<p>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.</p>

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

J.A. Aguilar Saavedra

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

Switzerland

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

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

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

<p>We report the precise energy scan measurement of the cross section line shape of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>. The analysis is based on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collision data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>495</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>pb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> collected with the BESIII detector at BEPCII. By analyzing the cross section line shape, we extract the relative phase <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Φ</mi></math> between the strong and electromagnetic amplitudes of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> resonance, a fundamental parameter in charmonium physics, based on the assumption that the relative phase between the electromagnetic amplitude of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> resonance and the continuum is zero. Two distinct solutions for the branching fraction <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> are observed: a constructive interference solution with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo>=</mo><mo stretchy="false">(</mo><mn>7.49</mn><mo>±</mo><mn>0.41</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Φ</mi><mo>=</mo><mo stretchy="false">(</mo><mn>110.1</mn><mo>±</mo><mn>6.7</mn><mo stretchy="false">)</mo><mo>°</mo></mrow></math>, and a destructive interference solution with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo>=</mo><mo stretchy="false">(</mo><mn>10.94</mn><mo>±</mo><mn>0.48</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Φ</mi><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>106.8</mn><mo>±</mo><mn>5.7</mn><mo stretchy="false">)</mo><mo>°</mo></math>. A significant correlation between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Φ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi></math> is established, demonstrating that interference effects must be taken into account in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> branching fraction measurements. Additionally, the first results for both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> strong form factor, which characterizes the strong coupling between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>, and the energy-dependent electromagnetic form factor of the charged kaon in this energy region are reported.</p>

M. Ablikim

Russia

M.N. Achasov

P. Adlarson

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

Y. Ban

H.R. Bao

X.L. Bao

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M.B. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

S.A. Cetin

X.Y. Chai

J.F. Chang

T.T. Chang

G.R. Che

Y.Z. Che

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.M. Chen

T. Chen

W. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.K. Chen

J. Cheng

L.N. Cheng

South Korea

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

H.L. Dai

J.P. Dai

X.C. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denisenko

M. Destefanis

First Energy-Scan Measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> around the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> Resonance