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, $\mathrm{\Delta }G$, 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 ${\pi }^0$, $\eta$, $J\mathrm{/}\psi$ etc. are measured in wide rapidity range. In this talk, $A_{LL}$ in ${\pi }^0$ production in central rapidity and $J\mathrm{/}\psi$ production in forward rapidity will be discussed. The ${\pi }^0$ is reconstructed through its diphoton decay channel within the rapidity range of $\mid \eta \mid$ $<$ 0.35 and azimuthal angle of $180{}^{\circ }$. Similarly, $J\mathrm{/}\psi$ is reconstructed via dimuon decay channel within the rapidity range of 1.2 $<$ $\mid \eta \mid$ $<$ 2.2. Preliminary results for $A_{LL}$ in ${\pi }^0$ and $J\mathrm{/}\psi$ 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 $\mathrm{\Delta }G$ constraint will be discussed. In year 2013, the total integrated luminosity was 150 $p{b}^{-1}$ 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 ${\pi }^0$ and 0.002 for $J\mathrm{/}\psi$.