CHIRAL DYNAMICS and NUCLEAR MATTER Wolfram Weise ECT * Trento and T - - PowerPoint PPT Presentation

CHIRAL DYNAMICS and NUCLEAR MATTER

Wolfram Weise

ECT* Trento and Technische Universität München

EMMI Workshop “Cold Dense Nuclear Matter: from Short-Range Nuclear Correlations to Neutron Stars” GSI 15 October 2015

Chiral EFT approaches to nuclear many-body systems Nuclear matter, neutron matter and neutron stars Beyond mean field: fluctuations and Functional Renormalisation Group Thermodynamics of the chiral order parameter Pion mass in the nuclear medium

1

Outlook: Chiral SU(3) dynamics and hypernuclear matter

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

PHASES and STRUCTURES of QCD

• facts and visions -
• J. Wambach,
• K. Heckmann,
• M. Buballa

arXiv:1111.5475v2 [hep-ph]

? ? ?

2

   

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                  

              



CHIRAL PHASE TRANSITION

? ?

CHIRAL SYMMETRY RESTORATION

from Nambu-Goldstone to Wigner-Weyl Realisation of Chiral Symmetry PHASE TRANSITION or smooth CROSSOVER ?

T [MeV]

P MeV fm3

• nuclear

physics terrain

Chiral first-order phase transition and critical point ?

. . . based on chiral quark models which do not respect nuclear physics constraints

Needed: systematic approach to nuclear thermodynamics

.

3

PIONS, NUCLEONS and NUCLEI in the context of LOW-ENERGY QCD CONFINEMENT of quarks and gluons in hadrons Spontaneously broken CHIRAL SYMMETRY LOW-ENERGY QCD with light (u,d) quarks: Effective Field Theory of (weakly) interacting Nambu-Goldstone Bosons (pions)

Q << 4π fπ ∼ 1 GeV

Chiral EFT represents QCD at energy/momentum scales Strategies at the interface between QCD and nuclear physics : In-medium Chiral Perturbation Theory based on non-linear sigma model (with inclusion of nucleons) Chiral Nucleon-Meson model based on linear sigma model

non-perturbative Renormalization Group approach expansion of free energy density in powers of Fermi momentum

4

¯ K∗

¯ K

ρ

π

a1

0.5 1.0 mass [GeV]

0− 1−

1+

Goldstone Boson Dipole Axial Dipole

Goldstone Boson

mesons baryons

1 2

+

3 2

+

N

ω

∆

VACUUM condensates

Goldstone Gap

4π fπ

GAP

0+

f0

ρ, ω

Spontaneously Broken CHIRAL SYMMETRY

PION

Characteristic Symmetry Breaking SCALE: PION DECAY CONSTANT

π

µ

ν

Axial current

4π fπ ∼ 1 GeV

Triplet

• f

NAMBU - GOLDSTONE BOSONS:

π+, π0, π−

5

fπ = 92.2 ± 0.2 MeV

6

SCALES and SCHEMES

1 GeV

Q

Λχ = 4π fπ

(energy / momentum)

UV IR

0.5

mπ

λ ⌧ Λχ, mσ

LINEAR SIGMA MODEL NON-LINEAR SIGMA MODEL Chiral EFT

π, σ

N0

N

π

Vlow−k

DOMAIN

Nuclear Physics

. .

UV IR

Renormalization Group Achim Schwenk’s talk

1.0 2.0 1 2 3 4

ρ(b)

[fm−2]

b [fm] xB = 0.1

0.5

1 2 3 1.0

ρ(b)

[fm−2]

0.5

b [fm]

xB = 0.44

,

→ PROTON

and “old”

• D
• D
• D

=

• Transverse distributions of quarks in the proton

core - plus - cloud structure ?

• M. Guidal, H. Moutarde, M.

Vanderhaeghen

• Rep. Prog. Phys. 76 (2013) 066202

valence + sea quarks

7

(core + (pion) cloud)

x = 0.1 x = 0.4

Q2 = 2.5 GeV2 Deeply Virtual Compton Scattering (expectations for DVCS @ JLab - 12 GeV) compact core: valence quarks b < 0.5 fm

V

1 2 3 I II III

r [µ−1]

π

N N

• ne-pion exchange

π

π

two-pion exchange N short distance N

NN potential

N N N N

π π π

• ne-pion

exchange two-pion exchange

Chiral Effective

Field Theory & Lattice QCD

contact terms

explicit treatment of NN Central Potential from Lattice QCD

• S. Aoki, T. Hatsuda, N. Ishii
• Prog. Theor. Phys. 123 (2010) 89

NN Interaction

two-pion exchange

Hierarchy of SCALES

r [m−1

π ]

8

Interacting systems of PIONS (light / fast) and NUCLEONS (heavy / slow): + + . . .

