Date

Search for vector-like leptons with long-lived particle decays in the CMS muon system in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration Chekhovsky, Vladimir ; Hayrapetyan, Aram ; Makarenko, Vladimir ; et al.
CMS-EXO-23-015, 2025.
Inspire Record 2902874 DOI 10.17182/hepdata.156846

A first search is presented for vector-like leptons (VLLs) decaying into a light long-lived pseudoscalar boson and a standard model $\tau$ lepton. The pseudoscalar boson is assumed to have a mass of 2 GeV and to decay exclusively into a pair of photons. It is identified using the CMS muon system. The analysis is carried out using a data set of proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment in 2016-2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. Selected events contain at least one pseudoscalar boson decaying electromagnetically in the muon system and at least one hadronically decaying $\tau$ lepton. No significant excess of data events is observed compared to the background expectation. Upper limits are set at 95% confidence level on the vector-like lepton production cross section as a function of the VLL mass and the pseudoscalar boson mean proper decay length. The observed and expected exclusion ranges of the VLL mass extend up to 700 and 670 GeV, respectively, depending on the pseudoscalar boson lifetime.

10 data tables

Distributions of the number of hits in the cluster (Nhits) for the DT category in the signal region (SR). The last histogram bin contains all overflow events.

Distributions of the number of hits in the cluster (Nhits) for the CSC category in the signal region (SR). The last histogram bin contains all overflow events.

Distributions of the number of hits in the cluster (Nhits) for the DT category in the out-of-time (OOT) region. The last histogram bin contains all overflow events.

More…

Version 2
Search for supersymmetry in final states with disappearing tracks in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration Hayrapetyan, Aram ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
Phys.Rev.D 109 (2024) 072007, 2024.
Inspire Record 2705044 DOI 10.17182/hepdata.144178

A search is presented for charged, long-lived supersymmetric particles in final states with one or more disappearing tracks. The search is based on data from proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS detector at the CERN LHC between 2016 and 2018, corresponding to an integrated luminosity of 137 fb$^{-1}$. The search is performed over final states characterized by varying numbers of jets, b-tagged jets, electrons, and muons. The length of signal-candidate tracks in the plane perpendicular to the beam axis is used to characterize the lifetimes of wino- and higgsino-like charginos produced in the context of the minimal supersymmetric standard model. The d$E$/d$x$ energy loss of signal-candidate tracks is used to increase the sensitivity to charginos with a large mass and thus a small Lorentz boost. The observed results are found to be statistically consistent with the background-only hypothesis. Limits on the pair production cross section of gluinos and squarks are presented in the framework of simplified models of supersymmetric particle production and decay, and for electroweakino production based on models of wino and higgsino dark matter. The limits presented are the most stringent to date for scenarios with light third-generation squarks and a wino- or higgsino-like dark matter candidate capable of explaining the known dark matter relic density.

60 data tables

Comparison between the data and SM background predictions for the number of b-tagged jets in the long track final state.

Comparison between the data and SM background predictions for the number of jets in the long track final state.

Comparison between the data and SM background predictions for the hard missing transverse momentum in the long track final state.

More…

Measurements of the inclusive W and Z boson production cross sections and their ratios in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV

The CMS collaboration Chekhovsky, Vladimir ; Hayrapetyan, Aram ; Makarenko, Vladimir ; et al.
CMS-SMP-22-017, 2025.
Inspire Record 2900021 DOI 10.17182/hepdata.157226

Measurements are presented of the W and Z boson production cross sections in proton-proton collisions at a center-of-mass energy of 13.6 TeV. Data collected in 2022 and corresponding to an integrated luminosity of 5.01 fb$^{-1}$ with one or two identified muons in the final state are analyzed. The results for the products of total inclusive cross sections and branching fractions for muonic decays of W and Z bosons are 11.93 $\pm$ 0.08 (syst) $\pm$ 0.17 (lumi) $^{+0.07}_{-0.07}$ (acc) nb for W$^+$ boson production, 8.86 $\pm$ 0.06 (syst) $\pm$ 0.12 (lumi) $^{+0.05}_{-0.06}$ (acc) nb for W$^-$ boson production, and 2.021 $\pm$ 0.009 (syst) $\pm$ 0.028 (lumi) $^{+0.011}_{-0.013}$ (acc) nb for the Z boson production in the dimuon mass range of 60-120 GeV, all with negligible statistical uncertainties. Furthermore, the corresponding fiducial cross sections, as well as cross section ratios for both fiducial and total phase space, are provided. The ratios include charge-separated results for W boson production (W$^+$ and W$^-$) and the sum of the two contributions (W$^\pm$), each relative to the measured Z boson production cross section. Additionally, the ratio of the measured cross sections for W$^+$ and W$^-$ boson production is reported. All measurements are in agreement with theoretical predictions, calculated at next-to-next-to-leading order accuracy in quantum chromodynamics.

