Nuclear Physics with Lattice QCD

Physics Accomplishments

Pion-Pion Scattering     Kaon-Pion Scattering     Kaon-Kaon Scattering     Multi-Pion Scattering       Nucleon-Nucleon Scattering       Hyperon-Nucleon Scattering     fK/fpi     Mn - Mp

    Pion-Pion Scattering
pipi 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 tree-level in chiral perturbation theory [Weinberg--long ago ].
We have calculated this scattering length at the percent level at pion masses down to 290 MeV, and find remarkable agreement with the tree-level prediction of Weinberg, as shown in the left panel.   Our prediction for the scattering length at the physical pion mass obtained with one-loop mixed-action chiral perturbation theory is shown along with other determinations/calculations, showing remarkable consistency.

Precise Determination of the I=2 pi pi Scattering Length from Mixed-Action Lattice QCD.

Silas R. Beane, Thomas C. Luu, Kostas Orginos, Assumpta Parreno, Martin J. Savage, Aaron Torok, Andre Walker-Loud
Published in Phys.Rev.D77:014505,2008.
e-Print: arXiv:0706.3026 [hep-lat]
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I = 2 pi-pi scattering from fully-dynamical mixed-action lattice QCD.
By NPLQCD Collaboration (Silas R. Beane et al.)
Published in Phys.Rev.D73:054503,2006.
e-Print: hep-lat/0506013

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pipi results

Kaon-Pion Scattering
Pi K Scattering
The pion-kaon scattering length is something that is of interest i strong interaction physics as it explores the role of the strange quark in the pseudo-Goldstone sector.  The counterterm(s) that contribute at NLO are different from that entering pion-pion and kaon-kaon scattering.  We are able to make a remarkably precise prediction for this scattering length.
Pi K a verse a

Kaon-Kaon Scattering
MKAKK verse MK
The scattering of two K+'s provides a window into the nf = 2+1 nature of low-energy 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 tree-level 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.
By NPLQCD Collaboration (Silas R. Beane et al.).
e-Print: arXiv:0709.1169 [hep-lat]

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Multi-Pion Scattering
We have recently calculated the energy of multi-pion systems up to and including systems of 12 pions. The first many-body calculation in lattice QCD.  the expression in the left panel is the energy of n-pions out to order 1/L^7, which includes the 3-pion vertex, first entering at 1/L^6.  The right panel shows the 3-body interaction in NDA units of 1/mpi fpi^4.

Multi-Pion Systems in Lattice QCD and the Three-Pion Interaction.
Silas R. Beane, William Detmold, Thomas C. Luu, Kostas Orginos, Martin J. Savage, Aaron Torok .
e-Print: arXiv:0710.1827 [hep-lat]

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The Energy of n Identical Bosons in a Finite Volume at O(L**-7).
William Detmold, Martin J. Savage
e-Print: arXiv:0801.0763 [hep-lat]

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n-Boson Energies at Finite Volume and Three-Boson Interactions.
Silas R. Beane , William Detmold, Martin J. Savage
Published in Phys.Rev.D76:074507,2007.
e-Print: arXiv:0707.1670 [hep-lat]

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3 body force

Nucleon-Nucleon Scattering
NN 1S0
In 2005 we performed the first fully-dynamical lattice QCD calculation of the nucleon-nucleon 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 scale-invariant 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.

Nucleon-nucleon scattering from fully-dynamical lattice QCD.
S.R. Beane  , P.F. Bedaque  , K. Orginos , M.J. Savage  .
Published in Phys.Rev.Lett.97:012001,2006.
e-Print: hep-lat/0602010

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NN 3S1

Hyperon-Nucleon Scattering
n Sigma- phase shift
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.  Hyperon-Nucleon scattering may play an important role in the evolution of supernova, but the cross-sections for such processes are very hard to measure, with a grand total of 35 data points exisiting at present.
The left panel shows the phase-shift 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.

Hyperon-Nucleon Scattering from Fully-Dynamical Lattice QCD.
By NPLQCD Collaboration (Silas R. Beane et al.).
Published in Nucl.Phys.A794:62-72,2007.
e-Print: hep-lat/0612026

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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 charged-current 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  alow-energy 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 (William-Mary Coll. & Jefferson Lab) , M.J. Savage (Washington U., Seattle) . NT-UW-06-15, JLAB-THY-06-503, UMD-40762-365, UNH-06-05, Jun 2006. 14pp.
Published in Phys.Rev.D75:094501,2007.
e-Print: hep-lat/0606023
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Neutron-Proton Mass-Splitting 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 charge-symmetry breaking) is due to the difference in the masses of the up and down quarks, ultimately determined by the values of the Yukawa-couplings 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 neutron-proton mass difference of M_n-M_p = 1.293318 +- 0.000009 MeV  results from an estimated electromagnetic contribution of M_n-M_p  = -0.76 +-  0.30 MeV
and the remaining mass difference is due to a strong isospin breaking contribution of M_n-M_p = 2.05 +- 0.30  MeV.

We calculated M_n-M_p = 2.26 +- 0.57 +- -.42 +- 0.10 MeV from partially-quenched lattice QCD calculations.

Strong-isospin violation in the neutron-proton mass difference from fully-dynamical lattice QCD and PQQCD.
Silas R. Beane (New Hampshire U. & Jefferson Lab) , Kostas OrginosJefferson Lab & William-Mary Coll.) , Martin J. Savage (Washington U., Seattle) .
Published in Nucl.Phys.B768:38-50,2007.  e-Print: hep-lat/0605014
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