scholarly journals I=2ππS-wave scattering phase shift from lattice QCD

2012 ◽  
Vol 85 (3) ◽  
Author(s):  
S. R. Beane ◽  
E. Chang ◽  
W. Detmold ◽  
H. W. Lin ◽  
T. C. Luu ◽  
...  
Keyword(s):  
Phase Shift ◽  
Lattice Qcd ◽  
Wave Scattering ◽  
Scattering Phase

scholarly journals ρ resonance from the I = 1 ππ potential in lattice QCD

2018 ◽  
Vol 175 ◽  
pp. 05007 ◽  
Author(s):  
Daisuke Kawai
Keyword(s):  
Phase Shift ◽  
Lattice Qcd ◽  
Complex Energy Plane ◽  
Complex Energy ◽  
S Matrix ◽  
Resonant Behavior ◽  
Scattering Phase ◽  
The Difference ◽  
Energy Plane

We calculate the phase shift for the I = 1 ππ scattering in 2+1 flavor lattice QCD at mπ = 410 MeV, using all-to-all propagators with the LapH smearing. We first investigate the sink operator independence of the I = 2 ππ scattering phase shift to estimate the systematics in the LapH smearing scheme in the HAL QCD method at mπ = 870 MeV. The difference in the scattering phase shift in this channel between the conventional point sink scheme and the smeared sink scheme is reasonably small as long as the next-toleading analysis is employed in the smeared sink scheme with larger smearing levels. We then extract the I = 1 ππ potential with the smeared sink operator, whose scattering phase shift shows a resonant behavior (ρ resonance). We also examine the pole of the S-matrix corresponding to the ρ resonance in the complex energy plane.

scholarly journals ππ P-wave resonant scattering from lattice QCD

2018 ◽  
Vol 175 ◽  
pp. 05022
Author(s):  
Srijit Paul ◽  
Constantia Alexandrou ◽  
Luka Leskovec ◽  
Stefan Meinel ◽  
John W. Negele ◽  
...  
Keyword(s):  
Phase Shift ◽  
Lattice Qcd ◽  
Pion Mass ◽  
Resonant Scattering ◽  
P Wave ◽  
Statistics Analysis ◽  
Resonance Parameters ◽  
Lattice Size ◽  
Scattering Phase

We present a high-statistics analysis of the ρ resonance in ππ scattering, using 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV and a lattice size of approximately 3:6 fm. The computation of the two-point functions are carried out using combinations of forward, sequential, and stochastic propagators. For the extraction of the ρ-resonance parameters, we compare different fit methods and demonstrate their consistency. For the ππ scattering phase shift, we consider different Breit-Wigner parametrizations and also investigate possible nonresonant contributions. We find that the minimal Breit-Wigner model is suffcient to describe our data, and obtain amρ = 0:4609(16)stat(14)sys and gρππ = 5:69(13)stat(16)sys. In our comparison with other lattice QCD results, we consider the dimensionless ratios amρ/amN and amπ/amN to avoid scale setting ambiguities.

scholarly journals 2+ States of 8Be

1969 ◽  
Vol 22 (3) ◽  
pp. 293 ◽  
Author(s):  
FC Barker
Keyword(s):  
Excited State ◽  
Phase Shift ◽  
Excited States ◽  
Wave Scattering ◽  
Matrix Theory ◽  
Half Maximum ◽  
R Matrix ◽  
Particle Spectra ◽  
Scattering Phase ◽  
D Wave

Analysis by many-level R-matrix theory of the d-wave "'-'" scattering phase shift suggests the existence of broad 2+ excited states of 8Be, but their properties depend sensitively on the assumed channel radius a2. A simultaneous fit to the 9Be(p, d)8Be deuteron spectrum near the 2, 9 MeV peak requires a2 "'" 7�1 fm, while a simultaneous fit to the ",-particle spectra following 8Li and 8B p-decays requires a2 "'" 6� 7 fm. For the best overall fit with a2 = 6�75 fm, the first 2+ excited state is at 2� 84 MeV excitation energy with a width at half maximum of 1�30 MeV. It is shown that data from other reactions which appeared to give much larger widths for this level can be fitted using the same R-matrix parameters. A second 2+ excited state is obtained at about 9 MeV with a width of about 10 MeV. Properties of the narrow 2+ states at 16�6 and 16�9 MeV are also discussed.

scholarly journals The γπ → ππ anomaly from lattice QCD and dispersion relations

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Malwin Niehus ◽  
Martin Hoferichter ◽  
Bastian Kubis
Keyword(s):  
Phase Shift ◽  
Lattice Qcd ◽  
Effective Field ◽  
Dispersion Relations ◽  
Chiral Anomaly ◽  
Physical Point ◽  
Inverse Amplitude Method ◽  
Quark Mass Dependence ◽  
Scattering Phase ◽  
First Time

