Magnetically generated currents in the QGP Umut Grsoy Utrecht - PowerPoint PPT Presentation

Magnetically generated currents in the QGP Umut Gürsoy Utrecht University Oxford University, 29.5.2014 arXiv:1401.3805 with D. Kharzeev and K. Rajagopal arXiv:1212.3894 with I. Iatrakis, E. Kiritsis, F. Nitti, A. O’ Bannon Magnetically generated currents in the QGP – p.1

QCD under external magnetic fields e /e for eB ≈ 10 13 G. • Schwinger pair production if F > m 2 • Magnetic catalysis: B (de)catalyzes � ¯ qq � , T c ( B ) is complicated Bali et al ’12 • rho-meson condensation ⇒ superconducting QCD vacuum! Chernodub ’10 • Changes in the phase diagram in µ − T − B Magnetically generated currents in the QGP – p.2

QCD under external magnetic fields e /e for eB ≈ 10 13 G. • Schwinger pair production if F > m 2 • Magnetic catalysis: B (de)catalyzes � ¯ qq � , T c ( B ) is complicated Bali et al ’12 • rho-meson condensation ⇒ superconducting QCD vacuum! Chernodub ’10 • Changes in the phase diagram in µ − T − B This talk: Electric currents in QGP generated by magnetic fields • Chiral anomaly Kharzeev, McLerran, Warringa ’07 • Faraday + Hall in expanding plasmas U.G, Kharzeev, Rajagopal ’14 Magnetically generated currents in the QGP – p.2

Heavy ion collisions and magnetic fields • Initial magnitude of B B • Bio-Savart: B 0 ∼ γZe b R 3 ⇒ ∼ 10 18 (10 19 ) G at RHIC (LHC). • B 0 ∼ 10 10 − 10 13 G (neutron stars), 10 15 (magnetars) • More relevantly eB ≈ 5 − 15 × m 2 π RHIC (LHC). Magnetically generated currents in the QGP – p.3

PART I: Chiral Magnetic Current Magnetically generated currents in the QGP – p.4

Chiral Anomaly in QCD Magnetically generated currents in the QGP – p.5

Chiral Anomaly in QCD • massless fermions are chiral: left and right-handed quarks. • Classically QGP chiral symmetric: N L = N R as T ≈ 500 MeV ≫ m u , m d • Axial current ∂ µ J µ 5 = ∂ µ � ¯ ψγ µ ψ � L − � ¯ ψγ µ ψ � R � � = 0 N f g 2 • However there is a QM anomaly: ∂ µ j µ 5 = − F µν µν ˜ a . 16 π 2 F a Magnetically generated currents in the QGP – p.5

Chiral Anomaly in QCD • massless fermions are chiral: left and right-handed quarks. • Classically QGP chiral symmetric: N L = N R as T ≈ 500 MeV ≫ m u , m d • Axial current ∂ µ J µ 5 = ∂ µ � ¯ ψγ µ ψ � L − � ¯ ψγ µ ψ � R � � = 0 N f g 2 • However there is a QM anomaly: ∂ µ j µ 5 = − F µν µν ˜ a . 16 π 2 F a • Due to topologically non-trivial gluon configurations g 2 F µν µν ˜ d 4 x F a � • Gluon winding number: Q w = ∈ Z . a 32 π 2 • Atiyah-Singer index theorem: ∆( N L − N R ) = 2 N f Q w Magnetically generated currents in the QGP – p.5

How to produce Q w in QGP? E Sphaleron Topologically non-trivial gluon fields Caloron Instanton Qw -1 1 -2 0 2 • Sphalerons: thermally induced changes in Q w • The most dominant Q w decay Moore et al ’97 due to sphalerons • Sphaleron decay rate: d ( N L − N R ) ≈ 192 . 8 α 5 s T 4 dtd 3 x Magnetically generated currents in the QGP – p.6

Chiral Magnetic Current Magnetically generated currents in the QGP – p.7

Chiral Magnetic Current s · � • Under B spin degeneracy of quarks lifted due H ∼ − q� B : Magnetically generated currents in the QGP – p.7

Chiral Magnetic Current s · � • Under B spin degeneracy of quarks lifted due H ∼ − q� B : • Macroscopic manifestation of the axial anomaly • Anomalous magnetohydrodynamics: � 2 π 2 µ 5 � e 2 J = B Kharzeev et al ’07, Son, Surowka ’09 • µ 5 encodes the imbalance N L � = N R Magnetically generated currents in the QGP – p.7

• If Q w � = 0 ( or µ 5 finite ) • If there is an external magnetic field • There exists J µ ∝ B due to chiral anomaly • In QGP the main source of Q w is sphalerons • Sphaleron decay rate: d ( N L − N R ) ≈ 192 . 8 α 5 s T 4 dtd 3 x Magnetically generated currents in the QGP – p.8

• If Q w � = 0 ( or µ 5 finite ) • If there is an external magnetic field • There exists J µ ∝ B due to chiral anomaly • In QGP the main source of Q w is sphalerons • Sphaleron decay rate: d ( N L − N R ) ≈ 192 . 8 α 5 s T 4 dtd 3 x • But QGP is strongly interacting... Why trust perturbative calculations? Magnetically generated currents in the QGP – p.8

Holographic calculation UV IR Horizon Finite T, N c ≫ 1 , α s ≫ 1 QFT ⇔ GR on black holes in 5D T QFT r Maldacena ’97; Witten; Gubser, Klebanov, Polyakov ’98 1. �O ( x 1 ) O ( x 2 ) � computed from ˆ ∇ 2 φ = m 2 φ on the BH. Magnetically generated currents in the QGP – p.9

