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

TL;DR

This paper measures the production rates of a Higgs boson decaying into bottom quarks associated with W or Z bosons as a function of the bosons' transverse momentum, using ATLAS data at 13 TeV, confirming Standard Model predictions.

Contribution

First measurement of $VH$, $H o bar{b}$ production as a function of gauge boson transverse momentum at 13 TeV with detailed fiducial cross-sections.

Findings

Results agree with Standard Model predictions.

Set limits on effective Lagrangian parameters affecting Higgs couplings.

Provides detailed differential cross-section measurements.

Abstract

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.

Figures

Tables

Table 1. 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 subscript 𝑚 top m_{\mathrm{top}} is the reconstructed mass of a semileptonically decaying top-quark candidate in the 1-lepton channel. The calculation of m top subscript 𝑚 top m_{\mathrm{top}} uses the four-momenta of one of the two b 𝑏 b -jet candidates, the lepton, and the hypothetical neutrino produced in the event. The neutrino four-momentum is derived using the W 𝑊 W boson mass constraint  [ 15 ] and m top subscript 𝑚 top m_{\mathrm{top}} is then reconstructed from the combination of the b 𝑏 b -jet candidate and the value of the neutrino longitudinal momentum that yields the smallest top-quark candidate mass. The m top ≤ 225 subscript 𝑚 top 225 m_{\mathrm{top}}\leq 225   GeV  requirement in the 1-lepton signal region is needed to maintain orthogonality with the W 𝑊 W +HF control region.

Channel	Categories
	$75$ GeV  GeV		$p_{\text{T}}^{V,r}>150$ GeV
	$2$ jets	$\ge 3$ jets	$2$ jets	$3$ jets	$\ge 3$ jets
0-lepton	$-$	$-$	SR	SR	$-$
1-lepton
$m_{bb}\ge 75$ GeV or $m_{\mathrm{top}}\le 225$ GeV	$-$	$-$	SR	SR	$-$
GeV and $m_{\mathrm{top}}>225$ GeV	$-$	$-$	CR	CR	$-$
2-lepton
$ee$ and $\mu \mu$ channels	SR	SR	SR	$-$	SR
$e\mu$ channel	CR	CR	CR	$-$	CR

Table 2. Table 2: 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 𝑉 𝐻 VH 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 𝑍 𝐻 ZH , p T Z < 150 ​ GeV superscript subscript 𝑝 T 𝑍 150 GeV p_{\text{T}}^{Z}<150\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV} regions (from q ​ q ¯ 𝑞 ¯ 𝑞 q\bar{q} and g ​ g 𝑔 𝑔 gg ) into four regions, based on whether p T Z < 75 ​ GeV superscript subscript 𝑝 T 𝑍 75 GeV p_{\text{T}}^{Z}<75\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV} or 75 < p T Z < 150 ​ GeV 75 superscript subscript 𝑝 T 𝑍 150 GeV 75<p_{\text{T}}^{Z}<150\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV} ; (ii) by adding a p T Z < 250 superscript subscript 𝑝 T 𝑍 250 p_{\text{T}}^{Z}<250   GeV  requirement to the g ​ g → Z ​ H → 𝑔 𝑔 𝑍 𝐻 gg\to ZH , p T Z > 150 superscript subscript 𝑝 T 𝑍 150 p_{\text{T}}^{Z}>150   GeV  regions (with zero or at least one extra particle-level jet), and (iii) by adding a separate g ​ g → Z ​ H , p T Z > 250 formulae-sequence → 𝑔 𝑔 𝑍 𝐻 superscript subscript 𝑝 T 𝑍 250 gg\to ZH,p_{\text{T}}^{Z}>250   GeV  region. The three regions W ​ H 𝑊 𝐻 WH , p T W < 150 superscript subscript 𝑝 T 𝑊 150 p_{\text{T}}^{W}<150   GeV , q ​ q ¯ → Z ​ H → 𝑞 ¯ 𝑞 𝑍 𝐻 q\bar{q}\to ZH , p T Z < 75 superscript subscript 𝑝 T 𝑍 75 p_{\text{T}}^{Z}<75   GeV  and g ​ g → Z ​ H → 𝑔 𝑔 𝑍 𝐻 gg\to ZH , p T Z < 75 superscript subscript 𝑝 T 𝑍 75 p_{\text{T}}^{Z}<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
			$N_{\mathrm{lep}}$	$p_{\text{T}}^{V,r}$ interval	$N_{\mathrm{jet}}$
$WH$, $p_{\text{T}}^W>150\text{GeV}$	$WH$,	$q\overline{q}\to WH$, , 0-jet	1	$>150$ GeV	2, 3
		$q\overline{q}\to WH$, , $\ge 1$-jet
	$WH$, $p_{\text{T}}^W>250\text{GeV}$	$q\overline{q}\to WH$, $p_{\text{T}}^W>250\text{GeV}$
$ZH$,	$ZH$,	$q\overline{q}\to ZH$,	2	75–150 GeV	2, $\ge 3$
		$gg\to ZH$,
$ZH$, $p_{\text{T}}^Z>150\text{GeV}$	$ZH$,	$q\overline{q}\to ZH$, , 0-jet
		$gg\to ZH$, , 0-jet
		$q\overline{q}\to ZH$, , $\ge 1$-jet	0	$>150$ GeV	2, 3
		$gg\to ZH$, , $\ge 1$-jet	2	$>150$ GeV	2, $\ge$3
	$ZH$, $p_{\text{T}}^Z>250\text{GeV}$	$q\overline{q}\to ZH$, $p_{\text{T}}^Z>250\text{GeV}$
		$gg\to ZH$, $p_{\text{T}}^Z>250$ GeV

