CMS-HIG-25-002

CMS-HIG-25-002 ; ATL-PHYS-PUB-2025-018
Highlights of the HL-LHC physics projections by ATLAS and CMS
ATLAS and CMS Collaborations
31 March 2025
Submitted to EPPSU
Abstract: The High-Luminosity LHC (HL-LHC) physics programme will be crucial for deepening our understanding of fundamental physics, enabling in particular precision studies of the Higgs sector and enhancing sensitivity to rare processes and potential new physics. With unprecedented integrated luminosity, it will offer a unique opportunity to probe the standard model (SM) with extreme accuracy and explore connections to open questions in particle physics, astroparticle physics, and cosmology. The physics reach of the upgraded ATLAS and CMS detectors at the end of their programme will not only be significant in its own right but will also serve as a critical foundation for decision-making on future colliders, shaping the 2026 update of the European Strategy for Particle Physics.
Links: e-print arXiv:2504.00672 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	References	CMS Publications

Highlights of the HL-LHC physics projections by ATLAS and CMS: File submitted to the European Strategy Update.
CMS Collaboration author list.

Figures
png pdf	Figure 1: The projected uncertainty in the combined coupling signal strength modifiers (left) and their ratios (right) with 3 ab $^{-1}$ of $pp$ collisions under the S2 systematic uncertainty scenario, assuming that the Higgs boson decays only to final states predicted by the SM.
png pdf	Figure 1-a: The projected uncertainty in the combined coupling signal strength modifiers (left) and their ratios (right) with 3 ab $^{-1}$ of $pp$ collisions under the S2 systematic uncertainty scenario, assuming that the Higgs boson decays only to final states predicted by the SM.
png pdf	Figure 1-b: The projected uncertainty in the combined coupling signal strength modifiers (left) and their ratios (right) with 3 ab $^{-1}$ of $pp$ collisions under the S2 systematic uncertainty scenario, assuming that the Higgs boson decays only to final states predicted by the SM.
png pdf	Figure 2: Left: Expected ATLAS+CMS $\kappa_{3}$ likelihood scans for single decay channels and the combination for 3 ab $^{-1}$ for the S3 scenario, obtained fixing $\kappa_{3}^\mathrm{true}=$ 1. Right: The ATLAS+CMS projections for $\kappa_{2V}$ in the S2 and S3 scenarios, fixing $\kappa_{2V}^\mathrm{true}=$ 1.
png pdf	Figure 2-a: Left: Expected ATLAS+CMS $\kappa_{3}$ likelihood scans for single decay channels and the combination for 3 ab $^{-1}$ for the S3 scenario, obtained fixing $\kappa_{3}^\mathrm{true}=$ 1. Right: The ATLAS+CMS projections for $\kappa_{2V}$ in the S2 and S3 scenarios, fixing $\kappa_{2V}^\mathrm{true}=$ 1.
png pdf	Figure 2-b: Left: Expected ATLAS+CMS $\kappa_{3}$ likelihood scans for single decay channels and the combination for 3 ab $^{-1}$ for the S3 scenario, obtained fixing $\kappa_{3}^\mathrm{true}=$ 1. Right: The ATLAS+CMS projections for $\kappa_{2V}$ in the S2 and S3 scenarios, fixing $\kappa_{2V}^\mathrm{true}=$ 1.
png pdf	Figure 3: Comparison of the ESPPU 2020 and ESPPU 2026 projected 3 ab $^{-1}$ HH sensitivities from various final states, and their combinations.
png pdf	Figure 4: Left: The ATLAS+CMS projection on the precision of the determination of $\kappa_{3}$ as a function of $\kappa_{3}^\mathrm{true}$ . The 68% and 95% confidence intervals are shown in the upper plot, while the lower plot shows the $\kappa_{3}$ deviation from the simulated $\kappa_{3}^\mathrm{true}$ value and its 68% and 95% confidence intervals. Right: 95% CL constraints from the $\mathrm{HHH}$ search projection on $\kappa_3$ and $\kappa_4$ . Results are shown for 3 ab $^{-1}$ per experiment at $\sqrt{s}=$ 14 TeV in scenario S3 with data-driven background uncertainties. Unitarity limits, as calculated in Ref. [57], are overlaid in the region bounded by the grey dashed line.
