We present the first lattice QCD calculation of the next-to-leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation for the space-like kernel, which is combined with the spatially summed vector correlator computed on CLS ensembles with $\textit{N}$ = 2 + 1 flavors of O($\textit{a}$)-improved Wilson fermions, covering six lattice spacings between 0$\textit{.}$039 and 0$\textit{.}$097 fm and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain as our final, continuum-extrapolated result $$ {a}_{\mu}^{\mathrm{hvp},\kern0.30em \mathrm{nlo}} $$ = −101.57(26) (54) × 10 . It lies below the estimate provided by the 2025 White Paper of the Muon ($\textit{g}$ – 2) Theory Initiative by 1.4$\textit{σ}$ but is two times more precise. It also exhibits a strong tension of 4.6$\textit{σ}$ with data-driven evaluations based on hadronic cross section measurements excluding the recent result by CMD-3.

Germany

Arnau Beltran

Alessandro Conigli

Switzerland

Simon Kuberski

Harvey Meyer

Konstantin Ottnad

Hartmut Wittig

Higher-order hadronic vacuum polarization contribution to the muon $\textit{g}$ − 2 from lattice QCD

This Letter presents the first evidence of the simultaneous production of two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> bosons and one photon with the ATLAS detector at the Large Hadron Collider. The measurement is performed using the full Run-2 dataset, recorded from 2015 to 2018, of proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>140</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>. The fully leptonic final state with four leptons and one photon is analyzed, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>Z</mi><mi>Z</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>′</mo><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>′</mo><mo>−</mo></mrow></msup><mi>γ</mi></mrow></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo><mo>,</mo><msup><mo>ℓ</mo><mo>′</mo></msup><mo>=</mo><mi>e</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>. This final state is measured in a fiducial region where photon final-state radiation is minimized, and the photon has a transverse momentum of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>p</mi></mrow><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mo>&gt;</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. Eight events are selected, with a background estimate of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.92</mn><mo>±</mo><mn>0.15</mn></math>. This results in an observed (expected) significance of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi><mi>γ</mi></math> final state of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4.4</mn><mi>σ</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4.0</mn><mi>σ</mi></math>). The measured cross section for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>Z</mi><mi>Z</mi><mi>γ</mi><mo stretchy="false">→</mo><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>′</mo><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>′</mo><mo>−</mo></mrow></msup><mi>γ</mi></mrow></math> in the fiducial region is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>Z</mi><mi>Z</mi><mi>γ</mi></mrow></msub><mo>=</mo><mn>0.14</mn><msubsup><mrow><mn>4</mn></mrow><mrow><mo>−</mo><mn>0.051</mn></mrow><mrow><mo>+</mo><mn>0.065</mn></mrow></msubsup><msubsup><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mn>0.004</mn></mrow><mrow><mo>+</mo><mn>0.008</mn></mrow></msubsup><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow><mtext> </mtext><mtext> </mtext><mi>fb</mi></mrow></math>, in agreement with the standard model prediction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>fid</mi></mrow><mrow><mi>SM</mi></mrow></msubsup><mo>=</mo><mn>0.130</mn><mo>±</mo><mn>0.006</mn><mtext> </mtext><mtext> </mtext><mi>fb</mi></mrow></math>.