17 data tables

Corrected normalized distribution of the transverse momentum of the leading muon in the Z boson signal region. Simulated contributions from Z boson, electroweak, and ttbar production, as well as their sum, and the data are shown.

Corrected normalized distribution of the transverse momentum of the trailing muon in the Z boson signal region. Simulated contributions from Z boson, electroweak, and ttbar production, as well as their sum, and the data are shown.

Corrected normalized distribution of the missing transverse momentum in the Z boson signal region. Simulated contributions from Z boson, electroweak, and ttbar production, as well as their sum, and the data are shown.

More…

Search for nonresonant pair production of Higgs bosons in the $b\bar{b}b\bar{b}$ final state in $pp$ collisions at $\sqrt{s}= 13$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Braden Keim ; Abeling, Kira ; et al.
Phys.Rev.D 108 (2023) 052003, 2023.
Inspire Record 2621476 DOI 10.17182/hepdata.137769

A search for nonresonant Higgs boson pair production in the $b\bar{b}b\bar{b}$ final state is presented. The analysis uses 126 fb$^{-1}$ of $pp$ collision data at $\sqrt{s}={13}$ TeV collected with the ATLAS detector at the Large Hadron Collider, and targets both the gluon-gluon fusion and vector-boson fusion production modes. No evidence of the signal is found and the observed (expected) upper limit on the cross-section for nonresonant Higgs boson pair production is determined to be 5.4 (8.1) times the Standard Model predicted cross-section at 95% confidence level. Constraints are placed on modifiers to the $HHH$ and $HHVV$ couplings. The observed (expected) $2\sigma$ constraints on the $HHH$ coupling modifier, $\kappa_\lambda$, are determined to be $[-3.5, 11.3]$ ($[-5.4, 11.4]$), while the corresponding constraints for the $HHVV$ coupling modifier, $\kappa_{2V}$, are $[-0.0, 2.1]$ ($[-0.1, 2.1]$). In addition, constraints on relevant coefficients are derived in the context of the Standard Model effective field theory and Higgs effective field theory, and upper limits on the $HH$ production cross-section are placed in seven Higgs effective field theory benchmark scenarios.

38 data tables

Distributions of the reconstructed m<sub>HH</sub> in data (shown by the black points), the estimated background (shown by the yellow histograms) in the VBF signal region with |&Delta;&eta;<sub>HH</sub>| &lt; 1.5. The hatching shows the total uncertainty of the background estimate. The distribution of the expected background is obtained using the best-fit values of the nuisance parameters in the fit to the data with the background-only hypothesis. Distributions for three choices of couplings are shown: the SM, &kappa;<sub>&lambda;</sub>= 6, and &kappa;<sub>2V</sub> = 0 (with all other couplings set to their SM values in the last two models), scaled so as to be visible on the plot. The lower panels show the ratio of the observed data yield to the predicted background in each bin. Events in the overflow bins are counted in the yields of the final bins. In the HEPData entry, the raw value per histogram bin is provided, while in the published paper the values in the histogram are scaled by the bin width.

Distributions of the reconstructed m<sub>HH</sub> in data (shown by the black points), the estimated background (shown by the yellow histograms) in the VBF signal region with |&Delta;&eta;<sub>HH</sub>| &gt; 1.5. The hatching shows the total uncertainty of the background estimate. The distribution of the expected background is obtained using the best-fit values of the nuisance parameters in the fit to the data with the background-only hypothesis. Distributions for three choices of couplings are shown: the SM, &kappa;<sub>&lambda;</sub>= 6, and &kappa;<sub>2V</sub> = 0 (with all other couplings set to their SM values in the last two models), scaled so as to be visible on the plot. The lower panels show the ratio of the observed data yield to the predicted background in each bin. Events in the overflow bins are counted in the yields of the final bins. In the HEPData entry, the raw value per histogram bin is provided, while in the published paper the values in the histogram are scaled by the bin width.

