Cross-Section Measurements of the VZ Production

Abstract

The chapter describes a spin-off of the $VH(b \bar{b})$ boosted analysis which performs cross-section measurements of the VZ process. The analysis is new and not completed but preliminary results are shown in the section. For the first time, $ZZ(b\bar{b})$ and $WZ(b\bar{b})$ cross-sections at $\sqrt{s}= 13$ $\text {TeV}$ are measured in two $p_{\text {T}}^{V}$ regions

The chapter describes a spin-off of the $VH(b \bar{b})$ boosted analysis which performs cross-section measurements of the VZ process. The analysis is new and not completed but preliminary results are shown in the section. For the first time, $ZZ(b\bar{b})$ and $WZ(b\bar{b})$ cross-sections at $\sqrt{s}= 13$ $\text {TeV}$ are measured in two $p_{\text {T}}^{V}$ regions.

9.1 Motivation and VZ Composition

In the $VH(b\bar{b})$ boosted analysis the default fit is (1+1) PoIs fit where the VH and the VZ contributions are extracted simultaneously. The VH and VZ processes have a similar topologies and the simultaneous fit allows to test the analysis on an irreducible background. For this reason the VZ results is used a cross-check of the VH analysis.

Some tests have been performed to evaluate the sensitivity of the analysis on the VH and VZ processes. The tests show that the analysis has a better sensitivity to the diboson process than to the Higgs production mode, in particular the precision on the ZZ process is twice better with respect to the precision on the ZH process. The idea of this spin-off analysis is to re-use the $VH(b\bar{b})$ boosted analysis to perform cross-section measurements of the VZ process.

The study of the WZ and ZZ production modes in p-p collisions provides an important test of the gauge boson sector of the SM. The CMS Collaboration already presented a measurement of the VZ cross-section in the $VZ \rightarrow Vb\bar{b}$ decay modes where the V boson decays leptonically re-using the $VH(b\bar{b})$ analysis [1]. In this analysis the cross-sections are measured simultaneously for the WZ and ZZ production with $p_{\text {T}}^{V}$ > 100 $\text {GeV}$ using a dataset corresponding to an integrated luminosity of 18.9 fb$^{-1}$ with $\sqrt{s}=8$ $\text {TeV}$.

The analysis presented here is an unprecedented attempt to measure $VZ(b\bar{b})$ cross-sections at $\sqrt{s}=13$ $\text {TeV}$, in the high $p_{\text {T}}^{V}$ regime. As already mentioned in Sect. 3.4.4, the VZ process includes the WZ and ZZ processes. The ZZ production mode is split into two contributions: $qq \rightarrow ZZ$ and $gg\rightarrow ZZ$. The ZZ events that contribute to the analysis are events in which one Z boson decays leptonically and the other Z boson decay hadronically. For the WZ events the main contribution in the analysis is from events in which the W boson decays leptonically and the Z boson decays hadronically. The major input is from events in which the Z boson decays into a $b\bar{b}$ pair. There is also a small contribution from events in which the W boson decays hadronically and the Z boson decays leptonically. Table 9.1 briefly summarizes the different fractions of the MC VZ contributions in the $VH(b\bar{b})$ analysis. About 90% of the VZ events in the analysis are $VZ(b\bar{b)}$ events in which the Z boson decays into a pair of b-quarks and the V boson decays leptonically. Almost 3.3% of the events are $W(qq')Z(\nu \nu /ll)$ events, in which the vector boson that decays hadronically is a W boson instead of the Z boson. The remaining 5.2% of the VZ events are $VZ(q\bar{q})$ events in which the Z boson decays hadronically but not into a $b\bar{b}$ pair.

Table 9.1 Monte Carlo VZ fraction in the analysis summing the contributions of the three lepton channels and all the analysis regions. The asterisk * indicates the events in which the hadronic decay of Z boson is not b-quarks

9.2 VZ Simplified Template Cross-Section Bins

A STXS-like framework is used to perform the cross-section measurement for the VZ process. The use of the STXS framework for the VZ mass was never use before and it per se a challenge. The definition of the VZ STXS bins replicates the one already discussed for the VH process. Each bin is defined using the generator values of the measured quantities. Only the VZ events in which the Z boson decays hadronically and the V boson decays leptonically are considered as signal events. The $W(qq')Z(\nu \bar{\nu }/l\bar{l})$ events are considered as background events of the analysis.

