Muons

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

5.3 Physics objects

5.3.2 Muons

a straight line, and information from the muon chambers improves the 𝑝

T

measurement significantly, because they provide essential information about the track curvature.

One can define additional muon identification (ID) criteria based on several kine- matic variables: the number of hits and the fit quality of the track; the compatibility between the tracker hits and the segments in the muon stations; and the compati- bility between the muon track and the primary vertex. The global track fit 𝜒²and a kink-finder 𝜒²are used as indicators of the fit quality of the global muon track.

The compatibility between the tracker track and muon station segments is evaluated with a position match 𝜒2, and a variable called the segment compatibility. The compatibility between the track and the primary vertex is evaluated with the track impact parameters (closest distance of approach in the x-y plane or z axis). Based on these variables, muons can be further classified into three different types as follows:

• Loose muon ID: Muons that are either a tracker or a global muon, with no further requirements.

• Medium muon ID: A medium muon satisfies the loose ID criterion, and pos- sesses valid hits on more than 80% of the number of tracker layers that it tra- verses. Additionally, the muon must be classified either as agood global muon or should pass a tight segment compatibility requirement (> 0.451). A good global muon has a global track-fit 𝜒²/ndof < 3, the kink-finder 𝜒² <

20, the position match 𝜒²< 12, and a segment compatibility > 0.303.

• Tight muon ID: A tight muon is a global muon with a global track-fit𝜒2/ndof

< 10, has at least one hit in the muon chamber and at least six hits in the inner tracker (with > 1 pixel hits). It also satisfies certain track impact parameter (w.r.t. the primary vertex) requirements, which are d^{𝑥 𝑦} < 0.2 cm and d^𝑧 < 0.5 cm.

Events in the𝐻 → 𝜇 𝜇 analysis are required to have at least two oppositely charged Medium ID muons with 𝑝

T > 20 GeV and |𝜂| <2.4. Furthermore, each of the muons is also required to pass a relative isolation requirement in which the sum of the 𝑝

T of charged and neutral hadrons, and photons, lying within a cone of Δ𝑅 =√︁

Δ𝜂2+Δ𝜙2=0.4 around the muon, is less than 25% of the 𝑝

Tof the muon.

If a photon in the isolation cone is associated with the final state radiation (FSR)

of the muon (see Section 5.3.2.2), then it is not included in the isolation sum. A Δ𝛽-correction is also applied to the isolation sum which subtracts half of the𝑝

Tsum of charged hadron candidates lying within the isolation cone but originating from pile-up vertices. This correction helps to remove the contamination from neutral particles produced by pile-up interactions that spuriously enter into the vicinity of the candidate muon.

The sensitivity of this search depends critically on the muon 𝑝

Tresolution and also on the resolution of the𝑀_{𝜇 𝜇} mass peak. The𝑝

Tresolution of muons worsens with increasing muon |𝜂|, the resolution being around 1–2% in the central barrel region of the detector (|𝜂| < 0.9) , and degrading to 2 to 3.5% for muons passing through the endcaps of the muon system (|𝜂|> 1.2), as shown in Fig. 5.2. The next few subsections will discuss ways to correct for any mis-reconstruction of the muon 𝑝T originating from software bias, uncertainties in the magnetic field or detector misalignment.

Figure 5.2: Resolution, as a function of 𝑝

T, for single, isolated muons in the barrel (|𝜂|< 0.9), transition (0.9 <|𝜂|< 1.4), and endcap regions (1.4 <|𝜂|< 2.5). For each bin, the solid (open) symbols correspond to the half-width for 68% (90%) intervals of the residuals distribution [89].

5.3.2.1 Rochester Corrections

The muon momentum scale and resolution are calibrated in bins of muon𝑝

T,𝜂and charge, using𝑍 → 𝜇 𝜇decays as a standard candle, following the method described in Ref. [136]. The correction method is briefly summarized as follows

• Negative and positive muons are divided separately into different𝜂and𝜙bins, for both data and simulation. In each bin, the 1/𝑝

Tdistributions for both data and simulation are corrected, so that the mean value (<1/𝑝

T >) becomes the same as that in the𝑍 → 𝜇 𝜇simulation (which is assumed to be very precisely modelled).