The observed 95&#37; CL exclusion limits as a function of &kappa;<sub>&lambda;</sub> (obtained using the signal strength &mu;<sub>ggF+VBF</sub> as the POI) from the combined ggF and VBF signal regions, as shown by the solid black line. The value of &kappa;<sub>2V</sub> is fixed to 1. The blue and yellow bands show respectively the 1&sigma; and 2&sigma; bands around the expected exclusion limits, which are shown by the dashed black line. The expected exclusion limits are obtained using a fit to the data with the background-only hypothesis. The dark red line shows the predicted combined ggF and VBF HH cross-section as a function of &kappa;<sub>&lambda;</sub>.

More…

Small-$x$ evolution of gluon fields from incoherent J/$\psi$ photoproduction in ultraperipheral PbPb collisions

The CMS collaboration Chekhovsky, Vladimir ; Hayrapetyan, Aram ; Makarenko, Vladimir ; et al.
CMS-HIN-23-009, 2025.
Inspire Record 2899343 DOI 10.17182/hepdata.156185

Incoherent J/$\psi$ photoproduction in heavy ion ultraperipheral collisions (UPCs), in which the photon interacts with localized, fluctuating gluonic hotspots rather than the entire nucleus, provides a unique probe of those fluctuations. This study presents the first measurement of the dependence of this photoproduction yield on the photon-nucleon center-of-mass energy ($W_\gamma^\mathrm{N}$), using PbPb UPCs at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The data corresponds to an integrated luminosity of 1.52 nb$^{-1}$, recorded by the CMS experiment. The measurement covers a wide $W_\gamma^\mathrm{N}$ range of $\approx$40-400 GeV, probing gluons carrying a fraction of nucleon momentum $x$ in the range between 5.9 $\times$ 10$^{-3}$ and 6.5 $\times$ 10$^{-5}$. The measured incoherent J/$\psi$ photoproduction cross section is suppressed relative to theoretical predictions without nuclear effects. However, the ratio of incoherent to coherent photoproduction remains constant across the probed $W_\gamma^\mathrm{N}$ and $x$ range. Together, these results pose significant challenges to current theoretical models which include gluon saturation or nuclear shadowing effects.

8 data tables

The differential incoherent $\mathrm{J}/\psi$ photoproduction cross section as a function of $|y|$, in different neutron multiplicity classes.

The differential incoherent $\mathrm{J}/\psi$ photoproduction cross section as a function of $y$, in different neutron multiplicity classes.

The incoherent $\mathrm{J}/\psi$ photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$ or Bjorken $x$, measured in PbPb ultra-peripheral collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$ values used correspond to the center of each rapidity range. The theoretical uncertainties is due to the uncertainties in the photon flux.

More…

Disentangling sources of momentum fluctuations in Xe+Xe and Pb+Pb collisions with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Aakvaag, Erlend ; Abbott, Braden Keim ; et al.
Phys.Rev.Lett. 133 (2024) 252301, 2024.
Inspire Record 2806288 DOI 10.17182/hepdata.153671

High-energy nuclear collisions create a quark-gluon plasma, whose initial condition and subsequent expansion vary from event to event, impacting the distribution of the event-wise average transverse momentum ($P([p_{\mathrm{T}}])$). Distinguishing between contributions from fluctuations in the size of the nuclear overlap area (geometrical component) and other sources at fixed size (intrinsic component) presents a challenge. Here, these two components are distinguished by measuring the mean, variance, and skewness of $P([p_{\mathrm{T}}])$ in $^{208}$Pb+$^{208}$Pb and $^{129}$Xe+$^{129}$Xe collisions at $\sqrt{s_{{\mathrm{NN}}}} = 5.02$ and 5.44 TeV, respectively, using the ATLAS detector at the LHC. All observables show distinct changes in behavior in ultra-central collisions, where the geometrical variations are suppressed as the overlap area reaches its maximum. These results demonstrate a new technique to disentangle geometrical and intrinsic fluctuations, enabling constraints on initial condition and properties of the quark-gluon plasma, such as the speed of sound.

