Multiparticle cumulants method can be used to reveal long-range collectivity in small and large colliding systems. The four-particle symmetric cumulant <math><mrow><mi>s</mi><msub><mi>c</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub><mrow><mo>{</mo><mn>4</mn><mo>}</mo></mrow></mrow></math>, three-particle asymmetric cumulant <math><mrow><mi>a</mi><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>{</mo><mn>3</mn><mo>}</mo></mrow></mrow></math>, and the normalized cumulants <math><mrow><mi>n</mi><mi>s</mi><msub><mi>c</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub><mrow><mo>{</mo><mn>4</mn><mo>}</mo></mrow></mrow></math> and <math><mrow><mi>n</mi><mi>a</mi><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>{</mo><mn>3</mn><mo>}</mo></mrow></mrow></math> from the transverse momentum conservation and flow are calculated. The interplay between the two effects is also investigated. Our results are in a good agreement with the recent ATLAS measurements of multiparticle azimuthal correlations with the subevent cumulant method, which provides insight into the origin of collective flow in small systems.

China

Jia-Lin Pei

Guo-Liang Ma

Poland

Adam Bzdak

Symmetric cumulant <math><mrow><mi>s</mi><msub><mi>c</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub><mrow><mo>{</mo><mn>4</mn><mo>}</mo></mrow></mrow></math> and asymmetric cumulant <math><mrow><mi>a</mi><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>{</mo><mn>3</mn><mo>}</mo></mrow></mrow></math> from transverse momentum conservation and flow

We calculate the baryon number cumulants within acceptance with short-range correlations and global baryon number conservation in terms of cumulants in the whole system without baryon conservation. We extract leading and next-to-leading order terms of the large baryon number limit approximation. These approximations are checked to be very close to the exact results.

Michał Barej

Cumulants from short-range correlations and baryon number conservation at next-to-leading order

We calculate the baryon factorial cumulants assuming arbitrary short-range correlations and the global baryon number conservation. The general factorial cumulant generating function is derived. Various relations between factorial cumulants subjected to baryon number conservation and the factorial cumulants without this constraint are presented. We observe that for <math><mi>n</mi><mi>th</mi></math> factorial cumulant the short-range correlations of more than <math><mi>n</mi></math> particles are suppressed with increasing number of particles. The recently published [V. Vovchenko et al., Phys. Lett. B 811, 135868 (2020)] relations between the cumulants in a finite acceptance with global baryon conservation and the grand-canonical susceptibilities are reproduced.

Factorial cumulants from short-range correlations and global baryon number conservation

The unitarily extended Bialas–Bzdak model of elastic proton–proton scattering is applied, without modifications, to describe the differential cross-section of elastic proton–antiproton collisions in the TeV energy range, and to extrapolate these differential cross-sections to LHC energies. In this model-dependent study we find that the differential cross-sections of elastic proton–proton collision data at 2.76 and 7 TeV energies differ significantly from the differential cross-section of elastic proton–antiproton collisions extrapolated to these energies. The elastic proton–proton differential cross-sections, extrapolated to 1.96 TeV energy with the help of this extended Bialas–Bzdak model do not differ significantly from that of elastic proton–antiproton collisions, within the theoretical errors of the extrapolation. Taken together these results provide a model-dependent, but statistically significant evidence for a crossing-odd component of the elastic scattering amplitude at the at least 7.08 sigma level. From the reconstructed Odderon and Pomeron amplitudes, we determine the  $$\sqrt{s}$$  <math> <msqrt> <mi>s</mi> </msqrt> </math>   dependence of the corresponding total and differential cross-sections.

Hungary

T. Csörgő

I. Szanyi

Observation of Odderon effects at LHC energies: a real extended Bialas–Bzdak model study