png pdf	Figure 4-a: Left: The ATLAS+CMS projection on the precision of the determination of $\kappa_{3}$ as a function of $\kappa_{3}^\mathrm{true}$ . The 68% and 95% confidence intervals are shown in the upper plot, while the lower plot shows the $\kappa_{3}$ deviation from the simulated $\kappa_{3}^\mathrm{true}$ value and its 68% and 95% confidence intervals. Right: 95% CL constraints from the $\mathrm{HHH}$ search projection on $\kappa_3$ and $\kappa_4$ . Results are shown for 3 ab $^{-1}$ per experiment at $\sqrt{s}=$ 14 TeV in scenario S3 with data-driven background uncertainties. Unitarity limits, as calculated in Ref. [57], are overlaid in the region bounded by the grey dashed line.
png pdf	Figure 4-b: Left: The ATLAS+CMS projection on the precision of the determination of $\kappa_{3}$ as a function of $\kappa_{3}^\mathrm{true}$ . The 68% and 95% confidence intervals are shown in the upper plot, while the lower plot shows the $\kappa_{3}$ deviation from the simulated $\kappa_{3}^\mathrm{true}$ value and its 68% and 95% confidence intervals. Right: 95% CL constraints from the $\mathrm{HHH}$ search projection on $\kappa_3$ and $\kappa_4$ . Results are shown for 3 ab $^{-1}$ per experiment at $\sqrt{s}=$ 14 TeV in scenario S3 with data-driven background uncertainties. Unitarity limits, as calculated in Ref. [57], are overlaid in the region bounded by the grey dashed line.
png pdf	Figure 5: Expected 95% CL upper limits on the $\mathrm{ \sigma(pp \to S \to HH }$ cross section as a function of the scalar mass $m_{\mathrm{S}}$ , produced via gluon fusion using the narrow width approximation. The projection is derived assuming 3 ab $^{-1}$ per experiment for the S2 scenario at 14 TeV. For comparison, production cross section curves for the model described in Section 7 are shown, for two values of the scalar portal coupling $a_2$ .
png pdf	Figure 6: (Top) BEH potentials in various models which predict a first-order phase transition [70]. The models are compared with the SM BEH potential. Two approaches (SMEFT 6 and HH-driven) are used to show the expected uncertainties on the Higgs self-coupling achieved by combining ATLAS and CMS at 3 ab $^{-1}$ in the S3 scenario. The dashed lines show the boundary of the regions for which the alternative models predict a strong first-order phase transition. The arrows indicate the region where the strong first-order phase transition happens. Further details can be found in the text. The bottom panel shows the difference between the potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ . Here, the 68% and 95% CL uncertainty bands on the shape of $V(\phi)$ are shown, for the HH-driven and SMEFT 6 potentials (see text). (Bottom) A zoom into the $V(\phi)-V_{SM}(\phi)$ difference around the minimum of $V(\phi)$ , corresponding to the validity range of the HH-driven band.
png pdf	Figure 6-a: (Top) BEH potentials in various models which predict a first-order phase transition [70]. The models are compared with the SM BEH potential. Two approaches (SMEFT 6 and HH-driven) are used to show the expected uncertainties on the Higgs self-coupling achieved by combining ATLAS and CMS at 3 ab $^{-1}$ in the S3 scenario. The dashed lines show the boundary of the regions for which the alternative models predict a strong first-order phase transition. The arrows indicate the region where the strong first-order phase transition happens. Further details can be found in the text. The bottom panel shows the difference between the potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ . Here, the 68% and 95% CL uncertainty bands on the shape of $V(\phi)$ are shown, for the HH-driven and SMEFT 6 potentials (see text). (Bottom) A zoom into the $V(\phi)-V_{SM}(\phi)$ difference around the minimum of $V(\phi)$ , corresponding to the validity range of the HH-driven band.
