A tetraquark or not a tetraquark: A holography inspired stringy hadron (HISH) perspective

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

A rotating string model versus baryon spectra

We continue our program of describing hadrons as rotating strings with massive endpoints. In this paper we propose models of baryons and confront them with the baryon Regge trajectories. We show that these are best fitted by a model of a single string with a quark at one endpoint and a diquark at the other. This model is preferred over the Y-shaped string model with a quark at each endpoint. We show how the model follows from a stringy model of the holographic baryon which includes a baryonic vertex connected with N_c strings to flavor probe branes. From fitting to baryonic data we find that there is no clear evidence for a non-zero baryonic vertex mass, but if there is such a mass it should be located at one of the string endpoints. The available baryon trajectories in the angular momentum plane (J,M^2), involving light, strange, and charmed baryons, are rather well fitted when adding masses to the string endpoints, with a single universal slope of 0.95 GeV^-2. Most of the results for the quark masses are then found to be consistent with the results extracted from the meson spectra in a preceding paper, where the value of the slope emerging from the meson fits was found to be 0.90 GeV^-2. In the plane of quantum radial excitations, (n,M^2), we also find a good agreement between the meson and baryon slopes. The flavor structure of the diquark is examined, where our interest lies in particular on baryons composed of more than one quark heavier than the u and d quarks. For these baryons we present a method of checking the holographic interpretation of our results.Comment: v2: typos corrected, references added, 41 pages; v3: added some sentences to clarify the relation between our model and the holograhic string, 42 page

Large N Chern-Simons with massive fundamental fermions - A model with no bound states

In a previous paper, we analyzed the theory of massive fermions in the fundamental representation coupled to a U(N) Chern-Simons gauge theory in three dimensions at level K. It was done in the large N, large K limits where Lambda=N/K was kept fixed. Among other results, we showed there that there are no high mass quark anti-quark bound states. Here we show that there are no bound states at all.Comment: 14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1306.6465. A reference and acknowledgement adde

On bound-states of the Gross Neveu model with massive fundamental fermions

In the search for QFT's that admit boundstates, we reinvestigate the two dimensional Gross-Neveu model, but with massive fermions. By computing the self-energy for the auxiliary boundstate field and the effective potential, we show that there are no bound states around the lowest minimum, but there is a meta-stable bound state around the other minimum, a local one. The latter decays by tunneling. We determine the dependence of its lifetime on the fermion mass and coupling constant.Comment: 10 pages, 2 figures Version to be published in JHE

Rotating strings confronting PDG mesons

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-bbar 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.Comment: v2: typos fixed and reference added, 47 pages / v3: added section in appendix detailing the states used in the fits, 51 page

Glueballs as rotating folded closed strings

In previous papers we argued that mesons and baryons can be described as rotating open strings in holographic backgrounds. Now we turn to closed strings, which should be the duals of glueballs. We look at the rotating folded closed string in both flat and curved backgrounds. A basic prediction of the closed string model is that the slope of Regge trajectories is half that of open strings. We propose that a simple method to identify glueballs is to look for resonances that belong to trajectories with a slope of approximately 0.45 GeV^-2, half the meson slope. We therefore look at the experimental spectra of flavorless light mesons to see if such a scheme, where some of the states are placed on open string trajectories and some on closed ones, can fit known experimental data. We look at the f_0 (J^PC = 0^++) and f_2 (2^++) resonances. As there is no preference for a single scheme of sorting the different states into meson and glueball trajectories, we present several possibilities, each identifying a different state as the glueball. We supplement each scheme with predictions for the masses of excited glueballs. We show that the width of the decay into two mesons is different for glueballs and mesons thus providing a supplementary tool to distinguish between them. In addition, we look at some lattice QCD results for glueball spectra and check their compatibility with the closed string model. One of the main conclusions of this paper is that an extension of experimental data on the spectrum of flavorless hadrons is needed, in particular in the region between around 2.4 GeV and 3 GeV.Comment: v1: 43 pages, v2: references added, 44 pages, v3: references added, 44 page

On the spectra of scalar mesons from HQCD models

We determine the holographic spectra of scalar mesons from the fluctuations of the embedding of flavor D-brane probes in HQCD models. The models we consider include a generalization of the Sakai Sugimoto model at zero temperature and at the "high-temperature intermediate phase", where the system is in a deconfining phase while admitting chiral symmetry breaking and a non-critical 6d model at zero temperature. All these models are based on backgrounds associated with near extremal N_c D4 branes and a set of N_f<<N_c flavor probe branes that admit geometrical chiral symmetry breaking. We point out that the spectra of these models include a 0^{--} branch which does not show up in nature. At zero temperature we found that the masses of the mesons M_n depend on the "constituent quark mass" parameter m^c_q and on the excitation number n as M_n^2 m^c_q and M^2_n n^{1.7} for the ten dimensional case and as M_n m^c_q and M_n n^{0.75} in the non-critical case. At the high temperature intermediate phase we detect a decrease of the masses of low spin mesons as a function of the temperature similar to holographic vector mesons and to lattice calculations.Comment: 22 pages, 12 figure