Proton Decay Matrix Elements: USQCD collaboration FY 2007

Proton Decay Matrix Elements

A project in USQCD collaboration in FY2007 & 2008

Y. Aoki (PI), C. Dawson, T. Izubuchi, A. Lichtl, A. Soni

mail to: yaoki AT bnl.gov

Proton decay is a smoking gun of the physics beyond the standard model and is naturally expected in grand unified theories (GUTs). Lower limit of the proton lifetime from the deep mine experiments has been providing important constraints on the GUT models. The theoretical estimate of the lifetime requires short range information which differs from one GUT model to the other, and the low energy matrix elements with an initial proton and a final pseudoscalar meson, which are model independent. We are aiming to provide a reliable estimate of the matrix elements using lattice QCD.

There are three key points for which this calculation makes the results more reliable than the existing ones.

Usage of the 2+1 flavor dynamical domain wall fermion ensemble generated by RBC and UKQCD collaborations. This will eliminate the quenching error of the existing calculation. Usage of the chiral fermion allows only the same mixing of operators as in the continuum theory, that will help reduce the systematic error, too.

Usage of a non-perturbative renormalization. By that we do notneed to rely on the lattice perturbation theory which has larger systematic error. The method was tested in our previous quenched and 2 flavor dynamical domain wall fermion calculations.

Usage of the direct method to calculate the matrix elements. This will eliminate the uncontrolled error of the more conventional indirect method, where only two new low energy constants besides the ordinary low energy constants of the nucleon chiral Lagrangian will control the matrix elements of all the decay modes. We calculate the matrix elements through the three-point function for each decay modes.

Our target is to reach as small as 20-30% error on the matrix elements, where the error does not include those from the scaling violation. To control the error from the scaling violation, we need to repeat our calculation on ensembles on the different lattice spacing, which would be the future work.

Project status FY2007:

Non-perturbative renormalization of the operator: Done.

Tuning the smearing parameters for the nucleon and pseudoscalar operators: Done.

Measurement of the matrix element by the direct method:

mf=0.01: 75% done.
mf=0.02: Done
mf=0.03: Yet.

Project status FY2008:

Measurement of the matrix element by the direct method:

mf=0.005: Yet.