The azimuthal correlation angle, $\Delta\phi$, between the scattered lepton and the leading jet in deep inelastic $e^{\pm}p$ scattering at HERA has been studied using data collected with the ZEUS detector at a centre-of-mass energy of $\sqrt{s} = 318 \;\mathrm{GeV}$, corresponding to an integrated luminosity of $326 \;\mathrm{pb}^{-1}$. A measurement of jet cross sections in the laboratory frame was made in a fiducial region corresponding to photon virtuality $10 \;\mathrm{GeV}^2 < Q^2 < 350 \;\mathrm{GeV}^2$, inelasticity $0.04 < y < 0.7$, outgoing lepton energy $E_e > 10 \;\mathrm{GeV}$, lepton polar angle $140^\circ < \theta_e < 180^\circ$, jet transverse momentum $2.5 \;\mathrm{GeV} < p_\mathrm{T,jet} < 30 \;\mathrm{GeV}$, and jet pseudorapidity $-1.5 < \eta_\mathrm{jet} < 1.8$. Jets were reconstructed using the $k_\mathrm{T}$ algorithm with the radius parameter $R = 1$. The leading jet in an event is defined as the jet that carries the highest $p_\mathrm{T,jet}$. Differential cross sections, $d\sigma/d\Delta\phi$, were measured as a function of the azimuthal correlation angle in various ranges of leading-jet transverse momentum, photon virtuality and jet multiplicity. Perturbative calculations at $\mathcal{O}(\alpha_{s}^2)$ accuracy successfully describe the data within the fiducial region, although a lower level of agreement is observed near $\Delta\phi \rightarrow \pi$ for events with high jet multiplicity, due to limitations of the perturbative approach in describing soft phenomena in QCD. The data are equally well described by Monte Carlo predictions that supplement leading-order matrix elements with parton showering.
<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Inclusive measurement of the differential cross sections, $d\sigma/d\Delta\phi$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. The effect of initial- and final-state radiation has been corrected in data, based on a simulation study performed in the RAPGAP framework. The quantities $\delta_\mathrm{stat}$ and $\delta_\mathrm{syst}$ represent the statistical and systematic uncertainties relative to the central value, respectively. The uncertainty in the luminosity measurement ($1.9\%$) is not included in these values. The quantities $\delta(\mathcal{O}(\alpha_{s}^{k}))$ represent the combined uncertainty of the scale dependence in the calculation and the model dependence in the hadronisation correction in the $\mathcal{O}(\alpha_{s}^{k})$ calculations.
<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.
<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.
A new measurement of inclusive-jet cross sections in the Breit frame in neutral current deep inelastic scattering using the ZEUS detector at the HERA collider is presented. The data were taken in the years 2004 to 2007 at a centre-of-mass energy of $318\,\text{GeV}$ and correspond to an integrated luminosity of $347\,\text{pb}^{-1}$. Massless jets, reconstructed using the $k_t$-algorithm in the Breit reference frame, have been measured as a function of the squared momentum transfer, $Q^2$, and the transverse momentum of the jets in the Breit frame, $p_{\perp,\text{Breit}}$. The measured jet cross sections are compared to previous measurements and to perturbative QCD predictions. The measurement has been used in a next-to-next-to-leading-order QCD analysis to perform a simultaneous determination of parton distribution functions of the proton and the strong coupling, resulting in a value of $\alpha_s(M_Z^2) = 0.1142 \pm 0.0017~\text{(experimental/fit)}$${}^{+0.0006}_{-0.0007}~\text{(model/parameterisation)}$${}^{+0.0006}_{-0.0004}~\text{(scale)}$, whose accuracy is improved compared to similar measurements. In addition, the running of the strong coupling is demonstrated using data obtained at different scales.
<b>Note: in the paper, uncertainties are given in percent. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Double-differential inclusive-jet cross sections, $\sigma$. Also listed are the unfolding uncertainty $\delta_\text{unf}$, the sum of the uncorrelated systematic uncertainties $\delta_\text{uncor}$ and the correlated systematic uncertainties associated with the jet-energy scale $\delta_\text{JES}$, the MC model $\delta_\text{model}$, the relative normalisation of the background from unmatched detector-level jets $\delta_\text{fake}$, the relative normalisation of the background from low-$Q^2$ DIS events $\delta_\text{Low-$Q^2$}$, the $(E-p_\text{Z})$-cut boundaries $\delta_{E-p_\text{Z}}$, the track-matching-efficiency correction $\delta_\text{TME}$. Uncertainties for which a single number is listed should be taken as symmetric in the other direction. Not listed explicitly is the luminosity uncertainty of $1.9\%$, which is fully correlated across all points. The last four columns show the QED Born-level correction $c_\text{QED}$ that has been applied to the data as well as the $Z$, $c_Z$, and hadronisation correction $c_\text{Had}$ and associated uncertainty that need to be applied to the theory predictions.