The VZ events are categorized according to the production and decay modes in order to have five categories: $gg \rightarrow Z(q \bar{q} )Z(\nu \bar{\nu })$, $qq \rightarrow Z(q\bar{q} ) Z (\nu \bar{\nu } )$, $qq \rightarrow Z( q \bar{q} ) W(l \nu )$, $gg \rightarrow Z (q \bar{q} )Z(l \bar{l})$ and $qq \rightarrow Z(q\bar{q}) Z ( l\bar{l} )$. Each category is divided according to the transverse momentum of the vector boson which decays leptonically. The events are split applying four cuts at $p_{\text {T}}^{V}$ = 75 $\text {GeV}$, 150 $\text {GeV}$, 250 $\text {GeV}$ and 400 $\text {GeV}$. This configuration with 25 bins is called maximum splitting and it is shown in Fig. 9.1a. The measurement presented in this thesis uses a coarser splitting referred as main splitting. The different ZZ productions and Z leptonic decay modes are all merged together. All the VZ events with $p_{\text {T}}^{V}$ < 250 $\text {GeV}$ are fixed to their SM values in the fit. Figure 9.1b shows the VZ STXS categorization in the main splitting scheme and the four STXS bins where the cross-section measurements have been performed.

Fig. 9.1

a Maximum splitting and b main splitting of the VZ events in STXS bins. The boundaries of the truth $p_{\text {T}}^{V}$ regions are expressed in $\text {GeV}$. In the main splitting the measurements are performed only in the bin shown in red, the bins shown in white are fixed to their SM values

The goal of this new analysis is achieved by replacing the VZ signal strength $\mu _{VZ}$ with the cross-section measurements in the four STXS bins (see Fig. 9.2) performing a (4$+$4) PoIs fit. The eight PoIs extracted from the fit are: $\sigma ^{ZH}_{250-400}$, $\sigma ^{ZH}_{400}$, $\sigma ^{WH}_{250-400}$, $\sigma ^{WH}_{400}$, $\sigma ^{ZZ}_{250-400}$, $\sigma ^{ZZ}_{400}$, $\sigma ^{WZ}_{250-400}$, $\sigma ^{WZ}_{400}$.

Fig. 9.2

Pictorial representation of the PoIs for the signal strength measurement of the VZ process (left) compared to the cross-section measurements (right)

Some modifications to the framework used for the VH analysis are required. The measurement of the cross-sections needs to split the VZ simulated events and to update the VZ systematics uncertainties. The overall theoretical uncertainties should be removed and residual uncertainties need to be considered while performing a cross-section measurement. The VZ analysis is at the early stage and the systematic uncertainties have been not yet changed, meaning that the VZ uncertainties are over-conservative. Only the $p_{\text {T}}^{V}$ acceptance uncertainty on the VZ events is neglected since the cross-section measurements have been performed in the two $p_{\text {T}}^{V}$ regions independently. The theoretical uncertainties on the predicted cross-sections have been specifically derived for the VZ measurement following the recommendations available in literature and they are presented in Sect. 9.3. To validate the split of the VZ inputs, a merging procedure of the VZ events has been applied and the (1+1) PoIs fit has been performed as a cross check.

The expected cross-sections times the branching ratios of the $VZ(b\bar{b})$ events in each bin of the maximum splitting scheme were not available in literature and they have been evaluated for this analysis. Figure 9.3 shows the obtained cross-sections times branching ratios of the $VZ(b\bar{b})$ events in the maximum splitting scheme. The considered branching ratios are the branching ratio of the leptonic decay of the V boson and the branching ratio of the decay of the Z boson into $b\bar{b}$ pair since more than 90% of the VZ events selected in the analysis have a Z boson which decays into b-quarks. The cross-sections times branching ratios are obtained by computing from simulated VZ samples the fractions of events in each bin, and multiplying such fractions by the theoretical predictions of the inclusive cross-section. The theoretical prediction of the inclusive cross-section are calculated at NLO in QCD (see Sect. 3.4.4). The qq-initiated MC samples have been generated at LO and NLO in QCD depending on the parton multiplicity, while the gg-initiated MC samples have been generated at LO in QCD.

Fig. 9.3

SM $VZ(b\bar{b})$ cross-sections times branching ratios in each bin of the maximum splitting scheme at $\sqrt{s}$ = 13 $\text {TeV}$

Fig. 9.4

SM $VZ(b\bar{b})$ cross-sections times branching ratios in each bin of the main splitting scheme at $\sqrt{s}$ = 13 $\text {TeV}$

The expected $VZ(b\bar{b})$ cross-sections times the branching ratios in each bin of the main splitting are shown in Fig. 9.4.

