m. lujan hadron electric polarizability with n-hyp clover fermions michael lujan andrei alexandru,...
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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
M. Lujan
Motivation
Quantum mechanical example
Background field method
Choice of electric field
Use of Dirichlet boundary conditions
Preliminary Results
outline
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M. Lujan
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..
Michael Lujan
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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M. Lujan
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)
M. Lujan
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.
M. Lujan
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
M. Lujan
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
M. Lujan
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.
M. Lujan
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)
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 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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