velocity. A plane-wave analysis predicts four propagation modes: the classical P and S waves and two slow waves, namely, the Biot and thermal modes. We obtain the frequency-domain Green's function in homogeneous media as the displacements-temperature solution of the thermo-poroelasticity equations. The numerical examples validate the presence of the wave modes predicted by the plane-wave analysis. The S wave is not affected by heat diffusion, whereas the P wave shows an anelastic behaviour, and the slow modes present a diffusive behaviour depending on the viscosity, frequency and thermoelasticity properties. In heterogeneous media, the P wave undergoes mesoscopic attenuation through energy conversion to the slow modes. The Green's function is useful to study the physics in thermoelastic media and test numerical algorithms.

scholarly journals S-wave kaon–nucleon potentials with all-to-all propagators in the HAL QCD method

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Kotaro Murakami ◽  
◽  
Yutaro Akahoshi ◽  
Sinya Aoki
Keyword(s):  
Lattice Qcd ◽  
Pion Mass ◽  
Phase Shifts ◽  
Quark Propagator ◽  
Repulsive Interaction ◽  
S Wave ◽  
Experimental Phase ◽  
Future Studies ◽  
Zero Momentum ◽  
The One

Abstract Employing an all-to-all quark propagator technique, we investigate kaon–nucleon interactions in lattice QCD. We calculate the S-wave kaon–nucleon potentials at the leading order in the derivative expansion in the time-dependent HAL QCD method, using (2+1)-flavor gauge configurations on $32^3 \times 64$ lattices with lattice spacing $a \approx 0.09$ fm and pion mass $m_{\pi} \approx 570$ MeV. We take the one-end trick for all-to-all propagators, which allows us to put the zero-momentum hadron operators at both source and sink and to smear quark operators at the source. We find a stronger repulsive interaction in the $I=1$ channel than in the $I=0$. The phase shifts obtained by solving the Schrödinger equations with the potentials qualitatively reproduce the energy dependence of the experimental phase shifts, and have similar behavior to previous results from lattice QCD without all-to-all propagators. Our study demonstrates that the all-to-all quark propagator technique with the one-end trick is useful for studying interactions in meson–baryon systems in the HAL QCD method, so we will apply it to meson–baryon systems which contain quark–antiquark creation/annihilation processes in our future studies.

Sign in / Sign up

Export Citation Format

Share Document