π π

N N

+

π

π

Leff = Lπ(U, ∂U) + LN(ΨN, U, ...)

U(x) = exp[iτaπa(x)/fπ]

CHIRAL EFFECTIVE FIELD THEORY

Construction of Effective Lagrangian: Symmetries short distance dynamics: contact terms Realization of Low-Energy QCD based on Non-Linear Sigma Model plus (heavy) baryons

9

NUCLEAR INTERACTIONS from CHIRAL EFFECTIVE FIELD THEORY

Weinberg Bedaque & van Kolck Bernard, Epelbaum, Kaiser, Meißner; . . .

O Q0 Λ0

• O

Q2 Λ2

• O

Q3 Λ3

• O

Q4 Λ4

• Systematically organized HIERARCHY

10

Explicit DEGREES of FREEDOM

∆(1230)

Large spin-isospin polarizability of the Nucleon

β∆ = g2

A

f 2

π(M∆ − MN) ∼ 5 fm3

M∆ − MN ≃ 2 mπ << 4π fπ

(small scale)

N N

π π

∆

strong 3-body interaction

N

N

N

π π

Dominance of Pionic Van der Waals - type intermediate range central potential

• N. Kaiser, S. Fritsch, W. W. , NPA750 (2005) 259
• N. Kaiser, S. Gerstendörfer, W. W. , NPA637 (1998) 395

Vc(r) = − 9 g2

A

32π2 f 2

π

β∆ e−2mπr r6 P(mπr)

• J. Fujita, H. Miyazawa (1957)

Pieper, Pandharipande, Wiringa, Carlson (2001)

N ∆

∆(1230) in pion-nucleon scattering

11

π+p

plab [GeV/c]

σtot [mb]

Explicit DEGREES of FREEDOM (contd.)

∆(1230)

Kaiser et al. , Ordonez et al. Krebs, Epelbaum, Meißner (2007)

Important physics of ∆(1230) promoted to NLO Improved convergence

12

13

Important :

Explicit treatment of two-pion exchange dynamics

+

contact terms

N, ∆

+

3-body forces

π

π

N N N N

+

contact terms

+

“Discovery” of two-pion exchange at LHC: elastic pp scattering at deviation from standard exponential behaviour

dσ dt ∝ ebt

−0.05 −0.04 −0.03 −0.02 −0.01 0.01 0.02 0.03 0.04 0.05 0.06 dσ/dt − ref ref , ref = 527.1 e−19.39 |t| 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 |t| [GeV2] data, statistical uncertainties full systematic uncertainty band

• syst. unc. band without normalisation

Nb = 1 Nb = 2 Nb = 3

P P P

π π

• G. Antchev et al. (TOTEM coll.)
• Nucl. Phys. B 899 (2015) 527
• L. Jenkovszky, A. Lengyel

Acta Phys. Pol. B 46 (2015) 863

• V. A. Khoze, A.D. Martin,

M.G. Ryskin

• J. Phys. G 42 (2015) 025003

√s = 8 TeV Short digression:

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 r [fm]

• 400
• 300
• 200
• 100

100 200 [MeV]

π

π+2π

N

N N

π π

nge

N N

π

∆(1232)

Isovector Tensor Potential

[MeV] VT r [fm]

Important pieces of the CHIRAL NUCLEON-NUCLEON INTERACTION

ISOVECTOR TENSOR FORCE

s1 s2 VT

note: no meson CENTRAL ATTRACTION from TWO-PION EXCHANGE

N

N N

π π

note: no boson

σ ρ

Van der WAALS - like force:

Vc(r) ∝ −exp[−2mπr] r6 P(mπr)

... at intermediate and long distance

• N. Kaiser, S. Gerstendörfer, W.W. : Nucl. Phys. A 637 (1998) 395

∆(1232)

14

Expansion of ENERGY DENSITY powers of Fermi momentum

E(kF)

Loop expansion of (In-Medium) Chiral Perturbation Theory

[modulo functions fn(kF/mπ)

in

]

IN-MEDIUM CHIRAL PERTURBATION THEORY Nuclear thermodynamics: compute free energy density

(3-loop order)

• N. Kaiser, S. Fritsch, W. W.