42 data tables

Data from Figure 1, panel a, $\left\langle[p_{T}]\right\rangle$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 1, panel b, $\left\langle[p_{T}]\right\rangle$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 1, panel b, $\left\langle[p_{T}]\right\rangle$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

More…

Proton emission in ultraperipheral Pb-Pb collisions at $\sqrt{\textit{s}_{\mathrm{\textbf{NN}}}}=5.02$ TeV

The ALICE collaboration Acharya, Shreyasi ; Agarwal, Apar ; Aglieri Rinella, Gianluca ; et al.
CERN-EP-2024-288, 2024.
Inspire Record 2846998 DOI 10.17182/hepdata.157600

The first measurements of proton emission accompanied by neutron emission in the electromagnetic dissociation (EMD) of $^{208}$Pb nuclei in the ALICE experiment at the LHC are presented. The EMD protons and neutrons emitted at very forward rapidities are detected by the proton and neutron Zero Degree Calorimeters of the ALICE experiment. The emission cross sections of zero, one, two, and three protons accompanied by at least one neutron were measured in ultraperipheral $^{208}$Pb-$^{208}$Pb collisions at a center-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}=5.02$~TeV. These 0p, 1p, 2p, and 3p cross sections are described by the RELDIS model, and according to this model, they are associated with the production of various isotopes of Pb, Tl, Hg, and Au in the EMD of $^{208}$Pb. The cross sections of the emission of a single proton accompanied by the emission of one, two, or three neutrons in EMD were also measured. The data are significantly overestimated by the RELDIS model, which predicts that the (1p,1n), (1p,2n), and (1p,3n) cross sections are very similar to the cross sections for the production of the thallium isotopes $^{206,205,204}$Tl.

2 data tables

Measured cross sections of the emission of a given number of protons k accompanied by at least one neutron i in UPC of Pb nuclei.

Measured cross sections of the emission of a given number of neutrons i accompanied by a single proton in UPC of Pb nuclei.


Multiplicity-dependent jet modification from di-hadron correlations in pp collisions at $\sqrt{s} = 13$ TeV

The ALICE collaboration Acharya, Shreyasi ; Agarwal, Apar ; Aglieri Rinella, Gianluca ; et al.
CERN-EP-2024-229, 2024.
Inspire Record 2826253 DOI 10.17182/hepdata.157587

Short-range correlations between charged particles are studied via two-particle angular correlations in pp collisions at $\sqrt{s}=13$ TeV. The correlation functions are measured as a function of the relative azimuthal angle $\Delta\varphi$ and the pseudorapidity separation $\Delta\eta$ for pairs of primary charged particles within the pseudorapidity interval $|\eta| < 0.9$ and the transverse-momentum range $1 < p_{\rm T} < 8$ GeV/$c$. Near-side ($|\Delta\varphi|<1.3$) peak widths are extracted from a generalised Gaussian fitted over the correlations in full pseudorapidity separation ($|\Delta\eta|<1.8$), while the per-trigger associated near-side yields are extracted for the short-range correlations ($|\Delta\eta|<1.3$). Both are evaluated as a function of charged-particle multiplicity obtained by two different event activity estimators. The width of the near-side peak decreases with increasing multiplicity, and this trend is reproduced qualitatively by the Monte Carlo event generators PYTHIA 8, AMPT, and EPOS. However, the models overestimate the width in the low transverse-momentum region ($p_{\rm T} < 3$ GeV/$c$). The per-trigger associated near-side yield increases with increasing multiplicity. Although this trend is also captured qualitatively by the considered event generators, the yield is mostly overestimated by the models in the considered kinematic range. The measurement of the shape and yield of the short-range correlation peak can help us understand the interplay between jet fragmentation and event activity, quantify the narrowing trend of the near-side peak as a function of transverse momentum and multiplicity selections in pp collisions, and search for final-state jet modification in small collision systems.

40 data tables

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $1.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 2.0$ GeV/$c$. The multiplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $2.0 < p_\mathrm{T, trig} < 3.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $2.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 3.0$ GeV/$c$. The multiplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

More…

Observation of the charged-particle multiplicity dependence of $\sigma_{\psi(2S)}/\sigma_{\text{J}/\psi}$ in pPb collisions at 8.16 TeV

The CMS collaboration Chekhovsky, Vladimir ; Hayrapetyan, Aram ; Makarenko, Vladimir ; et al.
CMS-HIN-24-001, 2025.
Inspire Record 2896594 DOI 10.17182/hepdata.154161

Bound states of charm and anticharm quarks, known as charmonia, have a rich spectroscopic structure that can be used to probe the dynamics of hadron production in high-energy hadron collisions. Here, the cross section ratio of excited ($\psi$(2S)) and ground state (J/$\psi$) vector mesons is measured as a function of the charged-particle multiplicity in proton-lead (pPb) collisions at a center-of-mass (CM) energy per nucleon pair of 8.16 TeV. The data corresponding to an integrated luminosity of 175 nb$^{-1}$ were collected using the CMS detector. The ratio is measured separately for prompt and nonprompt charmonia in the transverse momentum range 6.5 $\lt$$p_\text{T}$$\lt$ 30 GeV and in four rapidity ranges spanning $-$2.865 $\lt$$y_\text{CM}$$\lt$ 1.935. For the first time, a statistically significant multiplicity dependence of the prompt cross section ratio is observed in proton-nucleus collisions. There is no clear rapidity dependence in the ratio. The prompt measurements are compared with a theoretical model which includes interactions with nearby particles during the evolution of the system. These results provide additional constraints on hadronization models of heavy quarks in nuclear collisions.

