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.

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 Parton Distribution Functions and Lattice QCD

2019 ◽  
Vol 206 ◽  
pp. 01003
Author(s):  
Huey-Wen Lin
Keyword(s):  
Lattice Qcd ◽  
Parton Distribution ◽  
Pion Mass ◽  
Effective Field ◽  
Distribution Functions ◽  
Large Momentum ◽  
Parton Distribution Functions ◽  
Proton Structure ◽  
Nonperturbative Renormalization ◽  
First Time

Recently, there have been rapid developments in lattice-QCD calculations of proton structure, especially in the parton distribution functions (PDFs). We overcame a longstanding obstacle and for the first time in lattice-QCD are able to directly calculate the Bjorken-x dependence of the quark, helicity and transversity distributions. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-x dependence of finite-momentum PDFs, called “quasi-PDFs”, can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized non-perturbatively in RI/MOM-scheme. Following a nonperturbative renormalization of the parton quasi-distribution in a regularization-independent momentum-subtraction scheme, we establish its matching to the $ \overline {{\rm{MS}}} $ PDF and calculate the non-singlet matching coefficient at next-to-leading order in perturbation theory. In this proceeding, I will show the progress that has been made in recent years, highlighting the latest state-of-the art PDF calculations at the physical pion mass. Future impacts on the large-x global PDF fits are also discussed.

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 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 Interactions of two and three mesons including higher partial waves from lattice QCD

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Tyler D. Blanton ◽  
Andrew D. Hanlon ◽  
Ben Hörz ◽  
Colin Morningstar ◽  
Fernando Romero-López ◽  
...  
Keyword(s):  
Lattice Qcd ◽  
Effective Field Theory ◽  
Energy Levels ◽  
Particle Energy ◽  
Effective Field ◽  
Chiral Perturbation ◽  
Wave Interactions ◽  
Statistical Precision ◽  
K Matrix ◽  
First Time

Abstract We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three Nf = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.

scholarly journals Scattering of two and three physical pions at maximal isospin from lattice QCD

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Matthias Fischer ◽  
Bartosz Kostrzewa ◽  
Liuming Liu ◽  
Fernando Romero-López ◽  
Martin Ueding ◽  
...  
Keyword(s):  
Lattice Qcd ◽  
Particle Interaction ◽  
Chiral Expansion ◽  
Leading Order ◽  
Direct Computation ◽  
Physical Point ◽  
Dependent Part ◽  
Quark Mass Dependence ◽  
Energy Dependent ◽  
Good Agreement

AbstractWe present the first direct $$N_f=2$$ N f = 2 lattice QCD computation of two- and three-$$\pi ^+$$ π + scattering quantities that includes an ensemble at the physical point. We study the quark mass dependence of the two-pion phase shift, and the three-particle interaction parameters. We also compare to phenomenology and chiral perturbation theory (ChPT). In the two-particle sector, we observe good agreement to the phenomenological fits in s- and d-wave, and obtain $$M_\pi a_0 = -0.0481(86)$$ M π a 0 = - 0.0481 ( 86 ) at the physical point from a direct computation. In the three-particle sector, we observe reasonable agreement at threshold to the leading order chiral expansion, i.e. a mildly attractive three-particle contact term. In contrast, we observe that the energy-dependent part of the three-particle quasilocal scattering quantity is not well described by leading order ChPT.

scholarly journals Neutron electric dipole moment using lattice QCD simulations at the physical point

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
C. Alexandrou ◽  
A. Athenodorou ◽  
K. Hadjiyiannakou ◽  
A. Todaro
Keyword(s):  
Dipole Moment ◽  
Lattice Qcd ◽  
Electric Dipole Moment ◽  
Electric Dipole ◽  
Neutron Electric Dipole Moment ◽  
Physical Point

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
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