August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 1
A running coupling explanation of the surprising transparency of the QGP at LHC
Alessandro BuzzattiMiklos Gyulassy
Phys. Rev. Lett. 108, 0223101 (2012) arXiv:1207.6020 (2012)
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 2
Outline
โข CUJETโ Presentation of the modelโ Systematic errors
โข Flavor dependent RAA at RHIC and LHCโ Level crossing
โข Alpha runningโ Comparison with CMS and ALICE data
โข Conclusions
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 3
Jet Tomography
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 4
Energy loss โ Radiative
Incoherent limit: Gunion-Bertsch
โ Incoming quark is on-shell and masslessโ The non-abelian nature of QCD alters the spectrum
from the QED resultโ Multiple scattering amplitudes are summed
incoherently
๐=ยฟ
๐=ยฟ๐=ยฟ
๐ โฒ
Formation time physics
โข
โ Incoherent multiple collisionsโ LPM effect (radiation suppressed by multiple scatterings within one coherence
length)โ Factorization limit (acts as one single scatterer)
๐ ๐๐๐๐โฅ๐
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 5
DGLV model
Opacity series expantion
Radiation antenna
๐ป๐๐๐LPM effect
๐ผ๐๐ฃ๐๐๐ ๐ ๐๐๐๐๐๐ก๐๐๐๐ก๐๐๐๐๐๐ ๐ ๐๐๐๐๐๐ก๐ Scattering center distribution
Soft Radiation (, )Soft Scattering (, )
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 6
CUJETโข Geometry
โ Glauber modelโ Bjorken longitudinal expansion
โข Energy lossโ DGLV โ MD Radiative energy loss modelโ Energy loss fluctuations (Poisson expansion)โ Full path length integration:
โ Elastic energy loss contributionsโข Detailed convolution over initial production spectraโข In vacuum Fragmentation Functions
๐ (๐ )=๐๐ป (๐โฅ+๏ฟฝฬ๏ฟฝ๐ ,๐) ๐ (๐ )=๐ด๐ ๐๐+๐๐๐ (๐ )(๐โ ๐)
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 7
CUJETโข Geometry
โ Glauber modelโ Bjorken longitudinal expansion
โข Energy lossโ DGLV โ MD Radiative energy loss modelโ Energy loss fluctuations (Poisson expansion)โ Full path length integration:
โ Elastic energy loss contributionsโข Detailed convolution over initial production spectraโข In vacuum Fragmentation Functions
Possibility to evaluate systematic theoretical uncertainties such as sensitivity to formation and decoupling phases of the QGP evolution, local running coupling and screening scale variations, and other effects out of reach with analytic approximations;
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 8
Bjorken expansion
โข The local thermal equilibrium is established at
โข Before equilibrium
(entropy equation)
( is the observed rapidity density)
MONOTONIC density dependence
Temporal envelopes: linear, divergent, freestreaming
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 9
Systematic errors
โข Opacity order expansionโข Choice of interaction potentialโข Pre-equilibrium phaseโ ALSO:
โข pp Spectraโข Running coupling scales
1. One free parameter in the model: 2. Fit to 10GeV RHIC Pion data 3. All other predictions are fully constrained
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 10
Outline
โข CUJETโ Presentation of the modelโ Systematic errors
โข Flavor dependent RAA at RHIC and LHCโ Level crossing
โข Alpha runningโ Comparison with CMS and ALICE data
โข Conclusions
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 11
RHIC Results
, , ,
u
c
b
g
Inversion of RAA flavor hierarchy at sufficiently high pt
AB and M. Gyulassy, Phys. Rev. Lett. 108, 0223101 (2012)
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 12
LHC Results
Parameters constrained by RHIC
AB and M. Gyulassy, Phys. Rev. Lett. 108, 0223101 (2012)
Competing effect between Energy loss orderingโฆ
