CERN Physics Department What we may learn from AdS/CFT about the phenomenology of Heavy Ion Collisions Urs Achim Wiedemann CERN Physics Department TH Unit Durham, 19 December 2007 based on work in collaboration with Qudsia Ejaz, Thomas Faulkner, Hong Liu, Krishna Rajagopal

Beyond the Standard Model How does collectivity emerge from elementary interactions?

Beyond the Standard Model How does collectivity emerge from elementary interactions? p+p @ 14 TeV ATLAS CMS LHCb ALICE Heavy Ions @ 5.5 TeV ALICE CMS ATLAS Beyond the Standard Model

Beyond the Standard Model String theory The Standard Model How does collectivity emerge from elementary interactions? Novel techniques for thermal QFTs Topic of this talk Beyond the Standard Model String inspired model building

Why do we need collider energies Question: Why do we need collider energies to test properties of dense QCD matter which arise on typical scales ?

Answer 1: Large quantitative gains Increasing the center of mass energy implies Denser initial system, higher initial temperature Longer lifetime Bigger spatial extension Stronger collective phenomena A large body of experimental data from RHIC supports this argument.

Answer 2: Qualitatively novel access to properties of dense matter For a detailed experimentation with dense QCD matter, one ideally wants to do DIS on the QGP. … and we can by using auto-generated probes at high Large allows us to embed well-controlled large- processes (hard probes) in dense nuclear matter. Q: How sensitive are hard probes?

Bjorken’s original estimate and its correction Bjorken 1982: consider jet in p+p collision, hard parton interacts with underlying event collisional energy loss (Bjorken realized later that this estimate was numerically erroneous.) Bjorken conjectured monojet phenomenon in proton-proton Today we know (th): radiative energy loss dominates Baier Dokshitzer Mueller Peigne Schiff 1995 p+p: Negligible ! Monojet phenomenon! A+A: observed at RHIC,

High pT Hadron Spectra Centrality dependence: 0-5% 70-90% L large L small

Centrality dependence: Au+Au vs. d+Au Final state suppression Initial state enhancement partonic energy loss

“DIS on QGP”

Parton Propagation in an External Color Field High-energy scattering determined by eikonal Wilson line During scattering, transverse coordinates are frozen, color rotates lala

Example: virtual photoabsorption cross section Incoming virtual photon to O(g0) Outgoing from target Target average: For total cross section, square Model: Exponent of real quantity Saturation scale A.H.Mueller … lala

Example: gluon production in q+A Incoming free quark wave function dressed to O(g) Outgoing from target Number of produced gluons Target average involves adjoint Wilson loop: Bertsch Gunion spectrum + Brownian Motion Kovner Wiedemann, PRD 64 (2001) 114002 Kovchegov Mueller 1998 lala

The medium-modified Final State Parton Shower Wiedemann, NPB 588 (2000) 303 Radiation off produced parton Target average includes Brownian motion: BDMPS transport coefficient Expectation value of light-like Wilson line

The medium-modified Final State Parton Shower Medium characterized by transport coefficient: Wang, Gyulassy (1994); Baier, Dokshitzer, Mueller, Peigne, Schiff (1996); Zakharov (1997); Wiedemann (2000); Gyulassy, Levai, Vitev (2000); Wang ... Salgado,Wiedemann PRD68:014008 (2003) energy loss of leading parton pt-broadening of shower

Quenching parameter from HI phenomenology Eskola, Honkanen, Salgado, Wiedemann Nucl Phys A747 (2005) 511 Can we understand the order or magnitude of this fit parameter from 1st principles of a thermal QFT?

