A search for cascade decays of charged sleptons and sneutrinos using final states characterized by three leptons (electrons or muons) and missing transverse momentum is presented. The analysis is based on a dataset with 140 fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of $\sqrt{s}$=13 TeV recorded by the ATLAS detector at the Large Hadron Collider. This paper focuses on a supersymmetric scenario that is motivated by the muon anomalous magnetic moment observation, dark mattter relic density abundance, and electroweak naturalness. A mass spectrum involving light higgsinos and heavier sleptons with a bino at intermediate mass is targeted. No significant deviation from the Standard Model expectation is observed. This search enables to place stringent constraints on this model, excluding at the 95% confidence level charged slepton and sneutrino masses up to 450 GeV when assuming a lightest neutralino mass of 100 GeV and mass-degenerate selectrons, smuons and sneutrinos.
Distribution of $m_{3\ell}$ in SROS-on-$eee$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. The hatched band includes all statistical and systematic uncertainties.
Distribution of $m_{3\ell}$ in SROS-on-$e\mu\mu$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. The hatched band includes all statistical and systematic uncertainties.
Distribution of $E_{\text{T}}^{\text{miss}}$ in SROS-on-b-$eee$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. The hatched band includes all statistical and systematic uncertainties.
This paper presents the measurement of charged-hadron and identified-hadron ($K^\mathrm{0}_\mathrm{S}$, $Λ$, $Ξ^\mathrm{-}$) yields in photo-nuclear collisions using 1.7 $\mathrm{nb^{-1}}$ of $\sqrt{s_\mathrm{NN}} = 5.02$ TeV Pb+Pb data collected in 2018 with the ATLAS detector at the Large Hadron Collider. Candidate photo-nuclear events are selected using a combination of tracking and calorimeter information, including the zero-degree calorimeter. The yields as a function of transverse momentum and rapidity are measured in these photo-nuclear collisions as a function of charged-particle multiplicity. These photo-nuclear results are compared with 0.1 $\mathrm{nb^{-1}}$ of $\sqrt{s_\mathrm{NN}} = 5.02$ TeV $p$+Pb data collected in 2016 by ATLAS using similar charged-particle multiplicity selections. These photo-nuclear measurements shed light on potential quark-gluon plasma formation in photo-nuclear collisions via observables sensitive to radial flow, enhanced baryon-to-meson ratios, and strangeness enhancement. The results are also compared with the Monte Carlo DPMJET-III generator and hydrodynamic calculations to test whether such photo-nuclear collisions may produce small droplets of quark-gluon plasma that flow collectively.
The multiplicity distribution (#it{N}_{ch}^{rec}) from Pb+Pb photo-nuclear collisions.
The multiplicity distribution (#it{N}_{ch}^{rec}) from p+Pb collisions.
The Charged-hadron yields as a function of pT in different y selections in Pb+Pb photo-nuclear collisions.
This paper presents a first measurement of the cross-section for the charged-current Drell-Yan process $pp\rightarrow W^{\pm} \rightarrow \ell^{\pm} ν$ above the resonance region, where $\ell$ is an electron or muon. The measurement is performed for transverse masses, $m_{\text{T}}^{\text{W}}$, between 200 GeV and 5000 GeV, using a sample of 140 fb$^{-1}$ of $pp$ collision data at a centre-of-mass energy of $\sqrt{s}$ = 13 TeV collected by the ATLAS detector at the LHC during 2015-2018. The data are presented single differentially in transverse mass and double differentially in transverse mass and absolute lepton pseudorapidity. A test of lepton flavour universality shows no significant deviations from the Standard Model. The electron and muon channel measurements are combined to achieve a total experimental precision of 3% at low $m_{\text{T}}^{\text{W}}$. The single- and double differential $W$-boson charge asymmetries are evaluated from the measurements. A comparison to next-to-next-to-leading-order perturbative QCD predictions using several recent parton distribution functions and including next-to-leading-order electroweak effects indicates the potential of the data to constrain parton distribution functions. The data are also used to constrain four fermion operators in the Standard Model Effective Field Theory formalism, in particular the lepton-quark operator Wilson coefficient $c_{\ell q}^{(3)}.$
The mass of the top quark is measured using top-antitop-quark pair events with high transverse momentum top quarks. The dataset, collected with the ATLAS detector in proton--proton collisions at $\sqrt{s}=13$ TeV delivered by the Large Hadron Collider, corresponds to an integrated luminosity of 140 fb$^{-1}$. The analysis targets events in the lepton-plus-jets decay channel, with an electron or muon from a semi-leptonically decaying top quark and a hadronically decaying top quark that is sufficiently energetic to be reconstructed as a single large-radius jet. The mean of the invariant mass of the reconstructed large-radius jet provides the sensitivity to the top quark mass and is simultaneously fitted with two additional observables to reduce the impact of the systematic uncertainties. The top quark mass is measured to be $m_t = 172.95 \pm 0.53$ GeV, which is the most precise ATLAS measurement from a single channel.
