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تسجيل مستخدم جديدHigh-energy scattering amplitudes in QED, QCD and supergravity
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تأليف
Agustin Sabio Vera
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This is a personal recollection of several results related to the study of the high energy limit of scattering amplitudes in gravitational theories. They would not have been possible without the encouragement and constant support from Lev Nikolaevich Lipatov.
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We analyse the high-energy limit of the gluon-gluon scattering amplitude in QCD, and display an intriguing relation between the finite parts of the one-loop gluon impact factor and the finite parts of the two-loop Regge trajectory.
Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in $mathcal{N}=2$ super-Yang-Mills (SYM) theory coupled to $N_f$ fundamental hypermultiplets. Our results are valid in $Dle 6$ dimensions, where th
e upper bound corresponds to six-dimensional chiral $mathcal{N}=(1,0)$ SYM theory. By exploiting a close connection with $mathcal{N}=4$ SYM theory - and, equivalently, six-dimensional $mathcal{N}=(1,1)$ SYM theory - we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding $D$-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning $N_f$ enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in $D=4$. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with $mathcal{N}=(1,1)$ and $mathcal{N}=(2,0)$ supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in $D=5-2epsilon$ and show that it non-trivially cancels out as expected.
We introduce photon and gluon propagators in which the scalar polarization component is subtracted systematically by making use of the BRST invariance of the off-shell vector boson created from physical on-shell states. The propagator has the light-c
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We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a s
imilar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.,cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics.
In any consistent massive quantum field theory there are well known bounds on scattering amplitudes at high energies. In conformal field theory there is no scattering amplitude, but the Mellin amplitude is a well defined object analogous to the scatt
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