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Berkeley Summer School, June 9-‐12, 2014
Extrac;ng lumpy glue in the proton-‐IPSat model
rq
qz
1-z
*�
s
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RMS 0
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Ap
Bp
bs
b-ssd
s2dB�d
s2dA�d
Bartels,Golec-‐Biernat,Kowalski Kowalski,Teaney Kowalski,Motyka,WaI
µ̃2 = µ20 +
4
r?
2
Tp(b?) = e�b2?
2BG
Average gluon radius of the proton extracted from HERA diffrac;ve data
Extrac;ng lumpy glue in the proton-‐IPSat model Very good agreement of IPSat model with combined HERA data
Rezaiean,Siddikov,Van der Klundert,RV:1212.2974
Inclusive DIS off proton Exclusive DIS off proton
Lumpy nuclei: constrained by (limited) DIS data Kowalski, Lappi, RV, PRL (2008)
Heavy ion phenomenology in weak coupling Collisions of lumpy gluon ``shock” waves
Fµ⌫,a = @µA⌫,a � @⌫A
⌫,a + gfabcAµ,bA⌫,c
DµFµ⌫,a = �
⌫+⇢
aA(x?)�(x
�) + �
⌫�⇢
aB(x?)�(x
+)
x
± = t± z
Leading order solu;on: Solu;on of QCD Yang-‐Mills eqns
Tμν from Yang-‐Mills dynamics
Ini;al longitudinal pressure is nega;ve: Goes to PL =0 from below with ;me evolu;on
Glasma energy density and pressure
Mul;par;cle produc;on: lasing gluons
Mul;par;cle produc;on in the Glasma naturally gives:
Long range rapidity correla;ons – key input into hydro
Nega;ve Binomial Distribu;ons (NBDs):
Output of model – no addi;onal parameter unlike ``Glauber” Fluctua;ons related to shapes – also unlike Glauber.
k=1: Bose-‐Einstein dist.; k=∞: Poisson distribu;on
Gelis,Lappi,McLerran, arXiv:0905.3234
NBDs in heavy ion collisions
10-5
10-4
10-3
0 500 1000 1500 2000 2500P
(dN
g/dy
)dNg/dy
Glasma centrality selection
0-5%
5-10
%
10-2
0%
20-3
0%
30-4
0%40
-50%
50-6
0%
Schenke,Tribedy,RV: arXiv:1206.6805
Only model of heavy ion collisions where mul;plicity dist./centrality selec;on Is not an external input
Matching boost invariant Yang-‐Mills to hydrodynamics
State of the art phenomenology: Solve rela;vis;c viscous hydrodynamic equa;ons with Glasma (Yang-‐Mills) ini;al condi;ons
Match event by event Glasma (YM)+2+1-‐D viscous hydro
Energy dist. of YM fields YM+hydro
Matching boost invariant Yang-‐Mills to hydrodynamics
Energy density and (ux,uy) from
Matching boost invariant Yang-‐Mills to hydrodynamics
Matching to viscous hydro is “brutal” : assume very rapid isotropiza;on at ini;al hydro ;me
Large systema;c uncertainty: how does isotropiza;on/thermaliza;on occur on ;mes < 1 fm/c ?
Heavy ion phenomenology in weak coupling Hydrodynamics: efficient transla;on of spa;al anisotropy into momentum anisotropy
dN
d�=
N
2⇡(1 + 2v1 cos(�) + 2v2 cos(2�) + 2v3 cos(3�) + 2v4 cos(4�) + · · · )
MUSIC: 3+1-‐D event-‐by-‐event viscous rela;vis;c hydro model Schenke,Jeon, Gale
Heavy ion phenomenology in weak coupling Results from the IP-‐Glasma +MUSIC model:
AdS/CFT bound = 0.08
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.5 1 1.5 2
v n
pT [GeV]
narrow: �/s(T)wide: �/s=0.12
30-40%
PHENIX v2 PHENIX v3 PHENIX v4 STAR v2 STAR v3 STAR v4 STAR v5
0
0.05
0.1
0.15
0.2
0 0.5 1 1.5 2
�vn2 �
1/2
pT [GeV]
ATLAS 20-30%, EPnarrow: �/s(T)wide: �/s=0.2
v2 v3 v4 v5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 10 20 30 40 50
�v n2 �1/2
centrality percentile
�/s = 0.2ALICE data vn{2}, pT>0.2 GeV v2
v3 v4 v5
Gale,Jeon,Schenke,Tribedy,Venugopalan, PRL (2013) 012302
RHIC data require lower average value of η/s rela;ve to LHC
Heavy ion phenomenology in weak coupling
Heavy ion phenomenology in weak coupling
Remarkable agreement of IP-‐Glasma+MUSIC with data out to fairly peripheral overlap geometries…
Schenke,Venugopalan, arXiv:1405.3605
The ridge in p+p and p+A through colored glass
The ridge Tsunami
u What is the underlying QCD mechanism of the ridge?
