Multijet events at large transverse momentum ($p_\mathrm{T}$) are measured at $\sqrt{s}$ = 13 TeV using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The multiplicity of jets with $p_\mathrm{T}$$>$ 50 GeV that are produced in association with a high-$p_\mathrm{T}$ dijet system is measured in various ranges of the $p_\mathrm{T}$ of the jet with the highest transverse momentum and as a function of the azimuthal angle difference $\Delta\phi_{1,2}$ between the two highest $p_\mathrm{T}$ jets in the dijet system. The differential production cross sections are measured as a function of the transverse momenta of the four highest $p_\mathrm{T}$ jets. The measurements are compared with leading and next-to-leading order matrix element calculations supplemented with simulations of parton shower, hadronization, and multiparton interactions. In addition, the measurements are compared with next-to-leading order matrix element calculations combined with transverse-momentum dependent parton densities and transverse-momentum dependent parton shower.
Jet multiplicity measured for a leading-pT jet ($p_{T1}$) with 200 < $p_{T1}$ < 400 GeV and for an azimuthal separation between the two leading jets of $0 < \Delta\Phi_{1,2} < 150^{\circ}$. The full breakdown of the uncertainties is displayed, with PU corresponding to Pileup, PREF to Trigger Prefering, PTHAT to the hard-scale (renormalization and factorization scales), MISS and FAKE to the inefficienties and background, LUMI to integrated luminosity. With JES, JER and stat. unc. following the notation in the paper.
Jet multiplicity measured for a leading-pT jet ($p_{T1}$) with 200 < $p_{T1}$ < 400 GeV and for an azimuthal separation between the two leading jets of $150 < \Delta\Phi_{1,2} < 170^{\circ}$. The full breakdown of the uncertainties is displayed, with PU corresponding to Pileup, PREF to Trigger Prefering, PTHAT to the hard-scale (renormalization and factorization scales), MISS and FAKE to the inefficienties and background, LUMI to integrated luminosity. With JES, JER and stat. unc. following the notation in the paper.
Jet multiplicity measured for a leading-pT jet ($p_{T1}$) with 200 < $p_{T1}$ < 400 GeV and for an azimuthal separation between the two leading jets of $170 < \Delta\Phi_{1,2} < 180^{\circ}$. The full breakdown of the uncertainties is displayed, with PU corresponding to Pileup, PREF to Trigger Prefering, PTHAT to the hard-scale (renormalization and factorization scales), MISS and FAKE to the inefficienties and background, LUMI to integrated luminosity. With JES, JER and stat. unc. following the notation in the paper.
Measurements of target asymmetries and double-polarization observables for the reaction $γp\to pπ^0π^0$ are reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility (Bonn University) using the Bonn frozen-spin butanol (C$_4$H$_9$OH) target, which provided transversely polarized protons. Linearly polarized photons were produced via bremsstrahlung off a diamond crystal. The data cover the photon energy range from $E_γ$=650 MeV to $E_γ$=2600 MeV and nearly the complete angular range. The results have been included in the BnGa partial wave analysis. Experimental results and the fit agree very well. Observed systematic differences in the branching ratios for decays of $N^*$ and $Δ^*$ resonances are attributed to the internal structure of these excited nucleon states. Resonances which can be assigned to SU(6)$\times$O(3) two-oscillator configurations show larger branching ratios to intermediate states with non-zero intrinsic orbital angular momenta than resonances assigned to one-oscillator configurations.
Target asymmetry for $\pi^0\pi^0$ as a function of the polar angle for bins of the incident photon energy in the range of $E_\gamma$ = 650-2600 MeV.
Target asymmetry for $\pi^0\pi^0$ as a function of the $\pi^0\pi^0$ invariant mass for bins of the incident photon energy in the range of $E_\gamma$ = 650-2600 MeV.
Target asymmetry for $\pi^0\pi^0$ as a function of the $\phi^*$ angle for bins of the incident photon energy in the range of $E_\gamma$ = 650-2600 MeV.