png pdf	Figure 6-b: (Top) BEH potentials in various models which predict a first-order phase transition [70]. The models are compared with the SM BEH potential. Two approaches (SMEFT 6 and HH-driven) are used to show the expected uncertainties on the Higgs self-coupling achieved by combining ATLAS and CMS at 3 ab $^{-1}$ in the S3 scenario. The dashed lines show the boundary of the regions for which the alternative models predict a strong first-order phase transition. The arrows indicate the region where the strong first-order phase transition happens. Further details can be found in the text. The bottom panel shows the difference between the potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ . Here, the 68% and 95% CL uncertainty bands on the shape of $V(\phi)$ are shown, for the HH-driven and SMEFT 6 potentials (see text). (Bottom) A zoom into the $V(\phi)-V_{SM}(\phi)$ difference around the minimum of $V(\phi)$ , corresponding to the validity range of the HH-driven band.
png pdf	Figure 7: Top left: Bounds on the heavy scalar model, in the plane of the scalar portal coupling, $a_2$ , versus the scalar singlet mixing angle $\theta$ [73]. The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0 GeV and $b_4=$ 0.25. The other contours show the 95% CL exclusion in this plane from the resonant searches into $S\rightarrow \mathrm{HH} /\mathrm{ZZ}$ signatures, from the $H$ coupling to $Z$ and from $\kappa_3$ constraints. Top right: The same contours are shown in the plane of the deviation of the Higgs boson coupling to the $Z$ with respect to the SM one, versus $\kappa_{3}$ . The dark blue points show the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0, and $b_4=$ 0.25. Bottom left: Exclusion bounds in the plane of the Higgs boson to $\mathrm{ZZ}$ coupling with respect to the SM one versus $\kappa_{3}$ ; 68% and 95% exclusion bounds are displayed. The dark blue points populate the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for all choices of $m_{\mathrm{S}}$ , $b_3$ , and $b_4$ . Bottom right: Projections for the HL-LHC measurements of the Higgs boson and top quark mass. The top quark mass measurement in ${\mathrm{t}\overline{\mathrm{t}}} \text{+jet}$ is shown from ATLAS at 8 TeV [75] and CMS at 13 TeV [76]. The ATLAS+CMS projection is shown with profiling of the systematic uncertainties in the extraction of the top quark mass, based on the S2 scenario. Figure adapted from Ref. [77] with unchanged value and uncertainty in the strong coupling $\alpha_\mathrm{S}$ . The band between the stable and metastable region represents the uncertainty in $\alpha_\mathrm{S}$ .
png pdf	Figure 7-a: Top left: Bounds on the heavy scalar model, in the plane of the scalar portal coupling, $a_2$ , versus the scalar singlet mixing angle $\theta$ [73]. The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0 GeV and $b_4=$ 0.25. The other contours show the 95% CL exclusion in this plane from the resonant searches into $S\rightarrow \mathrm{HH} /\mathrm{ZZ}$ signatures, from the $H$ coupling to $Z$ and from $\kappa_3$ constraints. Top right: The same contours are shown in the plane of the deviation of the Higgs boson coupling to the $Z$ with respect to the SM one, versus $\kappa_{3}$ . The dark blue points show the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0, and $b_4=$ 0.25. Bottom left: Exclusion bounds in the plane of the Higgs boson to $\mathrm{ZZ}$ coupling with respect to the SM one versus $\kappa_{3}$ ; 68% and 95% exclusion bounds are displayed. The dark blue points populate the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for all choices of $m_{\mathrm{S}}$ , $b_3$ , and $b_4$ . Bottom right: Projections for the HL-LHC measurements of the Higgs boson and top quark mass. The top quark mass measurement in ${\mathrm{t}\overline{\mathrm{t}}} \text{+jet}$ is shown from ATLAS at 8 TeV [75] and CMS at 13 TeV [76]. The ATLAS+CMS projection is shown with profiling of the systematic uncertainties in the extraction of the top quark mass, based on the S2 scenario. Figure adapted from Ref. [77] with unchanged value and uncertainty in the strong coupling $\alpha_\mathrm{S}$ . The band between the stable and metastable region represents the uncertainty in $\alpha_\mathrm{S}$ .