Values and uncertainties for the parameters of interest in the profile likelihood fit to $\overline{m_J}$, $m_{jj}$, and $m_{tj}$ using data. The parameters of interest are the top quark mass, $m_t$, and the ratio of the measured cross-section to the Standard Model expectation of the $t\bar{t}$ cross-section, $\mu$.
Post-fit central values and uncertaintes for the nuisance parameters (including MC stat uncertainty terms) used in the profile likelihood fit to $\overline{m_J}$, $m_{jj}$, and $m_{tj}$ using data.
Covariance matrix for the profile likelihood fit to $\overline{m_J}$, $m_{jj}$, and $m_{tj}$ using data.
This paper presents a search for massive, charged, long-lived particles with the ATLAS detector at the Large Hadron Collider using an integrated luminosity of 140 $fb^{-1}$ of proton-proton collisions at $\sqrt{s}=13$ TeV. These particles are expected to move significantly slower than the speed of light. In this paper, two signal regions provide complementary sensitivity. In one region, events are selected with at least one charged-particle track with high transverse momentum, large specific ionisation measured in the pixel detector, and time of flight to the hadronic calorimeter inconsistent with the speed of light. In the other region, events are selected with at least two tracks of opposite charge which both have a high transverse momentum and an anomalously large specific ionisation. The search is sensitive to particles with lifetimes greater than about 3 ns with masses ranging from 200 GeV to 3 TeV. The results are interpreted to set constraints on the supersymmetric pair production of long-lived R-hadrons, charginos and staus, with mass limits extending beyond those from previous searches in broad ranges of lifetime.
The contour for the excluded mass--lifetime region for stau pair production obtained with the di-track search. All masses and lifetimes shown that are below the curve and above 200 GeV are excluded by the observed data (while the expected exclusion is between the upper curve down to 210 GeV for lifetimes above 3000 ns). The sensitivity extends indefinitely to longer lifetimes.
The contour for the excluded mass--lifetime region for stau pair production obtained with the di-track search. All masses and lifetimes shown that are below the curve and above 200 GeV are excluded by the observed data (while the expected exclusion is between the upper curve down to 210 GeV for lifetimes above 3000 ns). The sensitivity extends indefinitely to longer lifetimes.
The contour for the excluded mass--lifetime region for stau pair production obtained with the di-track search. All masses and lifetimes shown that are below the curve and above 200 GeV are excluded by the observed data (while the expected exclusion is between the upper curve down to 210 GeV for lifetimes above 3000 ns). The sensitivity extends indefinitely to longer lifetimes.
The multiplicities of positive and negative pions, kaons and unidentified hadrons produced in deep-inelastic scattering are measured in bins of the Bjorken scaling variable $x$, the relative virtual-photon energy $y$ and the fraction of the virtual-photon energy transferred to the final-state hadron $z$. Data were obtained by the COMPASS Collaboration using a 160 GeV muon beam of both electric charges and a liquid hydrogen target. These measurements cover the kinematic domain with photon virtuality $Q^2 > 1$ (GeV/$c)^2$, $0.004 < x < 0.4$, $0.1 < y < 0.7$ and $0.2 < z < 0.85$, in accordance with the kinematic domain used in earlier published COMPASS multiplicity measurements with an isoscalar target. The calculation of radiative corrections was improved by using the Monte Carlo generator DJANGOH, which results in up to 12% larger corrections in the low-$x$ region.