• A smearing is applied to the resolution of the 1/𝑝

Tdistribution in the simula- tion, such that it matches the resolution in data.

• After all the above steps, there may still be some residual offset in each𝑚_{𝜇 𝜇} bin, when compared to the 𝑍 → 𝜇 𝜇 simulation. The last step is to apply the ratio of this offset and the nominal Z mass, as a correction factor to the muon 𝑝

T. The correction is applied in an iterative manner, until the offset is minimized.

5.3.2.2 Final state radiation (FSR) recovery

In a small fraction of signal events (9%), a muon in the final state may radiate a photon, thereby losing some of its momentum. This causes a slight degradation in the resolution of the signal 𝑀_{𝜇 𝜇} peak. To recover this loss in the resolution, a procedure was developed to look for FSR photons within the isolation cone of the muon and can be summarized as follows

• Consider all reconstructed muons with 𝑝

T > 20 GeV and |𝜂| < 2.4 as candi- dates for FSR recovery.

• For a given muon, consider all photons (𝛾) withΔ𝑅(𝜇, 𝛾) < 0.5, 𝑝

T > 2 GeV, 0.0< |𝜂| < 1.4442 or 1.566 < |𝜂|< 2.5 as possible FSR candidates.

• Ignore photons that are associated with the bremsstrahlung of a reconstructed electron.

• In order to strongly suppress the contamination from H→ Z𝛾 → 𝜇 𝜇𝛾decays, FSR photon candidates are required to have 𝑝

𝛾 T/𝑝

𝜇

T < 0.4.

• Impose a loose isolation requirement on the photon : 𝐼_𝛾/𝑝

T(𝛾) = (Σ^{𝑃 𝐹}

𝑖 𝑝^𝑖

T(Δ𝑅(𝛾 , 𝑖) < 0.3))/𝑝

T(𝛾) < 1.8, where 𝑝

T(𝛾) is the 𝑝

T

of the FSR photon candidate and the index𝑖refers to the PF candidates other than the muon within a cone of𝑅 =0.3 around the photon.

• Require photon to be collinear with the muon : Δ𝑅(𝜇, 𝛾)/𝑝

T(𝛾)² < 0.012

• In case of multiple FSR photon candidates, only the one with the smallest value ofΔ𝑅(𝜇, 𝛾)/𝑝

T(𝛾)²is considered.

If an FSR photon is associated with a muon, its momentum is added to that of the original muon. This procedure increases the signal efficiency by about 3% and improves the𝑀_{𝜇 𝜇}resolution by around 2%.

5.3.2.3 GeoFit Corrections

In CMS, the muon 𝑝

Tvalues are primarily computed using the measured radius of curvature (𝑅) of the reconstructed muon track from hits in the inner tracker. This reconstruction has inherent uncertainties, which affect both the track trajectory and measured 𝑝

T. As prompt muons originate directly from the collision vertex, the measured point of closest approach between the muon track and the collision vertex in the𝑥−𝑦plane (known as the track impact parameter: 𝑑

0) should be exactly zero for muons coming from W/Z/H decays. However, if the muon track radius estimation is incorrect, the𝑑

0value will be non-zero, and is related to the mis-measurement in radius of curvature (Δ𝑅) as follows (see [137] for derivation):

|𝑑

0| ∼ Δ𝑅 𝑅2

. (5.1)

Since in homogeneous magnetic fields, 𝑝

T ∼ 𝑅, we can re-write the above equation as

|𝑑

0| ∼ |𝛿 𝑝

T| 𝑝2

T

. (5.2)

Therefore, the precision of the muon𝑝

Tmeasurement can be improved by including the interaction point position as an additional hit of the muon track. The correspond- ing adjustment in the 𝑝

T,𝛿 𝑝

T, is given by Eqn.5.2. The resulting improvement in the expected𝑚_{𝜇 𝜇}resolution in signal events ranges from 5% to 10%, depending on muon 𝑝

T,𝜂, and the data-taking period (see Fig.5.3).