A Novel Gauge Invariant Multistate Smearing Technique

We present an investigation of a gauge invariant smearing technique that allows the construction of smearing functions with arbitrary radial behavior, by foresaking the space-filling nature of traditional smearing techniques. This is applied to both heavy–heavy, heavy–light, and light–light systems with one particular choice of radial “wavefunction”—the hydrogenic solutions—and we find good stability for both fitted masses and amplitudes of the radially excited states. The dependence of the amplitudes on the smearing radius is demonstrated to be well understood, while near optimal smearing radii may be found with extremely low statistics using a property of the smeared-local correlator. The smearing technique is inexpensive since it is noniterative, achieves a good signal-to-noise ratio, and can be altered to use wavefunctions from, say, potential models or the Bethe–Salpether equations in future simulations.