arXiv subjects

Adam Bzdak

Publications and source records attributed to Adam Bzdak.

At least 19 recordsLinked to original sources

arXiv2026

Bayesian extraction of TMC-free collectivity in proton-proton and proton-nucleus collisions at the LHC

A central challenge in understanding the origin of collective flow-like signatures in small collision systems calls for a reliable method to disentangle collective flow from substantial background correlations, especially those arising from transverse momentum conservation (TMC). A Bayesian inference framework is developed to integrate TMC calculations with the LHC-ATLAS data on long-range multiparticle azimuthal correlation observables, thereby extracting TMC-free collectivity in small systems. Our analysis indicates that while the TMC-free elliptic and triangular flow ($v_{2}$ and $v_{3}$) are similar, the $p$+$p$ and $p$+Pb systems exhibit distinct TMC backgrounds, TMC-flow interplay, and $v_{2}$-$v_{3}$ correlations. We demonstrate that the extracted $v_{2}$ and $v_{3}$ are well described by the measured four-particle $v_2\{4\}$ and two-particle $v_3\{2\}$ in $p$+Pb collisions, whereas these measurements systematically underestimate the TMC-free flow in $p$+$p$ collisions, due to competing contributions from TMC effects. This establishes a robust and data-driven framework, enabling a quantitatively controlled interpretation of collective signals and opening a new avenue for understanding the origin of collectivity in small collision systems.

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arXiv2026

How transverse momentum conservation breaks azimuthal correlation factorization

The breakdown of azimuthal two-particle correlation factorization, quantified by the ratios $r_2$ and $r_3$, serves as a sensitive probe of transverse-momentum-dependent flow fluctuations. While hydrodynamic models predict $r_3 \leq 1$, experimental data from CMS in p-Pb collisions exhibit $r_3 > 1$, presenting a clear puzzle. We show that transverse momentum conservation (TMC) is the key mechanism dictating this factorization breakdown in small systems. We systematically calculate the effect of TMC as a function of the momentum difference between particles across various multiplicity and momentum ranges. Our results are in quantitative agreement with CMS p-Pb data for both $r_2$ and $r_3$. A central finding is a sign rule: under TMC, the deviation $r_n - 1$ follows $\left ( - 1 \right )^{n+1} $, being negative for even and positive for odd harmonic orders $n$. This work quantifies a dominant non-flow contribution to the factorization ratios $r_n$ in small systems, and demonstrates that this kinematic effect must be subtracted or accounted for before $r_n$ can be used as a reliable probe of genuine flow fluctuations.

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arXiv2025

Acceptance dependence of factorial cumulants, long-range correlations, and the antiproton puzzle

We analyze joint factorial cumulants of protons and antiprotons in relativistic heavy-ion collisions and point out that they obey the scaling $\hat{C}_{nm}^{p,\bar{p}} \propto \langle N_p \rangle^n \langle N_{\bar{p}} \rangle^m$ as a function of acceptance when only long-range correlations are present in the system, such as global baryon conservation and volume fluctuations. This hypothesis can be directly tested experimentally without the need for corrections for volume fluctuations. We show that if correlations among protons and antiprotons are driven by global baryon conservation and volume fluctuations only, the equality $\hat{C}_{2}^{p} / \langle N_p \rangle^2 = \hat{C}_{2}^{\bar{p}} / \langle N_{\bar{p}} \rangle^2$ holds for large systems created in central collisions. We point out that the experimental data of the STAR Collaboration from phase I of RHIC beam energy scan are approximately consistent with the scaling $\hat{C}_{nm}^{p,\bar{p}} \propto \langle N_p \rangle^n \langle N_{\bar{p}} \rangle^m$, but the normalized antiproton correlations are stronger than that of protons, $-\hat{C}_{2}^{\bar{p}} / \langle N_{\bar{p}} \rangle^2 > -\hat{C}_{2}^{p} / \langle N_p \rangle^2$. Existing theoretical baselines, based on global baryon conservation and volume fluctuations, cannot explain the data, to which we refer as the antiproton puzzle. We also discuss high-order factorial cumulants which can be measured with sufficient precision within phase II of RHIC-BES.

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arXiv2025

Effect of transverse momentum conservation and flow on symmetric cumulants $sc_{2,3} \left \{ 4 \right \}$ and $sc_{2,3,4} \left \{ 6 \right \}$

Symmetric cumulants can improve our understanding of the joint probability distribution function $ P\left ( v_{m},v_{n},v_{k}, \dots,\Psi _{m},\Psi _{n},\Psi _{k},\dots \right )$, potentially offering new insights into the nature of the fluctuations of the quark-gluon plasma produced in relativistic heavy-ion collisions. In this work, the four-particle symmetric cumulants $sc_{2,3} \left \{ 4 \right \}$, six-particle symmetric cumulants $sc_{2,3,4} \left \{ 6 \right \}$, and the normalized cumulants $nsc_{2,3} \left \{ 4 \right \}$ and $nsc_{2,3,4} \left \{ 6 \right \}$ originating from transverse momentum conservation, collective flow, and the interplay between the two effects are calculated. Our results on $sc_{2,3} \left \{ 4 \right \}$ are consistent with the ATLAS data using the subevent cumulant method, facilitating a more profound understanding of the origins of the symmetric cumulant in small systems. Our results on $sc_{2,3,4} \left \{ 6 \right \}$ serve as theoretical predictions for future experimental measurements in small systems.

