STRANGENESS NEUTRALITY AND THE QCD PHASE STRUCTURE

Transcription

1 STRANGENESS NEUTRALITY AND THE QCD PHASE STRUCTURE Fabian Rennecke Brookhaven National Laboratory [Fu, Pawlowski, FR, hep-ph/ ] [Fu, Pawlowski, FR, hep-ph/ ] NUCLEAR PHYSICS COLLOQUIUM FRANKFURT 18/09/2018

2 OUTLINE The QCD phase diagram & heavy-ion collisions Strangeness neutrality Low-energy QCD & functional RG Strangeness neutrality, correlations & phase structure

3 QCD PHASE DIAGRAM T μ B

4 QCD PHASE DIAGRAM T τ μ B μ Q? E,B ω μ S

5 PROBING THE PHASE DIAGRAM phase diagram probed at freeze-out; timescale ~10 fm/c from strong and weak decays with the same final products [PDG] typical timescales of strong and (flavor-changing) weak decays: ~1 fm/c vs ~10 13 fm/c quark number conservation of the strong interactions at the freeze-out! baryon number, strangeness & isospin are conserved

6 PROBING THE PHASE DIAGRAM net quark content determined by incident nuclei net strangeness has to be zero fixes μs : strangeness neutrality net charged fixed fixes μq increasing baryon chemical potential with decreasing beam energy (at mid-rapidity) μb is a `free parameter NA49 preliminary 3 10 STAR Preliminary (MeV) B µ 10 2 BES (STAR) Andronic et al s NN (GeV) [L. Kumar (STAR), J.Phys. G38 (2011)] [NA49, compiled by C. Blume]

7 PROBING THE PHASE DIAGRAM net quark content determined by incident nuclei net strangeness has to be zero fixes μs : strangeness neutrality net charged fixed fixes μq increasing baryon chemical potential with decreasing beam energy (at mid-rapidity) μb is a `free parameter NA49 preliminary (MeV) B µ STAR Preliminary Effect of particle number conservation on the phase structure/thermodynamics? [NA49, compiled by C. Blume] BES (STAR) Andronic et al s NN (GeV) [L. Kumar (STAR), J.Phys. G38 (2011)]

8 NOMENCLATURE chemical potentials: q = 0 1 da s µ = 0 µ u µ d µ s 1 C A = µ B 3 µ B µ Q 1 3 µ B 1 3 µ Q 1 3 µ Q µ S charge 1 C A baryon strangeness here: µ Q =0 cumulants of conserved charges pressure BS ij = T i+j p(t,µ B,µ S i S net baryon number: net strangeness: hbi = hn B N Bi = BS 10 VT 3 hsi = hn S N S i = BS 01 VT 3

9 BARYON-STRANGENESS CORRELATION strangeness neutrality C BS 3 BS 11 BS 02 = 3 hbsi hbihsi hs 2 i hsi 2 = 3 hbsi hs 2 i [Koch, Majumder, Randrupp, nucl-th/ ] diagnostic tool for deconfinement: QGP all strangeness is carried by strict relation beween B and S: if all flavors are independent: C BS =1 s, s B s = S s /3 BS 11 = BS 02 /3 hadronic phase mesons can carry only strangeness, baryons both BS 11 BS 02 : only strange baryons : strange baryons & mesons C BS 6=1

10 STRANGENESS NEUTRALITY HIC: colliding nuclei have zero strangeness hsi =0 strangeness neutrality implicitly defines µ S0 (T,µ B )=µ S (T,µ B ) hsi=0 BS 01 T,µ B,µ S0 =0 ) d BS 01 S0 dµ B = 1 3 C BS

11 STRANGENESS NEUTRALITY HIC: colliding nuclei have zero strangeness hsi =0 strangeness neutrality implicitly defines µ S0 (T,µ B )=µ S (T,µ B ) hsi=0 BS 01 T,µ B,µ S0 =0 ) d BS 01 =0, dµ B = 1 3 C BS particle number conservation phases of QCD access B-S correlation through strangeness neutrality!

