Q Q dynamics with external magnetic fields

Transcription

1 Q Q dynamics with external magnetic fields Marco Mariti University of Pisa 33rd International Symposium on Lattice Field Theory, Kobe 15/07/2015 In collaboration with: C. Bonati, M. D Elia, M. Mesiti, F. Negro, A. Rucci, F. Negro, F.Sanfilippo

2 QCD with external B fields QCD with B fields at the strong scale eb m 2 π Relevant in many contexts Neutron stars, B T [Duncan and Thompson, 1992] Off-central heavy ion collisions, B T [Skokov et al., 2009] Early universe, B T [Vachaspati, 1991] e Tesla 0.06 GeV 2 LHC eb factory: expected fields up to eb 0.3 GeV 2 Lifetime of eb after collisions still under debate

3 eb effects on gluon dynamics eb couples with quarks. Nevertheless, at this scale electromagnetic interactions lead to non trivial non perturbative effects also in the gluon sector Lattice results: Sea and Valence contributions to the chiral condensate [D Elia, Negro (2011)] Inverse catalysis [Bruckmann et al. (2013)] Anisotropies in the plaquettes [Ilgenfritz et al. (2014); Bali et al. (2013)] Anisotropy of the static QQ potential at T = 0 [Bonati et al. (2014)] T = 0 results Outline Updated results for V QQ (B) at T = 0 with continuum extrapolations Magnetic angular dependence anisotropy coefficients Finite T results Preliminary study of Debye screening masses above T c Dependence on eb at T = 200, 250 MeV for fields up to eb = 1.03 GeV 2

4 Magnetic field on the lattice Gauge fields interactions enter through the covariant derivative. Continuum: µ + iga a µt a µ + iga a µt a + iea µ On the lattice: add proper u(1) phases to the SU(3) links : U µ (n) U µ (n) exp (iqa µ (n)) Periodic boundary conditions e iqba = e iqb(a LxLya2 ) Quantization condition qb = 2πb L xl ya 2 con b Z B = Bẑ gauge fixing ay = Bx, then: b= u (q) y (n) = e ia2 qbn x u (q) x (n) nx=l x = e i a2 ql xbn y For b / Z string become visible. Non-uniform B b=

5 Static Q Q potential Interaction between NR quarks QQ well described by the so called Cornell potential V (r) = C + α r + σr; σ string tension α Coulomb term Good effective description of meson spectra and confinement The static potential have been largely investigated from first principles on the lattice One consider the Wilson loop W (r, T ) related to the energy to create a couple QQ at distance r annihilated after a time T ( W (ˆr, V (ˆr) = lim log ˆT ) + 1) ˆT W (ˆr, ˆT ) In PRD 89 (2014) we investigated the effects induced by external magnetic fields on the potential at T = 0

6 Static Q Q potential Fixed magnetic field direction B = Bẑ Defined orthogonal (W XY ) and parallel (W Z ) Wilson loops according to the spatial direction of the loop W XY ( r, T ) = W (rˆx, T ) + W (rŷ, T ) ; W Z ( r, T ) = W (rẑ, T ) 2 Kept separeted these components and measured the potential from them V XY (ˆr) = c XY + α XY ˆr + ˆσ XY ˆr 2 V Z (ˆr) = c Z + α Z ˆr + ˆσ Z ˆr 2

7 Anisotropic static Q Q potential We used Symanzik improved gauge action Staggered fermions with 2-level sout smearing improvement Phyisical quark masses 1 HYP smearing on T -direction 24 APE smearing on spatial directions (36 APE for new data) Lattice setups L a [fm] b old data NEW av(n s a) eb = 0.0 GeV 2 eb = 0.7 GeV 2 XY eb = 0.7 GeV 2 XYZ eb = 0.7 GeV 2 Z n s Anisotropies washed out averaging over all directions Compute O(eB)/O(0) for O = α, r 0, σ

8 Anisotropic static Q Q potential Continuum extrapolations σ(b)/σ(b=0) L=24 XY L=32 XY L=40 XY L=48 XY L=24 Z L=32 Z L=40 Z L=48 Z r 0 (B)/r 0 (B=0) L=24 XY L=32 XY L=40 XY L=48 XY L=24 Z L=32 Z L=40 Z L=48 Z 0.8 α(b)/α(b=0) eb [GeV 2 ] 1.6 L=24 XY L=32 XY L=40 XY 1.4 L=48 XY L=24 Z L=32 Z 1.2 L=40 Z L=48 Z eb [GeV 2 ] eb [GeV 2 ] Continuum extrapolations confirm anisotropies σ XY > σ Z while α Z > α XY For σ expected deviations larger than 10% above 1 GeV 2

