DUALITY OF DYNAMICAL AND THERMAL DESCRIPTIONS IN PARTON DISTRIBUTION FUNCTIONS

We suggest a duality between the standard (dynamical) and statistical distributions of partons in the nucleons. The temperature parameter entering into the statistical form for the quark distributions is estimated. It is shown that the freeze-out temperature in central heavy-ion collisions at zero chemical potential or the effective width of the energy distribution of pions has a similar value which was estimated in this paper for the valence massless quarks in a free nucleon.

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Coupled Boltzmann transport equations of heavy quarks and quarkonia in quark-gluon plasma

Journal of High Energy Physics ◽

10.1007/jhep01(2021)046 ◽

2021 ◽

Vol 2021 (1) ◽

Cited By ~ 1

Author(s):

Xiaojun Yao ◽

Weiyao Ke ◽

Yingru Xu ◽

Steffen A. Bass ◽

Berndt Müller

Keyword(s):

Quark Gluon Plasma ◽

Heavy Ion ◽

Gluon Plasma ◽

Transport Equations ◽

Distribution Functions ◽

Heavy Flavor ◽

Boltzmann Transport ◽

Coupled Transport ◽

Parton Distribution Functions ◽

Ion Collisions

Abstract We develop a framework of coupled transport equations for open heavy flavor and quarkonium states, in order to describe their transport inside the quark-gluon plasma. Our framework is capable of studying simultaneously both open and hidden heavy flavor observables in heavy-ion collision experiments and can account for both, uncorrelated and correlated recombination. Our recombination implementation depends on real-time open heavy quark and antiquark distributions. We carry out consistency tests to show how the interplay among open heavy flavor transport, quarkonium dissociation and recombination drives the system to equilibrium. We then apply our framework to study bottomonium production in heavy-ion collisions. We include ϒ(1S), ϒ(2S), ϒ(3S), χb(1P) and χb(2P) in the framework and take feed-down contributions during the hadronic gas stage into account. Cold nuclear matter effects are included by using nuclear parton distribution functions for the initial primordial heavy flavor production. A calibrated 2 + 1 dimensional viscous hydrodynamics is used to describe the bulk QCD medium. We calculate both the nuclear modification factor RAA of all bottomonia states and the azimuthal angular anisotropy coefficient v2 of the ϒ(1S) state and find that our results agree reasonably with experimental measurements. Our calculations indicate that correlated cross-talk recombination is an important production mechanism of bottomonium in current heavy-ion experiments. The importance of correlated recombination can be tested experimentally by measuring the ratio of RAA(χb(1P)) and RAA(ϒ(2S)).

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Z-boson production in p-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ = 8.16 TeV and Pb-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ = 5.02 TeV

Journal of High Energy Physics ◽

10.1007/jhep09(2020)076 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

S. Acharya ◽

◽

D. Adamová ◽

A. Adler ◽

J. Adolfsson ◽

...

Keyword(s):

Z Boson ◽

Decay Channel ◽

Theoretical Calculations ◽

Center Of Mass ◽

Laboratory Frame ◽

Distribution Functions ◽

Boson Production ◽

Free Nucleon ◽

Parton Distribution Functions ◽

Nuclear Modifications

Abstract Measurement of Z-boson production in p-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 8.16 TeV and Pb-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 5.02 TeV is reported. It is performed in the dimuon decay channel, through the detection of muons with pseudorapidity −4 < ημ< −2.5 and transverse momentum $$ {p}_{\mathrm{T}}^{\mu } $$ p T μ > 20 GeV/c in the laboratory frame. The invariant yield and nuclear modification factor are measured for opposite-sign dimuons with invariant mass 60 < mμμ< 120 GeV/c2 and rapidity 2.5 <$$ {y}_{\mathrm{cms}}^{\mu \mu} $$ y cms μμ < 4. They are presented as a function of rapidity and, for the Pb-Pb collisions, of centrality as well. The results are compared with theoretical calculations, both with and without nuclear modifications to the Parton Distribution Functions (PDFs). In p-Pb collisions the center-of-mass frame is boosted with respect to the laboratory frame, and the measurements cover the backward (−4.46 <$$ {y}_{\mathrm{cms}}^{\mu \mu} $$ y cms μμ < −2.96) and forward (2.03 <$$ {y}_{\mathrm{cms}}^{\mu \mu} $$ y cms μμ < 3.53) rapidity regions. For the p-Pb collisions, the results are consistent within experimental and theoretical uncertainties with calculations that include both free-nucleon and nuclear-modified PDFs. For the Pb-Pb collisions, a 3.4σ deviation is seen in the integrated yield between the data and calculations based on the free-nucleon PDFs, while good agreement is found once nuclear modifications are considered.