Holographic calculation UV IR Horizon Finite T, N c ≫ 1 , α s ≫ 1 QFT ⇔ GR on black holes in 5D T QFT r Maldacena ’97; Witten; Gubser, Klebanov, Polyakov ’98 1. �O ( x 1 ) O ( x 2 ) � computed from ˆ ∇ 2 φ = m 2 φ on the BH. 2. Recall ωJ µ 5 ( ω ) ∝ Tr F ˜ F ( ω ) . Introduce CP odd axion a ( r, x ) d 4 xa 0 ( x )Tr F ˜ 3. The source term � F ( x ) with a ( r, x ) → a 0 ( x ) at the boundary. Magnetically generated currents in the QGP – p.9

Holographic calculation of ∆( N L − N R ) • Initial excess N 5 ≡ N L − N R near thermal equilibrium. • Described by perturbation L → L + ǫ Tr F ˜ F dt N 5 → ωJ 05 ∝ � Tr F ˜ F Tr F ˜ • Linear response theory: d F ( ω ) � N 5 • Should calculate the decay rate Γ CS ∼ � Tr F ˜ F Tr F ˜ F ( ω ) � • Holography: Study ˆ ∇ 2 a ( r, x ) = 0 on the 5D BH. Magnetically generated currents in the QGP – p.10

Holographic calculation of ∆( N L − N R ) Magnetically generated currents in the QGP – p.11

Holographic calculation of ∆( N L − N R ) AdS/CFT: Γ CS = ( g 2 N c ) 2 256 π 3 T 4 , Son, Starinets ’02 Magnetically generated currents in the QGP – p.11

Holographic calculation of ∆( N L − N R ) AdS/CFT: Γ CS = ( g 2 N c ) 2 256 π 3 T 4 , Son, Starinets ’02 Phenomenologically interesting region T ≈ T c where conformality breaks down: Trace of the energy-momentum tensor 1.8 1.6 SU(3) 4 SU(4) 4 , normalized to the SB limit of p / T 1.4 SU(5) SU(6) SU(8) 1.2 improved holographic QCD model 1 0.8 0.6 ∆ / T 0.4 0.2 0 0.5 1 1.5 2 2.5 3 3.5 T / T c Magnetically generated currents in the QGP – p.11

Improved holographic QCD U.G., Nitti, Kiritsis ’07 d 5 x √− g � c Z (Φ)( ∂α ) 2 � R − ( ∂ Φ) 2 + V (Φ) − S GR 1 c = � • M 3 p N 2 2 N 2 1 + c 1 λ + c 4 λ 4 � � • Parametrize Z ( λ ) = Z 0 • Result: Γ CS ( T c ) ≥ C s ( T c ) T c χ O’Bannon, U.G, Iatrakis, Kiritsis, Nitti ’12 • where χ = ∂ 2 ǫ ( θ ) is the topological susceptibility ∂θ 2 � CS �� Κ 2 Z 0 � 2 Π � � s T � N c 2 � 2.0 1.5 1.0 0.5 T � T c 1 2 3 4 5 6 7 for ihQCD to reproduce lattice 0 + − glueball spectrum within 1 σ . Magnetically generated currents in the QGP – p.12

Summary - part I • Calculated the Γ CS in non-conformal holography • CME is proportional to Γ CS • Comparison of AdS/CFT with non-AdS/non-CFT at T c : Γ CFT ≈ 0 . 045 T 4 c vs. Γ CS > 1 . 64 T 4 c CS • Precise value at T c ambiguous but a lower limit exists. √ Γ CS • Linear response ⇒ µ 5 ∝ V 3 χ • “Realistic” holography in favor of the chiral magnetic effect in HICs Magnetically generated currents in the QGP – p.13

Summary - part I • Calculated the Γ CS in non-conformal holography • CME is proportional to Γ CS • Comparison of AdS/CFT with non-AdS/non-CFT at T c : Γ CFT ≈ 0 . 045 T 4 c vs. Γ CS > 1 . 64 T 4 c CS • Precise value at T c ambiguous but a lower limit exists. √ Γ CS • Linear response ⇒ µ 5 ∝ V 3 χ • “Realistic” holography in favor of the chiral magnetic effect in HICs Outlook: • To fix the ambiguity, determine Z ( φ ) ⇒ compare Tr F ∧ F Euclidean correlators with lattice • Determine Γ CS ( B, T ) • What is µ 5 if generated far from equilibrium? Magnetically generated currents in the QGP – p.13

PART II: Faraday + Hall currents ongoing work with D. Kharzeev and K. Rajagopal Magnetically generated currents in the QGP – p.14

“Classical” currents in charged and expanding medium: E F = − ∂ � • Faraday currents � J F ∼ σ � E F with ∇ × � B ∂t • Hall currents � J H ∼ σ � E H with � u × � E H = � B • Also a “quantum” current � J CME ∼ µ 5 � B considered in part I. Magnetically generated currents in the QGP – p.15

Calculating the magnetic field in HICs • Maxwell with a point-like moving source source: � � ∇ 2 � t � B − σ∂ t � x ⊥ − � B − ∂ 2 x ′⊥ ) B = − eβ ∇ × zδ ( z − βt ) δ ( � ˆ • Integrate over participant and spectator distributions: • Simplifying assumption hard-sphere distribution for spectators and participants • For participants empirical distribution over Y: Kharzeev et al. 2007 f ( Y b ) = (4 sinh( Y 0 / 2)) − 1 e Y b / 2 , − Y 0 ≤ Y b ≤ Y 0 Magnetically generated currents in the QGP – p.16

Time profile of B at LHC • with σ = 0 . 023 fm − 1 and with σ = 0 : Magnetically generated currents in the QGP – p.17