Towards a theory of bottom-up holographic models for linear Regge trajectories of light mesons

Abstract

We develop a bottom-up holographic theory of linear meson Regge trajectories that generalizes and unites into one logical framework various approaches proposed in the past and scattered in the literature. The starting point of the theory is a quadratic in fields holographic five-dimensional action in which the Poincaré invariance along the holographic coordinate is violated in the most general way compatible with the linear Regge behavior of the discrete spectrum in four dimensions. The linearity of radial spectrum ensures the correct structure of OPE of two-point correlation functions. It is further demonstrated how different Soft Wall (SW) like holographic models existing in the literature plus some new ones emerge from our general setup. Various interrelations between the emerging models are studied. These models include the known SW models with different sign in the exponential background, the SW models with certain generalized backgrounds, with modified metrics, and models with the mass term depending on the holographic coordinate in a simple polynomial way. We argue that this dependence allows to describe the effects caused by the main non-local phenomena of strongly coupled 4D gauge theory -the confinement and spontaneous chiral symmetry breaking -in terms of a local 5D dual field theory in the AdS space. We provide a detailed comparison of our approach with the Light Front holographic QCD, with the spectroscopic predictions of the dual Veneziano like amplitudes, and with the experimental Regge phenomenology. A renormalization recipe is formulated that allows to avoid the problem of unphysical massless pole arising in the vector case in a general situation. The given recipe can be used to predict the intercept of linear radial trajectory related with the ground state mass. We apply our general approach to a holographic study of confinement, chiral symmetry breaking, and the pion form factor.

Revisiting the pion Regge trajectories

“…. The obtained averaged slopes α nr = 1.10 and α l = 1.10 with m R = 0.135 GeV are equal to the slope obtained in Ref [20,91]. [ M 2 ≈1.10(l+ n r + 0.62) ].…”

“…The Regge trajectory is one of the effective approaches for studying hadron spectra [2][3][4][5][6][7][8][9][10][11]. The orbital and radial Regge trajectories [12] for pion are often taken as being approximately linear in the (M 2 , l) plane and in the (M 2 , n r ) plane, respectively, M 2 = α 1 l+α 2 n r +c [13][14][15][16][17][18][19][20], where M is the mass, α 1 and α 2 are the Regge slopes, l is the orbital angular momentum, n r is the radial quantum number, and c is a constant. The pion Regge trajectories are in fact nonlinear when they are examined more precisely, see Fig.…”

Incorporation of heavy-quark mass into soft-wall holographic models

“…In the spirit of "No-wall" holographic model of Ref. [40] (see also a more detailed discussion in [7]), let us eliminate the exponential background in the action (2.7) by the field transformation Φ = e −cz φ.…”

“…The substitution of (2.24) into (2.25) gives the potential (2.14) as expected. Note that a similar transformation of the standard quadratic SW model will result in a O(z 4 ) contribution to the effective mass (2.24) (this contribution determines the slope of Regge spectrum) while the O(z) contribution will be absent [7].…”

“…This phenomenological approach to strong interactions has various heuristic motivations [6] and by now it counts several hundreds of publications on variety of applications in hadron physics (Regge spectroscopy, hadron formfactors, QCD phase diagram, etc. [7]). As a rule, the constructed holographic models describe the sector of light quark flavors, while the progress in holographic description of heavy flavors looks relatively modest.…”