Fig. 9.5

a VZ events and b VZ fraction from each STXS bin (x-axis) in every reconstructed event category (y-axis). The HP and LP SRs in 0- and 1-lepton channels have been merged and the contribution in the CRs is not shown because it is negligible

9.2.1 Comparison to Reconstructed Categories

The expected VZ event yield in each reconstructed event category (y-label) originating from the STXS bin (x-label) is shown in Fig. 9.5a. The number of reconstructed events with a truth $p_{\text {T}}^{V}$ < 250 $\text {GeV}$ is low because the analysis selects only events with $p_{\text {T}}^{V}$ $\ge$ 250 $\text {GeV}$. The events in these regions are fixed in the fit to their SM values because the statistics is not enough to perform a meaningful measurement.

The fraction of VZ events in each reconstructed event category (y-label) originating from the STXS bins (x-label) is shown Fig. 9.5b. The 2-lepton channel shows a very good correspondence between the truth and the reconstructed categories with a matching of 95%, followed by the 1-lepton channel with a matching of 80–90%. Differently in the 0-lepton channel there is a 20% contribution from the WZ events. The same trend has been observed considering VH signal process in which 20% of the events reconstructed in the 0-lepton channel are coming from the WH process. The WZ events reconstructed in the 0-lepton channel are events where the W boson decays in $\tau + \nu$ and then the $\tau$ lepton decays hadronically.

9.3 Theoretical Cross-Sections Uncertainties

The theoretical uncertainties on the cross-sections, as the theoretical predictions on the cross-sections, were not available in literature and they have been derived for this thesis. These uncertainties take into account the missing higher-order terms in the QCD expansion and uncertainties induced by the choices of the parton distribution functions (PDFs) and $\alpha _S$. The uncertainties have been derived specifically for each source of uncertainties and then summed in quadrature to obtain the total uncertainty on the theoretical prediction. A brief description of the different components of the theoretical cross-sections uncertainties is reported in the following sub-sections.

9.3.1 QCD Scale Uncertainties

The QCD scale uncertainties account for the impact of the higher order terms in the expansion of the cross-section that have been neglected. The scale variations are evaluated in the inclusive $p_{\text {T}}^{V}$ bins because,due to cancellations, in the exclusive $p_{\text {T}}^{V}$ bins the variations could underestimate the uncertainties. The scale variations in the inclusive $p_{\text {T}}^{V}$ bins are then propagated to the exclusive $p_{\text {T}}^{V}$ bins using the Stewart-Tackmann method [2].

Fig. 9.6

Relative QCD scale variations in inclusive $p_{\text {T}}^{V}$ bins for a $gg \rightarrow ZZ$, b $qq \rightarrow ZZ$ and c $qq \rightarrow WZ$ production modes. The black line represents the absolute value of the maximum variation and it coincides with one of the six variations

The QCD scale uncertainties are computed by varying the renormalisation scale $\mu _R$ and factorisation scale $\mu _F$ independently between 1/2 and 2 times their original values $\mu _R^{norm}$ and $\mu _F^{norm}$. The six scale variations considered are:

$$\begin{aligned} \left[ \frac{\mu _R}{\mu ^{norm}_R}, \frac{\mu _F}{\mu ^{norm}_F} \right] : [0.5, 1][1,0.5][2,1][1,2][0.5, 0.5][2,2] \end{aligned}$$

(9.1)

The computed variations are relative variations with respect to the nominal values $\left[ \frac{\mu _R}{\mu ^{norm}_R}, \frac{\mu _F}{\mu ^{norm}_F} \right] = [1,1]$ and they are evaluated in each inclusive $p_{\text {T}}^{V}$ region ($p_{\text {T}}^{V}$ > 0 $\text {GeV}$, $p_{\text {T}}^{V}$ > 75 $\text {GeV}$, $p_{\text {T}}^{V}$ > 150 $\text {GeV}$, $p_{\text {T}}^{V}$ > 250 $\text {GeV}$, $p_{\text {T}}^{V}$ > 400 $\text {GeV}$) for $gg \rightarrow ZZ$, $qq \rightarrow ZZ$ and $qq \rightarrow WZ$ production modes. The absolute value of the maximum of the six variations represents the relative QCD uncertainties in each inclusive $p_{\text {T}}^{V}$ bin. Figure 9.6 shows the relative QCD variations of each process together with the absolute value of the maximum variation which coincides with one of the six variations. The absolute value of the maximum variation is of the order of 40–50% for the $gg \rightarrow ZZ$ process, and 10–20% for the $qq \rightarrow ZZ$ and $qq \rightarrow WZ$ processes. Using the Stewart-Tackmann method the absolute values of the maximum variation are calculated in the exclusive $p_{\text {T}}^{V}$ bins and they represent the QCD scale variation. The QCD scale variations on the measured STXS bins for the $gg \rightarrow ZZ$, $qq \rightarrow ZZ$ and $qq \rightarrow WZ$ processes are summarised in Table 9.2. The QCD uncertainties on the $gg\rightarrow ZZ$ process are larger with respect to the QCD uncertainties of the qq-initiated processes due to the limited precision of the MC sample.

