QCD isospin breaking in meson masses, decay constants and quark mass ratios

Amorós, G.; Bijnens, Johan; Talavera, P.

doi:10.1016/s0550-3213(01)00121-3

Cited by 231 publications

(400 citation statements)

References 69 publications

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“…In fact using the L 1 , L 2 , and L 3 values of Ref. [22], we obtainl 1 = 5.64 ± 0.84 andl 2 = 1.95 ± 0.23 which do not agree well with the values quoted in Ref. [4], but are in agreement with our bounds.…”

Section: Unitarity Relations For the Linear Sigma Modelcontrasting

confidence: 67%

Dispersion relation bounds forππscattering

2008

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Axiomatic principles such as analyticity, unitarity, and crossing symmetry constrain the second derivative of the π π scattering amplitudes in some channels to be positive in a region of the Mandelstam plane. Since this region lies in the domain of validity of chiral perturbation theory, we can use these positivity conditions to bound linear combinations ofl1 andl2. We compare our predictions with those derived previously in the literature using similar methods. We compute the one-loop π π scattering amplitude in the linear sigma model (LSM) using the MS scheme, a result hitherto absent in the literature. The LSM values forl1 andl2 violate the bounds for small values of mσ/mπ. We show how this can occur, while still being consistent with the axiomatic principles.

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Section: Unitarity Relations For the Linear Sigma Modelcontrasting

confidence: 67%

Dispersion relation bounds forππscattering

2008

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“…Note that thel i used in the formulae for R Mπ , R Fπ differ from these values by a term logarithmic in [30] (the uncertainties in L 6 and L 9 are our estimate).…”

Section: Simplified Formulaementioning

confidence: 75%

“…[29,22]; for the SU(3) low energy constants L r i (µ) we refer to the O(p 4 ) fit of Ref. [30]. In the former case, the full correlation matrix is given in [29] in the latter case it has been communicated privately [31], but in either case the final errors are almost the same, regardless whether the full correlation matrix is used or just the diagonal part.…”

Section: Numerical Analysismentioning

confidence: 99%

Finite volume effects for meson masses and decay constants

2005

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We present a detailed numerical study of finite volume effects for masses and decay constants of the octet of pseudoscalar mesons. For this analysis we use chiral perturbation theory and asymptotic formulaeà la Lüscher and propose an extension of the latter beyond the leading exponential term. We argue that such a formula, which is exact at the one-loop level, gives the numerically dominant part at two loops and beyond. Finally, we discuss the possibility to determine low energy constants from the finite volume dependence of masses and decay constants.

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“…The precision required in present phenomenological applications makes necessary to include corrections of O(p 6 ). While many two-loop χPT calculations have been already performed [7,8,9,10,11,12,13,14,15], the large number of unknown low-energy couplings (LECs) appearing at this order puts a clear limit to the achievable accuracy [16].…”

Section: The Large-n C Limitmentioning

confidence: 99%

Towards a determination of the chiral couplings at NLO in 1/N_C: L₈^r(μ) and C₃₈^r(μ)

Rosell

Pich

Sanz-Cillero

2007

J. High Energy Phys.

126

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We present a dispersive method which allows to investigate the low-energy couplings of chiral perturbation theory at the next-to-leading order (NLO) in the 1/N C expansion, keeping full control of their renormalization scale dependence. Using the resonance chiral theory Lagrangian, we perform a NLO calculation of the scalar and pseudoscalar twopoint functions, within the single-resonance approximation. Imposing the correct QCD short-distance constraints, one determines their difference Π(t) ≡ Π S (t) − Π P (t) in terms of the pion decay constant and resonance masses. Its low momentum expansion fixes then the low-energy chiral couplings L 8 and C 38 . At µ 0 = 0.77 GeV, we obtain L r 8 (µ 0 ) SU (3) = (0.6 ± 0.4) · 10 −3 and C r 38 (µ 0 ) SU (3) = (2 ± 6) · 10 −6 .

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QCD isospin breaking in meson masses, decay constants and quark mass ratios

Cited by 231 publications

References 69 publications

Dispersion relation bounds forππscattering

Dispersion relation bounds forππscattering

Finite volume effects for meson masses and decay constants

Towards a determination of the chiral couplings at NLO in 1/N_C: L₈^r(μ) and C₃₈^r(μ)

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QCD isospin breaking in meson masses, decay constants and quark mass ratios

Cited by 231 publications

References 69 publications

Dispersion relation bounds forππscattering

Dispersion relation bounds forππscattering

Finite volume effects for meson masses and decay constants

Towards a determination of the chiral couplings at NLO in 1/NC: L8r(μ) and C38r(μ)

Contact Info

Product

Resources

About

Towards a determination of the chiral couplings at NLO in 1/N_C: L₈^r(μ) and C₃₈^r(μ)