The beyond-the-standard-model scenario presented in this work is motivated by the observations of neutrino masses, the anomalous magnetic moments of the electron and muon, and dark matter in the Universe. We explain these observations by extending the standard model with two generations of vector-like fermions and an inert scalar doublet, all of which are odd under a $Z_2$ symmetry. The light neutrino masses and mixings are generated radiatively while maintaining consistency with bounds on lepton flavor violation. Loop diagrams featuring the same fields also explain the anomalous magnetic moments. Similarly, the correct dark matter relic abundance is reproduced without conflicting with direct detection constraints, or those from big bang nucleosynthesis or cosmic microwave background observations. Finally, prospective signatures at the LHC are discussed.

India

Vandana Sahdev

Neutrino masses, anomalous magnetic moments and dark matter with vector-like fermions and an inert scalar doublet * V.S. acknowledges the support from research grant no. CRG/2018/004889 of the SERB, India; T.R. Seshadri for providing resources during the initial stages of the work; and Brajesh Choudhary for providing access to computers bought under the aegis of Grant No. SR-MF/PS-0212014-DUB (G) of the DST (India)

This Letter presents a combination of searches for Higgs boson pair (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>H</mi></math>) production performed by the ATLAS and CMS Collaborations using proton-proton collision datasets recorded at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> during the Large Hadron Collider Run 2, corresponding to integrated luminosities ranging between 126 and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>140</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The upper limit at the 95% confidence level on the total <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>H</mi></math> signal strength, defined as the ratio of the measured cross section to the standard model (SM) prediction, corresponds to 2.5, with an expected value of 1.7 (2.8) assuming the absence (presence) of the SM <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>H</mi></math> signal. The strength of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>H</mi></math> signal is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>0.8</mn><mrow><mo>−</mo><mn>0.7</mn></mrow><mrow><mo>+</mo><mn>0.9</mn></mrow></msubsup></math> relative to the SM prediction. The observed significance is found to be 1.1 standard deviations whereas 1.3 are expected for the SM <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>H</mi></math> signal. Constraints are set on the Higgs boson trilinear self-coupling and on the couplings of two Higgs bosons to two vector bosons, both normalized to the SM predictions and denoted as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>κ</mi><mi>λ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>κ</mi><mrow><mn>2</mn><mi>V</mi></mrow></msub></math>, respectively. The observed individual constraints at the 95% confidence level are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>−</mo><mn>0.71</mn><mo>&lt;</mo><msub><mrow><mi>κ</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>&lt;</mo><mn>6.1</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.73</mn><mo>&lt;</mo><msub><mi>κ</mi><mrow><mn>2</mn><mi>V</mi></mrow></msub><mo>&lt;</mo><mn>1.3</mn></math>, while the expected constraints assuming the presence of the SM <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>H</mi></math> signal are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>1.3</mn><mo>&lt;</mo><msub><mi>κ</mi><mi>λ</mi></msub><mo>&lt;</mo><mn>6.7</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.66</mn><mo>&lt;</mo><msub><mi>κ</mi><mrow><mn>2</mn><mi>V</mi></mrow></msub><mo>&lt;</mo><mn>1.4</mn></math>.

France

G. Aad

Norway

E. Aakvaag

United States

B. Abbott

United Arab Emirates

S. Abdelhameed

Germany

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

B. Aitbenchikh

Sweden

T.P.A. Åkesson

Japan

D. Akiyama

N.N. Akolkar

S. Aktas

G.L. Alberghi

Canada

J. Albert

Switzerland

U. Alberti

P. Albicocco

G.L. Albouy

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

Z.M.K. Alsolami

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

Portugal

S.P. Amor Dos Santos

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

Combination of ATLAS and CMS Searches for Higgs Boson Pair Production at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>

