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Akihiko Monnai (RIKEN BNL Research Center) In collabora;on with:
Berndt Müller (Duke University/BNL)
Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
New Fron)ers in QCD 2013 13th December 2013, Yukawa Ins;tute for Theore;cal Physics, Kyoto, Japan
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 2 / 31
Overview 1. Introduc;on
-‐ The quark-‐gluon plasma -‐ High-‐energy heavy ion collisions
2. Thermaliza;on of gluons -‐ Collinear gluon spliOng and recombina;on -‐ Fokker-‐Planck type diffusion -‐ Numerical es;ma;ons: gluon distribu;on
3. Thermal & chemical equilibra;on of quarks -‐ Quark and gluon spliOng/recombina;on processes -‐ Numerical es;ma;ons: quark and gluon distribu;ons
4. Summary and outlook
Introduc;on 2
Next slide: 3 / 31
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan
1. Introduc;on
Next: 2. Gluon spliOng in early thermaliza;on
Introduc;on
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 4 / 31
Introduc;on n Quark-‐gluon plasma (QGP): many-‐body system of deconfined
quarks and gluons
Introduc;on
Hadron phase QGP phase
(crossover) sQGP (wQGP?)
The QGP is supposed to have filled the early universe; It can be produced in heavy ion experiments at RHIC & LHC
Heavy ion QGP is found to exhibit near-‐perfect fluidity Early local equilibra;on (τ < 0.6-‐1 fm) is implied
Graphics by AM
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 5 / 31
Introduc;on n Modeling a “LiLle Bang”
Thermaliza;on of gluons
τ < 0 fm/c: color glass condensate (saturated gluons)
τ ~ 1-‐10 fm/c: QGP/hadronic fluid (strongly coupled)
τ > 10 fm/c: hadronic gas (weakly coupled)
τ ~ 0-‐1 fm/c: CGC -‐> QGP ? (pre-‐equilibrated)
Pre-‐equilibrated QCD medium is a high-‐energy fron;er in hadron physics Dynamical descrip;on is required for understanding QCD maLer
Graphics by AM
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 6 / 31
Mo;va;on n Color glass condensate (CGC)
n QGP fluid
Collinear gluon spliOng
Gluons emiLed from gluons emit gluons in a fast-‐travelling nucleon
NA49 Collabora;on (2003)
x
xP(x
)
H1PDF 2009c )
Q2 = 10 GeV2xuv
xdv
xS/20
xg /20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
10-4
10-3
10-2
10-1
H1 Collabora;on (2009)
They start to overlap and saturated
Azimuthal momentum anisotropy v2 is large compared with spa;al one ε2
gluon gluon gluon gluon
gluon gluon gluon
gluon
gluon
gluon
QCD maLer at the ini;al stage of heavy ion collisions is dominated by gluons
ε2
QCD maLer is locally equilibrated at some point and behaves as a fluid
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 7 / 31
Mo;va;on n Early (local) equilibra;on
Collinear gluon spliOng
One of the long standing issues in heavy ion physics -‐ Naïve CGC and glasma lead to nega;ve longitudinal pressure
Equilibra;on requires
We focus on thermaliza;on and provide a model based on collinear spliOng to introduce low momentum partons
-‐ CGC has large frac;on of high-‐momentum gluons
Cf: parton cascade picture boLom-‐up approaches Bose condensate
K. Geiger and B. Müller (1992) R. Baier et. al. (2001), P. Arnold et al. (2003)
Isotropiza;on Thermaliza;on
& pL p
f pT
J.-‐P. Blaizot et al. (2012, 2013), X.-‐G. Huang and J. Liao (2013)
Next slide: 8 / 31
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan
2. Thermaliza;on of gluons
Mo;va;on
Next: 3. Thermal and chemical equilibra;on of quarks
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 9 / 31
Collinear spliOng model n Gluon spliOng
A spliOng modifies the parton distribu;on f as
Time evolu;on of gluon distribu;on by collinear spliOng
where , and
is the spliOng rate