France

G. Aad

Norway

E. Aakvaag

United States

B. Abbott

United Arab Emirates

S. Abdelhameed

K. Abeling

N.J. Abicht

S.H. Abidi

M. Aboelela

Morocco

A. Aboulhorma

Israel

H. Abramowicz

Italy

B.S. Acharya

A. Ackermann

C. Adam Bourdarios

Poland

L. Adamczyk

S.V. Addepalli

United Kingdom

M.J. Addison

J. Adelman

Türkiye

A. Adiguzel

T. Adye

A.A. Affolder

Y. Afik

Spain

M.N. Agaras

A. Aggarwal

Romania

C. Agheorghiesei

A. Ahmad

F. Ahmadov

S. Ahuja

China

X. Ai

G. Aielli

A. Aikot

M. Ait Tamlihat

Sweden

T.P.A. Åkesson

Japan

D. Akiyama

N.N. Akolkar

S. Aktas

G.L. Alberghi

Canada

J. Albert

U. Alberti

P. Albicocco

S. Alderweireldt

Z.L. Alegria

CERN

M. Aleksa

I.N. Aleksandrov

C. Alexa

Greece

T. Alexopoulos

F. Alfonsi

M. Algren

M. Alhroob

Czechia

B. Ali

H.M.J. Ali

S. Ali

S.W. Alibocus

South Africa

M. Aliev

G. Alimonti

C. Allaire

B.M.M. Allbrooke

D.R. Allen

J.S. Allen

J.F. Allen

Australia

C.S. Alley

E.R. Almazan

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

A. Alvarez Fernandez

M. Alves Cardoso

M.G. Alviggi

M. Aly

Brazil

Y. Amaral Coutinho

A. Ambler

C. Amelung

M. Amerl

T. Amezza

B. Amini

K. Amirie

A. Amirkhanov

D. Amperiadou

S. An

C. Anastopoulos

T. Andeen

J.K. Anders

A.C. Anderson

A. Andreazza

S. Angelidakis

A. Angerami

A.V. Anisenkov

A. Annovi

C. Antel

E. Antipov

M. Antonelli

F. Anulli

M. Aoki

T. Aoki

M.A. Aparo

L. Aperio Bella

M. Apicella

C. Appelt

A. Apyan

M. Arampatzi

Evidence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Z</mi><mi>Z</mi><mi>γ</mi></mrow></math> Production with the ATLAS Detector

We investigate the behavior of the nonradial gravity-pulsation discontinuity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-mode in neutron stars with a strong first-order phase transition which give rise to hybrid star configurations. These modes are of utmost relevance, since they can be potentially excited in isolated as well as binary neutron star systems in the inspiral phase, thus allowing us to indirectly detect the presence of a deconfinement transition. In order to do this, we consider four categories of hybrid stars that present distinctive features in their equations of state. We employ the constant speed of sound parametrization, which accounts for a sharp phase transition between confined hadronic matter and deconfined quark matter. Then, working within the relativistic Cowling approximation to obtain the frequencies of nonradial oscillations, we find that, depending on the hybrid star category, the relations between discontinuity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-mode frequencies and masses as well as tidal deformabilities display a highly distinct behavior across the diverse hybrid star categories that appear in the slow hadron-quark conversion regime. This distinct phenomenology provides smoking-gun evidence to clearly distinguish and further classify hybrid stars with a strong transition from purely hadronic stars using upcoming gravitational-wave data. In addition, we present for each of the categories studied the relation between the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-mode frequency and the normalized energy density jump. Finally, we present a novel universal relation for the discontinuity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-mode able to encompass the four categories, including long branches of slow stable hybrid stars and address its asteroseismological capability.

M.C. Rodriguez

José C. Jiménez

Ignacio F. Ranea-Sandoval

Classification of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>-modes for neutron stars with a strong transition: Novel universal relation including slow stable hybrid stars

According to the GEVAG (Generalized Entropy Varying-G) framework, any modification to the Bekenstein-Hawking area law would also lead to a varying-$\textit{G}$ gravity theory in which the effective gravitational constant $\textit{G}$ becomes area-dependent. Among a myriad of generalized entropy functions explored in the literature, of special interest is the logarithmic correction of quantum gravity. In this work, we apply GEVAG to investigate the effect of logarithmic correction on very early-time cosmology, including the conditions for inflation. We found that if the coefficient of the logarithmic correction term is negative, $\textit{G}$ becomes twice that of the current value; whereas, a positive coefficient leads to a very small value of $\textit{G}$ , which may ameliorate the “arrow of time” problem. We make some comparisons with the constant-$\textit{G}$ approach and reveal the advantages of the GEVAG approach. For example, it can evade the sudden singularity that could otherwise arise when the coefficient of the logarithmic correction term is negative. We also check the validity of the generalized second law and comment on the range of the various parameters.

Chen-Hao Wu

Yen Ong

Cosmology with logarithmic corrected horizon entropy according to the generalized entropy and variable-$\textit{G}$ correspondence

