Date

Temperature Measurement of Quark-Gluon Plasma at Different Stages

The STAR collaboration Aboona, B.E. ; Adam, J. ; Adamczyk, L. ; et al.
Nature Commun. 16 (2025) 9098, 2025.
Inspire Record 2755369 DOI 10.17182/hepdata.147195

In a Quark-Gluon Plasma (QGP), the fundamental building blocks of matter, quarks and gluons, are under extreme conditions of temperature and density. A QGP could exist in the early stages of the Universe, and in various objects and events in the cosmos. The thermodynamic and hydrodynamic properties of the QGP are described by Quantum Chromodynamics (QCD) and can be studied in heavy-ion collisions. Despite being a key thermodynamic parameter, the QGP temperature is still poorly known. Thermal lepton pairs ($e^+e^-$ and $\mu^+\mu^-$) are ideal penetrating probes of the true temperature of the emitting source, since their invariant-mass spectra suffer neither from strong final-state interactions nor from blue-shift effects due to rapid expansion. Here we measure the QGP temperature using thermal $e^+e^-$ production at the Relativistic Heavy Ion Collider (RHIC). The average temperature from the low-mass region (in-medium $\rho^0$ vector-meson dominant) is $(1.99 \pm 0.24) \times 10^{12}$ K, consistent with the chemical freeze-out temperature from statistical models and the phase transition temperature from LQCD. The average temperature from the intermediate mass region (above the $\rho^0$ mass, QGP dominant) is significantly higher at $(3.40 \pm 0.55)\times 10^{12}$ K. This work provides essential experimental thermodynamic measurements to map out the QCD phase diagram and understand the properties of matter under extreme conditions.

5 data tables

The inclusive dielectron invariant mass spectra of 27 GeV in 0-80% centrality.

The inclusive dielectron invariant mass spectra of 54.4 GeV in 0-80% centrality.

The charged multiplicity normalzied excess yield of 27 GeV in 0-80% centrality.

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Evidence for $B^{+}\to K^{+}\nu\bar{\nu}$ Decays

The Belle-II collaboration Adachi, I. ; Adamczyk, K. ; Aggarwal, L. ; et al.
Phys.Rev.D 109 (2024) 112006, 2024.
Inspire Record 2725943 DOI 10.17182/hepdata.146803

We search for the rare decay $B^{+}\rightarrow K^{+}\nu\bar{\nu}$ in a $362\ \rm{fb}^{-1}$ sample of electron-positron collisions at the $\Upsilon(4S)$ resonance collected with the Belle II detector at the SuperKEKB collider. We use the inclusive properties of the accompanying $B$ meson in $\Upsilon(4S) \to B\kern 0.18em\overline{\kern -0.18em B}{}$ events to suppress background from other decays of the signal $B$ candidate and light-quark pair production. We validate the measurement with an auxiliary analysis based on a conventional hadronic reconstruction of the accompanying $B$ meson. For background suppression, we exploit distinct signal features using machine learning methods tuned with simulated data. The signal-reconstruction efficiency and background suppression are validated through various control channels. The branching fraction is extracted in a maximum likelihood fit. Our inclusive and hadronic analyses yield consistent results for the $B^{+}\rightarrow K^{+}\nu\bar{\nu}$ branching fraction of $\left[2.7\pm 0.5(\mathrm{stat})\pm 0.5(\mathrm{syst})\right] \times 10^{-5}$ and $\left[1.1^{+0.9}_{-0.8}(\mathrm{stat}){}^{+0.8}_{-0.5}(\mathrm{syst})\right] \times 10^{-5}$, respectively. Combining the results, we determine the branching fraction of the decay $B^{+}\rightarrow K^{+}\nu\bar{\nu}$ to be $\left[2.3 \pm 0.5(\mathrm{stat})^{+0.5}_{-0.4}(\mathrm{syst})\right]\times 10^{-5}$, providing the first evidence for this decay at $3.5$ standard deviations. The combined result is $2.7$ standard deviations above the standard model expectation.

