Quark, Gluoni e Supercalcolo

Massimo D’Elia

Congressino del Dipartimento di Fisica Pisa, 17 aprile 2013

The Standard Model of Particle Physicsprovides the best known description ofstrong and electroweak interactions

+Higgsboson

• Quarks are spin-1/2 particles and carry 3 different color charges.

They also carry fractional electric (+2/3 e, -1/3 e) and weak charges.

• Quarks interact strongly via 8 spin-1 particles called gluons .

Interactions are described by Quantum ChromoDynamics (QCD)

• Quarks and gluons have never been observed as free states, th ey are ”confined”

into hadrons. Experiments provide a suppression of free qua rks, as compared

with cosmological expectations, in excess of 10−15. Why?

QCD is very similar to Quantum ElectrodynamicsQuantum gauge theories describing matter fields which inter act via gauge bosons

LQCD =∑

f

ψfi

(

iDµijγ

Eµ −mfδij

)

ψfj − 1

4Ga

µνGµνa

LQED =∑

f

ψf (iDµγµ −mf)ψf − 1

4FµνF

µν

Why are they so different?

The local symmetry group for QCD is non-Abelian: SU(3) matrices.

Gluon fields are color charged and

interact among themselves

Gluon interactions lead to vacuum anti-screening of color c harges,which appear smaller and smaller as one gets closer to them

That is at the origin of ASYMPTOTIC FREEDOM

(D. Gross, D. Politzer, F. Wilczek, 1974)

HIGH ENERGIES =⇒ The coupling is small. Per-

turbation theory works well.

LOW ENERGIES =⇒ The coupling is large,

perturbation theory fails, QCD is non-perturbative.

COLOR CONFINEMENT is a large-distance prob-

lem, related to the non-perturbative regime of QCD.

A yet unsolved problem ...

Why should we care to solve QCD in the non-perturbative regim e?

• Understanding strongly interacting gauge theories is a for midabletheoretical problem of utmost importance by itself

• We must understand strongly interacting matter as we observ e itaround us (hadronic, nuclear matter)

• Is strongly interacting matter confined forever?

N. Cabibbo and G. Parisi (1975): a new, deconfined state of

matter, corresponding to quark liberation, may exist in ex-

treme conditions of high temperature or high baryon density .

Quark-Gluon Plasma (QGP)? Tc ∼ 200 MeV ∼ 2 1012 ◦K

• The physics of the early Universe and of compact astrophysic al ob-jects may be described by states of matter completely away fr om ourcommon experience. Predictions must be extracted from QCD

The QCD phase diagram: a schematic draft

HADRONIC PHASE

c

uark luonQ G Plasma

µBµ

C

T

µN1 GeV

170 MeV

matternuclear

1 orderst

(T ,Ε µ )?Ε

RHICSPS

LHC

baryon chemical potential

collisions

heavy ion(Little Bangs)

Ear

ly

(Big

Ban

g)U

nive

rse

neutron stars

Color superconductivity?

T

What we would like to know:

• Location and nature of the transition to deconfined matter

• Location and properties of other possible exotic phases

Experimental input? Heavy Ion Collisions (SPS, RHIC, LHC, . .. FAIR)

QGP fireball? revealed by detectorsFinal Hadron Gas

– Only the final products of the little bangs are directly accessible. Particle multi-

plicities and ratios are well described by thermal distribu tion reached at chemi-

cal freeze-out. (like the Cosmic Microwave Background after Big Bang)

Evidence for a new state of matter:

anisotropic flow of final products in non-

central collision, best fluid ever created,

shear viscosity η/s ∼ 0.1 − 0.2.

Is it what QCD predicts?

Theoretical Problem: Solving a system with infinitely many

degrees of freedom in a strongly coupled regime.

- Taking ideas from condensed matter theory is the most natur al thing

to happen. An example:

One of the proposed mechanisms for color confinement

(G. t’Hooft and S. Mandelstam, 1975):

dual superconductivity of the QCD vacuum

• Ground state characterized by condensation of dual topolog ical de-

grees of freedom carrying a magnetic charge: magnetic monopoles

• =⇒ dual Meissner effect, expulsion of chromoelectric fields

• formation of chromoelectric flux tubes =⇒ confining potential.

Various theoretical tools can be used to illuminate the prob lem, a short

list of some of them used actively here in Pisa:

• Approaches based on supersymmetric gauge theories, where t he role of dual,

topological objects emerges more clearly (K. Konishi)

• Approaches based on the holograpich correspondence betwee n gauge theories

in D dimensions and string theories in D+1 dimensions (gauge /gravity duals)

(F. Bigazzi)

• Effective field theory approaches based on the idea of univer sality, in particular

to study aspects related to the phase transition and to the ro le of effective chiral

degrees of freedom (E. Meggiolaro, E. Vicari)

Is it possible to systematically approach the problem start ing from the

QCD first principles?

