Hadronic production of a Higgs boson in association with two jets at ...

1.1. The Standard Model of Particle Physics 11Showers and jetsImmediately upon looking at an image of a high-energy collision one can spot acollection of hadrons which are grouped into a roughly cone sized area. Thesehadrons, which have travelled roughly collinear to each other, are known as jets.Therefore, to compare theory to experiment one needs a suitable jet algorithm todefine exactly what is meant by a jet and the properties it has. Several jet algorithmsexist [27–31], the one we will use in this thesis is known as the k T algorithm andworks in the following way [32]:• The algorithm begins with a set of preclusters, which for our theoretical calculationswith MCFM means partons. Each precluster is expressed in thefollowing form(E,p) = E(1, cosφsin θ, sin φ sin θ, cosθ) (1.23)where E is the precluster energy and φ and θ are the azimuthal and polarangles respectively.• For each precluster define the square of the transverse momenta and rapidity,d 2 i = p2 T,i , p2 T = p2 x + p2 y and y = 1 2 ln E + p zE − p z, (1.24)• For each pair (i, j) (i ≠ j) of preclusters define,d ij= min(p 2 T,i , p2 T,j )∆R2 ijD 2= min(p 2 T,i , p2 T,j )(y i − y j ) 2 + (φ i − φ j ) 2D 2 (1.25)where D ≈ 1 is a parameter of the jet algorithm.• Find the minimum of all the d i and d ij and call it d min .• If d min is a d ij remove preclusters i and j from the list and replace them witha new merged precluster (E ij , p ij ), given byE ij = E i + E jp ij = p i + p j (1.26)