u How far can can we extend the collec;ve flow paradigm to small size systems – and do we see systema;c devia;ons?
u Is there “spooky quantum mechanics” at work a la photon or spin entanglement ?
u Are hadroniza;on paIerns universal QCD physics or do they reflect thermal abundances ?
High mul;plici;es + small systems = gluon satura;on What does it take to produce~ 150 hadrons per 5 units of rapidity in a single p+p event ?
For λ=0.14, get about 13 gluons produced in 5 units ~ min.bias hadron mul;plicity λ=0.3: ~45 gluons in 5 units, λ=0.4: ~90 gluons in 5 units, in ball park… Very rapid growth of gluon dist. in such events…
High mul;plici;es + small systems = gluon satura;on What does it take to produce~ 150 hadrons per 5 units of rapidity in a single p+p event ?
For λ=0.14, get about 13 gluons produced in 5 units ~ min.bias hadron mul;plicity λ=0.3: ~45 gluons in 5 units, λ=0.4: ~90 gluons in 5 units, in ball park… Very rapid growth of gluon dist. In such events…
π
π
π π
π
Satura;on regulates this by adding increasingly “smaller” gluons of size 1/Qs(x) with decreasing x (increasing energy)
dNprot.g
d⌘⇡ 1.1CF
2⇡2
S?Q2
S,prot.
↵S
Ng ~ 100 in 5 units for QS2 ~ 2 GeV2 : a semi-‐hard scale !
Lappi: arXiv 0711.3039
Ini;al state collima;on from jet+Glasma
Quan;ta;ve modeling of these ini;al state correla;ons gives good descrip;on of p+p high mul;plicity correla;on data and features of p+A correla;on data
(Next talk by Kevin Dusling) Dusling, Venugopalan, arXiv:1210.3701, arXiv:1211.3701, arXiv:1302.7018
High mul;plicity events: two par;cle correla;ons
u Full YM+JIMWLK evolu;on – not available yet
u Approxima;ons: I) BK Gaussian trunca;on approxima;on -‐evolu;on but no rescaIering II) YM results for MV model: rescaIering but no evolu;on
Dusling,Gelis,Lappi,RV:0911.2720; Lappi,Srednyak,RV:0911.2068; Kovchegov,Wertepny: 1212.1195
Gelis,Lappi,RV arXiv:0804.2630 [hep-‐ph]; arXiv:0807.1306 [hep-‐ph]
Glasma graphs RG evolution:
+ + … Keeping leading logs to all orders (NLO+NNLO+…)
= LO graph with evolved sources avg. over sources in each event and over all events gives correla;on
Dumitru,Gelis,McLerran,RV: 0804.3858 Gelis, Lappi, RV, arXiv: 0807.1306
Glasma graphs RG evolution:
+ + … Keeping leading logs to all orders (NLO+NNLO+…)
= LO graph with evolved sources avg. over sources in each event and over all events gives correla;on
Dumitru,Gelis,McLerran,RV: 0804.3858 Gelis, Lappi, RV, arXiv: 0807.1306
From solns. of Yang-‐Mills eqns.with two light cone sources Includes all mult. scat. contribu;ons (gρ1)n and (gρ2)n
Glasma graphs
Correla;ons are induced by color fluctua;ons that vary event to event – for Gaussian weight func;onals in ρ, have color screening radius ~ 1/QS
Glasma graphs
Correla;ons are induced by color fluctua;ons that vary event to event – for Gaussian weight func;onals in ρ, have color screening radius ~ 1/QS
Glasma graphs generate long range rapidity correla;ons…
Glasma graphs