15 data tables

- - - - - - - - Overview of HEPData Record - - - - - - - -<br/><br/></ul><b>Post-fit yields:</b><ul><li><a href="146803?version=1&table=Postfit%20yields%20Y(4S)%3A%20fit%20variable%20(ITA)">Y(4S) fit variable (ITA)</a><li><a href="146803?version=1&table=Postfit%20yields%20off-resonance%3A%20fit%20variable%20(ITA)">Off-resonance fit variable (ITA)</a><li><a href="146803?version=1&table=Postfit%20yields%20Y(4S)%3A%20%24%5Ceta(%5Crm%7BBDT%7D_%7B2%7D)%24%20(ITA)">Y(4S) $\eta(\rm{BDT}_{2})$ (ITA)</a><li><a href="146803?version=1&table=Postfit%20yields%20Y(4S)%3A%20%24q%5E%7B2%7D%24%20(HTA)">Y(4S) $q^{2}$ (ITA)</a><li><a href="146803?version=1&table=Postfit%20yields%20Y(4S)%3A%20%24%5Ceta(%5Crm%7BBDT%7D_%7B2%7D)%24%20(ITA%2C%20signal-rich)">Y(4S) $\eta(\rm{BDT}_{2})$ (ITA, signal-rich)</a><li><a href="146803?version=1&table=Postfit%20yields%20Y(4S)%3A%20%24q%5E%7B2%7D%24%20%20(ITA%2C%20signal-rich)">Y(4S) $q^{2}$ (ITA, signal-rich)</a><li><a href="146803?version=1&table=Postfit%20yields%20Y(4S)%3A%20fit%20variable%20(HTA)">Y(4S) fit variable (HTA)</a><li><a href="146803?version=1&table=Postfit%20yields%20Y(4S)%3A%20%24q%5E%7B2%7D%24%20(HTA)">Y(4S) $q^{2}$ (HTA)</a></ul><b>Signal selection efficiency:</b><ul><li><a href="146803?version=1&table=Selection%20efficiency%20(ITA)">ITA</a><li><a href="146803?version=1&table=Selection%20efficiency%20(HTA)">HTA</a></ul><b>Likelihoods:</b><ul><li><a href="146803?version=1&table=Profile%20likelihoods%20(HTA)">HTA</a><li><a href="146803?version=1&table=Profile%20likelihoods%20(ITA)">ITA</a><li><a href="146803?version=1&table=Profile%20likelihoods%20(Combined)">Combined</a></ul><b>Branching fraction summary:</b><ul><li><a href="146803?version=1&table=Branching%20fraction%20summary">Branching fraction summary</a></ul></ul>HistFactory json with full statistical model for combined likelihood and minimal fitting example are included under Resources.<ul>

Observed yields and fit results in bins of the $\eta(\rm{BDT}_{2})\times q^2_{\mathrm{rec}}$ space obtained by the ITA simultaneous fit to the off- and on-resonance data, corresponding to an integrated luminosity of 42 and 362 fb$^{-1}$, respectively. The yields are shown individually for the $B^+ \rightarrow K^{+}\nu\bar\nu$ signal, neutral and charged $B$-meson decays and the sum of the five continuum categories. The yields are obtained in bins of the $\eta(\rm{BDT}_{2})\times q^2_{\mathrm{rec}}$ space.

Observed yields and fit results in bins of the $\eta(\rm{BDT}_{2})\times q^2_{\mathrm{rec}}$ space obtained by the ITA simultaneous fit to the off- and on-resonance data, corresponding to an integrated luminosity of 42 and 362 fb$^{-1}$, respectively. The yields are shown individually for the $B^+ \rightarrow K^{+}\nu\bar\nu$ signal, neutral and charged $B$-meson decays and the sum of the five continuum categories. The yields are obtained in bins of the $\eta(\rm{BDT}_{2})\times q^2_{\mathrm{rec}}$ space.

