1. M. Lujan Hadron Electric Polarizability with n-HYP Clover Fermions Michael Lujan Andrei Alexandru, Walter Freeman, and Frank Lee The George Washington University 2013 Lattice Conference, Mainz 1The George Washington University

2. M. Lujan Motivation Quantum mechanical example Background field method Choice of electric field Use of Dirichlet boundary conditions Preliminary Results outline The George Washington University2

3. M. Lujan Motivation The George Washington University 3 - H. R. Fiebig, W. Wilcox, and R. M. Woloshyn, Nucl. Phys. B324, 47 (1989) - A. Alexandru and F. X. Lee (2009), 0911.2520 - W. Detmold, B. C. Tiburzi, and A. Walkder-Loud, ariXiv:1001.1131v2 [hep-lat] - W. Detmold, B. C. Tiburzi and A. Walker-Loud, arXiv:0809.0721 [hep-lat]. - M. Engelhardt [LHPC Collaboration], Phys. Rev. D 76, 114502 (2007) [arXiv:0706.3919 [hep- lat]] - J. Christensen, W. Wilcox, F. X. Lee, and L.-M. Zhou, Phys. Rev. D 72, 034503 (2005) - W. Detmold, B. C. Tiburzi, and A. Walker-Loud, arXiv:0809.0721 [hep-lat];, Phys. Rev. D 79 094505, (2009). many other contributions.

4. Michael Lujan Quantum Mechanical Example 1 st order 2 nd order An external electric field changes the energy. We want to calculate this energy or mass shift. Ground state 4

5. M. Lujan Atomic vs. Nuclear 5

6. M. Lujan Background field method The George Washington University6 1)Choose a vector potential that produces a constant electric field 2)Measure the energy shift  get the polarizability Focus on neutral particles. Valence calculation Volume effects, chiral behavior, partial quenching

7. M. Lujan Electric Field Scaling The George Washington University7 u d -1e/3 2e/3 Important: what value of electric field should we use? Too large will provoke higher order effects. Too small we have numerical precision issues. Another motivation is to help with calculations for charging the sea quark. (NEXT PRESENTATION)

8. M. Lujan The Ensembles: 2-flavor n-HYP Clover The George Washington University8 1)24 3 x 48 a = 0.126 fm M π ~ 300 MeV 300 configurations η=0.0051 2) 24 3 x 64 a = 0.126 fm M π ~ 220 MeV 500 configurations η=0.0001 3) 48 x 24 2 x 48 a = 0.126 fm M π ~ 300 MeV 300 configurations η=0.0001 * 5 propagators per configuration per source (0, +E, +2E, -E, -2E) * 5 – 6 kappa values, study the pion mass dependence. * About 20 point sources per configuration ~ 6 GPU hours per configuration per source ~ 150,000 GPU hours for this project COMPUTATIONAL COST Note: 24 3 x48 lattice has a different has a different value of η than the other two. It was used to avoid values of numerical precision.

9. M. Lujan Fitting Method The George Washington University9 C =C =

10. M. Lujan Boundary effects and mass shift The George Washington University10 We use Dirichlet B.C. in x and t: Allows us to use any value of the electric field we want Try to minimize effects by placing the source away from the Dirichlet walls. The B.C. in x induces a non-zero momenta ~ π/L Free particle will have an altered energy : E 2 =m 2 +(π/L) 2 Is calculated with no electric field in a periodic box

11. M. Lujan Benefits of multiple sources The George Washington University11 pion neutron

12. M. Lujan Preliminary Results: neutral “pion” The George Washington University12 Negative trend continues--as seen in other studies. No difference can be said about partial quenching for these range masses. No volume dependence is seen

13. M. Lujan Preliminary Results: Neutron The George Washington University13 There seems to be a rise in the central value, should do a jackknife difference for these values. Perhaps a partial quenching effect is seen--need to increase statistics.

14. M. Lujan Preliminary Results: Neutron cont… The George Washington University14 We don’t, yet, see a steep rise toward the experimental value. Will the rise towards the experimental value become more apparent for m π < 200 MeV? Volume effects, what will the 48 lattice show? Dynamical effects, the exclusion of charged sea quarks…(next presentation)

15. M. Lujan This work: Studying three ensembles using dynamical generated n-HYP clover fermions. Volume study, chiral study, partial quenching. We looked at the neutron, pion. The pion seems to still have the same negative trend even for large boxes and smaller quark masses. Neutron is beginning to show a rise at around < 250 MeV Future work Volume study for the neutron, currently the signal is note so clear. The effects of charging the sea quarks—all the propagators and correlators we compute for this valence study is directly used in the study with charged sea quarks. Also charged particles. The data is already there. Summary and outlook The George Washington University15

16. M. Lujan END The George Washington University16

17. M. Lujan Preliminary Results: Neutron The George Washington University17 with corrected magnetic moment