Fields In Heavy Ion Collisions Research Articles

Polarization dynamics in the paramagnet of a charged quark-gluon plasma

It is commonly understood that the strong magnetic field produced in heavy ion collisions is short-lived. The electric conductivity of the quark-gluon plasma is unable to significantly extend the lifetime of the magnetic field. We propose an alternative scenario to achieve this: with finite baryon density and spin polarization by the initial magnetic field, the quark-gluon plasma behaves as a paramagnet, which may continue to polarize the quark after fading of the initial magnetic field. We confirm this picture by calculations in both quantum electrodynamics and quantum chromodynamics. In the former case, we find a splitting in the damping rates of probe fermions with an opposite spin component along the magnetic field. In the latter case, we find a similar splitting in damping rate of the probe quark in quark-gluon plasma in both high and low density limits. The splitting provides a way of polarizing strange quarks by the quark-gluon plasma paramagnet consisting of light quarks, which effectively extends the lifetime of the magnetic field in heavy ion collisions. Published by the American Physical Society 2024

Global spin alignment of vector mesons and strong force fields in heavy-ion collisions

Global spin alignment of vector mesons and strong force fields in heavy-ion collisions

Dynamical magnetic fields in heavy-ion collisions

The magnetic fields in heavy-ion collisions are important ingredients for many interesting phenomena, such as the Chiral Magnetic Effect, Chiral Magnetic Wave, the directed flow $v_1$ of $D^0$ mesons and the splitting of the spin polarization of the $\Lambda$/$\bar{\Lambda}$. Quantitative studies of these phenomena however suffer from limited understanding on the dynamical evolution of these fields in the medium created by the collisions, which remains a critical and challenging problem. The initial magnetic fields from the colliding nuclei decay very fast in the vacuum but their lifetime could be extended through medium response due to electrically conducting quarks and antiquarks. Here we perform a detailed analysis of such medium effect on the dynamical magnetic fields by numerically solving the Maxwell's equations concurrently with the expanding medium described by viscous hydrodynamics, under the assumption of negligible back reaction of the fields on the fluid evolution. Our results suggest a considerable enhancement of late time magnetic fields, the magnitude of which depends sensitively on the fireball expansion as well as the medium electric conductivity both before and during hydrodynamic stage.

Electromagnetic field effects and anomalous chiral phenomena in heavy-ion collisions at intermediate and high energy

<sec>Heavy-ion collisions can produce high-temperature and high-density quantum chromodynamics (QCD) matter under extremely strong electromagnetic fields, which triggers off many important anomalous chiral phenomena, such as the chiral magnetic effect and chiral magnetic wave. The anomalous chiral phenomena can help to find the evidence of <inline-formula><tex-math id="M2">\begin{document}$\cal{CP}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M2.png"/></alternatives></inline-formula> symmetry breaking in the strong interaction, deepen the understanding of the QCD vacuum fluctuations, and disclose the mystery of asymmetry of antimatter-matter in the universe. </sec><sec>In this paper, firstly, the magnetic fields are investigated for small and large colliding systems at relativistic heavy ion collider (RHIC) and large hadron collider (LHC). These studies indicate that collision energy and initial nucleon structure have significant effects on magnetic fields. And, the lifetimes of magnetic field in different media are very different in heavy-ion collisions. Then, in order to study the chiral magnetic effect, some experimental observables are studied by using a multi-phase transport model without or with different strengths of the chiral magnetic effect. For small systems, if QGP exists, the chiral magnetic effect could be observed in the peripheral collisions. For isobaric collisions, the correlators with respect to the spectator plane can imply a much cleaner signal of chiral magnetic effect than that with respect to the participant plane. Our results support that the strength of chiral magnetic effect may be absent or small in isobaric collisions. Next, some new strategies are applied to study the chiral magnetic wave. Moreover, a novel mechanism for the electric quadrupole moment can also explain the charge-dependent elliptic flow of pions generated by the chiral magnetic wave. In addition, some interesting phenomena also occur, owing to the magnetic field in heavy-ion collisions at intermediate energy. The directed flow and elliptic flow of photons have no effect on magnetic field at <inline-formula><tex-math id="M3">\begin{document}$p_{\rm T}<25$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M3.png"/></alternatives></inline-formula> GeV. However, because of the magnetic field, the directed flow of photons decreases and the elliptic flow of photons increases at <inline-formula><tex-math id="M4">\begin{document}$p_{\rm T}>25$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20230245_M4.png"/></alternatives></inline-formula> GeV. Besides, the magnetic field has a significant effect on giant dipole resonance, i.e. the magnetic field increases the angular momentum and enhances some observables of the giant dipole resonance spectrum. In conclusion, magnetic field plays a key role in heavy-ion collisions at both high energy and intermediate energy. It provides an unprecedented opportunity for studying the microscopic laws of nuclear physics. However, there are still many unsolved problems that need further studying in the future.</sec>

