arXiv subjects
Publications and source records attributed to Yoshitaka Hatta.
I summarize our recent work towards finding and utilizing analytic solutions of relativistic hydrodynamic. In the first part I discuss various exact solutions of the second-order conformal hydrodynamics. In the second part I compute flow harmonics $v_n$ analytically using the anisotropically deformed Gubser flow and discuss its dependence on $n$, $p_T$, viscosity, the chemical potential and the charge.
We investigate the close connection between the quantum phase space Wigner distribution of small-$x$ gluons and the color dipole scattering amplitude, and propose to study it experimentally in the hard diffractive dijet production at the planned electron-ion collider. The angular correlation between the nucleon recoiled momentum and the dijet transverse momentum will probe the nontrivial correlation in the phase space Wigner distribution. This experimental study will not only provide us with three-dimensional tomographic pictures of gluons inside high energy proton, but also give a unique and interesting signal for the small-$x$ dynamics with QCD evolution effects.
Recently, the STAR collaboration at RHIC has presented experimental evidence for the correlation between the elliptic flow difference of charged pions and charge asymmetry as a possible signal of the chiral magnetic wave. We demonstrate that the STAR results can be understood within the standard viscous hydrodynamics.
We define the QCD Husimi distribution as the phase space distribution of partons inside the nucleon. Compared to the more well-known Wigner distribution, the Husimi distribution is better behaved and positive. It thus allows for a probabilistic interpretation and can be used to define the `entropy' of the nucleon as a measure of complexity of the partonic structure. A possible connection to the Color Glass Condensate approach at small-$x$ is also discussed.
We present a new solution of relativistic hydrodynamics in 1+3 dimensions which depends on both the transverse coordinate and rapidity. At early times the flow expands dominantly longitudinally in a non-boost-invariant manner, and at late times it expands nearly spherically. These two regimes are shown to be related by symmetry. The effect of viscosity is also discussed.
We generalize the Gubser solution of viscous hydrodynamics by including the finite density effect and analytically compute the flow harmonics $v_n$. We explicitly show how $v_n$ and their viscous corrections depend on the chemical potential. The difference in $v_n$ between particles and antiparticles is also analytically computed and shown to be proportional to various chemical potentials and the viscosity. Excellent agreement is obtained between the results and the available experimental data from the SPS, RHIC and the LHC.
Evolution of quark-gluon plasma (QGP) near equilibrium can be described by the second-order relativistic viscous hydrodynamic equations. Consistent and analytically verifiable numerical solutions are critical for phenomenological studies of the collective behavior of QGP in high-energy heavy-ion collisions. A novel analytical solution based on the conformal Gubser flow which is a boost-invariant solution with transverse fluid velocity is presented. Due to the non-linear nature of the equation, the analytical solution is non-perturbative and exhibits features that are rather distinct from solutions to usual linear hydrodynamic equations. It is used to verify with high precision the numerical solution with a newly developed state-of-the-art $(3+1)$-dimensional second-order viscous hydro code (CLVisc). The perfect agreement between the analytical and numerical solutions demonstrates the reliability of the numerical simulations with the second-order viscous corrections. This lays the foundation for future phenomenological studies that allow one to gain access to the second-order transport coefficients.
We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the Israel-Stewart equation in the literature. This allows us to compare the solutions of the kinetic and hydrodynamic equations at an analytical level. We then derive a novel boost-invariant solution of the Boltzmann equation which has an unconventional dependence on the proper time. The existence of such a solution is also suggested in second order hydrodynamics and fluid-gravity correspondence.
In the context of nucleon structure, the Wigner distribution has been commonly used to visualize the phase-space distribution of quarks and gluons inside the nucleon. However, the Wigner distribution does not allow for a probabilistic interpretation because it takes negative values. In pursuit of a positive phase-space distribution in QCD, we introduce the Husimi distribution and demonstrate its advantages via a simple one-loop example. We also comment on a possible connection to the semiclassical approach to saturation physics at small-$x$.
Based on a viscous hydrodynamic model with anisotropically perturbed Gubser flow and isothermal Cooper-Frye freezeout at early times, we analytically compute the flow harmonics $v_n(p_T)$ and study how they scale with the harmonic number $n$ and transverse momentum, as well as the system size, shear and bulk viscosity coefficients, and collision energy. In particular, we find that the magnitude of shear viscous corrections grows linearly with $n$. The mixing between different harmonics is also discussed. While this model is rather simple as compared to realistic heavy-ion collisions, we argue that the scaling results presented here may be meaningfully compared to experimental data collected over many energies, system sizes, and geometries.
In this paper, we present a fully analytical description of the early-stage formation of elliptic flow in relativistic viscous hydrodynamics. We first construct an elliptic deformation of Gubser flow which is a boost invariant solution of the Navier-Stokes equation with a nontrivial transverse profile. We then analytically calculate the momentum anisotropy of the flow as a function of time and discuss the connection with the empirical formula by Bhalerao {\it et al.} regarding the viscosity dependence of elliptic flow.
In this paper we present the details of our previous work on exact solutions in second-order conformal hydrodynamics together with a number of new solutions found by mapping Minkowski space onto various curved spacetimes such as anti-de Sitter space and hyperbolic space. We analytically show how the solutions of ideal hydrodynamics are modified by the second-order effects including vorticity. We also find novel boost-invariant exact solutions which exist only in second-order hydrodynamics and have an unusual dependence on the proper time.
We present some exact solutions of relativistic second-order hydrodynamic equations in theories with conformal symmetry. Starting from a spherically expanding solution in ideal hydrodynamics, we take into account general conformal second-order corrections, and construct, for the first time, fully analytical axisymmetric exact solutions including the case with nonzero vorticity. These solutions are time-reversible despite having a nonvanishing shear stress tensor and provide a useful quantitative measure of the second-order effects in relativistic hydrodynamics.
We show that the total gluon helicity $ΔG$ in a polarized nucleon can be calculated on a Euclidean lattice through a universality class of QCD operators that describe the helicity or polarization of the onshell gluon radiation. We in particular find some operators whose matrix elements in a nucleon of momentum $P^z$ are directly related to $ΔG$ with only power-law $(1/P^z)^n (n\ge 2)$ corrections.
In the collinear twist-three approach, we calculate for the first time the gluon contribution to double (longitudinal-transverse) spin asymmetry A_{LT} for open charm production in proton-proton collisions measurable at RHIC. Utilizing the Ward-Takahashi identity for the non-pole part of the hard scattering amplitude, we derive a factorized, gauge invariant formula for the asymmetry. The result may be combined with the previous studies of single-spin asymmetry in the same channel and allows for a systematic analysis of three-gluon correlations inside a transversely polarized nucleon.
I review the recent progress in understanding the complete gauge invariant decomposition of the nucleon spin with particular emphasis on its twist structure.
In the context of inter-jet energy flow, we present the first quantitative result of the resummation of non-global logarithms at finite N_c. This is achieved by refining Weigert's approach in which the problem is reduced to the simulation of associated Langevin dynamics in the space of Wilson lines. We find that, in e+e- annihilation, the exact result is rather close to the result previously obtained in the large-N_c mean field approximation. However, we observe enormous event-by-event fluctuations in the Langevin process which may have significant consequences in hadron collisions.
We derive exact relations among the polarized gluon and three-gluon distributions in the transversely polarized nucleon which are relevant to single and double spin asymmetries in various hard processes. We also discuss the partonic decomposition of the transverse nucleon spin and point out a potential problem with frame-independence.