A numerical treatment is the best present first-principle ap proach

The starting point is the path-integral approach to Quantum Mechan-

ics and Quantum Field Theory, opened by R. Feynman in 1948.

〈0|O|0〉 ⇒∫

Dϕe−S[ϕ]O[ϕ]

The QCD path integral is discretized on a finite space-time la ttice

=⇒ finite number of integration variables

For QCD, integration variables are 3 × 3 unitary matrices, Uµ(n),

living on lattice links (link variables) (K.G. Wilson, 1974)

The path-integral is then computed by Monte-Carlo algorith ms

which sample field configurations proportionally to e−S[U ]

∫

DUe−S[U ]O[U ] ≃ O =1

M

M∑

i=1

O[U{i}]

1T

QCD partition function in terms of Euclidean path integral

Tr(

e−HQCD

T

)

⇒∫

DUe−SG[U ] detM [U ]

T =1

τ=

1

Nta(β,m)

τ is the extension of the compactified time

As long as DUe−SG detM [U ] is positive, it can be interpreted as a probability dis-

tribution DUP [U ] over gauge link configurations.

Sample averages give access to various equilibrium propert ies:

• vacuum expectation values needed to characterize the groun d state

• thermal quantities (energy density, specific heat, etc. ) ne eded to study the tran-

sition and the properties of the different phases

Uncertainties

• statistical: finite sample, error ∼ 1/√

sample size.

• systematic: finite box size L, finite lattice spacing a, unphysical quark masses.

Given enough computer power, uncertainties can be kept unde r control. Results from

different groups, adopting different discretizations, co nverge to consistent results.

How much computer power? A typical simulation may deal with more than 108

degrees of freedom and invert a sparse matrix connecting the m more then 106 times.

Projects employing L ≫ 1 fm, a . 0.1 fm and physical quark masses, require more

than 100 Teraflop*year ( ∼ 1022 floating point operations)

The full control over systematic effects has some exception s:

• QCD at high baryon density: DUe−SG detM [U ] is complex

• computation of non-equilibrium properties (e.g., transpo rt prop. like viscosity)

Lattice QCD and Supercomputing: a successful partenership ?

• At the time he proposed lattice QCD (1974) K.G.Wilson did not even dream of

making actual numerical simulations

• At the time somebody started dreaming (M. Creutz, 1979), ava ilable computer

power was of few Mflops ( 106 floating point operations per second)

• Nowadays many supercomputers around the world reach few Pet aflops ( 1015 flops)

That enables us today to make precise computations

An example:

the hadron spectrum at the percentprecision levelAoki, S., et al., 2010, Phys.Rev. D81, 074503.

Lattice QCD in Pisa

Activity in Pisa goes back to the early ’80s, i.e. to the early days of Lattice Gauge

Theories.

It is impossible to list all the people who have worked at some stage in the field

Incomplete list of people active in the field in the last 10 yea rs:

B. Alles, C. Bonati, M. Campostrini, G. Cossu, L. Del Debbio, A. Di Giacomo, M. Gior-

dano, M. D., M. Hasenbush, G. Lacagnina, L. Lepori, B. Lucini , M. Mariti, E. Meggiolaro,

G. Paffuti, A. Patella, C. Pica, F. Pucci, P. Rossi, E. Vicari .

I will give a rapid overview only of recent results regarding deconfinement and QCD

in ”extreme conditions”

Results about the finite T transition

The liberation of color degrees of freedom is clearly visibl e in thermodynamical quan-

tities and coincides with chiral symmetry restoration.

energy density u/d and s number fluctuations chiral condensate

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

120 140 160 180 200 220 240 260 280 300

T [MeV]

fK scale

χl/T2: Nτ=8

Nτ=6χs/T

2: Nτ=8Nτ=6

0

0.2

0.4

0.6

0.8

1

120 140 160 180 200

T [MeV]

∆l,sfK scale

asqtad: Nτ=8Nτ=12

HISQ/tree: Nτ=6Nτ=8

Nτ=12Nτ=8, ml=0.037ms

stout cont.

arXiv:1007.2580 arXiv:1111.1710 arXiv:1111.1710

Temperature and nature of the transitionS. Borsanyi et al. JHEP 1009, 073 (2010) Tc = 155(6) MeV (stout link stag. discretization, amin ≃ 0.08 fm)

A. Bazavov et al., PRD 85, 054503 (2012) Tc = 154(9) MeV (HISQ/tree stag. discretization, amin ≃ 0.1 fm)

- Physical point consistent with a smooth crossover (Aoki et al., Nature 443, 675 (2006))

- Chiral point (2 massless quarks) still an open issue: does i t boil ( 1st order) or not?

M. D., A. Di Giacomo and C. Pica, PRD 72, 114510; Bonati, Cossu , M.D., Di Giacomo, ’07 and in progress

QCD at finite baryon density

Problems with complex measure can be solved by a few approxim ate methods, e.g.

by simulating at imaginary potentials plus analytic contin uation.

