Measurement of $VH$, $H\to b\bar{b}$ production as a function of the vector-boson transverse momentum in 13 TeV $pp$ collisions with the ATLAS detector

Cross-sections of associated production of a Higgs boson decaying into bottom-quark pairs and an electroweak gauge boson, $W$ or $Z$, decaying into leptons are measured as a function of the gauge boson transverse momentum. The measurements are performed in kinematic fiducial volumes defined in the `simplified template cross-section' framework. The results are obtained using 79.8 fb$^{-1}$ of proton-proton collisions recorded by the ATLAS detector at the Large Hadron Collider at a centre-of-mass energy of 13 TeV. All measurements are found to be in agreement with the Standard Model predictions, and limits are set on the parameters of an effective Lagrangian sensitive to modifications of the Higgs boson couplings to the electroweak gauge bosons.


Introduction
with its large branching ratio of 58%. This paper presents a measurement of 'reduced' stage-1 V H STXS (defined in Section 3) using H → bb decays with 79.8 fb −1 of 13 TeV pp collisions collected by ATLAS between 2015 and 2017. The results are used to investigate the strength and tensor structure of the interactions of the Higgs boson with vector bosons using an effective Lagrangian approach [22].

Data and simulation samples
The data were collected with the ATLAS detector [23,24] between 2015 and 2017, triggered by isolated charged leptons or large transverse momentum imbalance, E miss T . Only events with good data quality were kept.
The Monte Carlo simulation samples used for the measurements presented here are identical to those used for the measurement of the inclusive V H, H → bb signal strength [15]. Several samples of simulated events were produced for the signal (qq → W H, qq → Z H and gg → Z H) and main background (tt, single-top, V+jets and diboson) processes. They were used to optimise the analysis criteria and to determine the expected signal and background distributions of the discriminating variables used in the final fit to the data. The multijet background is largely suppressed by the selection criteria and is estimated using data-driven techniques.
The signal templates in each STXS region were obtained from simulated qq → W H and qq → Z H events with zero or one additional jet, calculated at next-to-leading order (NLO), generated with the P -B v2 + G S + M NLO generators [25][26][27][28]. The contribution from loop-induced gg → Z H production was simulated at leading order (LO) using the P -B v2 generator [25]. Additional scale factors were applied to the qq → V H processes as a function of the generated vector-boson transverse momentum (p V T ) to account for electroweak (EW) corrections at NLO. These factors were determined from the ratio between the V H differential cross-sections computed with and without these corrections by the H program [29,30]. The mass of the Higgs boson was fixed at 125 GeV.

Event selection and categorisation
The object reconstruction, event selection and classification into categories used for the measurements, are identical to those described in Ref. [15]. The selection and the event categories are briefly summarised below.
Events are retained if they are consistent with one of the typical signatures of V H, H → bb production and decay, with Z → νν, W → ν or Z → ( = e, µ). Vector-boson decays into τ-leptons are not targeted explicitly. However, they satisfy the selection criteria with reduced efficiency in the case of leptonic τ-lepton decays.
In particular, events are kept if they contain at most two isolated electrons or muons, and two good-quality high-p T (> 45, 20 GeV) jets with |η| < 2.5 satisfying b-jet identification ('b-tagging') requirements (which have an average efficiency of 70% for jets containing b-hadrons that are produced in inclusive tt events [43]). The two b-jet candidates are used to reconstruct the Higgs boson candidate; their invariant mass is denoted by m bb . Additional jets are required to have p T > 20 GeV for |η| < 2.5 or p T > 30 GeV for 2.5 < |η| < 4.5, and not be identified as b-jets.
Events with either zero, one or two isolated electrons or muons are classified as '0-lepton', '1-lepton' or '2-lepton' events, respectively. The 0-lepton events and the 1-lepton events are required to have transverse momentum imbalance, as expected from the neutrinos from Z → νν or W → ν decays; in the 2-lepton events, the leptons must have the same flavour and an invariant mass close to the Z boson mass.
Additional requirements are applied to suppress background from QCD production of multijet events in the 0-lepton and 1-lepton channels. To suppress the large tt background, events with four or more jets are discarded in the 0-lepton and 1-lepton channels. Finally, a requirement on the reconstructed transverse momentum p V,r T of the vector boson V is applied. It is computed, depending on the number, N lep , of selected electrons and muons, as either the missing transverse momentum E miss T (N lep = 0), the magnitude of the vector sum of the missing transverse momentum and the lepton p T (N lep = 1), or the dilepton p T (N lep = 2). The minimum value of p V,r T is 150 GeV in the 0-and 1-lepton channels, and 75 GeV in the 2-lepton channel.
Events satisfying the previous criteria are classified into eight categories (also called signal regions in the following), shown in Table 1, with different signal-to-background ratios. These categories are defined by the number of jets, N jet (including the two b-jet candidates), N lep , and p V,r T . Additional categories (also called control regions in the following) containing events satisfying alternative selections are introduced to constrain some background processes such as W boson production in association with jets containing heavy-flavour hadrons, or top-quark pair production. The signal contribution in such categories is expected to be negligible. Table 1: Summary of the reconstructed-event categories. Categories with relatively large fractions of the total expected signal yields are referred to as 'signal regions' (SR), while those with negligible expected signal yield, mainly designed to constrain some background processes, are called 'control regions' (CR). The quantity m top is the reconstructed mass of a semileptonically decaying top-quark candidate in the 1-lepton channel. The calculation of m top uses the four-momenta of one of the two b-jet candidates, the lepton, and the hypothetical neutrino produced in the event. The neutrino four-momentum is derived using the W boson mass constraint [15] and m top is then reconstructed from the combination of the b-jet candidate and neutrino longitudinal momentum that yields the smallest top-quark candidate mass.

