Mariane Mangin-Brinet

Tsukuba Global Science Week – 21.09.2018

Ø Introduction

Ø What is lattice QCD
Ø Why do we need it?
Ø How does it work?
Ø How is it organized?
Ø Reaching the physical pion mass

Ø Nucleon physics

Ø nucleon mass
Ø axial chargeØ Momentum fraction <x>u-d and helicity <x>Δu-ΔdØ Renormalisation
Ø Conclusion
Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Prior warning (and apologizes...):
ØPresentation limited to what is studied in L.P.S.C. à necessarily
restricted compared to the richness of the fieldØMany subjects of interest in LQCD will not be mentioned (nuclearinteractions, finite temperature, flavor physics, ....)
Ø Work performed in the framework of the European Twisted Mass
Collaboration (ETMC). Many other competitive international
collaborations exist (PACS-CS, MILC, HPQCD, BMW, ALPHA ....)
Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Courtesy Fermilab Visual Media Services

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Courtesy Fermilab Visual Media Services

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

GluonFermions + quark-gluon interaction

Courtesy Fermilab Visual Media Services- Formulated by K. Wilson in 1974 (Phys.Rev. D10 (1974) 2445-2459): gauge theories on a space-timelattice and demonstration that lattice gauge theories at strong coupling lead to confinement- Regularization of QCD (inherent to all field theories) by space-time discretization- has become a standard tool
Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

• Perturbative QCD (pQCD) very successful in describing many phenomena• BUT limited to an energy range where !S << 1Salient feature of QCD : Asymptotic freedom
pQCD cannot describe physics at GeV scale

Particle Data Group, 2010

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

• Perturbative QCD (pQCD) very successful in describing many phenomena• BUT limited to an energy range where !S << 1Salient feature of QCD : Asymptotic freedom

Simple example of positronium :pQCD cannot describe physics at GeV scaleNo finite order diagram fore+ ee+e- has a positronium pole

Bound states cannot be described by perturbations

Positronium pole arises from adivergent infinite sum of diagrams

pQCD cannot describe bound states, whatever scaleUnderstanding bound states in QCD is crucial, because of confinement

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

• Perturbative QCD (pQCD) very successful in describing many phenomena• BUT limited to an energy range where !S << 1Salient feature of QCD : Asymptotic freedom

Simple example of positronium :pQCD cannot describe physics at GeV scaleNo finite order diagram fore+ ee+e- has a positronium pole

Bound states cannot be described by perturbations

Positronium pole arises from adivergent infinite sum of diagrams

pQCD cannot describe bound states, whatever scale
Understanding bound states in QCD is crucial, because of confinement

Spontaneous breaking of chiral symmetry
Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018• Only rigorous and systematic non perturbative method to solve QCD ab initio• Aim: provide solutions of this fundamental theory of matter without uncontrolled
uncertainties and with precisions rivaling those of experiments.

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

• QCD must be regularized in IR and UV• LQCD is a possible regularization• Principle:• space-time is discretized:• quark :on the lattice sites• gluon :on the lattice links• discretized action:a• formulation of QFT in terms of Feynman path integrals with complex time (tit)• observables obtained by•computed by Monte Carlo methods, inspired by statistical physics

Calculations based on stochastic methods: very demanding in terms of computing power.
Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

• Different QCD action discretizations è different international collaborations• Pooling of computing resources and manpower inside a given collaboration• Typical steps of a lattice QCD simulation:
1. Gauge field (or configurations) generation using Monte Carlo methods (HMC) on
HPC - most demanding part of the computation
2. Quark propagators calculation by solving a large linear system (HPC)
3. Analysis (or post-treatment), i.e. computations of expectation values of operators,
chosen depending on the problem we are interested + statistical study (CPU/GPUfarms)
4. Control of systematics (discretization effects,…) by repeating steps 1.2.3. forseveral lattice parameters (lattice spacing, volume,….)Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Adapted from A. Ukawa, Tsukuba University, « Lattice QCD at the turning point » (2010)
1975

1980

1985

0.8 fm83.16

1.6 fm163.32

1990

1995

2000

2005

2010

2015

1973 QCD
1974 Lattice QCD« quenched »2.4 fm243.483 fm
323.643 fm
643.118

5 fm
483.96/643.128

Nf=0
Nf=2 (u,d)« unquenched »or« full QCD »Nf=2+1 (u,d,s)
Nf=2+1+1 (u,d,s,c)R. Gupta, arXiv:hep-lat/9807028
CP-PACS Collaboration

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Described by an « interpolating field »: J N (x) = "abc [uT a (x)C 5 db (x)] uc (x)Observables computed studying the expectation values of operators built from thisinterpolating field
Simplest example: ab-initio computation of nucleon mass (I)Excitedstates

groundstate

Annihilate a state with quantum
number of the nucleon at spacetime x(",⃗ t)

Mariane Mangin-Brinet

Tsukuba Global Science Week

Create a state with quantum
number of the nucleon at
space-time (0,0)(0, 0)« 2 point-function »21.09.2018

Nucleon mass (II)QCD with u,d (degenerate), s and c quarks

slightly different
discretizations

Mass of most of the visible
matter in the Universe=STRONG INTERACTION!

