# Presentation: 004101

## Mach cone shock waves at RHIC

## Outline

- Jet-Medium coupling
- Mach cone structures from colored and colorless sound
- Mach cone shockwaves in a dynamical model simulation
- Shockwaves go with the flow
- Ridge
- Conclusions

## Jet-Medium Coupling

- What happens to the jets’ lost energy? What part is “heating” the
- plasma, what part is redistributed into excitations of the medium?

- Colorful Modes:  	longitudinal modes => Mach cones	J. Ruppert & B. Müller (Phys.Lett.B618:123-130,2005)	transverse modes  => Cherenkov (like) radiation	I. Dremin, (e.g Nucl.Phys.A767:233-247,2006), 	A. Majumder et al. (e.g. Phys.Rev.Lett.96:172302,2006)
- 2)  Colorless (hydrodynamical) mode => Mach conesH. Stöcker et al. (e.g. Nucl.Phys.A750:121-147,2005),J. Casalderra-Solana et. al. (e.g. Nucl.Phys.A774:577-580,2006),T. Renk & J. Ruppert (e.g. Phys.Rev.C73:011901,(2006))

- I. Dremin’s talk

## Mach cones from colored sound?

- What is the wake structure induced by a high-pT color charge traversing the QCD medium?
- Can Mach waves in the QGP be created?
- Information on part of plasma’s properties is contained in longitudinal and transverse components of the dielectric tensor
- Two scenarios of interest:
- High temperature pQCD plasma
- Plasma as a quantum liquid

- J. Ruppert & B. Müller, Phys. Lett. **B618** (2005) 123

## Plasmon branches

- Generic result: if a space-like transverse plasmon branch exist Cherenkov-like gluon radiation could be induced. Koch, Majumder, Wang, Phys. Rev. Lett 96:172302, 2007

- Generic result: if a space-like longitudinal plasmon branch exist Mach cone structures could be induced.
- J. Ruppert & B. Müller, Phys. Lett. **B618** (2005) 123

- Colored sound

- Longitudinal modes

- Transverse modes

## Making colorful wakes

- Hard scattered parton (=jet-precursor) acts as a point-like probe current:

- Energy loss of the
- incident color charges:
- Thoma, Gyulassy, Nucl.Phys.
-  B351:491 (1990), Weldon,
- Phys. Rev. D26, 1394 (1983)

- Induced charge- and current densities:

- Ruppert & B. Müller,
- Phys. Lett. **B618** (2005) 123

## Colored wakes in the QCD Medium

- 1. High temperature pQCD plasma:
- Color charge density wake
- 	is a co-moving screening cloud:

- J. Ruppert & B. Müller,
- Phys. Lett. **B618** (2005) 123

- 2. Plasma as a quantum liquid:
- Subsonic jet: analogous results to pQCD plasma case
- Supersonic jet: excitation of longitudinal plasma modes (colored sound) with Mach cone emission angle:

## Mach cones in a hydrodynamical framework

- Radiative energy could be deposited in collective hydrodynamical modes.
- H. Stöcker et al. (e.g. Nucl.Phys.A750:121-147,2005),
- J. Casalderray, E. Shuryak, D. Teaney,
- Nucl.Phys.A774:577-580,2006

- Idea similar to studies of waves in the nuclear medium which can be excited if supersonically travelling source occurs:
- See e.g. A. E. Glassgold,
- W. Heckroth, and KM Watson, Ann. Phys. (Paris) 6, 1 (1959), Scheid et al. Phys.Rev. Lett. 32 (1974), 741

- J. Casalderray, E. Shuryak, D. Teaney,
- Nucl.Phys.A774:577-580,2006

- Colorless sound

## Strong shock excitation only created with specific source term!

- Non isentropic excitations: the main excitation mechanism is entropy production and the flow field introduces vorticity.

- Isentropic excitations: No significant entropy production. Medium excitation by sound wave emission.

- QM 2006, Casalderray-Solana

- Weak correlation signal with point-likesource: Chaudhuri & Heinz, Phys.Rev.Lett.97:062301,2006

- Source term not yet derivedfundamentally. Has to
- express  non-equilibrium
- coupling of jet’s secondaries

## Hadron production in different pT regions

- Hadron production in different pT regions

- Jets created in hard collisions --> Fragmentation regime >6 GeVLost energy - redistributed in the medium --> hydro window <2 GeV
- Intermediate window --> recombination region

- Momentum cuts allow to concentrate on energy redistributionin the medium of hard partons to the soft bulk medium

## Correlation Measurements: Theoretical modeling in a dynamical medium I

- (Fig. Casalderray-Solana)

- Assume: energy lost from hard partonsexcites collective mode with fraction f

- Follow flow of energy/momentum in
- dynamical medium =>dispersion relation

- Renk & Ruppert, Phys.Rev.C73:011901,2006,
- Phys. Lett. B646:19-23,2007, and
- Phys. Rev. C 76, 014908 (2007)

- (Fig. Renk)

