Introduction QCD Lattice Physics Challenges

The symmetries of QCD(and consequences)

Sinéad M. RyanTrinity College Dublin

�antum Universe Symposium, Groningen, March 2018

Understand nature in terms of fundamental building blocks

Introduction QCD Lattice Physics Challenges

The Rumsfeld Classification

“As we know, there are known knowns.There are things we know we know.

We also know, there are known unknowns.That is to say we know there are some things we do not know.

But there are also unknown unknowns,the ones we don’t know we don’t know.”

– Donald Rumsfeld, U.S. Secretary of Defense, Feb. 12, 2002

Introduction QCD Lattice Physics Challenges

Some known knowns�antum ChromoDynamics - the theory of quarks and gluons

Embarassingly successful

Precision tests of SM can reveal newphysics - more important than ever!

Why focus on the 4.6%?

QCD is the only experimentally studied strongly-interacting quantum fieldtheory - highlights many subtleties.A paradigm for other strongly-interacting theories in BSM physics.There are still puzzles and surprises in this well-studied arena.

Introduction QCD Lattice Physics Challenges

What is QCD?A gauge theory for SU(3) colour interactions of quarks and gluons: Color motivated byexperimental measurements; not a “measureable” quantum number. Lagrangian invariantunder colour transformations.

Elementary fields: �arks Gluons

(qα)af

colour a = 1, . . . , 3spin 1/2 Dirac fermions�avour f = u, d, s, c, b, t

Aaμ

�

colour a = 1, . . . , 8spin 1bosons

L = q̄f�

iγmuDμ − mf�

qf −1

4GaμνG

aμν

with Gaμν = ∂μAaν − ∂νA

aμ + gf

abcAbμAcν

andiγμDμq = γμ

�

i∂μ + gAaμta�

q

Generates gluon self-interactions - might expect consequences!

Introduction QCD Lattice Physics Challenges

Elucidating the effect of the self-interactions: QED vs QCD

αs(Q2) =1

33−2Nf12π ln

�

Q2

Λ2

�

In QED: coupling runs and bare e− isscreened at large distances - reducingSame but di�erent for QCD withanti-screening from gluon interactionsdominates!

Asymptotic freedom

Coupling small at high energies - energeticquarks are (almost) free.

Nobel prize 2004 for Gross, Politzer and Wilczek.

The interaction between quarks, between gluons and between quarks and gluonsgrows rapidly with separation

At hadronic scales, r ∼ 0.2fm ∼ 14 rproton it is huge! A perturbative expansion notappropriate...

Introduction QCD Lattice Physics Challenges

Confinement: a consequence of QCD interactions

�arks and gluons are not observed in nature - only in bound states (colour singlets)

Confinement not yet derived from QCD

Verified by numerical simulation from first principles

Strong force overcomes repulsive EM force to “glue” protons in the nucleus.

Introduction QCD Lattice Physics Challenges

Gluons and QCD

QCD describes structure and interactions ofnuclear ma�er

Without gluons there are no protons, noneutrons and no atomic nuclei

Gluons dominate the structure of the QCDvacuum

Essential features of QCD (asymptotic freedom, chiral symmetry breaking, colourconfinement) are driven by gluons.

Unique aspect for QCD is gluon self interactions.

99% of mass of visible universe arises from glue.

Half the nucleon momentum is carried by gluons.

Introduction QCD Lattice Physics Challenges

Some symmetries of QCD

The structure of QCD fully defined by the requirement of invariance under localgauge transformations: ie physical content unchanged if quarks and gluonstransform under colour SU(3).

Isospin symmetry: a global transformation - SU(2) rotation in flavour space (QCDinteractions are flavour-blind). Acts on up and down quarks and L is invariant foridentical or vanishing masses.

Chiral Symmetry: For massless QCD, le� and right handed pieces of L areseparately invariant. A global symmetry. ψ = ψR + ψL, ψR,L =

12 (1± γ

5)ψ:ψ(x)→ exp

−i∑8

b=1 abtbγ5

ψ(x)

Introduction QCD Lattice Physics Challenges

Spontaneous Chiral Symmetry Breaking: chiral symmetry broken by propertiesof the QCD vacuum (cf Higgs mechanism). The (approximately massless) pions arethe Goldstone bosons of the broken symmetry.

QCD vacuum state is not invariant under the same symmetries as L

Chiral condensate is an order parameter

〈qq̄〉 =�

6= 0 (broken phase)= 0 (unbroken)

Many others: flavour, isospin, ...

Introduction QCD Lattice Physics Challenges

Dynamical mass generation through non-linear interactions

Very li�le to do with Higgs!

Massless gluons and almost masslesquarks interact - generating most of themass of nucleonsProton: uud

mu = 2.3+0.7−0.5 MeV/c

2

md = 4.8+0.7−0.3 MeV/c

2

MP = 938.3 MeV/c2

Mπ = 130 MeV/c2

The pion is the Goldstone boson of dynamical chiral symmetry breaking.