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Determination of $|V_{cb}|$ using $\overline{B}^0\to D^{*+}\ell^-\bar\nu_\ell$ decays with Belle II

The Belle-II collaboration Adachi, I. ; Adamczyk, K. ; Aggarwal, L. ; et al.
Phys.Rev.D 108 (2023) 092013, 2023.
Inspire Record 2705370 DOI 10.17182/hepdata.145129

We determine the CKM matrix-element magnitude $|V_{cb}|$ using $\overline{B}^0\to D^{*+}\ell^-\bar\nu_\ell$ decays reconstructed in $189 \, \mathrm{fb}^{-1}$ of collision data collected by the Belle II experiment, located at the SuperKEKB $e^+e^-$ collider. Partial decay rates are reported as functions of the recoil parameter $w$ and three decay angles separately for electron and muon final states. We obtain $|V_{cb}|$ using the Boyd-Grinstein-Lebed and Caprini-Lellouch-Neubert parametrizations, and find $|V_{cb}|_\mathrm{BGL}=(40.57\pm 0.31 \pm 0.95\pm 0.58)\times 10^{-3}$ and $|V_{cb}|_\mathrm{CLN}=(40.13 \pm 0.27 \pm 0.93\pm 0.58 )\times 10^{-3}$ with the uncertainties denoting statistical components, systematic components, and components from the lattice QCD input, respectively. The branching fraction is measured to be ${\cal B}(\overline{B}^0\to D^{*+}\ell^-\bar\nu_\ell)=(4.922 \pm 0.023 \pm 0.220)\%$. The ratio of branching fractions for electron and muon final states is found to be $0.998 \pm 0.009 \pm 0.020$. In addition, we determine the forward-backward angular asymmetry and the $D^{*+}$ longitudinal polarization fractions. All results are compatible with lepton-flavor universality in the Standard Model.

8 data tables

Measured partial decay rates $\Delta\Gamma$ (in units of $10^{-15}$ GeV)

Average of normalized decay rates over $\overline{B}^0\to D^{*+} e^- \bar\nu_e$ and $\overline{B}^0\to D^{*+} \mu^- \bar\nu_\mu$ decays

Full experimental (statistical and systematic) correlations (in \%) of the partial decay rates for the $\overline{B}^0\to D^{*+} e^- \bar\nu_e$ and $\overline{B}^0\to D^{*+} \mu^- \bar\nu_\mu$ decays.

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Results on Elastic Cross Sections in Proton-Proton Collisions at $\sqrt{s} = 510$ GeV with the STAR Detector at RHIC

The STAR collaboration Abdulhamid, M.I. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Lett.B 852 (2024) 138601, 2024.
Inspire Record 2704122 DOI 10.17182/hepdata.144920

We report results on an elastic cross section measurement in proton-proton collisions at a center-of-mass energy $\sqrt{s}=510$ GeV, obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section is measured in the four-momentum transfer squared range $0.23 \leq -t \leq 0.67$ GeV$^2$. We find that a constant slope $B$ does not fit the data in the aforementioned $t$ range, and we obtain a much better fit using a second-order polynomial for $B(t)$. The $t$ dependence of $B$ is determined using six subintervals of $t$ in the STAR measured $t$ range, and is in good agreement with the phenomenological models. The measured elastic differential cross section $\mathrm{d}\sigma/\mathrm{dt}$ agrees well with the results obtained at $\sqrt{s} = 546$ GeV for proton--antiproton collisions by the UA4 experiment. We also determine that the integrated elastic cross section within the STAR $t$-range is $\sigma^\mathrm{fid}_\mathrm{el} = 462.1 \pm 0.9 (\mathrm{stat.}) \pm 1.1 (\mathrm {syst.}) \pm 11.6 (\mathrm {scale})$~$\mu\mathrm{b}$.

2 data tables

Top panel: The $pp$ elastic differential cross section $d\sigma/dt$ fitted with an exponential $A e^{-B(t)|t|}$. Bottom panel: Residuals (Data - Fit)/Error. Uncertainties on the data points are smaller than the symbol size. The vertical scale uncertainty of 2.5% is not included in in the full error.

Results of the exponential function $A e^{-B(t)|t|}$ fit to the elastic differential cross section data as well as the integrated fiducial cross section are listed. Also listed are the corresponding values of the statistical and systematic uncertainties. The scale (luminosity and trigger efficiency) uncertainty of 2.5% applicable to the fit parameter $A$ and fiducial cross section $\sigma^\mathrm{fid}_\mathrm{el}$ is not included in the full error.


