A
bstract
The set of double-logarithmic (DL) contributions (
α t
ln
2
s
)
n
to the 4-graviton amplitude in
N
= 8 supergravity (SUGRA), with
α
being the gravitational coupling and (
s, t
) the ...Mandelstam invariants, is studied in impact parameter (
ρ
) representation. This sector of the amplitude shows interesting properties which shed light on the nature of quantum corrections in gravity. Besides having a convergent behaviour as
s
increases, which is not present in
N
<
4 SUGRA theories, there exists a critical line
ρ
c
(
s
) above which the Born amplitude prevails. The short distance region
ρ < ρ
c
(
s
) is dominated by the DL terms. As a consequence, when studied in terms of an eikonal approach in the forward limit, the scattering angle linked to the bending of the semiclassical trajectory of the graviton shows a transition from attractive gravity at large distances to a region at small
ρ
characterized by a repulsive DL contribution to the gravitational potential due to the gravitino content of the theory. In the complex angular momentum plane, this DL high energy asymptotics is driven by the rightmost pole singularity of a parabolic cylinder function. The resummation of DL quantum corrections in
N
= 8 SUGRA can be understood in terms of the counting of 1-rooted maps on orientable surfaces.
A
bstract
We study the four-gluon scattering amplitude in the high energy limit of QCD written in terms of its conformal expansion. We highlight the need to include both even and odd conformal spin ...contributions in order to map it to an iterative representation in rapidity and transverse momentum space which we have evaluated numerically. By Fourier expanding in a set of three azimuthal angles, we find a new form for the amplitude in terms of
4
F
3
hypergeometric functions. An alternative formulation is possible when connecting this Fourier expansion with Bessel kernels studied in analytic number theory.
We show that it is possible to describe the effective Pomeron intercept, determined from the HERA deep inelastic scattering data at small values of Bjorken x, by using next-to-leading order ...Balitsky-Fadin-Kuraev-Lipatov evolution together with collinear improvements. To obtain a good description over the whole range of Q(2), we use a non-Abelian physical renormalization scheme with the Brodsky-Lepage-Mackenzie optimal scale, combined with a parametrization of the running coupling in the infrared region.
A
bstract
Imposing infrared boundary conditions on the BFKL equation with running coupling transforms the complex momentum
ω
-plane cut present in the gluon Green function into an infinite series of ...positive Regge poles. In addition, a cut on the negative
ω
line remains. We consider a Hermitian kernel at leading order with running coupling and construct the gluon Green function performing the
ω
integration away from the real axis. We find a strong dependence of the asymptotic intercepts and collinear behaviour on the non-perturbative choice of the boundary conditions, in the form of an infrared phase. This is particularly manifest in the asymmetric infrared/ultraviolet structure of the associated diffusion in transverse momentum. We find that random walks into the infrared region are largely reduced in this approach.
The double copy structure of soft gravitons Vera, Agustín Sabio; Vázquez-Mozo, Miguel A.
The journal of high energy physics,
03/2015, Volume:
2015, Issue:
3
Journal Article
Peer reviewed
Open access
A
bstract
The subleading corrections to factorization theorems for soft bremsstrahlung in nonabelian gauge theories and gravity are investigated in the case of a five point amplitude with four ...scalars. Building on recent results, we write the action of the angular momentum operators on scattering amplitudes as derivatives with respect to the Mandelstam invariants to uncover a double copy structure in the contribution of the soft graviton to the amplitude, both in the leading term and the first correction. Using our approach, we study Gribov’s theorem as extended to nonabelian gauge theories and gravity by Lipatov, and find that subleading corrections can be obtained from those to Low’s theorem by dropping the terms with derivatives with respect to the center-of-mass energy, which are suppressed at high energies. In this case, the emitted gravitons are not necessarily soft.
A
bstract
We investigate tree-level five-point amplitudes in scalar-QCD expressed in terms of Sudakov variables and find the equivalent “gravitational” counterparts using the color-kinematics duality ...proposed by Bern, Carrasco, and Johansson. Taking the multi-Regge limit in the gravitational amplitudes, we show that those pieces in the coupling of two reggeized gravitons to one on-shell graviton directly stemming from the double copy of the vertex for two reggeized gluons to one on-shell gluon are universal and properly reproduced by the duality.
A
bstract
We present a study within the
k
T
-factorisation scheme on single bottom quark production at the LHC. In particular, we calculate the rapidity and transverse momentum differential ...distributions for single bottom quark/anti-quark production. In our setup, the unintegrated gluon density is obtained from the NL
x
BFKL Green function whereas we included mass effects to the L
x
heavy quark jet vertex. We compare our results to the corresponding distributions predicted by the usual collinear factorisation scheme. The latter were produced with Pythia 8.1.
A
bstract
A study of the double logarithmic in the center-of-mass energy,
s
, contributions to the four-graviton scattering amplitude is presented for four-dimensional
N
≥ 4 supergravities. This ...includes a novel representation for the coefficients of the perturbative expansion based on exactly solvable recurrences. A review is given of the structure in the complex angular momentum plane for the
t
-channel partial wave singularities of the different amplitudes. Working in impact parameter representation,
ρ
, it is shown that the resummation of double logarithms makes gravity weaker in regions of small
ρ
and large
s
. This screening of the gravitational interaction at short distances in the double logarithmic sector of the amplitudes is more acute as the number of gravitinos in the theory increases. It brings corrections to the eikonal phase which can change the sign of the graviton’s deflection angle and generate regions with repulsive interaction. For very small impact parameters there appears a constant negative shift in both the eikonal phase and Shapiro’s time delay which is not large enough to generate causality violation.
We present an effective action for the electroweak sector of the standard model valid for the calculation of scattering amplitudes in the high energy (Regge) limit. Gauge invariant Wilson lines are ...introduced to describe reggeized degrees of freedom whose interactions are generated by effective emission vertices. From this approach previous results at leading logarithmic accuracy for electroweak boson Regge trajectories are reproduced together with the corresponding interaction kernels. The proposed framework lays the path for calculations at higher orders in perturbation theory.
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