(2002-2004)

in-medium nucleon propagators

• incl. Pauli blocking

Small scales:

mπ, kF << 4πfπ ∼ 1 GeV energy, momentum,

15

“Medium insertion” in the nucleon propagator:

(γµpµ + MN)

• i

p2 − M2

N + iε − 2π δ(p2 − M2 N) θ(p0) θ(kF − |⃗

p)

• |~

p|)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

[

• 3]
• 20
• 10

10 20 30 40 50

0.1 0.2 0.3 0.4 20 40 −20 ρ [fm−3] E/A [MeV]

empirical 3-body + Pauli

• S. Fritsch, N. Kaiser, W. W.
• Nucl. Phys. A 750 (2005) 259

In-medium ChPT

(π, N, ∆)

basically: analytic calculation Input parameters: few contact terms Binding, saturation

Realistic (complex, momentum dependent) single-particle potential

Asymmetry energy

Fermi Liquid Theory:

Quasiparticle interaction and Landau parameters 3-loop

T = 0

J.W. Holt, N. Kaiser, W. W. (2011 - 2013) Recent reviews: J.W. Holt, N. Kaiser, W. W. Prog. Part. Nucl. Phys. 73 (2013) 35 J.W. Holt, M. Rho, W. W. arXiv:1411.6681, Phys. Reports (2015)

• C. Wellenhofer, J.W. Holt,
• N. Kaiser, W. W.
• Phys. Rev. C 89 (2014) 064009

Nuclear Energy Density Functional and finite nuclei

16

NUCLEAR MATTER

Nuclear thermodynamics: liquid-gas phase transition

... satisfying Hugenholtz - van Hove and Luttinger theorems (!)

0.05 0.1 0.15 0.2

ρ [fm

• 3]
• 1

1 2 3 4

P [MeV/fm

3] T=0MeV T=5MeV T=10MeV T = 1 5 M e V T=20MeV T = 2 5 M e V

T = 0 T = 25 MeV 20 15 10 5

NUCLEAR THERMODYNAMICS

π

π

N N N N

+

Van der Waals + Pauli contact terms Liquid - Gas Transition at Critical Temperature T = 15 MeV

c c

(empirical: T = 16 - 18 MeV) baryon density pressure nuclear matter: equation of state NUCLEAR CHIRAL (PION) DYNAMICS

N, ∆

BINDING & SATURATION: 3-loop in-medium ChEFT

+ 3-body

forces

17

! !"!# !"!$ !"!% !"!& !"' !"'# !"'$ !"'%

! # $ % & '! '# '$ '%

()*+,+-./0.1

• ./0.1

()* ()*

!"234,56

7+289:6

;90<=>?+3=)@<.>?+A+!"B!

gas gas liquid N = Z

PHASE DIAGRAM of NUCLEAR MATTER

In-medium chiral effective field theory

(3-loop calculation of free energy density)

Pion-nucleon dynamics including delta isobars Short-distance NN contact terms Three-body forces

• S. Fritsch, N. Kaiser, W. W.
• Nucl. Phys. A 750 (2005) 259
• S. Fiorilla, N. Kaiser, W. W.
• Nucl. Phys. A 880 (2012) 65

916 918 920 922 2 4 6 8 10 12 14 16

Critical point

m [MeV]

T [MeV]

gas

liquid

gas

liquid gas gas critical point symmetric (N = Z) nuclear matter

µB [MeV]

baryon chemical potential temperature T [MeV]

18

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 2 4 6 8 10 12 14 16

Neutron fraction 0.5 Neutron fraction 0.6 Neutron fraction 0.7 Neutron fraction 0.8 Neutron fraction 0.9 Neutron fraction 0.947 Critical points

r [fm-3]

T [MeV]

. . . . . .

N Z = 0.5

0.6 0.7 0.8 0.9 0.95

Z A = 0.5

0.4 0.3 0.2 0.05 0.1

PHASE DIAGRAM of NUCLEAR MATTER

Trajectory of CRITICAL POINT for asymmetric matter . . . determined almost completely by isospin dependent (one- and two-) pion exchange dynamics

as function of proton fraction Z/A

• S. Fiorilla, N. Kaiser, W. W.
• Nucl. Phys. A880 (2012) 65

19

0.1 0.2 0.3 0.4 0.5

Neutron Density (fm

• 3)

20 40 60 80 100 120

Energy per Neutron (MeV)

Esym = 33.7 MeV

different 3N

E/N [MeV]

20 40 60 80 100 120

ρn [fm−3]

3N

0.1 0.2 0.3 0.4 0.5 ChEFT QMC

J.W. Holt, N. Kaiser, W. W.

