Charmed Mesons in Matter Chihiro Sasaki Institute of Theoretical - PowerPoint PPT Presentation

Charmed Mesons in Matter Chihiro Sasaki Institute of Theoretical Physics, University of Wroclaw, Poland [1] C.S., Phys. Rev. D 90 , no. 11, 114007 (2014). [2] C.S. and K. Redlich, Phys. Rev. D 91 , no. 7, 074021 (2015).

Introduction: why charm? • crossover temperatures: not unique! T ss T qq - - chiral 200 MeV 155 MeV T poly.inflection T charges deconf • flavor basis vs. conserved charge basis: strange mesons deconfined at T ch ! µ u = 1 3 µ B + 2 µ d = 1 3 µ B − 1 µ s = 1 3 µ B − 1 3 µ Q , 3 µ Q , 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) charm quarks start to appear around T ch [Basavov et al. (’14)] (iii) survival charmed hadrons up to T/T c = 1 . 2 [Mukherjee et al. (’15)] • correlations between light and heavy-flavor physics, beyond HRG ⇒ how are heavy-light hadrons modified toward chiral crossover? D s ∼ c ¯ s is like K ∼ q ¯ s ? · · · NO!

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

Role of light flavor (chiral) symmetry • observation : 2nd lowest spin doublets D u,d (0 + ) : 2308 MeV D u,d (1 + ) : 2427 MeV [Belle (03)] [Belle (03)] D s (0 + ) : 2317 MeV D s (1 + ) : 2460 MeV [Babar (03)] [CLEO (03)] • mass difference of parity doublets: δm = 300 − 400 MeV ∼ Λ QCD • chiral doubling [Nowak-Rho-Zahed (92); Bardeen-Hill (93)] heavy quark sym D(1 + ) D(0 + ) chiral sym chiral sym D(0 - ) D(1 - ) heavy quark sym effective theory for heavy-light system based on the two relevant symmetries

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

Chiral condensates: role of charmed-meson MF 0.025 0.025 HISQ/tree : N τ =12 HISQ/tree: N τ =12 0.02 0.02 N τ =8 N τ =8 N τ =6 N τ =6 0.015 0.015 N τ =8, m l =0.037m s R R ∆ l ∆ s stout, cont. 0.01 0.01 0.005 0.005 0 0 -0.005 T [MeV] -0.005 T [MeV] 120 140 160 180 200 220 240 120 140 160 180 200 220 240 [HotQCD Collaboration (’12)] • lattice: qualitative diff. between � ¯ qq � 0.1 q=u,d ss � · · · SU(2+1): T ( u,d ) < T ( s ) and � ¯ s c c 0.08 • chiral model: σ q,s − approx. SU(3)!? σ q,s [GeV] 0.06 • induced chiral sym. breaking: 0.04 � 1 � 0.02 h ∗ 2 g q q = h q − D 2 π + 2 k q D 2 , q q 0 � 1 � s = h s − 1 0 0.5 1 1.5 2 h ∗ 2 g s 2 D 2 π + 2 k s D 2 √ . s s T/T pc

conventional approach: 1. set up at T = 0 , all the parameters are constant . 2. 4 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

Intrinsic thermal effects 0.1 1.2 q=u,d s 0.08 1 s (T=0) σ q,s [GeV] 0.06 0.8 s (T)/g π 0.04 0.6 g π 0.02 0.4 0 0.2 0.6 0.8 1 1.2 1.4 0.6 0.8 1 1.2 1.4 T/T pc T/T pc • concept of EFT: generating functional, Green’s functions � � Q D q D ge S QCD [ q,g ] ≡ Q D Ue S eff [ U ] Z = q q q Q • low-energy constants: high-frequency modes integrated out ⇒ in a hot/dense medium: effective couplings dep. on T/n • σ q,s profiles from lattice QCD ⇒ g π ( T ) and k ( T )

