2+1 flavor topological susceptibility from the asqtad ... · Conclusions First MILC χtopo Result...

Full QCD Topological Susceptibility since 2001MILC Asqtad Program: χtopo

2007 Methods and ResultsConclusions

2+1 flavor topological susceptibility from theasqtad action at 0.06 fm

C. Bernard, B. Billeter, C. DeTar, S. Gottlieb,U.M. Heller, J.E. Hetrick1,L. Levkova, J. Osborn

D. Renner, R. Sugar, D. Toussaint

1MILC CollaborationUniversity of the Pacific

Stockton, CA USA

LATTICE 2007Regensberg, Germany

J.E. Hetrick / MILC - LAT07 LATTICE 2007



Outline

1 Full QCD Topological Susceptibility since 2001An assignment from S. Dürr in 2001

2 MILC Asqtad Program: χtopoFirst MILC χtopo Result 2003Rooted Staggered Chiral Perturbation TheoryBilleter, DeTar, and Osborn: χtopo from RSχPT

3 2007 Methods and ResultsMethodsResultsCaveats

4 Conclusions




An assignment from S. Dürr in 2001

From: S. Dürr: hep-lat/0103011 (Nucl. Phys. B611 p.281 2001)

For small mq

χtopo ∼f 2πm2

π

2Nf

Where’s the m → 0suppression in the data?

“...roughly consistent with each other, butfollow theoretical expectations to a limited degree”




An assignment from S. Dürr in 2001

Data used for 2001 comparison:

CP-PACS: Iwasaki action + Wilson clover fermions (163x32, 243x48)

UKQCD: Wilson gauge + Wilson clover fermions (163x32)

SESAM/TχL: Wilson gauge and Wilson fermions (163x32, 243x40)

PISA: Wilson gauge + staggered fermions (164)

Advances since 2001:Highly Improved Actions — 2+1 flavor full QCDStaggered Chiral Perturbation TheoryBigger Computers




First MILC χtopo Result 2003Rooted Staggered Chiral Perturbation TheoryBilleter, DeTar, and Osborn: χtopo from RSχPT

MILC Improved Action ProgramAsqtad Action: O(αsa2) improved gauge and fermion actions

Topological Charge via Boulder Fµν F̃ µν and HYP Smearing

By 2003 — 2 lattice spacings: a = 0.13 and 0.09 fm

C. Bernard et. al. Phys. Rev. D68 114501 (2003)

a → 0 extrapolation isessentialData compared tocontinuum χPT:

χtopo ∼f 2πm2

π

4(1 + mu,d/2ms)

2 lattice spacings...Encouraging results





(Rooted) Staggered Chiral Perturbation Theory

Lee and Sharpe W. Lee and S. Sharpe, Phys. Rev. D60 114503 (1999) —1 flavor × 4 tastes

Aubin and Bernard C. Aubin and C. Bernard, Phys. Rev. D68 034014 (2003) — nf flavors × 4 tastes, and— nf flavors × (4 tastes)1/4

How to handle taste breaking effects at finite a.





Billeter, DeTar, and Osborn: Anomaly couples to φoIB. Billeter, C. DeTar, and J. Osborn, Phys. Rev. D70 077502 (2004)

From the Rooted Staggered ChiralLagrangian

L =f 2π

8Tr(∂µU†∂U) +

XCiOi

− µf 2π

4Tr[M(U† + U)] +

m2o

2φ2

oI + . . .

χtopo =f 2πm2

π,I/81 + m2

π,I/2mss,I + 3m2π,I/2m2

o

χm→0 ∼f 2πm2

π,I

8

χm→∞ ∼f 2πm2

o

12= 0.06/r 4

0

Pion taste multiplet masses m2π,t at fixed a,

versus quark mass mq

Lesson:Use m2

π,I not m2π,Goldstone




MethodsResultsCaveats

Topological Susceptibitily Measurements

Boulder extended Fµν F̃µν definitionT. DeGrand, A. Hasenfratz, and T. Kovacs Nucl. Phys. D505, 417 (1997)

Use 3 HYP Smoothing sweeps to find q(r) = Fµν F̃µν

Use⟨Q2

⟩/V =

∫dr 〈q(r)q(0)〉

Fit long distance behavior of 〈q(r)q(0)〉 to analytical form toη + η′ scalar propagator.





Long distance topological charge density correlator fit

Defining C(r) = 〈q(r)q(0)〉⟨Q2⟩ /V =

∑r≤rc

Cmeas(r) +∑r>rc

Cfit(r)

Cfit(r) = D(mη, r) + D(mη′ , r)

D(m, r) =m

4π2rK1(mr)





New Results from a = 0.06 fm 483× 144 lattices

Simultaneously Fitdata at differentlattice spacings andmasses to f (m, a)

1χtopor 4

0= f (m2

π,I , a)

= A0+(A1+A2a2+A3a4)/m2π,I

Continuum = f (m, 0)

Compare with L.O.2+1 + ∞ RSχPT





Autocorrelation of Q




Conclusions

2+1 flavor χtopo quite consistent with SχPT

0.06 fm data already very close to continuum for small mπ,I

1/4 root method is supported, since continuum formula for χtopo isquite sensitive to nf and mf


2+1 flavor topological susceptibility from the asqtad ... · Conclusions First MILC χtopo Result...

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