Table 3. Table 3: Best-fit values and uncertainties for the V ​ H 𝑉 𝐻 VH , V → → 𝑉 absent V\to  leptons reduced stage-1 simplified template cross-sections times the H → b ​ b ¯ → 𝐻 𝑏 ¯ 𝑏 H\to b\bar{b} 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. The total systematic uncertainty, equal to the difference in quadrature between the total uncertainty and the statistical uncertainty, differs from the sum in quadrature of the Th. Sig., Th. Bkg., and Exp. systematic uncertainties due to correlations. All leptonic decays of the V 𝑉 V bosons (including those to τ 𝜏 \tau -leptons, ℓ = e , μ , τ ℓ 𝑒 𝜇 𝜏 \ell=e,\mu,\tau ) are considered.

Measurement region	SM prediction			Result			Stat. unc.		Syst. unc. [fb]
(, $H\to b\overline{b}$)	[fb]			[fb]			[fb]		Th. sig.		Th. bkg.		Exp.
5-POI scheme
$W\to \ell \nu$;  GeV	$24.0$	$\pm$	$1.1$	$20$	$\pm$	$25$	$\pm$	$17$	$\pm$	2	$\pm$	13	$\pm$	9
$W\to \ell \nu$; $p_{\text{T}}^V>250$ GeV	$7.1$	$\pm$	$0.3$	$8.8$	$\pm$	$5.2$	$\pm$	$4.4$	$\pm$	0.5	$\pm$	2.5	$\pm$	0.9
$Z\to \ell \ell ,\nu \nu$;  GeV	$50.6$	$\pm$	$4.1$	$81$	$\pm$	$45$	$\pm$	$35$	$\pm$	10	$\pm$	21	$\pm$	19
$Z\to \ell \ell ,\nu \nu$;  GeV	$18.8$	$\pm$	$2.4$	$14$	$\pm$	$13$	$\pm$	$11$	$\pm$	1	$\pm$	6	$\pm$	3
$Z\to \ell \ell ,\nu \nu$; $p_{\text{T}}^V>250$ GeV	$4.9$	$\pm$	$0.5$	$8.5$	$\pm$	$4.0$	$\pm$	$3.7$	$\pm$	0.8	$\pm$	1.2	$\pm$	0.6
3-POI scheme
$W\to \ell \nu$; $p_{\text{T}}^V>150$ GeV	$31.1$	$\pm$	$1.4$	$35$	$\pm$	$14$	$\pm$	9	$\pm$	2	$\pm$	9	$\pm$	4
$Z\to \ell \ell ,\nu \nu$;  GeV	$50.6$	$\pm$	$4.1$	$81$	$\pm$	$45$	$\pm$	35	$\pm$	10	$\pm$	21	$\pm$	19
$Z\to \ell \ell ,\nu \nu$; $p_{\text{T}}^V>150$ GeV	$23.7$	$\pm$	$3.0$	$28.4$	$\pm$	$8.1$	$\pm$	6.4	$\pm$	2.4	$\pm$	3.6	$\pm$	2.3