Correla;ons are induced by color fluctua;ons that vary event to event – for Gaussian weight func;onals in ρ, have color screening radius ~ 1/QS
Glasma graphs generate long range rapidity correla;ons… Glasma graphs are suppressed rela;ve to “jet” graphs for QS << pT by powers of αS AND NC (At high pT, large x or large impact parameters)
Glasma graphs
Correla;ons are induced by color fluctua;ons that vary event to event – for Gaussian weight func;onals in ρ, have color screening radius ~ 1/QS
Glasma graphs enhanced by 1/αS
8 for high occupancy fields (factor of 105 !) (central impact parameters, small x, low pT, large nuclei)
Glasma graphs generate long range rapidity correla;ons… Suppressed for QS << pT by powers of αS AND NC (At high pT, large x or large impact parameters)
Angular structure from (mini-‐) Jet radia;on
GBFKL
p
q
Cdijet(p,q) / �A ⌦ �B ⌦GBFKL
NLO in the dense-‐dense framework but… unsuppressed in NC
Caveat: does not include mul;ple scaIering contribu;ons which may be significant for kT < QS
Quan;ta;ve descrip;on of pp ridge Dusling,RV:PRL108 (2012)262001
A(�p, �q) = ⇥(|�p � �q|���min
) ⇥(��max
� |�p � �q|)
Dependence on transverse area cancels in ra;o…
Rarer and rarer gluon configura;ons probed in the proton
Systema;cs of p+p correlated yield Data from CMS collabora;on Fits: Dusling,RV, arXiv:1302.7018
0.00
0.10
0.20
0.301 < pT
trig < 2 GeV1 < pT
asc < 2 GeV2 < pT
trig < 3 GeV 3 < pTtrig < 4 GeV 4 < pT
trig < 5 GeV 5 < pTtrig < 6 GeV
0.00
0.04
0.08
0.12 2 < pTasc < 3 GeV
0.00
0.01
0.03
0.043 < pT
asc < 4 GeV
0.00
0.01
0.02
0.03 4 < pTasc < 5 GeV
0.000
0.003
0.006
0.009
0 1 2 3 6q
5 < pTasc < 6 GeV
0 1 2 3 6q
0 1 2 3 6q
0 1 2 3 6q
0 1 2 3 6q
Dusling,RV, PRD 87, 051502 (R) (2013); arXiv:1302.7018
What about p+A ?
Ridge much bigger than p+p for the same mul;plicity
p+A ridge nearly as large as peripheral Pb+Pb
Systema;cs of p+Pb associated yield Dusling, RV: 1211.3701 1302.7018
0
0.02
0.04
0 1 2 3 4 5 6pT
trig=pTasc [GeV]
Associated Yield
p+Pb: CMS datap+p: CMS data
“Jet subtracted” p+Pb ridge
Similar subtrac;on in RHIC d+Au to extract ridge
The v3 surprise in LHC pA collisions CMS 1305.0609
v3 > 0 not obviously obtained from Glasma graphs in kT factoriza;on approxima;on
Only even moments obtained…
CMS summary talk at Quark MaIer
CMS summary talk at Quark MaIer
Also from ini;al state Universal hadroniza;on paIern?
Reflects more underlying stringy picture
Not obvious in hydro-‐see later slides
HBT radii same in pp at same Nch & v2 smaller
??
Recall IP-‐Glasma+MUSIC model in A+A
Remarkable agreement of IP-‐Glasma+MUSIC with data out to fairly peripheral overlap geometries…
Schenke,Venugopalan, arXiv:1405.3605
IP-‐Glasma model: mul;plicity distribu;ons Schenke,Tribedy,Venugopalan, arXiv 1311.3636
p+Pb 5.02 TeV
Color charge fluctua;ons: different color configura;ons for same gluon number But gluon # in wave func;ons can fluctuate too. Required to explain tails of mul;plicity distribu;ons.
