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

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

May 20, 2023 37 likes •168 views

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?

slide-1
SLIDE 1

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).

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SLIDE 2

Introduction: why charm?

  • crossover temperatures: not unique!

Tqq

  • Tss
  • chiral

deconf 155 MeV 200 MeV

Tcharges Tpoly.inflection

  • flavor basis vs. conserved charge basis: strange mesons deconfined at Tch!

µu = 1 3µB + 2 3µQ , µd = 1 3µB − 1 3µQ , µs = 1 3µB − 1 3µQ − µS .

  • charm? · · · lessons from lattice QCD:

(i) EoS not affected by dynamical c-quark around Tch

[Borsanyi et al. (’11)]

(ii) charm quarks start to appear around Tch [Basavov et al. (’14)] (iii) survival charmed hadrons up to T/Tc = 1.2

[Mukherjee et al. (’15)]

  • correlations between light and heavy-flavor physics, beyond HRG

⇒ how are heavy-light hadrons modified toward chiral crossover? Ds ∼ c¯ s is like K ∼ q¯ s? · · · NO!

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SLIDE 3

Symmetries of QCD in the heavy quark mass limit

  • flavor symmetries

chiral symmetry : mu,d/ΛQCD ≪ 1 , ms/ΛQCD < 1 . heavy quark symmetry : ΛQCD/mc,b ≪ 1 .

  • SU(2NQf) spin-flavor symmetry (mQ → ∞): [Shuryak (’81), Isgur-Wise (’89)]

light d.o.f. (q) do not feel the flavor and spin of the heavy quark (Q).

c c b b D D* B* B spin spin flavor flavor

spin partners: D(0−) and D(1−) B(0−) and B(1−)

  • real world:

mD∗ − mD = 142 MeV , mB∗ − mB = 46 MeV ≪ ΛQCD : 1/mQ corr. mDs − mDd = 100 MeV , mBs − mBd = 90 MeV ≪ ΛQCD : mq corr.

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SLIDE 4

Role of light flavor (chiral) symmetry

  • observation: 2nd lowest spin doublets

Du,d(0+) : 2308 MeV [Belle (03)] Du,d(1+) : 2427 MeV [Belle (03)] Ds(0+) : 2317 MeV [Babar (03)] Ds(1+) : 2460 MeV [CLEO (03)]

  • mass difference of parity doublets: δm = 300 − 400 MeV ∼ ΛQCD
  • chiral doubling

[Nowak-Rho-Zahed (92); Bardeen-Hill (93)]

D(0+) D(0-) D(1-) D(1+) heavy quark sym heavy quark sym chiral sym chiral sym

effective theory for heavy-light system based on the two relevant symmetries

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SLIDE 5

Embedding D, Ds in a linear sigma model

  • chiral fields Σ = σ + iπ, heavy-light meson fields H(0−, 1−), G(0+, 1+)

Σ → gLΣg†

R ,

HL,R → SHL,Rg†

L,R .

  • Lagrangian

L = LL(Σ) + LHL(H, Σ) , VHL = VHL(H2, H4; Σ) + V (exp)

HL

.

  • 6 parameters fixed with T = 0 physics

V (2)

HL : m0 , gq π , gs π Σ↔H2

, V (4)

HL : k0 , kq , ks Σ↔H4

  • isospin sym & mean field approximation: σq , σs , Dq , Ds

conventional approach ... then?

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SLIDE 6

Chiral condensates: role of charmed-meson MF

  • 0.005

0.005 0.01 0.015 0.02 0.025 120 140 160 180 200 220 240 T [MeV]

∆l

R

HISQ/tree : Nτ=12 Nτ=8 Nτ=6 Nτ=8, ml=0.037ms stout, cont.

  • 0.005

0.005 0.01 0.015 0.02 0.025 120 140 160 180 200 220 240 T [MeV]

∆s

R

HISQ/tree: Nτ=12 Nτ=8 Nτ=6

[HotQCD Collaboration (’12)]

0.02 0.04 0.06 0.08 0.1 0.5 1 1.5 2 σq,s [GeV] T/Tpc q=u,d s

  • lattice: qualitative diff. between ¯

qq and ¯ ss · · · SU(2+1): T (u,d)

c

< T (s)

c

  • chiral model: σq,s − approx. SU(3)!?
  • induced chiral sym. breaking:

h∗

q = hq − D2 q

1 2gq

π + 2kqD2 q

  • ,

h∗

s = hs − 1

√ 2D2

s

1 2gs

π + 2ksD2 s

  • .
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SLIDE 7

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. σq and σs as input

e.g. lattice chiral consansates

  • 2. Dq, Ds and 2 HL-couplings as output

⇒ gπ, k varying with T

  • 3. h∗

q/h∗ s ≪ 1 restored

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SLIDE 8

Intrinsic thermal effects

0.02 0.04 0.06 0.08 0.1 0.6 0.8 1 1.2 1.4 σq,s [GeV] T/Tpc q=u,d s 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 gπ

s(T)/gπ s(T=0)