Table 4. Table 4: The expected and observed 68 % percent \% CL (four top rows) and 95% CL (four bottom rows) intervals for the effective Lagrangian coefficients c ¯ H ​ W subscript ¯ 𝑐 𝐻 𝑊 \bar{c}_{HW} , c ¯ H ​ B subscript ¯ 𝑐 𝐻 𝐵 \bar{c}_{HB} , c ¯ W − c ¯ B subscript ¯ 𝑐 𝑊 subscript ¯ 𝑐 𝐵 \bar{c}_{W}-\bar{c}_{B} and c ¯ d subscript ¯ 𝑐 𝑑 \bar{c}_{d} when the other coefficients are assumed to vanish. Each row is composed of two sub-rows: the first one uses the interference between SM and non-SM amplitudes and the SM-independent contributions, while the second sub-row uses only the interference between SM and non-SM amplitudes.

Coefficient	Expected interval	Observed interval
Results at 68% confidence level
${\overline{c}}_{HW}$	[$-0.003$, 0.002]	[$-0.001$, 0.004]
(interference only	[$-0.002$, 0.003]	[$-0.001$, 0.005])
\hdashline${\overline{c}}_{HB}$	[$-0.066$, 0.013]	[$-0.078$, $-0.055$] $\bigcup$ [0.005, 0.019]
(interference only	[$-0.016$, 0.016]	[$-0.005$, 0.030])
\hdashline${\overline{c}}_W-{\overline{c}}_B$	[$-0.006$, 0.005]	[$-0.002$, 0.007]
(interference only	[$-0.005$, 0.005]	[$-0.002$, 0.008])
\hdashline${\overline{c}}_d$	[$-1.5$, 0.3]	[$-1.6$, $-0.9$] $\bigcup$ [$-0.3$, $0.4$]
(interference only	[$-0.4$, 0.4]	[$-0.2$, $0.7$])
Results at 95% confidence level
${\overline{c}}_{HW}$	[$-0.018$, 0.004]	[$-0.019$,$-0.010$] $\bigcup$ [$-0.005$, 0.006]
(interference only	[$-0.005$, 0.005]	[$-0.003$, $0.008$])
\hdashline${\overline{c}}_{HB}$	[$-0.078$, 0.024]	[$-0.090$, $0.032$]
(interference only	[$-0.033$, 0.033]	[$-0.022$, $0.049$])
\hdashline${\overline{c}}_W-{\overline{c}}_B$	[$-0.034$, 0.008]	[$-0.036$,$-0.024$] $\bigcup$ [$-0.009$, 0.010]
(interference only	[$-0.009$, 0.010]	[$-0.006$, $0.014$])
\hdashline${\overline{c}}_d$	[$-1.7$, $0.5$]	[$-1.9$, $0.7$]
(interference only	[$-0.8$, 0.8]	[$-0.6$, $1.1$])

Equations

$${\bar{c}}_{HW}=\frac{m_W^2}{g}\frac{c_{HW}}{{\Lambda }^2},{\bar{c}}_{HB}=\frac{m_W^2}{g^{\prime }}\frac{c_{HB}}{{\Lambda }^2},{\bar{c}}_W=\frac{m_W^2}{g}\frac{c_W}{{\Lambda }^2},{\bar{c}}_B=\frac{m_W^2}{g^{\prime }}\frac{c_B}{{\Lambda }^2},{\bar{c}}_d=v^2\frac{c_d}{{\Lambda }^2},$$

Full text

\LEcontact

Steve Lloyd s.l.lloyd@qmul.ac.uk

\AtlasTitleMeasurement 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 \AtlasAbstract 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.