Table 9.2 QCD scale uncertainties on the $gg \rightarrow ZZ$, $qq \rightarrow ZZ$ and $qq \rightarrow WZ$ production modes in the STXS bins where the cross-sections measurements have been performed

9.3.2 PDF Uncertainties

The parton distribution function (PDF) uncertainties have been evaluated using the variations of the NNPDF3.0 set [3]. This PDF set includes a nominal PDF and 100 PDF variations. The PDF uncertainties are computed in each STXS bin for $gg \rightarrow ZZ$, $qq \rightarrow ZZ$ and $qq \rightarrow WZ$ production modes using the sample standard deviation:

$$\begin{aligned} \delta _j = \sqrt{ \frac{1}{100} \sum \limits _{i=1}^{100} (y_{\text {PDF}i} - y_{\text {PDF}0})^2 } \end{aligned}$$

(9.2)

where $y_{\text {PDF}0}$ and $y_{\text {PDF}i}$ are the cross-sections in each STXS bin for the nominal PDF (PDF0) and the alternative PDF (PDFi). The variation of each alternative PDF is less than 1% in each STXS bin and the overall uncertainty is of the order of 3–4% for the $gg \rightarrow ZZ$ process and 1–2% for the qq-initiated processes. Table 9.3 summarises the PDF predictions for the three processes in the $p_{\text {T}}^{V}$ regions where the cross-section measurements have been performed.

Table 9.3 PDF uncertainties on the $gg \rightarrow ZZ$, $qq \rightarrow ZZ$ and $qq \rightarrow WZ$ production modes in the STXS bins where the cross-sections measurements have been performed

9.3.3 $\alpha _S$ Uncertainties

The $\alpha _S$ uncertainty have been computed using the variations of the NNPDF3.0 set. In addition to the 100 PDF variations with the same nominal value of $\alpha _S(m^2_Z) = 0.118$, the set contains also 2 PDF sets obtained for two alternative values of $\alpha _S(m^2_Z)$: $\alpha _S(m^2_Z) =0.117$ and $\alpha _S(m^2_Z) =0.119$. The $\alpha _S$ uncertainty is computed in each STXS bin for the three production modes ($gg \rightarrow ZZ$, $qq \rightarrow ZZ$, $qq \rightarrow WZ$) starting from the relative variations. The relative variations $\text {Var}_{\alpha _S=0.117}$ and $\text {Var}_{\alpha _S=0.119}$ are evaluated using the samples with $\alpha _S(m^2_Z) =0.117$ and $\alpha _S(m^2_Z) =0.119$ with respect to the nominal sample. The relative $\alpha _S$ uncertainty is the average of the absolute value of the relative variations $\text {Var}_{\alpha _S=0.117}$ and $\text {Var}_{\alpha _S=0.119}$:

$$\begin{aligned} \text {Var}_{\alpha _S} = \frac{|\text {Var}_{\alpha _S=0.119}| + |\text {Var}_{\alpha _S=0.117}|}{2} \end{aligned}$$

(9.3)

Figure 9.7 shows the relative $\alpha _S$ variations and the average of the variations, which is the relative $\alpha _S$ uncertainty, for the three production modes in the STXS bins. The relative $\alpha _S$ uncertainty is of the order of 1–2%. Table 9.4 summarises the relative $\alpha _S$ uncertainties in the STXS regions where the measurements have been performed.

Fig. 9.7

Absolute value of the relative $\alpha _S$ variations in STXS bins for a $gg \rightarrow ZZ$, b $qq \rightarrow ZZ$ and c $qq \rightarrow WZ$ production modes. The black line represents the relative $\alpha _S$ uncertainty

9.3.4 Summary

Thanks to the procedure previously described, the theoretical uncertainties on the theoretical cross-section predictions have been evaluated for the ZZ and WZ processes. Beyond the scope of this thesis, a similar procedure will be applied to evaluate the residual uncertainties necessary to improve the STXS measurements. The total theoretical uncertainty is estimated from the sum in quadrature of the QCD, PFD and $\alpha _S$ uncertainties. The total uncertainties have been evaluated for the $gg \rightarrow ZZ$, $qq \rightarrow ZZ$ and $qq \rightarrow WZ$ processes and then used into each region of the main splitting. Table 9.5 shows the total cross-section predictions in the bins of the main splitting together with the full set of uncertainties.

