$π-π$ scattering, QED and finite-volume quantization

Christ, Norman; Feng, Xu; Karpie, Joseph; Nguyen, Tuan

doi:10.48550/arxiv.2111.04668

“…Progress by our collaborations on these fronts is reported in Refs. [4,5]. A third, ∼12% systematic error arises due to discretization effects from simulating A 0 with only a single, relatively coarse (a −1 ≈ 1.4 GeV) lattice spacing.…”

Section: Pos(lattice2023)335mentioning

confidence: 99%

Exploiting hidden symmetries to accelerate the lattice calculation of $K\to\pi\pi$ decays with G-parity boundary conditions

Kelly

2023

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

0

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The RBC & UKQCD collaborations have successfully employed G-parity boundary conditions in the measurement of K → ππ decays to obtain a physical decay with the two-pion ground state, at the cost of a significant increase in computational expense. We report on new theoretical/algorithmic developments based upon the properties of the Dirac operator under complex conjugation that have been exploited to achieve highly significant computational cost reductions, and explain their impact on our ongoing effort to repeat the calculation on finer lattices.

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“…When calculating this amplitude, it will prove beneficial to actually determine the Euclidean space analogue and then analytically continue it into Minkowski space. The validity of this analytic continuation is discussed in full detail in [16].…”

Section: Analytic Treatment For Long Distancementioning

confidence: 99%

“…Coulomb corrections to pi-pi scattering diagrams, at least two pions must travel the long space-like distance 𝑅, which in Euclidean space is clearly exponentially suppressed [16].…”

Section: Pos(lattice2021)312mentioning

confidence: 99%

Coulomb corrections to pi-pi scattering

Christ¹,

Feng²,

Karpie³

et al. 2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

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The relationship between finite volume multi-hadron energy levels and matrix elements and two particle scattering phase shifts and decays is well known, but the inclusion of long range interactions such as QED is non-trivial. Inclusion of QED is an important systematic error correction to 𝐾 → 𝜋𝜋 decays. In this talk, we present a method of including a truncated, finiterange Coulomb interaction in a finite-volume lattice QCD calculation. We show how the omission caused by the truncation can be restored by an infinite-volume analytic calculation so that the final result contains no power-law finite-volume errors beyond those usually present in Luscher's finite-volume phase shift determination. This approach allows us to calculate the QED-corrected infinite-volume phase shift for 𝜋𝜋 scattering in Coulomb gauge, a necessary ingredient to 𝐾 → 𝜋𝜋, while neglecting the transverse radiation for now.

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“…It is only diagrams of type (𝑐), where the Coulomb interaction is between two well separated pions, which are not exponentially suppressed in 𝑅 when the energy is below the four pion threshold. In the other two types of diagrams, at least two pions must travel the long space-like distance 𝑅, which in Euclidean space is clearly exponentially suppressed [16].…”

Section: Analytic Treatment For Long Distancementioning

confidence: 99%

“…The full analytical evaluation of Eq. ( 12) is given in [16]. Here we summarize the important final result of the 𝑂 (𝛼) correction to the phase shift from the 𝑉 TC interaction as…”

Section: Analytic Treatment For Long Distancementioning

confidence: 99%

Coulomb corrections to pi-pi scattering

Christ¹,

Xing²,

Karpie³

et al. 2021

Preprint

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The relationship between finite volume multi-hadron energy levels and matrix elements and two particle scattering phase shifts and decays is well known, but the inclusion of long range interactions such as QED is non-trivial. Inclusion of QED is an important systematic error correction to 𝐾 → 𝜋𝜋 decays. In this talk, we present a method of including a truncated, finiterange Coulomb interaction in a finite-volume lattice QCD calculation. We show how the omission caused by the truncation can be restored by an infinite-volume analytic calculation so that the final result contains no power-law finite-volume errors beyond those usually present in Luscher's finite-volume phase shift determination. This approach allows us to calculate the QED-corrected infinite-volume phase shift for 𝜋𝜋 scattering in Coulomb gauge, a necessary ingredient to 𝐾 → 𝜋𝜋, while neglecting the transverse radiation for now.

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$π-π$ scattering, QED and finite-volume quantization

Cited by 3 publications

References 27 publications

Exploiting hidden symmetries to accelerate the lattice calculation of $K\to\pi\pi$ decays with G-parity boundary conditions

Exploiting hidden symmetries to accelerate the lattice calculation of $K\to\pi\pi$ decays with G-parity boundary conditions

Coulomb corrections to pi-pi scattering

Coulomb corrections to pi-pi scattering

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