\PreprintIdNumberCERN-EP-2019-019 \AtlasRefCodeHIGG-2018-50 \PreprintIdNumberCERN-EP-2019-019 \AtlasJournalRefJHEP 05 (2019) 141 \AtlasDOI10.1007/JHEP05(2019)141 \AtlasCoverSupportingNoteSimplified template cross-section measurements for the $VH(H\to b\bar{b})$ process with the ATLAS detectorhttps://cds.cern.ch/record/2636121 \AtlasCoverCommentsDeadline \AtlasCoverAnalysisTeam \AtlasCoverEgroupEditorsatlas-HIGG-2018-50-editors@cern.ch \AtlasCoverEgroupEdBoardatlas-HIGG-2018-50-editorial-board@cern.ch

1 Introduction

A particle consistent with the Standard Model (SM) predictions for the Higgs boson [1, 2, 3, 4] was observed in 2012 by the ATLAS and CMS collaborations [5, 6] at the LHC. Further analysis of ATLAS and CMS data collected in proton–proton ($pp$) collisions at centre-of-mass energies of 7 TeV, 8 TeV and 13 TeV in two LHC data-taking periods (Runs 1 and 2) has led to precise measurements of the mass of this particle (around 125 GeV) [7, 8, 9], tests of its spin and parity ($J^{P}=0^{+}$) against alternative hypotheses [10, 11], as well as to measurements of its production and decay rates [12, 13, 14].

Recently, experiments at the LHC observed Higgs boson production in association with weak gauge bosons $V=W,Z$ ($VH$ production) [15] and Higgs boson decays into pairs of bottom quarks ($H\to b\bar{b}$) [15, 16]. With these results, the four most important Higgs boson production modes predicted by the SM, gluon–gluon fusion (ggF), vector-boson fusion (VBF), and associated production of a Higgs boson with either a weak gauge boson ($VH$) or a top-quark pair ($t\bar{t}H$) are established. Similarly, several of the main modes of Higgs boson decays into fermionic ($b\bar{b}$, $\tau\tau$) and bosonic ($WW$, $ZZ$, $\gamma\gamma$) final states are observed. All results, typically expressed in the form of ‘signal strengths’, defined as the ratio of the observed to the expected product of the production cross-section times branching ratio into a certain final state, are consistent with SM predictions within uncertainties.

To probe the kinematic properties of Higgs boson production in more detail, to reduce the impact of theoretical uncertainties on the measurements and to make the measurements easier to compare with future updated calculations, the framework of simplified template cross-sections (STXS) has been introduced [17, 18]. In this framework, the cross-sections for the various Higgs boson production modes are measured in exclusive regions carefully defined by fiducial selections based on the kinematic properties of Higgs boson production. The extrapolation from the phase space selected by the analysis criteria to that for which the cross-section measurements are presented is thus reduced.

The STXS measurements are designed to proceed in stages of increasing granularity with more recorded data. In ‘stage 0’, cross-sections are measured separately for the four main production modes in a fiducial Higgs boson rapidity region $|y_{H}|<2.5$,111ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the $z$-axis along the beam pipe. The $x$-axis points from the IP to the centre of the LHC ring, and the $y$-axis points upwards. Cylindrical coordinates $(r,\phi)$ are used in the transverse plane, $\phi$ being the azimuthal angle around the $z$-axis. The pseudorapidity is defined in terms of the polar angle $\theta$ as $\eta=-\ln\tan(\theta/2)$. When dealing with massive particles, the rapidity $y=1/2\ln[(E+p_{z})/(E-p_{z})]$ is used, where $E$ is the energy and $p_{z}$ is the $z$-component of the momentum. mainly driven by the ATLAS and CMS detector acceptances for most of the reconstructed objects (leptons, photons and $b$-jets). In ‘stage 1’ these regions are split into 31 subregions according to kinematic properties such as the number of particle-level jets with transverse momentum $p_{\text{T}}>30$ GeV (excluding any jets from Higgs boson decays), the transverse momentum of the Higgs boson, or the transverse momentum of the weak gauge boson $V$ for $VH$, $V\to$ leptons production. In simulation, particle-level jets are built by clustering all generated stable particles ($c\tau>10$ mm), excluding the decay products of the Higgs boson as well as the neutrinos and charged leptons from the decays of the weak gauge boson, using the anti-$k_{t}$ clustering algorithm [19] with a radius parameter $R=0.4$.

