Collinear and soft divergences in perturbative quantum gravity are investigated to arbitrary orders in amplitudes for wide-angle scattering, using methods developed for gauge theories. We show that collinear singularities cancel when all such divergent diagrams are summed over, by using the gravitational Ward identity that decouples unphysical polarizations from the S-matrix. This analysis generalizes a result previously demonstrated in the eikonal approximation. We also confirm that the only virtual graviton corrections that give soft logarithmic divergences are of the ladder and crossed ladder type.

The infrared behavior of perturbative quantum gravity is studied using the method developed for QED by Faddeev and Kulish. The operator describing the asymptotic dynamics is derived and used to construct an IR-finite S matrix and space of asymptotic states. All-orders cancellation of IR divergences is shown explicitly at the level of matrix elements for the example case of gravitational potential scattering. As a practical application of the formalism, the soft part of a scalar scattering amplitude is related to the gravitational Wilson line and computed to all orders.Comment: 34 pages, 8 figure

Modifications of Heisenberg's uncertainty relation have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change in the quantum mechanical commutation relations involving position and momenta. In particular, the modifications to the spectrum of the hydrogen atom can be naturally interpreted as a varying (with energy) fine structure constant. From the data on the energy levels we attempt to constrain the scale of the new physics and find that it must be close to or larger than the weak scale. Experiments in the near future are expected to change this bound by at least an additional order of magnitude.

Using heavy quark effective field theory, exponentiation of Sudakov double logarithms, and perturbative factorization theorems for exclusive processes, we calculate the amplitude for the semileptonic decay of mesons with a single, very heavy quark into .rr and p for a large hadronic recoil momentum. A formula for these large-recoil widths is obtained in terms of two-particle wave functions of the heavy and light mesons and applied to semileptonic decays of the B.PACS number(s1: 13.20.He, 12.39.Hg

We discuss 1/Q corrections to hard processes in QCD where Q is a large mass parameter like the total energy in e + e − annihilation. The main problem we address ourselves to is whether these corrections to different processes (concentrating for definiteness on the Thrust and the Drell-Yan cross section) can be related to each other in a reliable way so that the phenomenology of the 1/Q corrections can be developed. We derive first the relation valid to lowest order using both the renormalon and finite-gauge-boson mass techniques to check its independence on the infrared cut-off procedure. We then argue that the 1/Q corrections are due to soft gluons which factorize into a universal factor such that the lowest order relations are preserved in higher orders. Euclidean space, such as the total cross section for e + e − → hadrons. The power like corrections can also be studied [2] by means of infrared renormalons since the latter are particular graphs sensitive to large distances. Thus, all the general properties are observed and the nonperturbative contribution results in an overall factor which can be large numerically.The advantage of the renormalon technique is that it can be applied to any infrared safe quantity and it is by using this technique and its variations that 1/Q corrections were discovered recently [3,4,5,6,7,8]. One of the modifications of the renormalon technique is introduction of finite gluon mass (λ) in the evaluation of the lowest order radiative corrections