The reaction $\gamma p \rightarrow p \pi^0 \eta$ has been studied with the CBELSA/TAPS detector at the electron stretcher accelerator ELSA in Bonn for incident photon energies from threshold up to 3.1 GeV. This paper has been motivated by the recently claimed observation of a narrow structure in the M$_{N\eta}$ invariant mass distribution at a mass of 1678 MeV/$c^2$. The existence of this structure cannot be confirmed in the present work. Instead, for E$_{\gamma}$ = 1400 - 1500 MeV and the cut M$_{p\pi^0} \le 1190 $ MeV/$c^2$ a statistically significant structure in the M$_{p\eta}$ invariant mass distribution near 1700 MeV/$c^2$ is observed with a width of $\Gamma\approx 35$ MeV/$c^2$ while the mass resolution is $\sigma_{res}$ = 5 MeV/$c^2$. Increasing the incident photon energy from 1420 to 1540 MeV this structure shifts in mass from $\approx$ 1700MeV/c$^2$ to $\approx$ 1725 MeV/$c^2$; the width increases to about 50 MeV/$c^2$ and decreases thereafter. The cross section associated with this structure reaches a maximum of $\approx$ 100 nb around E$_{\gamma} \approx$ 1490 MeV (W $\approx $ 1920 MeV), which coincides with the $p a_0$ threshold. Three scenarios are discussed which might be the origin of this structure in the M$_{p\eta}$ invariant mass distribution. The most likely interpretation is that it is due to a triangular singularity in the $\gamma p \rightarrow p a_0 \rightarrow p \pi^0 \eta$ reaction
Differential cross section for $\pi^0$ in the $\gamma p$ for the incident photon energy range of $E_\gamma$ = 1400-1500 MeV.
Differential cross section for $\eta$ in the $\gamma p$ for the incident photon energy range of $E_\gamma$ = 1400-1500 MeV.
Differential cross section for $p$ in the $\gamma p$ for the incident photon energy range of $E_\gamma$ = 1400-1500 MeV.
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>
A search is performed for W' bosons decaying to a top and a bottom quark in the all-hadronic final state, in proton-proton collisions at a center-of-mass energy of 13 TeV. The analyzed data were collected by the CMS experiment between 2016 and 2018 and correspond to an integrated luminosity of 137 fb$^{-1}$. Deep neural network algorithms are used to identify the jet initiated by the bottom quark and the jet containing the decay products of the top quark when the W boson from the top quark decays hadronically. No excess above the estimated standard model background is observed. Upper limits on the production cross sections of W' bosons decaying to a top and a bottom quark are set. Both left- and right-handed W' bosons with masses below 3.4 TeV are excluded at 95% confidence level, and the most stringent limits to date on W' bosons decaying to a top and a bottom quark in the all-hadronic final state are obtained.
The reconstructed m$_{tb}$ distributions in data and expected background in signal region for the data taking period of 2016. Yield in each bin is divided by the corresponding bin width.
The reconstructed m$_{tb}$ distributions in data and expected background in validation region for the data taking period of 2016. Yield in each bin is divided by the corresponding bin width.
The reconstructed m$_{tb}$ distributions in data and expected background in signal region for the data taking period of 2017. Yield in each bin is divided by the corresponding bin width.
A measurement of the double-polarization observable $E$ for the reaction $\gamma p\to \pi^0 p$ is reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility in Bonn using the Bonn frozen-spin butanol (C$_4$H$_9$OH) target, which provided longitudinally-polarized protons. Circularly-polarized photons were produced via bremsstrahlung of longitudinally-polarized electrons. The data cover the photon energy range from $E_\gamma =600$~MeV to $E_\gamma =2310$~MeV and nearly the complete angular range. The results are compared to and have been included in recent partial wave analyses.
Double-polarization observable E for different beam energies from 600 to 2310 MeV
A narrow pentaquark state, $P_c(4312)^+$, decaying to $J/\psi p$ is discovered with a statistical significance of $7.3\sigma$ in a data sample of ${\Lambda_b^0\to J/\psi p K^-}$ decays which is an order of magnitude larger than that previously analyzed by the LHCb collaboration. The $P_c(4450)^+$ pentaquark structure formerly reported by LHCb is confirmed and observed to consist of two narrow overlapping peaks, $P_c(4440)^+$ and $P_c(4457)^+$, where the statistical significance of this two-peak interpretation is $5.4\sigma$. Proximity of the $\Sigma_c^+\bar{D}^{0}$ and $\Sigma_c^+\bar{D}^{*0}$ thresholds to the observed narrow peaks suggests that they play an important role in the dynamics of these states.
Distribution of $(J/\psi p)$ system invariant mass from the decay of $\Lambda_{b}^{0}$ candidates in the channel $\Lambda_{b}^{0} \to J/\psi p K^{-}$.
Distribution of $(J/\psi p)$ system invariant mass from the decay of $\Lambda_{b}^{0}$ candidates in the channel $\Lambda_{b}^{0} \to J/\psi p K^{-}$. $\Lambda_{b}^{0}$ candidates are selected after the suppression of the dominant $\Lambda^{*} \to p K^{-}$ contributions using the $m_{Kp} > 1.9$ GeV$/c^2$ requirement.
$\cos \theta_{P_c}$-weighted ditribution of $(J/\psi p)$ system invariant mass from the decay of $\Lambda_{b}^{0}$ candidates in the channel $\Lambda_{b}^{0} \to J/\psi p K^{-}$. Here $\theta_{P_c}$ is the helicity angle of the pentaquark exotic state (the angle between $K^-$ and $J/\psi$ in the pentaquark state rest frame).
