Particle Theory in the 21 st Century Andreas Karch.

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Particle Theory in the 21st Century

Andreas Karch

The ultimate quest

What are the rules that govern the world atthe smallest scales? Why does the universe lookthe way it looks like at the largest scales?

Everything else is details; and its messy and complicated (like life).

The Theory of Everything

The Theory of Everything:

The standard model Lagrangian(as of July 3rd, 2012).

Prediction: Probability to interact two Ws with TeV scaleenergy > 1 ???????

Solution: Higgs! Is it there?

The Higgs! It’s real!(or at least something pretty close to it.)

Problem: Hard to calculate!

Solution: Lattice (no real time, no finite density). String Theory via holography

Problem:

That’s it? Aren’t we missing something?!?

Particle Physics in the 21st century:

• Open Problems within the standard model: QCD difficult to calculate. Non-perturbative. Lattice works (sometimes). Sometimes perturbation theory.

• Problems beyond SM: We know there is BSM (beyond the standard model) physics: Neutrino masses, Dark Matter, Dark Energy, GRAVITY.

BSM Physics

What physics could be hiding “around the corner”?

What novel experimental signatures would we belooking for?

Beware the nightmare scenario: “Just the Higgs”

Fortunately hints of non-Higgsness. Are they real?

QCD Physics

What happens when baryons melt?

Strongly coupled soup of quarks and gluons. What are its properties? We can realize itexperimentally (heavy-ion collisions). But can we cacluate?

This is the stuff the early universewas made from!

Applied String Theory“Holography”

(and a little applied field theory)

Holography = Solvable Toy Model

Solvable models of strong coupling dynamics.

• Study Transport, real time• Study Finite Density• Explore paradigms “beyond Landau”

(Challenging in real QCD, experimentally relevant)

(Non-Fermi Liquids? Phase Transitions? High Tcsuperconductors? Topological Insulators?)

Gives us qualitative guidance/intuition.

Not QCD! Expect errors of order 100%better than extrapolating perturbation theory to αs ~ 1

Challenge for Computers:

e.g. Lattice QCD

We do have methods for strong coupling:

But: typically relies on importance sampling.

Monte-Carlotechniques.

𝑒−𝑆weighting in Euclidean path integral.

FAILS FOR DYNAMIC PROCESSES OR AT FINITE DENSITY (sign problem)

Holographic Toy models.

Can we at leastget a qualitativeunderstanding ofhow dynamics looklike at strong coupling?

Holographic Toy models.

Can we at leastget a qualitativeunderstanding ofhow dynamics lookslike at strong coupling?

Holographic Theories:

“Large N”:

Holographic toy models have two key properties:

theory is essentially classical

“Large λ”:large separation of scales in the spectrum

mspin-2-meson

mspin-1-meson

~ λ1/4

QCD: 775 MeV1275 MeV

Successes and recent developments

• Viscosity and Hydrodynamics

• Energy Loss

• Thermalization

Viscosity of Quarks and Gluons

Shear Viscosity

Viscosity = Diffusion constant for momentum

Viscosity = [(force/area)] per unit velocity gradient

Viscosity in Heavy Ions.

How does the almondshaped fluid expand?

high pressure

low pressure

(Shear) Viscosity η

(1 cp = 10−2 p = 10−3 Pa·s)

Force per unit area per velocity gradient

Measuring Viscosity - an example

22(2.3 1011cp)

Recall: Viscosity of pitch: ~ 2.3 1011cp

RHIC’s measurement of hot QCD (= quark gluon plasma) (from colliding high energy gold nuclei)

Viscosity in Holography:

(KSS;Kovtun - UW grad student;Son – UW faculty,Starinets – UW postdoc)

• pinpoints correct observable• gives ball-park figure• large at weak coupling –

extrapolation from weak coupling is order of magnitude off!

Viscosity to entropy ratio:• close to 1/(4 π) in quark gluon plasma produced at RHIC --- strongly coupled! fluid, not plasma!

• 2-3 times that in cold atomic gases• at least factor of 10 times 1/(4 π) in all other substances known to mankind (including superfluid helium, water, …)

• 11 orders of magnitude larger that 1/(4 π) in pitch.

Energy LossEnergy Loss

Jet quenching.

See one of two back-to-back created particles.

The other one got “stuck” in the fireball

Jet quenching is a direct indication of large drag forces on quarks..

Sometimes HARD COLLISIONS produce non-thermalparticles inside the fire ball = probe of the plasma.

Jet Quenching at the LHC (Atlas)

Stopping Distance:

Quantify Energy loss in terms of Stopping Distance:

How far does quark of energy E travel beforeit gets thermalized into the plasma?

Perturbative QCD or QED: L ~ E1/2

Energy Loss: Heavy quarks

Constant E - field

(Herzog, Karch, Kozcaz, Kovtun, Yaffe)(all UW: postdoc, faculty, student2,faculty)

Energy Loss: Heavy quarks

Constant E - field

(Herzog, Karch, Kozcaz, Kovtun, Yaffe)(all UW: postdoc, faculty, student2,faculty)

SOLVE CLASSICALEQUATIONS OFMOTION!