Stage-0 STXS were measured recently with 36.1 fb*-1* of 13 TeV ATLAS data using $H\to\gamma\gamma$ [20] and $H\to ZZ^{*}\to 4\ell$ decays [21], with results in agreement with SM predictions. In addition, Refs. [20] and [21] contain some ‘reduced’ stage-1 STXS measurements of ggF and VBF regions, after merging together regions where the data lack sufficient sensitivity to Higgs boson production. Given the low $VH$ production cross-sections, the only Higgs boson decay mode that can currently be measured is $H\to b\bar{b}$, with its large branching ratio of 58%. This presents a measurement of ‘reduced’ stage-1 $VH$ STXS (defined in Section 3) using $H\to b\bar{b}$ 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].

2 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, $E_{\text{T}}^{\mathrm{miss}}$. 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 $VH$, $H\to b\bar{b}$ signal strength [15]. Several samples of simulated events were produced for the signal ($q\bar{q}\to WH$, $q\bar{q}\to ZH$ and $gg\to ZH$) and main background ($t\bar{t}$, 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 $q\bar{q}\to WH$ and $q\bar{q}\to ZH$ events with zero or one additional jet, calculated at next-to-leading order (NLO), generated with the Powheg-Box v2 + GoSam + MiNLO generators [25, 26, 27, 28]. The contribution from loop-induced $gg\to ZH$ production was simulated at leading order (LO) using the Powheg-Box v2 generator [25]. Additional scale factors were applied to the $q\bar{q}\to VH$ processes as a function of the generated vector-boson transverse momentum ($p_{\text{T}}^{V}$) to account for electroweak (EW) corrections at NLO. These factors were determined from the ratio between the $VH$ differential cross-sections computed with and without these corrections by the Hawk program [29, 30]. The mass of the Higgs boson was fixed at 125 GeV.

In the measurement of the $pp\to ZH$ cross-sections, the relative contributions of the $q\bar{q}\to ZH$ and $gg\to ZH$ processes are determined by the most accurate theoretical cross-section predictions currently available: next-to-next-to-leading order (NNLO) in QCD and NLO in EW [31, 32, 33, 34, 35, 36, 37] for $q\bar{q}\to ZH$, and next-to-leading order and next-to-leading logarithm (NLO+NLL) in QCD [38, 39, 40, 41, 42] for $gg\to ZH$.

3 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 $VH$, $H\to b\bar{b}$ production and decay, with $Z\to\nu\bar{\nu}$, $W\to\ell\nu$ or $Z\to\ell\ell$ ($\ell=e,\mu$). Vector-boson decays into $\tau$-leptons are not targeted explicitly. However, they satisfy the selection criteria with reduced efficiency in the case of leptonic $\tau$-lepton decays.