h+/h- multiplicities in (x, y, z) bins with corrections, applied corrections for VM and RC are provided in the table
pi+/pi- multiplicities in (x, y, z) bins with corrections, applied corrections for VM and RC are provided in the table
K+/K- multiplicities in (x, y, z) bins with corrections, applied corrections for VM and RC are provided in the table
Inclusive and differential measurements of the top-antitop ($t\bar{t}$) charge asymmetry $A_\text{C}^{t\bar{t}}$ and the leptonic asymmetry $A_\text{C}^{\ell\bar{\ell}}$ are presented in proton-proton collisions at $\sqrt{s} = 13$ TeV recorded by the ATLAS experiment at the CERN Large Hadron Collider. The measurement uses the complete Run 2 dataset, corresponding to an integrated luminosity of 139 fb$^{-1}$, combines data in the single-lepton and dilepton channels, and employs reconstruction techniques adapted to both the resolved and boosted topologies. A Bayesian unfolding procedure is performed to correct for detector resolution and acceptance effects. The combined inclusive $t\bar{t}$ charge asymmetry is measured to be $A_\text{C}^{t\bar{t}} = 0.0068 \pm 0.0015$, which differs from zero by 4.7 standard deviations. Differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the $t\bar{t}$ system. Both the inclusive and differential measurements are found to be compatible with the Standard Model predictions, at next-to-next-to-leading order in quantum chromodynamics perturbation theory with next-to-leading-order electroweak corrections. The measurements are interpreted in the framework of the Standard Model effective field theory, placing competitive bounds on several Wilson coefficients.
- - - - - - - - Overview of HEPData Record - - - - - - - - <br/><br/> <b>Results:</b> <ul> <li><a href="132116?version=2&table=Resultsforchargeasymmetryinclusive">$A_C^{t\bar{t}}$</a> <li><a href="132116?version=2&table=Resultsforchargeasymmetryvsmtt">$A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$</a> <li><a href="132116?version=2&table=Resultsforchargeasymmetryvspttt">$A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$</a> <li><a href="132116?version=2&table=Resultsforchargeasymmetryvsbetatt">$A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$</a> <li><a href="132116?version=2&table=Resultsforleptonicchargeasymmetryinclusive">$A_C^{\ell\bar{\ell}}$</a> <li><a href="132116?version=2&table=Resultsforchargeasymmetryvsllmll">$A_C^{\ell\bar{\ell}}$ vs $m_{\ell\bar{\ell}}$</a> <li><a href="132116?version=2&table=Resultsforchargeasymmetryvsllptll">$A_C^{\ell\bar{\ell}}$ vs $p_{T,\ell\bar{\ell}}$</a> <li><a href="132116?version=2&table=Resultsforchargeasymmetryvsllbetall">$A_C^{\ell\bar{\ell}}$ vs $\beta_{z,\ell\bar{\ell}}$</a> </ul> <b>Bounds on the Wilson coefficients:</b> <ul> <li><a href="132116?version=2&table=BoundsonWilsoncoefficientschargeasymmetryinclusive">$A_C^{t\bar{t}}$</a> <li><a href="132116?version=2&table=BoundsonWilsoncoefficientschargeasymmetryvsmtt">$A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$</a> </ul> <b>Ranking of systematic uncertainties:</b></br> Inclusive:<a href="132116?version=2&table=NPrankingchargeasymmetryinclusive">$A_C^{t\bar{t}}$</a></br> <b>$A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$:</b> <ul> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsbetattbin0">$\beta_{z,t\bar{t}} \in[0,0.3]$</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsbetattbin1">$\beta_{z,t\bar{t}} \in[0.3,0.6]$</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsbetattbin2">$\beta_{z,t\bar{t}} \in[0.6,0.8]$</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsbetattbin3">$\beta_{z,t\bar{t}} \in[0.8,1]$</a> </ul> <b>$A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$:</b> <ul> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsmttbin0">$m_{t\bar{t}}$ < $500$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsmttbin1">$m_{t\bar{t}} \in [500,750]$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsmttbin2">$m_{t\bar{t}} \in [750,1000]$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsmttbin3">$m_{t\bar{t}} \in [1000,1500]$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsmttbin4">$m_{t\bar{t}}$ > $1500$GeV</a> </ul> <b>$A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$:</b> <ul> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsptttbin0">$p_{T,t\bar{t}} \in [0,30]$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsptttbin1">$p_{T,t\bar{t}} \in[30,120]$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsptttbin2">$p_{T,t\bar{t}}$ > $120$GeV</a> </ul> Inclusive leptonic:<a href="132116?version=2&table=NPrankingleptonicchargeasymmetryinclusive">$A_C^{\ell\bar{\ell}}$</a></br> <b>$A_C^{\ell\bar{\ell}}$ vs $\beta_{z,\ell\bar{\ell}}$</b> <ul> <li><a href="132116?version=2&tableNPrankingchargeasymmetry=vsllbetallbin0">$\beta_{z,\ell\bar{\ell}} \in [0,0.3]$</a> <li><a href="132116?version=2&tableNPrankingchargeasymmetry=vsllbetallbin1">$\beta_{z,\ell\bar{\ell}} \in [0.3,0.6]$</a> <li><a href="132116?version=2&tableNPrankingchargeasymmetry=vsllbetallbin2">$\beta_{z,\ell\bar{\ell}} \in [0.6,0.8]$</a> <li><a href="132116?version=2&tableNPrankingchargeasymmetry=vsllbetallbin3">$\beta_{z,\ell\bar{\ell}} \in [0.8,1]$</a> </ul> <b>$A_C^{\ell\bar{\ell}}$ vs $m_{\ell\bar{\ell}}$</b> <ul> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsllmllbin0">$m_{\ell\bar{\ell}}$ < $200$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsllmllbin1">$m_{\ell\bar{\ell}} \in [200,300]$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsllmllbin2">$m_{\ell\bar{\ell}} \in [300,400]$Ge$</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsllmllbin3">$m_{\ell\bar{\ell}}$ > $400$GeV</a> </ul> <b>$A_C^{\ell\bar{\ell}}$ vs $p_{T,\ell\bar{\ell}}$</b> <ul> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsllptllbin0">$p_{T,\ell\bar{\ell}}\in [0,20]$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsllptllbin1">$p_{T,\ell\bar{\ell}}\in[20,70]$GeV</a> <li><a href="132116?version=2&table=NPrankingchargeasymmetryvsllptllbin2">$p_{T,\ell\bar{\ell}}$ > $70$GeV</a> </ul> <b>NP correlations:</b> <ul> <li><a href="132116?version=2&table=NPcorrelationschargeasymmetryinclusive">$A_C^{t\bar{t}}$</a> <li><a href="132116?version=2&table=NPcorrelationschargeasymmetryvsmtt">$A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$</a> <li><a href="132116?version=2&table=NPcorrelationschargeasymmetryvspttt">$A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$</a> <li><a href="132116?version=2&table=NPcorrelationschargeasymmetryvsbetatt">$A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$</a> <li><a href="132116?version=2&table=NPcorrelationsleptonicchargeasymmetryinclusive">$A_c^{\ell\bar{\ell}}$</a> <li><a href="132116?version=2&table=NPcorrelationschargeasymmetryvsllmll">$A_c^{\ell\bar{\ell}}$ vs $m_{\ell\bar{\ell}}$</a> <li><a href="132116?version=2&table=NPcorrelationschargeasymmetryvsllptll">$A_C^{\ell\bar{\ell}}$ vs $p_{T,\ell\bar{\ell}}$</a> <li><a href="132116?version=2&table=NPcorrelationschargeasymmetryvsllbetall">$A_C^{\ell\bar{\ell}}$ vs $\beta_{z,\ell\bar{\ell}}$</a> </ul> <b>Covariance matrices:</b> <ul> <li><a href="132116?version=2&table=Covariancematrixchargeasymmetryvsmtt">$A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$</a> <li><a href="132116?version=2&table=Covariancematrixchargeasymmetryvspttt">$A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$</a> <li><a href="132116?version=2&table=Covariancematrixchargeasymmetryvsbetatt">$A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$</a> <li><a href="132116?version=2&table=Covariancematrixleptonicchargeasymmetryvsllmll">$A_c^{\ell\bar{\ell}}$ vs $m_{\ell\bar{\ell}}$</a> <li><a href="132116?version=2&table=Covariancematrixleptonicchargeasymmetryvsllptll">$A_C^{\ell\bar{\ell}}$ vs $p_{T,\ell\bar{\ell}}$</a> <li><a href="132116?version=2&table=Covariancematrixleptonicchargeasymmetryvsllbetall">$A_C^{\ell\bar{\ell}}$ vs $\beta_{z,\ell\bar{\ell}}$</a> </ul>
The unfolded inclusive charge asymmetry. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed, and the impact of the linear term of the Wilson coefficient on the $A_C^{t\bar{t}}$ prediction is shown for two different values. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.