This Letter presents a measurement of prompt charged-particle production in proton-oxygen interactions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><msub><mi>s</mi><mi>NN</mi></msub></msqrt><mo>=</mo><mn>9.62</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> center-of-mass energy with the ATLAS detector, corresponding to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>634</mn><mtext> </mtext><mtext> </mtext><mi>μ</mi><mrow><msup><mrow><mi mathvariant="normal">b</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></mrow></math> of integrated luminosity. A total of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>246</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> selected events have at least one track with transverse momentum <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub><mo>&gt;</mo><mn>500</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and pseudorapidity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>η</mi><mo stretchy="false">|</mo><mo>&lt;</mo><mn>2.5</mn></math>. The measured fiducial proton-oxygen cross section is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>σ</mi><mrow><mi>fid</mi><mo>.</mo></mrow><mrow><mi>p</mi><mi mathvariant="normal">O</mi></mrow></msubsup><mo>=</mo><mn>396</mn><mo>±</mo><mn>6</mn><mo stretchy="false">(</mo><mrow><mi>exp</mi><mo>.</mo></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>9</mn><mo stretchy="false">(</mo><mrow><mi>lumi</mi><mo>.</mo></mrow><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>mb</mi></math> and the extrapolated inelastic proton-air cross section is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>σ</mi><mrow><mi>inel</mi><mo>.</mo></mrow><mrow><mi>p</mi><mo>+</mo><mi>air</mi></mrow></msubsup><mo>=</mo><mn>406</mn><mo>±</mo><mn>6</mn><mo stretchy="false">(</mo><mrow><mi>exp</mi><mo>.</mo></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>9</mn><mo stretchy="false">(</mo><mrow><mi>lumi</mi><mo>.</mo></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>28</mn><mo stretchy="false">(</mo><mrow><mi>th</mi><mo>.</mo></mrow><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>mb</mi></math>. Measurements of charged-particle multiplicity, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> distributions are an order-of-magnitude more precise than differences between hadronic-interaction models. These results enable improved modeling of cosmic-ray air showers, which is important for astroparticle physics.

J. Ackerschott

M. Apicella

C. Appelt

A. Apyan

M. Arampatzi

Measurement of Charged-Particle Production in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><msub><mi>s</mi><mrow><mi>NN</mi></mrow></msub></msqrt><mo>=</mo><mn>9.62</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> Proton-Oxygen Collisions as a Probe of Cosmic-Ray Air Showers with the ATLAS Detector

Entanglement is a key property of quantum systems. In this Letter the first measurements of quantum entanglement between spins in pairs of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> bosons are reported, using proton-proton collision data from the Large Hadron Collider (LHC) at center-of-mass energies of 13 and 13.6 TeV, recorded with the ATLAS detector. Measurements of angular observables sensitive to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><msup><mi>Z</mi><mo>*</mo></msup></math> spin-density-matrix elements in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>H</mi><mo stretchy="false">→</mo><mi>Z</mi><msup><mrow><mi>Z</mi></mrow><mrow><mo>*</mo></mrow></msup><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></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> process yield coefficients <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>1</mn></mrow></msub><mo>=</mo><mo>−</mo><mn>0.71</mn><mo>±</mo><mn>0.45</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>2</mn></mrow></msub><mo>=</mo><mn>0.08</mn><mo>±</mo><mn>0.44</mn></math>, consistent with their Standard Model predictions. A complementary hypothesis test using the full angular distribution, and relying on several Standard Model assumptions in the decays, provides substantially higher sensitivity to quantum correlations and disfavors the separable-state hypothesis at a significance of 4.7 standard deviations (expected <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4.9</mn><mi>σ</mi></math>) relative to the entangled Standard Model hypothesis. These results provide strong evidence of quantum entanglement between massive bosons (spin qutrits) at the electroweak scale.

J.A. Aguilar Saavedra

Measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>-Boson Pair Entanglement in Decays of Higgs Bosons at the ATLAS Experiment

A search is performed for the electroweak pair production of charginos and associated production of a chargino and neutralino, each of which decays through an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-parity-violating coupling into a lepton and a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>, or Higgs boson. This search targets the Higgs boson decay channel of the charginos and neutralinos, using events with three or more <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-tagged jets and one or two electrons or muons. The analyzed data corresponds 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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>56</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of proton-proton collision data produced by the Large Hadron Collider at center-of-mass energies of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13.6</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, respectively, collected by the ATLAS experiment between 2015 and 2023. The data are found to be consistent with predictions from the Standard Model. The results are interpreted as limits at 95% confidence level on model-independent cross sections for processes beyond the Standard Model. Limits are also set on the production of charginos and neutralinos for a minimal supersymmetric Standard Model with an additional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> gauge symmetry that is spontaneously broken. Charginos and neutralinos with masses between 150 GeV and 1100 GeV are excluded at 95% confidence level for a scenario in which they decay via Higgs bosons, assuming equal decay branching fractions to each lepton flavor. Additional limits on chargino and neutralino production are derived for flavor-specific decay scenarios where the charginos decay into a single lepton flavor.