<b>Note: in the paper, uncertainties are given in percent. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Breakdown of the uncorrelated uncertainty $\delta_\text{uncor}$ from Table 1. Shown are the uncertainties associated with the reweighting of the MC models ($\delta_\text{rew.}$), the electron-energy scale ($\delta_\text{EES}$), the electron-finding algorithm ($\delta_\text{EM}$), the electron calibration ($\delta_\text{EL}$), the variation of the $p_{T,\text{lab}}$ cut of the jets ($\delta_{p_T}$), the variation of the electron-track momentum-cut boundaries ($\delta_\text{trk.}$), the variation of the $p_T/\sqrt{E_T}$-cut boundaries ($\delta_\text{bal.}$), the variation of the $Z_\text{vertex}$-cut boundaries ($\delta_\text{vtx.}$), the variation of the $R_\text{RCAL}$-cut boundaries ($\delta_\text{rad.}$), the variation of the electron-track distance-cut boundaries ($\delta_\text{DCA}$), the relative normalisation of the background from photoproduction events ($\delta_\text{PHP}$), the polarisation correction ($\delta_\text{pol.}$), the FLT track-veto-efficiency correction ($\delta_\text{FLT}$) and the correction to QED Born-level ($\delta_\text{QED}$). For the asymmetric uncertainties, the upper number corresponds to the upward variation of the corresponding parameter and the lower number corresponds to the downward variation.
Correlation matrix of the unfolding uncertainty within the inclusive-jet cross-section measurement. Correlations are given in percent.
A search for flavor-changing neutral-current couplings between a top quark, an up or charm quark and a $Z$ boson is presented, using proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the ATLAS detector at the Large Hadron Collider. The analyzed dataset corresponds to an integrated luminosity of 139 fb$^{-1}$. The search targets both single-top-quark events produced as $gq\rightarrow tZ$ (with $q = u, c$) and top-quark-pair events, with one top quark decaying through the $t \rightarrow Zq$ channel. The analysis considers events with three leptons (electrons or muons), a $b$-tagged jet, possible additional jets, and missing transverse momentum. The data are found to be consistent with the background-only hypothesis and 95% confidence-level limits on the $t \rightarrow Zq$ branching ratios are set, assuming only tensor operators of the Standard Model effective field theory framework contribute to the $tZq$ vertices. These are $6.2 \times 10^{-5}$ ($13\times 10^{-5}$) for $t\rightarrow Zu$ ($t\rightarrow Zc$) for a left-handed $tZq$ coupling, and $6.6 \times 10^{-5}$ ($12\times 10^{-5}$) in the case of a right-handed coupling. These results are interpreted as 95% CL upper limits on the strength of corresponding couplings, yielding limits for $|C_{uW}^{(13)*}|$ and $|C_{uB}^{(13)*}|$ ($|C_{uW}^{(31)}|$ and $|C_{uB}^{(31)}|$) of 0.15 (0.16), and limits for $|C_{uW}^{(23)*}|$ and $|C_{uB}^{(23)*}|$ ($|C_{uW}^{(32)}|$ and $|C_{uB}^{(32)}|$) of 0.22 (0.21), assuming a new-physics energy scale $\Lambda_\text{NP}$ of 1 TeV.
Summary of the signal strength $\mu$ parameters obtained from the fits to extract LH and RH results for the FCNC tZu and tZc couplings. For the reference branching ratio, the most stringent limits are used.
Observed and expected 95% CL limits on the FCNC $t\rightarrow Zq$ branching ratios and the effective coupling strengths for different vertices and couplings (top eight rows). For the latter, the energy scale is assumed to be $\Lambda_{NP}$ = 1 TeV. The bottom rows show, for the case of the FCNC $t\rightarrow Zu$ branching ratio, the observed and expected 95% CL limits when only one of the two SRs, either SR1 or SR2, and all CRs are included in the likelihood.
