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Recent results from PHENIX on double helicity asymmetry ($A_{LL}$) measurement at $\sqrt{s}$ = 510 GeV

One of the major objectives of the RHIC spin program at BNL is the measurement of the gluon helicity contribution, $ΔG$, to the proton spin via measuring the double longitudinal spin asymmetry ($A_{LL}$) in various channels. In PHENIX (Pioneering High Energy Nuclear Interaction eXperiment) the $A_{LL}$ in $π^{0}$, $η$, $J/ψ$ etc. are measured in wide rapidity range. In this talk, $A_{LL}$ in $π^{0}$ production in central rapidity and $J/ψ$ production in forward rapidity will be discussed. The $π^{0}$ is reconstructed through its diphoton decay channel within the rapidity range of $\left| η\right|$ $<$ 0.35 and azimuthal angle of $180\,^{\circ}$. Similarly, $J/ψ$ is reconstructed via dimuon decay channel within the rapidity range of 1.2 $<$ $\left| η\right|$ $<$ 2.2. Preliminary results for $A_{LL}$ in $π^{0}$ and $J/ψ$ production from the data collected in the year 2013 at center of mass energy ($\sqrt{s}$) = 510 GeV will be presented. Also, their impact on $ΔG$ constraint will be discussed. In year 2013, the total integrated luminosity was 150 $pb^{-1}$ which is almost ten times the total luminosity recorded in the year 2009 at $\sqrt{s}$ = 200 GeV. Due to increase in the center of mass energy and integrated luminosity, the new measurements can cover the Bjorken x range down to 0.01 for $π^{0}$ and 0.002 for $J/ψ$.