Finite volume corrections to pi-pi scattering

Andre Walker-Loud; Ikuro Sato; Paulo F. Bedaque

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Finite volume corrections to pi-pi scattering

Paulo F. Bedaque, Ikuro Sato, Andre Walker-Loud

High Energy Physics - Lattice · Submitted 25 Jan 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we report on a one-loop chiral perturbation theory calculation of the leading exponential corrections in the case of I=2 pi-pi scattering near threshold.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.09 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Lattice QCD studies of hadron-hadron interactions are performed by computing the energy levels of the system in a finite box. The shifts in energy levels proportional to inverse powers of the volume are related to scattering parameters in a model independent way. In addition, there are non-universal exponentially suppressed corrections that distort this relation. These terms are proportional to exp(-m_pi L) and become relevant as the chiral limit is approached. In this paper we report on a one-loop chiral perturbation theory calculation of the leading exponential corrections in the case of I=2 pi-pi scattering near threshold.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Lattice QCD studies of hadron-hadron interactions are performed by computing the energy levels of the system in a finite box.	background 0.92	0.11	0.02	asserted 1.00
s1	The shifts in energy levels proportional to inverse powers of the volume are related to scattering parameters in a model independent way.	background 1.00	0.08	0.06	asserted 1.00
s2	In addition, there are non-universal exponentially suppressed corrections that distort this relation.	background 0.95	0.08	0.04	asserted 1.00
s3	These terms are proportional to exp(-m_pi L) and become relevant as the chiral limit is approached.	background 0.99	0.09	0.04	asserted 1.00
s4	In this paper we report on a one-loop chiral perturbation theory calculation of the leading exponential corrections in the case of I=2 pi-pi scattering near threshold.	contribution 1.00	0.95	0.56	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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The paper

Original abstract

Lattice QCD studies of hadron-hadron interactions are performed by computing the energy levels of the system in a finite box. The shifts in energy levels proportional to inverse powers of the volume are related to scattering parameters in a model independent way. In addition, there are non-universal exponentially suppressed corrections that distort this relation. These terms are proportional to exp(-m_pi L) and become relevant as the chiral limit is approached. In this paper we report on a one-loop chiral perturbation theory calculation of the leading exponential corrections in the case of I=2 pi-pi scattering near threshold.

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References

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Large-$N$ $\pi^+\pi^+$ scattering from twisted Eguchi--Kawai reduction
hep-lat 2026-10 accept novelty 7.0 of 10

The large-N value of the low-energy constant ℓππ/N is determined to be 0.345(21) from first-principles lattice QCD.
The $\pi\pi\to\pi\gamma^\star$ amplitude and the resonant $\rho\to\pi\gamma^\star$ transition from lattice QCD
hep-ph 2016-04 conditional novelty 7.0 of 10

Lattice QCD yields the first first-principles determination of the rho-to-pion transition form factor, extracted from the residue of the pi-pi to pi-gamma amplitude at the rho pole.
On the equivalence of left-hand-cut and three-body formalisms
hep-lat 2026-09 accept novelty 6.0 of 10

Two-body left-hand-cut and three-body formalisms for lattice QCD are analytically and numerically equivalent for particle-bound-state scattering with one-particle exchange.
Multichannel one-to-two transition amplitudes in a finite volume
hep-lat 2014-06 accept novelty 6.0 of 10

A generalized Lellouch-Luscher formula converts finite-volume lattice matrix elements of a current between a one-particle and a two-particle state into infinite-volume transition amplitudes, for any number of coupled ...
Two-particle multichannel systems in a finite volume with arbitrary spin
hep-lat 2014-01 accept novelty 6.0 of 10

A single master equation (Eq. 22) gives the finite-volume quantization condition for two-particle systems with arbitrary spin, arbitrary open coupled channels, arbitrary momentum, and twisted or periodic boundary conditions.

Show 3 more citing papers

Two-Nucleon Systems in a Finite Volume: (I) Quantization Conditions
hep-lat 2013-05 accept novelty 6.0 of 10

The paper derives and tabulates finite-volume quantization conditions relating two-nucleon lattice energy eigenvalues to S-, P-, D-, and F-wave scattering parameters, including partial-wave mixing, for three boost classes.
The I=2 pipi S-wave Scattering Phase Shift from Lattice QCD
hep-lat 2011-07 conditional novelty 6.0 of 10

Lattice QCD calculations of the I=2 pion-pion scattering phase shift yield threshold parameters that agree with Roy-equation determinations and with experiment.
Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-2 $\pi\pi$ scattering length
hep-lat 2015-06 conditional novelty 5.0 of 10

The first Nf=2+1+1 lattice QCD determination gives Mπa0 = -0.0442(2)stat(+4-0)sys for the isospin-2 ππ scattering length, consistent with chiral perturbation theory and prior lattice results.

How the literature uses it

23 arXiv papers cite this in 35 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 28 sentences without a confident label

Uses its method or tool 2 papers

In this work we use the formula developed in [ref] for the $ππ$ scattering.

I=2 $\pi$-$\pi$ scattering length with dynamical overlap fermion · Introduction · 1.00
For $a_0$ we apply the asymptotic finite size correction formula Eq. (31) from Ref. [ref] [equation] which is valid close to threshold (small $q^2$) only.

Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-2 $\pi\pi$ scattering length · Lüscher formula to $𝒪(1/L^5)$ · 0.99

Cites it as background 3 papers

In this regime, chiral effective field theory provides a useful description of low temperature dynamics.[ Chiral effective field theory has been used to study finite spacetime volume effects for a long time [ref] .] Leading finite-$β$ effects will come from pion loops, with the chiral loop expansion controlled by the small parameter $m_π^2/(4πf_π)^2 ≪1$, with $f_π ∼$.

Exponential reduction of finite volume effects with twisted boundary conditions · Introduction · 0.95
[ref] , the authors estimated exponentially suppressed corrections for $ππ$ and NN scatterings in the FV.

Two-particle scattering from finite-volume quantization conditions using the plane wave basis · Introduction · 0.94
In order to enlarge the applicability of Lüscher's method, extensions have been developed over the years which include: moving frames with non-vanishing center of mass momentum [ref] , asymmetric boxes [ref] , twisted boundary conditions [ref] , and more.

Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-2 $\pi\pi$ scattering length · Introduction · 0.84

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