โฆand pp Production spectra
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 13
Pions and Electrons at RHIC
LIGHT QUARKS HEAVY QUARKS
Wicks, Horowitz, Djordjevic, Gyulassy / NPA (2007)
CUJET solves the Heavy Quark puzzleโฆ
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 14
Pions at LHC
โฆbut doesnโt excel at explaining the surprising transparency at LHC
AB and M. Gyulassy, Phys. Rev. Lett. 108, 0223101 (2012)
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 15
Outline
โข CUJETโ Presentation of the modelโ Systematic errors
โข Flavor dependent RAA at RHIC and LHCโ Level crossing
โข Alpha runningโ Comparison with CMS and ALICE data
โข Conclusions
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 16
Alpha scales
โข Introduce one-loop alpha runningโข
โ
โ
0 1 2 3 4 50 .10 .20 .30 .40 .5 ๐ถ๐ด๐จ๐ฟ
๐ฌ๐๐๐๐๐๐=ยฟ
B. G. Zakharov, JETP Lett. 88 (2008) 781-786
S. Peigne and A. Peshier, Phys.Rev. D77 (2008) 114017
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 17
Alpha scales
โข Introduce one-loop alpha runningโข
โ Systematic uncertainties:
0 1 2 3 4 50 .10 .20 .30 .40 .5 ๐ถ๐ด๐จ๐ฟ
B. G. Zakharov, JETP Lett. 88 (2008) 781-786
Vary
Fit LHC Pion data at fixing
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 18
Focus on LHC
It is natural to use LHC results as our benchmark due to the extended range available
howeverRHIC remains an essential tool to constraint our models
STAR HFT sPHENIX
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 19
LHC Pions
CUJET effective alpha
See also B. Betz and M. Gyulassy, arXiv:1201.02181
Solid: LHCDashed: RHIC
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 20
ALICE and CMS PionsCMS CollaborationALICE Collaboration
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 21
ALICE and CMS PionsALICE Collaboration CMS Collaboration
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 22
PHENIX Pions
PHENIX Collaboration
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 23
ALICE and CMS Heavy Flavors
ALICE Collaboration CMS Collaboration
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 24
ConclusionsMODEL
โข CUJET offers a reliable and flexible model able to compute leading hadron Jet Energy loss and compare directly with dataโ Satisfactory results when looking at flavor and density dependence of RAA โ Possibility to study systematic theoretical uncertaintiesโ Easy to improve
ACHIEVEMENTSโข New RHIC electron predictions now consistent with uncertainties of data (Heavy
Quark puzzle)โข Strong prediction of novel level crossing pattern of flavor dependent RAA
โข Evidence of running alpha strong coupling constantโ Simultaneous agreement with RHIC and LHC data
FUTUREโข Necessity to fit as many orthogonal observable as possible
โ Non central collision RAA
โ Elliptic flow v2
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 25
BACKUP
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 26
Energy loss
โข Consider a simplified power law model for Energy loss: W. A. Horowitz and M. Gyulassy, arXiv:1104.4958B. Betz and M. Gyulassy, arXiv:1201.0218
10 20 30 40 50E G eV
0 .4
0 .2
0 .0
0 .2
0 .4
aE;L ,dN dy20 40 60 80 100
E G eV
0 .4
0 .2
0 .0
0 .2
0 .4
aE;L ,dN dy LHC RHICConstant alpha Constant alpha
Running alpha Running alpha
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 27
Initial pQCD spectra
Competing effects between increased density and harder production spectraโ RHIC density and spectraโ LHC density, RHIC spectraโ LHC density and spectra
GLUEUPCHARMBOTTOM
NLO-FONLL uncertainty
UPBOTTOM
Initial quark production spectra
RHIC
Ramona Vogt