• Phys. Rev. C 87 (2013) 014338

NEUTRON MATTER

In-medium chiral effective field theory (3-loop) with resummation of short distance contact terms (large nn scattering length, as = 19 fm) agreement with sophisticated many-body calculations

(e.g. recent Quantum Monte Carlo computations )

Neutron matter behaves almost (but not quite) like a unitary Fermi gas Bertsch parameter

ξ = ¯ E EFermi gas ≃ 0.5

• S. Gandolfi et al.

EPJ A50 (2014) 10

20

F(⃗ p1, ⃗ p2) = f(⃗ p1, ⃗ p2) + g(⃗ p1, ⃗ p2)⃗ σ1 · ⃗ σ2 + h(⃗ p1, ⃗ p2)S12(ˆ q) +

δE =

• ⃗

pst

ϵ⃗

p δn⃗ pst + 1

2

• ⃗

p1s1t1 ⃗ p2s2t2

F(⃗ p1s1t1; ⃗ p2s2t2)δn⃗

p1s1t1δn⃗ p2s2t2 + · · · ,

0.05 0.1 0.15 0.2 ρ [fm

• 3]

10 20 30 40 E/A [MeV] V2N+V3N (2.1 fm

• 1)

V2N+V3N (2.5 fm

• 1)

APR QMC

Chiral Fermi Liquid Approach to Neutron Matter

Quasiparticle interaction based on accurate NNLO chiral nucleon-nucleon interaction including three-body forces: . . . Chiral NN + 3N V(low-k) + 3N

J.W. Holt, N. Kaiser, W. W.

• Phys. Rev. C 87 (2013) 014338
• S. Gandolfi et al.

PRC80 (2009) 045802

Quantum Monte Carlo calculations with ChEFT Interactions exhibit systematic order-by-order convergence

• A. Gezerlis et al.
• Phys. Rev. Lett. 111 (2013) 032501

Akmal et al. 1998

21

Chiral Nucleon-Meson Model

(based on Linear Sigma Model)

and Functional Renormalization Group

22

Mesons, Nucleons, Nuclear Matter and Functional Renormalization Group

Chiral nucleon - meson model Effective potential constructed to reproduce standard nuclear thermodynamics around equilibrium Mean field calculations

• S. Floerchinger, Ch. Wetterich : Nucl. Phys. A 890-891 (2012) 11
• M. Drews, T. Hell, B. Klein, W. W. Phys. Rev. D88 (2013) 096011

and neutrons are combined field ψ = (ψp, ψn)T . the repulsive short-range

Mesonic and nucleonic particle-hole fluctuations treated non-perturbatively using FRG

• M. Drews, W. W. Phys. Lett. B738 (2014) 187 Phys. Rev. C91 (2015) 035802

L = ¯ ψiγµ∂µψ + 1 2∂µσ ∂µσ + 1 2∂µπ · ∂µπ − ¯ ψ

• g(σ + iγ5 τ · π) + γµ(gω ωµ + gρτ · ρµ)

⇥ ψ − 1 4F (ω)

µν F (ω)µν − 1

4F (ρ)

µν · F (ρ)µν

+1 2m2

V (ωµωµ +

)

2 ρ ρµ · ρµ

µ − U(σ, π),

23

200 400 600 800 1000 Μ MeV⇥ 50 100 150 200 T MeV⇥

.

line of constant density

ρ = 0.15 ρ0

nuclear liquid-gas phase transition

CHEMICAL FREEZE-OUT

Chemical freeze-out in baryonic matter at T < 100 MeV is not associated with (chiral) phase transition or rapid crossover

• S. Floerchinger, Ch. Wetterich : Nucl. Phys. A 890-891 (2012) 11
• A. Andronic,

P . Braun-Munzinger,

• J. Stachel
• Phys. Lett.

B 673 (2009) 142 B 678 (2009) 516

empirical freeze-out

from HI experiments

chiral crossover Chiral nucleon - meson model in mean-field approximation

24

Fixing the input: some comments

Potential

U(σ, π) = U0(χ) − m2

πfπ(σ − fπ)

chiral invariant part

parametrized in powers of

U0 square χ = 1

2(σ2 + π2),

breaking term:

explicit chiral symmetry breaking Vector fields encode short-distance NN dynamics,

(NOT to be identified with physical and mesons)

ω

ρ

self-consistently determined background mean fields (non-fluctuating)

Scalar (“sigma”) field

has mean-field (chiral order parameter) and fluctuating pieces. mass: NOT to be identified with pole in I = 0 s-wave pion-pion T matrix

