QCD Short-distance Constraints and Hadronic Approximations

This paper discusses a general class of ladder resummation inspired hadronic approximations. It is found that this approach naturally reproduces many successes of single meson per channel saturation models (e.g. VMD) and NJL based models. In particular the existence of a constituent quark mass and a gap equation follows naturally. We construct an approximation that satisfies a large set of QCD short-distance and large $N_c$ constraints and reproduces many hadronic observables. We show how there exists in general a problem between QCD short-distance constraints for Green Functions and those for form factors and cross-sections following from the quark-counting rule. This problem while expected for Green functions that do not vanish in purely perturbative QCD also persists for many Green functions that are order parameters.Comment: 27 page

On the two-loop contributions to the pion mass

We derive a simplified representation for the pion mass to two loops in three-flavour chiral perturbation theory. For this purpose, we first determine the reduced expressions for the tensorial two-loop 2-point sunset integrals arising in chiral perturbation theory calculations. Making use of those relations, we obtain the expression for the pion mass in terms of the minimal set of master integrals. On the basis of known results for these, we arrive at an explicit analytic representation, up to the contribution from K-K-eta intermediate states where a closed-form expression for the corresponding sunset integral is missing. However, the expansion of this function for a small pion mass leads to a simple representation which yields a very accurate approximation of this contribution. Finally, we also give a discussion of the numerical implications of our results.Comment: Typos corrected and minor changes in Table 2. Published version. 19 pages, 1 figure, 2 table

Low-energy dynamics of the γγ→ππ\gamma\gamma\to\pi\pi reaction

We calculate the one-quark-loop amplitude for the low energy $\gamma\gamma\to\pi\pi$ collision in the context of the Nambu and Jona-Lasinio model with scalar and pseudoscalar four quark couplings to all orders in the external momenta. We show that the NJL predictions for the $\gamma\gamma\to\pi^+\pi^-$ reaction are not far from the Born amplitude, which is close to the data, and is compatible with the chiral perturbation theory estimations. We determine the corrections given by the NJL model in leading order of $1/N_c$ to the chiral loop amplitude for $\gamma\gamma\to\pi^0\pi^0$. Numerical results for the $\gamma\gamma\rightarrow\pi\pi$ cross sections and for pion polarizabilities are given.Comment: 20 pages in LaTex, 3 figures in 1 Postscript fil

The number of colors in the decays pi^0, eta, eta-prime -> gamma gamma

The decays pi^0, eta, eta-prime -> gamma gamma are investigated up to next-to-next-to-leading order in the framework of the combined 1/N_c and chiral expansions. Without mixing of the pseudoscalar mesons the N_c independence of the pi^0 and eta decay amplitudes is shown to persist at the one-loop level, although the contribution of the Wess-Zumino-Witten term to the pertinent vertices is not canceled by the N_c dependent part of a Goldstone-Wilczek term. The decay amplitude of the singlet field, on the other hand, depends strongly on N_c and yields under the inclusion of mixing also a strong N_c dependence for the eta decay. Both the eta and eta-prime decay are suited to confirm the number of colors to be N_c=3.Comment: 18 pages, 1 figur

Tests of the naturalness of the coupling constants in ChPT at order p^6

We derive constraints on combinations of O(p^6) chiral coupling constants by matching a recent two-loop calculation of the pi-K scattering amplitude with a set of sum rules. We examine the validity of the natural expectation that the values of the chiral couplings can be associated with physics properties of the light resonance sector. We focus, in particular, on flavour symmetry breaking of vector resonances. A resonance chiral Lagrangian is constructed which incorporates flavour symmetry breaking more completely than was done before. We use pi-K unsubtracted sum rules as tests of the modelling of the resonance contributions to the chiral couplings. In some cases the O(p^6) couplings are found not to be dominated by the resonance contributions.Comment: 15 pages, 5 figures; v2: minor improvements, to appear in Eur. Phys. J.

Towards a determination of the chiral couplings at NLO in 1/N(C): L_8(mu) and C_38(mu)

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 two-point functions, within the single-resonance approximation. Imposing the correct QCD short-distance constraints, one determines their difference Pi(t)=Pi_S(t)-Pi_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 mu_0=0.77 GeV, we obtain L_8(mu_0)^{SU(3)} = (0.6+-0.4)10^{-3} and C_{38}(mu_0)^{SU(3)}=(2+-6)10^{-6}.Comment: Extended version published at JHEP01(2007)039. A NLO prediction for the O(p6) chiral coupling C_38 has been added. The original L_8 results remain unchange

The BKB_K Kaon Parameter in the Chiral Limit

We introduce four-point functions in the hadronic ladder resummation approach to large $N_c$ QCD Green functions. We determine the relevant one to calculate the $B_K$ kaon parameter in the chiral limit. This four-point function contains both the large momenta QCD OPE and the small momenta ChPT at NLO limits, analytically. We get $\hat B_K^\chi = 0.38 \pm 0.15$. We also give the ChPT result at NLO for the relevant four-point function to calculate $B_K$ outside the chiral limit, while the leading QCD OPE is the same as the chiral limit one.Comment: 17 page

Radiative Ke3 decays revisited

Motivated by recent experimental results and ongoing measurements, we review the chiral perturbation theory prediction for radiative Ke3 decays (neutral kaons). Special emphasis is given on the stability of the inner bremsstrahlung-dominated relative branching ratio vs. the Ke3 form factors, and on the separation of the structure dependent amplitude in differential distributions over the phase space. For the structure dependent terms, an assessment of the order p^6 corrections is given. In particular, a full next-to-leading order calculation of the axial component is performed. The experimental analysis of the photon energy spectrum is discussed, and other potentially useful distributions are introduced.Comment: Version published in Eur.Phys.J.C.: 23 pages (LaTeX), 10 figures. Minor changes in text, typos removed, references updated, Springer style file use

eta, eta-prime -> pi^+ pi^- gamma with coupled channels

The decays eta, eta-prime -> pi^+ pi^- gamma are investigated within an approach that combines one-loop chiral perturbation theory with a coupled channel Bethe-Salpeter equation which satisfies unitarity constraints and generates vector mesons dynamically from composite states of two pseudoscalar mesons. It is furthermore shown that the inclusion of the eta-prime as a dynamical degree of freedom does not renormalize the Wess-Zumino-Witten term.Comment: 21 pages, 11 figure

η→3π\eta \to 3 \pi at Two Loops In Chiral Perturbation Theory

We calculate the decay $\eta\to3\pi$ at next-to-next-to-leading order or order $p^6$ in Chiral Perturbation Theory. The corrections are somewhat larger than was indicated by dispersive estimates. We present numerical results for the Dalitz plot parameters, the ratio $r$ of the neutral to charged decay and the total decay rate. In addition we derive an inequality between the slope parameters of the charged and neutral decay. The experimental charged decay rate leads to central values for the isospin breaking quantities $R=42.2$ and $Q=23.2$.Comment: 35p, some misprints corrected and a wrong figure replace. Some sentences reformulated and Sect. 2 shortene