We provide a pedagogical review article on fundamentals and applications of the quantum dynamics in strong electromagnetic fields in QED and QCD. The fundamentals include the basic picture of the Landau quantization and the resummation techniques applied to the class of higher-order diagrams that are enhanced by large magnitudes of the external fields. We then discuss observable effects of the vacuum fluctuations in the presence of the strong fields, which consist of the interdisciplinary research field of nonlinear QED. We also discuss extensions of the Heisenberg-Euler effective theory to finite temperature/density and to non-Abelian theories with some applications. Next, we proceed to the paradigm of the dimensional reduction emerging in the low-energy dynamics in the strong magnetic fields. The mechanisms of superconductivity, the magnetic catalysis of the chiral symmetry breaking, and the Kondo effect are addressed from a unified point of view in terms of the renormalization-group method. We provide an up-to-date summary of the lattice QCD simulations in magnetic fields for the chiral symmetry breaking and the related topics as of the end of 2022. Finally, we discuss novel transport phenomena induced by chiral anomaly and the axial-charge dynamics. Those discussions are supported by a number of appendices.

The PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) has measured electrons from heavy flavor (charm and bottom) decays for 0.3 < p_T < 9 GeV/c at midrapidity (|y| < 0.35) in Au+Au collisions at sqrt(s_NN) = 200 GeV. The nuclear modification factor R_AA relative to p+p collisions shows a strong suppression in central Au+Au collisions, indicating substantial energy loss of heavy quarks in the medium produced at RHIC. A large azimuthal anisotropy, v_2, with respect to the reaction plane is observed for 0.5 < p_T < 5 GeV/c indicating non-zero heavy flavor elliptic flow. Both R_AA and v_2 show a p_T dependence different from those of neutral pions. A comparison to transport models which simultaneously describe R_AA(p_T) and v_2(p_T) suggests that the viscosity to entropy density ratio is close to the conjectured quantum lower bound, i.e., near a perfect fluid.

We have measured direct photons for p_T&lt;5~GeV/$c$ in minimum bias and 0\%--40\% most central events at midrapidity for Cu$+$Cu collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The $e^{+}e^{-}$ contribution from quasi-real direct virtual photons has been determined as an excess over the known hadronic contributions in the $e^{+}e^{-}$ mass distribution. A clear enhancement of photons over the binary scaled $p$$+$$p$ fit is observed for p_T&lt;4 GeV/$c$ in Cu$+$Cu data. The $p_T$ spectra are consistent with the Au$+$Au data covering a similar number of participants. The inverse slopes of the exponential fits to the excess after subtraction of the $p$$+$$p$ baseline are 285$\pm$53(stat)$\pm$57(syst)~MeV/$c$ and 333$\pm$72(stat)$\pm$45(syst)~MeV/$c$ for minimum bias and 0\%--40\% most central events, respectively. The rapidity density, $dN/dy$, of photons demonstrates the same power law as a function of $dN_{\rm ch}/d\eta$ observed in Au$+$Au at the same collision energy.

The PHENIX experiement has measured the electron-positron pair mass spectrum from 0 to 8 GeV/c^2 in p+p collisions at sqrt(s)=200 GeV. The contributions from light meson decays to e^+e^- pairs have been determined based on measurements of hadron production cross sections by PHENIX. They account for nearly all e^+e^- pairs in the mass region below 1 GeV/c^2. The e^+e^- pair yield remaining after subtracting these contributions is dominated by semileptonic decays of charmed hadrons correlated through flavor conservation. Using the spectral shape predicted by PYTHIA, we estimate the charm production cross section to be 544 +/- 39(stat) +/- 142(syst) +/- 200(model) \mu b, which is consistent with QCD calculations and measurements of single leptons by PHENIX.