Effective chemical potentials

µeff

n,p(

) = µn,p − gω ω0(

) ± gρ ρ3

0(

Relevant quantities:

Gρ = g2

ρ

m2

V

Gω = g2

ω

m2

V

contact terms in ChEFT

,

σ

Nucleon mass: m2

N = 2g χ

. . . in vacuum: mN = g fπ

Parameters: 2 coefficients in ,

U0

mσ ≃ 0.8 GeV , Gρ ∼ Gω/4 ≃ 1 fm2 determined by nuclear matter properties and symmetry energy

25

“σ(500)”

k ∂Γk ∂k = = 1 2 Tr k ∂Rk

∂k

Γ(2)

k

+ Rk .

Chiral nucleon-meson model beyond mean-field

Fluctuations: Wetterich’s RG flow equations

Rk(p2) = (k2 − p2) θ(k2 − p2)

k ∂k¯ Γk(T, µ) =

• +

⇤ ⇤ ⇤ ⇤ ⇤

T,µ

• +

⇤ ⇤ ⇤ ⇤ ⇤

T =0,µ=µc

(18)

Thermodynamics:

full propagator

• M. Drews, T. Hell, B. Klein, W. W. Phys. Rev. D 88 (2013) 096011

nucleons pions

effective action scale regulator:

• C. Wetterich:
• Phys. Lett. B 301 (1993) 90

T, µp, µn

T = 0, µ = µ0 (= mN − E0/A)

multi-pion exchange processes nucleon-hole excitations multi-nucleon correlations

26

Renormalization Group strategies

Non-perturbative treatment of

−

• i=n,p

4

1 2

k∂Uk,χ ∂k (T, µp, µn, χ, ω0, ρ3

0) =

1

tras

in M The 1 2

+

UV scale:

=

k5 12π2

• ⇧

⇤

1 + 2nB(Eσ) Eσ

+

3 1 + 2nB(Eπ)

⌦

Eπ

− 4

1 4 1 −

1 nF(EN − rµi,eff)

⌦

⌥

±

− EN

anal

)

⌦⇥ ⌃ ⌅,

. . . plus vector field equations, then full system of equations solved on a grid.

effective potential

Flow equations in practice

E2

π = k2 + U ⇤ k(χ) , E2 σ = k2 + U ⇤ k(χ) + 2χ U ⇤⇤ k (χ) ,

U ⇤

k(χ) = ∂Uk(χ)

∂χ , E2

N = k2 + 2g2χ ,

µeff

n,p(k) = µn,p − gω ω0(k) ± gρ ρ3 0(k) ,

− nB(E) = 1 eE/T −1 ,

Uk=0

± and nF(E) = 1 eE/T +1 . (9)

“full” effective action

. .

Γk=Λ Γk Γk=0

27

Λ ' Λχ = 4π fπ IR

0.0 0.5 1.0 1.5 2.0 2.5 3.0 20 10 10 20 n n0 E A

• FIG. 1. The energy per particle of symmetric nuclear matter com-

puted in the FRG-nucleon-meson-model (solid line) as compared to the Akmal-Pandharipande-Ravenhall EoS (dotted, [28]). and a QMC computation (dashed, [39])

Symmetric nuclear matter in the chiral FRG approach

• M. Drews, T. Hell, B. Klein, W. W.
• Phys. Rev. D 88 (2013) 096011

energy per nucleon at T = 0

FRG-Nucleon-Meson-Model (solid curve) in comparison with advanced many-body (variational and QMC) computations

density ρ/ρ0

28

900 910 920 930 940 5 10 15 20 25 Μ MeV⇥ T MeV⇥

ΧEFT mean field RG

0.0 0.2 0.4 0.6 0.8 1.0 5 10 15 20 25 Ρ⇤Ρ0 T MeV⇥

RG mean field ΧEFT

Results : Liquid - Gas Transition

• symmetric nuclear matter -
• M. Drews, T. Hell, B. Klein, W. W.
• Phys. Rev. D 88 (2013) 096011

close correspondence between (perturbative) in-medium ChEFT and (non-perturbative) FRG results

29

Asymmetric nuclear matter in the chiral FRG approach

FRG results (non-perturbative) are remarkably similar to (perturbative) in-medium Chiral EFT calculations

0.0 0.5 1.0 1.5 2.0 2.5 3.0 20 10 10 20 30 n n0 E A

0.5 0.4 0.3 0.2 0.1 x = 0

proton fraction

0.0 0.2 0.4 0.6 0.8 1.0 5 10 15 20 n n0 T MeV

0.5 0.4 0.3 0.2 0.1 x = 0.045

Liquid-gas phase transition:

evolution of coexistence regions from symmetric to asymmetric nuclear matter

• M. Drews, W. W. Phys. Lett. B738 (2014) 187 Phys. Rev. C91 (2015) 035802

critical point

ρ/ρ0 ρ/ρ0

30

900 910 920 930 940 950 960 1.00 1.05 1.10 1.15 1.20 Μ MeV mΠ, n mΠ

.

