10.4 Limits on Beyond the Standard Model Physics
10.4.3 Settings limits on Pseudo Observables
Using the results from the H → ZZ∗ → 4` fiducial analysis, we set limits on two simplified PO
scenarios:
1. εZ`L vs. εZ`R.
Sets limits on extra contact terms between Higgs and Z+left/right-handed leptons. We keep flavor universality to ensure εZµL,R = εZeL,R, and keep all the other POs at the their SM values. SoκZZ is fixed to 1, and all otherε= 0.
2. κZZ vs. εZ`L.
This is a scenario where, working at tree level in the linear EFT, one can be express the POs as linear combinations of the Wilson coefficients of the EFT Lagrangian [155]. εZ`R= 0.48εZ`L. We again keep flavor universality εZµL,R =εZeL,R, and set all of the otherε= 0.
Since the contact terms εZ`L and εZ`R are in theFL form factor, they have the same Lorentz structure as the SM, and so only affect the dilepton invariant mass spectra, and do not affect the lepton angular distributions. We therefore use the difference in χ2 between the measured and
predictedm12vs.m34differential cross section to constrain the possible contributions from the contact
terms. Using these constraints, we build a 2D profile likelihood assuming the SM values for all but the two free POs, and then set limits as shown in Figure1010.
Since the addition of these POs changes the Higgs boson production rate, in principle we could have set limits based on the inclusive Higgs boson cross section alone, but in that case, the contours in the left figure of 1010would have been a full ellipse. The added information from the invariant mass spectra improves the sensitivity. The shape information inm12vs.m34 also improves the limit
L ε 0.4 − −0.2 0 0.2 R ε 0.2 − 0 0.2 0.4 0.6 0.8 Λ -2ln 0 1 2 3 4 5 6 7 8 95% CL Obs SM 95% CL Exp ATLAS 4l → ZZ* → H -1 13 TeV, 36.1 fb L ε 0.4 − −0.2 0 0.2 0.4 κ 1.5 − 1 − 0.5 − 0 0.5 1 1.5 2 Λ -2ln 0 1 2 3 4 5 6 7 8 95% CL Obs SM 95% CL Exp ATLAS 4l → ZZ* → H -1 13 TeV, 36.1 fb
Figure 1010: Limits on pseudo-observables inH→4`decays. On the left plot, the limits are set for
εZ`L andεZ`R, which are contact terms between Higgs boson andZ+left/right-handed leptons. On the right, limits are set on a linear EFT inspired scenario expressed with
εZ`L and κZZ. κZZ modifies the strength of the Higgs boson coupling to Z bosons. The 95% confidence contour is surrounded by the red solid line. It is shifted with respect to the Standard Model (the black star and the black dotted line) but there are no significant deviations. The colors indicates the values of−2 lnλ.
Conclusion
This thesis has presented results on the Higgs boson inclusive and differential cross sections with the ATLAS detector using proton-proton collisions at√s= 13 TeV at the LHC. We have used data collected over the span of 2015 and 2016 totaling to an integrated luminosity of 36.1 fb−1. Two
types of cross sections were measured: the fiducial cross sections, limited to the phase space of
H →ZZ∗→4`and the acceptance of the ATLAS detector, and the total cross sections, measured
in the full phase space of the Higgs using data from bothH →ZZ∗→4` andH →γγ (diphoton)
decays. The fiducial cross sections are less model dependent in their measurement, while the total cross sections are more model dependent but benefit from the added statistics of two independent decay channels.
The inclusive cross section result measures the over-all probability of a Higgs boson being pro- duced from a proton-proton collision. The Standard Model (SM) predicted gluon-gluon fusion cross section (which is how 87% of Higgs bosons are produced inpp collisions) was perturbatively calcu- lated to N3LO in QCD, making it the most accurate theory prediction for Higgs boson cross sections to date. In the fiducial analysis, we measured the cross section to beσfid·BR(H →4`) = 3.62±0.50
(stat) +0.25/-0.20 (sys) fb, in agreement with the SM prediction of 2.91±0.13 fb. In the full phase space analysis using the combined data, the cross section was measured to beσtot = 57.0 +6.0/-5.9
(stat.) +4.0/-3.3 (syst.) pb, in agreement with the SM prediction of of 55.6±2.5 pb. Each mea- surement has ap-value of 19% and 84% respectively. Given this result, the measured cross sections are fully consistent with a Standard Model production of the Higgs boson.
The differential cross section presents the production of the Higgs boson from proton-proton collisions as a function of various observables. An observable like the Higgs transverse momentum,
pHT, is sensitive to new Higgs couplings to undiscovered particles or modified couplings to known SM
particles, which would show up as more Higgs bosons produced at largerpH
T. Njets is the number
of jets produced in association with the Higgs, and it is sensitive to Higgs production modes, i.e. a Higgs produced via VBF will always be associated with 2 jets while a Higgs produced viaggF is more likely to have no associated jets. BothpTandNjets can provide sensitivity to the couplings of
the Higgs. Section5.4explains each of the differential variables measured in the analysis and their sensitivity to different properties of the Higgs boson.
To summarize the fiducial and total phase space differential cross section results, we will focus on justpH
T andNjets and compare them to the baselineNNLOPS theory prediction. We measured in
the fiducial analysis ap-value of 25% and 33% forpH
T andNjets respectively, and in the total phase
space analysis a p-value of 29% and 43% for pH
T and Njets respectively. The measurements both
became more compatible with the Standard Model with the additional data fromH →γγ. While the results overall agree well with coming from the SM, the higher bins of pH
T and Njets, as seen
in Figures105,106 for the fiducial result and Figure108 for the total result, have little sensitivity. The sensitivity in these bins is limited by low statistics, which will improve when the analysis is repeated with the full Run 2 dataset of almost 150 fb−1.
In the absence of any discoveries beyond the Standard Model, limits were also set on alternative models which assume extra couplings between the Higgs boson and SM particles. These alternative models were derived within the framework of pseudo observables (PO). PO models relax certain assumptions that the Standard Model makes about the nature of the Higgs boson such as assuming the Higgs is part of an SU(2)L doublet, lepton universality, or CP invariance, and creates new
parameters that can be fit to with data. Both inclusive and differential distributions can constrain the PO models, and we used the measured m12vs.m34 differential cross section to constrain the
values of extra contact terms between the Higgs and Z+left/right-handed leptons, as shown in Figure1010.
Looking Ahead
Given that there is low sensitivity in many distributions at high Higgs and jet pT due to low
statistics, the full Run 2 dataset will be able to increase the sensitivity in these bins and reduce the uncertainty of the measurement. In case of revealed excesses from added data, using frameworks like the pseudo observables or dimension-6 Effective Field Theories to parameterize any beyond the Standard Model effects will become more relevant and important. The nature of these excesses would hopefully point to ideas of how to further investigate some of the open questions in particle
physics. Looking towards Run 3, more data will also be able to begin probing rarer properties of the Higgs, such as the Higgs self-coupling termλwith the investigation of di-Higgs production.
The Higgs boson, having only recently been discovered, still has many years of fruitful investiga- tion ahead of it. Better discrimination between production modes will better constrain the strength of its couplings to the fermions and vector bosons and reveal any deviations from the SM. Larger and larger statistics will make rarer decays or deviations more pronounced. The four lepton channel with its strong sensitivity stands to gain deeply from more data, and by the end of Run 3 will have its uncertainties dominated by systematics rather than statistics.
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