Quantum Chromodynamics on a space-time lattice - Prace Training

53 Pages·2013·8.27 MB·English

by  Akira Ukawa

25  June, 2013
HPC Summer School
New York, USA(cid:1)
Akira Ukawa
Center for Computational Science,
University of Tsukuba & RIKEN AICS(cid:1)
Quantum Chromodynamics
on a space-time lattice

– Building up the Femto Universe of(cid:7)hadrons
and nuclei on a computer –
1
Four decades of Lattice QCD
1975 1980 1985 1990 1995 2000 2005 2010 2020
1973 QCD
1974 lattice QCD
Physics
1st spec calculation 1981
Hamber-Parisi
Weingarten
0.8fm 1.6fm 3.0fm 2.4fm
Lattice size L
43x8 163x32 643x118 243x48
Nf=0 quenched
6.0fm
Algorithms
643x128
Nf=2 u,d
Nf =#sea
Nf=2+1 u,d,s
quarks
4th generation 5th generation
3rd generation 10Pfops
2nd generation 10Tfops
Machines 10Gflops 1Tfops
1st generation K comouter
APE100
1Gflops
APE1
QCDPAX
QCDOC BlueGene/Q
QCDSP
CP-PACS PACS-CS
Today’s agenda
" Lattice QCD as science
" Lattice QCD as computation
" A few epoch-making calculations
" (Other) challenges of Lattice QCD
" Conclusions and perspectives
3
Lattice QCD as science
4
The Standard Model
(cid:12)(cid:3)building blocks at the age 10-6 sec(cid:12)
!  Matter particles
u s t
& # & # & #

$ ! $ ! $ !
"  6 quarks d c b
% " % " % "
& e # &µ# &τ#
"  6 leptons
$ ! $ ! $ !
$ ! $ ! $ !
ν ν ν
% e" % µ" % τ"

!  Particles mediating interactions
γ
"  photon Electromagnetism
Weinberg-Salam
"  Weak bosons W, Z Weak interactions theory (1967)
"  gluons g Strong interaction
Quantum
Chromodynamics
!  Particle which breaks EW symmetry
(QCD) (1973)
(and gives rise to masses of particles)
"  Higgs boson H Englert-Brout, Higgs, … (1964)
( ) ( ) ( )
SU 3 ⊗ SU 2 ⊗U 1
!  Gauge field theory based on
 
QCD EM +Weak
Has to add Lee-Yang(cid:1)
Standard Model and Nobel Prize in Physics(cid:1)
1965 Tomonaga(cid:8)Schwinger(cid:8)Feynman
Renormalization theory(cid:1)
1949 QED
Spontaneous breakdown
2008 Nambu
of symmetry(cid:1)
1967 EW theory
1979 Glashow(cid:8)Salam(cid:8)Weinberg
1982 Wilson
Renormalization
group (cid:1)
2008 Kobayashi(cid:8)Maskawa
6 quarks and CP violation(cid:1)
1973 QCD 1999 tHooft(cid:8)Veltman
Renormalization of non-Abelian
gauge theories(cid:1)
2004 Gross(cid:8)Politzer(cid:8)Wilczek
Asymptotic freedom (cid:1)
6
Quarks, hadrons, nuclei and
Quantum Chromodynamics (QCD)(cid:1)
−15
The Femto Universe(cid:1) 1 fm = 1×10 m
Nuclei(cid:1)
H, He,…, C,…, O,…, Fe,…, U,…(cid:1)
hadrons
quarks(cid:1) e.g., proton and neutron(cid:1)
u
d
u
u
≈ 2 fm
1/3
≈ 1.6A fm
Natural elements (nuclei) are governed by Quantum
Chromodynamics (QCD)
Cf. Chemistry is governed by quantum electrodynamics (QED)
7
A few more words on quarks and hadrons(cid:1)
!  6 types of quark “flavors”
2
u c t
Q = + e
Carry fractional charge in
up charm top 3
s 1 units of electron charge(cid:1)
d b
Q = − e
down strange bottom 3
Heavier mass(cid:1)
!  various flavor combinations produce a few hundred
particles called “hadrons”
u u s
proton(cid:1) d neutron(cid:1) d Ω baryon(cid:1) s (cid:8)(cid:8)(cid:8)(cid:8)(cid:8)(cid:1)
u d s
See Particle Data Group http://pdg.lbl.gov/ for a full list(cid:1)
!  Yet, no isolated quarks have been found in experiments;
quarks are confined under normal circumstances
8
Quantum Chromodynamics
Gross-Wilczek-Politzer 1973
!  Quantum field theory of quarks and gluons
q (x) quark field
f defined at every 4-dim space-time point
A (x) gluon field
x = (x , x , x ,t)
µ
1 2 3
!  Quarks carry color(chromo) charge, and gluons mediate the
interaction between color charges
Cf. electrons carry electric charge, and photons mediate
the interaction between electric charges
!  Given the coupling strength and 6 quark masses, allows first-
principles calculations of all the properties of hadrons and
nuclei
e2
α = color
QCD coupling strength
s
4πc
m , m , m , m , m , m
6 quark masses
u d s c b t
(cid:4)fulfilling Yukawa(cid:3)s dream of 1934 in a refined way(cid:5)(cid:1)
9
Three fundamental features of QCD
!  Described by quark and gluon fields defined at every
point of space-time, and NOT by particles
q (x) A (x) x = (x , x , x ,t)
quark field gluon field
f µ 1 2 3

!  Local interaction only, i.e., no points separated by a
finite distance interact, only neighboring points do so
1
L (x) = Tr(F (x)F (x))+∑q (x)(γ ⋅(∂ −iA (x))+ m )q (x)
QCD µν µν f µ µ µ f f
8πα

s f
QCD Lagrangian
!  Relativistic quantum mechanical system; the
fundamental equation is an integral over fields
(Feynman), and NOT a partial differential equation
1
− ∫ d4xL (x)
O(A, q, q) = ∫ ∏dA(x)dq (x)dq(x) O(A, q, q)e QCD
Z
x
Physical quantities by
Feynman path integral
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