The unfolded differential charge asymmetry as a function of the invariant mass of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed, and the impact of the linear term of the Wilson coefficient on the $A_C^{t\bar{t}}$ prediction is shown for two different values. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.
A combination of measurements of the inclusive top-quark pair production cross-section performed by ATLAS and CMS in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV at the LHC is presented. The cross-sections are obtained using top-quark pair decays with an opposite-charge electron-muon pair in the final state and with data corresponding to an integrated luminosity of about 5 fb$^{-1}$ at $\sqrt{s}=7$ TeV and about 20 fb$^{-1}$ at $\sqrt{s}=8$ TeV for each experiment. The combined cross-sections are determined to be $178.5 \pm 4.7$ pb at $\sqrt{s}=7$ TeV and $243.3^{+6.0}_{-5.9}$ pb at $\sqrt{s}=8$ TeV with a correlation of 0.41, using a reference top-quark mass value of 172.5 GeV. The ratio of the combined cross-sections is determined to be $R_{8/7}= 1.363\pm 0.032$. The combined measured cross-sections and their ratio agree well with theory calculations using several parton distribution function (PDF) sets. The values of the top-quark pole mass (with the strong coupling fixed at 0.118) and the strong coupling (with the top-quark pole mass fixed at 172.5 GeV) are extracted from the combined results by fitting a next-to-next-to-leading-order plus next-to-next-to-leading-log QCD prediction to the measurements. Using a version of the NNPDF3.1 PDF set containing no top-quark measurements, the results obtained are $m_t^\text{pole} = 173.4^{+1.8}_{-2.0}$ GeV and $\alpha_\text{s}(m_Z)= 0.1170^{+ 0.0021}_{-0.0018}$.
Full covariance matrix including all systematic uncertainties expressed as nuisance parameters. With the exception of the cross section parameters, all parameters were normalised to 1 before the fit. Therefore, the diagonal elements represent the constraint in quadrature.
Full covariance matrix including all systematic uncertainties expressed as nuisance parameters. With the exception of the cross section parameters, all parameters were normalised to 1 before the fit. Therefore, the diagonal elements represent the constraint in quadrature.
We study the spin-exotic $J^{PC} = 1^{-+}$ amplitude in single-diffractive dissociation of 190 GeV$/c$ pions into $\pi^-\pi^-\pi^+$ using a hydrogen target and confirm the $\pi_1(1600) \to \rho(770) \pi$ amplitude, which interferes with a nonresonant $1^{-+}$ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile their experimental findings. We study the nonresonant contributions to the $\pi^-\pi^-\pi^+$ final state using pseudo-data generated on the basis of a Deck model. Subjecting pseudo-data and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the $J^{PC} = 1^{-+}$ amplitude and also for amplitudes with other $J^{PC}$ quantum numbers. We investigate for the first time the amplitude of the $\pi^-\pi^+$ subsystem with $J^{PC} = 1^{--}$ in the $3\pi$ amplitude with $J^{PC} = 1^{-+}$ employing the novel freed-isobar analysis scheme. We reveal this $\pi^-\pi^+$ amplitude to be dominated by the $\rho(770)$ for both the $\pi_1(1600)$ and the nonresonant contribution. We determine the $\rho(770)$ resonance parameters within the three-pion final state. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the $J^{PC} = 1^{-+}$ amplitude.
