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; ...] π ( z c ) D c pp E π d σ 2 ) d σ = ∫ dx 1 ∫ dx 2 ∫ dz c f a / p ( x a ,Q 2 ) f b / p ( x b ,Q 3 p π d ̂ 2 t d π z c AB pp d σ d σ = ∫ d r ) t B ( ∣ ⃗ r ∣ ) E π 2 bd 2 r t A ( ⃗ b − ⃗ ⊗ S ( ... )⊗ M ( ... )⊗ Q ( ... )⊗ F ( ... ) E π 3 p π 3 p π Dilute gas d d II. Dense gluon matter limit as initial condition + hydro: ρ 1 ρ 2 CGC: high CGC initial condition: density gluons α 1 , α 2 where and gluon fields of nuclei
Successful applications of I and II: Successful applications of I and II: I. pQCD model: --- hard probes --- high-p T physics --- jets --- h-h correlations --- ... W=200 GeV II. CGC model: --- soft physics --- multiplicities --- centrality dependence --- E T production --- rapidity distributions --- ...
Problems: Problems: Connection between I and II: Connection between I and II: I. pQCD model (Feynman graphs): --- LO, NLO, ... ? --- factorization (k T ) --- resummations --- soft physics --- heavy quark quenching --- ... II. CGC model (asymptotic): --- hard probes Large-x: valence partons --- jet physics random color charge, a (x) --- correlations Small-x: radiation field, --- ... created by a (x)
A further model for particle production: A further model for particle production: 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: III. Non-perturbative, non-asymptotic color transport: “pair-creation in strong fields” --- strong (Abelian) static E field: Schwinger mechanism probability of pair-creation: 2 + p T 2 m 2 p T =− e E 2 p T P ( p T ) d 3 ln ( 1 − exp [−π ]) d 4 π eE integrated probability at mass m: P m =( e E ) 2 2 ∞ 1 2 exp [−π n m 3 ∑ n = 1 eE ] 4 π n ratio of production rates (e.g. strange to light) 2 − m q 2 γ s = P ( s s ) m s P ( q q )= exp [−π ] eE = 0.9 GeV / fm eE --- 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.
Kinetic equation for fermion pair production: Kinetic equation for fermion pair production: W ( k 1, k 2, k 3 ) Wigner function: a , W = W s + W a = 1,2,... , N c 2 − 1 a t Color decomposition: where s;a γ s ;a γ μ γ s; a γ μ + c μν μ ν + d μ s;a = a s; a + b μ s;a σ 5 + i e 5 W Spinor decomposition: a =( 0, −⃗ A )=( 0,0,0, A 3 a ) A μ Color vector field (longit.): Kinetic equation for Wigner function: 0 γ ∂ ∂ t W + g ν ] }− [ F i ν , { W , γ ν } ] ) = ∂ k i ( 4 { W ,F 0, i }+ 2 { F i ν , [ W , γ 0 γ 8 0 γ 0, W ] + ig [ A i , [ γ i ,W ] ] . i ,W }− i m [ γ = i k i {γ 0 γ 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: s (⃗ k ,t )+⃗ k ⃗ s (⃗ k ,t ) k ,t )= m a b + 1 f f (⃗ ω(⃗ k ) 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) : 2 ( t /δ) ] E pulse ( t )= E 0 [ 1 − tanh Sauter A, Pulse field (dotted): E const ( t )= E pulse ( t ) at t < 0 B, Constant field (dashed): E const ( t )= E 0 t > 0 at E scaled ( t )= E pulse ( t ) at t < 0 C, Scaled field (solid): E 0 E scaled ( t )= t < 0 at κ ( 1 + t / t 0 ) 1 / 2 δ= 0.1 / E 0 at RHIC energy κ= 2 / 3 for scaled Bjorken expans. 1 / 2 t 0 = 0.01 / E 0 with
√ E ) for the Bjorken expansion at t= 2/ √ i ) for the Bjorken expansion at t= 2/ Numerical results (b i E 0 in SU(2): Numerical results (b 0 in SU(2): m = 0 b s T (k T ,k 3 ) b a T (k T ,k 3 ) b a 3 (k T ,k 3 ) b s 3 (k T ,k 3 )
√ E Numerical results for fermion distributions at t= 2/ √ E 0 in SU(2): Numerical results for fermion distributions at t= 2/ 0 in SU(2): f f (k 3 ): longitudinal mom. distr. f f (k T ): transv. mom. distr. k T / √ E 0 = 0.5 k 3 = 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 f f (k T ): transv. mom. distr. ratio: SU(2) / U(1) at k T / √ E 0 = 0.5 ⇒ ¾ at k T / 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) SU(N c ) / U(1) normalized to 1 N c =2 N c =3 f f (k T ): 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.)
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 of 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: E 0 = 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: E 0 = 0.1 ( = 0.05 fm ) Dashed line: E 0 = 0.5 ( = 0.25 fm ) E 0 = 0.68 GeV/fm , g=2 g ⋅ E 0 ∝ = 1.17 GeV/fm
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