0 π ∆ ∆ coupling constant

We calculate the π∆∆ coupling gπ0∆++∆++ using light cone QCD sum rule. Our result is gπ0∆++∆++ = (11.8 ± 2.0). PACS numbers: 12.39.Fe, 14.20.Gk The π∆∆ coupling constant g1, like the nucleon axial charge gA, is a basic parameter which enters the loop calculation in all processes involved with delta resonance [1] in chiral perturbation theory. Unfortunately it is not directly accessible experimentally. A special quartet scheme of chiral symmetry realization for evenand odd-parity baryon resonances was proposed in [2]. Based on such a scheme the authors found that the parity nonchanging couplings such as π∆±N ∗ ±, π∆±∆±, and πN ∗ ±N ∗ ± are forbidden at the leading order [2]. Such a result is very different from quark model prediction [3] and large Nc argument g1 = 9 5 gA [5]. Recently an attempt was made to extract this important coupling from the fit to the phase shift data of pion-nucleon scattering in the fourth order chiral perturbation theory analysis [4]. Because this coupling only appears in the third order loop contribution, it’s very hard to pin down the value precisely. However the preliminary result was g1 = −0.94 ∼ −2.65 [4]. These value for g1 comes out very differently from the large Nc prediction as noted in [4]. So an independent theoretical extraction may prove useful to help clarify the present ambiguous situation concerning this coupling. We have calculated πNN and πNN [6], ηNN [7] and ρNN , ωNN [8] coupling constants in the framework of light cone QCD sum rule (LCQSR). The extracted values of various couplings from LCQSR are in good agreement with those used in or obtained from phenomenological analysis. In this short note we extend the same formalism to calculate the π∆∆ coupling constant. Let’s first introduce some notations. For the ∆ resonance, we use the isospurion formalism, treating the ∆ field T i μ(x) as a vector spinor in both spin and isospin space with the constraint τ T i μ(x) = 0 [1]. The components of this field are T 3 μ = − √