theta dependence of the spectrum of SU(N) gauge theories

We study the theta dependence of the spectrum of four-dimensional SU(N) gauge theories, where theta is the coefficient of the topological term in the Lagrangian, for N >= 3 and in the large-N limit. We compute the O(theta(2)) terms of the expansions around theta = 0 of the string tension and the lowest glueball mass, respectively sigma(theta) = sigma (1 + s(2)theta(2) + ...)and M(theta) = M (1 + g(2)theta(2) +...), where sigma and M are the values at theta = 0. For this purpose we use numerical simulations of the Wilson lattice formulation of SU( N) gauge theories for N = 3, 4, 6. The O(theta(2)) coefficients turn out to be very small for all N >= 3. For example, s(2) = -0.08(1) and g(2) = -0.06(2) for N = 3. Their absolute values decrease with increasing N. Our results are suggestive of a scenario in which the theta dependence in the string and glueball spectrum vanishes in the large-N limit, at least for sufficiently small values of vertical bar theta vertical bar. They support the general l (theta) over bar arge- N scaling arguments that indicate 0/N as the relevant Lagrangian parameter in the large-N expansion.