Strong fields in heavy ion collisions at VLHC P. Lvai (Wigner RCP, - - PowerPoint PPT Presentation

Strong fields in heavy ion collisions at VLHC

• P. Lévai (Wigner RCP, Budapest, Hungary)

V.V. Skokov (BNL, Upton, USA)

• D. Berényi, A. Pásztor (ELTE, Budapest, Hungary)
• Phys. Rev. D71 (2005) 094010; D78 (2008) 054004.
• J. Phys. G36 (2009) 064068; G38 (2011) 124155.

arXiv: 1208.0448 QED Strong Fields Workshop Bolyai College, 4 February 2014, Budapest

• 1. Introduction

Plans on the Very Large Hadron Collider VLHC at CERN

Kick-off meeting: 12-14 February, 2014, Univ. of Geneva

http://indico.cern.ch/conferenceDisplay.py?confId=282344 Heavy Ion Program → → Interest on strong fields

• 2. Perturbative and non-perturbative

descriptions of particle production in heavy ion collisions Heavy Ion Collisions: BNL → CERN → RHIC → LHC → VLHC

Particle production mechanisms in high energy HI collisions: Particle production mechanisms in high energy HI collisions:

• I. Dilute parton gas limit as initial condition + parton cascade:

PDF(p,n) +pQCD + Glauber + [Shad; Multisc; Quench; Fluct; ...]

• II. Dense gluon matter limit as initial condition + hydro:

CGC initial condition: where and gluon fields of nuclei

α1,α2

ρ2 ρ1

Dilute gas CGC: high density gluons

Eπ d σ

AB

d

3 pπ

=∫ d

2bd 2r t A(⃗

r)t B(∣⃗ b−⃗ r∣) Eπ d σ

pp

d

3 pπ

⊗S(...)⊗M (...)⊗Q(...)⊗F(...) Eπ d σ

pp

d

3 pπ

=∫ dx1∫dx2∫dz cf a/p( xa,Q

2)f b/p( xb,Q 2) d σ

d ̂ t Dc

π(z c)

π zc

2

Successful applications of I and II: Successful applications of I and II:

• I. pQCD model:
• -- hard probes
• -- high-pT physics
• -- jets
• -- h-h correlations
• -- ...
• II. CGC model:
• -- soft physics
• -- multiplicities
• -- centrality dependence
• -- ET production
• -- rapidity distributions
• -- ...

W=200 GeV

Problems: Problems:

• I. pQCD model (Feynman graphs):
• -- LO, NLO, ... ?
• -- factorization (kT)
• -- resummations
• -- soft physics
• -- heavy quark quenching
• -- ...
• II. CGC model (asymptotic):
• -- hard probes
• -- jet physics
• -- correlations
• -- ...

Connection between I and II: Connection between I and II: Large-x: valence partons random color charge, a(x) Small-x: radiation field, created by a(x)

• III. Non-perturbative, non-asymptotic color transport:

“confined flux tube formation and breaking”

• -- phenomenological approximations are known (string, rope)
• -- phenomenology is applied successfully in string-based codes
• -- FRITIOF, PYTHIA, HIJING are using strings
• -- URQMD, HIJING-BB is using ropes (melted strings)
• -- good agreement with data at different energies
• -- ...

R

• -- formal QCD-based equations are known (Heinz, Mrowczynski)
• -- YM-field evolution in 3+1 dim, collision (Poschl, Müller)
• -- lattice-QCD calculations have been started (Krasnitz, Lappi)
• -- ...

A further model for particle production: A further model for particle production:

A further model for particle production: A further model for particle production:

• III. Non-perturbative, non-asymptotic color transport:

“pair-creation in strong fields”

• -- strong (Abelian) static E field: Schwinger mechanism

probability of pair-creation: integrated probability at mass m: ratio of production rates (e.g. strange to light)

• -- strong time dependent SU(N) color fields:

Kinetic Equation for the color Wigner function A.V. Prozokevich, S.A. Smolyansky, S.V. Ilyin, hep-ph/0301169.

