Differential two-particle normalized cumulants ( $$R_2$$ ) and transverse momentum correlations ( $$P_2$$ ) are measured as a function of the relative pseudorapidity and azimuthal angle difference $$( \Delta \eta , \Delta \varphi )$$ of charged particle pairs in minimum bias pp collisions at $$\sqrt{\textit{s}}$$ = 13 TeV. The measurements use charged hadrons in the pseudorapidity region of $$|\eta | < 0.8$$ and the transverse momentum range 0.2 $$< \textit{p}_{\mathrm T} < $$ 2.0 $$\textrm{GeV}/\textit{c}$$ in order to focus on soft multiparticle interactions and to complement prior measurements of these correlation functions in p–Pb and Pb–Pb collisions. The correlation functions are reported for both unlike-sign and like-sign pairs and their charge-independent and charge-dependent combinations. Both the $$R_2$$ and $$P_2$$ measured in pp collisions exhibit features qualitatively similar to those observed in p–Pb and Pb–Pb collisions. The $$\Delta \eta $$ and $$\Delta \varphi $$ root mean square widths of the near-side peak of the correlation functions are evaluated and compared with those observed in p–Pb and Pb–Pb collisions and show smooth evolution with the multiplicity of charged particles produced in the collision. The comparison of the measured correlation functions with predictions from PYTHIA8 shows that this model qualitatively captures their basic structure and characteristics but feature important differences. In addition, the $$R_2^{\textrm{CD}}$$ is used to determine the charge balance function of hadrons produced within the detector acceptance of the measurements. The integral of the balance function is found to be compatible with those reported by a previous measurement in Pb–Pb collisions.

France

S. Acharya

India

A. Agarwal

Switzerland

G. Aglieri Rinella

Italy

L. Aglietta

M. Agnello

N. Agrawal

Z. Ahammed

S. Ahmad

South Korea

S. Ahn

Slovakia

I. Ahuja

A. Akindinov

Germany

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

China

H. Alfanda

Mexico

R. Alfaro Molina

B. Ali

A. Alici

United States

N. Alizadehvandchali

A. Alkin

Norway

J. Alme

G. Alocco

T. Alt

A. Altamura

I. Altsybeev

J. Alvarado

M. Anaam

Romania

C. Andrei

United Kingdom

N. Andreou

A. Andronic

E. Andronov

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

L. Aphecetche

H. Appelshäuser

C. Arata

S. Arcelli

R. Arnaldi

Brazil

J. Arneiro

I. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

D. Averyanov

M. Azmi

Japan

H. Baba

A. Badalà

J. Bae

Y. Bae

Y. Baek

X. Bai

R. Bailhache

Y. Bailung

R. Bala

A. Balbino

A. Baldisseri

Poland

B. Balis

Z. Banoo

V. Barbasova

F. Barile

L. Barioglio

Greece

M. Barlou

B. Barman

Hungary

G. Barnaföldi

L. Barnby

E. Barreau

V. Barret

L. Barreto

C. Bartels

K. Barth

E. Bartsch

N. Bastid

Sweden

S. Basu

G. Batigne

D. Battistini

B. Batyunya

D. Bauri

Peru

J. Alba

Denmark

I. Bearden

C. Beattie

P. Becht

D. Behera

I. Belikov

A. Bell Hechavarria

F. Bellini

R. Bellwied

S. Belokurova

L. Beltran

Y. Beltran

G. Bencedi

A. Bensaoula

S. Beole

Y. Berdnikov

A. Berdnikova

L. Bergmann

M. Besoiu

L. Betev

Measurements of differential two-particle number and transverse momentum correlation functions in pp collisions at $$\sqrt{\textit{s}}$$ = 13 TeV

<p>Using <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 collected with the BESIII detector operating at the Beijing electron positron collider, the cross section 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>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mi>h</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> is measured at 59 points with center-of-mass energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math> ranging from 4.009 to 4.950 GeV with a total integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>22.2</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The cross section between 4.3 and 4.45 GeV exhibits a plateaulike shape and drops sharply around 4.5 GeV, which cannot be described by two resonances only. Three coherent Breit-Wigner functions are used to parametrize the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math>-dependent cross section line shape. The masses and widths are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><msubsup><mrow><mn>4223.6</mn></mrow><mrow><mo>−</mo><mn>3.7</mn><mo>−</mo><mn>2.9</mn></mrow><mrow><mo>+</mo><mn>3.6</mn><mo>+</mo><mn>2.6</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>58.5</mn></mrow><mrow><mo>−</mo><mn>11.4</mn><mo>−</mo><mn>6.5</mn></mrow><mrow><mo>+</mo><mn>10.8</mn><mo>+</mo><mn>6.7</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mrow><mn>4327.4</mn></mrow><mrow><mo>−</mo><mn>18.8</mn><mo>−</mo><mn>9.3</mn></mrow><mrow><mo>+</mo><mn>20.1</mn><mo>+</mo><mn>10.7</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Γ</mi><mn>2</mn></msub><mo>=</mo><mspace linebreak="goodbreak"></mspace><mo stretchy="false">(</mo><msubsup><mn>244.1</mn><mrow><mo>−</mo><mn>27.1</mn><mo>−</mo><mn>18.3</mn></mrow><mrow><mo>+</mo><mn>34.0</mn><mo>+</mo><mn>24.2</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mn>3</mn></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mn>4467.4</mn><mrow><mo>−</mo><mn>5.4</mn><mo>−</mo><mn>2.7</mn></mrow><mrow><mo>+</mo><mn>7.2</mn><mo>+</mo><mn>3.2</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><msup><mi>c</mi><mn>2</mn></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Γ</mi><mn>3</mn></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mn>62.8</mn><mrow><mo>−</mo><mn>14.4</mn><mo>−</mo><mn>7.0</mn></mrow><mrow><mo>+</mo><mn>19.2</mn><mo>+</mo><mn>9.9</mn></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The first uncertainties are statistical and the second are systematic. The inclusion of the relatively narrower third component proves crucial for reproducing the drop at around 4.5 GeV. The statistical significance of the three-resonance assumption over the two-resonance assumption is greater than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5</mn><mi>σ</mi></math>.</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

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. 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

Türkiye

S.A. Cetin

X.Y. Chai

J.F. 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.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z.J. Chen

Z.K. Chen

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.X. Ding

J. Dong

Observation of Three Resonant Structures in the Cross Section of <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><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msub><mi>h</mi><mi>c</mi></msub></math>