Stretched string with self-interaction at the Hagedorn point: Spatial sizes and black holes

Abstract

We analyze the length, mass and spatial distribution of a discretized transverse string in D ⊥ dimensions with fixed end-points near its Hagedorn temperature. We suggest that such a string may dominate the (holographic) Pomeron kinematics for dipole-dipole scattering at intermediate and small impact parameters. Attractive self-string interactions cause the transverse string size to contract away from its diffusive size, a mechanism reminiscent of the string-black-hole transmutation. The string shows sizable asymmetries in the transverse plane that translate to primordial azimuthal asymmetries in the stringy particle production in the Pomeron kinematics for current pp and pA collisions at collider energies. I. INTRODUCTIONRecent high multiplicity events in pA and pp collisions at the LHC [1-3] have revealed some similarities with heavy ion collisions at ultra-relativistic energies: 1) a prompt and large entropy deposition; 2) a large radial and elliptic flow. The results have renewed the interest in the formation of a fireball and the relevance of hydrodynamics in small hadronic collisions at high energy [4][5][6][7][8]. The purpose of this paper is to explore this idea further by using self-interacting strings close to their Hagedorn point. This study complements our recent investigation of cold and self-interacting strings at low-x [9].Hadron collisions at high energies are dominated by soft Pomeron and Reggeon exchanges. The Pomeron is an effective 0 ++ exchange corresponding to the highest Regge trajectory. Its small intercept α P (0) − 1 ≈ 0.08 is used to explain the small growth of the hadron-hadron cross section at large √ s with the rapidity interval χ = ln(s/s 0 ) in the context of Reggeon calculus [10][11][12][13]. First principle perturbative QCD calculations describes a harder Pomeron by re-summing the soft collinear Bremshtralung with a larger intercept and zero slope [14,15].Non-perturbative arguments based on duality suggests that the soft Pomeron involves a closed string exchange in the t-channel. The string world-sheet could be thought as a fishnet of planar gluon diagrams in QCD in the large number of colors limit. The quantum theory of planar diagrams in the double limit of strong coupling and large number of colors is tractable in supersymmetric theories using the holographic principle [16]. Many descriptions of the soft Pomeron in holographic duals to QCD have been suggested without supersymmetry, reproducing a number of results in both DIS and diffractive scattering [4,9,[17][18][19][20][21][22][23]. Recently, we have suggested that highly resolved and cold string with a number of quanta N ≡ 1/x can be used to account for low-x non-perturbative physics [9]. Perturbative low-x physics based on the color glass condensate has been discussed by many [24][25][26][27][28][29][30][31][32][33][34][35][36].One of the most remarkable feature of free strings is the exponential growth with their mass of the degeneracy in their spectra, which translates to a constant entropy to mass ratio [37,38]. Excited...

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