The cross-section for inelastic proton-proton collisions at a centre-of-mass energy of 13\,TeV is measured with the LHCb detector. The fiducial cross-section for inelastic interactions producing at least one prompt long-lived charged particle with momentum $p>2$\,GeV/$c$ in the pseudorapidity range $2<\eta<5$ is determined to be $\sigma_{\rm acc}= 62.2 \pm 0.2 \pm 2.5$\,mb. The first uncertainty is the intrinsic systematic uncertainty of the measurement, the second is due to the uncertainty on the integrated luminosity. The statistical uncertainty is negligible. Extrapolation to full phase space yields the total inelastic proton-proton cross-section $\sigma_{\rm inel}= 75.4 \pm 3.0 \pm 4.5$\,mb, where the first uncertainty is experimental and the second due to the extrapolation. An updated value of the inelastic cross-section at a centre-of-mass energy of 7\,TeV is also reported.
The cross-section for inelastic $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV, yielding one or more prompt long-lived charged particles in the kinematic range $p > 2.0$ GeV/$c$ and $2.0 < \eta < 5.0$ (LHCb acceptance). The quoted uncertainty that is almost completely systematic in nature as the purely statistical uncertainty is found negligible. A particle is long-lived if its proper (mean) lifetime is larger than 30 ps, and it is prompt if it is produced directly in the $pp$ interaction or if none of its ancestors is long-lived.
The total cross-section for inelastic $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 13$ TeV, extrapolated from Monte Carlo in similar way to measurement at $\sqrt{s}=7$ TeV.
Update of the total cross-section for inelastic $pp$ collisions at a centre-of-mass energy $\sqrt{s} = 7$ TeV due to improved calibration of the luminosity scale.
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).
A search for heavy neutral Higgs bosons and $Z^{\prime}$ bosons is performed using a data sample corresponding to an integrated luminosity of 36.1 fb$^{-1}$ from proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by the ATLAS detector at the LHC during 2015 and 2016. The heavy resonance is assumed to decay to $\tau^+\tau^-$ with at least one tau lepton decaying to final states with hadrons and a neutrino. The search is performed in the mass range of 0.2-2.25 TeV for Higgs bosons and 0.2-4.0 TeV for $Z^{\prime}$ bosons. The data are in good agreement with the background predicted by the Standard Model. The results are interpreted in benchmark scenarios. In the context of the hMSSM scenario, the data exclude $\tan\beta > 1.0$ for $m_A$ = 0.25 TeV and $\tan\beta > 42$ for $m_A$ = 1.5 TeV at the 95% confidence level. For the Sequential Standard Model, $Z^{\prime}_\mathrm{SSM}$ with $m_{Z^{\prime}} < 2.42$ TeV is excluded at 95% confidence level, while $Z^{\prime}_\mathrm{NU}$ with $m_{Z^{\prime}} < 2.25$ TeV is excluded for the non-universal $G(221)$ model that exhibits enhanced couplings to third-generation fermions.
Observed and predicted mTtot distribution in the b-veto category of the 1l1tau_h channel. Despite listing this as an exclusive final state (as there must be no b-jets), there is no explicit selection on the presence of additional light-flavour jets. Please note that the bin content is divided by the bin width in the paper figure, but not in the HepData table. In the paper, the first bin is cut off at 60 GeV for aesthetics but contains underflows down to 50 GeV as in the HepData table. The last bin includes overflows. The combined prediction for A and H bosons with masses of 300, 500 and 800 GeV and $\tan\beta$ = 10 in the hMSSM scenario are also provided.
Observed and predicted mTtot distribution in the b-tag category of the 1l1tau_h channel. Despite listing this as an exclusive final state (as there must be at least one b-jets), there is no explicit selection on the presence of additional light-flavour jets. Please note that the bin content is divided by the bin width in the paper figure, but not in the HepData table. In the paper, the first bin is cut off at 60 GeV for aesthetics but contains underflows down to 50 GeV as in the HepData table. The last bin includes overflows. The combined prediction for A and H bosons with masses of 300, 500 and 800 GeV and $\tan\beta$ = 10 in the hMSSM scenario are also provided.
Observed and predicted mTtot distribution in the b-veto category of the 2tau_h channel. Despite listing this as an exclusive final state (as there must be no b-jets), there is no explicit selection on the presence of additional light-flavour jets. Please note that the bin content is divided by the bin width in the paper figure, but not in the HepData table. The last bin includes overflows. The combined prediction for A and H bosons with masses of 300, 500 and 800 GeV and $\tan\beta$ = 10 in the hMSSM scenario are also provided.
Forum