Search for charginos and neutralinos with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-parity violating decays in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> and 13.6 TeV <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions with the ATLAS detector

The Lorentz-contracted electromagnetic fields of the ions in ultra-relativistic heavy-ion collisions generate intense quasi-real photon fluxes. These lead to photon-induced interactions that are observed in ultra-peripheral collisions (UPCs), such as vector meson and lepton-pair production. The high photon flux also enables the occurrence of multiple photon-induced processes in a single collision. Presented is the first measurement of the coincident production of <math altimg='si2.svg'><mrow><mi>&#947;</mi><mi>&#947;</mi><mo>&#8594;</mo><msup><mi>&#956;</mi><mo>+</mo></msup><msup><mi>&#956;</mi><mo>&#8722;</mo></msup></mrow></math> and <math altimg='si4.svg'><mrow><mi>&#947;</mi><mo linebreak='goodbreak'>+</mo><mi>A</mi><mo>&#8594;</mo><msup><mi>&#961;</mi><mn>0</mn></msup><mo linebreak='goodbreak'>+</mo><mi>A</mi></mrow></math> in UPC Pb+Pb collisions at centre-of-mass energies of 5.02 TeV and 5.36 TeV with the ATLAS detector at the Large Hadron Collider. The coincident <italic>&#961;</italic> 0 is identified via its decay into a <math altimg='si5.svg'><mrow><msup><mi>&#960;</mi><mo>+</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup></mrow></math> pair, with the selected <math altimg='si5.svg'><mrow><msup><mi>&#960;</mi><mo>+</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup></mrow></math> sample also containing the non-resonant continuum contribution. The rate of the coincident process relative to the exclusive <math altimg='si2.svg'><mrow><mi>&#947;</mi><mi>&#947;</mi><mo>&#8594;</mo><msup><mi>&#956;</mi><mo>+</mo></msup><msup><mi>&#956;</mi><mo>&#8722;</mo></msup></mrow></math> process is measured differentially in intervals of forward event activity, quantified by the Zero Degree Calorimeters. The relative rate of coincident <italic>&#961;</italic> 0 production, including non-resonant <math altimg='si5.svg'><mrow><msup><mi>&#960;</mi><mo>+</mo></msup><msup><mi>&#960;</mi><mo>&#8722;</mo></msup></mrow></math> contributions, is measured to be <math altimg='si6.svg'><mrow><mrow><mo>(</mo><mn>9.3</mn><mspace width='0.16em' /><mo>&#177;</mo><mn>0.4</mn><mspace width='0.16em' /><mrow><mo mathvariant='normal'>(</mo><mtext>stat</mtext><mo>.</mo><mo>)</mo></mrow><mspace width='0.16em' /><mo>&#177;</mo><mn>0.2</mn><mspace width='0.16em' /><mrow><mo mathvariant='normal'>(</mo><mtext>syst</mtext><mo>.</mo><mo>)</mo></mrow><mo>)</mo></mrow><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>3</mn></mrow></msup></mrow></math>, summed over forward event activity. Correlations between the dimuon kinematic properties, such as its mass, and the coincident <italic>&#961;</italic> 0 meson production rate, are also presented. These measurements confirm the presence of multi photon-induced processes in UPC collisions, and can provide new insight into the impact parameter dependence of photon-induced vector meson production.

Y. Abulaiti

M. Akbiyik

A.V. Akimov

W. Alkakhi

P.P. Allport

C.G. Ames

D. Amidei

K.R. Amos

Measurement of coincident photon-initiated processes in ultra-peripheral Pb+Pb collisions with the ATLAS detector

A search for quantum black holes in electron+jet or muon+jet final states with high invariant mass is performed. The analysis uses data from <math altimg='si13.svg'><mrow><msqrt><mi>s</mi></msqrt><mo linebreak='goodbreak'>=</mo><mn>13.6</mn><mspace width='0.33em' /><mtext>TeV</mtext></mrow></math> <italic>pp</italic> collisions recorded by the ATLAS detector between 2022 and 2024 during Run 3 of the Large Hadron Collider, corresponding to an integrated luminosity of <math altimg='si14.svg'><mrow><mn>164</mn><mspace width='0.33em' /><msup><mrow><mtext>fb</mtext></mrow><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></mrow></math>. This search is strongly motivated by a dramatic increase of the production cross-section by up to an order of magnitude for the highest masses considered, thanks to the small increase of 0.6&#8201;TeV in centre-of-mass energy between Run 2 and Run 3. No significant excess above the Standard Model background is observed, and 95% CL upper limits are set on the production cross-section times branching ratio in several benchmark models, reaching a mass scale of 9.4&#8201;TeV. These represent the strongest exclusion limits to date on quantum black hole production.

S.J. Arbiol Val

Search for quantum black holes in lepton+jet final states using proton–proton collisions at <math altimg='si13.svg'><mrow><msqrt><mi>s</mi></msqrt><mo linebreak='goodbreak'>=</mo><mn>13.6</mn><mspace width='0.33em' /><mtext>TeV</mtext></mrow></math> with the ATLAS detector

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.

Arnau Beltran

Alessandro Conigli

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>.

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