Cross-section measurements
The reduced V H, V → leptons stage-1 STXS regions used in this paper are summarised in Table 2, which also indicates which reconstructed-event categories are most sensitive in each region. All leptonic decays of the weak gauge bosons (including Z → ττ and W → τν) are considered for the STXS definition.
To avoid theory uncertainties from extrapolations to a phase space not accessible to the measurement, the p Z T < 150 GeV stage-1 regions are split into two subregions, p Z T < 75 GeV and 75 < p Z T < 150 GeV. Currently, there are not enough data events to distinguish qq → Z H from gluon-induced Z H production, despite their different kinematic properties. As the gg → Z H cross-section is only 16% of that of qq → Z H, no attempt is made to measure the qqand gg-initiated processes separately. The qq → Z H and gg → Z H regions are thus merged together, after having modified the gg → Z H fiducial region definition to match that of qq → Z H. Therefore, the gg → Z H, p Z T > 150 GeV stage-1 regions (with zero or at least one extra particle-level jet) are modified by adding a p Z T < 250 GeV requirement, and events with p Z T > 250 GeV and any number of particle-level jets are put in a separate gg → Z H, p Z T > 250 GeV region, leading to a total of 14 modified stage-1 regions. These regions are then merged together in reduced stage-1 regions, chosen to keep the total uncertainty in the measurements near or below 100%.
Two sets of reduced stage-1 regions are considered. In one, called the '5-POI (parameters of interest)' scheme, five cross-sections, three for Z H production (75 < p Z T < 150 GeV, 150 < p Z T < 250 GeV and p Z T > 250 GeV) and two for W H production (150 < p W T < 250 GeV and p W T > 250 GeV), are measured. In the other one, called the '3-POI' scheme, three cross-sections, two for Z H (75 < p Z T < 150 GeV and p Z T > 150 GeV) and one for W H (p W T > 150 GeV), are measured. The 5-POI scheme leads to measurements that have total uncertainties larger than those in the 3-POI scheme, but are more sensitive to enhancements at high p V T from potential anomalous interactions between the Higgs boson and the EW gauge bosons. The reconstructed-event categories do not distinguish between events with generated p V T below or above 250 GeV. Discrimination between the two p V T regions 150-250 GeV and > 250 GeV for events with generated p V T below or above 250 GeV is provided by the different shapes of the boosted-decision-tree discriminant (BDT V H ) used in the final fit to the data, as illustrated in Figure 1 in the case of the 1-lepton, 2-jet category. This arises from the fact that the reconstructed p V,r T is largely correlated with the BDT V H output, for which it constitutes one of the most discriminating input variables together with m bb and the angular separation of the two b-jets.
The product of the signal cross-section times the H → bb branching ratio and the total leptonic decay branching ratio for W or Z bosons is determined in each of the reduced stage-1 regions by a binned maximum-likelihood fit to the data. The cross-sections are not constrained to be positive in the fit. Signal and background templates of the discriminating variables, determined from the simulation or data control regions, are used to extract the signal and background yields. A simultaneous fit is performed to all the signal and control regions. Systematic uncertainties are included in the likelihood function as nuisance parameters.
The likelihood function is very similar to that described in Ref. [15]. In particular, the same observables are used, namely BDT V H in the signal regions and either the invariant mass m bb of the two b-jets or the event yield in the control regions. The treatment of the background and of its uncertainties is also unchanged. The only differences relative to the likelihood function in Ref.
[15] concern the treatment of the signal: • Instead of a single signal shape (for BDT V H or m bb ) or yield per category, multiple shapes or yields are introduced, one for each reduced stage-1 STXS region under study. The 3-POI and 5-POI 'reduced stage-1' sets of merged regions used for the measurements, the corresponding kinematic regions of the stage-1 V H simplified template cross-sections, and the reconstructed-event categories that are most sensitive in each merged region. The stage-1 regions are modified (i) by splitting the two Z H, p Z T < 150 GeV regions (from qq and gg) into four regions, based on whether p Z T < 75 GeV or 75 < p Z T < 150 GeV; (ii) by adding a p Z T < 250 GeV requirement to the gg → Z H, p Z T > 150 GeV regions (with zero or at least one extra particle-level jet), and (iii) by adding a separate gg → Z H, p Z T > 250 GeV region. The three regions W H, p W T < 150 GeV, qq → Z H, p Z T < 75 GeV and gg → Z H, p Z T < 75 GeV, in which the current analysis is not sensitive and whose corresponding cross-sections are fixed to the SM prediction in the fit, are not shown.