png pdf	Figure 7-b: Top left: Bounds on the heavy scalar model, in the plane of the scalar portal coupling, $a_2$ , versus the scalar singlet mixing angle $\theta$ [73]. The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0 GeV and $b_4=$ 0.25. The other contours show the 95% CL exclusion in this plane from the resonant searches into $S\rightarrow \mathrm{HH} /\mathrm{ZZ}$ signatures, from the $H$ coupling to $Z$ and from $\kappa_3$ constraints. Top right: The same contours are shown in the plane of the deviation of the Higgs boson coupling to the $Z$ with respect to the SM one, versus $\kappa_{3}$ . The dark blue points show the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0, and $b_4=$ 0.25. Bottom left: Exclusion bounds in the plane of the Higgs boson to $\mathrm{ZZ}$ coupling with respect to the SM one versus $\kappa_{3}$ ; 68% and 95% exclusion bounds are displayed. The dark blue points populate the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for all choices of $m_{\mathrm{S}}$ , $b_3$ , and $b_4$ . Bottom right: Projections for the HL-LHC measurements of the Higgs boson and top quark mass. The top quark mass measurement in ${\mathrm{t}\overline{\mathrm{t}}} \text{+jet}$ is shown from ATLAS at 8 TeV [75] and CMS at 13 TeV [76]. The ATLAS+CMS projection is shown with profiling of the systematic uncertainties in the extraction of the top quark mass, based on the S2 scenario. Figure adapted from Ref. [77] with unchanged value and uncertainty in the strong coupling $\alpha_\mathrm{S}$ . The band between the stable and metastable region represents the uncertainty in $\alpha_\mathrm{S}$ .
png	Figure 7-c: Top left: Bounds on the heavy scalar model, in the plane of the scalar portal coupling, $a_2$ , versus the scalar singlet mixing angle $\theta$ [73]. The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0 GeV and $b_4=$ 0.25. The other contours show the 95% CL exclusion in this plane from the resonant searches into $S\rightarrow \mathrm{HH} /\mathrm{ZZ}$ signatures, from the $H$ coupling to $Z$ and from $\kappa_3$ constraints. Top right: The same contours are shown in the plane of the deviation of the Higgs boson coupling to the $Z$ with respect to the SM one, versus $\kappa_{3}$ . The dark blue points show the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0, and $b_4=$ 0.25. Bottom left: Exclusion bounds in the plane of the Higgs boson to $\mathrm{ZZ}$ coupling with respect to the SM one versus $\kappa_{3}$ ; 68% and 95% exclusion bounds are displayed. The dark blue points populate the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for all choices of $m_{\mathrm{S}}$ , $b_3$ , and $b_4$ . Bottom right: Projections for the HL-LHC measurements of the Higgs boson and top quark mass. The top quark mass measurement in ${\mathrm{t}\overline{\mathrm{t}}} \text{+jet}$ is shown from ATLAS at 8 TeV [75] and CMS at 13 TeV [76]. The ATLAS+CMS projection is shown with profiling of the systematic uncertainties in the extraction of the top quark mass, based on the S2 scenario. Figure adapted from Ref. [77] with unchanged value and uncertainty in the strong coupling $\alpha_\mathrm{S}$ . The band between the stable and metastable region represents the uncertainty in $\alpha_\mathrm{S}$ .
png pdf	Figure 7-d: Top left: Bounds on the heavy scalar model, in the plane of the scalar portal coupling, $a_2$ , versus the scalar singlet mixing angle $\theta$ [73]. The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0 GeV and $b_4=$ 0.25. The other contours show the 95% CL exclusion in this plane from the resonant searches into $S\rightarrow \mathrm{HH} /\mathrm{ZZ}$ signatures, from the $H$ coupling to $Z$ and from $\kappa_3$ constraints. Top right: The same contours are shown in the plane of the deviation of the Higgs boson coupling to the $Z$ with respect to the SM one, versus $\kappa_{3}$ . The dark blue points show the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for $m_{\mathrm{S}}=$ 300 GeV, $b_3=$ 0, and $b_4=$ 0.25. Bottom left: Exclusion bounds in the plane of the Higgs boson to $\mathrm{ZZ}$ coupling with respect to the SM one versus $\kappa_{3}$ ; 68% and 95% exclusion bounds are displayed. The dark blue points populate the area where a strong first-order phase transition in the early universe is possible within the scalar singlet model discussed in the text for all choices of $m_{\mathrm{S}}$ , $b_3$ , and $b_4$ . Bottom right: Projections for the HL-LHC measurements of the Higgs boson and top quark mass. The top quark mass measurement in ${\mathrm{t}\overline{\mathrm{t}}} \text{+jet}$ is shown from ATLAS at 8 TeV [75] and CMS at 13 TeV [76]. The ATLAS+CMS projection is shown with profiling of the systematic uncertainties in the extraction of the top quark mass, based on the S2 scenario. Figure adapted from Ref. [77] with unchanged value and uncertainty in the strong coupling $\alpha_\mathrm{S}$ . The band between the stable and metastable region represents the uncertainty in $\alpha_\mathrm{S}$ .
