scholarly journals CHIRAL PERTURBATION THEORY IN THE FRAMEWORK OF NONCOMMUTATIVE GEOMETRY

1996 ◽  
Vol 11 (08) ◽  
pp. 1509-1522 ◽  
Author(s):  
FARHAD ARDALAN ◽  
KAMRAN KAVIANI
Keyword(s):  
Perturbation Theory ◽  
Noncommutative Geometry ◽  
Chiral Perturbation Theory ◽  
Skyrme Model ◽  
Coupling Constants ◽  
Chiral Perturbation ◽  
Similar Treatment ◽  
The Right ◽  
Good Agreement

We consider the noncommutative generalization of the chiral perturbation theory. The resultant coupling constants are severely restricted by the model and in good agreement with the data. When applied to the Skyrme model, our scheme reproduces the non-Skyrme term with the right coefficient. We comment on a similar treatment of the linear σ model.

Light front Hamiltonian for boson form of QED (1 + 1) in Pauli–Villars regularization

2019 ◽  
Vol 34 (21) ◽  
pp. 1950113
Author(s):  
V. A. Franke ◽  
M. Yu. Malyshev ◽  
S. A. Paston ◽  
E. V. Prokhvatilov ◽  
M. I. Vyazovsky
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chiral Condensate ◽  
Light Front ◽  
Coupling Constants ◽  
Hamiltonian Approach ◽  
Chiral Perturbation ◽  
Dimensional Models ◽  
Villars Regularization ◽  
Ultraviolet Regularization

Light front (LF) Hamiltonian for QED in [Formula: see text] dimensions is constructed using the boson form of this model with additional Pauli–Villars-type ultraviolet regularization. Perturbation theory, generated by this LF Hamiltonian, is proved to be equivalent to usual covariant chiral perturbation theory. The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some renormalization of coupling constants. The obtained results can be useful when one attempts to apply LF Hamiltonian approach for [Formula: see text]-dimensional models like QCD.

Resonant and non-resonant contributions of B → K∗(p1,𝜖1){Kπ,ππ,KK} decay modes

2019 ◽  
Vol 34 (06) ◽  
pp. 1950043
Author(s):  
Mahboobeh Sayahi
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Branching Ratio ◽  
Heavy Meson ◽  
Chiral Perturbation ◽  
Decay Modes ◽  
Qcd Factorization ◽  
Three Body ◽  
Good Agreement

In this paper, the non-leptonic three-body decays [Formula: see text], [Formula: see text], [Formula: see text] are studied by introducing two-meson distribution amplitude for the [Formula: see text], [Formula: see text] and [Formula: see text] pairs in naive and QCD factorization (QCDF) approaches, such that the analysis is simplified into quasi-two body decays. By considering that the vector meson is being ejected in factorization, the resonant and non-resonant contributions are analyzed by using intermediate mesons in Breit–Wigner resonance formalism and the heavy meson chiral perturbation theory (HMChPT), respectively. The calculated values of the resonant and non-resonant branching ratio of [Formula: see text], [Formula: see text] and [Formula: see text] decay modes are compared with the experimental data. For [Formula: see text] and [Formula: see text], the non-resonant contributions are about 70–80% of experimental data, for which the total results by considering resonant contributions are in good agreement with the experiment.

scholarly journals Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen ◽  
Martin A. Mojahed
Keyword(s):  
Perturbation Theory ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Strange Quark ◽  
Chemical Potential ◽  
Light Quark ◽  
Quark Condensate ◽  
Lattice Data ◽  
Chiral Perturbation ◽  
Good Agreement

AbstractWe calculate the light-quark condensate, the strange-quark condensate, the pion condensate, and the axial condensate in three-flavor chiral perturbation theory ($$\chi $$ χ PT) in the presence of an isospin chemical potential at next-to-leading order at zero temperature. It is shown that the three-flavor $$\chi $$ χ PT effective potential and condensates can be mapped onto two-flavor $$\chi $$ χ PT ones by integrating out mesons with strange-quark content (kaons and eta), with renormalized couplings. We compare the results for the light-quark and pion condensates at finite pseudoscalar source with ($$2+1$$ 2 + 1 )-flavor lattice QCD, and we also compare the axial condensate at zero pseudoscalar and axial sources with lattice QCD data. We find that the light-quark, pion, and axial condensates are in very good agreement with lattice data. There is an overall improvement by including NLO effects.

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.

TOWARD THE UNDERSTANDING OF K→3π DECAYS IN CHIRAL PERTURBATION THEORY

1989 ◽  
Vol 04 (09) ◽  
pp. 869-876 ◽  
Author(s):  
HAI-YANG CHENG ◽  
C.Y. CHEUNG ◽  
WAI BONG YEUNG
Keyword(s):  
Perturbation Theory ◽  
Chiral Lagrangians ◽  
Current Algebra ◽  
Chiral Perturbation Theory ◽  
Higher Order ◽  
Chiral Perturbation ◽  
Good Agreement

Corrections to current-algebra analysis of K→3π decay amplitudes are calculated using the dimension-four effective chiral Lagrangians, which are uniquely determined from the integration of nontopological chiral anomalies. We find that the constant and linear terms in the ΔI = ½ amplitude are in good agreement with experiment; the previous discrepancy of 20–35% between current algebra and experiment is thus accounted for by including the higher order chiral Lagrangians. Predictions for quadratic terms are also given for both ΔI = ½ and [Formula: see text] transitions.

ON THE SIGNIFICANCE OF RECENT LATTICE RESULTS FOR THE CHIRAL LAGRANGIAN

2008 ◽  
Vol 23 (21) ◽  
pp. 3187-3190
Author(s):  
H. LEUTWYLER
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Quark Condensate ◽  
Low Energy ◽  
Coupling Constants ◽  
Chiral Perturbation ◽  
Decay Constants ◽  
Energy Domain ◽  
The Masses ◽  
Ozi Rule

The report concerns only one of the issues discussed in my talk at ICFP 2007: the significance of recent lattice results for our understanding of the nonperturbative phenomena in the low energy domain of QCD. All of these results are consistent with the phenomenological estimates for the coupling constants of the chiral SU (2)× SU (2) Lagrangian and thereby corroborate the predictions based on these. In the case of SU (3)× SU (3), the results also confirm the old estimates obtained from chiral perturbation theory. In particular, the first two terms in the expansion of the masses and decay constants in powers of ms appear to represent a decent approximation for the full series. Some of the lattice results indicate that the quark condensate violates the OZI-rule rather strongly, but as there are some discrepancies concerning this issue, it is too early to draw conclusions.

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