## Theoretical modeling in a dynamical medium II

- Fireball evolution model describing hadronic mt spectra, HBT, photon emission and RAA (cf. Renk, Phys. Rev. C. 70 (2004) 021903)
- Space-time position dependent jet energy deposition into the medium (in BDMPS according to ASW quenching weights, anologously as in e. g. Renk, Ruppert, Nonaka, Bass, Phys.Rev.C75:031902,2007 )
- Fraction fmach of energy deposition into collective mode (sound)
- Local speed of sound u (and fireball thermodynamics) from lattice EOS
- Propagation of sound waves through evolving medium (incl. longitudinal and transverse expansion)
- Freeze-out using Cooper-Frye formula
- Monte-Carlo sampling using trigger conditions and acceptance cuts

- Renk & Ruppert, Phys.Rev.C73:011901,2006

## Monte Carlo

- Near side:
- Hard parton energy (and type)
- LO pQCD parton spectrum
- Vertex sampling from nuclear overlap
- Pobabilisitc energy loss in BDMPS
- Near and away side fragmentation
- Fragment and check against near side trigger threshold

- Away side:
- Intrinsic kT
- Chosen such that d-Au width of far side peak is reproduced
- Away side probabilistic energy loss from in-medium path
- Propagate excited mode
- Freeze-out according to Cooper-Frye
- Count hadrons above associate threshold

**Contains all information on trigger bias, pathlength distribution and **
**nuclear density. . .**

## Energy deposition

- Renk, Ruppert, Phys.Rev.C73:011901,2006

## 2-particle correlation and medium properties

- Faster evolution <=> larger angle
- More flow exposure <=> structures are washed out

- Tool to probe speed of sound and longitudinal and
- transverse flow.

- Renk, Ruppert

## Transverse flow I

- At 1 GeV, a Mach signal only appears if aligned with flow

- Renk, Ruppert, Phys.Rev.C73:011901,2006; Satarov, Stocker, Mishustin, Phys.Lett.B627:64-70,2005.

- Shockwave: additional boost for hadrons at freeze-out
- “Position space” vs. ”Momentum space”

- (Fig. T. Renk)

- Renk, Ruppert, Phys.Rev.C73:011901,2006

## Transverse flow II

- Wing of the cone “vanishes” for some geometries due
- to non - alignment flow - mach shock

- Due to momentum conservation: reappearance of strength  at lower pT

- Misidentification as ‘deflected jet’ possible

- Renk, Eur. Phys. J. C49 : 13-17,2007

## Shockwaves go with the flow

- Propagate with cs relative to local medium
- (Elongation in rapidity space)
- Longitudinal flow field at final zfinal determines
- boost in momentum space

- Elongation only for excitation propagating relative to
- the medium! Poses severe challenges to non-hydro scenarios.

- Renk, Ruppert, Phys.Lett.B646:19-23,2007

## Away side parton at midrapidity

- (Fig. T. Renk)

- Renk, Ruppert,
- Phys.Lett.B646:19-23,2007

## Rapidity-averaged away-side parton

- (Fig. T. Renk)

- Renk, Ruppert,
- Phys.Lett.B646:19-23,2007

## Including longitudinal flow

- Renk, Ruppert,
- Phys.Lett.B646:19-23,2007

- (Fig. T. Renk)

- Longitudinal flow: if near-side at mid-
- rapidity and cut for away-side at (small) forward-rapidity => away-side correlation signal still (almost) unchanged [rapidity cuts only show
- longitudinally elongated cone]

## Three particle correlations

- Assumption: calculated as factorized 2-particle correlations

- Calculated backround subtracted
- Each particle from shockwave is correlated with away side parton
- Neglect additional correclations among particles in shockwave
- (motivation: momentum conservation in cone shared among O(20+) particles)

- (Fig. T. Renk)

## 3-particle correlations and medium properties

- Correlation at y=0

- Strong flow distortion <=> diagonal contribution dominant

- Off-diagonal strength does not appear
- automatically for Mach cones

- Renk, Ruppert, Phys. Rev. C 76, 014908 (2007)

## Pt cut variations

- Complication due to recombination region -- not yet includedin dynamical model. Therefore arguments more qualitative here.

- J. Adams et. al. [STAR Collaboration] Phys. Rev. Lett. 95 (2005) 152301

- No apparent change in angle as function of passociate
- No apparent change in angle as function of ptrig
- Scaling law describes relative peak strength as a function of ptrig
- Disappearance of dip (punchthrough?)

- (Fig. T. Renk)

## Is the ridge a similar hydro phenomenon?

- Ridge vs. large angle correlation might be a resemblance of bow shock vs. Mach shock!

- Conclusive measurement would be determining
- the transition region of  4-particle correlation with di-hadron trigger

- (Figs. T. Renk)

- Large spread in rapidity would be a genuine hydro phenomenon also for smaller-angle soundwave

- Renk, Ruppert, hep-ph/0701154

## Conclusions

- Redistributed energy in collective (colorless) modes
- leading to Mach shocks explains:

- Measured correlation gives averaged speed of sound of the nuclear medium <cS> (angular measurement)
- Sensitive in details to evolution (especially 3 particle correlation)
- Relative independence of away-side correlation width with ptrig and passociate
- Presence of a dip on the away-side
- (weak) off-diagonal structures in 3 particle correlations
- Ridge might be a similar hydro phenomenon: bow shock

- Special thanks to T. Renk

## Color Octet vs. color singlet

- Colored sound