as number is doubled while momentum is conserved:
p
zp
(1 ! z)p
Collinear spliOng model
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 10 / 31
Collinear spliOng model n Gluon spliOng
Rough es;ma;on of parton emission rate
In sta;c frame In boosted frame
(In thermal system )
is implied
The ;me evolu;on can violate the second law of thermodynamics if spliOng con;nues on, i.e., not stable at thermal equilibrium
A mechanism that prevents “over-‐shrinking” in phase space should be present
Collinear spliOng model
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 11 / 31
Collinear spliOng model n Gluon recombina;on
Time evolu;on should stop at local equilibrium (2nd law of thermodynamics)
Recombina;on should occur when density Is large (in analogy with Balitsky-‐Kovshegov equa;on)
Parameteriza;on of recombina;on process
where is equilibrium distribu;on in medium
Degeneracy Effec;ve thermal mass
(1 ! z)p
zpp
Collinear spliOng model
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 12 / 31
Collinear spliOng model n Momentum smearing effect
Elas;c scaLering is taken into account by rela;vis;c Fokker-‐Planck equa;on
where and characterizes drag and diffusion effects
SpliOng occurs when a parton becomes off-‐shell by interac;ng with medium
Collinear spliOng model
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 13 / 31
Collinear spliOng model n Momentum smearing effect
n CGC-‐like ini;al condi;on
Rough es;ma;on of drag and diffusion coefficients
Numerical analyses
Rela;vis;c Einstein rela;on yields the drag coefficient
Analy;c solu;on of a diffusion equa;on for a delta func;on
Standard devia;on
Longitudinal momentum modifica;on
and are implied
Gluon distribu;on and
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 14 / 31
Numerical analyses n Time evolu;on in one-‐dimensional non-‐expanding system
Thermal & chemical …
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.2 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
g f
-410
-310
-210
-110
1
10
210 (t = 0.2 fm/c)init
gf (t = 0.2 fm/c)gf
eqgf
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 15 / 31
Numerical analyses n Time evolu;on in one-‐dimensional non-‐expanding system
Thermal & chemical …
p (GeV)0 1 2 3 4 5 6
g f
-410
-310
-210
-110
1
10
210 (t = 0.2 fm/c)init
gf (t = 0.4 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.4 fm/c)gf
eqgf
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 16 / 31
Numerical analyses n Time evolu;on in one-‐dimensional non-‐expanding system
Thermal & chemical …
p (GeV)0 1 2 3 4 5 6
g f
-410
-310
-210
-110
1
10
210 (t = 0.2 fm/c)init
gf (t = 0.6 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.6 fm/c)gf
eqgf
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 17 / 31
Numerical analyses n Time evolu;on in one-‐dimensional non-‐expanding system
・ Collinear gluon spliOng contributes visibly to quick thermaliza;on ・ Entropy produc;on is confirmed posi;ve
Thermal & chemical …
・ Recombina;on is a key; Is the dynamics in dense region strong enough in 3D to enforce isotropiza;on?
p (GeV)0 1 2 3 4 5 6
g f
-410
-310
-210
-110
1
10
210 (t = 0.2 fm/c)init
gf (t = 0.8 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.8 fm/c)gf
eqgf
Next slide: 18 / 31
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan
3. Thermal & chemical equilibra;on of quarks
Mo;va;on
Next: 4. Summary and outlook
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 19 / 31
Mo;va;on n Early (local) equilibra;on
Parton spliOng model
Equilibra;on requires more
Gluon medium eventually becomes quark-‐gluon plasma Is quark thermaliza;on fast enough? Is the QGP chemical equilibrated?
