We revisit the model of mesons as rotating strings with massive endpoints and confront it with meson spectra. We look at Regge trajectories both in the (J, M²) and (n, M²) planes, where J and n are the angular momentum and radial excitation number respectively. We start from states comprised of u and d quarks alone, move on to trajectories involving s and c quarks, and finally analyze the trajectories of the heaviest observed \( b\overline{b} \) mesons. The endpoint masses provide the needed transition between the linear Regge trajectories of the light mesons to the deviations from linear behavior encountered for the heavier mesons, all in the confines of the same simple model. From our fits we extract the values of the quark endpoint masses, the Regge slope (string tension) and quantum intercept. The model also allows for a universal fit where with a single value of the Regge slope we fit all the (J, M²) trajectories involving u, d, s, and c quarks. We include a list of predictions for higher mesons in both J and n.

In this note we collect and summarize the predictions of the Holography Inspired Stringy Hadron (HISH) model. Following a brief review of the model, we list the masses and widths of predicted excited...

Recently a novel hadronic state of mass 6.9 GeV, that decays mainly to a pair of charmonia, was observed in LHCb. The data also reveals a broader structure centered around 6490 MeV and suggests another unconfirmed resonance centered at around 7240 MeV, very near to the threshold of two doubly charmed $$\Xi _{cc}$$Ξ cc baryons. We argue in this note that these exotic hadrons are genuine tetraquarks and not molecules of charmonia. It is conjectured that they are V-baryonium , namely, have an inner structure of a baryonic vertex with a cc diquark attached to it, which is connected by a string to an anti-baryonic vertex with a $${\bar{c}} {\bar{c}}$$c ¯ c ¯ anti-diquark. We examine these states as the analogs of the V-baryonium states $$\Psi (4360)$$Ψ ( 4360 ) and Y(4630)/ $$\Psi (4660)$$Ψ ( 4660 ) which are charmonium-like tetraquarks. One way to test these claims is by searching for a significant decay of the state at 7.2 GeV into $$\Xi _{cc}{\overline{\Xi }}_{cc}$$Ξ cc Ξ ¯ cc . Such a decay would be the analog of the decay of the state Y(4630) into to $$\Lambda _c{\overline{\Lambda }}_c$$Λ c Λ ¯ c . We further argue that there should be trajectories of both orbital and radial excited states of the X(6900). We predict their masses. It is possible that a few of these states have already been seen by LHCb.

We suggest to use the state $Y(4630)$, which decays predominantly to $\Lambda_c\bar\Lambda_c$, as a window to the landscape of tetraquarks. We propose a simple criterion to decide whether a state is a genuine stringy exotic hadron - a tetraquark - or a "molecule". If it is the former it should be on a (modified) Regge trajectory. We present the predictions of the mass and width of the higher excited states on the $Y(4630)$ trajectory. We argue that there should exist an analogous "$Y_b$" state that decays to $\Lambda_b\bar\Lambda_b$ and describe its trajectory. We conjecture also a similar trajectory for tetraquarks containing strange quarks, and the modified Regge trajectories can in fact be predicted for any resonances found decaying to a baryon-antibaryon pair. En route to the results regarding tetraquarks, we also make some additional predictions on higher excited charmonium states. We briefly discuss the zoo of exotic stringy hadrons and in particular we sketch all the possibilities of tetraquark states.Comment: v1: 28 pages, v2: typos fixed, references added, 29 pages, v3: revised, published version, 30 page

We propose a novel measure of chaotic scattering amplitudes. It takes the form of a log-normal distribution function for the ratios $r_n={\delta }_n/{\delta }_{n+1}$ of (consecutive) spacings ${\delta }_n$ between two (consecutive) peaks of the scattering amplitude. We show that the same measure applies to the quantum mechanical scattering on a leaky torus as well as to the decay of highly excited string states into two tachyons. Quite remarkably, the $r_n$ obey the same distribution that governs the nontrivial zeros of Riemann $\zeta$ function.

We analyze the amplitudes of one highly excited string (HES) state with two or three tachyons in open bosonic string theory. We argue that these processes are chaotic by showing that the spacing ratios of successive peaks in the angular dependence of the amplitudes are distributed as predicted by the $\beta$-ensemble of random matrix theory (RMT). We show how the continuous parameter $\beta$ depends on the level and helicity of the scattered HES state. We derive the scattering amplitude of an HES and three tachyons and show that it takes the form of the Veneziano amplitude times a dressing factor, and that the dressing is chaotic as a function of the scattering angle, in the sense that its spacing ratios match with RMT predictions.