University	  of	  Tsukuba	  	  | Center	  for	  Computational	  Sciences

Research	  in	  Particle	  Physics
2+1	  flavor	  QCD	  at	  Physical	  Point
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 aprincipal subject in particle physics.
After quenched simulation, in which dynamical quarks are neglected,
and a succeeding 2 flavor QCD simulation with dynamical up and down
(1)
quarks by the CP-­‐PACS computer, those studies were extended to 2+1
flavor QCD by incorporating the dynamical strange quark, though thedegenerate up-­‐down quark mass was much heavier than the physicalvalue of 3 MeV (physical point). On the PACS-­‐CS and T2K computers, wehave succeeded in reaching the physical point by a reweighting
technique utilizing the simulated data at the up-­‐down quark mass of 4MeV. This calculation is followed by (8 fm) 3 volume simulation on the K
computer. The left figure presents relative difference of the light hadron
spectrum from the experiment at the physical point. In the figure theinputs are only the pion, kaon, and omega baryon masses to determine
the up-­‐down and strange quark masses, and the lattice cutoff,respectively. Our results at the physical point show good agreementwith the experiment albeit errors are still not quite small for some of thehadrons.
In nature, the masses for up and down quarks and also their electric charges are (2)different. Their effects are observed in mass splittings among isospin multiplets of0±
K
K
light hadrons, e.g., m -­‐m . Thus, we have embarked on 1+1+1 flavor QCD+QEDsimulation at the physical point incorporating the isospin breaking effects. The
right figure plots the ratio of K0 to K± propagators to detect their mass difference.
Our results (black symbol) show a good consistency with the expected slope from0±K
K
the experimental value of m -­‐m (red line).
[PACS-­‐CS	  Collaborations:	  Phys.	  Rev.	  D81,	  074503	  (2010);	  S.	  Aoki	  et	  al.,	  Phys.	  Rev.	  D86,	  034507	  (2012);	  K.-­‐I.	  Ishikawa	  et	  al.,	  https://arxiv.org/abs/1511.09222]

Direct	  calculation	  of	  energy-­‐momentum	  tensor	  for	  Quantum	  Chromodynamics
Energy-­‐momentum tensor (EMT) is a generator of the translation and is one of the most essential quantity in physics.
Lattice simulation is the only method to evaluate a quark and gluon contribution to EMT from the first principle. However
it is not straightforward to be studied on the lattice due to the explicit violation of the translation symmetry.
(3) 0

T=199 MeV (Nt=14)

T00/T

4-5
-10-15
-20
-25
00.5

11.5

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Recently a new method was proposed to calculate EMT by applying gradient flowequation. In the process of the gradient flow the violation of symmetry is smeared
and the EMT becomes renormalized automatically. Conversion to the proper EMT
operator related to the symmetry is performed by taking zero flow time limit(fig3).We applied the method to 2+1 flavor QCD for the first time and calculated thesimplest ingredient; energy density (fig4) and pressure (fig5) as a first step. The
result shows a good agreement with the conventional method at T ≤ 300 MeV withconsiderably improved statistical error.

t/a2(5)

gradient flowT-integration

1020815

6p/T4

e/T4(4)25

10

An important future direction of this study is acalculation of correlation functions of EMT at thephysical point, which is under way using the HA-­‐PACS and the COMA.

gradient flow
T-integration

425[Y.	  Taniguchi	  et	  al.,	  https://arxiv.org/abs/1609.01417]

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T (MeV)

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

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T (MeV)

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