P( pT)d

2 pT=− e E

4 π

3 ln(1−exp[−π

m

2+pT 2

eE ])d

2 pT

Pm=(e E)

2

4 π

3 ∑n=1 ∞

1 n

2 exp[−π n m 2

eE ] γs= P(s s) P(q q)=exp[−π ms

2−mq 2

eE ] eE=0.9GeV / fm

∂tW +g 8 ∂ ∂ ki (4{W ,F 0,i}+2{Fi ν,[W , γ

0γ ν]}−[ Fiν ,{W ,γ 0 γ ν}])=

=i ki{γ

0 γ i,W }−i m [γ 0,W ]+ig[ Ai ,[γ 0γ i ,W ]].

W (k1, k 2,k 3)

Kinetic equation for fermion pair production: Kinetic equation for fermion pair production: Wigner function: Color decomposition: Spinor decomposition: Color vector field (longit.): Kinetic equation for Wigner function:

for details see V.V. Skokov, PL: PRD71 (2005) 094010 for U(1) PRD78 (2008) 054004 for SU(2) PRD82 (2010) 054004 + prep.

Distribution function for fermions with mass m: W =W

s+W at a ,

where a=1,2,..., N c

2−1

W

s;a=a s; a+bμ s;a γ μ+cμν s;aσ μ ν+dμ s ;a γ μ γ 5+i e s; a γ 5

Aμ

a=(0,−⃗

A)=(0,0,0, A3

a)

f f(⃗ k ,t)=m a

s(⃗

k ,t)+⃗ k ⃗ b

s(⃗

k ,t) ω(⃗ k ) +1 2

Kinetic equation in the U(1) Abelian case – strong laser fields: Kinetic equation in the U(1) Abelian case – strong laser fields:

Kinetic equation in the U(1) Abelian case – strong laser fields: Kinetic equation in the U(1) Abelian case – strong laser fields:

Kinetic equation in the U(1) Abelian case – strong laser fields: Kinetic equation in the U(1) Abelian case – strong laser fields:

Kinetic equation in the U(1) Abelian case – strong laser fields: Kinetic equation in the U(1) Abelian case – strong laser fields:

Kinetic equation in the U(1) Abelian case – strong laser fields: Kinetic equation in the U(1) Abelian case – strong laser fields:

Application of kinetic equations: Application of kinetic equations: U(1) Abelian case – strong laser fields at ELI (Szeged, Prague): Time dependence (chirp, pulses) Space dependence (extension into x,y directions) → → See the talk of Daniel Berenyi SU(2), SU(3) non-Abelian case – heavy ion collisons (LHC, RHIC): Time dependence Space dependence Color dependence Numerically exhausting: grids, clouds, GPU-solutions → → Test field at WIGNER RCP GPU Laboratory

Heavy ion collisions: Time dependent external field, E(t) : Heavy ion collisions: Time dependent external field, E(t) : A, Pulse field (dotted): B, Constant field (dashed): C, Scaled field (solid):

E pulse(t)=E0[1−tanh

2(t /δ)]

Econst(t)=E pulse(t) at t <0 Econst(t)=E0 at t >0 Escaled(t )=E pulse(t) at t<0 Escaled (t )= E0 (1+t /t 0)

κ

at t<0

δ=0.1/E 0

1/2

at RHIC energy κ=2/3 for scaled Bjorken expans. with t 0=0.01/E 0

1/2

Sauter

Numerical results (b Numerical results (bi

i) for the Bjorken expansion at t= 2/

) for the Bjorken expansion at t= 2/√ √E E0

0 in SU(2):

in SU(2): bsT(kT,k3) baT(kT,k3) bs3(kT,k3) ba3(kT,k3) m = 0

Numerical results for fermion distributions at t= 2/ Numerical results for fermion distributions at t= 2/√ √E E0