Merged region
Merged region Stage 1 (modified) STXS region Reconstructed-event categories 3-POI scheme 5-POI scheme with largest sensitivity • Instead of a single parameter of interest, the inclusive signal strength, the fit has multiple parameters of interest, i.e. the cross-sections of the reduced stage-1 regions, multiplied by the H → bb and V → leptons branching ratios.
• Overall theoretical cross-section and branching ratio uncertainties, which affect the signal strength measurements but not the STXS measurements, are not included in the likelihood function.
The expected signal shapes of the discriminating variable distributions and the acceptance times efficiency (referred to as 'acceptance' in the following) in each reduced stage-1 region are determined from simulated samples of SM V H, V → leptons, H → bb events. The acceptance of each reconstructed-event category for signal events from the different regions of the 5-POI reduced stage-1 scheme is shown in Figure 2(a). The fraction of signal events in each reconstructed-event category originating from the different regions in the same scheme is shown in Figure 2 As shown in Figure 2(a), the current analysis is not sensitive to W H events with p W T < 150 GeV and to Z H events with p Z T < 75 GeV, since their acceptance in each category is at the level of 0.1% or smaller. Therefore, in the fits the signal cross-section in these regions is constrained to the SM prediction, within the theoretical uncertainties. Since these regions contribute only marginally to the selected event sample, the impact on the final results is negligible. A cross-check in which the relative signal cross-section uncertainty for the p W T < 150 GeV and p Z T < 75 GeV regions is conservatively set to 70% of the prediction (i.e. about seven times the nominal uncertainty) leads to variations of the measured STXS below 1%. The sources of systematic uncertainty are identical to those described in Ref.
[15], except for those associated with the Higgs boson signal simulation, which are re-evaluated [44]. In this re-evaluation the uncertainties are separated into two groups: • uncertainties affecting signal modelling -i.e. acceptance and shape of kinematic distributionsin each of the three or five reduced stage-1 regions (hereafter referred to as theoretical modelling uncertainties), and • uncertainties in the prediction of the production cross-section for each of these regions (hereafter referred to as theoretical cross-section uncertainties).
While theoretical modelling uncertainties enter the measurement of the STXS, theoretical cross-section uncertainties do not affect the results, but only the predictions with which they are compared. The consequent reduction of the impact of the theoretical uncertainties on the results with respect to the signal strength measurements is one of the main advantages of measuring STXS.
The two groups of systematic uncertainties are estimated for high-granularity STXS regions, and then merged into the reduced scheme under consideration. This approach makes it easy to compute the systematic uncertainties for merging schemes different from those presented here. The uncertainties are evaluated by    dividing the phase space into five p V T regions (with the following lower edges: 0 GeV, 75 GeV, 150 GeV, 250 GeV and 400 GeV), and each p V T region into three bins depending on the number of particle-level jets (zero, one, or at least two), independently for the qq → V H and gg → Z H processes. When two STXS regions are merged, their relative theoretical cross-section uncertainties lead to a modelling uncertainty. These uncertainties are evaluated as the remnant of the theoretical cross-section uncertainties for the high-granularity regions after the subtraction of the theoretical cross-section uncertainty for the merged region.
The high-granularity regions are used to calculate theoretical cross-section uncertainties for the missing higher-order terms in the QCD perturbative expansion and for the uncertainties induced by the choices of the parton distribution function (PDF) and α S . Fourteen independent sources of uncertainties due to the missing higher-order terms lead to total uncertainties of 3%-4% for qq → V H and 40%-50% for gg → Z H with p V T > 75 GeV [44]. Thirty-one independent sources of PDF and α S uncertainties, each of them usually smaller than 1%, lead to a total quadrature sum between 2% and 3% depending on the STXS region. The theoretical modelling uncertainties change the shapes of the reconstructed p V,r T and m bb distributions in the same way as described in Ref. [15]. Four independent sources for the QCD expansion and two independent sources for the PDF and α S choices are considered.
Systematic uncertainties in the signal acceptance and shape of the p V,r T and m bb distributions due to the parton shower (PS) and underlying event (UE) models are estimated from the variations of acceptance and shapes of simulated events after changing the P 8 PS parameters or after replacing P 8 with H 7 for the PS and UE models [15]. The signal acceptance uncertainties due to the PS and UE models (five independent sources) are typically of the order of 1% (5%-15%) with a maximum of 10% (30%) for the qq → V H (gg → Z H) production mode. Two independent nuisance parameters account for the systematic uncertainties induced by the PS and UE models in the p V,r T and m bb distributions. In addition, a systematic uncertainty due to the EW corrections is parameterised as a change in shape of the p V T distributions for the qq → V H processes [15].