9 Anisotropic static Q Q potential Electromagnetism: medium with anisotropic dielectric constant e r e ɛ (x) ɛ (y) ɛ (z) x 2 + y2 + z2 ɛ (x) ɛ (y) ɛ (z) α r α ɛ (α) xy (x 2 + y 2 ) + ɛ (α) z z 2 σr σ ɛ (σ) xy (x 2 + y 2 ) + ɛ (σ) z z 2 Can be reformulated as V (r, θ, B) = α(θ,b) r + σ(θ, B)r σ(θ, B) = σɛ (σ) 1 (B) 1 + ɛ (σ) 2 (B) sin2 (θ) σ(b)/σ(0) 1,6 1,4 1,2 1 L = 32 L = 48 eb = 1.03 GeV 2 α(θ, B) = α ɛ (α) 1 1+ɛ (α) 2 (B) sin 2 (θ) ɛ O 1 = ɛ O z ɛ O 2 = ɛ x y O /ɛ O z 1 θ angle between eb and W (r, T ) 0,8 0,6 0 π/8 π/4 3π/8 π/2 θ L = 48 ɛ (σ) 1 = 0.70(5) ɛ (σ) 2 = 2.17(52)

10 Finite T with external B fields Above T C strongly interacting matter deconfine Quark Gluon Plasma Color screening melts heavy quark bound states One can define screening masses for the chromo-electric and chromo-magnetic gauge fields m E and m M. Screening masses defined non perturbatively by inverse correlation lengths of proper gauge invariant operators Previous studies on the lattice Pure gauge [Kacmareck et al., PRD 62 (2000) ] N f = 2 dynamical Wilson fermions [Maezawa et al., PRD 81 (2010) ] N f = dynamical staggered fermions [Borsányi et al., JHEP04 (2015) 138]

11 Debye screening masses To separate m E and m M one can decompose Polyakov loops correlators into combinations symmetric under Eucledean time reflection and C L M = L+L 2 L E = L L 2 } L M± = L M ±L M 2 L E± = L E±L E 2 } M (E) even (odd) under Euclidean time reflection A 4 (t, x) A 4 ( t, x) A i (t, x) A i ( t, x) + ( ) even (odd) under C A µ (t, x) A µ(t, x) Because Tr L E+ = Tr L M = 0 one considers only: C M+ (r, T ) = x TrL M+(x)TrL M+ (x + r) x TrL(x) 2 C E (r, T ) = x TrL E (x)trl E (x + r) Debye screening masses defined from the exponential fall off of these correlators

12 Debye screening masses Preliminary study 0.01 T = 250 MeV C E+ B=0.0 GeV 2 C M- B=0.0 GeV 2 Improved action and physical quark masses (rt) C(r,T) Used our smallest lattice spacing a = fm with L = 48 for N T = 8, 10 1e rt We fit the correlators according to 36 steps APE smering on spatial directions C M+ (r, T ) a M (T ) e m M (T )r r C E (r, T ) a E (T ) e m E (T )r For eb 0 we keep XY and Z directions separate to look for anisotropies in the screening masses. r

13 Debye screening masses T = 200 MeV T = 200 MeV Z XY Z XY m M / T (eb) m E / T(eB) eb [GeV 2 ] eb [GeV 2 ] B = 0 results at T = 200 MeV: m M /T = 4.68(6) and m E /T = 9.52(21) (good agreement with JHEP04 (2015) 138 at the same lattice spacing) XY, Z results compatible with each other at present precision Increase of both masses with eb at T = 200 MeV

14 Debye screening masses T = 250 MeV T = 250 MeV 6 Z XY Z XY m M / T (eb) m E / T(eB) eb [GeV 2 ] eb [GeV 2 ] B = 0 results at T = 250 MeV: m M /T = 4.64(5) and m E /T = 9.44(18) (good agreement with JHEP04 (2015) 138 at the same lattice spacing) XY, Z results compatible with each other at present precision m E stay constant with eb, m M still increases.

15 Debye screening masses Magnetic corrections to the screening masses decrease with Tc 7 eb = 0.0 GeV 2 eb = 0.56 GeV 2 eb = 0.78 GeV 2 eb = 1.04 GeV eb = 0.0 GeV 2 eb = 0.56 GeV 2 eb = 0.78 GeV 2 eb = 1.04 GeV 2 m M / T 6 m E / T T [MeV] T [MeV] Extend this study to other temperatures above T c Continuum extrapolation Work in progress: measurement of Polyakov loop correlators for T < T c

16 Conclusions Summary Continuum extrapolation confirms anisotropies in the static QQ potential Angular dependence of the observables agrees with an anisotropic description of the mediuum In the deconfined phase, we found magnetic dependence in the screeneng masses m E, m M near T c No relevant anisotropies above T c Future studies Precision improvement and continuum limit for the anisotropy coefficients Extend our investigations above T c to determine T dependence of the magnetic corrections to the screening masses Extend our investigation at finite temperature for T < T c

17 THANK YOU