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the first $t^\prime$ bin from $0.100$ to $0.141\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 8(a). In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_0.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_0</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the second $t^\prime$ bin from $0.141$ to $0.194\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(a) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_1.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_1</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the third $t^\prime$ bin from $0.194$ to $0.326\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(b) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_2.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_2</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
We have performed the most comprehensive resonance-model fit of $\pi^-\pi^-\pi^+$ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction $\pi^- + p \to \pi^-\pi^-\pi^+ + p_\text{recoil}$ with a 190 GeV/$c$ pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, $0.5 < m_{3\pi} < 2.5$ GeV/$c^2$, and simultaneously in 11 bins of the reduced four-momentum transfer squared, $0.1 < t' < 1.0$ $($GeV$/c)^2$, are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{++}$, $2^{-+}$, $4^{++}$, and spin-exotic $1^{-+}$ quantum numbers. The model contains the well-known resonances $\pi(1800)$, $a_1(1260)$, $a_2(1320)$, $\pi_2(1670)$, $\pi_2(1880)$, and $a_4(2040)$. In addition, it includes the disputed $\pi_1(1600)$, the excited states $a_1(1640)$, $a_2(1700)$, and $\pi_2(2005)$, as well as the resonancelike $a_1(1420)$. We measure the resonance parameters mass and width of these objects by combining the information from the PWA results obtained in the 11 $t'$ bins. We extract the relative branching fractions of the $\rho(770) \pi$ and $f_2(1270) \pi$ decays of $a_2(1320)$ and $a_4(2040)$, where the former one is measured for the first time. In a novel approach, we extract the $t'$ dependence of the intensity of the resonances and of their phases. The $t'$ dependence of the intensities of most resonances differs distinctly from the $t'$ dependence of the nonresonant components. For the first time, we determine the $t'$ dependence of the phases of the production amplitudes and confirm that the production mechanism of the Pomeron exchange is common to all resonances.
Real and imaginary parts of the normalized transition amplitudes $\mathcal{T}_a$ of the 14 selected partial waves in the 1100 $(m_{3\pi}, t')$ cells (see Eq. (12) in the paper). The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the transition amplitudes in the column headers. The $m_{3\pi}$ values that are given in the first column correspond to the bin centers. Each of the 100 $m_{3\pi}$ bins is 20 MeV/$c^2$ wide. Since the 11 $t'$ bins are non-equidistant, the lower and upper bounds of each $t'$ bin are given in the column headers. The transition amplitudes define the spin-density matrix elements $\varrho_{ab}$ for waves $a$ and $b$ according to Eq. (18). The spin-density matrix enters the resonance-model fit via Eqs. (33) and (34). The transition amplitudes are normalized via Eqs. (9), (16), and (17) such that the partial-wave intensities $\varrho_{aa} = |\mathcal{T}_a|^2$ are given in units of acceptance-corrected number of events. The relative phase $\Delta\phi_{ab}$ between two waves $a$ and $b$ is given by $\arg(\varrho_{ab}) = \arg(\mathcal{T}_a) - \arg(\mathcal{T}_b)$. Note that only relative phases are well-defined. The phase of the $1^{++}0^+ \rho(770) \pi S$ wave was set to $0^\circ$ so that the corresponding transition amplitudes are real-valued. In the PWA model, some waves are excluded in the region of low $m_{3\pi}$ (see paper and [Phys. Rev. D 95, 032004 (2017)] for a detailed description of the PWA model). For these waves, the transition amplitudes are set to zero. The tables with the covariance matrices of the transition amplitudes for all 1100 $(m_{3\pi}, t')$ cells can be downloaded via the 'Additional Resources' for this table.
Decay phase-space volume $I_{aa}$ for the 14 selected partial waves as a function of $m_{3\pi}$, normalized such that $I_{aa}(m_{3\pi} = 2.5~\text{GeV}/c^2) = 1$. The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the decay phase-space volume in the column headers. The labels are identical to the ones used in the column headers of the table of the transition amplitudes. $I_{aa}$ is calculated using Monte Carlo integration techniques for fixed $m_{3\pi}$ values, which are given in the first column, in the range from 0.5 to 2.5 GeV/$c^2$ in steps of 10 MeV/$c^2$. The statistical uncertainties given for $I_{aa}$ are due to the finite number of Monte Carlo events. $I_{aa}(m_{3\pi})$ is defined in Eq. (6) in the paper and appears in the resonance model in Eqs. (19) and (20).