scholarly journals Low-energy interactions of Nambu-Goldstone bosons withDmesons in covariant chiral perturbation theory

2010 ◽  
Vol 82 (5) ◽  
Author(s):  
L. S. Geng ◽  
N. Kaiser ◽  
J. Martin-Camalich ◽  
W. Weise
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Goldstone Bosons

scholarly journals MASS AND WIDTH OF THE σ

2007 ◽  
Vol 22 (02n03) ◽  
pp. 257-265 ◽  
Author(s):  
HEINRICH LEUTWYLER
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Scattering Amplitude ◽  
Pole Position ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Goldstone Bosons ◽  
Quantum Numbers ◽  
Low Energies ◽  
Work Done

I report on recent work done in collaboration with Irinel Caprini and Gilberto Colangelo1. We observe that the Roy equations lead to a representation of the ππ scattering amplitude that exclusively involves observable quantities, but is valid for complex values of s. At low energies, this representation is dominated by the contributions from the two subtraction constants, which are known to remarkable precision from the low energy theorems of chiral perturbation theory. Evaluating the remaining contributions on the basis of the available data, we demonstrate that the lowest resonance carries the quantum numbers of the vacuum and occurs in the vicinity of the threshold. Although the uncertainties in the data are substantial, the pole position can be calculated quite accurately, because it occurs in the region where the amplitude is dominated by the subtractions. The calculation neatly illustrates the fact that the dynamics of the Goldstone bosons is governed by the symmetries of QCD.

scholarly journals New method for fitting the low-energy constants in chiral perturbation theory

2020 ◽  
Vol 102 (9) ◽  
Author(s):  
Qin-He Yang ◽  
Wei Guo ◽  
Feng-Jun Ge ◽  
Bo Huang ◽  
Hao Liu ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Low Energy ◽  
New Method ◽  
Chiral Perturbation ◽  
Energy Constants

CHIRAL PERTURBATION THEORY AT THE QUARK LEVEL

1992 ◽  
Vol 07 (29) ◽  
pp. 7305-7338 ◽  
Author(s):  
A.N. IVANOV ◽  
M. NAGY ◽  
N.I. TROITSKAYA
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Final State Interaction ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Final State ◽  
Large N ◽  
Quark Level ◽  
Energy Approximation

The chiral perturbation theory is developed at the quark level within the extended Nambu-Jona-Lasinio model, which we used for the low-energy approximation of QCD in the leading order of the large N expansion. In terms of constituent-quark loop diagrams we analyze all of the main low-energy effects caused by the first order corrections in the current-quark-mass expansions. For the correct description of the η→3π decays we confirm the important role of the final-state interaction quoted by Gasser and Leutwyler.

scholarly journals Dissecting the $$\Delta I=1/2$$ rule at large $$N_c$$

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Andrea Donini ◽  
Pilar Hernández ◽  
Carlos Pena ◽  
Fernando Romero-López
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Low Energy ◽  
Kaon Decay ◽  
Chiral Perturbation ◽  
Kaon Decays ◽  
Diagrammatic Analysis ◽  
Good Agreement

Abstract We study the scaling of kaon decay amplitudes with the number of colours, $$N_c$$Nc, in a theory with four degenerate flavours, $$N_f=4$$Nf=4. In this scenario, two current-current operators, $$Q^\pm $$Q±, mediate $$\Delta S=1$$ΔS=1 transitions, such as the two isospin amplitudes of non-leptonic kaon decays for $$K\rightarrow (\pi \pi )_{I=0,2}$$K→(ππ)I=0,2, $$A_0$$A0 and $$A_2$$A2. In particular, we concentrate on the simpler $$K\rightarrow \pi $$K→π amplitudes, $$A^\pm $$A±, mediated by these two operators. A diagrammatic analysis of the large-$$N_c$$Nc scaling of these observables is presented, which demonstrates the anticorrelation of the leading $${{\mathcal {O}}}(1/N_c)$$O(1/Nc) and $${{\mathcal {O}}}(N_f/N_c^2)$$O(Nf/Nc2) corrections in both amplitudes. Using our new $$N_f=4$$Nf=4 and previous quenched data, we confirm this expectation and show that these corrections are naturally large and may be at the origin of the $$\Delta I=1/2$$ΔI=1/2 rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, $$g^\pm $$g±, can be determined. A NLO estimate of the $$K \rightarrow (\pi \pi )_{I=0,2}$$K→(ππ)I=0,2 isospin amplitudes can then be derived, which is in good agreement with the experimental value.

scholarly journals First direct lattice calculation of the chiral perturbation theory low-energy constant ℓ7

2021 ◽  
Vol 104 (7) ◽  
Author(s):  
R. Frezzotti ◽  
G. Gagliardi ◽  
V. Lubicz ◽  
G. Martinelli ◽  
F. Sanfilippo ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Low Energy ◽  
Lattice Calculation ◽  
Chiral Perturbation ◽  
Energy Constant ◽  
Direct Lattice
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