The USQCD BSM ProjectGeorge T. Fleming
Yale University
SCGT12mini
KMI, Nagoya, Japan
19 March 2012

Participating USQCD Groups

U.S. DOE’s INCITE Program•

Innovative and Novel Computational Impact on Theory and Experiment•Current Leadership Class Resources:•••

Jaguar (Cray XT5) at Oak Ridge National Laboratory in Tennessee.

•Intrepid (IBM BlueGene/P) at Argonne National Laboratory in Illinois.

New Leadership Class Resources (starting next year):•Titan (Cray XT6, 292K AMD cores + ??? GPUs) at Oak Ridge.

•Mira (IBM BlueGene/Q, 48 racks, 768K cores) at Argonne.

USQCD receives one of the largest grants of time for lattice gauge theory,
which is divided amongst five projects, of which one is BSM physics.

Goals of the USQCD BSM Program•

U.S. DOE’s INCITE Program is an opportunity to apply very large resources
to lattice gauge theory studies of beyond the standard model (BSM) physics.

•Such large resources are ideal for producing ensembles of gauge
configurations in large lattice volumes.

•It is important that the ensembles are useful in producing results relevant forLHC phenomenology.

•For the ensembles to be of broad interest, the choice of model is chosen
through a consensus process.

•Each of the members of the BSM group are actively working on BSM
calculations on their own or as part of other scientific collaborations.

•Our current project is SU(3) Yang-Mills with Nf=8.

•Starting to plan for the next project once Nf=8 is completed.

SU(3), Nf=8 HISQ Lattice Generation• The best approach to connecting lattice gauge theory studies toelectroweak phenomenology is using the correspondence
between low energy constants (LECs) in the electroweak andhadronic chiral lagrangians.

• They parameterize many interesting possible deviations fromthe standard model, including the S parameter, WW scattering,
triple gauge vertices, ...

• To date, no lattice BSM calculation has been able to perform astandard extraction of the LECs:• The finite volume effects seem more severe than QCD.
• The radius of convergence seem to be smaller than in QCD.
• This project will be the first serious attempt to reach the chiralregime using lattices as large as 643×128.

Why do we need large volumes?
•Anticipated scales: a-1 ~ 4 MV ~ 16 MP ~ 50 FP ~ L-1.

• Bare coupling controls a⋅MV. Bare mass controls a⋅MP.
• Dynamics determines MV⋅FP.
• $$$ controls L/a. Realistically, L/a=64 is the current upper limit.
• Finite volume effects controlled by MP⋅L and FP⋅L.
• Empirical rules from QCD: MP⋅L > 4 and FP⋅L > 1.
•

Chiral expansion parameter: χ = MP2/(4πFP)2 ~ 0.06.

• Should the expansion parameter be proportional to Nf?
• Nf=2: χ→0.12 and Nf=8, χ→0.5.

Flavor Dependence of ChiPT����
2mB
12mB
2
Mπ = 2mB 1 +log
2α8 − α5 + Nf (2α6 − α4 ) +2(4πF )Nf(4πF )2��
��2mB 1Nf2mB
Fπ = F 1 +(α5 + Nf α4 ) −log2(4πF ) 22(4πF )2��
��
2N2mB
12mB
f −12�qq� = F B 1 +(2α8 + η2 ) + 2Nf α6 −log2(4πF ) 2Nf(4πF )2NLO terms in ChiPT have explicit linear dependence• Generically,
on N . An exception is the chiral log in (M ) .
πf2• The α ∼O(1) low energy constants.
• η ∼O(a ) contact term: UV-sensitive slope for condensate.
• Should we think of the expansion parameter proportional to N ?
i2-2f

Non-analytic flavor factors in NNLO ChiPTm log(m)m2 log2(m)

Mπ2

Nf-1

-3/8 Nf2 + 1/2 - 9/2 Nf-2

Fπ-1/2 Nf

3/16 Nf2 + 1/2〈qq〉-Nf + Nf-1

3/2 - 3/2 Nf-2

• J. Bijnens and J. Lu, JHEP11(2009)116 [arXiv:0910.5424]
NLO coeff for M is not generic and doesn’t persist to• Smallhigher orders.
chiral expansion parameter seems to grow with N so smaller• Thefermion masses and larger volumes are required as N increases.
π2ff

