A model for pion-pion scattering in large-N QCD

171

We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants s, t and u. We construct these modules for every value of the spacetime dimension D, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by s 2 at fixed t. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for D ≤ 6. For D ≥ 7 there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for D ≤ 6. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also violates our conjectured Regge growth bound, at least when D ≤ 6, even when the exchanged particles have low spin.

Section: Jhep02(2020)114mentioning

confidence: 99%

Section: A3 Constructing Counter Examplesmentioning

confidence: 99%

Classifying and constraining local four photon and four graviton S-matrices

Chowdhury

Gadde

Gopalka

et al. 2020

171

“…The spectrum of long rotating open strings was studied using the effective theory in [15]. 7 In this study, one starts from the free long rotating string and considers all possible higher derivative operators that are consistent with the symmetries of the problem. There are two types of corrections -due to the boundary and the bulk operators.…”

Section: Effective Theory Of Long Stringsmentioning

confidence: 99%

“…This is because here we are considering a Euclidean solution. 7 For the long static string, the set of universal corrections was classified in [24].…”

Section: Effective Theory Of Long Stringsmentioning

confidence: 99%

“…The analysis of [12] assumed that there is no accumulation point in the spectrum and that there is a separation of scales in the large s, t limit. Correspondingly, the result 1 In [6,7] an ansatz for the scattering amplitude was analyzed for which the leading Regge trajectory is piece-wise linear and flat for negative t. It consists of an infinite sum of the Veneziano amplitudes with different slopes approaching zero, all sharing the same mass spectrum.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On fine structure of strings: the universal correction to the Veneziano amplitude

Sever

Zhiboedov

2018

We consider theories of weakly interacting higher spin particles in flat spacetime. We focus on the four-point scattering amplitude at high energies and imaginary scattering angles. The leading asymptotic of the amplitude in this regime is universal and equal to the corresponding limit of the Veneziano amplitude. In this paper, we find that the first sub-leading correction to this asymptotic is universal as well. We compute the correction using a model of relativistic strings with massive endpoints. We argue that it is unique using holography, effective theory of long strings and bootstrap techniques.

On the N-pion extension of the Lovelace-Shapiro model

Bianchi

Consoli

Vecchia

2021

We reconsider a modification of the N-point amplitude of the Neveu-Schwarz (NS) model in which the tachyon becomes a pion by shifting its mass to zero and keeping the super-projective invariance of the integrand of the amplitude. For the scattering of four particles it reduces to the amplitude written by Lovelace and Shapiro that has Adler zeroes. We confirm that also the N-pion amplitude has Adler zeroes and show that it reduces to that of the non-linear σ-model for α′ → 0 keeping Fπ fixed. The four- and six-point flavour-ordered amplitudes satisfy tree-level unitarity since they can be derived from the correspondent amplitudes of the NS model in ten dimensions by suitably choosing the components of the momenta of the external mesons in the six extra dimensions. Negative norm states (ghosts) are shown to appear instead in higher-point amplitudes. We also discuss several amplitudes involving different external mesons.