Can baryon acoustic oscillations illuminate the parity-violating galaxy four-point correlation function?

Recent measurements of the galaxy four-point correlation function (4PCF) from the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey indicate potential statistical evidence for parity violation. If this signal is of genuine physical origin, it must stem from beyond-Standard Model physics, most likely during the very early Universe, prior to decoupling ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>z</a:mi> <a:mo>∼</a:mo> <a:mn>1020</a:mn> </a:mrow> </a:math> ). Since the baryon acoustic oscillation (BAO) features imprint at decoupling, they are expected in the parity-odd galaxy 4PCF. Thus detecting them would be an additional piece of evidence that the signal is genuine. We demonstrate, using a toy parity-violating model, how the BAO imprint on the parity-odd 4PCF. We then show how to do a model-independent search for BAO in the odd 4PCF. This is desirable since, if the signal is real, we may not know for some time what model of e.g. inflation produces it. If BAO are detected in the parity-odd sector, they can be used as a standard ruler as is already done in the two-point correlation function and three-point correlation function. We derive a simple formula relating the expected precision on the BAO scale to the overall parity-odd detection significance. Searching for the BAO in the odd 4PCF of redshift surveys such as DESI, Euclid, Spherex, and Roman will be a valuable additional avenue to determine if parity violation in the distribution of galaxies is real.