Heavy-light Flavor Correlations on the QCD Phase Boundary

Transcription

1 Heavy-light Flavor Correlations on the QCD Phase Boundary Chihiro Sasaki Institute of Theoretical Physics, University of Wroclaw, Poland [1] C.S., Phys. Rev. D 90, no. 11, (2014). [2] C.S. and K. Redlich, Phys. Rev. D 91, no. 7, (2015).

2 crossover temperatures: not unique! T qq - T ss - chiral 155 MeV 200 MeV T charges T poly.inflection deconf flavor basis vs. conserved charge basis: strange mesons deconfined at T ch! µ u = 1 3 µ B µ Q, µ d = 1 3 µ B 1 3 µ Q, µ s = 1 3 µ B 1 3 µ Q µ S. charm? lessons from lattice QCD: (i) EoS not affected by dynamical c quark around T ch [Borsanyi et al. ( 11)] (ii) charmed mesons deconfined together with light mesons [Basavov et al. ( 14)] correlations between light and heavy-flavor physics how are heavy-light hadrons modified toward chiral crossover? D s c s is like K q s? NO!

3 I. Chiral Structure of Heavy-light Mesons

4 Symmetries of QCD in the heavy quark mass limit flavor symmetries chiral symmetry : m u,d /Λ QCD 1, m s /Λ QCD < 1. heavy quark symmetry : Λ QCD /m c,b 1. heavy-light (Q q) mesons Q : heavy quark and q : light quark e.g. D mesons: Q = c, q = u, d, s physical picture (m Q ) flavor symmetry (c b): cloud does not feel the flavor of Q. spin symmetry: cloud does not feel the spin of Q. Spin and flavor symmetries of heavy quarks are entangled!

5 SU(2N Qf ) spin-flavor symmetry: [Shuryak ( 81), Isgur-Wise ( 89)] light d.o.f. (q) do not feel the flavor and spin of the heavy quark (Q). B b flavor c D spin spin B * b flavor c D * spin partners: D(0 ) and D(1 ), B(0 ) and B(1 ) real world: m D m D = 142 MeV, m B m B = 46 MeV Λ QCD 1/m Q corrections m Ds m Dd = 100 MeV, m Bs m Bd = 90 MeV Λ QCD m q corrections

6 Role of light flavor (chiral) symmetry observation: 2nd lowest spin doublets D u,d (0 + ) : 2308 MeV [Belle (03)] D u,d (1 + ) : 2427 MeV [Belle (03)] D s (0 + ) : 2317 MeV [Babar (03)] D s (1 + ) : 2460 MeV [CLEO (03)] mass difference of parity doublets: δm = MeV Λ QCD NOTE: potential model for D mesons (cf. hydrogen atom) does not work! chiral doubling [Nowak-Rho-Zahed (92); Bardeen-Hill (93)] chiral sym heavy quark sym D(0 + ) D(1 + ) D(0 - ) D(1 - ) heavy quark sym chiral sym effective theory for heavy-light system based on the two relevant symmetries

7 II. Thermodynamics

8 Embedding D, D s in a linear sigma model chiral fields Σ = σ + iπ, heavy-light meson fields H(0, 1 ), G(0 +, 1 + ) Lagrangian Σ g L Σg R, H L,R SH L,R g L,R. L = L L (Σ) + L HL (H, Σ), 6 parameters fixed with T = 0 physics V (2) HL : m 0, g } π q {{, gπ s } Σ H 2, V HL = V HL (H 2, H 4 ; Σ) + V (exp) HL. (4) VHL : k 0, k q, k }{{} s Σ H 4 isospin sym & mean field approximation: σ q, σ s, D q, D s conventional approach... then?

9 Chiral condensates: role of charmed-meson MF l R HISQ/tree : N τ =12 N τ =8 N τ =6 N τ =8, m l =0.037m s stout, cont s R HISQ/tree: N τ =12 N τ =8 N τ = T [MeV] T [MeV] [HotQCD Collaboration ( 12)] σ q,s [GeV] q=u,d s T/T pc lattice: qualitative diff. between qq and ss SU(2+1): T c (u,d) < T c (s) chiral model: σ q,s approx. SU(3)!? induced chiral sym. breaking: h q = h q D 2 q h s = h s 1 2 D 2 s ( ) 1 2 gq π + 2k q Dq 2 ( 1 2 gs π + 2k s Ds 2, ).