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arXiv2024

Symmetric cumulant $sc_{2,4} \left \{ 4 \right \}$ and asymmetric cumulant $ac_{2} \left \{ 3 \right \}$ from transverse momentum conservation and flow

Multiparticle cumulants method can be used to reveal long-range collectivity in small and large colliding systems. The four-particle symmetric cumulant $sc_{2,4} \left \{ 4 \right \}$, three-particle asymmetric cumulant $ac_{2} \left \{ 3 \right \}$, and the normalized cumulants $nsc_{2,4} \left \{ 4 \right \}$ and $nac_{2} \left \{ 3 \right \}$ 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.

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arXiv2023

Cumulants from fluctuating width of rapidity distribution

In relativistic heavy-ion collisions, the longitudinal fluctuations of the fireball density caused, e.g., by baryon stopping fluctuations result in event-by-event modifications of the shape of the proton rapidity density distribution. The multiparticle rapidity correlation functions due to the varying distribution width of the proton rapidity density in central Au+Au collisions at low energies are derived. The cumulant ratios are calculated and discussed in the context of the recent STAR Collaboration results. We find that the cumulant ratios for small width fluctuations seem to be universal.

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arXiv2022

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

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. Our results extend the findings of Refs. [1,2]. These approximations are checked to be very close to the exact results.

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arXiv2022

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

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 $n$-th factorial cumulant, the short-range correlations of more than $n$ particles are suppressed with the increasing number of particles. The recently published [1] relations between the cumulants in a finite acceptance with global baryon conservation and the grand-canonical susceptibilities are reproduced.

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arXiv2022

Multiparticle azimuthal cumulants from transverse momentum conservation and collective flow

We calculate the $n$th order of $2k$-particle azimuthal cumulants $c_n\{2k\}$ based on transverse momentum conservation (TMC) and collective flow $v_n$(n=2,3). We demonstrate that the TMC effect only leads to a nonzero $c_n\{2k\}$ with the sign of $(-1)^{nk}$ and the magnitude inversely proportional to $(N-2k)^{nk}$. The interplay between TMC and collective flow can change the signs of $c_2\{4\}$, $c_3\{2\}$ and $c_3\{4\}$ at some values of multiplicity $N$, which could provide a good probe to study the onset of collectivity and search for the substructure of proton in small colliding systems.

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arXiv2020

Factorial cumulants from global baryon number conservation

The proton, antiproton and mixed proton-antiproton factorial cumulants originating from the global conservation of baryon number are calculated analytically up to the sixth order. Our results can be directly tested in experiments.

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arXiv2020

The QCD phase diagram and statistics friendly distributions

The preliminary STAR data for proton cumulants for central collisions at \sqrt{s}=7.7 GeV are consistent with a two-component proton multiplicity distribution. We show that this two-component distribution is statistics friendly in that factorial cumulants of surprisingly high orders may be extracted with a relatively small number of events. As a consequence the two-component model can be tested and verified right now with the presently available STAR data from the first phase of the RHIC beam energy scan.

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arXiv2019

Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan

We review the present status of the search for a phase transition and critical point as well as anomalous transport phenomena in Quantum Chromodynamics (QCD), with an emphasis on the Beam Energy Scan program at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. We present the conceptual framework and discuss the observables deemed most sensitive to a phase transition, QCD critical point, and anomalous transport, focusing on fluctuation and correlation measurements. Selected experimental results for these observables together with those characterizing the global properties of the systems created in heavy ion collisions are presented. We then discuss what can be already learned from the currently available data about the QCD critical point and anomalous transport as well as what additional measurements and theoretical developments are needed in order to discover these phenomena.

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arXiv2019

Wounded nucleon, quark and quark-diquark emission functions versus experimental results from RHIC

Using the wounded nucleon, quark, and quark-diquark models, we extract the wounded source emission functions from the PHOBOS data for d+Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. We apply these models to compute charged particle multiplicity distributions as functions of pseudorapidity for p+p, p+Al, p+Au, d+Au, $^3$He+Au, Cu+Cu, Cu+Au, Au+Au, and U+U 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.

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arXiv2018

Mapping the QCD phase diagram with statistics friendly distributions

We demonstrate that the multiplicity distribution of a system located in the vicinity of a first-order phase transition can be successfully measured in terms of its factorial cumulants with a surprisingly small number of events. This finding has direct implications for the experimental search of a QCD phase transition conjectured to be located in the high baryon density region of the QCD phase diagram.

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arXiv2018

Net-baryon multiplicity distribution consistent with lattice QCD

We determine the net-baryon multiplicity distribution which reproduces all cumulants measured so far by lattice QCD. We present the dependence on the volume and temperature of this distribution. We find that for temperatures and volumes encountered in heavy ion reactions, the multiplicity distribution is very close to the Skellam distribution, making the experimental determination of it rather challenging. We further provide estimates for the statistics required to measure cumulants of the net-baryon and net-proton distributions.

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arXiv2018

Large proton cumulants from the superposition of ordinary multiplicity distributions

We construct a multiplicity distribution characterized by large factorial cumulants (integrated correlation functions) from a simple combination of two ordinary multiplicity distributions characterized by small factorial cumulants. We find that such a model, which could be interpreted as representing two event classes, reproduces the preliminary data for the proton cumulants measured by the STAR collaboration at $7.7$ GeV very well. This model then predicts very large values for the fifth and sixth order factorial cumulants, which can be tested in experiment.

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arXiv2018

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

The azimuthal cumulants, $c_2\{2\}$ and $c_2\{4\}$, originating from the global conservation of transverse momentum in the presence of hydro-like elliptic flow are calculated. We observe the sign change of $c_2\{4\}$ 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.

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arXiv2017

Wounded quark emission function at the top RHIC energy

The wounded nucleon and quark emission functions are extracted for different centralities in d+Au collisions at $\sqrt{s}=200\ \text{GeV}$ 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 $dN_{ch}/d\eta$ distributions in p+Au and $^3$He+Au collisions are presented.

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