In particular, events are kept if they contain at most two isolated electrons or muons, and two good-quality high-$p_{\text{T}}$ ($>45,20$ GeV) jets with $|\eta|<2.5$ satisfying $b$-jet identification (’$b$-tagging’) requirements (which have an average efficiency of 70% for jets containing $b$-hadrons that are produced in inclusive $t\bar{t}$ 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 $p_{\text{T}}>20$ GeV for $|\eta|<2.5$ or $p_{\text{T}}>30$ GeV for $2.5<|\eta|<4.5$, 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 $Z\to\nu\bar{\nu}$ or $W\to\ell\nu$ decays; in the 2-lepton events, the leptons must have the same flavour (and opposite charge for events with muons) 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 $t\bar{t}$ 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 $p_{\text{T}}^{V,\mathrm{r}}$ of the vector boson $V$ is applied. It is computed, depending on the number, $N_{\mathrm{lep}}$, of selected electrons and muons, as either the missing transverse momentum $E_{\text{T}}^{\mathrm{miss}}$ ($N_{\mathrm{lep}}=0$), the magnitude of the vector sum of the missing transverse momentum and the lepton $p_{\text{T}}$ ($N_{\mathrm{lep}}=1$), or the dilepton $p_{\text{T}}$ ($N_{\mathrm{lep}}=2$). The minimum value of $p_{\text{T}}^{V,\mathrm{r}}$ 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, $N_{\mathrm{jet}}$ (including the two $b$-jet candidates), $N_{\mathrm{lep}}$, and $p_{\text{T}}^{V,\mathrm{r}}$. 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 ($W$+HF), or top-quark pair production. The signal contribution in such categories is expected to be negligible.

4 Cross-section measurements

The reduced $VH$, $V\to$ leptons stage-1 STXS regions used in this 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 $Z\to\tau\tau$ and $W\to\tau\nu$) are considered for the STXS definition.

Compared to the original stage-1 proposal presented in Ref. [17], the following changes have been made for the reduced $VH$, $V\to$ leptons stage-1 STXS regions of Table 2:

• •

the $p_{\text{T}}^{Z}<150\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$ stage-1 regions are split into two subregions, $p_{\text{T}}^{Z}<75\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$ and $75<p_{\text{T}}^{Z}<150$ GeV, to avoid theory uncertainties from extrapolations to a phase space not accessible to this measurement;

• •

an additional $gg\to ZH$, $p_{\text{T}}^{Z}\leavevmode\nobreak\ >250$ GeV region has been introduced, similarly to what is already done for $q\bar{q}\to ZH$.

These two changes lead to a total of 14 modified stage-1 regions, which are then combined together in reduced stage-1 regions, chosen to keep the total uncertainty in the measurements near or below 100%, in the following way:

• •

the $q\bar{q}\to ZH$ and $gg\to ZH$ regions are merged. There are currently not enough data events to distinguish $q\bar{q}\to ZH$ from gluon-induced $ZH$ production despite their different kinematic properties;

• •

the $150<p_{\text{T}}^{V}<250$ GeV regions with zero or at least one particle-level jet are merged.

Two sets of reduced stage-1 regions are considered. In one, called the ‘5-POI (parameters of interest)’ scheme, five cross-sections, three for $ZH$ production ($75<p_{\text{T}}^{Z}<150$ GeV, $150<p_{\text{T}}^{Z}<250$ GeV and $p_{\text{T}}^{Z}>250$ GeV) and two for $WH$ production ($150<p_{\text{T}}^{W}<250$ GeV and $p_{\text{T}}^{W}>250$ GeV), are measured. In the other one, called the ‘3-POI’ scheme, three cross-sections, two for $ZH$ ($75<p_{\text{T}}^{Z}<150$ GeV and $p_{\text{T}}^{Z}>150$ GeV) and one for $WH$ ($p_{\text{T}}^{W}>150$ 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 $p_{\text{T}}^{V}$ from potential anomalous interactions between the Higgs boson and the EW gauge bosons.

The reconstructed-event categories do not distinguish between events with generated $p_{\text{T}}^{V}$ below or above 250 GeV. Discrimination between the two $p_{\text{T}}^{V}$ regions 150–250 GeV and $>250$ GeV is provided by the different shapes of the boosted-decision-tree discriminant ($\mathrm{BDT}_{VH}$) 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 $p_{\text{T}}^{V,\mathrm{r}}$ is largely correlated with the $\mathrm{BDT}_{VH}$ 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 $H\to b\bar{b}$ 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 $\mathrm{BDT}_{VH}$ 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 $\mathrm{BDT}_{VH}$ or $m_{bb}$) or yield per category, multiple shapes or yields are introduced, one for each reduced stage-1 STXS region under study.

• •

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 $H\to b\bar{b}$ and $V\to$ 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 $VH$, $V\to$ leptons, $H\to b\bar{b}$ 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(b).

