The behavior of vector mesons in extreme environments provides a unique probe of non-perturbative Quantum Chromodynamics. We investigate the conditions for Bose-Einstein condensation (BEC) of spin-1 <italic>&#961;</italic> mesons in dense rotating hadronic matter, a regime relevant to the peripheral heavy-ion collisions and the interiors of rapidly rotating neutron stars. When the <italic>&#961;</italic> meson chemical potential ( <italic>&#956;<inf>&#961;</inf></italic>) approaches its effective mass ( <math altimg='si1.svg'><msubsup><mi>m</mi><mi>&#961;</mi><mo>*</mo></msubsup></math>), a phase transition to BEC occurs. We demonstrate that this transition is non-trivially influenced by global rotation, which couples to the spin of the <italic>&#961;</italic> mesons, leading to a macroscopic spin alignment of the condensate along the axis of rotation. This interplay between condensation and rotation results in distinct polarization patterns, which can serve as a possible signature of a BEC in experiments. The results suggest that rapidly rotating neutron stars may harbor an anisotropic, spin-polarized <italic>&#961;</italic>-condensed phase, which could impact their equation of state.

India

Kshitish Kumar Pradhan

Mexico

Dushmanta Sahu

Raghunath Sahoo

Emergent spin polarization from <italic>&#961;</italic> meson condensation in rotating hadronic matter

Thermoelectric phenomena are traditionally associated with the interconversion of thermal and electrical energy in many-body systems. In the context of high-temperature quantum chromodynamics (QCD) matter produced in relativistic heavy-ion collisions, thermoelectric responses can provide insight into the evolving microscopic dynamics and the redistribution of effective degrees of freedom across the phase transition region. In this work, for the first time, we present a phenomenological study of the thermoelectric figure of merit ( <italic>ZT</italic>) in hot QCD matter, with a particular focus on its behavior across the hadronic and quark-gluon plasma phases. Using model-based calculations for the electrical conductivity, Seebeck coefficient, and thermal conductivity, we analyze the temperature dependence of <italic>ZT</italic> and identify characteristic features near the QCD phase transition temperature. Our results indicate that <italic>ZT</italic> exhibits nontrivial behavior near the transition region, reflecting the changing transport properties and active degrees of freedom in the medium. This phenomenological study of the thermoelectric figure of merit provides a complementary perspective to traditional transport studies and may provide critical insights for advancing the understanding of QCD matter through the transition region.

Kamaljeet Singh

Thermoelectric figure of merit and the deconfinement phase transition

Pion condensation in ultrarelativistic collisions presents a compelling theoretical phenomenon with significant implications for the dynamics of hadronic matter. Various theoretical frameworks offer insight into the nature of high-temperature Bose-Einstein condensation (BEC). The present study investigates the dissipative behavior of a relativistic pion gas undergoing BEC in ultrarelativistic heavy-ion collisions. Further, we obtain viscosity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math>), bulk viscosity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi></math>), and speed of sound (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>c</mi><mi>s</mi></msub></math>) by employing the Boltzmann transport equation with the relaxation time approximation. Findings show a substantial drop in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>/</mo><mi>s</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ζ</mi><mo>/</mo><mi>s</mi></math> with the fractional increase in condensation. This effect is becoming more evident in larger systems approaching the thermodynamic limit. Alongside the reduction in viscosities, the speed of sound also decreases with increasing condensation, indicating a softening of the equation of state. The analysis of finite-size effects reveals that larger systems exhibit more pronounced signatures of BEC. These results suggest that pion condensation can influence the hydrodynamic evolution of the hadronic phase in heavy-ion collisions, with consequential implications for interpreting collective flow observables and the underlying equation of state.

