Systematic study for particle transverse momentum asymmetry in minimum bias pp collisions at LHC energies

In PYTHIA6 (PYTHIA8) once the transverse momentum $p_T$ of a generated particle is randomly sampled, $p_x$ and $p_y$ are set on the circle with radius of $p_T$ randomly. This may largely suppress the development of the final hadronic state transverse momentum anisotropy from the initial state spatial asymmetry. We modify PYTHIA6.4 by randomly setting $p_x$ and $p_y$ on the circumference of an ellipse with the half major and minor axes being $p_T(1+δ_p)$ and $p_T(1-δ_p)$, respectively. The modified PYTHIA6.4 is then employed to systematically study the charged particle transverse momentum asymmetry in the minimum bias pp collisions at $\sqrt s$=0.9, 7, and 14 TeV. The ALICE data on the transverse sphericity as a function of charged multiplicity, $<S_T>(N_{ch})$, are well reproduced with the modified PYTHIA6.4. It is found that the predicted charged particle $v_2$ upper limit is a measurable value, $\sim 0.12$, in the minimum bias pp collisions at $\sqrt s$=7 TeV. We suggest a systematic measurement for the particle transverse momentum sphericity, eccentricity (ellipticity), and elliptic flow parameter.

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