In-medium charmed-meson masses 2.4 2.4 0 + 0 + 0 - 0 - 2.3 2.3 2.2 2.2 M D s [GeV] M D [GeV] 2.1 2.1 2 2 1.9 1.9 1.8 1.8 0.6 0.8 1 1.2 1.4 0.6 0.8 1 1.2 1.4 T/T pc T/T pc • chiral splitting at T pc : δM D ≃ δM D s · · · insensitive to light flavors! ⇒ heavy quark symmetry ( 0 ) � D s • light mesons at T pc : δM π - σ ≪ δM K - κ ( 0 ) � D · · · SU(2+1) � = SU(3) ( 0 � ) D • cf. chiral SU(4): ( 0 � ) [Roder-Ruppert-Rischke (’03)] D s δM D ≪ δM D s

Generalized susceptibilities • generating functional vs. effective action � d 4 xJ ( x ) φ cl ( x ) Γ[ φ cl ] = − W [ J ] − • fluctuation of φ � � − 1 δ 2 W [ J ] δ 2 Γ[ φ ] � φ ( x ) φ ( y ) � − � φ ( x ) �� φ ( y ) � = δJ ( x ) δJ ( y ) = δφ cl ( x ) δφ cl ( y ) ∵ 1 = δ 2 W δ 2 Γ δJδJ δφ cl δφ cl • multiple fields � φ = ( φ 1 , φ 2 , · · · , φ n ) δ ij = δ 2 W δ 2 Γ , { i, j, k } = 1 , 2 , · · · , n δJ i δJ k δφ k δφ j – 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

Correlations between light and heavy-light mesons [CS-Redlich (’14)] σ q,s vs. D q,s D q,s vs. D q,s 3.5 2 σ q D q D q D q 1.8 3 σ s D q D q D s σ q D s D s D s 1.6 2.5 σ s D s 1.4 χ (T)/ χ (T=0) 2 χ (T)/ χ (T=0) 1.2 1.5 1 1 0.8 0.5 0.6 0 0.4 -0.5 0.2 0.6 0.8 1 1.2 1.4 0.6 0.8 1 1.2 1.4 T/T pc T/T pc qualitative changes set in at T ∼ T pc : (NOTE: χ ch ∼ ∂σ q,s /∂m q,s ) χ ch ˆ χ D ˆ χ σD = − ˆ ˆ C HL ˆ χ D , χ Dσ = − ˆ ˆ C HL ˆ χ ch , χ DD = ˆ C D − ˆ χ ch ˆ ˆ C HL ˆ C HL ≡ ˆ χ D . in-medium D s as a probe of O(4)!

Lattice observables - consistent with the model 1.0 HTLpt χ uc mn / χ c - 0.5 EQCD c 1 /p C c 2 /p C 2 sc M [GeV] m n: 22 1 + c 3 /p C c 4 /p C 3.5 13 0.5 0.4 0 + 31 11 1 − 0.3 3 0 − 0.0 0.2 2.5 0.1 -0.5 0.0 2 T [MeV] T [MeV] T [MeV] -0.1 -1.0 100 150 200 250 300 350 400 450 500 160 180 200 220 240 260 280 300 320 340 150 170 190 210 230 250 270 290 310 330 • screening D s masses [Bazavov et al. (’14)] - the same tend • 4th-order c - s corr.: survival D s up to T = 1 . 2 T ch [Mukherjee et al. (’15)] D s changes its property - medium modification sets in at ∼ T ch . • fluctuations and correlations of conserved charges X χ (non − reg) = F X ( σ q,s , D q,s ; χ ch ) X Chiral vs. confinement at finite density • hybrid model suggests a splitting of the 2 phase tr. [Benic-Mishustin-CS (’15)] • Dirac-eigenmode expansion on lattice (talk by T. Doi)

Summary • Synthesis of light and heavy quark dynamics m q m c , m s m c , T m c ≪ 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 D s ,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 – intrinsic density dependence - role of higher-lying hadrons – chiral restoration vs. deconfinement