Methods are used to re-weight individual events in an SM signal sample to produce a sample of a given CP-odd coupling strength, instead of generating individual signal samples with the required number of events for each coupling strength. This allows convenient access to arbitrary coupling strength values without the need to decide on these in advance. In order to simulate any degree of CP-mixing, a matrix element-based re-weighting procedure is applied to the existingPowheg+Pythia8 SM VBF signal sample. The re-weighting takes as input truth-level information for each event, more specifically the Bjorken x values of the incoming partons, the four-vectors of the outgoing Higgs boson1 and of the final-state partons (before any hadronisation), as well as the flavour of the involved partons. Using these, the weights are obtained as the ratio of the matrix element squared evaluated for the CP-mixed case one wishes to reweight to, and the SM matrix element squared. All of the matrix element calculations for the re-weighting are performed using code extracted from Hawk. Version 2.0 is the only version that includes anomalous HVV couplings. For the CP-mixed scenarios the parameter ˜dB is set equal to ˜d(see
eqs. 1.53).
Powhegincludes matching of matrix elements and parton shower at NLO,
meaning that there can be three different kinds of events (withqand ¯qinterchange- able): qq → qqH, qg → qqqH¯ and qq → qqgH. The re-weighting uses the corre- sponding matrix element at LO fromHawkfor the 2→2 +H or 2→3 +Hprocess, taking into account the flavours of incoming and outgoing partons. This procedure is expected to give a very good approximation to a real and full NLO re-weighting.
4.3.1 Validation of the Re-weighting Procedure
The validation of the re-weighting procedure is achieved by comparing a sample of SM simulated events after the re-weighting, and a sample of events directly generated assuming the same amount of CP-mixing. The Monte Carlo generators considered in this study are Vbfnlo and Mg5_aMC@NLO [68]. Both the HAWK routines
and Vbfnlo implement the same parametrisation of the effective lagrangian (see
1
VBF@NLO parameter Description
PARAMETR2 = true Parametrisation of the L3-Collaboration D_EVEN = 0.0 d, CP-even DB_EVEN = 0.0 dB DG1Z_EVEN = 0.0 Delta_g1_Z DKGAM_EVEN = 0.0 Delta_kappa_gamma D_ODD = 0.1 d˜, CP-odd DB_ODD = 0.1 d˜B KGAM_ODD = 0.0 kappa_gamma
HVV1 = 4 All anomalous couplings activated
TREEFACW = 1.0 SM HWW tensor factor (sin(alpha-beta) in MSSM) TREEFACZ = 1.0 SM HZZ tensor factor (sin(alpha-beta) in MSSM) LOOPFAC = 0.0 SM loop factor multiplying HZγ and Hγγ
Table 4.2: Parameters set in theVbfnloinput file anom_HVV.dat corresponding tod˜= ˜dB = 0.1. VBF-like cuts pT(p)>25GeV |η(p)|<4.5 |∆η(p1, p2)|>2.8 |∆R(p1, p2)|>0.4 M(p1p2)>500GeV
Table 4.3: List of minimal selection requirements applied to all the comparions discussed in this section. The cuts are applied to parton-level quantities for both LO and NLO comparisons.
equation 1.44), hence it is easier to make sure that the re-weighted sample and the one generated with Vbfnlo correspond to the same BSM model. Table 4.2 shows the value of the parameter used to simulate events with Vbfnlo.
Vbfnlocan only generate events at leading order (and differential distributions at next-to-leading order) that are then stored in standard Les Houches files (LHE) [164]. The four-vectors of the incoming and outgoing partons and of the Higgs boson, re- treived from theVbfnloLHE files, are used as input to the re-weighting code. The minimal set of VBF-like cuts applied to the partons is listed in table 4.3.
Additionally, theMg5_aMC@NLOprogram can simulate events with anoma- lous couplings also at NLO. This makes it possible to test how good an approxima- tion it is to separately re-weight the 2→ 2 +H and 2→ 3 +H processes instead of developing a full NLO re-weighting. This is important for the analysis since the SM VBF signal sample that is re-weighted is generated at next-to-leading order by
Mg5_aMC@NLO parameters numerical values cα = 0.6 KSM = 1.¯6 kAW W =−2.03 kAZZ =−2.03 kAγγ =−155.97 kAZγ = 0
Table 4.4: Input parameters for Mg5_aMC@NLO corresponding to d˜= ˜dB =
0.1. All other anomalous couplings term are set to zero.
σVbfnlo [fb] σMg5_aMC@NLO [fb] 1451±1 1447±2
Table 4.5: Cross sections for VBF production of a CP-mixed state, corresponding tod˜= ˜dB = 0.1
Powheg+Pythia. InMg5_aMC@NLO, the effective Lagrangian is expressed in
terms of the couplings of the Higgs bosons to the photon A, and the W and Z bosons (see 1.48). The relation between those couplings and ˜dare shown by equations 1.49. Table 4.4 shows the numerical values of the input parameters used to generate the
Mg5_aMC@NLOsamples using the characterisation model [165] that correspond
to ˜d = ˜dB = 0.1. Good agreement is found when comparing the cross sections
calculated by Mg5_aMC@NLO and Vbfnlo for the same CP-mixed state (see table 4.5).
The LHE files generated by Mg5_aMC@NLO at NLO carry only parton level information and are therefore subsequently showered by interfacing Mg5_-
aMC@NLOwith Pythia8. A Rivet [166] routine is used to store the information
on the partons in a ROOT file. The weigths and Optimal Observable are calculated from these root files. Figure 4.5 shows comparisons between distributions of events generated by Mg5_aMC@NLO directly with a CP-odd coupling strength of ˜d=
˜
dB = 0.1 and SM events re-weighted with the same CP-odd coupling strength.
Neither ∆φsignjj nor the Optimal Observable show any significant disagreement in this comparison.
Fraction of events / 0.2 0 0.01 0.02 0.03 0.04 0.05 0.06 generated re-weighted (HAWK) Madgraph5_aMC@NLO = 0.1, NLO d ~ ATLASSimulation jj sign φ ∆ -3 -2 -1 0 1 2 3 generated/reweighted 0.850.9 0.951 1.051.1 1.15 (a) Fraction of events / 0.5 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 generated re-weighted (HAWK) Madgraph5_aMC@NLO = 0.1, NLO d ~ ATLASSimulation OO -10 -8 -6 -4 -2 0 2 4 6 8 10 generated/reweighted 0.850.9 0.951 1.051.1 1.15 (b)
Figure 4.5: Distribution of∆φsignjj and Optimal Observable forMg5_aMC@NLO
Standard Model events after re-weighting (in red) and Mg5_aMC@NLO events
generated with d˜= ˜dB= 0.1. Both processeses are generated at NLO, and parton-
level information is used as input to the re-weighting.