We investigate the possible corrections to the linear Regge trajectories for the lightquark meson sector by matching two-point correlators of quark currents to the Operator Product Expansion. We find that the allowed modifications to the linear behavior must decrease rapidly with the principal quantum number. After fitting the lightest states in each channel and certain low-energy constants the whole spectrum for meson masses and residues is obtained in a satisfactory agreement with phenomenology. The perturbative corrections to our results are discussed.Keywords: QCD; sum rules; large-Nc.The observed masses squared of mesons with given quantum numbers form linear trajectories 1,2 depending on the number of radial excitation n. This is a strong indication that QCD admits an effective string description, as this type of spectrum is characteristic e.g. of the bosonic string. In the bosonic string model the slope of all trajectories must be equal since this quantity is proportional to the string tension depending on gluedynamics only. However, there exist sizeable deviations from the string picture. In the present analysis we examine possible corrections to the linear trajectories in the vector (V), axial-vector (A), scalar (S), and pseudoscalar (P) channels 3 . Our method is based on the consideration of the two-point correlators of V,A,S,P quark currents in the large-N c limit of QCD 4 . On the one hand, by virtue of confinement they are saturated by an infinite set of narrow meson resonances, that is, they can be represented by the sum of related meson poles in Euclidean space:expressing the quark-hadron duality 5 . Here J ≡ S, P, V, A; Γ = i, γ 5 , γ µ , γ µ γ 5 . Further we denote F S,P ≡ G S,P m S,P . On the other hand, their high-energy asymptotics 1

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A possible explanation for the appearance of light fermions and Higgs bosons on the four-dimensional domain wall is proposed. The mechanism of light particle trapping is accounted for by a strong self-interaction of five-dimensional pre-quarks. We obtain the low-energy effective action which exhibits the invariance under the so called τ -symmetry. Then we find a set of vacuum solutions which break that symmetry and the five-dimensional translational invariance. One type of those vacuum solutions gives rise to the domain wall formation with consequent trapping of light massive fermions and Higgs-like bosons as well as massless sterile scalars, the so-called branons. The induced relations between lowenergy couplings for Yukawa and scalar field interactions allow to make certain predictions for light particle masses and couplings themselves, which might provide a signature of the higher dimensional origin of particle physics at future experiments. The manifest translational symmetry breaking, eventually due to some gravitational and/or matter fields in five dimensions, is effectively realized with the help of background scalar defects. As a result the branons acquire masses, whereas the ratio of Higgs and fermion (presumably top-quark) masses can be reduced towards the values compatible with the present-day phenomenology. Since the branons do not couple to fermions and the Higgs bosons do not decay into branons, the latter ones are essentially sterile and stable, what makes them the natural candidates for the dark matter in the Universe.