Browsing by Author "Horowitz, William A"

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    Gluon radiation beyond Poisson using MHV techniques
    (2018) Rasoanaivo, Andriniaina Narindra; Horowitz, William A
    For the first time, MHV techniques are applied to radiative energy loss processes in QCD. First, we provide a pedagogical introduction to MHV techniques with explicit computational example on qq → ɡɡ cross section and splitting functions which reproduces known results. Next, we derive the multiple photon emissions current to reproduce the Poisson distribution of photon radiated from a high energetic quark. Then we derive the equivalent current for the case of multiple gluon emissions in vacuum. We then use the previous result to compute the two gluon correlation. We also study the radiation current induced from a change in the color state of an energetic quark: we start with the case of 1, 2, and 3 gluon induced radiations and then conjecture the analytic expression for n gluon emissions. We then prove this conjecture for the case where the emitted gluons are symmetric and antisymmetric under gluon permutations.
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    NLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem
    (2017) Ibrahim, Abdullah Khalil Hassan; Horowitz, William A
    We calculate to next-to-leading order accuracy the high-energy elastic scattering cross section for an electron off of a classical point source. We use the MS renormalization scheme to tame the ultraviolet divergences while the infrared singularities are dealt with using the well known Kinoshita-Lee-Nauenberg theorem. We show for the first time how to correctly apply the Kinoshita-Lee-Nauenberg theorem diagrammatically in a next-to-leading order scattering process. We improve on previous works by including all initial and final state soft radiative processes, including absorption and an infinite sum of partially disconnected amplitudes. Crucially, we exploit the Monotone Convergence Theorem to prove that our delicate rearrangement of this formally divergent series is uniquely correct. This rearrangement yields a factorization of the infinite contribution from the initial state soft photons that then cancels in the physically observable cross section. Since we use the MS renormalization scheme, our result is valid up to arbitrarily large momentum transfers between the source and the scattered electron as long as α log(1/δ) << 1 and α log(1/δ) log(Δ/E) << 1, where Δ and δ are the experimental energy and angular resolutions, respectively, and E is the energy of the scattered electron. Our work aims at computing the NLO corrections to the energy loss of a high energetic parton propagating in a quark-gluon plasma.
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    Towards the quark gluon plasma via MHV techniques
    (2018) Rabemananjara, Tanjona Radonirina; Horowitz, William A
    We study the multiple radiative gluon emission off a massless and highly energetic quark in the pQCD picture. We introduce the Maximally Helicity Violating (MHV) techniques to cope with the complexities in computing cross sections in multi-jet QCD. The multiphoton emission in QED is reviewed to emphasize the efficiency of the MHV approach. We show that the computation of the multiple photon emission current provides insight into the understanding of the multiple radiative gluon emission in QCD. We then compute the momentum distribution for one, two and three soft and collinear radiative gluons from a hard struck quark. Our MHV results exhibit non-Abelian information about the correlation of gluons. As a phenomenological analysis, we study the energy spectrum for emitting radiative gluons using our MHV results. By comparing the MHV and the standard Poisson approximation of uncorrelated multiple emission results, we see that there is significant difference between the two methods.