The symbol and alphabet of two-loop NMHV amplitudes from Q equations

We study the symbol and the alphabet for two-loop NMHV amplitudes in planar N = 4 super-Yang-Mills from the Q equations, which provide a first-principle method for computing multi-loop amplitudes. Starting from one-loop (NMHV)-M-2 ratio functions, we explain in detail how to use Q equations to obtain the total differential of two-loop n-point NMHV amplitudes, whose symbol contains letters that are algebraic functions of kinematics for n >= 8. We present explicit formula with nice patterns for the part of the symbol involving algebraic letters for all multiplicities, and we find 17 - 2m multiplicative-independent letters for a given square root of Gram determinant, with 0