7 data tables

Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $6.5<p_T<30.0\,GeV$ and $ -2.865 < y_{CM} < -2$ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$

Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $6.5<p_T<30.0\,GeV$ and $ -2 < y_{CM} < -1$ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$

Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $6.5<p_T<30.0\,GeV$ and $ -1 < y_{CM} < 1$ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$

More…

Observation of top-quark pair production in lead-lead collisions at $\sqrt{s_\mathrm{NN}}=5.02$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Aakvaag, Erlend ; Abbott, Braden Keim ; et al.
CERN-EP-2024-282, 2024.
Inspire Record 2849226 DOI 10.17182/hepdata.156982

Top-quark pair production is observed in lead-lead (Pb+Pb) collisions at $\sqrt{s_\mathrm{NN}}=5.02$ TeV at the Large Hadron Collider with the ATLAS detector. The data sample was recorded in 2015 and 2018, amounting to an integrated luminosity of 1.9 nb$^{-1}$. Events with exactly one electron and one muon and at least two jets are selected. Top-quark pair production is measured with an observed (expected) significance of 5.0 (4.1) standard deviations. The measured top-quark pair production cross-section is $\sigma_{t\bar{t}} = 3.6\;^{+1.0}_{-0.9}\;\mathrm{(stat.)}\;^{+0.8}_{-0.5}\;\mathrm{(syst.)} ~\mathrm{\mu b}$, with a total relative uncertainty of 31%, and is consistent with theoretical predictions using a range of different nuclear parton distribution functions. The observation of this process consolidates the evidence of the existence of all quark flavors in the pre-equilibrium stage of the quark-gluon plasma at very high energy densities, similar to the conditions present in the early universe.

5 data tables

The figure shows the post-fit distribution of events as a function of the dilepton invariant mass ($m_{e\mu}$), in lead-lead (Pb+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, with an integrated luminosity of 1.9 nb$^{-1}$. The data correspond to the SR1 (Signal Region 1 (SR\(_1\)):} Events with exactly one muon and one oppositely charged electron, a dilepton invariant mass \( m_{e\mu} \geq 30 \, \mathrm{GeV} \), at least two jets with \( p_T \geq 35 \, \mathrm{GeV} \), and a dilepton transverse momentum \( p_T^{e\mu} > 40 \, \mathrm{GeV} \). This region is expected to be signal-dominated) channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield.

The figure shows the post-fit distribution of events as a function of the dilepton invariant mass ($m_{e\mu}$), in lead-lead (Pb+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, with an integrated luminosity of 1.9 nb$^{-1}$. The data correspond to the SR2 (Signal Region 2 (SR\(_2\)):} Events meeting the same criteria as SR\(_1\), but with a dilepton transverse momentum \( p_T^{e\mu} \leq 40 \, \mathrm{GeV} \). This region includes events with a lower \( p_T^{e\mu} \) and has a larger background contribution) channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield.

The impact of systematic uncertainties on the fitted signal-strength parameter $\hat{\mu}$ for the combined fit of all channels. Only the 10 most significant systematic uncertainties are shown and listed in decreasing order of their impact on $\mu$ on the $y$-axis. The empty (filled) blue/cyan boxes correspond to the pre-fit (post-fit) impact on $\mu$, referring to the upper $x$-axis. The impact of each systematic uncertainty, $\Delta \mu$, is calculated by comparing the nominal best-fit value of $\mu$ with the result of the fit when fixing the corresponding nuisance parameter $\theta$ to its best-fit value $\hat{\theta}$ shifted by its pre-fit (post-fit) uncertainties $\hat{\theta} \pm \Delta \theta(\hat{\theta} \pm \Delta \hat{\theta})$. The black points, which refer to the lower $x$-axis, show the pulls of the fitted nuisance parameters, i.e., the deviations of the fitted parameters $\hat{\theta}$ from their nominal values $\theta_0$, normalized to their nominal uncertainties $\Delta \theta$. The black lines show the post-fit uncertainties of the nuisance parameters, relative to their nominal uncertainties, which are indicated by the dashed lines.

More…