New constraints on Lorentz invariance violation with polarized gamma-ray bursts

Lorentz invariance violations (LIV) can yield vacuum birefringence, which results in an energy-dependent rotation of the polarization vector of linearly polarized emission from astrophysical sources. It is believed that if the relative rotation angle ($\Delta\Theta$) of the polarization vector of high energy photons with respect to that of low energy photons is larger than $\pi/2$, then the net polarization of the signal would be significantly depleted and could not be as high as the observed level. Hence, the measurement of high polarization implies that $\Delta\Theta$ should not be too large. In this work, we assemble recent detections of prompt emission polarization in gamma-ray bursts (GRBs), all of whom have high detection significance. Following the method shown in Lin et al. (2016), we give a detailed calculation on the polarization evolution arising from the LIV effect for each GRB, and confirm that, even if $\Delta\Theta$ is approaching to $\pi/2$, the net polarization is not severely suppressed, and more than 60\% of the initial polarization can be conserved. Applying this method to our GRB polarimetric data, we improve existing sensitivities to LIV involving photons by factors ranging from two to ten. In addition, we prove that our constraints are not greatly affected by uncertainties in the spectral parameters of GRBs.