Static q-qbar potential

Static quark-antiquark potential E(L) The T-dependence of E(L) has been studied in lattice QCD. Bielefeld Group, hep-lat/0509001 time transverse distance L Ltime Consider thermal expectation value of static Wilson loop in fundamental representation. For we define a static quark-antiquark potential Lattice results support the argument of Matsui and Satz 1986 that quarkonium ‘melts’ due to color screening above the QCD phase transition. Exponent of imaginary quantity

J/Psi: a q-qbar pair moving through the medium produced in heavy ion collisions BUT: Connecting lattice QCD to heavy ion phenomenology requires model-dependent input - formation time? - formation mechanism? - collective motion of ‘medium’ Can one get insight from 1st principles of a thermal QFT on some of these so-far model-dependent inputs? Within reach in HICs at the LHC

Quarkonium dissociation at finite pt Wilson loops defining a static quark-antiquark potential at relative rapidity (or velocity ) with respect to the medium. Not calculable in lattice QCD but of phenomenological interest.

AdS/CFT

String Theory Calculations of Properties of Matter AdS/CFT correspondence relates Strong coupling problems Classical Problem in a curved in non-abelian QFT higher-dimensional space Maldacena, 1997 String coupling and string tension T’Hooft coupling Translation into field theoretic quantities Black hole horizon Curvature radius Finite T Lattice QCD is difficult to apply to problems involving real-time dynamics (moving QQbar pair, light-like Wilson loops, …) hydrodynamic properties (Problem of analytical continuation to if lowest Matsubara frequency in imaginary time formalism is .) ….

Wilson loops from AdS/CFT AdS/CFT - Recipe Finite temperature N=4 SYM dual to AdS5 Schwarzschild black hole: Translation into field theoretic quantities: Hawking temperature is QGP temperature String tension determines t’Hooft coupling Maldacena (1998) Rey and Lee (1998) Black hole horizon Our (3+1)-dim world Wilson loop C in our world horizon : area of string world sheet with boundary C. Curvature radius

Finding S(C) Wilson loop can be considered Not more difficult than finding the catenary Wilson loop can be considered as the space-time trajectory of a quark-antiquark pair. Key: open string connecting the quark pair can venture into the radial 5th dimension. Finding S(C): finding the shape of the string hanging from the spatial infinity of a black hole.

Calculating the loop in boosted metric AdS BH metric boosted in x3-direction: Parameterization of two-dimensional world-sheet bounded by C: Boundary condition: Nambu-Goto action: Our task: find catenary

Time-like vs. space-like world sheet Time-like world sheet: e.o.m. action length Lagrangian Hamiltonian Space-like world sheet:

Quenching parameter Space-like world sheet

Results for quenching parameter determine subtraction term S0 (via single string drag solution) Herzog, Karch, Kovtun, Kozcaz, Yaffe hep-th/0605158 S. Gubser, hep-th/0605182 consider ordered limit: expand S(C) for small L: Liu, Rajagopal, Wiedemann, hep-ph/0605178 What if the medium is moving with rapidity at angle w.r.t. jet trajectory? Liu, Rajagopal, Wiedemann, hep-ph/0612168

N=4 SYM Numerology Is this comparison meaningful? In QGP of QCD, parton energy loss described perturbatively up to non-perturbative quenching parameter. We calculate quenching parameter in N=4 SYM (not necessarily a calculation of full energy loss of SYM) If we relate N=4 SYM to QCD by fixing for T = 300 MeV for T = 400 MeV This is close to values from experimental fits. Is this comparison meaningful?

Comment on: Is comparison meaningful? N=4 SYM theory conformal Physics near vacuum and at very high energy is very different from that of QCD no asmptotic freedom no confinement superymmetric no chiral condensate no dynamical quarks, 6 scalar and 4 Weyl fermionic fields in adjoint representation

At finite temperature: Is comparions meaningful? conformal no asmptotic freedom no confinement superymmetric (badly broken) no chiral condensate no dynamical quarks, 6 scalar and 4 Weyl fermionic fields in adjoint representation N=4 SYM theory at finite T QCD at T ~ few x Tc near conformal (lattice) not intrinsic properties of QGP at strong coupling not present may be taken care of by proper normalization

Quenching parameter for other theories General CFTs with gravity dual: (large N and strong coupling) Liu, Rajagopal, Wiedemann, hep-ph/0612168 a central charge s entropy Near conformal theories: corrections small Buchel, hep-th/0605178 Finite coupling and Nc corrections: hard Armesto, Edelstein, Mas hep-ph/0606245 R-charge chemical potentials: Avramis, Sfetsos; Armesto, Edelstein, Mas; Lin, Matsuo; … Corrections small when chemical potentials small

Static q-qbar potential Time-like world sheet

Screening length shows velocity scaling The screening length of the static q-qbar potential scales with velocity This indicates that the q-qbar dissociation temperatures scales like For any quark mass, there is a maximal velocity beyond which there is no potential between the pair.