In-medium pion mass

Test case and contact with phenomenology : compare with s-wave pion-nuclear optical potential from pionic atoms chiral FRG result

. .

Good agreement of FRG calculation with empirical in-medium pion mass shift, both in sign and magnitude

small dominant

mπ(µ) mπ

π π

N N

U(ρ) = − 2π mπ  bo − (b2

0 − 2b2 1)

⌧1 r

• ρ

mπ(ρ) mπ ' 1 + U(ρ) mπ ' 1.1 ρ ρ0

ρ0 = 0.16 fm−3 ρ = 1.25 ρ0

31

phenomenology:

π−

In-medium pion mass (contd.)

ChEFT RG linear density

FRG ChEFT

LO (b0 term)

mπ(n) mπ(vac) density n/n0

Non-perturbative FRG result in comparison with in-medium Chiral Perturbation Theory

. . .

. . .

• S. Goda, D. Jido:

PTEP (2014) 33D03

“mean field” “fluctuations”

• M. Drews, W. W.
• Phys. Rev. C91 (2015) 035802

ρ/ρ0

mπ(ρ) mπ(vac)

32

• =

mπ

• 1 + ρ b+

2m2

π

− g2

Ak4 F

24π4f 4

π

F( mπ 2kF ) + 1 8 + m2

π

b+ 2m2

π

− g2

A

8mN 2 2k4

F

π4f 4

π

• ECs, B , c , c , c , have been determined by the in-vacuum physical quan

m∗

π

in-medium ChEFT (NLO):

π−

0.00 0.05 0.10 0.15 0.20 0.25 0.0 0.2 0.4 0.6 0.8 1.0 n fm3⇥ ⌅ ⇤ f⇤

RG ⇥EFT 910 920 930 940 950 0.0 0.2 0.4 0.6 0.8 1.0 Μ MeV⇥ Σ ⇤ fΠ RG ΧEFT

0.65 0.7 0.7 0.75 0.8 0.85 0.9 700 750 800 850 900 950 20 40 60 80 100 Μ MeV⇥ T MeV⇥

Comparison of chiral effective field theory and NM-FRG results

Chiral Order Parameters

No tendency towards chiral phase transition

for baryon chemical potentials and temperatures

contour plots of

density dependence

• f chiral order parameters

T = 0 dependence of chiral order parameters

• n baryon chemical potential

T = 0

µ 1 GeV

T 100 MeV

• M. Drews, T. Hell, B. Klein, W. W.
• Phys. Rev. D 88 (2013) 096011

density

σ(T, µ) fπ

σ fπ σ fπ

ρ [fm−3]

σ(T = 0, ρ) fπ

h¯ qqiρ h¯ qqi0

33

920 925 930 935 940 945 950 955 0.0 0.2 0.4 0.6 0.8 1.0 Μ MeV Σ fΠ 1 2 3 4 5 6 7 0.0 0.2 0.4 0.6 0.8 1.0 n ê n0 Σ ê fΠ

Chiral Order Parameter

mean field

FRG

65 70 75 80 85 90 95 2 1 1 2 3 Σ MeV Uk0 MeV fm3 µ = 930 MeV µ = 923 MeV µ = 915 MeV

symmetric nuclear matter neutron matter

effective potential

important role of fluctuations beyond mean-field approximation: DISAPPEARANCE of first-order chiral phase transition FRG

mean field

density

fπ

σ0

σ fπ

σ fπ

• M. Drews, W. W.
• Phys. Rev. C91 (2015) 035802

ρ/ρ0

34

News from NEUTRON STARS

35

quark matter ??

STRANGE QUARK MATTER NUCLEONIC MATTER

New constraints from 2-solar-mass NEUTRON STARS

36

• J. Antoniadis et al.

