Person: Kelley, Randall
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Kelley
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Randall
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Kelley, Randall
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Publication Resummation of Jet Mass at Hadron Colliders(American Physical Society (APS), 2013) Chien, Yang-Ting; Kelley, Randall; Schwartz, Matthew; Zhu, Hua XingA method is developed for calculating the jet mass distribution at hadron colliders using an expansion about the kinematic threshold. In particular, we consider the mass distribution of jets of size R produced in association with a hard photon at the Large Hadron Collider. Expanding around the kinematic threshold, where all the energy goes into the jet and the photon, provides a clean factorization formula and allows for the resummation of logarithms associated with soft and collinear divergences. All of the large logarithms of jet mass are resummed at next-to-leading logarithmic level, and all the global logarithms at next-to-next-to-leading logarithmic level. A key step in the derivation is the factorization of the soft function into pieces associated with single scales and a remainder which contains nonglobal structure. This step, which is standard in traditional resummation, is implemented in effective field theory which is then used to resum the large logarithms using the renormalization group in a systematically improvable manner.Publication Threshold hadronic event shapes with effective field theory(American Physical Society (APS), 2011) Kelley, Randall; Schwartz, MatthewHadronic event shapes, that is, event shapes at hadron colliders, could provide a great way to test both standard and non-standard theoretical models. However, they are significantly more complicated than event shapes at e+e- colliders, involving multiple hard directions, multiple channels and multiple color structures. In this paper, hadronic event shapes are examined with Soft-Collinear Effective Theory (SCET) by expanding around the dijet limit. A simple event shape, threshold thrust, is defined. This observable is global and has no free parameters, making it ideal for clarifying how resummation of hadronic event shapes can be done in SCET. Threshold thrust is calculated at next-to-leading fixed order (NLO) in SCET and resummed to next-to-next-to-leading logarithmic accuracy (NNLL). The scale-dependent parts of the soft function are shown to agree with what is expected from general observations, and the factorization formula is explicitly shown to be renormalization group invariant to 1-loop. Although threshold thrust is not itself expected to be phenomenologically interesting, it can be modified into a related observable which allows the jet pT distribution to be calculated and resummed to NNLL+NLO accuracy. As in other processes, one expects resummation to be important even for moderate jet momenta due to dynamical threshold enhancement. A general discussion of threshold enhancement and non-global logs in hadronic event shapes is also included.Publication Threshold Hadronic Event Shapes with Effective Field Theory(American Physical Society, 2011) Kelley, Randall; Schwartz, MatthewHadronic event shapes, that is, event shapes at hadron colliders, could provide a great way to test both standard and nonstandard theoretical models. However, they are significantly more complicated than event shapes at e\(^+\)e\(^-\) colliders, involving multiple hard directions, multiple channels, and multiple color structures. In this paper, hadronic event shapes are examined with soft-collinear effective theory (SCET) by expanding around the dijet limit. A simple event shape, threshold thrust, is defined. This observable is global and has no free parameters, making it ideal for clarifying how resummation of hadronic event shapes can be done in SCET. Threshold thrust is calculated at next-to-leading fixed order (NLO) in SCET and resummed to next-to-next-to-leading logarithmic (NNLL) accuracy. The scale-dependent parts of the soft function are shown to agree with what is expected from general observations, and the factorization formula is explicitly shown to be renormalization group invariant to 1-loop. Although threshold thrust is not itself expected to be phenomenologically interesting, it can be modified into a related observable which allows the jet p\(_T\) distribution to be calculated and resummed to NNLL+NLO accuracy. As in other processes, one expects resummation to be important even for moderate jet momenta due to dynamical threshold enhancement. A general discussion of threshold enhancement and nonglobal logs in hadronic event shapes is also included.Publication The Two-loop Hemisphere Soft Function(American Physical Society, 2011) Kelley, Randall; Schabinger, Robert; Schwartz, Matthew; Zhu, HuaThe hemisphere soft function is calculated to order \(\alpha_s^2\). This is the first multi-scale soft function calculated to two loops. The renormalization scale dependence of the result agrees exactly with the prediction from effective field theory. This fixes the unknown coefficients of the singular parts of the two-loop thrust and heavy-jet mass distributions. There are four such coefficients, for 2 event shapes and 2 color structures, which are shown to be in excellent agreement with previous numerical extraction. The asymptotic behavior of the soft function has double logs in the \(C_F C_A\) color structure, which agree with non-global log calculations, but also has sub-leading single logs for both the \(C_F C_A\) and \(C_F T_F n_f\) color structures. The general form of the soft function is complicated, does not factorize in a simple way, and disagrees with the Hoang-Kluth ansatz. The exact hemisphere soft function will remove one source of uncertainty on the \(\alpha_s\) fits from \(e^+e^-\) event shapes.Publication Early (and Later) LHC Search Strategies for Broad Dimuon Resonances(Springer Verlag, 2011) Kelley, Randall; Randall, Lisa; Shuve, BrianResonance searches generally focus on narrow states that would produce a sharp peak rising over background. Early LHC running will, however, be sensitive primarily to broad resonances. In this paper we demonstrate that statistical methods should suffice to find broad resonances and distinguish them from both background and contact interactions over a large range of previously unexplored parameter space. We furthermore introduce an angular measure we call ellipticity, which measures how forward (or backward) the muon is in eta, and allows for discrimination between models with different parity violation early in the LHC running. We contrast this with existing angular observables and demonstrate that ellipticity is superior for discrimination based on parity violation, while others are better at spin determination.Publication One-Loop Matching and Next-to-Next-to-Leading Log Resummation for all Partonic 2→2 Processes in QCD(American Physical Society, 2011) Kelley, Randall; Schwartz, MatthewThe Wilson coefficients for all 4-parton operators which arise in matching QCD to soft-collinear effective theory (SCET) are computed at 1-loop. Any dijet observable calculated in SCET beyond leading order will require these results. The Wilson coefficients are separated by spin and color, although most applications will involve only the spin-averaged hard functions. The anomalous dimensions for the Wilson coefficients are given to 2-loop order, and the renormalization group equations are solved explicitly. This will allow for analytical resummation of dijet observables to next-to-next-to-leading logarithmic accuracy. For each channel, there is a natural basis in which the evolution is diagonal in color space. The same basis also diagonalizes the color evolution for the soft function. Even though soft functions required for SCET calculations are observable dependent, it is shown that their renormalization group evolution is almost completely determined by a universal structure. With these results, it will be possible to calculate hadronic event shapes or other dijet observables to next-to-leading order with next-to-next-to-leading log resummation.