Only 1% of the proton’s mass comes from the constituent quarks’ intrinsic masses.

The proton is an emergent (long-range) phenomena resulting from the collectivebehaviour of quarks and gluons - QCD!

Introduction QCD Lattice Physics Challenges

QCD: a practical tool for understanding matter?

There are two regimes:

Deep inside the proton

at short distances quarks behave as free particles

weak coupling

⇒ perturbation theory works

At “observable” distances

at long distance (1fm) quarks confined

strong coupling

⇒ perturbation theory fails: nonperturbative approach needed.

from Science & Technology Review

Observable properties of QCD from numericalsimulation

Does it work?

Introduction QCD Lattice Physics Challenges

Life on a lattice

Start from the QCD Lagrangian:

L = Ψ̄�

iγμDμ − m�

Ψ− 14 Gaμν

Gμνa

Gluon fields on links of a hypercube; quark fields on sites.

Approaches to fermion discretisation - Wilson, Staggered,Overlap.

Derivatives→ finite di�erences

Observables determined from finite-dimensional (Euclidean) path integrals of the QCDaction

〈O〉 = 1/Z∫

DUDψ̄Dψ O[U, ψ̄, ψ]e−S[U,ψ̄,ψ]

borrowing ideas from statistical mechanics.

Introduction QCD Lattice Physics Challenges

Scale of theory tools

ETM collaboration

Introduction QCD Lattice Physics Challenges

The lattice simulation landscape

from K. Jansen et al

Introduction QCD Lattice Physics Challenges

The light hadron spectrum I

BMW collaboration: a precision realisation of the low-energy spectrum of QCD

Introduction QCD Lattice Physics Challenges

The light hadron spectrum II

BMW: first principles demonstration of the correct neutron-proton mass di�erence

Introduction QCD Lattice Physics Challenges

QCD admits a rich and exotic spectrum

Introduction QCD Lattice Physics Challenges

Predictions: the glueball spectrum

0

2

4

6

8

10

12

--+--+++

0

1

2

3

4

5

r 0 M

G

0++

2++

3++

0-+

2-+

0+-

1+-

2+-

3+-

1--2--

3--

Morningstar & Peardon, 1999

Introduction QCD Lattice Physics Challenges

Predictions: (exotic) hybrid meson in charmonium

DDDD

DsDsDsDs

0-+0-+ 1--1-- 2-+2-+ 1-+1-+ 0++0++ 1+-1+- 1++1++ 2++2++ 3+-3+- 0+-0+- 2+-2+-0

500

1000

1500

M-

MΗ

cHM

eVL

Hadron Spectrum Collaboration, 2012

Some Current Challenges in QCD

Introduction QCD Lattice Physics Challenges

Going beyond simple bound states: resonances in a Euclideantheory

On la�ice volumes extract the spectrum. Lüscher formalism (1991) allows to deducephase shi� information

det

cot δ(E∗n ) + cotϕ(En, ~P, L)

= 0

the more distinct spectrum points the be�er the phase shi� picture

Introduction QCD Lattice Physics Challenges

The XYZs

Ryan Mitchell & Steve Olsen

The new strong exotic ma�er has beenaround for 15 years ... and we still don’tunderstand it ..

Will need precision la�ice resonancestudies including multi-hadrons andbound states ...

Introduction QCD Lattice Physics Challenges

The QCD phase diagram:

La�ice can:

Explore T ≥ 0, μ = 0 - fate ofhadrons in medium

La�ice can’t:Simulate at μ 6= 0

Fermion determinant iscomplex, no positive weightin path integralSign problem: Monte Carlomethods fail!

Introduction QCD Lattice Physics Challenges

The cost of doing businessGenerating gauge ensembles at physical quark masses on large volumes requiresmillions of core hours.

Computational Cost ∼ c × (Number of con�gurations)×�

1

Mπ

�6× (L)5 ×

�

a−1�7

Once the gauge configurations are generated just have to invert the Dirac matrix Mto get the fermion propagators ... how hard can that be?Let’s calculate:

a la�ice might have 24× 24× 24× 48 = 663, 552 sitesa fermion (quark) has 4 Dirac components3 colours in SU(3)⇒ M is easily 106 × 106‼

Requires high memory/network bandwidth, but also highly parallelisableTera/Peta bytes of data is also generated!

Introduction QCD Lattice Physics Challenges

Summary

QCD describes the properties of observed ma�er in terms of fundamental variablesand their interactions.

Symmetries (and their breaking) have dramatic consequences.

Many open questions and unsolved problems - phenomenological and theoretical -remain.

Many knowns and unknowns to understand!

Thanks for listening!

Introduction QCD Lattice Physics Challenges

Summary

QCD describes the properties of observed ma�er in terms of fundamental variablesand their interactions.

Symmetries (and their breaking) have dramatic consequences.

Many open questions and unsolved problems - phenomenological and theoretical -remain.

Many knowns and unknowns to understand!

Thanks for listening!

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