12 LOW-ENERGY MODELING OF QCD

13 PQM MODEL Polyakov-loop enhanced quark-meson model k = Z 1/T 0 dx 0 Z d 3 x n q D + C q + qh 5 q +tr D D + Ũk( )+U glue (L, L) o

14 PQM MODEL Polyakov-loop enhanced quark-meson model k = Z 1/T 0 dx 0 Z d 3 x n q D + C q + qh 5 q +tr D D + Ũk( )+U glue (L, L) o scalar and pseudoscalar meson nonets: {,f 0,a 0 0,a + = T a ( a +i a 0 ) 3,a 0, apple0, apple 0, apple +, apple } {, 0, 0, +,,K 0, K0,K +,K } open strange mesons l s, s l 5 = T a ( a +i 5 a ) quarks (assume light isospin symmetry): q = 0 1 l B la s

15 PQM MODEL Polyakov-loop enhanced quark-meson model k = Z 1/T 0 dx 0 Z d 3 x n q D + C q + qh 5 q +tr D D + Ũk( )+U glue (L, L) o chemical potential matrix µ 1 B 0 0 µ µ B 0 A µ B µ S vector source for the chemical potential C = 0 µ covariant derivative couples chemical potentials to mesons D +[C, ]

16 PQM MODEL Polyakov-loop enhanced quark-meson model k = Z 1/T 0 dx 0 Z d 3 x n q D + C q + qh 5 q +tr D D + Ũk( )+U glue (L, L) o effective meson potential: Ũ k = U k ( 1, 2 ) j l l j s s c k anomalous U(1)A breaking via t Hooft determinant =det +det U(3) x U(3) symmetric potential (as a function of two chiral invariants) i =tr( ) i explicit chiral symmetry breaking: finite light & strange current quark masses

17 PQM MODEL Polyakov-loop enhanced quark-meson model k = Z 1/T 0 dx 0 Z d 3 x n q D + C q + qh 5 q +tr D D + Ũk( )+U glue (L, L) o temporal gluon background field in cov. derivative: Polyakov loop: L = 1 N c D Tr f P e ig R 0 d A 0( ) E D ig 0 A 0 Polyakov loop potential: [Lo et. al., hep-lat/ ] U glue (L, L) T 4 = 1 2 a(t ) LL + b(t )ln M H (L, L) c(t )(L3 + L 3 )+d(t )( LL) 2 Haar measure M H (L, L) =1 6 LL + 4(L 3 + L 3 ) 3( LL) 2 parameters fitted to reproduce lattice pressure and Polyakov loop susceptibilities approximate Nf and μ dependence from QCD and HTL/HDL arguments [Herbst et. al., hep-ph/ , ] [Haas et. al., hep-ph/ ] `statistical confinement

18 FUNCTIONAL RG introduce regulator to partition function to suppress momentum modes below energy scale k (Euclidean space): Z Z k [J] = D' e S['] S k[']+ R x J' S k ['] = 1 2 scale dependent effective action: Z d 4 q (2 ) 4 '( k[ ]=sup J q)r k(q)'(q) Z k 2 J(x) (x) ln Z k [J] S k [J] x R k (p 2 ) k 2 k 2 = h'i J 1 tr k (p 2 ) p 2 evolution equation for Γk: [Wetterich t k = 1 2 STr apple (2) k + R k 1@t R t = k d dk successively integrate out fluctuations from UV to IR (Wilson RG) k 0 = Γk is eff. action that incorporates all fluctuations down to scale k lowering k: zooming out / coarse graining full quantum effective action (generates 1PI correlators)