M. D. and M.P. Lombardo, Phys. Rev. D 67, 014505 (2003); Phys. Rev. D 70, 074509 (2004).

M. D. and F. Sanfilippo, Phys. Rev. D 80, 014502 (2009); Phys. R ev. D 80, 111501 (2009);

C. Bonati, G. Cossu, M. D. and F. Sanfilippo, Phys. Rev. D 83, 05 4505 (2011);

P. Cea, L. Cosmai, M. D. and A. Papa, JHEP 0702, 066 (2007); Phy s. Rev. D 77, 051501 (2008); Phys. Rev. D 80, 034501 (2009)

Reliable only for small values of µB .

Comparison of various methods to extract

Tc(µB)/Tc(0) as a function of µB (4 stag. flavors)

P. Cea, L. Cosmai, M. D., A. Papa, PRD 81, 094502 (2010).

- We can reliably compute the curvature of the tran-

sition line, Tc(µB)

- We still cannot solve neutron stars

Strong interactions in strong magnetic fields

- in non-central heavy ion collisions, largest mag-

netic fields ever created ( B up to 1015 Tesla at LHC)

- possible strong fields in the early Universe, at the

time of the QCD transition ( B up to 1016 Tesla)

Many new phenomena are predicted, going from a change in the l ocation and nature

of the phase transition to changes in the properties of stron gly interacting matter

M. D., S. Mukherjee, F. Sanfilippo, Phys. Rev. D 82, 051501 (20 10);

M. D. and F. Negro, Phys. Rev. D 83, 114028 (2011);

M.D. and F. Negro, Phys. Rev. Lett. 109, 072001 (2012);

M. D., M. Mariti and F. Negro, Phys. Rev. Lett. 110, 082002 (20 13)

Coming soon: Magnetic susceptibility of the Quark-Gluon Plasma

(C. Bonati, M. D., M. Mariti, F. Negro, F. Sanfilippo, in progr ess)

- What about the mechanism underlying the confining/deconfin ing transition?

Dual superconductivity?

Two possible strategies to check the mechanism by lattice si mulations:

• Look for order parameters signalling magnetic charge conde nsation in the QCD

vacuum (A. Di Giacomo et al, 1995 →)

• Look directly for magnetic defects (monopoles) in lattice c onfigurations and at

their statistical properties, looking for evidence for con densation

(A. D’Alessandro, M.D., E. Shuryak, arXiv:1002.4161)

Computational resources

Lattice QCD simulations are ideally suited for paralleliza tion and have been a major

stimulus for the development of High Performance Computing resources.

An example is the series of APE machines ”made in INFN”

first APE project, 1988, 250 Mflops APEnext, 2006, 10 Tflops

People in the first APE project (Comput. Phys. Commun. 45, 345 (1987)): M. Albanese , F. Costantini,

G. Fiorentini, F. Flore, M.P. Lombardo, R. Tripiccione, P. B acilieri, L. Fonti, P. Giacomelli, E. Remiddi,

M. Bernaschi, N. Cabibbo, E. Marinari, G. Parisi, G. Salina, S. Cabasino, F. Marzano, P. Paolucci, S.

Petrarca, F. Rapuano, P. Marchesini, R. Rusack

Major computational resources available to our group today

- GPUs provide O(1) Teraflop cheap power on a Graphic Card

- That’s why we got interested in them (A. Di Giacomo et al, 2009)

C. Bonati, G. Cossu, M. D., P. Incardona, Comp. Phys. Comm. 18 3, 853 (2012)

- O(30) GPUs installed at INFN-PISA

- Other available at INFN-GENOA and INFN-ROME (QUONG)

- CNS4-cluster at INFN-PISA - 15 Tflop

- A share on the 2 Petaflop BlueGene/Q machine at CINECA:

- Next future developments: Progetto Premiale INFN ”SUMA”

A Glance at the Future ...

Impressive recent activity regarding the simulation of non -Abelian gauge

theories on optical lattices

- D. Banerjee, M. Dalmonte, M. Muller, E. Rico, P. Stebler, U. -J. Wiese and P. Zoller,

Phys. Rev. Lett. 109, 175302 (2012)

- E. Zohar, J. I. Cirac and B. Reznik, Phys. Rev. Lett. 110, 055 302 (2013)

- L. Tagliacozzo, A. Celi, A. Zamora and M. Lewenstein, Annal s Phys. 330, 160 (2013)

- D. Banerjee, M. Bogli, M. Dalmonte, E. Rico, P. Stebler, U. - J. Wiese and P. Zoller,

Phys. Rev. Lett. 110, 125303 (2013)

- E. Zohar, J. I. Cirac and B. Reznik, Phys. Rev. Lett. 110, 125 304 (2013)

- ...

- Is Quantum Computation the frontier of Lattice QCD?

- Is Lattice QCD the frontier of Quantum Computation?