Captain R. Singh

Bose-Einstein condensation and dissipative dynamics in a relativistic pion gas

RHIC and LHC have injected <math altimg='si2.svg'><mrow><msup><mrow /><mn>16</mn></msup><mrow><mi mathvariant='normal'>O</mi></mrow></mrow></math> nuclei in their accelerator complexes with a focus on investigating collectivity and the origin of quark-gluon plasma signatures in small collision systems. The <math altimg='si2.svg'><mrow><msup><mrow /><mn>16</mn></msup><mrow><mi mathvariant='normal'>O</mi></mrow></mrow></math> nuclei are known to possess clusters of <math altimg='si1.svg'><mi>&#945;</mi></math>-particles ( <math altimg='si19.svg'><mrow><msup><mrow /><mn>4</mn></msup><mrow><mi mathvariant='normal'>H</mi></mrow><mi>e</mi></mrow></math>) inside the nucleus. This paper attempts to study the clustered-nuclear-geometry dependence of anisotropic flow coefficients such as elliptic flow ( <math altimg='si20.svg'><msub><mi>v</mi><mn>2</mn></msub></math>) and triangular flow ( <math altimg='si21.svg'><msub><mi>v</mi><mn>3</mn></msub></math>), which are sensitive to the nuclear geometry of colliding nuclei. The study is performed in pO and OO collisions at <math altimg='si6.svg'><mrow><msqrt><msub><mi>s</mi><mrow><mrow><mi mathvariant='normal'>N</mi></mrow><mi>N</mi></mrow></msub></msqrt><mo linebreak='goodbreak'>=</mo><mn>9.61</mn></mrow></math> TeV and 7 TeV respectively, employing a hybrid model encompassing IP-Glasma + MUSIC + iSS + UrQMD. The results of the clustered nuclear geometry are compared with those of the Woods&#8211;Saxon nuclear profile. Both initial and final state anisotropies are estimated. This study is thus one of its first kind, where the study of anisotropic flow coefficients for pO and OO collisions is presented using a hybrid hydrodynamics model. While the effect of <math altimg='si1.svg'><mi>&#945;</mi></math>-clustering in pO is found to be small, it is significant for each observable studied in OO collisions. It is also observed that the magnitude of this effect has a noteworthy dependence on the size of the 4He.

Hungary

Aswathy Menon Kavumpadikkal Radhakrishnan

Suraj Prasad

Finland

Neelkamal Mallick

Gergely Gábor Barnaföldi

Probing the sensitivity of anisotropic flow coefficients to the initial nuclear structure in pO and OO collisions at the LHC

Heavy-ion collision experiments such as the Large Hadron Collider and the Relativistic Heavy Ion Collider offer a unique platform to study several key properties of the quark-gluon plasma (QGP), a deconfined state of strongly interacting matter. Quarks, being the electrically charged particles, can induce an electric current in the medium in response to the temperature gradients. Hence, the QGP medium can behave like a thermoelectric medium. The thermoelectric coefficients, such as the Seebeck and Thomson coefficients, can help us to understand the intricate transport phenomenon of the medium. In peripheral collisions, the intense, transient, and time-dependent magnetic field created due to spectator protons significantly influences the thermoelectric properties of the QGP medium, affecting the charge and heat transport. This work uses the quasiparticle model to calculate the Thomson coefficient in QGP. The Thomson effect, describing the continuous heating or cooling of the charge-carrying medium in the presence of temperature gradients, remains largely unexplored in QGP. The Seebeck effect, which relates temperature gradients to induced electric fields, has been widely studied in the literature. For the first time, we calculate the magneto-Thomson and transverse Thomson coefficients. We have studied their dependence on temperature, baryon chemical potential, center of mass energy, and time-dependent magnetic field with different decay parameters. The transverse Thomson effect originates due to the presence of the Nernst effect in the presence of a magnetic field. Our results provide new insights into the higher-order thermoelectric transport properties of the QGP medium in the context of heavy-ion collisions.

Thermoelectric Thomson coefficient of quark-gluon plasma in the presence of a time-varying magnetic field

Anisotropic flow and fluctuations are sensitive observables of the initial state effects in heavy ion collisions and are characterized by the medium properties and final state interactions. Using event-shape observables, one can constrain the probability distributions of anisotropic flow coefficients, thus reducing the linear and nonlinear contributions in the measured higher-order harmonics. In this paper, we use transverse spherocity as an event shape observable to study the flow coefficients and elliptic flow fluctuations. Transverse spherocity is found to have a strong correlation with elliptic flow and its fluctuations. We exploit this feature of transverse spherocity to remove the contribution to elliptic flow from higher-order harmonics. The study is performed in Pb–Pb collisions at <math altimg='si1.svg'><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi mathvariant='normal'>NN</mi></mrow></msub></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>5.02</mn></math> TeV using a multi-phase transport model. The multi-particle Q-cumulant method estimates the anisotropic flow coefficients, which reduces the non-flow contributions. We observe a stronger system response to the flow coefficients for the events with smaller values of elliptic flow.

