In this work, we develop machine learning techniques to study nonperturbative scattering amplitudes. We focus on the two-to-two scattering amplitude of identical scalar particles and study a toy model where we set the double discontinuity to zero, thereby simplifying the problem numerically. Neural networks provide an efficient parameterization for scattering amplitudes, offering a flexible toolkit to describe the details of their nonperturbative structure. Combined with the bootstrap approach based on the dispersive representation of the amplitude and machine learning’s gradient descent algorithms, they offer a new method to explore the space of consistent S-matrices. We derive bounds on the values of the first two low-energy Taylor coefficients of the amplitude and characterize the resulting amplitudes that populate the allowed region. Crucially, we parallel our neural network analysis with the standard S-matrix bootstrap, both primal and dual, and observe perfect agreement across all approaches.

France

Mehmet Gümüş

Damien Leflot

Piotr Tourkine

Switzerland

Alexander Zhiboedov

The S-matrix bootstrap with neural optimizers. Part I. Zero double discontinuity

A search for leptons displaced from the primary vertex is performed with the ATLAS detector at the Large Hadron Collider. The search includes the full proton-proton collision dataset collected during Run 2 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> and a partial dataset collected during Run 3 in 2022–2023 at <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>, corresponding to integrated luminosities of <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> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>56.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, respectively. Final states with displaced electrons or muons are considered, and novel triggers introduced in Run 3 are employed that use large impact parameter tracking to reconstruct displaced tracks with low momentum. In addition, photon reconstruction and multivariate techniques are employed to broaden the sensitivity to channels with large background rates or highly displaced electrons, respectively. The results are consistent with the Standard Model background expectations and are used to set model-independent limits on the production of displaced electrons and muons. The analysis is also interpreted in the context of a gauge-mediated supersymmetry breaking model with pair-produced long-lived sleptons and a dark sector model with pair-produced chargino-like states. The results include 95% confidence level exclusions of selectrons with lifetimes from 4 ps to 60 ns and a mass of 150 GeV, and exclusions of selectrons, smuons, and staus with a lifetime of 0.3 ns for masses up to 740, 830, and 440 GeV, respectively. Dark charginos with masses up to 380 GeV are excluded for a mass difference with the neutral state of 40 GeV, and mass differences down to 17 GeV are excluded for dark charginos with a 100 GeV mass.

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

H. Abreu

Y. Abulaiti

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

F. Ahmadov

S. Ahuja

China

X. Ai

G. Aielli

A. Aikot

M. Ait Tamlihat

B. Aitbenchikh

M. Akbiyik

Sweden

T.P.A. Åkesson

A.V. Akimov

Japan

D. Akiyama

N.N. Akolkar

S. Aktas

K. Al Khoury

G.L. Alberghi

Canada

J. Albert

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

W. Alkakhi

C. Allaire

B.M.M. Allbrooke

J.S. Allen

J.F. Allen

Chile

C.A. Allendes Flores

P.P. Allport

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

Z.M.K. Alsolami

M. Alvarez Estevez

A. Alvarez Fernandez

M. Alves Cardoso

M.G. Alviggi

M. Aly

Brazil

Y. Amaral Coutinho

A. Ambler

C. Amelung

M. Amerl

C.G. Ames

D. Amidei

B. Amini

K. Amirie

Portugal

S.P. Amor Dos Santos

K.R. Amos

D. Amperiadou

S. An

V. Ananiev

C. Anastopoulos

T. Andeen

J.K. Anders

A.C. Anderson

S.Y. Andrean

A. Andreazza

S. Angelidakis

A. Angerami

A.V. Anisenkov

A. Annovi

C. Antel

E. Antipov

Search for displaced leptons 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 discovery of numerous new hadrons over the past two decades has provided unprecedented opportunities to understand the nonperturbative QCD and hadron structure. The hadronic molecule picture plays an important role in explaining these new hadrons and enriching the configurations of exotic hadronic states. In this Letter, using the model-independent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mi>K</mi></math> potential extracted from the relevant experimental data, a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><mi>D</mi><mi>K</mi></math> three-body hadronic molecule is predicted with a mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mn>4310</mn></mrow><mrow><mo>−</mo><mn>24</mn></mrow><mrow><mo>+</mo><mn>14</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. This state shows decoupling to conventional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></math> charmonia or the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></msub><msubsup><mi>D</mi><mrow><mi>s</mi><mn>0</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></math> two-body molecular state. It can be regarded as a compelling three-body hadronic molecular candidate. We further demonstrate that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mrow><mo>*</mo><mo>±</mo></mrow></msup><msup><mi>D</mi><mo>∓</mo></msup><msup><mi>K</mi><mo>+</mo></msup></math> decays could be promising channels for searching for the predicted state in future high-luminosity LHCb runs.