Science 340 (2013) 6131

New constraints from NEUTRON STARS

M = 2.01 ± 0.04

.8 M⇥ conditions

PSR J0348+0432

P .B. Demorest et al. Nature 467 (2010) 1081

Shapiro delay measurement

Text

PSR J1614+2230

.8 M⇥ conditions

M = 1.97 ± 0.04

37

8 10 12 14 16 18 0.0 0.5 1.0 1.5 2.0 R km

[1, 2] constraints [3] constraints [37] M/M

NEUTRON STAR MATTER from Chiral Nucleon-Meson Approach and FRG

Neutron matter plus proton admixture (beta equilibrium) Symmetry energy range: 30 - 37 MeV

Chiral FRG

Trümper constraint

• Prog. Part. Nucl. Phys.

66 (2011) 674

• M. Drews, W. W.
• Phys. Rev. C91 (2015) 035802

Lattimer-Steiner constraint

EPJ A50 (2014) 40

ChEFT

• T. Hell, W. W.
• Phys. Rev.

C90 (2014) 045801

Chiral many-body dynamics using “conventional” (pion & nucleon) degrees of freedom is consistent with neutron star constraints

38

2 4 6 8 10 12 1 2 3 4 5 r km n n0

No ultrahigh densities in the neutron star core

Density profile of two-solar-mass neutron star

• M. Drews, W. W.
• Phys. Rev. C91 (2015) 035802

ρmax ∼ 5 ρ0

ρ(r) ρ0

(ρ0 = 0.16 fm−3)

r [km]

39

Chiral FRG calculation

maximum n-star core density:

0.5 fm 1.2 fm baryonic core pionic field ρB = 0.6 fm−3

normal nuclear matter: dilute

0.5 fm 2 fm baryonic core pionic field ρB = 0.15 fm−3

iriirr .rqr ur tsol sr ruJ s'0

• -w l2t salBcs

qfual le sJrs,(qd luBuodur leql .re^e,{oq :\,:'.qo {l ll'slapou ed,{1-auu,{19 ur oseJ eql lcBJ ur sr srql .rBeddEstp plno,t\ \tr:jii:rp srql 'oo <='w r4]ln r.uopso{ 3o saa.rEap uosetu Jolce^ .,u3zo{,, Jo lrurl eql r :rrt rtr)\'uorlnqrrlsrp reqr.unu uo,{reg

• ql qlr^\ uoloqd rEIeJSosr
• ql slceuuoc

:.Ut. .roi!Lu-ra Eurle8edord eql ol onp,{ldrurs sr (!.r) pue s(];) uae,,n1eq ecueJogrp ir::t:uir. aql'tuJ6t'O:s(?l) lecurdrue aql qlr,^d luaruea:3u pooE fra,L ul .ruJg.0 ' ,u .r.rrctgo auo'(lepour lur.uturul) I olqel ur se ruJ9.g=.r,($.r):Hl qlr^\

• cueH

'ltu ' (o,r) + " "9 ,{q ,{lrsuap Joqrunu uo,{req

• r{l

Jo (gl): rl.l snrpur arunbs ueeu eql ol r:ri:r \r trll) snrper eSreqc Jel€csosr

• renbs

ueotu eql teql ,(lalerpauur s,rolloJ 1I ' lt yog 1tb 1,t[-t tp " | ,!+?*

• '

' J i * u z 1 t 1 ,

• 1

f t t ' , [ r t t p " l + , : ( , b ) ] c

, (r),,g8i: e)or(Iw _.L)

:(lopou letururtu :cgt.E) uorlenba plog uosaru_r, iur..1 '1egg'7) rope3 ruro3 e3:eqc releJsosr

• r{l

reprsuoc,srql elerlsnllr

• 1

'uolrlos eql eprsur raqlunu uo,{:eq Jo uorlnqrr}stp \.rlnieeru Hcrr{rrr.r,(!.r):H/ sntper eql ueqlraE.rul ,(lgeraptsuoJ sr uoloqd eqt.{q

'plau uosoru-o aqt .iq paunu:a1ep Xlrsuap

• ' 'jl\)l)

rpleJsost aqt o1 saldnol uotoqd:e;ersost aql sealJq\\.{llsuap:B.reqt uo,{.rcq petrlp[!Jou . , I/ rl0H lapou leulultu oql JoJ (Itrun ot pazlleurou) suortnqlrlsrp a8:eq:r:elucsosl S.ilC Ir!J]r

aL 0r 80 90 t0 z0

Z [' u]l

\uoluos awtt$ls sD ''uoapnN I 'lD D /Duss!aI,! .c_.n 01rJ,4 UeC 3,4A

1 2 0.2 0.4 0.6 0.8 1.0 1.2 r [fm] [fm−1] 4πr2 ρB(r) 4πr2 ρS(r)

charge density

baryon density isoscalar

Densities and Scales in Compressed Baryonic Matter

neutron star core matter: compressed but not superdense chiral (soliton) model

• f the nucleon

compact baryonic core mesonic cloud in-medium pion field treated properly in chiral EFT