We report measurements of the branching fractions for $B^0\to\pi^+\pi^-$, $K^+\pi^-$, $K^+K^-$ and $K^0\pi^0$, and $B^+\to\pi^+\pi^0$, $K^+\pi^0$, $K^0\pi^+$ and $K^+\bar{K}{}^0$. The results are based on 10.4 fb$^{-1}$ of data collected on the $\Upsilon$(4S) resonance at the KEKB $e^+e^-$ storage ring with the Belle detector, equipped with a high momentum particle identification system for clear separation of charged $\pi$ and $K$ mesons. We find ${\cal B}(B^0\to\pi^+\pi^-) =(0.56^{+0.23}_{-0.20}\pm 0.04)\times 10^{-5}$,${\cal B}(B^0\to K^+\pi^-) =(1.93^{+0.34 +0.15}_{-0.32 -0.06})\times 10^{-5}$,${\cal B}(B^+\to K^+\pi^0) =(1.63^{+0.35 +0.16}_{-0.33 -0.18})\times 10^{-5}$,${\cal B}(B^+\to K^0\pi^+) =(1.37^{+0.57 +0.19}_{-0.48 -0.18})\times 10^{-5}$, and${\cal B}(B^0\to K^0\pi^0) =(1.60^{+0.72 +0.25}_{-0.59 -0.27})\times 10^{-5}$, where the first and second errors are statistical and systematic. We also set upper limits of ${\cal B}(B^+\to\pi^+\pi^0)<1.34\times 10^{-5}$,${\cal B}(B^0\to K^+K^-)<0.27\times 10^{-5}$, and${\cal B}(B^+\to K^+\bar{K}{}^0)<0.50\times 10^{-5}$ at the 90% confidence level.

The invariant yield of electrons from open-heavy-flavor decays for $1

We report the measurement of cumulants ($C_n, n=1\ldots4$) of the net-charge distributions measured within pseudorapidity (|\eta|&lt;0.35) in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=7.7-200$ GeV with the PHENIX experiment at the Relativistic Heavy Ion Collider. The ratios of cumulants (e.g. $C_1/C_2$, $C_3/C_1$) of the net-charge distributions, which can be related to volume independent susceptibility ratios, are studied as a function of centrality and energy. These quantities are important to understand the quantum-chromodynamics phase diagram and possible existence of a critical end point. The measured values are very well described by expectation from negative binomial distributions. We do not observe any nonmonotonic behavior in the ratios of the cumulants as a function of collision energy. The measured values of $C_1/C_2 = \mu/\sigma^2$and$C_3/C_1 = S\sigma^3/\mu$ can be directly compared to lattice quantum-chromodynamics calculations and thus allow extraction of both the chemical freeze-out temperature and the baryon chemical potential at each center-of-mass energy.

The differential cross section for the production of direct photons in p+p collisions at sqrt(s)=200 GeV at midrapidity was measured in the PHENIX detector at the Relativistic Heavy Ion Collider. Inclusive-direct photons were measured in the transverse-momentum range from 5.5--25 GeV/c, extending the range beyond previous measurements. Event structure was studied with an isolation criterion. Next-to-leading-order perturbative-quantum-chromodynamics calculations give a good description of the spectrum. When the cross section is expressed versus x_T, the PHENIX data are seen to be in agreement with measurements from other experiments at different center-of-mass energies.

The PHENIX Collaboration has measured the ratio of the yields of $\psi(2S)$ to $\psi(1S)$ mesons produced in $p$$+$$p$, $p$$+$Al, $p$$+$Au, and $^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV over the forward and backward rapidity intervals 1.2&lt;|y|&lt;2.2. We find that the ratio in $p$$+$$p$ collisions is consistent with measurements at other collision energies. In collisions with nuclei, we find that in the forward ($p$-going or $^{3}$He-going) direction, the relative yield of $\psi(2S)$ mesons to $\psi(1S)$ mesons is consistent with the value measured in \pp collisions. However, in the backward (nucleus-going) direction, the $\psi(2S)$ is preferentially suppressed by a factor of $\sim$2. This suppression is attributed in some models to breakup of the weakly-bound $\psi(2S)$ through final state interactions with comoving particles, which have a higher density in the nucleus-going direction. These breakup effects may compete with color screening in a deconfined quark-gluon plasma to produce sequential suppression of excited quarkonia states.

The cross section and transverse single-spin asymmetries of $\mu^{-}$ and $\mu^{+}$ from open heavy-flavor decays in polarized $p$+$p$ collisions at $\sqrt{s}=200$ GeV were measured by the PHENIX experiment during 2012 at the Relativistic Heavy Ion Collider. Because heavy-flavor production is dominated by gluon-gluon interactions at $\sqrt{s}=200$ GeV, these measurements offer a unique opportunity to obtain information on the trigluon correlation functions. The measurements are performed at forward and backward rapidity (1.4&lt;|y|&lt;2.0) over the transverse momentum range of $1.25

We present a detailed measurement of charged two-pion correlation functions in 0%-30% centrality $\sqrt{s_{_{NN}}}=200$ GeV Au$+$Au collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose-Einstein correlation functions stemming from L\'evy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter $\lambda$, the L\'evy index of stability $\alpha$ and the L\'evy length scale parameter $R$ as a function of average transverse mass of the pair $m_T$. We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same L\'evy-stable source functions. The $\lambda(m_T)$ measurements indicate a decrease of the strength of the correlations at low $m_T$. The L\'evy length scale parameter $R(m_T)$ decreases with increasing $m_T$, following a hydrodynamically predicted type of scaling behavior. The values of the L\'evy index of stability $\alpha$ are found to be significantly lower than the Gaussian case of $\alpha=2$, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.