Measurement of in-medium jet modification using direct photon+jet and $\pi^{0}$+jet correlations in $p+p$ and central Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV

The STAR collaboration Aboona, B.E. ; Adam, J. ; Adamczyk, L. ; et al.
Phys.Rev.Lett. 134 (2025) 232301, 2025.
Inspire Record 2693040 DOI 10.17182/hepdata.144263

The STAR Collaboration presents measurements of the semi-inclusive distribution of charged-particle jets recoiling from energetic direct-photon ($\gamma_{\rm dir}$) and neutral-pion ($\pi^{0}$) triggers in p+p and central Au+Au collisions at $\sqrt{s_\mathrm{NN}}$ GeV over a broad kinematic range, for jet resolution parameters $R$=0.2 and 0.5. Medium-induced jet yield suppression is observed to be larger for $R$=0.2 than for 0.5, reflecting the angular range of jet energy redistribution due to quenching. The predictions of model calculations incorporating jet quenching are not fully consistent with the observations. These results provide new insight into the physical origins of jet quenching.

8 data tables

I_{AA} of Au+Au 0%-15% collisions at sqrt{s_{NN}} = 200 GeV for R = 0.2 of gamma_{dir}+jet with E_{T,trig}= 15-20 GeV.

I_{AA} of Au+Au 0%-15% collisions at sqrt{s_{NN}} = 200 GeV for R = 0.5 of gamma_{dir}+jet with E_{T,trig}= 15-20 GeV.

I_{AA} of Au+Au 0%-15% collisions at sqrt{s_{NN}} = 200 GeV for R = 0.2 of pi^{0}+jet with E_{T,trig}= 11-15 GeV.

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Semi-inclusive direct photon+jet and $\pi^{0}$+jet correlations measured in $p+p$ and central Au+Au collisions at $\sqrt{s_\mathrm{NN}} = 200$ GeV

The STAR collaboration Aboona, B.E. ; Adam, J. ; Adamczyk, L. ; et al.
Phys.Rev.C 111 (2025) 064907, 2025.
Inspire Record 2693062 DOI 10.17182/hepdata.144264

The STAR experiment at RHIC reports new measurements of jet quenching based on the semi-inclusive distribution of charged-particle jets recoiling from direct photon ($\gamma_{\rm dir}$) and neutral pion ($\pi^{0}$) triggers in pp and central Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV, for triggers in the range $9<E_{\rm T}^{\rm trig}<20$ GeV. The datasets have integrated luminosities of 3.9$ {\rm nb}^{-1}$ for Au+Au and 23$ {\rm pb}^{-1}$ for pp collisions. Jets are reconstructed using the anti-$k_{\rm T}$ algorithm with resolution parameters $R$=0.2 and 0.5. The large uncorrelated jet background in central Au+Au collisions is corrected using a mixed-event approach, which enables precise charged-particle jet measurements at low transverse momentum $p_{\rm T,jet}^{\rm ch}$ and large $R$. Recoil-jet distributions are reported in the range $p_{\rm T,jet}^{\rm ch}<25$\gev. Comparison of the distributions measured in pp and Au+Au collisions reveals strong medium-induced jet yield suppression for $R=0.2$, with markedly less suppression for $R=0.5$. Comparison is also made to theoretical models incorporating jet quenching. These data provide new insight into the mechanisms underlying jet quenching and the angular dependence of medium-induced jet-energy transport, and provide new constraints on modelling such effects.

80 data tables

Rho distribution of SE recoil jet R=0.5 for AuAu 0-15% at sqrt{s_{NN}}=200 GeV from gamma_{rich}+jet event sample.

Rho distribution of ME recoil jet R=0.5 for AuAu 0-15% at sqrt{s_{NN}}=200 GeV from MB event sample.

Rho distribution of ME-30MeV recoil jet R=0.5 for AuAu 0-15% at sqrt{s_{NN}}=200 GeV from MB event sample.

