VBF specific kinematic variables

Chapter 5: First evidence of a Higgs boson decay to a pair of muons

5.6 VBF category

5.6.1 VBF specific kinematic variables

To build a multi-variate discriminant for the VBF signal, several kinematic variables were considered to separate the VBF signature from the Drell-Yan / Electro-weak Z background. They are discussed in details in this section.

5.6.1.1 Di-muon kinematics

We consider the following kinematic variables from the dimuon system:

• The invariant mass of the two selected muons𝑚(𝜇 𝜇): this tends to peak near the Higgs mass for the signal, whereas background processes have a more smoothly falling𝑚(𝜇 𝜇)spectrum.

• The transverse momentum of the dimuon system 𝑝_𝑇(𝜇 𝜇).

• The pseudorapidity of the dimuon system𝜂(𝜇 𝜇) : The dimuon system from the VBF signal process is mostly produced centrally in the detector, unlike other background processes.

• The dimuon mass resolution𝛿 𝑀(𝜇 𝜇)or the relative mass resolution𝛿 𝑀(𝜇 𝜇)/𝑀(𝜇 𝜇).

These variables are illustrated in Fig.5.6for both the signal and major background processes.

Figure 5.6: Variable comparisons between VBF Higgs signal (blue) and Drell-Yan + Electro-weak Z backgrounds (orange). (Top Left) 𝑚(𝜇 𝜇), (Top Right) 𝑝_𝑇(𝜇 𝜇) and (Bottom)𝛿 𝑀(𝜇 𝜇)/𝑀(𝜇 𝜇).

5.6.1.2 Leading and sub-leading jet kinematics

We consider the𝑝_𝑇,𝜂and𝜙from the two leading candidate VBF-like jets. Some of these variables are illustrated in Fig. 5.7for both the signal and major background processes.

Figure 5.7: Variable comparisons between VBF Higgs signal (blue) and Drell-Yan + Electro-weak Z backgrounds (orange). (Top Left) 𝑝_𝑇(𝑗

1), (Top Right) 𝑝_𝑇(𝑗

2) , (Bottom Left)𝜂(𝑗

1)and (Bottom Right)𝜂(𝑗

2).

5.6.1.3 Di-jet kinematics

We consider the following kinematic variables from the dijet system:

• The invariant mass of the two selected jets𝑚(𝑗 𝑗): tends to have higher values for the signal process as compared to other background processes.

• The pseudorapidity difference between the two selected jets |Δ𝜂(𝑗 𝑗) | =

|𝜂(𝑗

1) −𝜂(𝑗

2) |: This difference is higher for VBF-like jets that are produced back-to-back in the forward regions of the detector.

These variables are illustrated in Fig.5.8for both the signal and major back- ground processes.

Figure 5.8: Variable comparisons between VBF Higgs signal (blue) and Drell-Yan + Electro-weak Z backgrounds (orange). (Left)𝑚(𝑗 𝑗) and (Right)|Δ𝜂(𝑗 𝑗) |. 5.6.1.4 Kinematics of the dimuon + dijet system

We consider the following kinematic variables from the dimuon + dijet system:

• The mass of the system composed by the two jets and the two muons is given by 𝑀_{𝜇 𝜇 𝑗 𝑗}.

• The Zeppenfeld variable defined by

𝑧^★= 𝑦^★

| 𝜂(𝑗

1) −𝜂(𝑗

2) | where

𝑦^★=𝜂(𝜇 𝜇) − 𝜂(𝑗

1) +𝜂(𝑗

2) 2

.

This variable checks the "centrality" of the dimuon system w.r.t. the two VBF jets, with a value of|𝑧^∗| < 0.5 when the dimuon pseudorapidity falls in between the two jet pseudorapidities, and|𝑧^∗|> 0.5 otherwise.

• The transverse momentum balance defined by 𝑅(𝑝

T) = ( ®𝑝(𝑗

1) + ®𝑝(𝑗

2) + ®𝑝(𝜇

1) + ®𝑝(𝜇

2))𝑇

𝑝T(𝑗

1) +𝑝

T(𝑗

2) + 𝑝

T(𝜇 𝜇) .

Background processes tend to have longer tails in this variable than VBF events, as background events may contain additional decay products apart from the selected muons and jets.

• The minimum of the pseudorapidity difference between the selected jets (in- dividually) and the dimuon system

min(|𝜂(𝑗

1) −𝜂(𝜇 𝜇) |,|𝜂(𝑗

2) −𝜂(𝜇 𝜇) |).

These variables are illustrated in Fig.5.9for both the signal and major background processes.