We present azimuthal angular correlations between charged hadrons and energy deposited in calorimeter towers in central $d$$+$Au and minimum bias $p$$+$$p$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The charged hadron is measured at midrapidity |\eta|&lt;0.35, and the energy is measured at large rapidity (-3.7&lt;\eta&lt;-3.1, Au-going direction). An enhanced near-side angular correlation across |\Delta\eta| &gt; 2.75 is observed in $d$$+$Au collisions. Using the event plane method applied to the Au-going energy distribution, we extract the anisotropy strength $v_2$ for inclusive charged hadrons at midrapidity up to $p_T=4.5$ GeV/$c$. We also present the measurement of $v_2$ for identified $\pi^{\pm}$ and (anti)protons in central $d$$+$Au collisions, and observe a mass-ordering pattern similar to that seen in heavy ion collisions. These results are compared with viscous hydrodynamic calculations and measurements from $p$$+$Pb at $\sqrt{s_{_{NN}}}=5.02$ TeV. The magnitude of the mass-ordering in $d$$+$Au is found to be smaller than that in $p$$+$Pb collisions, which may indicate smaller radial flow in lower energy $d$$+$Au collisions.

Recently, multiparticle-correlation measurements of relativistic $p/d/^3$He$+$Au, $p$$+$Pb, and even $p$$+$$p$ collisions have shown surprising collective signatures. Here we present beam-energy-scan measurements of 2-, 4-, and 6-particle angular correlations in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}$=200, 62.4, 39, and 19.6 GeV. We also present measurements of 2- and 4-particle angular correlations in $p$$+$Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV. We find the 4-particle cumulant to be real-valued for $d$$+$Au collisions at all four energies. We also find that the 4-particle cumulant in $p$$+$Au has the opposite sign as that in $d$$+$Au, indicating that the correlations are geometrical and therefore collective in origin. Further we find that the 6-particle cumulant agrees with the 4-particle cumulant in $d$$+$Au collisions at 200 GeV, which indicates that nonflow effects are subdominant and provides strong evidence of collectivity.

The PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) has measured omega meson production via leptonic and hadronic decay channels in p+p, d+Au, Cu+Cu, and Au+Au collisions at sqrt(s_NN) = 200 GeV. The invariant transverse momentum spectra measured in different decay modes give consistent results. Measurements in the hadronic decay channel in Cu+Cu and Au+Au collisions show that omega production has a suppression pattern at high transverse momentum, similar to that of pi^0 and eta in central collisions, but no suppression is observed in peripheral collisions. The nuclear modification factors, R_AA, are consistent in Cu+Cu and Au+Au collisions at similar numbers of participant nucleons.

The jet fragmentation function is measured with direct photon-hadron correlations in p+p and Au+Au collisions at sqrt(s_NN)=200 GeV. The p_T of the photon is an excellent approximation to the initial p_T of the jet and the ratio z_T=p_T^h/p_T^\gamma is used as a proxy for the jet fragmentation function. A statistical subtraction is used to extract the direct photon-hadron yields in Au+Au collisions while a photon isolation cut is applied in p+p. I_ AA, the ratio of jet fragment yield in Au+Au to that in p+p, indicates modification of the jet fragmentation function. Suppression, most likely due to energy loss in the medium, is seen at high z_T. The fragment yield at low z_T is enhanced at large angles. Such a trend is expected from redistribution of the lost energy into increased production of low-momentum particles.

We investigate photon emission at the hadronization stage from a quark-gluon plasma created in relativistic heavy-ion collisions. A recombination-model picture suggests that a quark and an antiquark bind into a meson state in hadronization, which would apparently violate the energy conservation if there is nothing else involved. We consider here a hadronization process where the recombination accompanies a photon emission. This is an analog of the "{\it radiative recombination}" known in plasma physics, such as $e^- + p^+ \to {\rm H}^0 +\gamma$, which occurs when an electromagnetic plasma goes back to a neutral atomic gas. The "radiative hadronization" picture will bring about (i) an enhancement of the photon yield, (ii) significant flow of photons similar to that of hadrons, and (iii) the photon transverse momentum ($p_T$) distribution with a thermal profile whose effective temperature is given by blue-shifted temperature of quarks. Here as a simplest and phenomenological realization of the radiative hadronization, we modify the recombination model to involve a photon emission and evaluate the photon yield with this modified model. Adding this contribution to the direct photon yield along with thermal photon contribution calculated with a hydrodynamic model and a parametrized contribution of prompt photons, we study the $p_T$ spectrum and elliptic flow of the photons produced in heavy-ion collisions at RHIC and LHC energies.

