M. Lujan

Hadron Electric Polarizability with n-HYP Clover Fermions

Michael LujanAndrei Alexandru, Walter Freeman, and

Frank LeeThe George Washington University

2013 Lattice Conference, Mainz

1The George Washington University

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Motivation

Quantum mechanical example

Background field method

Choice of electric field

Use of Dirichlet boundary conditions

Preliminary Results

outline

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Motivation

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- 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..

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Quantum Mechanical Example

1st order

2nd order

An external electric field changes the energy. We want to calculate this energy or mass shift.

Ground state

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Atomic vs. Nuclear

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Background field method

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1) Choose a vector potential that produces a constant electric field2) Measure the energy shift get the polarizability

• Focus on neutral particles.

• Valence calculation

• Volume effects, chiral behavior, partial quenching

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Electric Field Scaling

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u d

-1e/32e/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)

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The Ensembles: 2-flavor n-HYP Clover

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1) 243 x 48• a = 0.126 fm• Mπ ~ 300 MeV• 300 configurations• η=0.0051

2) 243 x 64• a = 0.126 fm• Mπ ~ 220 MeV• 500 configurations• η=0.0001

3) 48 x 242 x 48

• a = 0.126 fm• Mπ ~ 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: 243x48 lattice has a different has a different value of η than the other two.It was used to avoid values of numerical precision.

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Fitting Method

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Boundary effects and mass shift

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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 : E2=m2+(π/L)2

Is calculated with no electric field in a periodic box

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Benefits of multiple sources

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pion neutron

neutron

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Preliminary Results: neutral “pion”

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• 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

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Preliminary Results: Neutron

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• 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.

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Preliminary Results: Neutron cont…

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We don’t, yet, see a steep rise toward the experimental value.•Will the rise towards the experimental value become more apparent for mπ < 200 MeV?•Volume effects, what will the 48 lattice show?•Dynamical effects, the exclusion of charged sea quarks…(next presentation)

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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 workVolume 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

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END

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Preliminary Results: Neutron

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with corrected magnetic moment