0 in SU(2):

in SU(2): ff(k3): longitudinal mom. distr. ff(kT): transv. mom. distr. kT/√E0 = 0.5 k3 = 0 ⇒ exponential (pulse) ⇒ polinomial (scaled)

Transverse momentum distr: scaling between U(1) and SU(2) at high-pT Transverse momentum distr: scaling between U(1) and SU(2) at high-pT ff(kT): transv. mom. distr. ratio: SU(2) / U(1) at kT/√E0 = 0.5 ⇒ ¾ at kT/s > 3 in U(1) and SU(2) (scaling in the Kinetic Eq.) [Bjorken scaled]

Transverse momentum distr: scaling in SU(3) at high-pT (m=0) Transverse momentum distr: scaling in SU(3) at high-pT (m=0) ff(kT): transv. mom. distr. Ratios (scaled time evol.): in SU(3) SU(2) / U(1) ⇒ 3/4 3 cases of E(t) SU(3) / U(1) ⇒ 4/3 [similar to SU(2)] (scaling in the Kinetic Eq.)

SU(Nc) / U(1) normalized to 1 Nc=2 Nc=3

• 3. Quark-pair production in strong SU(2) field
• -- quark mass dependence ---

Mass dependent fermion production in SU(2): Mass dependent fermion production in SU(2): Quark-pair production depends on the mass: m(light) = 8 MeV m(strange) = 150 MeV m(charm) = 1200 MeV m(bottom) = 4200 MeV Usually 'm' mass behaves as a scale (see electron mass in QED). But, what about zero mass limit? What is the scale in that case? Since we have non-zero fermion production, then some scale must exist. The characteristic time of the changes in E(t) ??  ⇒⇒ 

Mass dependent fermion production in SU(2) [pulse-like time dep.] Mass dependent fermion production in SU(2) [pulse-like time dep.] Fermion number (n) depends on the characteristic time

• f the pulse width:  =  in the pulse scenario

Mass dependent fermion production in SU(2) [pulse-like time dep.] Mass dependent fermion production in SU(2) [pulse-like time dep.] Transverse momentum spectra at different pulse width: E0 = 0.01; 0.1; 0.2

Mass dependent fermion production in SU(2) [pulse-like time dep.] Mass dependent fermion production in SU(2) [pulse-like time dep.] t: time in the CM frame : pulse width (t) Full line: E0 = 0.1 (= 0.05 fm ) Dashed line: E0 = 0.5 (= 0.25 fm ) E0 = 0.68 GeV/fm , g=2  g⋅E0 ∝  = 1.17 GeV/fm

Mass dependent fermion production in SU(2) [pulse-like time dep.] Mass dependent fermion production in SU(2) [pulse-like time dep.] flavour suppression factor m scaling !!!! Blue line: E0 = 0.1 (= 0.05 fm ) At large  heavy quarks are suppressed. Enhanced heavy fermion production at small  eff =  + m-1 [ meff ⇒⇒ -1 ]

γ

Q=lim (t →∞)nQ(t)/nu(t)

Mass dependent fermion production in SU(2) [pulse-like time dep.] Mass dependent fermion production in SU(2) [pulse-like time dep.] Collisional energy dependence of the quark flavour suppression + E0(t) = E0 ( 0 /  ) where  : 0, 1/2, 1

Mass dependent fermion production in SU(2) Mass dependent fermion production in SU(2) Numerical values for suppression factors : Schwinger 130 AGeV 200 AGeV 1 ATeV 2 ATeV 5.5 ATeV s 0.74 0.84 0.88 0.96 0.98 0.99 c 3 10-9 9 10-3 0.06 0.66 0.82 0.91 b ≈ 0 ≈ 0 10-6 0.15 0.45 0.72

