Constraint on Lorentz invariance violation for spectral lag transition in GRB 160625B using profile likelihood

Abstract We reanalyze the spectral lag data for GRB 160625B using frequentist inference in order to constrain the energy scale $$(E_{QG})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>QG</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> of Lorentz Invariance Violation (LIV). For this purpose, we use profile likelihood to deal with the astrophysical nuisance parameters. This is in contrast to Bayesian inference implemented in previous works, where marginalization was carried out over the nuisance parameters. We show that with profile likelihood, we do not find a global minimum for $$\chi ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> as a function of $$E_{QG}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>QG</mml:mi> </mml:mrow> </mml:msub> </mml:math> below the Planck scale for both linear and quadratic models of LIV, whereas bounded credible intervals were previously obtained using Bayesian inference. Therefore, we can set one-sided lower limits in a straightforward manner. We find that $$E_{QG} \ge 2.55 \times 10^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>QG</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≥</mml:mo> <mml:mn>2.55</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>16</mml:mn> </mml:msup> </mml:mrow> </mml:math> GeV and $$E_{QG} \ge 1.85 \times 10^7$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>QG</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≥</mml:mo> <mml:mn>1.85</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>7</mml:mn> </mml:msup> </mml:mrow> </mml:math> GeV at 95% c.l., for linear and quadratic LIV, respectively. Therefore, this is the first proof-of-principles application of profile likelihood method to the analysis of GRB spectral lag data to constrain LIV.