Results
The measured reduced stage-1 V H cross-sections times the H → bb and V → leptons branching ratios, σ × B, in the 5-POI and 3-POI schemes, together with the SM predictions, are summarised in Table 3. The results of the 5-POI scheme are also illustrated in Figure 3. The SM predictions are shown together with the theoretical cross-section uncertainty for the merged regions computed as described in the previous section. The measurements are in agreement with the SM predictions.
The cross-sections measured in the p V T > 150 GeV intervals are not equal to the sum of those measured for 150 < p V T < 250 GeV and p V T > 250 GeV. This is because the signal template for p V T > 150 GeV in the 3-POI fit is computed from the sum of the templates of the two regions assuming that the ratio of yields in those regions is that predicted by the SM, while in the 5-POI fit the normalisations of the two templates are floated independently.
The cross-sections are measured with relative uncertainties varying between 50% and 125% in the 5-POI case, and between 29% and 56% for the 3-POI. The largest uncertainties are statistical, except for the W H cross-sections with p W T > 150 GeV in the 3-POI case and with 150 < p W T < 250 GeV in the 5-POI case. In the 5-POI case, an anti-correlation of the order of 40%-60% is observed between the cross-sections in the ranges p V T > 250 GeV and 150 < p V T < 250 GeV, which are measured with the same reconstructed-event categories.
The dominant systematic uncertainties are due to the limited number of simulated background events and the theoretical modelling of the background processes. The uncertainties due to the theoretical modelling of the V H signal are small, with relative values ranging between 6% and 12%. The uncertainties in the predictions are 2-3 times larger for Z H than for W H in the same p V T interval due to the limited precision of the theoretical calculations of the gg → Z H process. Table 3: Best-fit values and uncertainties for the V H, V → leptons reduced stage-1 simplified template cross-sections times the H → bb branching ratio, in the 5-POI (top five rows) and 3-POI (bottom three rows) schemes. The SM predictions for each region, computed using the inclusive cross-section calculations and the simulated event samples described in Section 2, are also shown. The contributions to the total uncertainty in the measurements from statistical (Stat. unc.) or systematic uncertainties (Syst. unc.) in the signal modelling (Th. sig.), background modelling (Th. bkg.), and in experimental performance (Exp.) are given separately. All leptonic decays of the V bosons (including those to τ-leptons, = e, µ, τ) are considered.