Table 9.4 $\alpha$ uncertainties on the $gg \rightarrow ZZ$, $qq \rightarrow ZZ$ and $qq \rightarrow WZ$ production modes in the STXS bins where the cross-sections measurements have been performed

Table 9.5 Cross-section predictions and theoretical uncertainties for the VZ process at $\sqrt{s}$ = 13 $\text {TeV}$ in each region of the main splitting

9.4 Results of the Multi-PoIs Fit

The results of the (4$+$4) PoIs fit are obtained from a binned maximum profile likelihood fit to the data of the $m_J$ distribution. Considering the data collected during the full Run 2 at a center-of-mass energy of $\sqrt{s}=13$ $\text {TeV}$, corresponding to an integrated luminosity of 139 fb$^{-1}$, the significances of the VH and VZ processes in each bin are summarised in Table 9.6. The significances of the VH processes are compatible with the ones obtained from the (4$+$1) PoIs fit (see Table 8.5). The observed VZ significances vary between 1.5 and $2.5\sigma$. Figure 9.8 shows the correlations of the eight parameters of interest which are of the order of 10–20%. The correlations between the VH bins are the same obtained from the (4$+$1) PoIs fit.

Table 9.6 Expected and observed significance for the measured cross-sections in the eight bins

Fig. 9.8

Observed correlations among the cross-sections in the different regions. The colour indicates the size of the correlation

Figure 9.9 shows the comparison of the measured VH and VZ cross-sections with respect to the expected SM values. The theoretical uncertainties on the SM predictions of the cross-sections times branching ratios ($\sigma \times BR$) are shown as grey area. The VZ theoretical uncertainties are bigger than the VH theoretical uncertainties. The large VZ uncertainties are due to the limited precision of some VZ MC samples which are simulated at LO in QCD. All the VH and VZ measurements are in agreement with the SM predictions. The WH and WZ bins have almost the same precision while the ZZ bins has a twice better precision with respect to the ZH bins.

Fig. 9.9

Measured VH and VZ cross-sections times branching ratios divided by the SM predictions. The grey area shows the theoretical uncertainty on the SM prediction

The measured VZ cross-sections times $Z\rightarrow b\bar{b}$ and $V \rightarrow$ leptons branching ratios, together with the SM predictions, are summarized in Table 9.7 and illustrated in Fig. 9.10. The VZ cross-sections are measured with relative uncertainties varying between 60 and 95% with almost the equal contribution of the statistical and systematic uncertainties. The analysis has large VZ systematic uncertainties which are over-conservative and highly ranked in the VZ bins. The next natural step of the analysis is to improve the VZ uncertainty computation considering only residual uncertainties while performing the cross-section measurements. The VZ contribution on the systematic uncertainties will likely go down.

Table 9.7 Measured and predicted VZ cross-sections times BRs with corresponding uncertainties in the four STXS bins of the main splitting at $\sqrt{s}$ = 13 $\text {TeV}$

Fig. 9.10

Measured VZ cross-sections times branching ratios in the four STXS bins at $\sqrt{s}$ = 13 $\text {TeV}$

In this new measurement, the NPs of all the systematics have been fully scrutinized. The obtained NPs have been compared to the ones of the (4$+$1) PoIs fit. The pulls and the constraints of all the NPs do not change. In some cases some NPs show up in the pull plot because they are not pruned any more. In these particular cases the NP is neither pulled nor constrained. Furthermore the normalization factors of the major backgrounds ($V+$jets and $t\bar{t}$ ) are the same.

9.4.1 What’s Next?

As shown in this chapter, it is possible to performed a VZ cross-section measurement starting from the $VH(b\bar{b})$ boosted analysis. Nevertheless a more reliable study of the VZ systematic uncertainties is needed since now they are over-conservative. The new VZ uncertainty scheme will be based on the same methods applied for the theoretical VZ uncertainties and it will give a more reliable estimation of the systematic uncertainties specifically needed for the cross-section measurements.

The next natural step is the EFT interpretation of the results. The VZ cross-section can be parametrized as a function of Wilson coefficients while performing the (4$+$4) PoIs fit. Preliminary results shows that parametrizing the VH and VZ cross-sections with the Wilson coefficients, there is an improvements of 5–10% of the expected Wilson coefficient limit. The preliminary tests have been done performing a one-dimensional fit and considering the linear and quadratic parametrisation of the cross-section. The results looks promising and can help to improve limits for some operators.