We developed a unified framework based on a special (non-regular) embedding of the exceptional group $$E_6$$ in which the main stage of symmetry breaking chain realizes $$E_6\rightarrow G(2) \times SU(3)_A$$ . The exceptional factor $\textit{G}$(2) plays the role of a hidden strong sector, while $$SU(3)_A$$ acts as an ancestor of the electroweak gauge group. A minimal scalar sector is organized around a $$\textbf{650}$$ -based $$E_6$$ Higgs sector. Its $$G(2)\times SU(3)_A$$ components $$(\textbf{7},\textbf{1})$$ and $$(\textbf{1},\textbf{8})$$ implement the subsequent breaking steps $$G(2)\rightarrow SU(3)_C$$ and $$SU(3)_A\rightarrow SU(2)_L\times U(1)_A$$ . The $\textit{speciality}$ of this symmetry breaking establishes the feature of $\textit{darkness}$. Defining a hypercharge from the $$t_{8}$$ generator of $$SU(3)_A$$ is not sufficient to recover the exact Standard Model hypercharges and the correct Weinberg weak angle, leading to the necessity of an $$E_7$$ uplift which introduces only a proper additional $$U(1)_X$$ factor to fix the abelian sector. The special embedding naturally suppresses tree-level leptoquark couplings that typically mediate proton decay in regular grand unified theories. The scalar potential for the Higgs sectors has been constructed, deriving the heavy gauge-bosons spectrum and presenting a consistent one-loop running of the gauge couplings across the intermediate scales, which is shown to satisfy an $$E_6$$ unification. The exotic states are organized in $$E_7$$ -derived vectorlike pairs and are made ultraheavy, while a chirality-selecting projection keeps only the desired Standard Model zero modes. All non-Standard Model Higgs fields and $\textit{broken}$ massive vectors are found to be invisible to colliders searches. The $\textit{G}$(2) gluons ensemble confines into heavy dark glueballs with parametrically suppressed communication with $$SU(3)_A$$ and $$U(1)_X$$ sectors. Cosmological history is analyzed in details, including topological defects, inflation and reheating, demonstrating that monopole relics are naturally diluted. The resulting framework provides a minimal and internally consistent exceptional apparatus which includes the Standard Model and a dark matter sector which is secluded by the group-theoretic orthogonality.

Nicolò Masi

Toward a special $$E_6\rightarrow G(2) \times SU(3)_A$$ embedding for Standard Model and dark matter and an $$E_7$$ completion proposal

We extend the results of Lappi et al. [<a href="http://dx.doi.org/10.1140/epjc/s10052-023-12365-2">Eur. Phys. J. C 84, 84 (2024)</a>] to show that it is possible to obtain expressions for the longitudinal, singlet, and gluon structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> in deep inelastic scattering directly in terms of the measured functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>ln</mi><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> modulo nonsinglet corrections expected to be small at very small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The latter can be treated at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> using existing quark distributions. Our results are presented consistently to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>, correcting and extending the mixed-order results of Lappi et al..

Iran

G.R. Boroun

Loyal Durand

Phuoc Ha

Direct determination of the structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>d</mi><msup><mi>Q</mi><mn>2</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>

This Letter reports on the first evidence of inclusive Higgs-boson production at high transverse momentum in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>b</mi><mover accent="true"><mrow><mi>b</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> final state, reconstructed in a single large-radius jet. The results are based on proton-proton collision data recorded by the ATLAS detector at the Large Hadron Collider at a center-of-mass energies of 13 and 13.6 TeV, corresponding to a total integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>301</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>fb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>. The study profits from the large background suppression provided by the use of a new transformer-based algorithm for jet identification and the sharper mass and transverse momentum, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math>, resolution from a dedicated regression model. The yield relative to the standard model prediction for Higgs bosons produced at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math> larger than 450 GeV is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1.53</mn><mo>±</mo><mn>0.2</mn><msubsup><mrow><mn>7</mn><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mn>0.27</mn></mrow><mrow><mo>+</mo><mn>0.33</mn></mrow></msubsup><mrow><mo>±</mo></mrow><mn>0.17</mn></mrow></math>, where the first uncertainty is statistical, the second is experimental systematic, and the third accounts for theory systematic, corresponding to an observed (expected) significance of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3.8</mn><mi>σ</mi><mo stretchy="false">(</mo><mn>2.5</mn><mi>σ</mi><mo stretchy="false">)</mo></math> relative to the background-only hypothesis. Results are also obtained in three Higgs boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math> intervals and found to be compatible with standard model predictions, where the first uncertainty is statistical, the second is experimental systematic, and the third accounts for theory systematic.

S.J. Arbiol Val

Evidence of Higgs Boson Inclusive Production at High Transverse Momentum Decaying to a Pair of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-Quarks with the ATLAS Detector

A measurement of correction factors for the hadronic jet energy scale and resolution in the ATLAS detector is presented. These correction factors account for differences between simulated and observed data. They are obtained by analysing a selection of top quark events collected in proton–proton collisions by ATLAS between the years 2015 and 2018 at a centre-of-mass energy $$\sqrt{s} = 13$$ $$\text {T{eV}}$$ as well as in 2022 and 2023 at $$\sqrt{s} = 13.6$$ $$\text {T{eV}}$$ . The impact of different jet energy scale or resolution corrections on the reconstructed mass of the hadronically decaying $\textit{W}$ boson from top-quark decays in simulation is quantified. The correction factors are extracted from a fit to the parameterised reconstructed $\textit{W}$-boson mass distribution to data. The energy scale and resolution corrections are measured as a function of the jet transverse momentum between 20 and 200 GeV and absolute pseudorapidity less than 0.8. The uncertainties in the energy scale range from about 0.93% to about 1.7% for jets between 35 and 200 $$\text {G{eV}}$$ , while for the energy resolution the uncertainties range from about 14 to 28%. The method presented will be used in conjunction with other techniques to further improve ATLAS jet energy scale and resolution precision.