Study of the Roberge-Weiss phase caused by external uniform classical electric field using lattice QCD approach

The effect of an external electric field on the quark matter is an important question due to the presence of strong electric fields in heavy ion collisions. In the lattice QCD approach, the case of a real electric field suffers from the ‘sign problem’, and a classical electric field is often used similar as the case of chemical potential. Interestingly, in axial gauge a uniform classical electric field actually can correspond to an inhomogeneous imaginary chemical potential that varies with coordinate. On the other hand, with imaginary chemical potential, Roberge-Weiss (R-W) phase transition occurs. In this work, the case of a uniform classical electric field is studied by using lattice QCD approach, with the emphasis on the properties of the R-W phase. Novel phenomena show up at high temperatures. It is found that, the chiral condensation oscillates with z at high temperatures, and so is the absolute value of the Polyakov loop. It is verified that the charge density also oscillates with z at high temperatures. The Polyakov loop can be described by an ansatz Ap + Σq=u,dCq exp (LτQqiazeEz), where Ap is a complex number and Cd> 0, Cu ≥ 0 are real numbers that are fitted for different temperatures and electric field strengths. As a consequence, the behavior of the phase of Polyakov loop is different depending on whether the Polyakov loop encloses the origin, which implies a possible phase transition.

Spacetime structure of (3+1)D color fields in high energy nuclear collisions

We perform an analytic calculation of the color fields in heavy-ion collisions by considering the collision of longitudinally extended nuclei in the dilute limit of the Color Glass Condensate effective field theory of high-energy QCD. Based on general analytic expressions for the color fields in the future light cone, we evaluate the rapidity profile of the transverse pressure within a simple specific model of the nuclear collision geometry and compare our results to 3+1D classical Yang-Mills simulations.

Continuous evolution of electromagnetic field in heavy-ion collisions

In relativistic heavy-ion collisions the electromagnetic field exists before the hot nuclear matter emergence. Requiring the field continuity we compute it in the central rapidity region by taking into account the electromagnetic response of the Quark Gluon Plasma. We show that the electromagnetic field is nearly time-independent from about 1 fm/c after the collision until the freezeout. In particular, its value is about 10% of the initial magnitude of the magnetic field. Our result provides a theoretical basis for the common assumption that the electromagnetic field produced in relativistic heavy-ion collisions varies slowly with time.

The signature of charge dependent directed flow observables by electromagnetic fields in heavy ion collisions

We discuss the generation of the directed flow v_1(p_T,y_z) induced by the electromagnetic field as a function of p_T and y_z. Despite the complex dynamics of charged particles due to strong interactions generating several anisotropies in the azimuthal angle, it is possible at p_T > m to directly correlate the splitting in v_1 of heavy quarks with different charges to some main features of the magnetic field, and in particular its values at formation and freeze-out time. We further found that the slope of the splitting dDelta v_1/dy_z|_{y_z=0} of positively and negatively charged particles at high p_T can be formulated as dDelta v_1/dy_z|_{y_z=0}=-alpha frac{partial ln f}{partial p_T}+frac{2alpha -beta }{p_T}, where f is the p_T spectra of the charged particles and the constants alpha and beta (order of MeV) are constrained by the y component of magnetic fields and the sign of alpha is simply determined by the difference Delta [tB_y(t)] in the center of colliding systems at the formation time of particles and at the time when particles leave the effective range of electromagnetic fields or freeze out. The formula is derived from general considerations and is confirmed by several related numerical simulations; it supplies a useful guide to quantify the effect of different magnetic field configurations and provides an evidence of why the measurement of Delta v_1 of charm, bottom and leptons from Z^0 decay and their correlations are a powerful probe of the initial e.m. fields in ultra-relativistic collisions.