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Finite Temperature QCD Sum Rules: A Review

Advances in High Energy Physics ◽

10.1155/2017/9291623 ◽

2017 ◽

Vol 2017 ◽

pp. 1-24 ◽

Cited By ~ 19

Author(s):

Alejandro Ayala ◽

C. A. Dominguez ◽

M. Loewe

Keyword(s):

Finite Temperature ◽

Chemical Potential ◽

Sum Rules ◽

Light Quark ◽

Axial Vector ◽

Heavy Ion ◽

Qcd Sum Rules ◽

Rho Meson ◽

Ion Collisions ◽

Rule Method

The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for deconfinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing analysing the Weinberg sum rules and predicting the dimuon spectrum in heavy-ion collisions in the region of the rho-meson. Also, in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.

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Aspects of Relativistic Heavy-Ion Collisions

Universe ◽

10.3390/universe6050061 ◽

2020 ◽

Vol 6 (5) ◽

pp. 61 ◽

Cited By ~ 3

Author(s):

Georg Wolschin

Keyword(s):

Heavy Ion Collisions ◽

Initial Conditions ◽

Hadron Collider ◽

Heavy Ion ◽

Charged Hadron ◽

Distribution Functions ◽

Relativistic Heavy Ion Collisions ◽

Short Time Scale ◽

Relativistic Heavy Ion Collider ◽

Ion Collisions

The rapid thermalization of quarks and gluons in the initial stages of relativistic heavy-ion collisions is treated using analytic solutions of a nonlinear diffusion equation with schematic initial conditions, and for gluons with boundary conditions at the singularity. On a similarly short time scale of t ≤ 1 fm/c, the stopping of baryons is accounted for through a QCD-inspired approach based on the parton distribution functions of valence quarks, and gluons. Charged-hadron production is considered phenomenologically using a linear relativistic diffusion model with two fragmentation sources, and a central gluonic source that rises with ln 3 ( s N N ) . The limiting-fragmentation conjecture that agrees with data at energies reached at the Relativistic Heavy-Ion Collider (RHIC) is found to be consistent with Large Hadron Collider (LHC) data for Pb-Pb at s N N = 2.76 and 5.02 TeV. Quarkonia are used as hard probes for the properties of the quark-gluon plasma (QGP) through a comparison of theoretical predictions with recent CMS, ALICE and LHCb data for Pb-Pb and p-Pb collisions.

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Effects of Superstatistics on the Location of the Effective QCD Critical End Point

Ukrainian Journal of Physics ◽

10.15407/ujpe64.8.665 ◽

2019 ◽

Vol 64 (8) ◽

pp. 665

Author(s):

A. Ayala ◽

M. Hentschinski ◽

L. A. Hernández ◽

M. Loewe ◽

R. Zamora

Keyword(s):

Phase Diagram ◽

Chemical Potential ◽

Heavy Ion ◽

Relativistic Heavy Ion Collisions ◽

Chiral Symmetry Restoration ◽

Interaction Volume ◽

Qcd Phase Diagram ◽

End Point ◽

Ion Collisions ◽

Effective Description

Effects of the partial thermalization during the chiral symmetry restoration at the finite temperature and quark chemical potential are considered for the position of the critical end point in an effective description of the QCD phase diagram. We find that these effects cause the critical end point to be displaced toward larger values of the temperature and lower values of the quark chemical potential, as compared to the case where the system can be regarded as completely thermalized. These effects may be important for relativistic heavy ion collisions, where the number of subsystems making up the whole interaction volume can be linked to the finite number of participants in the reaction.

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The Sivers asymmetry in hadronic dijet production

Journal of High Energy Physics ◽

10.1007/jhep02(2021)066 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Zhong-Bo Kang ◽

Kyle Lee ◽

Ding Yu Shao ◽

John Terry

Keyword(s):

Spin Asymmetry ◽

Star Collaboration ◽

Heavy Ion ◽

Distribution Functions ◽

Relativistic Heavy Ion Collider ◽

Parton Distribution Functions ◽

Dijet Production ◽

Transverse Momentum Dependent ◽

Spin Asymmetries ◽

Polarized Proton

Abstract We study the single spin asymmetry in the back-to-back dijet production in transversely polarized proton-proton collisions. Such an asymmetry is generated by the Sivers functions in the incoming polarized proton. We propose a QCD formalism in terms of the transverse momentum dependent parton distribution functions, which allow us to resum the large logarithms that arise in the perturbative calculations. We make predictions for the Sivers asymmetry of hadronic dijet production at the kinematic region that is relevant to the experiment at the Relativistic Heavy Ion Collider (RHIC). We further compute the spin asymmetries in the selected positive and negative jet charge bins, to separate the contributions from u- and d-quark Sivers functions. We find that both the sign and size of our numerical results are roughly consistent with the preliminary results from the STAR collaboration at the RHIC.

