Hadronic production of a Higgs boson in association with two jets at ...
Hadronic production of a Higgs boson in association with two jets at ...
Hadronic production of a Higgs boson in association with two jets at ...
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4.6. Summary 130p µ 2 = (+0.34445032281, +0.14635282800, −0.10707762397, +0.29285022975),p µ 3 = (+0.22091667641, +0.08911915938, +0.19733901856, +0.04380941793),p µ 4= (+0.12789262211, −0.05808504045, −0.07361667438, −0.08696686795).(4.49)The results are presented <strong>in</strong> table 4.1 where we have chosen the renormalis<strong>at</strong>ionscale to be µ 2 = m 2 H .2Helicity A (0) M F,g4 M F,f4 M F,s4− − −− -116.526220-18.681775 i -9.540396-0.001010 i -0.176850+0.001010 i 0.176850-0.001010 i+ − −− 10.308088-0.824204 i -10.809925+0.056646 i -0.388288+0.198369 i 0.296783-0.155132 i− − ++ 20.511457-0.888525 i -10.991033+0.320009 i 0.268501-0.068414 i 0.066595-0.015451 i− + −+ 4.683784+4.242678 i -10.332320+0.149216 i 0.028668-0.066437 i 0.166800+0.038844 iTable 4.1: Numerical values for the f<strong>in</strong>ite parts <strong>of</strong> the <strong>Higgs</strong> + 4 gluon helicityamplitudes <strong>at</strong> the phase space po<strong>in</strong>t given <strong>in</strong> eq. (6.2).4.6 SummaryIn this chapter we have calcul<strong>at</strong>ed the last (analytically) unknown build<strong>in</strong>g block <strong>of</strong>the <strong>Higgs</strong> plus four gluon amplitude, the φ-NMHV amplitude A (1)4 (φ, 1+ , 2 − , 3 − , 4 − ).We chose to split the calcul<strong>at</strong>ion <strong>in</strong>to <strong>two</strong> parts, one be<strong>in</strong>g cut-constructible (to whichwe applied the techniques <strong>of</strong> four-dimensional unitarity) and a r<strong>at</strong>ional part, whichis <strong>in</strong>sensitive to four-dimensional cuts. We used the unitarity methods described<strong>in</strong> chapters 2 and 3 to calcul<strong>at</strong>e the cut-constructible pieces. We used Feynmandiagrams to calcul<strong>at</strong>e the r<strong>at</strong>ional pieces proportional to N f and BCFW recursionrel<strong>at</strong>ions to calcul<strong>at</strong>e the rema<strong>in</strong><strong>in</strong>g pieces. We checked our results for the φ-MHVand φ-NMHV amplitudes aga<strong>in</strong>st the semi-numerical code <strong>of</strong> Ref. [104].In the next chapter we will compute the rema<strong>in</strong><strong>in</strong>g helicity amplitude, the φqq-NMHV amplitude, complet<strong>in</strong>g the analytic calcul<strong>at</strong>ion <strong>of</strong> φ + parton amplitudes.We shall observe th<strong>at</strong> although similar to the calcul<strong>at</strong>ion carried out <strong>in</strong> this chapter,2 We have been <strong>in</strong>formed by John Campbell, th<strong>at</strong> the entries for M F,g4 and M F,q4 <strong>in</strong> Table 4.1are <strong>in</strong> agreement <strong>with</strong> results obta<strong>in</strong>ed us<strong>in</strong>g the sem<strong>in</strong>umerical code described <strong>in</strong> Ref. [104].