png pdf	Figure 8: Expected significance of the longitudinally polarized $WW$ scattering as a function of the luminosity in the S2 scenario.
png pdf	Figure 9: Left: Expected experimental uncertainty in the $\mathrm{t\bar{t}t\bar{t}}$ cross section measurement. Right: Projected 95% confidence intervals on the new physics energy scale $\Lambda$ from the combined constraints of $\mathrm{t \bar t Z }$ and $\mathrm{t \bar t \gamma}$ cross section measurements on EFT operators related to the electroweak dipole moments of the top quark, derived for EFT operator couplings $C_i=$ 1.
png pdf	Figure 9-a: Left: Expected experimental uncertainty in the $\mathrm{t\bar{t}t\bar{t}}$ cross section measurement. Right: Projected 95% confidence intervals on the new physics energy scale $\Lambda$ from the combined constraints of $\mathrm{t \bar t Z }$ and $\mathrm{t \bar t \gamma}$ cross section measurements on EFT operators related to the electroweak dipole moments of the top quark, derived for EFT operator couplings $C_i=$ 1.
png pdf	Figure 9-b: Left: Expected experimental uncertainty in the $\mathrm{t\bar{t}t\bar{t}}$ cross section measurement. Right: Projected 95% confidence intervals on the new physics energy scale $\Lambda$ from the combined constraints of $\mathrm{t \bar t Z }$ and $\mathrm{t \bar t \gamma}$ cross section measurements on EFT operators related to the electroweak dipole moments of the top quark, derived for EFT operator couplings $C_i=$ 1.
png pdf	Figure 10: ESPPU 2026 projections of coupling modifier uncertainties (left) and their ratios (right), compared to the previous HL-LHC projections [2]. The shown percentages represent the relative difference between the two projections. The precision of $\kappa_{\mathrm{Z}}$ is slightly lower due to the refined treatment of the $\mathrm{ZH}$ theory uncertainty.
png pdf	Figure 10-a: ESPPU 2026 projections of coupling modifier uncertainties (left) and their ratios (right), compared to the previous HL-LHC projections [2]. The shown percentages represent the relative difference between the two projections. The precision of $\kappa_{\mathrm{Z}}$ is slightly lower due to the refined treatment of the $\mathrm{ZH}$ theory uncertainty.
png pdf	Figure 10-b: ESPPU 2026 projections of coupling modifier uncertainties (left) and their ratios (right), compared to the previous HL-LHC projections [2]. The shown percentages represent the relative difference between the two projections. The precision of $\kappa_{\mathrm{Z}}$ is slightly lower due to the refined treatment of the $\mathrm{ZH}$ theory uncertainty.
png pdf	Figure 11: $\mathrm{HH}$ significances per final state channel, combined between ATLAS and CMS, in a comparison between integrated luminosities for the S2 systematics scenario (left) and in a comparison between systematics scenarios at 3 ab $^{-1}$ (right).
png pdf	Figure 11-a: $\mathrm{HH}$ significances per final state channel, combined between ATLAS and CMS, in a comparison between integrated luminosities for the S2 systematics scenario (left) and in a comparison between systematics scenarios at 3 ab $^{-1}$ (right).
png pdf	Figure 11-b: $\mathrm{HH}$ significances per final state channel, combined between ATLAS and CMS, in a comparison between integrated luminosities for the S2 systematics scenario (left) and in a comparison between systematics scenarios at 3 ab $^{-1}$ (right).