As shown in Figure 2(a), the current analysis is not sensitive to $WH$ events with $p_{\text{T}}^{W}<150$ GeV and to $ZH$ events with $p_{\text{T}}^{Z}<75$ 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 $p_{\text{T}}^{W}<150$ GeV and $p_{\text{T}}^{Z}<75$ 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 distributions – in 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 $p_{\text{T}}^{V}$ regions (with the following lower edges: 0 GeV, 75 GeV, 150 GeV, 250 GeV and 400 GeV), and each $p_{\text{T}}^{V}$ region into three bins depending on the number of particle-level jets (zero, one, or at least two), independently for the $q\bar{q}\to VH$ and $gg\to ZH$ 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 $\alpha_{\text{S}}$. Fourteen independent sources of uncertainties due to the missing higher-order terms lead to total uncertainties of 3%–4% for $q\bar{q}\to VH$ and 40%–50% for $gg\to ZH$ with $p_{\text{T}}^{V}>$ 75 GeV [44]. Thirty-one independent sources of PDF and $\alpha_{\text{S}}$ 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 $p_{\text{T}}^{V,\mathrm{r}}$ 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 $\alpha_{\text{S}}$ choices are considered.

Systematic uncertainties in the signal acceptance and shape of the $p_{\text{T}}^{V,\mathrm{r}}$ 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 Pythia 8 PS parameters or after replacing Pythia 8 with Herwig 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 $q\bar{q}\to VH$ ($gg\to ZH$) production mode. Two independent nuisance parameters account for the systematic uncertainties induced by the PS and UE models in the $p_{\text{T}}^{V,\mathrm{r}}$ and $m_{bb}$ distributions. In addition, a systematic uncertainty due to the EW corrections is parameterised as a change in shape of the $p_{\text{T}}^{V}$ distributions for the $q\bar{q}\to VH$ processes [15].

5 Results

The measured reduced stage-1 $VH$ cross-sections times the $H\to b\bar{b}$ and $V\to$ leptons branching ratios, $\sigma\times B$, 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 $p_{\text{T}}^{V}>150$ GeV intervals are not equal to the sum of those measured for $150<p_{\text{T}}^{V}<250$ GeV and $p_{\text{T}}^{V}>250$ GeV. This is because the signal template for $p_{\text{T}}^{V}>150$ 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 $WH$ cross-sections with $p_{\text{T}}^{W}>150$ GeV in the 3-POI case and with $150<p_{\text{T}}^{W}<250$ 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 $p_{\text{T}}^{V}>250$ GeV and $150<p_{\text{T}}^{V}<250$ 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 $VH$ signal are small, with relative values ranging between 6% and 12%. The uncertainties in the predictions are 2–3 times larger for $ZH$ than for $WH$ in the same $p_{\text{T}}^{V}$ interval due to the limited precision of the theoretical calculations of the $gg\to ZH$ process.

6 Constraints on anomalous Higgs boson interactions

The strength and tensor structure of the Higgs boson interactions are investigated using an effective Lagrangian approach [22]. Extra terms of the form $c_{i}^{(D)}\mathcal{O}_{i}^{(D)}/\Lambda^{D-4}$, where $\Lambda$ is the energy scale of the new interactions, ${O}_{i}^{(D)}$ are dimension-$D$ operators, and $c_{i}^{(D)}$ 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 $\Lambda$.

The results presented in this 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 EW symmetry breaking. Among such operators, four directly affect the $VH$ cross-sections because they introduce new Higgs boson interactions with $W$ bosons ($\mathcal{O}_{HW}$, $\mathcal{O}_{W}$) and $Z$ bosons (all four operators):

• •

$\mathcal{O}_{HW}=i\left(D^{\mu}H\right)^{\dagger}\sigma^{a}\left(D^{\nu}H\right)W^{a}_{\mu\nu}$,

• •

$\mathcal{O}_{HB}=i\left(D^{\mu}H\right)^{\dagger}\left(D^{\nu}H\right)B_{\mu\nu}$,

• •

\mathcal{O}_{W}=\frac{i}{2}\left(H^{\dagger}\sigma^{a}\overset{\text{\scriptsize\leftrightarrow}}{D^{\mu}}H\right)D^{\nu}W^{a}_{\mu\nu},

• •

\mathcal{O}_{B}=\frac{i}{2}\left(H^{\dagger}\overset{\text{\scriptsize\leftrightarrow}}{D^{\mu}}H\right)\partial^{\nu}B_{\mu\nu}.

