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.

0.15(mh/m1)lat / (mh/m1)exp-1
0.10

Vector meson

Octet baryon

Decuplet baryon

Input

After quenched simulation and a succeeding 2 flavor QCD simulation bytheCP-­‐PACS,
thosestudies
wereextended
to2+1
flavor
QCDby0.05
incorporating the dynamical strange quark, though the degenerate up-­‐down quark mass was much heavier than the physical value. On the PACS-­‐
0.00
CS and T2K computers, we have succeeded in reaching the physical pointby a reweighting technique. This calculation is followed by a larger volume<0.05
simulation on the K computer. Fig. 1 presents relative difference of the/ K dss l K* q N R Y U 6 Y U 1light hadron spectrum from the experiment. In the figure the inputs are<0.10
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.
Pseudoscalarmeson

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 Oakforest-­‐PACS computer which ranks in the 3rd position in the HPCG benchmark
and in the 6th position
intheTOP500
listatSC16.
Fig.
2showsaTABLE XI. Entropy density (ϵ + p)/T 4 : coeﬃcient of the nonlinear fit within the linear window
4 andcomparisonofpseudoscalar
decay
constants,
fandf,
on(10fm)
πK
2and χ /DOF.
(5fm)4. We detect 0.66% and 0.25% finite volume effect on fπ and fK,T
const
linear
1/tt2
χ2 /DOF
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)completely
by using
the master-­‐field
simulations.
366 26.70(10) −10.20(11) 0.000000(0.000000)

1.300(38)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)0.05740.0680fπ

0.0572fK

0.06790.05700.06780.05680.0677
0.0566
0.0676
0.05640.0562(5fm)

44(10fm)

0.0675(5fm)

44(10fm)

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	  flow30
−4.80(22)0.000000(0.000000)
gradientflow
T-integration
25−4.89(33) 0.000000(0.000000)

energy-­‐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 non-­‐10
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 are0
100 200 300 400 500 600
makingthefirst
systematic
applicationof
themethodtoQCD
withT (MeV)
dynamical quarks.
Fig.	  3,	  Y.	  Taniguchi	  et.	  al.,	  Phys.	  Rev.	  D	  96,	  no.	  1,	  014509	  (2017)
2.421(80)0.000170(60) The(e+p)/T4

244 18.05(22)35linear fit

30(e+p)/T

425
20
15
10
500100

200

300

400

500

600

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-­‐8FIG. 15. Entropy density (ϵ + p)/T 4 as a function of temperature. Errors include both statisticaland contact	  systematic aerrors.
ddress:	  pr@ccs.tsukuba.ac.jp

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