The energy dependence of the single-transverse-spin asymmetry, A_N, and the cross section for neutron production at very forward angles were measured in the PHENIX experiment at RHIC for polarized p+p collisions at sqrt(s)=200 GeV. The neutrons were observed in forward detectors covering an angular range of up to 2.2 mrad. We report results for neutrons with momentum fraction of x_F=0.45 to 1.0. The energy dependence of the measured cross sections were consistent with x_F scaling, compared to measurements by an ISR experiment which measured neutron production in unpolarized p+p collisions at sqrt(s)=30.6--62.7 GeV. The cross sections for large x_F neutron production for p+p collisions, as well as those in e+p collisions measured at HERA, are described by a pion exchange mechanism. The observed forward neutron asymmetries were large, reaching A_N=-0.08+/-0.02 for x_F=0.8; the measured backward asymmetries, for negative x_F, were consistent with zero. The observed asymmetry for forward neutron production is discussed within the pion exchange framework, with interference between the spin-flip amplitude due to the pion exchange and nonflip amplitudes from all Reggeon exchanges. Within the pion exchange description, the measured neutron asymmetry is sensitive to the contribution of other Reggeon exchanges even for small amplitudes.

The PHENIX experiment measured the centrality dependence of two-pion Bose-Einstein correlation functions in $\sqrt{s_{_{NN}}}=200$~GeV Au$+$Au collisions at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory. The data are well represented by L\'evy-stable source distributions. The extracted source parameters are the correlation-strength parameter $\lambda$, the L\'evy index of stability $\alpha$, and the L\'evy-scale parameter $R$ as a function of transverse mass $m_T$ and centrality. The $\lambda(m_T)$ parameter is constant at larger values of $m_T$, but decreases as $m_T$ decreases. The L\'evy scale parameter $R(m_T)$ decreases with $m_T$ and exhibits proportionality to the length scale of the nuclear overlap region. The L\'evy exponent $\alpha(m_T)$ is independent of $m_T$ within uncertainties in each investigated centrality bin, but shows a clear centrality dependence. At all centralities, the L\'evy exponent $\alpha$ is significantly different from that of Gaussian ($\alpha=2$) or Cauchy ($\alpha=1$) source distributions. Comparisons to the predictions of Monte-Carlo simulations of resonance-decay chains show that in all but the most peripheral centrality class (50%-60%), the obtained results are inconsistent with the measurements, unless a significant reduction of the in-medium mass of the $\eta'$ meson is included. In each centrality class, the best value of the in-medium $\eta'$ mass is compared to the mass of the $\eta$ meson, as well as to several theoretical predictions that consider restoration of $U_A(1)$ symmetry in hot hadronic matter.

We report electronic structure and physical properties of metal doped picene as well as selective synthesis of the phase exhibiting 18 K superconducting transition. First, Raman scattering is used to characterize the number of electrons transferred from the dopants to picene molecules. The charge transfer leads to a softening of Raman scattering peaks, which enables us to determine the number of transferred electrons. From this we have identified that three electrons are transferred to each picene molecule in the superconducting doped-picene solids. Second, we report the pressure dependence of Tc in 7 and 18 K phases of K3picene. The 7 K phase shows a negative pressure-dependence, while the 18 K phase exhibits a positive pressure-dependence which cannot be understood with a simple phonon mechanism of BCS superconductivity. Third, we report a new synthesis method for superconducting K3picene by a solution process with monomethylamine, CH3NH2. This method enables one to prepare selectively the K3picene sample exhibiting 18 K superconducting transition. The discovery of suitable way for preparing K3picene with Tc = 18 K may facilitate clarification of the mechanism of superconductivity.

The jet cross-section and jet-substructure observables in $p$$+$$p$ collisions at $\sqrt{s}=200$ GeV were measured by the PHENIX Collaboration at the Relativistic Heavy Ion Collider (RHIC). Jets are reconstructed from charged-particle tracks and electromagnetic-calorimeter clusters using the anti-$k_{t}$ algorithm with a jet radius $R=0.3$ for jets with transverse momentum within $8.0