19 PQM + FUNCTIONAL RG dynamical chiral symmetry breaking though Uk `statistical confinement through A0 background (Uglue) beyond mean-field (resummation of infinite class of diagrams through the FRG) thermal quark distributions modified through feedback from A0 n F (E) = 1 e (E µ)/t +1 A 0 6=0! N F (E; L, L) = 1+2 Le (E µ)/t 2(E µ)/t + Le 1+3 Le (E µ)/t +3Le 2(E µ)/t + e3(e µ)/t! ( 1 e 3(E µ)/t +1, L! 0 (confinement) 1 e (E µ)/t +1, L! 1 (deconfinement) `interpolation between baryon and quark d.o.f. correct `Nc - scaling of particle number fluctuations [Fukushima, hep-ph/ ] [Fu & Pawlowski, hep-ph/ ] [Ejiri et al., hep-ph/ ] [Skokov et al., hep-ph/ ] thermodynamics from Euclidean (off-shell) formulation simple hierarchy of relevant fluctuations: the lighter the particle, the more relevant it is fluctuations of kaons and s-quarks (coupled to A0) reasonable for qualitative description of the relevant strangeness effects (for moderate μ)

20 FLUCTUATIONS AND THE PHASE STRUCTURE AT STRANGENESS NEUTRALITY

21 MODEL VS LATTICE EOS thermodynamic potential: = e U 0 + U glue EoM thermodynamics: / µ B =0 - - (- χ )/ χ chiral transition temperature p = = p + Ts+ µ B n B + µ S n S I = 3p c 2 s s /@T n B = n S = BS 10 T 3 BS 01 T 3 / - - (- χ )/ χ [HotQCD, hep-lat/ & ] [Wuppertal-Budapest, hep-lat/ ] - - (- χ )/ χ

22 MODEL VS LATTICE EOS thermodynamic potential: = e U 0 + U glue EoM / μ / = thermodynamics: - (- χ )/ χ p = = p + Ts+ µ B n B + µ S n S I = 3p c 2 s s /@T / (- χ )/ χ n B = n S = BS 10 T 3 BS 01 T 3 / [HotQCD, hep-lat/ & ] [Wuppertal-Budapest, hep-lat/ ] - (- χ )/ χ

23 MODEL VS LATTICE EOS thermodynamic potential: = e U 0 + U glue EoM / μ / = thermodynamics: - (- χ )/ χ n B (T,µ B )/T µ Q =µ S =0 HRG p = µ B /T=2 = p + Ts+ µ B n B + µ S n S I = 3p c 2 s s /@T n B = n S = BS 10 T 3 BS 01 3 T [MeV] µ B /T=2.5 µ B /T=1 O(µ B 6 ) O(µ B 4 ) O(µ B 2 ) / / (- χ )/ χ [HotQCD, hep-lat/ & ] [Wuppertal-Budapest, hep-lat/ ] - (- χ )/ χ

24 STRANGENESS DENSITY as a function of μs / μ B = 300 MeV T = 50 MeV T = 120 MeV T = 200 MeV strangeness number density decreases with increasing μs strangeness neutrality: zero crossing µ S0 µ S (T,µ B ) ns =0 - μ [] almost linear at larger T: higher strangeness cumulants suppressed?

25 STRANGENESS CHEMICAL POTENTIAL as a function of μb at strangeness neutrality μ [] T [MeV] free quarks: 1/3 slope directly related to baryonstrangeness B = 1 3 C BS CBS for any T and μ μ []

26 BARYON-STRANGENESS CORRELATION at strangeness neutrality B = C BS hstrange baryonsi hstrange baryons & mesonsi 8 >< < 1 mesons dominate = 1 mesons & baryons (or uncorrelated flavor) >: > 1 baryons dominate μ B [MeV] competition between baryonic and mesonic sources of strangeness! maxima at the chiral transition! HotQCD [] direct sensitivity to the QCD phase transition lattice results: [HotQCD, hep-lat/ ]

27 BARYON-STRANGENESS CORRELATION strangeness conservation vs non-conservation <S> =0 μ S = 0 μ B [MeV] [] sizable impact of strangeness neutrality!