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Flow and vorticity with varying chemical potential in relativistic heavy ion collisions

International Journal of Modern Physics E ◽

10.1142/s0218301320500019 ◽

2020 ◽

Vol 29 (01) ◽

pp. 2050001

Author(s):

Abhisek Saha ◽

Soma Sanyal

Keyword(s):

Shear Viscosity ◽

Heavy Ion Collisions ◽

Collision Energy ◽

Chemical Potential ◽

Transport Model ◽

Heavy Ion ◽

Relativistic Heavy Ion Collisions ◽

Viscous Effects ◽

Ion Collisions ◽

Lower Collision

We study the vorticity patterns in relativistic heavy ion collisions with respect to the collision energy. The collision energy is related to the chemical potential used in the thermal — statistical models that assume approximate chemical equilibrium after the relativistic collision. We use the multiphase transport model (AMPT) to study the vorticity in the initial parton phase as well as the final hadronic phase of the relativistic heavy ion collision. We find that as the chemical potential increases, the vortices are larger in size. Using different definitions of vorticity, we find that vorticity plays a greater role at lower collision energies than at higher collision energies. We also look at other effects of the flow patterns related to the shear viscosity at different collision energies. We find that the shear viscosity obtained is almost a constant with a small decrease at higher collision energies. We also look at the elliptic flow as it is related to viscous effects in the final stages after the collision. Our results indicate that the viscosity plays a greater role at higher chemical potential and lower collision energies.

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Centrality dependence of thermal freeze-out conditions at LHC in Pb+Pb collisions at sNN = 2.76TeV

Modern Physics Letters A ◽

10.1142/s0217732315501679 ◽

2015 ◽

Vol 30 (33) ◽

pp. 1550167 ◽

Cited By ~ 2

Author(s):

Saeed Uddin ◽

Inam-ul Bashir ◽

Riyaz Ahmed Bhat ◽

Waseem Bashir

Keyword(s):

Experimental Data ◽

Chemical Potential ◽

Heavy Ion ◽

Collective Flow ◽

Flow Profile ◽

Alice Experiment ◽

Ion Collisions ◽

Momentum Spectra ◽

Transverse Momentum Spectra ◽

Freeze Out

We have analyzed the available midrapidity [Formula: see text] transverse momentum spectra of identified particles such as protons [Formula: see text], kaons [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for different centralities of Pb+Pb collisions at the LHC energy [Formula: see text]. We have used our earlier proposed unified statistical thermal freeze-out model. The model incorporates the effect of nuclear transparency in such energetic collisions and the resulting asymmetry in the collective-flow profile along the longitudinal and the transverse directions. Our calculated results are found to be in good agreement with the experimental data measured by the ALICE experiment. The model calculation fits the experimental data for different particle species which provide thermal freeze-out conditions in terms of temperature and collective-flow parameters. The analysis shows a rise in the thermal freeze-out temperature and a mild decrease in the transverse collective-flow velocity as we go from central to the peripheral collisions. The baryon chemical potential is assumed to be nearly zero for the bulk of the matter [Formula: see text], a situation expected in the heavy ion collisions at LHC energies in the Bjorken approach owing to nearly complete nuclear transparency. The contributions from the decay of the heavier resonances are also taken into account in our calculations.

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SKYRMION FORMATION IN 1+1 DIMENSIONS WITH CHEMICAL POTENTIAL

International Journal of Modern Physics A ◽

10.1142/s0217751x06029508 ◽

2006 ◽

Vol 21 (06) ◽

pp. 1199-1219 ◽

Cited By ~ 1

Author(s):

V. SUNIL KUMAR ◽

BISWANATH LAYEK ◽

AJIT M. SRIVASTAVA ◽

SOMA SANYAL ◽

VIVEK K. TIWARI

Keyword(s):

Chemical Potential ◽

Defect Density ◽

Basic Mechanism ◽

Heavy Ion ◽

Tube Formation ◽

Relativistic Heavy Ion Collisions ◽

Potential Term ◽

Ion Collisions ◽

Spatially Varying ◽

Superfluid Vortices

Formation of topological objects during phase transitions has been discussed extensively in literature. In all these discussions, defects and antidefects form with equal probabilities. In contrast, many physical situations, such as formation of baryons in relativistic heavy-ion collisions at present energies, flux tube formation in superconductors in the presence of external magnetic field, and formation of superfluid vortices in a rotating vessel, require a mechanism which can bias (say) defects over antidefects. Such a bias can crucially affect defect–antidefect correlations, apart from its effects on defect density. In this paper we initiate an investigation for the basic mechanism of biased formation of defects. For Skyrmions in 1+1 dimensions, we show that incorporation of a chemical potential term in the effective potential leads to a domain structure where order parameter is spatially varying. We show that this leads to biased formation of Skyrmions.

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