Effective string constants and massive fermion suppression in SU(2) Effective string constants and massive fermion suppression in SU(2) Schwinger formula for static field and static string: Suppression factor: Results of our dynamical calculation can be fit by an effective string tension, eff:

dN dt d

3x

= κ

2

4 π

3 exp(−πm 2/ κ)

γ

Q=exp(−π(mQ 2 −mq 2)/ κ)

γ∞

Q(κeff Q )=γ (Q)(τ)

Effective string constants and massive fermion suppression in SU(2) Effective string constants and massive fermion suppression in SU(2) Pulse width and collisional energy dependence

• f the flavour dependent effective string constant
• --- too much difference (and what about for light quarks)

Effective string constants and massive fermion suppression in SU(2) Effective string constants and massive fermion suppression in SU(2) Solution: Let us keep a fixed string constant for the light quarks and fix flavour specific effective string constant for the heavier quarks (strange, charm, bottom):

̂ κeff

u =1.17GeV /fm

̂ γ∞

Q=( ̂

κeff

Q

̂ κeff

u ) 2

exp(−π mQ

2

̂ κeff

Q +π mu 2

̂ κeff

u )=γ Q(τ)

Effective string constants and massive fermion suppression in SU(2) Effective string constants and massive fermion suppression in SU(2) Pulse width and collisional energy dependence

• f the flavour specific effective string constants
• -> strange string constant is nice, for heavy Q we get large values

Effective string constants and massive fermion suppression in SU(2) Effective string constants and massive fermion suppression in SU(2) Numerical values for flavour specific effective string constants in GeV/fm: 130 AGeV 200 AGeV 1 ATeV 2 ATeV 5.5 ATeV u,d 1.17 1.17 1.17 1.17 1.17 s 1.24 1.26 1.32 1.33 1.34 c 3.32 4.2 6.1 6.3 6.5 b 10.3 14.7 32 36 38 Saturation at higher LHC energies !!!!

Latest calculations on charged hadron R Latest calculations on charged hadron RAA

AA in Pb+Pb at 2.76 ATeV

in Pb+Pb at 2.76 ATeV Anomalous proton (baryon) production

• M. Gyulassy, V. Topor Pop: increased string constant

in HIJING 2.0 BB model

• D. Berényi, A. Pásztor, V.V. Skokov, P.L.:

Introduce extra quark and diquark yield from time-dependent strong chromo-electric field 3 quark coalescence → → it is working in the region pT= 4-20 GeV/c arXiv: 1208.0448

Latest calculations on charged hadron R Latest calculations on charged hadron RAA

AA in Pb+Pb at 2.76 ATeV

in Pb+Pb at 2.76 ATeV pQCD + Quenching + (Thermal + Schwinger diquark) coalesc. pQCD + Quenching + (Thermal + Schwinger diquark) coalesc.

• P. Lévai et al. 2012
• P. Lévai et al. 2012

RAA(p) > RAA(pion) for 2 < pT < 15 GeV/c

Latest calculations on proton/pion ratio in Pb+Pb at 2.76 ATeV Latest calculations on proton/pion ratio in Pb+Pb at 2.76 ATeV pQCD + Quenching + (Thermal + Schwinger diquark) coalesc. pQCD + Quenching + (Thermal + Schwinger diquark) coalesc.

• P. Lévai et al. 2012
• P. Lévai et al. 2012

extra proton yield at intermediate- and high-pT

Conclusions:

• 1. Particle production mechanisms are not fully explored

in non-Abelian cases, especially in case of strong fields.

• 2. If the overlap of heavy ions is very short, and the time scale
• f the initial phase is also short, then heavy quark production

is not suppressed by the heavy mass.

• 3. Short pulse: the time scale of the initial 'pulse' determines

the heavy quark production and not the charm mass.

• 4. Thus: heavy quark production can carry message about

the time scale of the initial overlap at LHC energies. (strange quark mass is too close to light quark mass)