Comparison between data and background prediction before the fit (Pre-Fit) for the mass of the SM top-quark candidate in SR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The four FCNC LH signals are also shown separately, normalized to five times the cross-section corresponding to the most stringent observed branching ratio limits. The first (last) bin in all distributions includes the underflow (overflow). The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).
We report results from a search for neutrino-induced neutral current (NC) resonant $\Delta$(1232) baryon production followed by $\Delta$ radiative decay, with a $\langle0.8\rangle$~GeV neutrino beam. Data corresponding to MicroBooNE's first three years of operations (6.80$\times$10$^{20}$ protons on target) are used to select single-photon events with one or zero protons and without charged leptons in the final state ($1\gamma1p$ and $1\gamma0p$, respectively). The background is constrained via an in-situ high-purity measurement of NC $\pi^0$ events, made possible via dedicated $2\gamma1p$ and $2\gamma0p$ selections. A total of 16 and 153 events are observed for the $1\gamma1p$ and $1\gamma0p$ selections, respectively, compared to a constrained background prediction of $20.5 \pm 3.65 \text{(sys.)} $ and $145.1 \pm 13.8 \text{(sys.)} $ events. The data lead to a bound on an anomalous enhancement of the normalization of NC $\Delta$ radiative decay of less than $2.3$ times the predicted nominal rate for this process at the 90% confidence level (CL). The measurement disfavors a candidate photon interpretation of the MiniBooNE low-energy excess as a factor of $3.18$ times the nominal NC $\Delta$ radiative decay rate at the 94.8% CL, in favor of the nominal prediction, and represents a greater than $50$-fold improvement over the world's best limit on single-photon production in NC interactions in the sub-GeV neutrino energy range
Data and MC comparison of the reconstructed $\pi^0$ momentum distribution for the 2$\gamma$1p selected events
Data/MC ratio as a function of reconstructed $\pi^0$ momentum for the 2$\gamma$1p selection
Data and MC comparison of the reconstructed $\pi^0$ momentum distribution for the 2$\gamma$0p selected events
Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy $\sqrt{s}=319$ GeV are measured. The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of $136$ pb${}^{-1}$. Charged particle multiplicities are measured as a function of photon virtuality $Q^2$, inelasticity $y$ and pseudorapidity $\eta$ in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined and the KNO scaling behaviour is investigated. The multiplicity distributions as a function of $Q^2$ and the Bjorken variable $x_{\rm Bj}$ are converted to the hadron entropy $S_{\rm hadron}$, and predictions from a quantum entanglement model are tested.
Charged particle multiplicity distribution $P(N)$ measured as a function of the number of charged particles $N$ in 4x4 kinematic bins of $Q^2$ and $y$.
Charged particle multiplicity distribution $P(N)$ measured as a function of the number of charged particles $N$ in three overlapping pseudorapidity ranges $-1.2<\eta_{lab}\vert<0.2$, $-0.5<\eta_{lab}\vert<0.9$ and $0.2<\eta_{lab}\vert<1.6$, subdivided into 4x4 kinematic bins of $Q^2$ and $y$.
Charged particle multiplicity distribution $P(N)$ measured as a function of the number of charged particles $N$ with the additional restriction to select only particles from the current region of the Breit frame $0<\eta^{*}<4$, in 4x4 kinematic bins of $Q^2$ and $y$.
Angular distributions of the decay B$^+$$\to$ K$^*$(892)$^+\mu^+\mu^-$ are studied using events collected with the CMS detector in $\sqrt{s} =$ 8 TeV proton-proton collisions at the LHC, corresponding to an integrated luminosity of 20.0 fb$^{-1}$. The forward-backward asymmetry of the muons and the longitudinal polarization of the K$^*$(892)$^+$ meson are determined as a function of the square of the dimuon invariant mass. These are the first results from this exclusive decay mode and are in agreement with a standard model prediction.
The measured signal yields, FL, AFB in bins of the dimuon invariant mass squared. The first uncertainty is statistical and the second is systematic.
