Next to Leading Order Calculations for Higgs Boson + Jets

Abstract

Due to the recent Higgs boson discovery, an important target for particle physics is to investigate its properties to determine if it is the standard model Higgs boson or some other variety. The Large Hadron Collider is now in Run Two, collecting even more data at higher precisions, which requires predictions at next to leading order or higher orders. Therefore it is important to have an efficient and automatic calculation of the next to leading order amplitudes for the Higgs boson. This thesis discusses the methods needed to perform these calculations.

These calculations are specifically developed in order to add them to the BlackHat library, which already provides these types of calculations for amplitudes involving quarks, gluons and W and Z bosons. Both this thesis and BlackHat use recursive methods, as these are more efficient than using the Feynman rules directly. Specifically the BCFW recursion relation is used to calculate tree amplitudes and generalised unitarity is used to calculate one loop amplitudes. These methods are first used in 4 dimensions to calculate the cut constructable parts of the amplitudes, then the extension of these techniques to higher numbers of dimensions is discussed, allowing the rational terms to be extracted using D dimensional generalised unitarity. In general, two different even integer dimensions higher than 4 are required for a numeric implementation of D dimensional generalised unitarity with spinors, which therefore requires working in both 6 and 8 dimensions. To enable an efficient implementation, a technique is introduced that allows only 6 dimensional calculations to be used rather than both 6 and 8 dimensional calculations and a reduction of 6 dimensional calculations to be in terms of only 4 dimensional objects is developed. The methods presented in this thesis provide a solid groundwork for Higgs boson amplitudes to be implemented into BlackHat.