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Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy \pi\pi Scattering
High Energy Physics - Phenomenology · Submitted 27 Mar 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The result $l_2^r ( M_{\rho} ) = ( 1.6 \pm 0.4 \pm 0.9 ) \times 10^{-3} ( {\bar l_2} = 4.17 \pm 0.19 \pm 0.43$) reproduces the correct D-waves but it is incompatible with existing Standard \chi PT analyses of $K_{l4}$ form factors beyond one loop.
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The abstract, sentence by sentence
Four of the six parameters defining the two-loop \pi\pi scattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard \chi PT expressions, we obtain the threshold parameters, low-energy phases and the O(p^4) constants $l_1^r, l_2^r$. The result $l_2^r ( M_{\rho} ) = ( 1.6 \pm 0.4 \pm 0.9 ) \times 10^{-3} ( {\bar l_2} = 4.17 \pm 0.19 \pm 0.43$) reproduces the correct D-waves but it is incompatible with existing Standard \chi PT analyses of $K_{l4}$ form factors beyond one loop.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Four of the six parameters defining the two-loop \pi\pi scattering amplitude have been determined using Roy dispersion relations. | background 0.88 | 0.13 | 0.06 | asserted 1.00 |
| s1 | Combining this information with the Standard \chi PT expressions, we obtain the threshold parameters, low-energy phases and the O(p^4) constants $l_1^r, l_2^r$. | method 0.74 | 0.86 | 0.09 | asserted 1.00 |
| s2 | The result $l_2^r ( M_{\rho} ) = ( 1.6 \pm 0.4 \pm 0.9 ) \times 10^{-3} ( {\bar l_2} = 4.17 \pm 0.19 \pm 0.43$) reproduces the correct D-waves but it is incompatible with existing Standard \chi PT analyses of $K_{l4}$ form factors beyond one loop. | result 0.88 | 0.80 | 0.76 | asserted 1.00 |
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Original abstract
Four of the six parameters defining the two-loop \pi\pi scattering amplitude have been determined using Roy dispersion relations. Combining this information with the Standard \chi PT expressions, we obtain the threshold parameters, low-energy phases and the O(p^4) constants $l_1^r, l_2^r$. The result $l_2^r ( M_{\rho} ) = ( 1.6 \pm 0.4 \pm 0.9 ) \times 10^{-3} ( {\bar l_2} = 4.17 \pm 0.19 \pm 0.43$) reproduces the correct D-waves but it is incompatible with existing Standard \chi PT analyses of $K_{l4}$ form factors beyond one loop.
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Given the relevance of eq:XPTLag in Standard Model pion scattering, the amplitudes for $G= SU(2)$ isospin pions have been computed through two-loop order [ref] .
Even-point Multi-loop Unitarity and its Applications: Exponentiation, Anomalies and Evanescence · Even-point Effective Field Theories · 0.81
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