Final results are presented from the inclusive measurement of deep-inelastic polarised-muon scattering on longitudinally polarised deuterons using a $^6$LiD target. The data were taken at $160~{\rm GeV}$ beam energy and the results are shown for the kinematic range $1~({\rm GeV}/c)^2 < Q^2 < 100~({\rm GeV}/c)^2$ in photon virtuality, $0.004<x<0.7$ in the Bjorken scaling variable and $W > 4~{\rm GeV}/c^2$ in the mass of the hadronic final state. The deuteron double-spin asymmetry $A_1^{\rm d}$ and the deuteron longitudinal-spin structure function $g_1^{\rm d}$ are presented in bins of $x$ and $Q^2$. Towards lowest accessible values of $x$, $g_1^{\rm d}$ decreases and becomes consistent with zero within uncertainties. The presented final $g_1^{\rm d}$ values together with the recently published final $g_1^{\rm p}$ values of COMPASS are used to again evaluate the Bjorken sum rule and perform the QCD fit to the $g_1$ world data at next-to-leading order of the strong coupling constant. In both cases, changes in central values of the resulting numbers are well within statistical uncertainties. The flavour-singlet axial charge $a_0$, {which is identified in the $\overline{\rm MS}$ renormalisation scheme with the total contribution of quark helicities to the nucleon spin}, is extracted from only the COMPASS deuteron data with negligible extrapolation uncertainty: $a_0 (Q^2 = 3~({\rm GeV}/c)^2) = 0.32 \pm 0.02_{\rm stat} \pm0.04_{\rm syst} \pm 0.05_{\rm evol}$. Together with the recent results on the proton spin structure function $g_1^{\rm p}$, the results on $g_1^{\rm d}$ constitute the COMPASS legacy on the measurements of $g_1$ through inclusive spin-dependent deep inelastic scattering.
Values of $A_1^d$ and $g_1^d$ for the COMPASS deuteron data at 160 GeV in $x$ bins averaged over $Q^2$.
Values of $A_1^d$ and $g_1^d$ for the COMPASS deuteron data at 160 GeV in (x, $Q^2$) bins.
Values of $g_1^{NS}$ for the COMPASS data in $x$ bins averaged over $Q^2$.
A precision measurement of jet cross sections in neutral current deep-inelastic scattering for photon virtualities $5.5<Q^2<80\,{\rm GeV}^2$ and inelasticities $0.2<y<0.6$ is presented, using data taken with the H1 detector at HERA, corresponding to an integrated luminosity of $290\,{\rm pb}^{-1}$. Double-differential inclusive jet, dijet and trijet cross sections are measured simultaneously and are presented as a function of jet transverse momentum observables and as a function of $Q^2$. Jet cross sections normalised to the inclusive neutral current DIS cross section in the respective $Q^2$-interval are also determined. Previous results of inclusive jet cross sections in the range $150<Q^2<15\,000\,{\rm GeV}^2$ are extended to low transverse jet momenta $5<P_{T}^{\rm jet}<7\,{\rm GeV}$. The data are compared to predictions from perturbative QCD in next-to-leading order in the strong coupling, in approximate next-to-next-to-leading order and in full next-to-next-to-leading order. Using also the recently published H1 jet data at high values of $Q^2$, the strong coupling constant $\alpha_s(M_Z)$ is determined in next-to-leading order.
Inclusive jet cross sections measured as a function of $P_T^{\rm jet}$ for $Q^2$ = 5.5-8.0 GeV$^2$. The correction factors on the theoretical cross sections $c^{\rm had}$ are listed together with their uncertainties. The radiative correction factors $c^{\rm rad}$ are already included in the quoted cross sections. Note that the uncertainties labelled $\delta^{E_{e^\prime}}$ and $\delta^{\theta_{e^\prime}}$ in Table 6 of the paper (arXiv:1611.03421v3) should be swapped. See Table 5 of arXiv:1406.4709v2 for details of the correlation model.
Inclusive jet cross sections measured as a function of $P_T^{\rm jet}$ for $Q^2$ = 8.0-11.0 GeV$^2$. The correction factors on the theoretical cross sections $c^{\rm had}$ are listed together with their uncertainties. The radiative correction factors $c^{\rm rad}$ are already included in the quoted cross sections. Note that the uncertainties labelled $\delta^{E_{e^\prime}}$ and $\delta^{\theta_{e^\prime}}$ in Table 6 of the paper (arXiv:1611.03421v3) should be swapped. See Table 5 of arXiv:1406.4709v2 for details of the correlation model.
Inclusive jet cross sections measured as a function of $P_T^{\rm jet}$ for $Q^2$ = 11.0-16.0 GeV$^2$. The correction factors on the theoretical cross sections $c^{\rm had}$ are listed together with their uncertainties. The radiative correction factors $c^{\rm rad}$ are already included in the quoted cross sections. Note that the uncertainties labelled $\delta^{E_{e^\prime}}$ and $\delta^{\theta_{e^\prime}}$ in Table 6 of the paper (arXiv:1611.03421v3) should be swapped. See Table 5 of arXiv:1406.4709v2 for details of the correlation model.