Energy Loss, Light Quarks

(Chesler, Jensen, Karch, Yaffe – again all UW)

Stopping Distance:

Perturbative QCD: L ~ E1/2

Holography:

Maximal Stopping Distance: L ~ E1/3

others found:Typical Stopping Distance: L ~ E1/4

Experiment:1/3 preferred over 1/2 ???

ThermalizationThermalization

Why does the QCD fireball thermalize so rapidly?

too hard!

How quickly does the holographic fireball thermalize?

Shockwave-collision to black hole

(Chesler, Yaffe)

Energy/area in shock ~ μ3

(Chesler, Yaffe)

μ ~ 2.3 GeV

“RHIC”:

Hydro valid ~ 0.35 fm/c << 1 fm/c

But: there is so much more info in this plot!

Lots to explore! Strong coupling, non-equilibrium.

Hydrolization vs Thermalization

(Chesler, Teaney)

Note: Hydro works when transverse and longitudinal pressure differ by a factor of 2.

Hydrolization before Thermalization!

Hydro works. No well defined temperature.

(Chesler, Teaney)

t=0initial perturbation

(Chesler, Teaney)

shock followslightlike geodesic

Asymptotic metricsettles to final state plus small peturbations.

Hydrolization

(Chesler, Teaney)

shock reachesnear horizonregion

Fluctuation Spectrumthermal..

Thermalization

Applications to Condensed Matter

Physics.

Applications to Condensed Matter

Physics.

Strong Coupling in CM.

The theory of everything:

𝐻= ∑𝑁𝑢𝑐𝑙𝑒𝑖 ,𝐴

𝑃 𝐴2

𝑚𝐴

+ ∑𝑒 𝑙𝑒𝑐𝑡𝑟𝑜𝑛 ,𝑖

𝑝𝑖2

𝑚𝑒

−∑𝐴 , 𝑖

|𝑥𝑖−𝑥𝐴|+∑𝑖≠ 𝑗

¿ 𝑥 𝑖−𝑥 𝑗∨¿¿

How hard can it be?

Strong Coupling in CM

Already Helium too difficult tosolve analytically.

electron/electron Coulomb repulsion not weak!

if it is negligible, we have good theory control:

Band structure! Insulators and conductors.

but what to do when it is not?

Landau’s paradigms:

• Identify physical candidates for low energy degrees of freedom.

• Write down most general allowed interactions

• See how interactions scale in low energy limit

dominate transport

many interactions “irrelevant” = scale to zero

What could they be?

1) weakly coupled fermions.

Landau Fermi Liquid

• Fermi Surface• Low energy excitations near Fermi Surface• Only Cooper Pair Instability survives at low energies, all other interactions scale to zero

universal!

at low temperaturesresistivity grows as T2

What could they be?

1) weakly coupled bosons.

Landau’s Theory of Phase Transitions

free energyorder parameter = scalar field.

Scalar mass relevant; dominates at low energies.Can be tuned to zero close to a phase transition.

Is this all?

Degrees of freedom in high Tc superconductorsare neither!

Non-Fermi Liquid

at low temperaturesresistivity grows as T

Strange Metal

What else could it be?

This is the perfect question to aska solvable toy model:

Studying matter in holographictoy models, what are the possiblelow energy behaviors?

Matter=finite density of some conserved charge.

MIT/Leiden Fermions.

Holographic Realization of a large class of non-Fermi

Liquids.

Fermions in a charged black hole background.

(Lee)(Liu, McGreevy, Vegh)(Cubrovic, Zaanen, Schalm)

MIT/Leiden Fermions.

Characteristic Features:

Fermi surface (singularity in wavevector dependence of correlation functions).

No well defined particle excitation. (not a Fermi-liquid).

Low temperature resistivity grows as T2Δ-1

(Δ free parameter in model).

Interactions don’t scale away?

Fermi-surface, but interactions not irrelevant?

Low energy physics = fermions coupled to other light degrees of freedom!

Local Quantum Criticality.0+1 dimensional theories close to a Landau-like phase transition.

= AdS2

The big question:

Is any of this realized (to some approximation)in real systems?

Holography provides controlled examplesof novel quantum matter.

Summary.

Solvable models of strong

coupling dynamics.

Holography

A graduate career in theoretical physics?A graduate career in theoretical physics?

Particle Theory

Number of students >> Number of jobs

Think twice! Do you like theory so much that it is worth while job insecurity for the next 10 years, taking postdocs at random, far away places?

Particle Theory• about 5 students for 5 faculty• historically paid our students 10 hour RA for 3 years; students TA at least 10 hours throughout

• year 1: take the graduate classes, do reading, attend particle theory journal club on Fridays to get to know us. Maybe research in the summer

• year 2: take QFT, advanced SM, nuclear physics, particle physics. Do trial research with one of us.

• year 3: we typically start supporting students we decide to take on by the beginning of their 3rd year.

Particle Theory in the 21 st Century Andreas Karch.

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