T/Tpc

  • concept of EFT: generating functional, Green’s functions

Z =

  • DqDgeSQCD[q,g] ≡
  • DUeSeff[U]

Q q Q Q q q

  • low-energy constants: high-frequency modes integrated out

⇒ in a hot/dense medium: effective couplings dep. on T/n

  • σq,s profiles from lattice QCD ⇒ gπ(T) and k(T)
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SLIDE 9

In-medium charmed-meson masses

1.8 1.9 2 2.1 2.2 2.3 2.4 0.6 0.8 1 1.2 1.4 MD [GeV] T/Tpc 0+ 0- 1.8 1.9 2 2.1 2.2 2.3 2.4 0.6 0.8 1 1.2 1.4 MDs [GeV] T/Tpc 0+ 0-

  • chiral splitting at Tpc: δMD ≃ δMDs

· · · insensitive to light flavors! ⇒ heavy quark symmetry

  • light mesons at Tpc: δMπ-σ ≪ δMK-κ

· · · SU(2+1) = SU(3)

  • cf. chiral SU(4):

[Roder-Ruppert-Rischke (’03)]

δMD ≪ δMDs

) (

  • D

) (

  • D

) (

  • s

D ) (

  • s

D

slide-10
SLIDE 10

Generalized susceptibilities

  • generating functional vs. effective action

Γ[φcl] = −W[J] −

  • d4xJ(x)φcl(x)
  • fluctuation of φ

φ(x)φ(y) − φ(x)φ(y) = δ2W[J] δJ(x)δJ(y) =

  • δ2Γ[φ]

δφcl(x)δφcl(y) −1 ∵ 1 = δ2W δJδJ δ2Γ δφclδφcl

  • multiple fields

φ = (φ1, φ2, · · · , φn) δij = δ2W δJiδJk δ2Γ δφkδφj , {i, j, k} = 1, 2, · · · , n – 2 × 2 sus. matrix ⇒ χqq,qs,ss ∼ χch: light flavor correlations – 4 × 4 sus. matrix ⇒ χσD, χDD: heavy-light flavor correlations

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SLIDE 11

Correlations between light and heavy-light mesons

[CS-Redlich (’14)]

σq,s vs. Dq,s Dq,s vs. Dq,s

  • 0.5

0.5 1 1.5 2 2.5 3 3.5 0.6 0.8 1 1.2 1.4 χ(T)/χ(T=0) T/Tpc σqDq σsDq σqDs σsDs 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.6 0.8 1 1.2 1.4 χ(T)/χ(T=0) T/Tpc DqDq DqDs DsDs

qualitative changes set in at T ∼ Tpc: (NOTE: χch ∼ ∂σq,s/∂mq,s) ˆ χσD = −ˆ χch ˆ CHL ˆ χD , ˆ χDσ = −ˆ χD ˆ CHL ˆ χch , ˆ χDD = ˆ CD − ˆ CHL ˆ χch ˆ CHL ≡ ˆ χD . in-medium Ds as a probe of O(4)!

slide-12
SLIDE 12

Lattice observables - consistent with the model

2 2.5 3 3.5 100 150 200 250 300 350 400 450 500 M [GeV] T [MeV] sc

  • 1+

0+ 1− 0−

  • 0.1

0.0 0.1 0.2 0.3 0.4 0.5 160 180 200 220 240 260 280 300 320 340 T [MeV] χuc

mn/χc 2

HTLpt EQCD m n: 22 13 31 11

T [MeV] c1/pC c3/pC c2/pC c4/pC

  • 1.0
  • 0.5

0.0 0.5 1.0 150 170 190 210 230 250 270 290 310 330

  • screening Ds masses

[Bazavov et al. (’14)] - the same tend

  • 4th-order c-s corr.: survival Ds up to T = 1.2Tch

[Mukherjee et al. (’15)]

Ds changes its property - medium modification sets in at ∼ Tch.

  • fluctuations and correlations of conserved charges X

χ(non−reg)

X

= FX(σq,s, Dq,s; χch) 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)
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SLIDE 13

Summary

  • Synthesis of light and heavy quark dynamics

mq mc , ms mc , T mc ≪ 1

heavy quark symmetry as a reliable guide – at Tpc: chiral mass splittings of HL mesons insensitive to light flavors. δMD,B ≃ δMDs,Bs vs. δMπ-σ ≪ δMK-κ – remnant of O(4) in HL mixed fluctuations. – anomalous suppression of Ds decay widths as a sign of CSR in-medium Ds 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