We investigate the high-energy fixed-angle scattering of pions and $\textit{ρ}$-mesons in a bottom-up holographic QCD model. To this end, we generalise the approach of Polchinski and Strassler [1] to write an ansatz for meson scattering amplitudes based on superstring scattering amplitudes in asymptotically AdS space. We demonstrate that our generalisation of the Polchinski-Strassler proposal is necessary to describe $\textit{ρ}$-meson scattering consistently with the Nambu-Goldstone boson equivalence theorem. Our results for pion and $\textit{ρ}$-meson scattering amplitudes are in agreement with the constituent counting rule found in QCD. Moreover, our proposal for 2-to-2 scattering amplitudes provides a method for computing scattering angle dependence.

United Kingdom

Adi Armoni

Japan

Bartosz Pyszkowski

Shigeki Sugimoto

South Korea

Dorin Weissman

High-energy fixed-angle meson scattering and the constituent counting rule in holographic QCD

<p>We establish a new tool for studying strongly coupled matter: an effective theory of black holes in gravity, which maps to a hydrodynamic description of field theories via the gauge-gravity duality. Our approach is inspired by previously known effective theories found in the limit of a high number of dimensions. We argue that the new approach can accurately describe phase transitions in a wide class of theories, such as the Yang-Mills and other nearly critical field theories. As an application to a previously unsolved problem, we analyze the interface between confining and deconfining phases in holographic Yang-Mills theory.</p>

Matti Järvinen

Black hole effective theory for strongly interacting matter

We propose a novel indicator for chaotic quantum scattering processes, the scattering form factor (ScFF). It is based on mapping the locations of peaks in the scattering amplitude to random matrix eigenvalues, and computing the analog of the spectral form factor (SFF). We compute the spectral and scattering form factors of several non-chaotic systems. We determine the ScFF associated with the phase shifts of the leaky torus, closely related to the distribution of the zeros of Riemann zeta function. We compute the ScFF for the decay amplitude of a highly excited string states into two tachyons. We show that it displays the universal features expected from random matrix theory - a decline, a ramp and a plateau - and is in general agreement with the Gaussian unitary ensemble. It also shows some new features, owning to the special structure of the string amplitude, including a “bump” before the ramp associated with gaps in the average eigenvalue density. The “bump” is removed for highly excited string states with an appropriate state dependent unfolding. We also discuss the SFF for the Gaussian β-ensemble, writing an interpolation between the known results of the Gaussian orthogonal, unitary, and symplectic ensembles.

Italy

Massimo Bianchi

Greece

Maurizio Firrotta

Israel

Jacob Sonnenschein

From spectral to scattering form factor

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 <math><mi>β</mi></math>-ensemble of random matrix theory (RMT). We show how the continuous parameter <math><mi>β</mi></math> 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.

Measuring chaos in string scattering processes

We propose a novel measure of chaotic scattering amplitudes. It takes the form of a log-normal distribution function for the ratios <math><msub><mi>r</mi><mi>n</mi></msub><mo>=</mo><msub><mi>δ</mi><mi>n</mi></msub><mo>/</mo><msub><mi>δ</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></math> of (consecutive) spacings <math><msub><mi>δ</mi><mi>n</mi></msub></math> 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 <math><msub><mi>r</mi><mi>n</mi></msub></math> obey the same distribution that governs the nontrivial zeros of Riemann <math><mi>ζ</mi></math> function.

Measure for Chaotic Scattering Amplitudes

We study quantum properties of supersymmetric   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 and   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 extensions of the four dimensional bosonic Chiral Higher Spin Gravities (HiSGRAs). We discuss the spectra, the classical actions and define the Feynman rules in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 and   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 superspaces in the light-front gauge. Using these Feynman rules, we compute tree and one-loop amplitudes for these systems. A dimensional reduction to a system with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supersymmetry and with massive higher spin fields is performed and quantum properties of this system are discussed.

Mirian Tsulaia

Supersymmetric quantum chiral higher spin gravity

We study the emergence of partonic behavior in scattering processes at large Mandelstam’s variable s from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler [1] in two ways. (i) We analyze several holographic confining backgrounds, in particular the hard wall model, the soft wall model and Witten’s model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small s but fade away for large s. In the fixed angle approximation we find in the hard and soft wall models that   <math> <mi>A</mi> </math>  $$ \mathcal{A} $$  ∼ s 2−∆/2 whereas in Witten’s model   <math> <mi>A</mi> </math>  $$ \mathcal{A} $$  ∼ s 3−∆/2 and   <math> <mi>A</mi> </math>  $$ \mathcal{A} $$  ∼ s 7/3−2∆/3 for the 11D and 10D formulations, respectively. In the Regge regime   <math> <mi>A</mi> </math>  $$ \mathcal{A} $$  ∼ s 2 t  −2+α  (log s/t) −1+α  where α is the power found in the fixed angle regime. Using the pole expansion the result for each model is Re [  <math> <mi>A</mi> </math>  $$ \mathcal{A} $$ ] ∼ s  −1, Im [  <math> <mi>A</mi> </math>  $$ \mathcal{A} $$ ] ∼ s  α . We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.

United States

Partonic behavior of string scattering amplitudes from holographic QCD models

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  $$\Xi _{cc}$$  <math> <msub> <mi>Ξ</mi> <mrow> <mi>cc</mi> </mrow> </msub> </math>   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  $${\bar{c}} {\bar{c}}$$  <math> <mrow> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   anti-diquark. We examine these states as the analogs of the V-baryonium states  $$\Psi (4360)$$  <math> <mrow> <mi>Ψ</mi> <mo>(</mo> <mn>4360</mn> <mo>)</mo> </mrow> </math>   and Y(4630)/ $$\Psi (4660)$$  <math> <mrow> <mi>Ψ</mi> <mo>(</mo> <mn>4660</mn> <mo>)</mo> </mrow> </math>   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  $$\Xi _{cc}{\overline{\Xi }}_{cc}$$  <math> <mrow> <msub> <mi>Ξ</mi> <mrow> <mi>cc</mi> </mrow> </msub> <msub> <mover> <mi>Ξ</mi> <mo>¯</mo> </mover> <mrow> <mi>cc</mi> </mrow> </msub> </mrow> </math>  . Such a decay would be the analog of the decay of the state Y(4630) into to  $$\Lambda _c{\overline{\Lambda }}_c$$  <math> <mrow> <msub> <mi>Λ</mi> <mi>c</mi> </msub> <msub> <mover> <mi>Λ</mi> <mo>¯</mo> </mover> <mi>c</mi> </msub> </mrow> </math>  . 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.

Deciphering the recently discovered tetraquark candidates around 6.9 GeV

Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

On the quantization of folded strings in non-critical dimensions

In this note we describe hadrons: mesons and baryons as strings with electric charges on their endpoints. We consider here only the neutral system with opposite charges, coupled to an external constant electromagnetic field. We derive certain classical solutions including rotating folded open strings. We write down the mode expansion and canonically quantize the system. The OPEs associated with such strings are determined. We rederive the non-commutativity of the zero modes and the fact that the charges modify the spacetime metric. We show that the quantum worldsheet energy momentum tensor on the boundary is affected by the endpoint charges and differs from the corresponding Noether current. We determine the generalization of the Veneziano scattering amplitude for such strings in the critical dimension. Phenomenological implications are addressed and in particular we show that the external magnetic field can be tuned so that the amplitude vanishes for particular kinematic setups. We discuss the generalization of such strings to non-critical four dimensional spacetime. In particular we renormalize the divergence of the Polchinski-Strominger effective action associated with the rotating folded string.