One of the most spectacular observations in heavy ion physics has been that thermalization may occur in small system collisions. For example, harmonic flow coefficients vn(pT) measured in high multiplicity p+A reactions are well reproduced by viscous hydrodynamics calculations. Small system collisions in fact serve as good tests of hydrodynamics because they should be more difficult to thermalize; in other words, shear stress and bulk pressure corrections are expected to be larger than in A+A collisions.
At freezeout, shear stress and bulk pressure manifest as nonthermal $\delta f$ corrections to the particle distributions. Hydrodynamic variables cannot fix the momentum dependence of the corrections, nor how these vary with hadron species. Therefore, to compute observables, hydro calculations rely on a model for $\delta f_i$. In practice, ad hoc postulated forms are used based on Grad's quadratic ansatz, completely disregarding the microscopic dynamics of the system. On the other hand, a self-consistent set of corrections can be obtained from kinetic theory, which depend on the scattering rates between the various species.
Self-consistent shear viscous corrections can generate a characteristic meson vs baryon difference in harmonic flow coefficients, much akin to quark number scaling. The difference arises because meson-meson cross sections tend to be smaller than meson-baryon cross sections (additive quark model). It is not yet known, however, how bulk viscosity and self-consistent bulk corrections affect harmonic flow. This is especially interesting in small systems because bulk pressure can be large. Extending the work of Molnar and Wolff (PRC95, 024903) we calculate self-consistent bulk viscous corrections in a multi-species hadron gas. Then, we use the self-consistent corrections to calculate harmonic flow observables in p+Pb collisions at the LHC, and show how bulk viscosity manifests in the momentum and species dependence of the harmonic flow coefficients.
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