N. Abicht

S. Abidi

B. Acharya

C. Bourdarios

S. Addepalli

M. Addison

A. Affolder

M. Agaras

Azerbaijan

M. Tamlihat

B. Aitbenchikh

T. Åkesson

N. Akolkar

G. Alberghi

G. Albouy

Z. Alegria

I. Aleksandrov

Saudi Arabia

H. Ali

S. Alibocus

W. Alkakhi

B. Allbrooke

D. Allen

J. Allen

C. Alley

Z. Alsolami

A. Fernandez

M. Cardoso

M. Alviggi

Y. Coutinho

Portugal

S. Santos

J. Anders

A. Anderson

A. Anisenkov

M. Aparo

L. Bella

Calibration of the jet energy scale and resolution of small-radius jets using semileptonic $$t\bar{t}$$ events with the ATLAS detector

Inclusive, differential and production-mode cross-section measurements of the Higgs boson are performed in the $\textit{H}$ → $\textit{ZZ}$ → 4$\textit{ℓ}$ decay channel. The analysis uses proton–proton collision data produced at the Large Hadron Collider at a centre-of-mass energy of $$ \sqrt{s}=13.6 $$ TeV and recorded with the ATLAS detector, corresponding to an integrated luminosity of 164 fb . The inclusive fiducial cross-section for the $\textit{H}$ → $\textit{ZZ}$ → 4$\textit{ℓ}$ process is measured to be $$ {\sigma}_{\mathrm{fid}}={3.65}_{-0.33}^{+0.35} $$ fb, in agreement with the Standard Model prediction of $$ {\sigma}_{\mathrm{fid}}^{\mathrm{SM}}=3.68\pm 0.17 $$ fb. Differential cross-sections are measured as a function of key kinematic observables of the Higgs boson and the four-lepton final state. Cross-sections are measured for the main production-modes in several exclusive regions of the Higgs boson production phase space and combined to measure an overall Higgs boson signal strength, defined as the measured cross-section normalised to the SM prediction, of $\textit{μ}$ = 0.99 ± 0.13. The results are interpreted in terms of modifications of Higgs boson couplings using the $\textit{κ}$ framework, within the Standard Model Effective Field Theory, and in scenarios probing the Higgs boson self-coupling. All the results are consistent with Standard Model expectations.

E. Almazan

S. Arbiol Val

Measurements of the Higgs boson production, fiducial and differential cross-sections in the four lepton decay channel using 164 fb $\textit{−}$1 of data collected at $$ \sqrt{s}=13.6 $$ TeV with the ATLAS detector

This paper presents the first search for non-resonant Higgs boson pair production in association with a top-quark pair ( $$ t\overline{t} HH $$ ) using proton–proton collision data collected with the ATLAS detector at the Large Hadron Collider. The data sample corresponds to an integrated luminosity of 196 fb , comprising 140 fb at a centre-of-mass energy of $$ \sqrt{s}=13 $$ TeV and 56 fb at 13.6 TeV. The search targets three distinct final states expected from $$ t\overline{t} HH $$ decays: (i) one lepton (electron or muon) with at least five $\textit{b}$-quarks, (ii) at least two $\textit{b}$-quarks accompanied by two leptons with the same electric charges or multiple leptons, and (iii) at least three $\textit{b}$-quarks with two photons. The $$ t\overline{t} HH $$ production cross-section, relative to its Standard Model prediction, is measured to be $$ {\mu}_{t\overline{t} HH}=-{3}_{-12}^{+11} $$ . This result corresponds to a 95% confidence-level upper limit of 20 times the Standard Model prediction for the $$ t\overline{t} HH $$ production cross-section, with an expected limit of 21. The Higgs effective field theory Wilson coefficient $$ {c}_{t\overline{t} HH} $$ is also constrained at the same confidence level to the range of $$ -3.9&lt;{c}_{t\overline{t} HH}&lt;3.3 $$ , compared with the expected range of $$ -4.0&lt;{c}_{t\overline{t} HH}&lt;3.5 $$ .

Search for Higgs boson pair production in association with top-quark pairs using 196 fb $\textit{−}$1 of proton–proton collision data at $$ \sqrt{s}=13 $$ and 13.6 TeV with the ATLAS detector