University of Tsukuba | Center for Computational Sciences

Research in Particle Physics
2+1 flavor QCD at Physical Point on very large lattices (master-field simulations)
Hadrons are the constituents of atomic nuclei. The computation of theirmass spectrum from the quantum chromodynamics (QCD), thefundamental theory of strong interaction described by quarks and gluons,
has been a principal subject in particle physics.
After quenched simulation and a succeeding 2 flavor QCD simulation by
the CP-PACS, those studies were extended to 2+1 flavor QCD byincorporating the dynamical strange quark, though the degenerate updown quark mass was much heavier than the physical value. On the PACSCS and T2K computers, we have succeeded in reaching the physical pointby a reweighting technique. This calculation is followed by a larger volume
simulation on the K computer. Fig. 1 presents relative difference of thelight hadron spectrum from the experiment. In the figure the inputs are
only the pion, kaon, and omega baryon masses to determine the up-down
Fig1, K-.I. Ishikawa et. al., https://arxiv.org/abs/1511.09222 and strange quark masses, and the lattice cutoff, respectively. Our results
at the physical point show good agreement with the experiment albeit
errors are still not quite small for some of the hadrons.

Our current project is aiming to control and remove systematic errors
due to the previous simulations on a finite volume with a finite latticespacing. We are performing so called master-field simulations on verylarger (10fm)4 volume with several lattice spacings using the OakforestPACS computer which ranks in the 3rd position in the HPCG benchmark
and in the 6th position
intheTOP500listatSC16.
Fig.
2showsaTA BLE X I . E ntropy density (ϵ + p)/ T 4 : coefficient of the nonlinear ﬁ t within the linear window
4 andcomparison
ofpseudoscalar
decay
constants,
fandf,
on(10fm)
πK2and χ / D OF .
(5fm)4. We detect 0.66% and 0.25% finite volume effect on fπ and fK,T
const
linear
1/ tt2χ 2 / D OF
respectively. The effect is very small but negligible to compare the549 9.494(36) − 2.282(52)5.7875(92)0.000000(0.000000) 925.2(3.8)
corresponding experiments.
Now,
we can control and remove the finite
439volume
24.207(84)effect− 11.540(58)2.138(16)0.000000(0.000000)
0.161(11)completelyby using
the master-field
simulations.
366 26.70(10) − 10.20(11) 0.000000(0.000000)

1.300(38)0.05740.0680fK

fπ

0.05720.06790.05700.06780.05680.0677
0.0566

0.0676
0.05640.0562(5fm)

44(10fm)

0.0675(5fm)

4(10fm)4

Fig2, K-.I. Ishikawa et. al., https://arxiv.org/abs/1807.06237

0.01099(49)Energy-momentum tensor in 2+1 flavor QCD using gradient flow

314 22.04(22)− 5.07(19) 0.000000(0.000000)

1.019(57)0.00403(27)274 19.88(17)− 4.79(15) 0.000000(0.000000)

1.999(50)0.00306(26)244 18.05(22)30− 4.80(22)0.000000(0.000000)
gradientflow
T-integration
25− 4.89(33) 0.000000(0.000000)

2.421(80)0.000170(60) The(e+p)/T4energy-momentum tensor is a fundamental observable in
219 15.99(31)2.54(11)0.000213(81) physics. It is the source of the gravity. Its diagonal elements contain200 15.02(38) − 4.89(43)0.000000(0.000000)
2.41(15)0.00021(10) the energy density and the pressure, while its off-diagonal elements
20
183 11.76(56) − 3.85(53)0.000000(0.000000)
1.95(19)0.000082(50) represent the stress. In order to calculate the energy-momentum
15
169 10.4(1.0) − 6.16(82) 0.000000(0.000000)
2.99(24)0.00201(22) tensor on the lattice, we need to perform a complicated non10
157 10.10(91) − 6.10(79) 0.000000(0.000000)
2.76(24)0.00246(31) perturbative renormalization due to violation of the translational5
137 3.4(1.4)− 1.8(1.4) 0.000000(0.000000)
1.09(43)0.00085(25) invariance on the lattice. For this purpose we adopt the gradient
0flow as a renormalization scheme proposed by H. Suzuki. We are
0100 200 300 400 500 600
makingthefirst
systematic
application
ofthemethodtoQCD
withT (MeV)dynamicalquarks.
Fig. 3, Y. Taniguchi et. al., Phys. Rev. D 96, no. 1, 014509 (2017)35

linear fit

30(e+p)/T

425
20
1510
500100200300400500600

Fig. 3 shows the entropy density as a function of temperature. The
degenerate u and d quark mass is heavier than experiment in thisplot. Red symbols are our new results using the gradient flow
method. Black symbols are our old results using a conventional
method. Both agree well with each other off the shaded region inwhich lattice artifact is considered to be large.
Fig. 4 is the same as Fig. 3 but the ud quark mass is set to its physicalvalue.

T (MeV)

Fig. 4, K. Kanaya et. al., EPJ Web of Conference, 175, 07023, pp.1-8

F I G . 15. E ntropy density (ϵ + p)/ T 4 as a function of temperature. E rrors include both statisticaland contact
systematic address:
errors.
pr@ccs.tsukuba.ac.jp

https://www.ccs.tsukuba.ac.jp/