png pdf	Figure 12: Expected 95% CL upper limits on the $\mathrm{ \sigma(pp \to S \to ZZ)}$ (left) and $\mathrm{ \sigma(pp \to S t \bar t \to t \bar t t \bar t) }$ (right) cross sections as a function of the scalar mass $m_{\mathrm{S}}$ , produced via gluon fusion using the narrow width approximation. The projection is derived assuming 3 ab $^{-1}$ per experiment for the S2 scenario at 14 TeV.
png pdf	Figure 12-a: Expected 95% CL upper limits on the $\mathrm{ \sigma(pp \to S \to ZZ)}$ (left) and $\mathrm{ \sigma(pp \to S t \bar t \to t \bar t t \bar t) }$ (right) cross sections as a function of the scalar mass $m_{\mathrm{S}}$ , produced via gluon fusion using the narrow width approximation. The projection is derived assuming 3 ab $^{-1}$ per experiment for the S2 scenario at 14 TeV.
png pdf	Figure 12-b: Expected 95% CL upper limits on the $\mathrm{ \sigma(pp \to S \to ZZ)}$ (left) and $\mathrm{ \sigma(pp \to S t \bar t \to t \bar t t \bar t) }$ (right) cross sections as a function of the scalar mass $m_{\mathrm{S}}$ , produced via gluon fusion using the narrow width approximation. The projection is derived assuming 3 ab $^{-1}$ per experiment for the S2 scenario at 14 TeV.
png pdf	Figure 13: BEH potentials in various models which predict first-order phase transition [73]. The models are compared with the SM BEH potential. Two approaches (SMEFT 6 and HH-driven) are used to show the expected uncertainties on the Higgs self-coupling achieved by combining ATLAS and CMS at 2 ab $^{-1}$ (top-left) and at 3 ab $^{-1}$ (top-right) in the S2 scenario, in a wide range of the BEH field value. The bottom panels show the difference between the potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ . Here, the 68% and 95% CL uncertainty bands on the shape of $V(\phi)$ are shown, for the HH-driven and SMEFT 6 potentials (see text). The bottom plots show the zoom into the $V(\phi)-V_{SM}(\phi)$ difference around the minimum of $V(\phi)$ , corresponding to the validity range of the HH-driven band.
png pdf	Figure 13-a: BEH potentials in various models which predict first-order phase transition [73]. The models are compared with the SM BEH potential. Two approaches (SMEFT 6 and HH-driven) are used to show the expected uncertainties on the Higgs self-coupling achieved by combining ATLAS and CMS at 2 ab $^{-1}$ (top-left) and at 3 ab $^{-1}$ (top-right) in the S2 scenario, in a wide range of the BEH field value. The bottom panels show the difference between the potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ . Here, the 68% and 95% CL uncertainty bands on the shape of $V(\phi)$ are shown, for the HH-driven and SMEFT 6 potentials (see text). The bottom plots show the zoom into the $V(\phi)-V_{SM}(\phi)$ difference around the minimum of $V(\phi)$ , corresponding to the validity range of the HH-driven band.
png pdf	Figure 13-b: BEH potentials in various models which predict first-order phase transition [73]. The models are compared with the SM BEH potential. Two approaches (SMEFT 6 and HH-driven) are used to show the expected uncertainties on the Higgs self-coupling achieved by combining ATLAS and CMS at 2 ab $^{-1}$ (top-left) and at 3 ab $^{-1}$ (top-right) in the S2 scenario, in a wide range of the BEH field value. The bottom panels show the difference between the potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ . Here, the 68% and 95% CL uncertainty bands on the shape of $V(\phi)$ are shown, for the HH-driven and SMEFT 6 potentials (see text). The bottom plots show the zoom into the $V(\phi)-V_{SM}(\phi)$ difference around the minimum of $V(\phi)$ , corresponding to the validity range of the HH-driven band.