28 STRANGENESS CHEMICAL POTENTIAL as a function of T at strangeness neutrality μ [] μ B [MeV] use as input for EoS at finite μb []

29 STRANGENESS CHEMICAL POTENTIAL role of open strange meson dynamics quark/baryon vs meson dynamics? equation for μs0 from the fermion part of the RG flow µ S0 fermions µ B 2 apple T L(T,µB 2 ln ) L(T,µ B ) [Fukushima, hep-ph/ ] full result fermions Eq. (??) only μ [] open strange meson fluctuations crucial! []

30 STRANGENESS NEUTRALITY EoS at strangeness neutrality / μ B = 300 MeV n S = 0 μ S = μ B /3 μ S = 0 / μ B = 540 MeV n S = 0 μ S = μ B /3 μ S = 0 / μ B = 675 MeV n S = 0 μ S = μ B /3 μ S = 0 [] [] [] μ B = 300 MeV n S = 0 μ S = μ B /3 μ S = 0 μ B = 540 MeV n S = 0 μ S = μ B /3 μ S = 0 μ B = 675 MeV n S = 0 μ S = μ B /3 μ S = 0 / / / [] [] [] μ B = 300 MeV n S = 0 μ S = μ B /3 μ S = 0 μ B = 540 MeV n S = 0 μ S = μ B /3 μ S = 0 μ B = 675 MeV n S = 0 μ S = μ B /3 μ S = 0 [] [] []

31 STRANGENESS NEUTRALITY phase structure at strangeness neutrality LS = L L j L js S T j L js S T =0 L = 1 N c D Tr f P e ig R 0 d A 0( ) E = μ = = μ = [] [] LS ns =0 LS µs =0 L ns =0 L µs =0 - LS ns =0 μ [] L ns =0 μ [] transition to QGP at larger T (for fixed μb) smaller curvature of the phase boundary CEP at smaller μb & larger T (?)

32 STRANGENESS NEUTRALITY isentropes at strangeness neutrality QGP evolves hydrodynamically at late stages `almost perfect fluid: small viscosity over entropy density QGP evolves close to isentropes in hydro regime s/n B = const. = [] μ S =0 n S =0 μ []

33 SUMMARY & OUTLOOK strangeness neutrality in heavy ion collisions intimate relation between strangeness conservation and phases of QCD as probed in heavy-ion collisions baryon-strangeness correlation via strangeness neutrality finite μb requires finite μs: sensitive to interplay of QCD d.o.f. relevant for phase structure and thermodynamics at finite μb ~30% effects already at moderate μb, CBS is most sensitive `delayed transition to the QGP in the phase diagram For the (near) future: study larger μ and the CEP repeat analysis also with charge chemical potential going beyond LPA including gluon fluctuations: dynamical hadronization self-consistent computation of the A0 potential computation of off-diagonal cumulants

34 SUMMARY & OUTLOOK strangeness neutrality in heavy ion collisions intimate relation between strangeness conservation and phases of QCD as probed in heavy-ion collisions baryon-strangeness correlation via strangeness neutrality finite μb requires finite μs: sensitive to interplay of QCD d.o.f. relevant for phase structure and thermodynamics at finite μb ~30% effects already at moderate μb, CBS is most sensitive `delayed transition to the QGP in the phase diagram For the (near) future: study larger μ and the CEP repeat analysis also with charge chemical potential going beyond LPA thank you including gluon fluctuations: dynamical hadronization self-consistent computation of the A0 potential computation of off-diagonal cumulants

35 BACKUP

36 STRANGENESS AND CHARGE CONSERVATION particle number conservation implicitly defines two functions: this implies: µ Q0 (T,µ B )=µ Q (T,µ B ) ns =0,n Q =rn B µ S0 (T,µ B )=µ S (T,µ B ) ns =0,n Q =rn B r = Z B = 1 3 C BS QS 11 S B = BS 11 ( SQ 11 r BS S 11 ) 2 ( BQ 11 r B 2 ) S 2 ( Q 2 r BQ 11 ) SQ 11 ( SQ 11 r BS 11 ) generalization of `freeze-out relations used on the lattice to any T and μ Β

37 2+1 FLAVOR PQM AT LARGE CHEMICAL POTENTIAL gluon contribution to the pressure at large chemical potential p glue = U glue (L, L) μ B = 750 MeV / - - / - μ B = 0 μ B = 750 MeV [] - [] model becomes unphysical at large μb likely due to missing feedback from the matter to the gauge sector / input potential not accurate at large L L