Necessity of self-consistent calculations for the electromagnetic field in probing the nuclear symmetry energy using pion observables in heavy-ion collisions

Within an isospin- and momentum-dependent transport model, we investigate the necessity of selfconsistent calculations for the electromagnetic field in probing the nuclear symmetry energy using pion observables in heavy-ion collisions at intermediate energies. To this end, we perform the $^{96}$Ru + $^{96}$Ru collisions at 400 MeV/nucleon with two calculations scenarios for the electromagnetic field including the selfconsistent calculation and the most used Li\'{e}nard-Wiechert formula, while the latter is a simplified one of the complete Li\'{e}nard-Wiechert formula by neglecting the radiation field for practical calculations in heavy-ion collisions at intermediate and/or relativistic energies. As a comparison, we also consider the static Coulomb field formula for calculations of the electromagnetic field in heavy-ion collisions. It is shown that the most used simplified Li\'{e}nard-Wiechert formula is not enough for the electromagnetic field calculation because the absent radiation field in this formula also affects significantly the charged pions as well as their $\pi^{-}/\pi^{+}$ ratio. Moreover, we also examine effects of the electromagnetic field in these scenarios on the double $\pi^{-}/\pi^{+}$ ratio of two isobar reaction systems of $^{96}$Ru + $^{96}$Ru and $^{96}$Zr + $^{96}$Zr at 400 MeV/nucleon. It is shown that the double $\pi^{-}/\pi^{+}$ ratio of two reactions tends to be less affected by the electromagnetic field calculation scenario and thus can still be an effective probe of the nuclear symmetry energy in heavy-ion collisions. Therefore, according to these findings, it is suggested that the selfconsistent calculation for the electromagnetic field should be carefully taken into account when using the pion observables to probe the nuclear symmetry energy in heavy-ion collisions.

Charge-dependent flow induced by electromagnetic fields in heavy ion collisions

The colliding heavy ions create extremely strong magnetic and electric fields that significantly affect the evolution of the produced quark-gluon plasma (QGP). The knowledge of these fields is essential for establishing the role of topological fluctuations in the QGP through the chiral magnetic effect and related anomaly-induced phenomena. In this talk, we describe our work on the evolution of the QGP in electric and magnetic fields in the framework of hydrodynamics supplemented, in a perturbative fashion, by the dynamical electromagnetism. The evolution of the QGP fluid is described within the iEBE-VISHNU framework. We find that the electromagnetically induced currents result in a a charge-odd directed flow Δν1 and a charge-odd Δν3 flow both of which are odd in rapidity. While the predicted magnitude of these charge-odd flows agrees with the data from RHIC and LHC, the sign of the predicted asymmetry between the flows of positive and negative hadrons is opposite to the data.

Chiral magnetic effect reveals the topology of gauge fields in heavy-ion collisions

The topological structure of vacuum is the cornerstone of non-Abelian gauge theories describing strong and electroweak interactions within the standard model of particle physics. However, transitions between different topological sectors of the vacuum (believed to be at the origin of the baryon asymmetry of the Universe) have never been observed directly. An experimental observation of such transitions in Quantum Chromodynamics (QCD) has become possible in heavy-ion collisions, where the chiral magnetic effect converts the chiral asymmetry (generated by topological transitions in hot QCD matter) into an electric current, under the presence of the magnetic field produced by the colliding ions. The Relativistic Heavy Ion Collider program on heavy-ion collisions such as the Zr-Zr and Ru-Ru isobars, thus has the potential to uncover the topological structure of vacuum in a laboratory experiment. This discovery would have far-reaching implications for the understanding of QCD, the origin of the baryon asymmetry in the present-day Universe, and for other areas, including condensed matter physics.