png pdf	Figure 13-c: BEH potentials in various models which predict first-order phase transition [73]. The models are compared with the SM BEH potential. Two approaches (SMEFT 6 and HH-driven) are used to show the expected uncertainties on the Higgs self-coupling achieved by combining ATLAS and CMS at 2 ab $^{-1}$ (top-left) and at 3 ab $^{-1}$ (top-right) in the S2 scenario, in a wide range of the BEH field value. The bottom panels show the difference between the potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ . Here, the 68% and 95% CL uncertainty bands on the shape of $V(\phi)$ are shown, for the HH-driven and SMEFT 6 potentials (see text). The bottom plots show the zoom into the $V(\phi)-V_{SM}(\phi)$ difference around the minimum of $V(\phi)$ , corresponding to the validity range of the HH-driven band.
png pdf	Figure 13-d: BEH potentials in various models which predict first-order phase transition [73]. The models are compared with the SM BEH potential. Two approaches (SMEFT 6 and HH-driven) are used to show the expected uncertainties on the Higgs self-coupling achieved by combining ATLAS and CMS at 2 ab $^{-1}$ (top-left) and at 3 ab $^{-1}$ (top-right) in the S2 scenario, in a wide range of the BEH field value. The bottom panels show the difference between the potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ . Here, the 68% and 95% CL uncertainty bands on the shape of $V(\phi)$ are shown, for the HH-driven and SMEFT 6 potentials (see text). The bottom plots show the zoom into the $V(\phi)-V_{SM}(\phi)$ difference around the minimum of $V(\phi)$ , corresponding to the validity range of the HH-driven band.
png pdf	Figure 14: The difference between the BEH potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ in four scenarios: SMEFT 6 (top left), SMEFT 8 (top right), exponential (bottom left), and logarithmic (bottom right) potentials. The 68% and 95% uncertainty bands from the ATLAS+CMS combination is compared to the boundary of the regions for which each model predicts a strong first-order phase transition. The $\phi$ range corresponds to the validity range of the HH-driven band. The projection is derived in S3 scenario assuming 3 ab $^{-1}$ per experiment.
png pdf	Figure 14-a: The difference between the BEH potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ in four scenarios: SMEFT 6 (top left), SMEFT 8 (top right), exponential (bottom left), and logarithmic (bottom right) potentials. The 68% and 95% uncertainty bands from the ATLAS+CMS combination is compared to the boundary of the regions for which each model predicts a strong first-order phase transition. The $\phi$ range corresponds to the validity range of the HH-driven band. The projection is derived in S3 scenario assuming 3 ab $^{-1}$ per experiment.
png pdf	Figure 14-b: The difference between the BEH potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ in four scenarios: SMEFT 6 (top left), SMEFT 8 (top right), exponential (bottom left), and logarithmic (bottom right) potentials. The 68% and 95% uncertainty bands from the ATLAS+CMS combination is compared to the boundary of the regions for which each model predicts a strong first-order phase transition. The $\phi$ range corresponds to the validity range of the HH-driven band. The projection is derived in S3 scenario assuming 3 ab $^{-1}$ per experiment.
png pdf	Figure 14-c: The difference between the BEH potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ in four scenarios: SMEFT 6 (top left), SMEFT 8 (top right), exponential (bottom left), and logarithmic (bottom right) potentials. The 68% and 95% uncertainty bands from the ATLAS+CMS combination is compared to the boundary of the regions for which each model predicts a strong first-order phase transition. The $\phi$ range corresponds to the validity range of the HH-driven band. The projection is derived in S3 scenario assuming 3 ab $^{-1}$ per experiment.
png pdf	Figure 14-d: The difference between the BEH potential $V(\phi)$ and its SM expectation $V_{SM}(\phi)$ in four scenarios: SMEFT 6 (top left), SMEFT 8 (top right), exponential (bottom left), and logarithmic (bottom right) potentials. The 68% and 95% uncertainty bands from the ATLAS+CMS combination is compared to the boundary of the regions for which each model predicts a strong first-order phase transition. The $\phi$ range corresponds to the validity range of the HH-driven band. The projection is derived in S3 scenario assuming 3 ab $^{-1}$ per experiment.
