University	  of	  Tsukuba	  	  | Center	  for	  Computational	  Sciences

Research	  in	  Particle	  Physics
2+1	  flavor	  QCD	  at	  Physical	  Point

Pseudoscalar
meson

Vector meson

Octet baryon

Decuplet baryon

Input

Hadrons are the constituents of atomic nuclei. The computation of their mass spectrum from the quantum chromodynamics(QCD), the fundamental theory of strong interaction described by quarks and gluons, has been a principal subject in particle
physics.
After quenched simulation, in which dynamical quarks are neglected, and a(1)succeeding 2 flavor QCD simulation with dynamical up and down quarks by the0.15
CP-­‐PACS, those studies were extended to 2+1 flavor QCD by incorporating the(mh/m1)lat / (mh/m1)exp-1
dynamicalstrange
quark,
thoughthedegenerateup-­‐downquark
mass
wasmuch0.10
heavier than the physical value of 3 MeV (physical point). On the PACS-­‐CS and T2K
computers, we have succeeded in reaching the physical point by a reweighting
0.05
technique utilizing the simulated data at the up-­‐down quark mass of 4 MeV. This
0.00
calculation is followed by (8 fm)3 volume simulation on the K computer. The leftfigure presents relative difference of the light hadron spectrum from the<0.05
experiment at the physical point. In the figure the inputs are only the pion, kaon,/ K dss l K* q N R Y U 6 Y U 1and omega baryon masses to determine the up-­‐down and strange quark masses,<0.10
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 ofthe hadrons. In nature, the masses for up and down quarks and also their electric charges are different. Their effects areobserved in mass splittings among isospin multiplets of light hadrons, e.g., mK -­‐mK . (2)Thus, we have embarked on 1+1+1 flavor QCD+QED simulation at the physicalpoint incorporating the isospin breaking effects. The right figure plots the ratioof K0 to K± propagators to detect their mass difference. Our results (blacksymbol) show a good consistency with the expected slope from theexperimental value of mK -­‐mK (red line).Our current project is aiming to control
and remove systematic errors due to the previous simulations on a finite
volume with a finite lattice spacing. We are performing the simulations onlarger volumes with several lattice spacings using the Oakforest-­‐PACS computer
which ranks in the 3rd position in the HPCG benchmark and in the 6th positionin the TOP500 list at SC16.
00±±

Proton	  radius	  problem

rms electric charge radius [fm]Proton radius problem is one of urgent problems to be solved in particle physics. The charge radius of the proton is different
in the two experiments using the elastic electron scattering and the muonic hydrogen atom, which are expressed by theblack and green stars, respectively, in the figure of the isovector charge radius (Fig.3): the difference of the charge radiusbetween the proton and neutron.
We (PACS Collaboration) tackles this problem using lattice QCD
calculation.
The
current
purpose,however,
istoreproduce
the(3) 1.2
Expt. (PDG)
experimental values, because the charge radius at larger pion mass
Expt. (µ-H atom)
1.1
PNDME
than the physical one is significantly smaller than the experiments.
LHPC
1MainzTowards this purpose, we calculate the isovector charge radius in 2+1
ETMC13
ETMC170.9
flavorQCD
atalmost
physicalpoint
onalarge
volume,wheretheRBC-UKQCD
PACS
spatial extent is 8.1 fm, using several computing resources including
0.8
COMA and Oakforest-­‐PACS.
0.7
Our result of the charge radius is plotted by the red square in Fig.3.
Since the statistical error of our result is large, at present we cannot
0.6
conclude which experiment is preferable from the lattice QCD
0.5
calculation. One of important future works is to reduce the statistical
0.4
error. Another important future work is to include the QED and isospin
00.02 0.04 0.06 0.08
0.1 0.12 0.14 0.16
22
breaking effects. We attempt these calculations using Oakforest-­‐PACS.
mπ [(GeV) ][N. Tsukamoto et al. for PACS Collaboration, https://arxiv.org/abs/1710.10782]

contact	  address:	  pr@ccs.tsukuba.ac.jp

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