χPT Radius of Convergence
1.0

Nf=2 NLO, NNLO
0.5

Fm NLO,NNLO
Fm LO

Nf=6 NLO, NNLO

0.0

� 0.5

� 1.0
0.000

0.002

0.004

0.006

0.008

0.010

0.012

mof decreasing radius of convergence with increasing N• Evidence
on 32 ×64 lattices [E.T. Neil et al., PoS(CD09)088].
32 ×64, m≅0.01: M ⋅L~4 and F ⋅L~1. 48 ×96 or larger• Onlattices needed to reach smaller fermion masses.

f33ππ

3calculation used domain wall fermions (DWF) which are one• Thisof the most computationally expensive fermion formulations.
483×96 not feasible before next year (BlueGene/Q, ...)

Tuning the SU(3), Nf=8 HISQ Action
HISQ Nf=8, β=4.0, tmin=100.8
3a1,i5, 16 x32

a MX (X = a1,i5 ; ρi ; a0,s; π5 )

3a0,s, 16 x32
3

ρi, 16 x32

0.6

3π5, 16 x32
3a1,i5, 24 x48
3a0,s, 24 x48
3

ρi, 24 x48

0.4

3π5, 24 x48

0.2

000.005

0.010.015

0.02

am0.025

0.03

0.035

0.04

Sat Mar 10 14:21:17 2012•

We have tuned the bare coupling β=10/g02 to β=4.0 where we find that a⋅MV
≈ 0.25 in the chiral limit.

•Finite volume effects for 163×32 become significant for a⋅m<0.03 suggestingMP⋅L ≤ 5 to avoid large finite volume effects.

•Taste-breaking appears to be remain quite small even at this relatively strong
bare coupling.

Tc as a cross-check on scale setting• In QCD, Tc / MV ~ 1/5. Perhaps for Nf=8, Tc / MV ≤ 1/5.
• Our goal is a-1~ 4 MV. At that lattice spacing, Tc < 0.05 a-1.
• So, if we can guess βc on an Nt=20 lattice, then our desired
β>βc at Nt=20.

• Start by finding βc on 83×4, 123×6, 163×8, 203×10, ...
• Extrapolate βc vs. Nt to Nt > 20 using beta function plus lattice
artifactsexp

�Nτ−1− 2β01g2S

��

β11+
2β02
β0 gS

��scTcTc (0)4=1++O(a)β12� 2ΛNSτ
2β0

Running of βc from chiral susc.
468
10121620
24

1.64(10)2.67(26)
3.03(34)

1.66(13)2.60(19)
3.12(24)
3.48(27)
3.77(28)
4.20(29)
4.53(30)
4.80(30)

54.5
4symmetric

2βc (input) βc (fit)β = 10 / g0

Nt

HISQ, Nf=8, m→0 at fixed Nt

3.5
3broken2.5
2βc (predicted)
βc (meas)1.5048•Note that β=4.0 is around βc for Nt = 12–17, not Nt > 20.

•

Does this mean for Nf=8, Tc / Mρ ≈ 1/4? Not as expected!

12a Nt162024E. Neil (FNAL)

FP and S parameter using valence DWFNf �[ΠVV (0) − Π�AA (0)] + ∆SSM��2 ∞1ds Nf=[RV (s) − RA (s)]3π 0 s2�����2 31m− 1− 1− hΘ(s − m2h )4sS = 4π•

We know how to compute S parameter reliably
using domain wall fermions (DWF).

•Using DWF valence fermions and HISQ seafermions, we can also compute S on our HISQ
lattices.

•Important for validating computation of Sparameter using only HISQ fermions for valenceand sea.

•

Another indication of where finite volume effects
become significant.

•Also get rough estimate of FP from the intercept.

•Work by D. Schaich.

Outlook for USQCD BSM Project in 2012

Concluding remarks• The USQCD BSM Project has access to some of the world’s
largest supercomputing resources.

• The project generates large lattices for the immediate benefit of
the USQCD collaboration. All lattices will be made available
worldwide after first publication.

• Our first publication should include details of zero-temperature
spectrum, finite temperature phase transition, determination ofχPT LECs, condensate enhancement, etc.