D3-D7-brane construction of mesons 9+1-dim Minkowski space, N D3-branes and Nf D7-branes D3: 0 1 2 3 . . . . . . . D7: 0 1 2 3 4 5 6 7 . . Position of D7-brane, e.g. x8=L, x9 = 0. Low-lying meson spectrum in gauge theory Fluctuations of x8, x9 on D7-branes Mass spectrum of these mesonic excitations analyzed Kruczenski, Mateos, Myers, Winters; Babington, Erdmenger, Evans, Guralnik, Kirsch; …

D7-brane embedding at finite temperature 9+1-dim Minkowski space, N D3-branes and Nf D7-branes D3: 0 1 2 3 . . . . . . . D7: 0 1 2 3 4 5 6 7 . . Position of D7-brane, e.g. x8=L, x9 = 0. Low-lying meson spectrum in gauge theory Fluctuations of x8, x9 on D7-branes Mass spectrum of these mesonic excitations analyzed Kruczenski, Mateos, Myers, Winters; Babington, Erdmenger, Evans, Guralnik, Kirsch; …

Meson dispersion relation at finite temperature Mesons at arbitrary high momentum propagate with finite limiting velocity v0, which can be very small. For very large quark mass, we are consistent with result for static quark potential Ejaz, Faulkner, Liu, Rajagopal, Wiedemann; arXiv:0712.0590

THE END of this talk Many chapters on comparing AdS/CFT to QCD written already In thermal sector: - Shear viscosity in QCD diffusion constants thermal spectral functions quenching drag quark-antiquark static potential … Policastro, Son, Starinets, PRL 87, 081601 (2001)… Policastro, Son, Starinets, hep-th/0205052, … Teaney, hep-th/0602044, … Liu, Rajagopal, Wiedemann hep-ph/0605178 PRL, …. Herzog et al hep-th/0605158; Gubser hep-th/0605182 Casalderrey-Solana, Teaney hep-ph/0605199 Liu, Rajagopal, Wiedemann hep-ph/0607062; … ‘Comparison’ neither straightforward nor obviously far-fetched - rich testing ground for understanding non-perturbative properties of non-abelian thermal gauge field theories Many chapters to be written …

BACK-UP Let me now turn to the properties of the bulk matter produced in a nucleus-nucleus collision.

Quark-antiquark static potential

Quark-antiquark static potential - angular dep.

Space-like World Sheet Lagrangian Hamiltonian Space-like world sheet for: e.o.m. action length

Energy Loss in a Strongly Expanding Medium In A-A collisions, the density of scattering centers is time-dependent: Salgado, Wiedemann PRL 89, 092303 (2002) = 1.5, 1.0, 0.5, 0 Dynamical Scaling Law: same spectrum obtained for equivalent static transport coefficient: In a nucleus-nucleus collision, the medium expands strongly and the density decreases in time. For example, for a 1-dimensional Bjorken expansion, this expansion parameter alpha equals one. If transverse expansion matters, alpha is larger than one. Now, remarkably, calculations of parton energy loss in such an expanding medium show a scaling law. The radiated gluon energy for different expansion scenarios can be mapped onto a single curve if rescaled in terms of this linear line-averaged transport coefficient. In practice, this means that you can analyzed effects of parton energy loss in heavy ion collisions as if the medium were static. At the end of the analysis, one simply translates the extracted static average transport coefficient into the corresponding dynamical one. Calculations for a static medium apply to expanding systems Rescaled spectrum