DWF@10 : BNL, NY : 15-17 March 2007 1

Baryon spectrum from 2+1 flavours of DWF QCD

Baryon spectrum from 2+1 flavours of DWF QCD

Chris Maynard

RBC and UKQCD collaborations

Chris Allton, Tom Blum, Paul Cooney, Luigi del Debbio, Meifeng Lin, Aurora Trivini, Takeshi Yamazaki, James Zanotti

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OutlineOutline

Motivation– Why baryons

Ensemble details– What has been measured

Baryon spectrum (degenerate)– Nucleons– Decuplet baryons

Outlook and conclusions

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Why baryons are importantWhy baryons are important

N. Isgur 1947-2001 nucl-th/0007008– Why N*'s are Important"

Nucleons are the stuff of which world is made Simplest system in which the quintessentially

nonabelian character of QCD is manifest– Nc quarks in proton because there are Nc colours

Baryons are sufficiently complex to reveal physics hidden from us in Mesons– Non-analytic chiral behaviour

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Roper Resonance

QM HO potential

Spectrum not completely understoodSpectrum not completely understood

Excited states do not fit “naturally” in Quark Model e.g. the Roper resonance

N(1440) JP=1/2+

Lattice QCD can give definitive answer

Excited states are hard

Is Roper radial excitation of nucleon, or something else

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Matrix elementsMatrix elements

Diverse phenomenology Structure functions

– Collider physics

Strangeness content of nucleon– Cold Dark Matter

Neutron electro-dipole moment– SUSY phenomenology

Proton decay– GUT and SUSY GUT models

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EnsemblesEnsembles

mu volume Ntraj Ntp Nind

0.03 163x32 4000 2 70

0.02 163x32 4000 4 70

0.01 163x32 4000 4 70

0.03 243x64 3000 2 50

0.02 243x64 3600 2 50

0.01 243x64 4000 2 80

0.005 243x64 4500 1 80

Iwasaki gauge action =2.13, 2+1 flavours (ms=0.04) LS=16 mres=0.003 a-1=1.60(3) (rho,r0, method of planes)

L= 2fm

L= 3fm

243 is still running and more measurements to comeResults are preliminary

Not complete

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NucleonsNucleons

RBC and UKQCD separate measurement datasets for matrix elements

Combined analysis for m=0.01 V=243

– 60 configurations– 5 Smearing combinations (6 for N*)

• Local-local LL• Gaussian-local (R=4) GL• Gaussian-Gaussian GG• Box (L=16) (extra N* operator) BL • Gaussian-local (R=7) G2L (4 tps)

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Nucleon massNucleon mass

Fit effective mass

1 fit parameter No fit-range

systematic error Only for m=0.01

1(

)(lneff

tc

tcm

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Nstar massNstar mass

3-6 timeslices per correlator

Result is fit-range sensitive for individual correlators

Uber-fit is fit-range insensitive

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Finite size effectsFinite size effects

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Nucleon FSENucleon FSE

No obvious FSE for Nucleon– 2 and 3 fm box

– mP ~ 390Mev

– mPL ~ 3.9 and 5.8

– mP/mV ~ 0.45

No FSE expected– m=0.005 mPL ~

4.6

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Nstar FSENstar FSE

No obvious FSE for Nstar– No expectation– N* Uber fit for 243

– N* noisey for 163

No FSE– Statistics limited

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Edinburgh plotEdinburgh plot

Displays all 2+1 flavour DWF data

Apparently lies on universal curve– LS, gauge

coupling, volume

Lightest data noisy due to vector correlator

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Chiral extrapolationChiral extrapolation

Linear extrap. vs mP

2

m=0.01 uberfit– No fit systematic

m=0.005 datum low?– Chiral effect?

– mP ~ 310MeV

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Chiral extrapolation IIChiral extrapolation II

NLO PT term– mP

3

Radius of convergence?

Maybe lightest– Definitely not

heaviest

Just for fun!

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Decuplet baryonsDecuplet baryons

Valence degenerate

mV=mu=mSea

mV=mstrange

Effective mass plot for m=0.01– Not fitting Meff

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Chiral extrapolationChiral extrapolation

Data consistent with linear extrapolation

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Baryon SpectrumBaryon Spectrum

Three lowest lying valence degenerate states– Negative parity

partners

Reasonable agreement with experiment– a-1=1.60(3) GeV

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Baryon spectrumBaryon spectrum

Ultimately expect non-linear chiral behaviour– Can’t get spectrum right

with linear

NLO PT fit not realistic– goes in right direction– maybe just statistics

Require lighter quarks and better statistics

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ConclusionsConclusions

Preliminary results for Baryon spectrum– Broadly agrees with experiment– starting to reach interesting regime

– mu/ms < 1/5, mP/mV ~ 0.38, mP ~ 310 MeV

– Measurements still running

Complex chiral behaviour must be explored to get spectrum right

Finer lattice spacing simulation under way– control lattice artefacts