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 28
Initial pQCD spectra
Competing effects between increased density and harder production spectraโ RHIC density and spectraโ LHC density, RHIC spectraโ LHC density and spectra
GLUEUPCHARMBOTTOM
NLO-FONLL uncertainty
UPBOTTOM
Initial quark production spectra
RHIC
Ramona Vogt
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 29
Initial pQCD spectra
Competing effects between increased density and harder production spectraโ RHIC density and spectraโ LHC density, RHIC spectraโ LHC density and spectra
LHC
GLUEUPCHARMBOTTOM
NLO-FONLL uncertainty
UPBOTTOM
Initial quark production spectra
Ramona Vogt
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 30
sensitivity
THICK: Linear with THIN: Divergent with or Freestreaming with DAHSED: Divergent or Freestreaming with
B
D
๐
e
BD
๐ RHIC LHC
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 31
Effective Potential
Static potential (DGLV)
โข Static scattering centersโข Color-electric screened Yukawa
potential (Debye mass)โข Full opacity series
Dynamical potential (MD)
โข Scattering centers recoilโข Includes not screened color-
magnetic effects (HTL gluon propagators)
โข Only first order in opacity
|๐๐(๐๐)|๐=๐๐
๐(๐ ๐)๐
(๐๐+๐(๐๐)๐)๐|๐๐(๐๐)|
๐= ๐๐
๐ (๐๐)๐
๐๐ (๐๐+๐ (๐๐)๐ )
Interpolating potential (CUJET)
โข Introduces effective Debye magnetic massโข Interpolates between the static and HTL dynamical limitsโข Magnetic screening allows full opacity series
|๐๐(๐๐)|๐=
๐(๐๐)๐
๐๐(๐ ๐)๐
(๐๐+๐๐(๐ ๐)๐ ) (๐๐+๐๐ (๐๐)๐ )
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 32
Beyond first order in opacityInterpolate between DGLV and MD with a new effective potential
It is possible to study the limit 0 for values of - The mean free path is divergent for =0
N=1
N=1+2+3
๐(๐๐+๐๐)๐
๐ซ๐ฎ๐ณ๐ฝโ
๐(๐๐+๐๐๐ )(๐๐+๐๐๐)
๐ด๐ซโ
๐๐๐(๐๐+๐๐)
ratio improves for N>1 and 0 , but likely not enough.
N=1+โฆ+5
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 33
Magnetic monopoles
Magnetic monopole enhancementโ Nonlinear density dependence
near Tc
AdS/CFT
RHIC dataL2 modelNear Tc enhancementL3 model
Jinfeng Liao, arXiv:1109.0271
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 34
Elastic energy loss and Fluctuations
Bjorken elastic collisionsโข Soft scatteringโข Thoma-Gyulassy model
๐ ๐ฌ๐ ๐ =โ๐ช๐น๐ ๐ถ๐๐ป ๐ ๐๐๐[๐ฉ ]
Energy loss fluctuationsโข The probability of losing a fractional energy is the convolution of
Radiative and Elastic contributions
โข Radiative: โข Elastic:
Poisson expansion of the number of INCOHERENTLY emitted gluons
Gaussian fluctuations
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 35
distributionEn=20GeV, x=0.25, bottom quark, plasma thickness 5fmOrder in opacity equal to N dead cone effect
N=1 (thin plasma)
N=โ (thick plasma)
๐ ๐ต๐ ๐๐ป๐
(๐๐ป๐ +๐๐๐ด ๐๐)๐
N=5 (finite opacity)
๐จ๐บ๐พ ๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 36
Energy loss
STATIC
EXPANDING
Energy loss vs L
Ratio u/b and u/c
EL / TOT
RAD/TOT
3 fm
6 fm
Ratio Rad and El to Total
Convergence for m>>E
up ; charm ; bottom
b
u
c
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 37
Temporal envelope
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 380 .2 0 .4 0 .6 0 .8 1 .0
x
0 .2
0 .4
0 .6
0 .8
1 .0
xdN dxkT sensitivity
๐+ยฟ ยฟ
โข Collinear approximation: โ DGLV formula has the same functional form for or โ Different kinematic limits:
L = 5, bottom quark
Solid lines: MDDashed lines: DGLV
๐๐ฌ
August 16st, 2012 โ Quark Matter 2012, Washington DC Alessandro Buzzatti โ Columbia University 39
Scaling violationโข BDMPS predicts the scaling of the induced intensity x-spectrum with
through the z variable