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Tests of light-lepton universality in angular asymmetries of $B^0 \to D^{*-} \ell \nu$ decays

The Belle-II collaboration Adachi, I. ; Adamczyk, K. ; Aggarwal, L. ; et al.
Phys.Rev.Lett. 131 (2023) 181801, 2023.
Inspire Record 2685572 DOI 10.17182/hepdata.144759

We present the first comprehensive tests of light-lepton universality in the angular distributions of semileptonic $B^0$-meson decays to charged spin-1 charmed mesons. We measure five angular-asymmetry observables as functions of the decay recoil that are sensitive to lepton-universality-violating contributions. We use events where one neutral $B$ is fully reconstructed in $\Upsilon\left(4S\right)\to{}B \overline{B}$ decays in data corresponding to $189~\mathrm{fb}^{-1}$ integrated luminosity from electron-positron collisions collected with the Belle II detector. We find no significant deviation from the standard model expectations.

2 data tables

Observed values of all angular asymmetry variables.

Full experimental covariance matrix of all angular asymmetry variables.


Version 3
Search for a long-lived spin-0 mediator in $b\to s$ transitions at the Belle II experiment

The Belle-II collaboration Adachi, I. ; Adamczyk, K. ; Aggarwal, L. ; et al.
Phys.Rev.D 108 (2023) L111104, 2023.
Inspire Record 2665757 DOI 10.17182/hepdata.147283

Additional spin-0 particles appear in many extensions of the standard model. We search for long-lived spin-0 particles $S$ in $B$-meson decays mediated by a $b\to s$ quark transition in $e^+e^-$ collisions at the $\Upsilon(4S)$ resonance at the Belle II experiment. Based on a sample corresponding to an integrated luminosity of $189 \mathrm{\,fb}^{-1}$, we observe no evidence for signal. We set model-independent upper limits on the product of branching fractions $\mathrm{Br}(B^0\to K^*(892)^0(\to K^+\pi^-)S)\times \mathrm{Br}(S\to x^+x^-)$ and $\mathrm{Br}(B^+\to K^+S)\times \mathrm{Br}(S\to x^+x^-)$, where $x^+x^-$ indicates $e^+e^-, \mu^+\mu^-, \pi^+\pi^-$, or $K^+K^-$, as functions of $S$ mass and lifetime at the level of $10^{-7}$.

166 data tables

Expected and observed candidates for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) as a function of the reduced mediator candidate mass.

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Global polarization of $\Lambda$ and $\bar{\Lambda}$ hyperons in Au+Au collisions at $\sqrt{s_{\rm NN}}=19.6$ and $27$ GeV

The STAR collaboration Abdulhamid, M.I. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Rev.C 108 (2023) 014910, 2023.
Inspire Record 2659670 DOI 10.17182/hepdata.140936

In relativistic heavy-ion collisions, a global spin polarization, $P_\mathrm{H}$, of $\Lambda$ and $\bar{\Lambda}$ hyperons along the direction of the system angular momentum was discovered and measured across a broad range of collision energies and demonstrated a trend of increasing $P_\mathrm{H}$ with decreasing $\sqrt{s_{NN}}$. A splitting between $\Lambda$ and $\bar{\Lambda}$ polarization may be possible due to their different magnetic moments in a late-stage magnetic field sustained by the quark-gluon plasma which is formed in the collision. The results presented in this study find no significant splitting at the collision energies of $\sqrt{s_{NN}}=19.6$ and $27$ GeV in the RHIC Beam Energy Scan Phase II using the STAR detector, with an upper limit of $P_{\bar{\Lambda}}-P_{\Lambda}<0.24$% and $P_{\bar{\Lambda}}-P_{\Lambda}<0.35$%, respectively, at a 95% confidence level. We derive an upper limit on the na\"ive extraction of the late-stage magnetic field of $B<9.4\cdot10^{12}$ T and $B<1.4\cdot10^{13}$ T at $\sqrt{s_{NN}}=19.6$ and $27$ GeV, respectively, although more thorough derivations are needed. Differential measurements of $P_\mathrm{H}$ were performed with respect to collision centrality, transverse momentum, and rapidity. With our current acceptance of $|y|<1$ and uncertainties, we observe no dependence on transverse momentum and rapidity in this analysis. These results challenge multiple existing model calculations following a variety of different assumptions which have each predicted a strong dependence on rapidity in this collision-energy range.

5 data tables

The first-order event-plane resolution determined by the STAR EPD as a function of collision centrality is roughly doubled in comparison to previous analyses using the STAR BBC. We see $R_{\rm EP}^{(1)}$ peak for mid-central collisions.