Tian-Wei Wu

Ming-Zhu Liu

Li-Sheng Geng

Implication of the Existence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup><mtext> </mtext><msub><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><mi>D</mi><mi>K</mi></mrow></math> Bound State on the Nature of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>2317</mn><mo stretchy="false">)</mo></mrow></math>, and a New Configuration of Exotic State

The current neutrino experiments provide an opportunity for testing the inverse see-saw mechanism through charged lepton flavor violating processes and neutrinoless double beta decay. Motivated by this, in this paper we study the <math altimg='si1.svg'><msub><mrow><mi mathvariant='bold'>S</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>&#8855;</mo><msub><mrow><mi mathvariant='bold'>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> discrete symmetry in the <math altimg='si2.svg'><mi>B</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mi>L</mi></math> gauge model where the active light neutrino mass matrix comes from the aforementioned mechanism. In this framework, the effect of complex vacuum expectation values of the Higgs doublets on the fermion masses is explored and, under certain assumptions on the Yukawa couplings, we find that the neutrino mixing is controlled by the Cobimaximal pattern, but a sizeable deviation from the charged lepton sector breaks the well known predictions on the atmospheric angle ( <math altimg='si3.svg'><msup><mrow><mn>45</mn></mrow><mrow><mo>&#8728;</mo></mrow></msup></math>) and the Dirac CP-violating phase ( <math altimg='si4.svg'><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><msup><mrow><mn>90</mn></mrow><mrow><mo>&#8728;</mo></mrow></msup></math>). In addition, due to the presence of heavy neutrinos at the TeV scale, charged lepton flavor violation (CLFV) and neutrinoless double beta decay get notable contributions. Analytical formulae for these observables are obtained, and then a numerical calculation allows us to fit quite well the lepton mixing for the normal and inverted hierarchies, however, the branching ratios decay values for CLFV disfavor the latter one. Along with this, the region of parameter space for the <math altimg='si5.svg'><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub></math> effective neutrino mass lies below the GERDA bounds for both the normal and inverted hierarchies. On the other hand, with a particular benchmark, the quark mass matrices are found to have textures that allow us to fit with great accuracy the CKM mixing matrix.

Mexico

Juan Carlos Gómez-Izquierdo

Catalina Espinoza

Lucia E. Gutiérrez Luna

Myriam Mondragón

Inverse see-saw mechanism with <bold>S</bold> <inf>3</inf> flavor symmetry

A measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>W</mi></mrow><mi>Z</mi><mi>γ</mi></mrow></math> triboson production cross section is presented. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy 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> recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>138</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The analysis focuses on the final state with three charged leptons, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>±</mo></mrow></msup></mrow><mi>ν</mi><mrow><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup></mrow></mrow></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo><mo>=</mo><mi>e</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>μ</mi></mrow></math>, accompanied by an additional photon. The observed (expected) significance of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>W</mi></mrow><mi>Z</mi><mrow><mi>γ</mi></mrow></math> signal is 5.4 (3.8) standard deviations. The cross section is measured in a fiducial region, where events with an ℓ originating from a tau lepton decay are excluded, to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.48</mn><mo>±</mo><mn>1.11</mn><mtext> </mtext><mtext> </mtext><mi>fb</mi></math>, which is compatible with the prediction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3.69</mn><mo>±</mo><mn>0.24</mn><mtext> </mtext><mtext> </mtext><mi>fb</mi></math> at next-to-leading order in quantum chromodynamics. Exclusion limits are set on anomalous quartic gauge couplings and on the production cross sections of massive axionlike particles.

Armenia

V. Chekhovsky

A. Hayrapetyan

V. Makarenko

A. Tumasyan

Austria

W. Adam

J.W. Andrejkovic

L. Benato

T. Bergauer

S. Chatterjee

K. Damanakis

M. Dragicevic

P.S. Hussain

M. Jeitler

N. Krammer

A. Li

D. Liko

I. Mikulec

J. Schieck

R. Schöfbeck

D. Schwarz

M. Sonawane

W. Waltenberger

C.E. Wulz

Belgium

T. Janssen

H. Kwon

T. Van Laer

P. Van Mechelen

N. Breugelmans

J. D’Hondt

S. Dansana

A. De Moor

M. Delcourt

F. Heyen

Y. Hong

S. Lowette

I. Makarenko

D. Müller

S. Tavernier

M. Tytgat

G.P. Van Onsem

S. Van Putte

D. Vannerom

B. Bilin

B. Clerbaux

A.K. Das

I. De Bruyn

G. De Lentdecker

H. Evard

L. Favart

P. Gianneios

A. Khalilzadeh

Observation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi><mi>Z</mi><mi>γ</mi></math> production and constraints on new physics scenarios in proton-proton collisions 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>