Mass Ordering of Spectra from Fragmentation of Saturated Gluon States in High-Multiplicity Proton-Proton Collisions

The mass ordering of mean transverse momentum $⟨p_T⟩$ and of the Fourier harmonic coefficient $v_2(p_T)$ of azimuthally anisotropic particle distributions in high energy hadron collisions is often interpreted as evidence for the hydrodynamic flow of the matter produced. We investigate an alternative initial state interpretation of this pattern in high-multiplicity proton-proton collisions at the LHC. The QCD Yang-Mills equations describing the dynamics of saturated gluons are solved numerically with initial conditions obtained from the color-glass-condensate-based impact-parameter-dependent glasma model. The gluons are subsequently fragmented into various hadron species employing the well established Lund string fragmentation algorithm of the pythia event generator. We find that this initial state approach reproduces characteristic features of bulk spectra, in particular, the particle mass dependence of $⟨p_T⟩$ and $v_2(p_T)$.

Figure 1

Left: Initial gluon distribution for a single IP-Glasma event; a single configuration of the sampled gluons in momentum space is shown by black points. Right: Strings extended in rapidity and clustered in transverse momentum. Red and blue points represent the momentum of the quarks and antiquarks attached at the string ends. Strings connecting the sampled gluons are shown by grey lines.

Figure 2

Probability distribution of scaled charged hadron multiplicity measured over $|\eta |<0.5$ in $p+p$ collisions at 7 TeV. The data points are from Ref. [64].

Figure 3

Mass ordering of $⟨p_T⟩$ plotted against scaled charged hadron multiplicity $N_{\mathrm{c}\mathrm{h}}/⟨N_{\mathrm{c}\mathrm{h}}⟩$. Data points for identified particles from the ALICE [67] and CMS [69] Collaborations are in the range $|y|<0.5$ and $|y|<1$, respectively. The values corresponding to $⟨N_{\mathrm{c}\mathrm{h}}⟩$ are obtained from Ref. [71] and Ref. [64] for ALICE and CMS data correspondingly. The $⟨p_T⟩$ values for charged hadrons are obtained from Ref. [68].

Figure 4

Dihadron correlation function using inclusive charged hadrons as both trigger and associated particles.

Figure 5

Mass ordering of $v_2\{2\}(p_T)$ extracted from the azimuthal dependence of two-particle ridge correlations in the $\mathrm{CGC}+\text{Lund}$ framework.