Figure 5.9: Variable comparisons between VBF Higgs signal (blue) and Drell-Yan + Electro-weak Z backgrounds (orange). (Top left)𝑝_𝑇(𝜇 𝜇 𝑗 𝑗), (Top right)𝑧^★, (Bottom left)𝑅(𝑝

T)and (Bottom right) min(|𝜂(𝑗

1) −𝜂(𝜇 𝜇) |,|𝜂(𝑗

2) −𝜂(𝜇 𝜇) |).

5.6.1.5 Quark-Gluon Likelihood discriminator for jets

Jets in VBF events are expected to originate solely from quarks whereas events produced via other mechanisms can have jets that originate from both gluons or quarks. The Quark-Gluon likelihood (QGL) [148] is a probability tagger that discriminates gluon-jets from quark-jets using jet constituent information. VBF events usually have high QGL values and the QGL distributions peak at 1 for both leading and subleading jets. The background shapes can peak both at 0 and 1.

However, a gluon jet most likely originates from an initial or final state radiation and tends to have a softer 𝑝

T spectrum. Therefore, sub-leading jets in background processes often come from gluon hadronization and thus, the QGL output of the subleading jet is more discriminating than the leading one for our scenario. Data- driven polynomial corrections to the QGL shape are also applied to the event weights (derived using Z+jets and dijet events in [148]).

These variables are illustrated in Fig.5.10for both the signal and major background processes.

Figure 5.10: Variable comparisons between VBF Higgs signal (blue) and Drell-Yan + Electro-weak Z backgrounds (orange). (Left) QGL(𝑗

1) and (Right) QGL(𝑗

2).

Some jets have spurious QGL values of -1, which indicates the jet had very few constituents for a QGL value to be calculated effectively.

5.6.1.6 Soft activity variables

We consider the following soft-jet kinematic variables in the event:

• 𝑁^soft

5 or the number of track jets (see Section5.3.7) with𝑝_𝑇 > 5 GeV : These jets are only comprised of charged tracks that do not belong to the selected muons or VBF-jets. Such a selection helps to distinguish the signal process from other backgrounds, since the signal VBF process has very limited extra hadronic activity.

• 𝐻soft

𝑇 𝑥 or the scalar sum of the transverse momenta of all the track jets with 𝑝

T

> x GeV, where𝑥 ∈ [2,5,10]: this also checks for additional soft activity in the event.

These variables are illustrated in Fig. 5.11 for both the signal and major background processes.

5.6.1.7 Collins-Soper frame variables

As discussed previously, the Drell-Yan process is an irreducible background for 𝐻 → 𝜇 𝜇. However, as the Z/𝛾 boson is a spin-1 particle and the Higgs is a spin-0 particle, the angular distributions of the two muons produced are different in the two processes. In particular, if we look at the frame where the original boson is

Figure 5.11: Variable comparisons between VBF Higgs signal (blue) and Drell-Yan + Electro-weak Z backgrounds (orange). (Left) 𝑁soft

5 and (Right)𝐻soft 𝑇 5.

produced at rest (and the two muons fly back-to-back), we could reconstruct certain angular variables that could help us distinguish between the two processes. This frame is known as the Collin-Soper frame [149] and is illustrated in Fig.5.12. The hadron plane is defined as the plane containing the two colliding partons. The y-axis is chosen as the normal vector to the hadron plane, and the z-axis is chosen such that it bisects the angle 2𝛽 between the vectors of the two colliding partons. The sign of the z-axis is taken as the sign of the z-component of the dimuon momentum in the laboratory frame. The x-axis is chosen accordingly (for a right-handed cartesian coordinate system). The decay products of a spin-0 particle have no preferential direction and this result in a constant angular distribution for muons originating from a Higgs decay. The dimuon system from the Drell-Yan process is however affected by the spin-1 nature the Z/𝛾 and have an angular distribution roughly described by

𝑑𝜎

𝑑Ω ∝ 1+cos²𝜃_{𝐶 𝑆} where𝜃_{𝐶 𝑆} is shown in Fig.5.12.

For our purposes here, we consider the following two angles:

• cos(𝜃_{𝐶 𝑆}) : The cosine of the angle between the collinear muons in the dimuon rest frame (green plane) and the z-axis

• cos(𝜙_{𝐶 𝑆}) : The cosine of the angle between the lepton-plane and the hadron- plane.

The cos(𝜃_{𝐶 𝑆}) variable is illustrated in Fig.5.13for both the signal and major back- ground processes.

Figure 5.12: An illustration of the Collins-Soper frame.

Figure 5.13: Variable comparisons between VBF Higgs signal (blue) and Drell-Yan + Electro-weak Z backgrounds (orange): cos(𝜃_{𝐶 𝑆}).

Each variable described in this section has been studied in detail in the Z control region for the three data taking periods and any observed differences between the data and the MC were corrected for according to Section5.3and5.4(see Fig.5.14, 5.15, and5.16). Some residual mis-modelling of the simulation compared to data are observed, but are known to be covered by the uncertainties due to jet energy scale and resolution.