Isotropiza;on Chemical equilibra;on
& pL
p
fg pT
Thermaliza;on
p
f
p
fq
boson
fermion
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 20 / 31
p
p
p
zp
(1 ! z)p
zp
(1 ! z)p
zp
(1 ! z)p
Parton spliOng model n Gluons + quarks
Time evolu;on of parton distribu;ons by collinear processes
Gluon emission from quark
Quark pair produc;on
Gluon spliOng
SpliOng func;ons
Quark-‐an;quark symmetry assumed
Parton spliOng model
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 21 / 31
Parton spliOng model n Gluons + quarks
Parameteriza;on of recombina;on processes
Equilibrium distribu;ons
(1 ! z)p
zpp
pzp
(1 ! z)p
pzp
(1 ! z)p
: fixed from momentum conserva;on
Parton spliOng model
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 22 / 31
Parton spliOng model n Momentum smearing effect
n Ini;al condi;on (CGC-‐like)
Fokker-‐Plank equa;on holds for each component
Numerical analyses
where
Gluon distribu;on
Quark distribu;on
and
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 23 / 31
Numerical analyses n Time evolu;ons (t = 0.2 fm/c)
p (GeV)0 1 2 3 4 5 6
q f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
qf (t = 0.2 fm/c)qf
eqqf
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.2 fm/c)gf
eqgf
Numerical analyses
Gluon distribu;on Quark distribu;on
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 24 / 31
Numerical analyses n Time evolu;ons (t = 0.4 fm/c)
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.4 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
q f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
qf (t = 0.4 fm/c)qf
eqqf
Numerical analyses
Gluon distribu;on Quark distribu;on
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 25 / 31
Numerical analyses n Time evolu;ons (t = 0.6 fm/c)
p (GeV)0 1 2 3 4 5 6
q f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
qf (t = 0.6 fm/c)qf
eqqf
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.6 fm/c)gf
eqgf
Numerical analyses
Gluon distribu;on Quark distribu;on
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 26 / 31
Numerical analyses n Time evolu;ons (t = 0.8 fm/c)
p (GeV)0 1 2 3 4 5 6
q f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
qf (t = 0.8 fm/c)qf
eqqf
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.8 fm/c)gf
eqgf
Numerical analyses
Gluon distribu;on Quark distribu;on
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 27 / 31
Numerical analyses n Time evolu;ons (t = 1.0 fm/c)
p (GeV)0 1 2 3 4 5 6
q f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
qf (t = 1.0 fm/c)qf
eqqf
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 1.0 fm/c)gf
eqgf
・ Distribu;ons approach the thermal ones; chemical equilibra;on is rela;vely fast but would be slower than thermaliza;on (~1.5-‐2.0 fm) ・ Shape of quark distribu;on reflects that of gluon distribu;on as quarks are pair-‐created from gluons ・ “Fermi pressure” would not develop as # of quarks are not enough
Numerical analyses
Gluon distribu;on Quark distribu;on
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 28 / 31
Numerical analyses n SpliOng with no recombina;on (logarithmic scale)
・ Quark number becomes too large for fermions near p = 0; spliOng should be suppressed, leading to slower chemical equilibra;on
p (GeV)0 1 2 3 4 5 6
g f
-410
-310
-210
-110
1
10
210
310 (t = 0.2 fm/c)init
gf (t = 0.8 fm/c)sp
gfeqgf
p (GeV)0 1 2 3 4 5 6
q f
-410
-310
-210
-110
1
10
210 (t = 0.2 fm/c)init
qf (t = 0.8 fm/c)sp
qfeqqf
・ The shape of quark distribu;on follows that of gluon distribu;on
Numerical analyses
Gluon distribu;on Quark distribu;on
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 29 / 31
Numerical analyses n Comparison of fg (pure gauge), fg and fq (Nf = 3)
・ Quark-‐gluon equilibra;on may be less “efficient” but more realis;c
p (GeV)0 1 2 3 4 5 6
g f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.8 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
g f
-410
-310
-210
-110
1
10
210 (t = 0.2 fm/c)init
gf (t = 0.8 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
g f0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
gf (t = 0.8 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
g f
-410
-310
-210
-110
1
10
210 (t = 0.2 fm/c)init
gf (t = 0.8 fm/c)gf
eqgf
p (GeV)0 1 2 3 4 5 6
q f
0
5
10
15
20
25
30
35
40 (t = 0.2 fm/c)init
qf (t = 0.8 fm/c)qf
eqqf
p (GeV)0 1 2 3 4 5 6
q f
-410
-310
-210
-110
1
10
210 (t = 0.2 fm/c)init
qf (t = 0.8 fm/c)qf
eqqf
Summary and outlook
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 30 / 31
Summary and outlook n Collinear quark and gluon spliOng in early thermaliza;on
n Future prospects include
The end
Low momentum gluons are quickly produced
Describes transi;on from CGC to QGP Thermaliza;on might be faster than chemical equilibra;on
Three dimensional modeling for analyses on effects of expansion and isotropiza;on Non-‐thermalized partons lead to off-‐equilibrium energy-‐momentum tensor at the ini;al ;me of hydrodynamic stage
Quark produc;on is reasonable fast; recombina;on would be important for fermions
Akihiko Monnai (RBRC) Pre-‐equilibrium dynamics of QCD maLer by gluon spliOng
NFQCD 2013, 13th December 2013, YITP, Kyoto, Japan Next slide: 31 / 31
The end n Thank you for listening! n Website: hLp://tkynt2.phys.s.u-‐tokyo.ac.jp/~monnai/