A combination is presented of all inclusive deep inelastic cross sections previously published by the H1 and ZEUS collaborations at HERA for neutral and charged current $e^{\pm}p$ scattering for zero beam polarisation. The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV. The data correspond to an integrated luminosity of about 1 fb$^{-1}$ and span six orders of magnitude in negative four-momentum-transfer squared, $Q^2$, and Bjorken $x$. The correlations of the systematic uncertainties were evaluated and taken into account for the combination. The combined cross sections were input to QCD analyses at leading order, next-to-leading order and at next-to-next-to-leading order, providing a new set of parton distribution functions, called HERAPDF2.0. In addition to the experimental uncertainties, model and parameterisation uncertainties were assessed for these parton distribution functions. Variants of HERAPDF2.0 with an alternative gluon parameterisation, HERAPDF2.0AG, and using fixed-flavour-number schemes, HERAPDF2.0FF, are presented. The analysis was extended by including HERA data on charm and jet production, resulting in the variant HERAPDF2.0Jets. The inclusion of jet-production cross sections made a simultaneous determination of these parton distributions and the strong coupling constant possible, resulting in $\alpha_s(M_Z)=0.1183 \pm 0.0009 {\rm(exp)} \pm 0.0005{\rm (model/parameterisation)} \pm 0.0012{\rm (hadronisation)} ^{+0.0037}_{-0.0030}{\rm (scale)}$. An extraction of $xF_3^{\gamma Z}$ and results on electroweak unification and scaling violations are also presented.
HERA combined reduced cross sections $\sigma_{r,\rm NC}^{+}$ for NC $e^{+}p$ scattering at $\sqrt{s} = 318$ GeV; $\delta_{\rm stat}$, $\delta_{\rm uncor}$ and $\delta_{\rm cor}$ represent the statistical, uncorrelated systematic and correlated systematic uncertainties, respectively; $\delta_{\rm rel}$, $\delta_{\gamma p}$, $\delta_{\rm had}$ and $\delta_{1}$ to $\delta_{4}$ are the correlated sources of uncertainties arising from the combination procedure. The uncertainties are quoted in percent relative to $\sigma_{r,\rm NC}^{+}$.
HERA combined reduced cross sections $\sigma_{r,\rm NC}^{+}$ for NC $e^{+}p$ scattering at $\sqrt{s} = 300$ GeV; $\delta_{\rm stat}$, $\delta_{\rm uncor}$ and $\delta_{\rm cor}$ represent the statistical, uncorrelated systematic and correlated systematic uncertainties, respectively; $\delta_{\rm rel}$, $\delta_{\gamma p}$, $\delta_{\rm had}$ and $\delta_{1}$ to $\delta_{4}$ are the correlated sources of uncertainties arising from the combination procedure. The uncertainties are quoted in percent relative to $\sigma_{r,\rm NC}^{+}$.
HERA combined reduced cross sections $\sigma_{r,\rm NC}^{+}$ for NC $e^{+}p$ scattering at $\sqrt{s} = 251$ GeV; $\delta_{\rm stat}$, $\delta_{\rm uncor}$ and $\delta_{\rm cor}$ represent the statistical, uncorrelated systematic and correlated systematic uncertainties, respectively; $\delta_{\rm rel}$, $\delta_{\gamma p}$, $\delta_{\rm had}$ and $\delta_{1}$ to $\delta_{4}$ are the correlated sources of uncertainties arising from the combination procedure. The uncertainties are quoted in percent relative to $\sigma_{r,\rm NC}^{+}$.
New results for the double spin asymmetry $A_1^{\rm p}$ and the proton longitudinal spin structure function $g_1^{\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\rm p}(x)$ by about a factor of two in the region $x\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\Delta \Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\rm p}$. The uncertainty of $\Delta \Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\rm NS}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{\rm A}/g_{\rm V}| = 1.22 \pm 0.05~({\rm stat.}) \pm 0.10~({\rm syst.})$, which validates the sum rule to an accuracy of about 9\%.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in ($x$, $Q^2$) bins.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in $x$ bins averaged over $Q^2$.
Values of $A_1^{\rm p}$ for the 2007 COMPASS data at 160 GeV in ($x$, $Q^2$) bins.
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