The corresponding $CP$-odd operators $\tilde{\mathcal{O}}_{HW}$, $\tilde{\mathcal{O}}_{HB}$, $\tilde{\mathcal{O}}_{W}$, and $\tilde{\mathcal{O}}_{B}$, are not considered.

Modifications of the $gg\to ZH$ production cross-section are only introduced by either higher-dimension ($D\geq 8$) operators or corrections that are formally at NNLO in QCD, and are not included in this study, in which the expected $gg\to ZH$ contribution is kept fixed to the SM prediction.

The operator $\mathcal{O}_{d}=y_{d}|H|^{2}\bar{Q}_{\mathrm{L}}Hd_{\mathrm{R}}$ (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 $\Gamma_{H}^{bb}$ and of the total Higgs boson width $\Gamma_{H}$, and therefore of the $H\to b\bar{b}$ branching ratio. This operator affects the measured cross-sections in the same way in each region.

Constraints are set on the coefficients of the five $\mathcal{O}_{W}$, $\mathcal{O}_{B}$, $\mathcal{O}_{HW}$, $\mathcal{O}_{HB}$ and $\mathcal{O}_{d}$ operators in the ‘Higgs Effective Lagrangian’ (HEL) implementation [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 $1/\Lambda^{2}$, and the SM-independent contributions that are quadratic in the coefficients and of order $1/\Lambda^{4}$. In the HEL implementation, the coefficients $c_{i}$ of interest are recast into the following dimensionless coefficients:

[TABLE]

where $g$ and $g^{\prime}$ 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 sum $\bar{c}_{W}+\bar{c}_{B}$ is strongly constrained by precision EW data [49] and is thus assumed here to be zero, and constraints are set on $\bar{c}_{HW}$, $\bar{c}_{HB}$, $\bar{c}_{W}-\bar{c}_{B}$ and $\bar{c}_{d}$. The relations between the HEL coefficients and the reduced STXS measured in this 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 determine $\bar{c}_{HW}$, $\bar{c}_{HB}$, $\bar{c}_{W}-\bar{c}_{B}$ and $\bar{c}_{d}$. Due to the large sensitivity to the Higgs boson anomalous couplings to vector bosons provided by the $p_{\text{T}}^{V}>250$ GeV cross-sections, the 5-POI results place tighter constraints on these coefficients (e.g. approximately a factor two for $\bar{c}_{HW}$) 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 one-dimensional projections are shown in Figure 4, and the 68% and 95% CL intervals for $\bar{c}_{HW}$, $\bar{c}_{HB}$, $\bar{c}_{W}-\bar{c}_{B}$ and $\bar{c}_{d}$ are summarised in Table 4. The parameters $\bar{c}_{HW}$ and $\bar{c}_{W}-\bar{c}_{B}$ are constrained at 95% CL to be no more than a few percent, while the constraint on $\bar{c}_{HB}$ is about five times worse, and the constraint on $\bar{c}_{d}$ 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 ($1/\Lambda^{4}$) 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.

7 Conclusion

Using 79.8 fb*-1* of $\sqrt{s}=13$ 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 $p_{\text{T}}^{V}$. 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 $p_{\text{T}}^{V}$ 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 $p_{\text{T}}^{V}$ ($>250$ 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.

Acknowledgements

We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.

We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, CRC and Compute Canada, Canada; COST, ERC, ERDF, Horizon 2020, and Marie Skłodowska-Curie Actions, European Union; Investissements d’ Avenir Labex and Idex, ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya, Spain; The Royal Society and Leverhulme Trust, United Kingdom.

The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [50].