The mid-central $P_{\rm H}$ measurements reported in this work are shown alongside previous measurements in the upper panel, and are consistent with previous measurements at the energies studied here. The difference between integrated $P_{\bar{\Lambda}}$ and $P_{\Lambda}$ is shown at $\sqrt{s_{\rm{NN}}}$=19.6 and 27 GeV alongside previous measurements in the lower panel. The splittings observed with these high-statistics data sets are consistent with zero. Statistical uncertainties are represented as lines while systematic uncertainties are represented as boxes. The previous $P_{\bar{\Lambda}}-P_{\Lambda}$ result at $\sqrt{s_{\rm NN}}=7.7$ GeV is outside the axis range, but is consistent with zero within $2\sigma$.

$P_{\rm H}$ measurements are shown as a function of collision centrality at $\sqrt{s_{\rm NN}}$=19.6 and 27 GeV. Statistical uncertainties are represented as lines while systematic uncertainties are represented as boxes. $P_{\rm H}$ increases with collision centrality at $\sqrt{s_{\rm NN}}$=19.6 and 27 GeV, as expected from an angular-momentum-driven phenomenon.

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Search for new physics in the $\tau$ lepton plus missing transverse momentum final state in proton-proton collisions at $\sqrt s $ = 13 TeV

The CMS collaboration Tumasyan, A. ; Adam, W. ; Andrejkovic, J.W. ; et al.
JHEP 09 (2023) 051, 2023.
Inspire Record 2626189 DOI 10.17182/hepdata.135472

A search for physics beyond the standard model (SM) in the final state with a hadron- ically decaying tau lepton and a neutrino is presented. This analysis is based on data recorded by the CMS experiment from proton-proton collisions at a center-of- mass energy of 13 TeV at the LHC, corresponding to a total integrated luminosity of 138 fb−1. The transverse mass spectrum is analyzed for the presence of new physics. No significant deviation from the SM prediction is observed. Limits are set on the production cross section of a W′ boson decaying into a tau lepton and a neutrino. Lower limits are set on the mass of the sequential SM-like heavy charged vector bo- son and the mass of a quantum black hole. Upper limits are placed on the couplings of a new boson to the SM fermions. Constraints are put on a nonuniversal gauge interaction model and an effective field theory model. For the first time, upper lim- its on the cross section of t-channel leptoquark (LQ) exchange are presented. These limits are translated into exclusion limits on the LQ mass and on its coupling in the t-channel. The sensitivity of this analysis extends into the parameter space of LQ models that attempt to explain the anomalies observed in B meson decays. The limits presented for the various interpretations are the most stringent to date. Additionally, a model-independent limit is provided.

15 data tables

The transverse mass distribution of $ au$ leptons and missing transverse momentum observed in the Run-2 data (black dots with statistical uncertainty) as well as the expectation from SM processes (stacked histograms). Different signal hypotheses normalized to 10 fb$^{-1}$ are illustrated as dashed lines for exemplary SSM W$\prime$ boson, QBH and EFT signal hypotheses. The ratios of the background-subtracted data yields to the expected background yields are presented in the lower panel. The combined statistical and systematic uncertainties in the background are represented by the grey shaded band in the ratio panel.

Bayesian upper exclusion limits at 95% CL on the product of the cross section and branching fraction of a W$\prime$ boson decaying to a $\tau$ lepton and a neutrino in the SSM model. For this model, W$\prime$ boson masses of up to 4.8 TeV can be excluded. The limit is given by the intersection of the observed (solid) limit and the theoretical cross section (blue dotted curve). The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively. The $\sigma \mathcal{B}$ for an SSM W' boson, along with its associated uncertainty, calculated at NNLO precision in QCD is shown.

Bayesian 95% CL model-independent upper limit on the product of signal cross sections and branching fraction for the $\tau+\nu$ decay for a back-to-back $\tau$ lepton plus $p_{T}^{miss}$ topology. To calculate this limit, all events for signal, background, and data are summed starting from a minimum $m_{T}$ threshold and then divided by the total number of events. No assumption on signal shape is included in this limit. The expected (dashed line) and observed (solid line) limits are shown as well as the 68% and 95% CL uncertainty bands (green and yellow, respectively).

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