Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInvestigation of the High Energy Behaviours of the Scalar Particle Scattering Amplitude in the Gravitational Field by Functional Approach
43
0
0.0
(
0
)
Authors
Nguyen Suan Han
Ask ChatGPT about the research
No Arabic abstract
Closed expressions for the Green function and amplitude of the scalar particle scattering in the external gravitational field $g_{mu u}(x)$ are found in the form of functional integrals. It is shown that, as compared with the scattering on the vector potential, the tensor character of the gravitational field leads to a more rapid increase of the cross section with increasing energy. Discrete energy levels of particles are obtained in the Newton potential.
rate research
Read More
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.
We compute an $s$-channel $2to2$ scalar scattering $phiphitoPhitophiphi$ in the Gaussian wave-packet formalism at the tree-level. We find that wave-packet effects, including shifts of the pole and width of the propagator of $Phi$, persist even when we do not take into account the time-boundary effect for $2to2$, proposed earlier. The result can be interpreted that a heavy scalar $1to2$ decay $Phitophiphi$, taking into account the production of $Phi$, does not exhibit the in-state time-boundary effect unless we further take into account in-boundary effects for the $2to2$ scattering. We also show various plane-wave limits.
The S-matrix in gravitational high energy scattering is computed from the region of large impact parameters b down to the regime where classical gravitational collapse is expected to occur. By solving the equation of an effective action introduced by Amati, Ciafaloni and Veneziano we find that the perturbative expansion around the leading eikonal result diverges at a critical value signalling the onset of a new regime. We then discuss the main features of our explicitly unitary S-matrix down to the Schwarzschilds radius R=2G s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact parameter. The nature of the singularity is studied with particular attention to the scaling behaviour of various observables at the transition. The numerical approach is validated by reproducing the known exact solution in the axially symmetric case to high accuracy.
We define form factors and scattering amplitudes in Conformal Field Theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as $p^2 to 0$. In particular, we study a form factor $F(s,t,u)$ obtained from a four-point function of identical scalar primary operators. We show that $F$ is crossing symmetric, analytic and it has a partial wave expansion. We illustrate our findings in the 3d Ising model, perturbative fixed points and holographic CFTs.
The amplitude A(s,t) for ultra-high energy scattering can be found in the leading eikonal approximation by considering propagation in an Aichelburg-Sexl gravitational shockwave background. Loop corrections in the QFT describing the scattered particles are encoded for energies below the Planck scale in an effective action which in general exhibits causality violation and Shapiro time advances. In this paper, we use Penrose limit techniques to calculate the full energy dependence of the scattering phase shift Theta_scat(hat_s},, where the single variable hat_s = Gs/m^2 b^(d-2) contains both the CM energy s and impact parameter b, for a range of scalar QFTs in d dimensions with different renormalizability properties. We evaluate the high-energy limit of Theta_scat(hat_s) and show in detail how causality is related to the existence of a well-defined UV completion. Similarities with graviton scattering and the corresponding resolution of causality violation in the effective action by string theory are briefly discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