Charge-dependent flow as evidence of strong electromagnetic fields in heavy-ion collisions

The extremely large electromagnetic fields generated in heavy-ion collisions provide access to novel observables that are expected to constrain various key transport properties of the quark-gluon plasma and could help solve one of the outstanding puzzles in QCD: the strong CP problem. In this review we present a brief overview of the theoretical and experimental characterization of these electromagnetic fields. After reviewing the current state, emphasizing one of the observables — the charge-dependent flow — we discuss the various discrepancies between the measurements and theoretical predictions. Finally, to help resolve the discrepancies, we suggest new measurements and theoretical ideas.

Improved quark coalescence model for spin alignment and polarization of hadrons

We propose an improved quark coalescence model for spin alignment of vector mesons and polarization of baryons by spin density matrix with phase space dependence. The spin density matrix is defined through Wigner functions. Within the model we propose an understanding of spin alignments of vector mesons $\phi$ and $K^{*0}$ (including $\bar{K}^{*0}$) in the static limit: a large positive deviation of $\rho_{00}$ for $\phi$ mesons from 1/3 may come from the electric part of the vector $\phi$ field, while a negative deviation of $\rho_{00}$ for $K^{*0}$ may come from the electric part of vorticity tensor fields. Such a negative contribution to $\rho_{00}$ for $K^{*0}$ mesons, in comparison with the same contribution to $\rho_{00}$ for $\phi$ mesons which is less important, is amplified by a factor of the mass ratio of strange to light quark times the ratio of $\left\langle \mathbf{p}_{b}^{2}\right\rangle $ on the wave function of $K^{*0}$ to $\phi$ ($\mathbf{p}_{b}$ is the relative momentum of two constituent quarks of $K^{*0}$ and $\phi$). These results should be tested by a detailed and comprehensive simulation of vorticity tensor fields and vector meson fields in heavy ion collisions.

New channels of prompt-photon production by magnetic fields in heavy-ion collisions

In this work I present recent results on the photon yield and elliptic flow coefficient in relativistic heavy-ion collisions for different centralities. In our calculation, we take into account gluon fusion and splitting channels which become available due to an intense and short-lived magnetic field. We show that with reasonable values for the saturation scale, our calculation helps to better describe the experimental results obtained at RHIC energies for the lowest part of the transverse photon momentum at different centralities.

Magnetic fields in heavy ion collisions: flow and charge transport

At the earliest times after a heavy-ion collision, the magnetic field created by the spectator nucleons will generate an extremely strong, albeit rapidly decreasing in time, magnetic field. The impact of this magnetic field may have detectable consequences, and is believed to drive anomalous transport effects like the Chiral Magnetic Effect (CME). We detail an exploratory study on the effects of a dynamical magnetic field on the hydrodynamic medium created in the collisions of two ultrarelativistic heavy-ions, using the framework of numerical ideal MagnetoHydroDynamics (MHD) with the ECHO-QGP code. In this study, we consider a magnetic field captured in a conducting medium, where the conductivity can receive contributions from the electromagnetic conductivity sigma and the chiral magnetic conductivity sigma _{chi }. We first study the elliptic flow of pions, which we show is relatively unchanged by the introduction of a magnetic field. However, by increasing the magnitude of the magnetic field, we find evidence for an enhancement of the elliptic flow in peripheral collisions. This effect is stronger at RHIC than the LHC, and it is evident already at intermediate collision centralities. Next, we explore the impact of the chiral magnetic conductivity on electric charges produced at the edges of the fireball. This initial sigma _chi can be understood as a long-wavelength effective description of chiral fermion production. We then demonstrate that this chiral charge, when transported by the MHD medium, produces a charge dipole perpendicular to the reaction plane which extends a few units in rapidity. Assuming charge conservation at the freeze-out surface, we show that the produced charge imbalance can have measurable effects on some experimental observables, like v_1 or langle sin phi rangle . This demonstrates the ability of a MHD fluid to transport the signature of the initial chiral magnetic fields to late times. We also comment on the limitations of the ideal MHD approximation and detail how further development of a dissipative-resistive model can provide a more realistic description of the QGP.

