A Combined NNLO Lattice-Continuum Determination of $L_{10}^r$

P. A. Boyle; L. Del Debbio; N. Garron; R. J. Hudspith; E. Kerrane; K. Maltman; J. M. Zanotti

doi:10.1103/PhysRevD.89.094510

A Combined NNLO Lattice-Continuum Determination of $L_{10}^r$

P. A. Boyle, L. Del Debbio, N. Garron, R. J. Hudspith, E. Kerrane, K. Maltman, J. M. Zanotti

School of Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

Abstract

The renormalized next-to-leading-order (NLO) chiral low-energy constant, $L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor $ud$ $V-A$ correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for $L_{10}^r$. Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with current versions of the strange hadronic $\tau$ branching fractions as input, we find $L_{10}^r(m_\rho )\, =\, -0.00346(32)$. This result represents the first NNLO determination of $L_{10}^r$ having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.

Original language	English
Journal	Physical Review D
Volume	89
Issue number	094510
DOIs	https://doi.org/10.1103/PhysRevD.89.094510
Publication status	Published - 29 May 2014

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hep-ph
hep-ex
hep-lat

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10.1103/PhysRevD.89.094510

PhysRevD.89.094510Final published version, 447 KB

Particle Theory at the Tait Institute
Ball, R. (Principal Investigator), Berera, A. (Co-investigator), Boyle, P. (Co-investigator), Del Debbio, L. (Co-investigator), Figueroa-O'Farrill, J. (Co-investigator), Gardi, E. (Co-investigator), Horsley, R. (Co-investigator), Kennedy, A. (Co-investigator), Kenway, R. (Co-investigator), Pendleton, B. (Co-investigator) & Simon Soler, J. (Co-investigator)
STFC
1/10/11 → 30/09/15
Project: Research

Cite this

@article{4b12835ca07b432db284ba681a8173e4,

title = "A Combined NNLO Lattice-Continuum Determination of $L_{10}^r$",

abstract = "The renormalized next-to-leading-order (NLO) chiral low-energy constant, $L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor $ud$ $V-A$ correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for $L_{10}^r$. Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with current versions of the strange hadronic $\tau$ branching fractions as input, we find $L_{10}^r(m_\rho )\, =\, -0.00346(32)$. This result represents the first NNLO determination of $L_{10}^r$ having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.",

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author = "{A. Boyle}, P. and {Del Debbio}, L. and N. Garron and {J. Hudspith}, R. and E. Kerrane and K. Maltman and {M. Zanotti}, J.",

note = "21 pages, 4 figures, 1 table. Updated references, one additional clarifying footnote in discussion section",

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AU - A. Boyle, P.

AU - Del Debbio, L.

AU - Garron, N.

AU - J. Hudspith, R.

AU - Kerrane, E.

AU - Maltman, K.

AU - M. Zanotti, J.

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PY - 2014/5/29

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N2 - The renormalized next-to-leading-order (NLO) chiral low-energy constant, $L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor $ud$ $V-A$ correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for $L_{10}^r$. Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with current versions of the strange hadronic $\tau$ branching fractions as input, we find $L_{10}^r(m_\rho )\, =\, -0.00346(32)$. This result represents the first NNLO determination of $L_{10}^r$ having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.

AB - The renormalized next-to-leading-order (NLO) chiral low-energy constant, $L_{10}^r$, is determined in a complete next-to-next-to-leading-order (NNLO) analysis, using a combination of lattice and continuum data for the flavor $ud$ $V-A$ correlator and results from a recent chiral sum-rule analysis of the flavor-breaking combination of $ud$ and $us$ $V-A$ correlator differences. The analysis also fixes two combinations of NNLO low-energy constants, the determination of which is crucial to the precision achieved for $L_{10}^r$. Using the results of the flavor-breaking chiral $V-A$ sum rule obtained with current versions of the strange hadronic $\tau$ branching fractions as input, we find $L_{10}^r(m_\rho )\, =\, -0.00346(32)$. This result represents the first NNLO determination of $L_{10}^r$ having all inputs under full theoretical and/or experimental control, and the best current precision for this quantity.

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JO - Physical Review D

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A Combined NNLO Lattice-Continuum Determination of $L_{10}^r$

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Particle Theory at the Tait Institute

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