Using the wounded nucleon, quark, and quark-diquark models, we extract the wounded source emission functions from the PHOBOS data for <math><mrow><mi>d</mi><mo>+</mo><mi>Au</mi></mrow></math> collisions at <math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV. We apply these functions to compute charged particle multiplicity distributions as functions of pseudorapidity for <math><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow><mo>,</mo><mo> </mo><mrow><mi>p</mi><mo>+</mo><mi>Al</mi></mrow><mo>,</mo><mo> </mo><mrow><mi>p</mi><mo>+</mo><mi>Au</mi></mrow><mo>,</mo><mo> </mo><mrow><mi>d</mi><mo>+</mo><mi>Au</mi></mrow><mo>,</mo><mo> </mo><mrow><mmultiscripts><mi>He</mi><mprescripts></mprescripts><none></none><mn>3</mn></mmultiscripts><mo>+</mo><mi>Au</mi></mrow><mo>,</mo><mo> </mo><mrow><mi>Cu</mi><mo>+</mo><mi>Cu</mi></mrow><mo>,</mo><mo> </mo><mrow><mi>Cu</mi><mo>+</mo><mi>Au</mi></mrow><mo>,</mo><mo> </mo><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></math>, and <math><mrow><mi>U</mi><mo>+</mo><mi>U</mi></mrow></math> collisions at the same energy and compare them with experimental data from the PHOBOS and PHENIX Collaborations. In symmetric collisions of heavy nuclei, the obtained distributions differ among the tested models. On the other hand, in asymmetric collisions, all three models give essentially the same distributions. The wounded quark-diquark and quark models are in reasonable agreement with data for all the investigated systems.

Paweł Gutowski

Wounded nucleon, quark, and quark-diquark emission functions versus experimental results from the BNL Relativistic Heavy Ion Collider at <math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV

The longitudinal proton-proton femtoscopy (Hanbury Brown–Twiss) correlation function, based on the idea that in a heavy-ion collision at <math><mrow><msqrt><mi>s</mi></msqrt><mo>≲</mo><mn>20</mn><mrow><mspace width="0.16em"></mspace><mi>GeV</mi></mrow></mrow></math> stopped protons are likely to be separated in configuration space, is evaluated. It shows a characteristic oscillation which appears sufficiently pronounced to be accessible in experiment. The proposed measurement is essential for estimating the baryon density in the central rapidity region and can be also viewed as an (almost) direct verification of the Lorentz contraction of the fast-moving nucleus.

Andrzej Bialas

United States

Volker Koch

Femtoscopy of stopped protons

The azimuthal cumulants, <math><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>{</mo><mn>2</mn><mo>}</mo></math> and <math><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>{</mo><mn>4</mn><mo>}</mo></math>, originating from the global conservation of transverse momentum in the presence of hydro-like elliptic flow are calculated. We observe the sign change of <math><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>{</mo><mn>4</mn><mo>}</mo></math> for small number of produced particles. This is in a qualitative agreement with the recent ATLAS measurement of multi-particle azimuthal correlations with the subevent cumulant method.

A remark on the sign change of the four-particle azimuthal cumulant in small systems

The wounded nucleon and quark emission functions are extracted for different centralities in <math><mi>d</mi><mo>+</mo><mi>Au</mi></math> collisions at <math><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn><mspace width="4pt"></mspace><mtext>GeV</mtext></mrow></math> using Monte Carlo simulations and experimental data. The shape of the emission function depends on centrality in the wounded nucleon model, whereas it is practically universal (within uncertainties) in the wounded quark model. Predictions for <math><mrow><mi>d</mi><msub><mi>N</mi><mrow><mi>c</mi><mi>h</mi></mrow></msub><mo>/</mo><mi>d</mi><mi>η</mi></mrow></math> distributions in <math><mi>p</mi><mo>+</mo><mi>Au</mi></math> and <math><mmultiscripts><mi>He</mi><mprescripts></mprescripts><none></none><mn>3</mn></mmultiscripts><mo>+</mo><mi>Au</mi></math> collisions are presented.

Wounded-quark emission function at the top energy available at the BNL Relativistic Heavy Ion Collider

In this note, using the simplified colour string model, we study the configuration space distribution of stopped nucleons in heavy-ion collisions. Given this model, we find that the stopped nucleons from the target and the projectile end up separated from each other by a distance which increases with the collision energy. In consequence, for the center-of-mass energies larger than 6 or 10~GeV (depending on the details of the model), it appears that the stopped nucleons are not necessarily in thermal and chemical equilibrium, and the net-baryon density reached is likely not much higher than that already present in the colliding nuclei.

Stopped Nucleons in Configuration Space

We calculate the <math><mi>k</mi></math>-particle <math><mo>(</mo><mrow><mi>k</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>8</mn></mrow><mo>)</mo></math> azimuthal cumulants resulting from the conservation of transverse momentum. We find that <math><mrow><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>{</mo><mi>k</mi><mo>}</mo></mrow><mo>&gt;</mo><mn>0</mn></mrow></math> and, depending on the transverse momenta, <math><mrow><msub><mi>c</mi><mn>2</mn></msub><mrow><mo>{</mo><mi>k</mi><mo>}</mo></mrow></mrow></math> can reach substantial values even for a relatively large number of particles. The impact of our results on the understanding of the onset of collectivity in small systems is emphasized.