Higher order flow coefficients – a messenger of QCD medium formed in heavy-ion collisions at the Large Hadron Collider

In ultrarelativistic collisions of nuclei at the Large Hadron Collider, the created QCD environment rapidly changes, leading to a nonadiabatic evolution of the quantum states involved. Considering this, we first examine the preequilibrium state of QCD matter and its effect on the initially produced charmonium using a temperature-independent Hamiltonian. As the QCD matter reaches local thermal equilibrium, this Hamiltonian transforms to its finite temperature counterpart. To model the preequilibrium stage, we use the bottom-up thermalization approach to determine the effective temperature of the QCD matter, followed by a Gubser-type expansion for the thermalized medium. Additionally, we consider collisional damping, gluonic dissociation, and regeneration mechanisms, which specifically modify the charmonium yield in the thermalized medium. Mainly, the gluonic dissociation and collisional damping cause a reduction in the yield conversely, regeneration through gluonic deexcitation enhances the yield of charmonium. Further, we explore the combined effects of these mechanisms on the collective yield of charmonium states with transverse momentum (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>p</mi><mi mathvariant="normal">T</mi></msub></math>) and event multiplicity in the proton-proton collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. Based on our findings, we contend that the combined effects of these mechanisms can serve as a robust probe for determining the possible existence of a thermalized QCD medium in such a small collision system.

Partha Bagchi

Jan-e Alam

Exploring QGP-like phenomena with charmonia in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo>+</mo><mi>p</mi></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>

The recent observation of global spin polarization of $$\Lambda $$ ( $$\bar{\Lambda }$$ ) hyperons and the spin alignment of $$\phi $$ and $$K^{*0}$$ vector mesons create remarkable interest in investigating the particle polarization in the relativistic fluid produced in heavy-ion collisions at GeV/TeV energies. Among other sources of spin polarization phenomena, the Debye mass of a medium plays a crucial role in particle polarization. Any modification brought to the effective mass due to the temperature, strong magnetic field ($\textit{eB}$), baryonic chemical potential ( $$\mu _{B}$$ ), medium anisotropy ( $$\xi $$ ), and vorticity, etc., certainly affects the particle spin polarization. In this work, we explore the global hyperon spin polarization and the spin alignment of vector mesons corresponding to the strong magnetic field, baryonic chemical potential, and medium anisotropy. We find that the degree of spin polarization is flavor-dependent for hyperons. Meanwhile, vector meson spin alignment depends on the hadronization mechanisms of initially polarized quarks and anti-quarks. Medium anisotropy significantly changes the degree of spin polarization compared to the magnetic field and baryon chemical potential.

Bhagyarathi Sahoo

Captain Singh

Impact of strong magnetic field, baryon chemical potential, and medium anisotropy on polarization and spin alignment of hadrons

The hot and dense hadronic medium formed during the heavy-ion collisions at the Relativistic Heavy Ion Collider and Large Hadron Collider energies can show thermoelectric effects in the presence of temperature gradients and nonzero baryon chemical potential. In this article, we study the thermoelectric coefficients of an interacting hot and dense hadron gas using the relativistic Boltzmann transport equation under the relaxation time approximation. We discuss the thermoelectric properties within different frameworks of hadron resonance gas models. In the presence of an external magnetic field, the thermoelectric coefficients become anisotropic, which leads to Hall-like thermoelectric coefficients, namely Nernst coefficients, along with the magneto-Seebeck coefficients. For the first time, we also estimate the Thomson coefficient of the medium, which comes into the picture due to the temperature dependence of the Seebeck coefficient of the medium. In the context of studying the thermoelectric generator performance, we calculate the values of the thermoelectric figure of merit of the medium.

Thermoelectric effects of an interacting hadron gas in the presence of an external magnetic field

In relativistic heavy-ion collisions, the formation of a deconfined and thermalized state of partons, known as quark-gluon plasma (QGP), leads to enhanced production of strange hadrons in contrast to proton-proton (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math>) collisions, which are taken as baseline. This observation is known as strangeness enhancement in heavy-ion collisions and is considered one of the important signatures that can signify the formation of QGP. However, in addition to strangeness enhancement, recent measurements hint at observing several heavy-ion-like features in high multiplicity <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions at energies available at the CERN Large Hadron Collider. Alternatively, event shape observables, such as transverse spherocity, transverse sphericity, charged particle flattenicity, and relative transverse activity classifiers, can fundamentally separate hard interaction-dominated jetty events from soft isotropic events. These features of event shape observables can probe the observed heavy-ion-like features in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions with significantly reduced selection bias and can bring all collision systems on equal footing. In this article, we present an extensive summary of the strange particle ratios to pions as a function of different event classifiers using the PYTHIA 8 model with color reconnection and rope hadronization mechanisms to understand the microscopic origin of strangeness enhancement in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions and also prescribe the applicability of these event classifiers in the context of strangeness enhancement. Charged-particle flattenicity is found to be most suited for the study of strangeness enhancement, and it shows a quantitative enhancement similar to that seen for the analysis based on the number of multiparton interactions.

CERN

Sushanta Tripathy

Probing strangeness with event topology classifiers in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions at energies available at the CERN Large Hadron Collider with the rope hadronization mechanism in PYTHIA