Electromagnetic Hadronic Form-Factors

The determination of light hadron physics properties is of considerable interest to experimental labs such as Jefferson Lab. Many quantities, such as hadron form-factors and generalized structure functions, are not well understood theoretically. The available and forthcoming high precision experimental data presents considerable challenges and many opportunities for corresponding lattice calculations. Including the contribution of light dynamical quarks is an important goal of this work, but the cost of generating these gauge ensembles is large. We have adopted a so-called “hybrid” scheme where staggered sea quarks are used (Asqtad action [1]) and domain wall valence quarks [2]. While unitarity is broken at finite lattice spacing, it is recovered in the continuum limit when the sea and valence quark masses are properly tuned. In this contribution, we study the efficacy of an uncommon method of calculating threepoint functions that avoids sequential source techniques. We calculate various electro-magnetic form-factors without the cost of a new sequential inversion for each new set of observables. The method is particularly suitable for valence quark actions amenable to a multi-mass solver, such as the Overlap quark action. The conclusion is that the method appears viable, but very light quark mass tests are needed (and on-going). A typical sequential source method for computing a matrix element such as 〈B(pf )|V (q)|A(pi)〉 for an initial state A with three-momenta pi and final state B at momenta pf with a two-quark insertion V involves either a sequential inversion through the insertion or the sink. To properly extract the matrix element for a set of momenta q = pf − pi, usually the sequential source for the sequential insertion is held at a fixed momenta. There are two common techniques. Sequential inversion through insertion: benefits are that one can vary the source and sink fields but the insertion momenta and operator are fixed. Sequential inversion through sink: benefits are one can vary the insertion operator and momenta, but the sink operator and momenta are fixed. In addition, for baryons the spin projection matrix between the source and sink must be fixed necessitating different sequential inversions to extract electric and magnetic quantities. The common problem is one vertex must have a definite momentum. As an alternative, one can instead make a sink (or source) quark propagator (as opposed to the state) have a definite momentum. Putting the sink (or source) quarks at definite momentum implies the hadron state has a fixed momenta via the translation/momentum operator on the lattice. The scheme then is to build the desired hadron state propagating from the source and sink where the quark propagators used for one of these states has a fixed momenta. Thus, one avoids sequential inversions computing 〈B(pf )|V (q)|A(pi)〉. For example, fixing the sink momenta to a fixed pf , one can extract the matrix element at all q by vary pi according to momentum conservation. To fix a quark’s momenta necessarily implies a wall source thus requiring the need for gauge fixing. Additional tricks can be used to improve statistics like using charge conjugation and time reversal (CT) in (anti-)periodic boundary conditions. This method also works for Dirichlet boundary conditions where one maintains equal source and sink separation from the Dirichlet