10 conventional approach: 1. set up at T = 0, all the parameters are constant gap equations at given T 3. approximate SU(3) h q/h s 1...!? resolution: 1. σ q and σ s as input e.g. lattice chiral consansates 2. D q, D s and 2 HL-couplings as output g π, k varying with T 3. h q/h s 1 restored

11 Intrinsic thermal effects σ q,s [GeV] q=u,d s g π s (T)/gπ s (T=0) T/T pc T/T pc concept of EFT: generating functional, Green s functions Z = DqDge S QCD[q,g] DUe S Q eff[u] q Q q q Q low-energy constants: high-frequency modes integrated out in a hot/dense medium: effective couplings dep. on T/n L: Tpc lat = 154 MeV quartic coupling such that m σ = 400 MeV HL: σ q,s profiles from lattice QCD gπ q,s (T ) etc.

12 In-medium charmed-meson masses M D [GeV] M Ds [GeV] T/T pc T/T pc chiral splitting at T pc : δm D δm Ds insensitive to light flavors! heavy quark symmetry light mesons at T pc : δm π-σ δm K-κ SU(2+1) SU(3) cf. chiral SU(4): [Roder-Ruppert-Rischke ( 03)] δm D δm Ds D( 0 ) D( 0 ) D s D s ( 0 ) ( 0 )

13 D s screening mass from lattice QCD [Bazavov-Karsch-Maezawa-Mukherjee-Petreczky ( 14) ] M [GeV] sc T [MeV] Quenched HL coupling and D s decays: anomalous suppression Γ(0 + /1 + 0 /1 + π 0 ) (g s π) 2 }{{} quenched due to CSR δ 2 π 0 η }{{} isospin violation

14 Generalized susceptibilities generating functional vs. effective action Γ[φ cl ] = W [J] d 4 xj(x)φ cl (x) fluctuation of φ φ(x)φ(y) φ(x) φ(y) = 1 = δ2 W δjδj δ 2 Γ δφ cl δφ cl multiple fields φ = (φ 1, φ 2,, φ n ) δ ij = δ2 W δj i δj k δ 2 Γ δφ k δφ j, δ2 W [J] δj(x)δj(y) = ( δ 2 Γ[φ] δφ cl (x)δφ cl (y) {i, j, k} = 1, 2,, n 2 2 sus. matrix χ qq,qs,ss χ ch : light flavor correlations 4 4 sus. matrix χ σd, χ DD : heavy-light flavor correlations ) 1

15 Correlations between light and heavy-light mesons [CS-Redlich ( 14)] σ q,s vs. D q,s D q,s vs. D q,s χ(t)/χ(t=0) σ q D q σ s D q σ q D s σ s D s χ(t)/χ(t=0) D q D q D q D s D s D s T/T pc T/T pc qualitative changes set in at T T pc : (NOTE: χ ch σ q,s / m q,s ) ˆχ σd = ˆχ ch Ĉ HL ˆχ D, ˆχ Dσ = ˆχ D Ĉ HL ˆχ ch, ˆχ DD = ĈD ĈHL ˆχ ch Ĉ HL ˆχ D. in-medium D s as a probe of O(4)!

16 Toward high-density QCD effective Lagrangian parameters vary with T! other hadrons: more and more states activated toward QCD p.t. role of higher KK modes in open moose model [Son, Stephanov ( 03)] correct high-energy behavior for current correlator nuclear matter saturation in Walecka model density-dep. parameters: many-body effects integrated out How to handle them? holographic QCD models: 1/N c corrections? 4d effective theories: higher resonances, careful treatment of broad resonances talk by Pok Man Lo microscopic approach: lattice QCD, DS/FRG

17 Summary Synthesis of light and heavy quark dynamics m q m c, m s m c, T mc 1 heavy quark symmetry as a reliable guide at T pc : chiral mass splittings of HL mesons insensitive to light flavors. δm D,B δm Ds,B s vs. δm π-σ δm K-κ remnant of O(4) in HL mixed fluctuations. anomalous suppression of D s decay widths as a sign of CSR in-medium D s as a probe of O(4)! Application to a dense system strange and charm number conservation role of higher-lying hadrons chiral restoration vs. deconfinement lat. Dirac-eigenmode expansion fluc. of conserved charges χ (non reg) X = F X (σ q,s, D q,s ; χ ch )