Red star: most recent ETMC result
Crossing of blue dashed andsolid lines: experimental point

Lattice 643.128
2+1+1
Physical quark masses
Lattice spacing a ∼ 0.08 fm

C. Alexandrou et al., arXiv:1807.00495 submitted to Phys.Rev. D

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Axial charge of the nucleon• gA= nucleon axial charge« 3 point-function »(#,⃗ t)(0, 0)• Well known from !-decay of the neutron• Key parameter for understanding thechiral structure of the nucleon• Considered as a « benchmark » quantity
for lattice QCD• Suffered from a longstanding uncertainty
due to its strong dependence in pion mass
Mariane Mangin-BrinetgA vs pion mass squared for different fermion actions (2010)

Tsukuba Global Science Week

21.09.2018

Axial charge of the nucleon• gA= nucleon axial charge
gA vs pion mass - chiral extrapolation« 3 point-function »1.4

1.35(#,⃗ t)(0, 0)

1.3• Well known from !-decay of the neutron• Key parameter for understanding thechiral structure of the nucleon• Considered as a « benchmark » quantity
for lattice QCD• Suffered from a longstanding uncertainty
due to its strong dependence in pion mass
Mariane Mangin-Brinet

gA

1.25

1.2

1.15

1.1

1.05

10

ETMC data - L24T48 - β=3.9
ETMC data - L32T64 - β=4.05
Fit Bernard&al hep-lat/0605010v1
Fit Procura&al hep-lat/0610105v2
physical point

0.1

0.2

0.3

0.4

0.5mπ (GeV)gA vs pion mass squared with chiral fits (2010)

Tsukuba Global Science Week

21.09.2018

Axial charge of the nucleon• gA= nucleon axial charge(#,⃗ t)(0, 0)• Well known from !-decay of the neutron• Key parameter for understanding thechiral structure of the nucleon• Considered as a « benchmark » quantity
for lattice QCD• Suffered from a longstanding uncertainty
due to its strong dependence in pion mass
Mariane Mangin-BrinetgA vs pion mass squared for different fermion actions (2015)
C. Alexandrou et al., Phys.Rev. D92 (2015) 11, 114513, arXiv: 1507.04936

Tsukuba Global Science Week

21.09.2018

Momentum fraction <x>u-d and helicity <x>Δu-Δd• An additional step in complexity : 3-point
function with derivative operator• Experimental values extracted from global
analysis of collider data★

• Has persistently come out too high fromlattice calculations• Concentrated effort to removing eachsource of systematic errors (pion mass,excited states,...)★

C. Alexandrou et al., Phys.Rev. D92 (2015) 11, 114513, arXiv: 1507.04936

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Momentum fraction <x>u-d and helicity <x>Δu-Δd• An additional step in complexity : 3-point
function with derivative operator• Experimental values extracted from global
analysis of collider data
• Has persistently come out too high fromlattice calculations• Concentrated effort to removing eachsource of systematic errors (pion mass,excited states,...)
Encouraging recent results
à Longstanding puzzle soon resolved ?
Mariane Mangin-Brinet

C. Alexandrou et al., Phys.Rev. D92 (2015) 11, 114513, arXiv: 1507.04936

Tsukuba Global Science Week

21.09.2018

• Essential ingredient of Lattice QCD calculations• Discretisation à provides a natural regularisation
What is computed on a lattice: « bare » observable: Obs(a) (regularized quantities)• Continuum limit à renormalisation
Renormalisation = procedure to take the limit

Mariane Mangin-Brinet: Obs(a) à Physical Observables

Tsukuba Global Science Week

21.09.2018

• Essential ingredient of Lattice QCD calculations• Discretisation à provides a natural regularisation
What is computed on a lattice: « bare » observable: Obs(a) (regularized quantities)• Continuum limit à renormalisation
Renormalisation = procedure to take the limit: Obs(a) à Physical Observables• Renormalization allows, from bare quantities computed on the lattice, to obtainphysical observables. It is thus mandatory to make meaningful predictions ofobservables• Direct influence of the accuracy ofon observables
Large program of RCs computation using RI-MOM type schemes developed in L.P.S.C. since several years
Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Dealing with lattice artifacts: an example of challenge to face
Treatment of lattice hypercubic artifacts• Scalar quantities in the continuum:rotationally invariant (O(4) group)• Scalar quantities on an hypercube :• Illustration see also B. Blossier et al, Phys.Rev. D91 (2015) no.11, 114507)

Quark renormalisation constant Zq vs (ap)2 before (blue points)
and after (green points) hypercubic artifacts correction

Mariane Mangin-Brinet(H(4) group) à lattice artifacts

Fermion bilinear renormalisation constants (Zq, scalar, pseudo-scalar,axial, vector, tensor) vs (ap)2 after hypercubic artifacts correction + running

Tsukuba Global Science Week

21.09.2018

Ø Importance of Nucleon physics for understanding QCD
Ø Also crucial for New Physics
Ø K. Wilson (Lattice 1989, Capri): «One lesson is that LQCD could require a 108 increase ofcomputing power AND spectacular algorithmic advances before ... interaction with experimenttakes place ».
At that time, a supercomputer would offer 20 Gflops + « Moore’s laws » à 108 = 40 years

à we are somehow 10 years in advanceØ Exciting time for LQCD, with many developments and exp./th. comparisons tocome in the next few years
Ø Developing « strong interactions » between L.P.S.C. and Tsukuba University
would be very fruitful
Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018

Mariane Mangin-Brinet

Tsukuba Global Science Week

21.09.2018