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

1.1. The Standard Model of Particle Physics 9the Lagrangian such as charges and masses are not the true physical quantitiesobserved in nature. At each loop order one must calculate counterterms which areabsorbed into the masses and charges. When combined with divergent integrals thesecounter terms lead to (UV) finite amplitudes at each order in perturbation theory.Infra-red divergences arise from two sources, when l 2 → 0 in a loop amplitude andwhen an external (spin-1) particle becomes soft (E 0 → 0) or collinear to anotherexternal particle 3 . In the second case, an (n+1) parton amplitude is observationallyequivalent to an n parton amplitude. In the first case the loop particle does notaffect the momentum flow of the diagram and the n parton m loop amplitude tendstowards an n parton (m − 1) loop amplitude. Therefore we see that in an IR regionone can combine (n + 1) parton (m − 1)-loop amplitudes with n-parton m loopamplitudes, resulting in IR pole cancellation. This procedure works systematicallyat all loop orders [18–20] and in our case we will need to combine (n + 1) partontree level amplitudes with n-parton one-loop amplitudes.1.1.3 An overview of a hadronic collisionIn this section we provide an extremely brief overview of a particle collision inan hadronic environment. We discuss factorisation of QCD amplitudes, jets andhadronisation.Factorisation and cross sectionsA hadronic collider such as the Tevatron or the LHC collides composite objectsrather than fundamental particles (such as electrons and positrons at LEP). Ingeneral a cross-section for a physical observable can be obtained from the followingformula [7,21],σ(S) = ∑ i,j∫dx 1 dx 2 f i (x 1 , µ 2 )f j (x 2 , µ 2 )ˆσ ij (ŝ = x 1 x 2 S, α S (µ 2 ), Q2µ 2 ) (1.22)3 Quark pairs can also produce collinear singularities through qq → g.