Abstract We propose a formalism to extract the γπ → ππ chiral anomaly F3π from calculations in lattice QCD performed at larger-than-physical pion masses. To this end, we start from a dispersive representation of the γ(*)π → ππ amplitude, whose main quark-mass dependence arises from the ππ scattering phase shift and can be derived from chiral perturbation theory via the inverse-amplitude method. With parameters constrained by lattice calculations of the P-wave phase shift, we use this combination of dispersion relations and effective field theory to extrapolate two recent γ(*)π → ππ calculations in lattice QCD to the physical point. Our formalism allows us to extract the radiative coupling of the ρ(770) meson and, for the first time, the chiral anomaly F3π = 38(16)(11) GeV−3. The result is consistent with the chiral prediction albeit within large uncertainties, which will improve in accordance with progress in future lattice-QCD computations.

Conduction electron surface scattering phase shift in lead

1979 ◽  
Vol 9 (4) ◽  
pp. L83-L84 ◽  
Author(s):  
A A Cottey
Keyword(s):  
Phase Shift ◽  
Conduction Electron ◽  
Surface Scattering ◽  
Scattering Phase

GENERAL FORMULA FOR THE SECOND VIRIAL COEFFICIENT

1961 ◽  
Vol 39 (11) ◽  
pp. 1563-1572 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Resolvent Operators ◽  
Simple Derivation ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Quantization Volume ◽  
Mechanical Expression ◽  
The Waves

A simple derivation is given of the quantum mechanical expression for the second virial coefficient in terms of the scattering phase shifts. The derivation does not require the introduction of a quantization volume and is based on the identity R(z)−R0(z) = R0(z)H1R(z), where R0(z) and R(z) are the resolvent operators corresponding to the unperturbed and total Hamiltonians H0 and H0 + H1 respectively. The derivation is valid in particular for a gas of excitons in a crystal for which the shape of the waves describing the relative motion of two excitons is not spherical, and, in general, varies with varying energy. The validity of the phase shift formula is demonstrated explicitly for this case by considering a quantization volume with a boundary the shape of which varies with the energy in such a way that for each energy the boundary is a surface of constant phase. The density of states prescribed by the phase shift formula is shown to result if the enclosed volume is required to be the same for all energies.

K+p interactions in the range 0.9–1.5 GeV/c and elastic scattering phase shift analysis

1970 ◽  
Vol 20 (2) ◽  
pp. 301-319 ◽  
Author(s):  
G. Giacomelli ◽  
P. Lugaresi-Serra ◽  
G. Mandrioli ◽  
A.M. Rossi ◽  
F. Griffiths ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Phase Shift Analysis ◽  
Shift Analysis ◽  
Scattering Phase

Estimating the error in variational scattering calculations

1978 ◽  
Vol 56 (10) ◽  
pp. 1358-1364 ◽  
Author(s):  
J. W. Darewych ◽  
R. Pooran
Keyword(s):  
Wave Scattering ◽  
Exponential Potential ◽  
S Wave ◽  
Order Error ◽  
Absolute Value ◽  
First Order ◽  
Scattering Phase ◽  
Square Well ◽  
Scattering Phase Shifts ◽  
Made In

We derive bounds to the absolute value of the error that is made in variational estimates of scattering phase shifts. These bounds, like the variational estimates, are second order in 'small' quantities and are, in this respect, an improvement on similar but first-order error bounds derived previously by Bardsley, Gerjuoy, and Sukumar. The s-wave scattering by a square well potential, in the Born approximation, and by an exponential potential, using a many parameter trial function, are used to illustrate the results.

scholarly journals Hermitizing the HAL QCD potential in the derivative expansion

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Sinya Aoki ◽  
Takumi Iritani ◽  
Koichi Yazaki
Keyword(s):  
Phase Shift ◽  
Wave Functions ◽  
Leading Order ◽  
Many Body ◽  
Derivative Expansion ◽  
Local Part ◽  
Scattering Phase ◽  
Many Body Systems ◽  
Local Term ◽  
Better Than

Abstract A formalism is given to hermitize the HAL QCD potential, which needs to be non-Hermitian except for the leading-order (LO) local term in the derivative expansion as the Nambu– Bethe– Salpeter (NBS) wave functions for different energies are not orthogonal to each other. It is shown that the non-Hermitian potential can be hermitized order by order to all orders in the derivative expansion. In particular, the next-to-leading order (NLO) potential can be exactly hermitized without approximation. The formalism is then applied to a simple case of $\Xi \Xi (^{1}S_{0}) $ scattering, for which the HAL QCD calculation is available to the NLO. The NLO term gives relatively small corrections to the scattering phase shift and the LO analysis seems justified in this case. We also observe that the local part of the hermitized NLO potential works better than that of the non-Hermitian NLO potential. The Hermitian version of the HAL QCD potential is desirable for comparing it with phenomenological interactions and also for using it as a two-body interaction in many-body systems.

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