Constraints on anomalous Higgs boson interactions
The i are numerical coefficients, are added to the SM Lagrangian to obtain an effective Lagrangian inspired by that in Ref. [45]. Only dimension D = 6 operators are considered in this study, since dimension D = 5 operators violate lepton or baryon number, while dimension D > 6 operators are further suppressed by powers of Λ.
The results presented in this paper focus on the coefficients of the operators in the 'Strongly Interacting Light Higgs' formulation [46]. This formalism is defined as the effective theory of a strongly interacting sector in which a light composite Higgs boson arises as a pseudo Goldstone boson, and is responsible for The corresponding CP-odd operatorsÕ HW ,Õ H B ,Õ W , andÕ B , are not considered.
Modifications of the gg → Z H production cross-section are only introduced by either higher-dimension (D ≥ 8) operators or corrections that are formally at NNLO in QCD, and are not included in this study, in which the expected gg → Z H contribution is kept fixed to the SM prediction.
The operator O d = y d |H| 2Q L Hd R (plus Hermitian conjugate) with Yukawa coupling strength y d , which modifies the coupling between the Higgs boson and down-type quarks, induces variations of the partial width Γ bb H and of the total Higgs boson width Γ H , and therefore of the H → bb branching ratio. This operator affects the measured cross-sections in the same way in each region.  [47], using the known relations between such coefficients and the stage-1 STXS based on leading-order predictions [48]. Such relations include interference terms between the SM and non-SM amplitudes that are linear in the coefficients and of order 1/Λ 2 , and the SM-independent contributions that are quadratic in the coefficients and of order 1/Λ 4 . In the HEL implementation, the coefficients c i of interest are recast into the following dimensionless coefficients: where g and g are the SU(2) and U(1) SM gauge couplings, and v is the vacuum expectation value of the Higgs boson field. These dimensionless coefficients are equal to zero in the SM.
The sumc W +c B is strongly constrained by precision EW data [49] and is thus assumed here to be zero, and constraints are set onc HW ,c H B ,c W −c B andc d . The relations between the HEL coefficients and the reduced STXS measured in this paper are obtained by averaging the relations for the regions that are merged with weights proportional to their respective cross-sections.
Simultaneous maximum-likelihood fits to the five STXS measured in the 5-POI scheme are performed to determinec HW ,c H B ,c W −c B andc d . Due to the large sensitivity to the Higgs boson anomalous couplings to vector bosons provided by the p V T > 250 GeV cross-sections, the 5-POI results place tighter constraints on these coefficients (e.g. approximately a factor two forc HW ) than do the 3-POI results. For this reason, constraints obtained with the 3-POI results are not shown here.
In each fit, all coefficients but one are assumed to vanish, and 68% and 95% confidence level (CL) one-dimensional intervals are inferred for the remaining coefficient. The negative-log-likelihood onedimensional projections are shown in Figure 4, and the 68% and 95% CL intervals forc HW ,c H B ,c W −c B andc d are summarised in Table 4. The parametersc HW andc W −c B are constrained at 95% CL to be no more than a few percent, while the constraint onc H B is about five times worse, and the constraint onc d is of order unity. For comparison, Table 4 also shows the 68% and 95% CL intervals for the dimensionless coefficients when the SM-independent contributions, which are of the same order (1/Λ 4 ) as the dimension-8 operators that are neglected, are not considered. The constraints are typically 50% stronger than when the SM-independent contributions are not neglected.

Conclusion
Using 79.8 fb −1 of √ s = 13 TeV proton-proton collisions collected by the ATLAS detector at the LHC, the cross-sections for the associated production of a Higgs boson decaying into bottom-quark pairs and an electroweak gauge boson W or Z decaying into leptons are measured as functions of the vector-boson transverse momentum p V T . The cross-sections are measured for Higgs bosons in a fiducial volume with rapidity |y H | < 2.5, in the 'simplified template cross-section' framework.
The measurements are performed for two different choices of the number of p V T intervals. The results have relative uncertainties varying between 50% and 125% in one case, and between 29% and 56% in the other. The measurements are in agreement with the Standard Model predictions, even in high p V T (> 250 GeV) regions that are most sensitive to enhancements from potential anomalous interactions between the Higgs boson and the electroweak gauge bosons.
One-dimensional limits on four linear combinations of the coefficients of effective Lagrangian operators affecting the Higgs boson couplings to the electroweak gauge bosons and to down-type quarks have also been set. For two of these parameters the constraint has a precision of a few percent.