Spin Hydrodynamic Generation in the Charged Subatomic Swirl

Recently there have been significant interests in the spin hydrodynamic generation phenomenon from multiple disciplines of physics. Such phenomenon arises from global polarization effect of microscopic spin by macroscopic fluid rotation and is expected to occur in the hot quark-gluon fluid (the “subatomic swirl”) created in relativistic nuclear collisions. This was indeed discovered in experiments which however revealed an intriguing puzzle: a polarization difference between particles and anti-particles. We suggest a novel application of a general connection between rotation and magnetic field: a magnetic field naturally arises along the fluid vorticity in the charged subatomic swirl. We establish this mechanism as a new way for generating long-lived in-medium magnetic field in heavy ion collisions. Due to its novel feature, this new magnetic field provides a nontrivial explanation to the puzzling observation of a difference in spin hydrodynamic generation for particles and anti-particles in heavy ion collisions.

Effect of Giant Resonances on Fluctuations of Electromagnetic Fields in Heavy Ion Collisions

We perform quantum calculations of fluctuations of the electromagnetic fields in $AA$ collisions at RHIC and LHC energies. Calculations are performed with the help of the fluctuation-dissipation theorem accounting for the giant dipole and quadrupole resonances. We find that in the quantum picture the field fluctuations are much smaller than that predicted by the classical Monte-Carlo simulation with the Woods-Saxon nuclear density used in previous analyses.

Charge-dependent flow induced by magnetic and electric fields in heavy ion collisions

We investigate the charge-dependent flow induced by magnetic and electric fields in heavy ion collisions. We simulate the evolution of the expanding cooling droplet of strongly coupled plasma hydrodynamically, using the iEBE-VISHNU framework, and add the magnetic and electric fields as well as the electric currents they generate in a perturbative fashion. We confirm the previously reported effect of the electromagnetically induced currents, that is a charge-odd directed flow $\Delta v_1$ that is odd in rapidity, noting that it is induced by magnetic fields (\`a la Faraday and Lorentz) and by electric fields (the Coulomb field from the charged spectators). In addition, we find a charge-odd $\Delta v_3$ that is also odd in rapidity and that has a similar physical origin. We furthermore show that the electric field produced by the net charge density of the plasma drives rapidity-even charge-dependent contributions to the radial flow $\langle p_T \rangle$ and the elliptic flow $\Delta v_2$. Although their magnitudes are comparable to the charge-odd $\Delta v_1$ and $\Delta v_3$, they have a different physical origin, namely the Coulomb forces within the plasma.

Sensitivity of observables to coarse-graining size in heavy-ion collisions

An open question in the field of heavy-ion collisions is to what extent the size of initial inhomogeneities in the system affects measured observables. Here we present a method to smooth out these inhomogeneities with minimal effect on global properties, in order to quantify the effect of short-range features of the initial state. We show a comparison of hydrodynamic predictions with original and smoothened initial conditions for four models of initial conditions and various observables. Integrated observables (integrated $v_n$, scaled $v_n$ distributions, normalized symmetric cumulants, event-plane correlations) as well as most differential observables ($v_n(p_T)$) show little dependence on the inhomogeneity sizes, and instead are sensitive only to the largest-scale geometric structure. However other differential observables such as the flow factorization ratio and sub-leading principal components are more sensitive to the granularity and could be a good tool to probe the short-scale dynamics of the initial stages of a heavy-ion collision, which are not currently well understood.

Promp photon yield and υ2 coefficent from gluon fusion induced by magnetic field in heavy-ion collisions

We compute the production of prompt photons and the υ2 harmonic coefficient in relativistic heavy-ion collisions induced by gluon fusion in the presence of an intense magnetic field, during the early stages of the reaction. The calculations take into account several parameters which are relevant to the description of the experimental transverse momentum distribution, and elliptic flow for RHIC and LHC energies. The main imput is the strenght of the magnetic field which varies in magnitude from 1 to 3 times the pion mass squared, and allows the gluon fusion that otherwise is forbidden in the absence of the field. The high gluon occupation number and the value of the saturation scale also play an important role in our calculation, as well as a flow velocity and geometrical factors. Our results support the idea that the origin of at least some of the photon excess observed in heavy-ion experiments may arise from magnetic field induced processes, and gives a good description of the experimental data.