png pdf	Figure 15: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 15-a: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 15-b: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 15-c: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 15-d: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 15-e: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 15-f: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 15-g: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 15-h: The dark blue hatched contours show the regions of the $a_2$ versus $\theta$ parameter space in the scalar singlet model where a strong first-order phase transition is possible. The other contours show the 95% CL exclusion in this plane from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays, from the H coupling to Z and from $\kappa_{3}$ constraints. The different plots correspond to representative parameter choices in the model.
png pdf	Figure 16: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 16-a: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 16-b: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 16-c: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 16-d: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 16-e: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 16-f: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 16-g: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 16-h: The dark blue hatched contours show the parameter space in the scalar singlet model where a strong first-order phase transition is possible in the plane of the Higgs coupling to the Z versus $\kappa_{3}$ . 95% CL exclusion contours from the searches for resonant $\mathrm{ S \to HH(ZZ) }$ decays and from $\kappa_{3}$ and $k_{\mathrm{Z}}$ are overlaid. The plots show the exclusion in different $M_{\mathrm{S}}$ versus $b_3$ slices of the parameter space when $b_4=$ 0.25
png pdf	Figure 17: Left: Expected uncertainty on $y_t$ as a function of the integrated luminosity, in the S2 scenario, obtained when the $\mathrm{ t\bar{t}H }$ contribution is freely floating. Right: Expected experimental uncertainty on $y_{t}$ as a function of the integrated luminosity, in the S2 scenario, obtained when the $\mathrm{ t\bar{t}H }$ events are parametrized as a function of $\kappa_{\mathrm{t}}$ .
png pdf	Figure 17-a: Left: Expected uncertainty on $y_t$ as a function of the integrated luminosity, in the S2 scenario, obtained when the $\mathrm{ t\bar{t}H }$ contribution is freely floating. Right: Expected experimental uncertainty on $y_{t}$ as a function of the integrated luminosity, in the S2 scenario, obtained when the $\mathrm{ t\bar{t}H }$ events are parametrized as a function of $\kappa_{\mathrm{t}}$ .
png pdf	Figure 17-b: Left: Expected uncertainty on $y_t$ as a function of the integrated luminosity, in the S2 scenario, obtained when the $\mathrm{ t\bar{t}H }$ contribution is freely floating. Right: Expected experimental uncertainty on $y_{t}$ as a function of the integrated luminosity, in the S2 scenario, obtained when the $\mathrm{ t\bar{t}H }$ events are parametrized as a function of $\kappa_{\mathrm{t}}$ .
png pdf	Figure 18: Evolution of the expected 95% CL bound on $C_i/\Lambda^2$ as a function of integrated luminosity for the SMEFT operator $\mathcal{O}^{8}_{Qt}$ obtained from the ATLAS+CMS combination of the inclusive $\mathrm{ t\bar{t}t\bar{t} }$ production cross section measurements in the S2 scenario. The impact of the experimental and total uncertainties are shown separately.

Tables
png pdf	Table 1: Projected uncertainties in percentage on the $H\rightarrow Z\gamma$ and $H\rightarrow \mu\mu$ signal strengths ( $\mu$ ) for the ATLAS [10] and CMS experiments [19], as well as their combination, for different integrated luminosities per experiment and uncertainty scenario S2. The $H\rightarrow \mu\mu$ analyses are combined assuming no experimental correlation between the two experiments, while the theoretical uncertainty is fully correlated.
png pdf	Table 2: Combined ATLAS and CMS expected statistical significance for $\mathrm{HH}$ production and the corresponding 68% confidence interval on $\kappa_{3}$ at 3 ab $^{-1}$ , derived assuming $\kappa_{3}^\mathrm{true}=$ 1. The last row reports the projected ATLAS+CMS percentage uncertainty on $\kappa_{3}$ in the various scenarios. The measurement labelled by the $\dagger$ symbol have been used in the ATLAS+CMS combination. When the $\dagger$ symbol is present on only one of the two experiments, this measurement has been extrapolated to 6 ab $^{-1}$ assuming the same sensitivity on that channel for the two experiments.
png pdf	Table 3: Expected 95% CL intervals on EFT coupling parameters, derived setting the new physics scale $\Lambda =$ 1 TeV and assuming a single non-zero EFT parameter at a time, in the context of deviations induced in the $\mathrm{ t\bar{t}t\bar{t} }$ process.

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