IP-‐Glasma model: system size Bzdak, Schenke,Tribedy,Venugopalan, arXiv 1304.3403
ε
r
System size in IP-‐Glasma nearly the same in p+p and p+Pb
IP-‐Glasma model: system size Schenke, Venugopalan: 1405.3605
ε
r
0
1
2
3
4
5
6
7
8
9
1 2 3 4 5 6 7 8 9
Rin
v, K
rm
ax
[fm
]
!Nch"1/3
#min = $QCD4
solid: m=0.2 GeV, K=1.25
dashed: m=0.1 GeV, K=1.15
ALICE Pb+Pb 2.76 TeV ALICE p+Pb 5.02 TeV ALICE p+p 7 TeV
m regulates the tail of gluon distribu;ons
Results for system size in the Glasma clearly leaves room for flow in Pb+Pb Flow not necessary in p+p to explain data up to quite rare Nch = 27. In p+Pb, whether there is room for flow in rare events is sensi;ve to how the tail of the gluon distribu;on is regulated…
Schenke, Venugopalan, arXiv:1405.3605
The ridge: flow in p+p and p+Pb ? Bzdak,Schenke,Tribedy,Venugopalan: 1304.3403
p+p at b=0
IP-‐Glasma+ MUSIC (hydro) gives much less v2 than Glauber models that have significantly larger spa;al sizes and shapes
Bozek,Torrieri,Broniowski, arXiv: 1307.5060 Kozlov,Luzum,Denicol,Jeon,Gale, arXiv:1405.3976
The ridge: flow in p+Pb?
In contrast to A+A, both shape and magnitude of IP-‐Glasma+MUSIC p+Pb results completely off from data
Schenke and Venugopalan, arXiv:1405.3605
The ridge: flow in p+Pb?
In contrast to A+A, both shape and magnitude of IP-‐Glasma+MUSIC p+Pb results completely off from data
Schenke and Venugopalan, arXiv:1405.3605
Maybe shapes are treated incorrectly in IP-‐Glasma ? Note they seem off even for mul;plicites where the IP-‐Glasma mul;plicity distribu;on agrees with the data…
Alterna;ve: hydro shouldn’t work for small size systems?
IP-‐Glasma model: mul;plicity distribu;ons Schenke,Tribedy,Venugopalan, arXiv 1311.3636
p+Pb 5.02 TeV
Color charge fluctua;ons: different color configura;ons for same gluon number But gluon # in wave func;ons can fluctuate too. Required to explain tails of mul;plicity distribu;ons.
Large x quarks in proton can have “eccentric” shapes.
Is this feasible for radiated gluons that pack the proton within constraints from confinement, causality & unitarity…?
G. A. Miller, arXiv:0802.3731
Addi;onal puzzles for the collec;vity picture in p+A
• Why is there no sign of “mini-‐jet” quenching in p+A ? • Why is v2 unchanged up to pT of 9 GeV
• Why is v2 much smaller in p+p than p+A for the same Nch and HBT radius ?
• Why is mass ordering in <pT> seen even at Nch = 6 ?
ALICE Overview – Jan Fiete Grosse-Oetringhaus 48
And the Jet at low pT?
• No modification at high pT • Double ridge at low pT
• Spectra modified at low pT?
• Ridge-subtracted jet-like yields • Ridge and jet seem additive in 2PC • Constant jet yields for ~60%
of p-Pb cross-section à no modification even at low pT
• Consistent with a picture of minijets in p-Pb collisions from superposition of NN collisions with incoherent fragmentation
à L. Milano (Tue PM)
Δϕ (rad)
yield vs multiplicity class
What happens to the "jet" at low pT?
high Nch low Nch
p-Pb
Significant vn moments in p+Pb out to large pT
Mass ordering seen down to low Nch
ALICE, 1307.6796
Hydro in small size systems: sensible or not ?
Two frequently used measures: Reynolds # and Knudsen #
Bzdak,Schenke,Tribedy,Venugopalan, arXiv:1304.3403 Denicol, Niemi, arXiv:1404.7327
Hydro good for Kn < 0.5, marginal for K < 1 transient regime; K > 1 free streaming
The “boIom-‐up” thermaliza;on process
Blaizot,Dominguez, Iancu,Mehtar-‐Tani
Berges,Boguslavskii,Schlich;ng,Venugopalan
A recent es;mate in this picture gives tequilibrium < 1 fm Kurkela,Lu, arXiv:1405.6318
Turbulent regime characterized by universal exponents
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