NPLQCD
Nuclear Physics with Lattice QCD 
Physics
Accomplishments 
PionPion Scattering  
The simplest hadronic scattering
process is that of two positivly charged pions. Highly
constrained by the approximate chiral symmetry of QCD, the scattering
length is uniquely predicted at treelevel in chiral perturbation
theory [Weinberglong ago ]. We have calculated this scattering length at the percent level at pion masses down to 290 MeV, and find remarkable agreement with the treelevel prediction of Weinberg, as shown in the left panel. Our prediction for the scattering length at the physical pion mass obtained with oneloop mixedaction chiral perturbation theory is shown along with other determinations/calculations, showing remarkable consistency. Precise Determination of the I=2 pi pi Scattering Length from MixedAction Lattice QCD. Silas R. Beane, Thomas C. Luu, Kostas Orginos, Assumpta Parreno, Martin J. Savage, Aaron Torok, Andre WalkerLoud Published in Phys.Rev.D77:014505,2008. ePrint: arXiv:0706.3026 [heplat]
I = 2 pipi scattering from fullydynamical mixedaction lattice QCD. By NPLQCD Collaboration (Silas R. Beane et al.) Published in Phys.Rev.D73:054503,2006. ePrint: heplat/0506013

KaonKaon Scattering  
The scattering of two K+'s provides
a window into the nf = 2+1 nature of lowenergy QCD. In chiral
perturbation theory the counterterms that enters at NLO is the same as
that for pi+ pi+ scattering. Surprisingly, the scattering
length is seen to be well reproduced by Weinbergs treelevel
prediction. This is unexpected as loops were thought to be
important at these masses, but apparently are not showing themselves. The K+ K+ scattering length from lattice QCD.

MultiPion Scattering  
We have recently calculated the
energy of multipion systems up to and including systems of 12 pions.
The first manybody calculation in lattice QCD. the expression in
the left panel is the energy of npions out to order 1/L^7, which
includes the 3pion vertex, first entering at 1/L^6. The right
panel shows the 3body interaction in NDA units of 1/mpi fpi^4. MultiPion Systems in Lattice QCD and the
ThreePion Interaction.
The Energy of n Identical Bosons in a Finite Volume
at O(L**7).
nBoson Energies at Finite Volume and ThreeBoson
Interactions.

NucleonNucleon Scattering  
In 2005 we performed the first
fullydynamical lattice QCD calculation of the nucleonnucleon
scattering length at pions as light as 350 MeV. The scattering length is found to be of natural size at the pion masses, unlike the unnaturally large scattering lengths found in nature. Only one of the points was at a pion mass within the regime of applicability of the NN effective field theories that have been develoiped during the last 15 years, and so we were unable to extrapolate to the physical point. However, in conjunction with the physical point we extrapolated to the chiral limit, finding very curious behaviour. It is possible that in the limit of vanishing quark masses that the scattering lengths in BOTH spin channels diverges, leading to a completely scaleinvariant interaction. We have no idea why nature would choose such behaviour, but it is something that must be explored further with lattice QCD calculations at lighter pion masses. Nucleonnucleon scattering from fullydynamical
lattice QCD.

HyperonNucleon Scattering  
One of the prime objective of
the NPLQCD collaboration is to compute scattering amplitudes for
processes that are inaccessible, or extremely hard to explore,
experimentally. HyperonNucleon scattering may play an important
role in the evolution of supernova, but the crosssections for such
processes are very hard to measure, with a grand total of 35 data
points exisiting at present. The left panel shows the phaseshift at one energy, in particular our calculation at a pion mass of ~500 MeV, compared with theory predictions at the physical pion mass. The right panel shows some of the available data and theory fits. HyperonNucleon Scattering from FullyDynamical
Lattice QCD.

fK / fpi 

Lattice determinations of the
pseudoscalar decay constants fK and fpi, when combined wityh the
experimentally measures branching fractions for K>mu nu(mu)(gamma)
and pi> mu nu(mu)(gamma) provide important theoretical input into
establishing the value of Vus, the chargedcurrent matrix element for
the s> u transition. Precise determination of Vus and Vud
together with the fact that the square of Vub is negligibly small,
provide aclean test of the tunitarity of the CKM matrix, and thus
provide alowenergy probe for physics beyond the standard model
with three generations of quarks. We calculated fK/fpi = 1.218 + 0.002 (+0.011)(0.024) . f(K)/f(pi) in Full QCD with Domain Wall Valence Quarks. S.R. Beane (New Hampshire U. & Jefferson Lab) , P.F. Bedaque (Maryland U. & LBL, Berkeley) , K. Orginos (WilliamMary Coll. & Jefferson Lab) , M.J. Savage (Washington U., Seattle) . NTUW0615, JLABTHY06503, UMD40762365, UNH0605, Jun 2006. 14pp. Published in Phys.Rev.D75:094501,2007. ePrint: heplat/0606023

NeutronProton MassSplitting due to Strong Isospin
Breaking  Charge Symmetry Breaking 

It is a basic property of our
universe that the neutron is slightly more massive than the
proton. The electroweak interactions are responsible for this
mass difference, which receives contributions from two sources.
The strong isospin breaking contribution (also known as chargesymmetry
breaking) is due to the difference in the masses of the up and down
quarks, ultimately determined by the values of the Yukawacouplings in
the Standard Model of electroweak interactions and the vacuum
expectation value of the Higgs field. The other contribution arises
from the fact that the proton and neutron carry different
electromagnetic charges. The experimental neutronproton mass
difference of M_nM_p = 1.293318 + 0.000009 MeV results from an
estimated electromagnetic contribution of M_nM_p = 0.76
+ 0.30 MeV and the remaining mass difference is due to a strong isospin breaking contribution of M_nM_p = 2.05 + 0.30 MeV. We calculated M_nM_p = 2.26 + 0.57 + .42 + 0.10 MeV from partiallyquenched lattice QCD calculations. Strongisospin violation in the neutronproton mass difference from fullydynamical lattice QCD and PQQCD. Silas R. Beane (New Hampshire U. & Jefferson Lab) , Kostas OrginosJefferson Lab & WilliamMary Coll.) , Martin J. Savage (Washington U., Seattle) . Published in Nucl.Phys.B768:3850,2007. ePrint: heplat/0605014