• N. Kaiser, U.-G. Meißner, W. W.
• Nucl. Phys. A 466 (1987) 685

⟨r2⟩1/2

B

≃ 0.5 fm ⟨r2⟩1/2

E,isoscalar ≃ 0.8 fm

40

Fluctuations beyond mean field include important multi-pion exchange mechanisms and low-energy nucleonic particle-hole excitations Chiral Effective Field Theory and Functional Renormalization Group: Nuclear Chiral Dynamics and Thermodynamics from symmetric to asymmetric nuclear matter and neutron (star) matter

SUMMARY

New constraints from neutron stars for the equation-of-state

• f dense & cold baryonic matter:

Mass - radius relation: stiff equation of state required ! No ultrahigh densities Conventional (nucleon-meson, “non-exotic”) EoS meets constraints Issue of strangeness: suppression of hyperons in neutron stars ?) No indication of first-order chiral phase transition

(ϱmax ∼ 5 ϱ0)

1st order phase transition: Fermi liquid interacting Fermi gas Fluctuations work against early restoration of chiral symmetry

41

42

Appendix:

HYPERONS in NEUTRON STARS

NEUTRON STAR MATTER including HYPERONS

with inclusion of hyperons: EoS too soft to support 2-solar-mass star unless strong short-range repulsion in YN and / or YNN interactions

M [M0] R [km] PNM N N + NN (I) N + NN (II) 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 11 12 13 14 15

PSR J1614-2230 PSR J0348+0432 n − matter

ΛN

ΛN

ΛN

ΛNN(1) ΛNN(2)

+ +

ChEFT QMC

R [km] M MO

.

• T. Hell, W.W.

PRC90 (2014) 045801

New Quantum Monte Carlo calculations using phenomenological hyperon-nucleon and hyperon-NN three-body interactions constrained by hypernuclei

• D. Lonardoni,
• A. Lovato,
• S. Gandolfi,
• F. Pederiva
• Phys. Rev. Lett.

114 (2015) 092301

Mass - radius relation of neutron stars QMC computations (hyper-neutron matter): ChEFT calculations (“conventional” n-star matter):

43

Hyperon - Nucleon Interaction

from CHIRAL SU(3) Effective Field Theory

LO NLO

Λ

Λ

Λ

Λ

Λ

Λ N

N

N

N

N

N K

π π

Σ

N

LO NLO repulsion LO phase shift NLO

moderate attraction at low momenta relevant for hypernuclei strong repulsion at higher momenta relevant for dense baryonic matter

• J. Haidenbauer, S. Petschauer, N. Kaiser,

U.-G. Meißner, A. Nogga, W. W.

• Nucl. Phys. A 915 (2013) 24

44

0.8 1.0 1.2 1.4 1.6 1.8 2.0 kF [fm−1] −80 −70 −60 −50 −40 −30 −20 −10 UΛ(kΛ = 0) [MeV]

χEFT LO 650 χEFT NLO 650 Nijmegen ’97

Density dependence of single particle potential

Λ

0.6 0.8 1.0 1.2 1.4 1.6 kF (1/fm)

• 60
• 45
• 30
• 15

UΛ (MeV)

LO NLO LO NLO

hypernuclei Brueckner calculations

using chiral SU(3) interaction

G(Ê) = V + V Q e(Ê) + i‘G(Ê)

= +

G G

Λ

Λ

dense matter

• J. Haidenbauer, U.-G. Meißner,
• Nucl. Phys. A 936 (2015) 29
• S. Petschauer, J. Haidenbauer, N. Kaiser, U.-G. Meißner, W. W.

EPJA (2015) ; arXiv:1507.08808 [nucl-th] 45

46

Supplementary Materials

ChEFT, resummed ⇤n , p , e , ⌅⌅ PNJL, Gv ⇥ 0.7 G , T ⇥ 0 MeV ⇤d , u , e⌅ ⇤d , u , e⌅ PNJL, Gv ⇥ 0 , T ⇥ 0 MeV SLy , FKW , polytropes

10 20 50 100 200 500 1000 0.1 1 10 100 ⇤ MeV fm 3⇥ P MeV fm 3⇥

pressure energy density

(n, p, e, µ)

Gv/G = 0.7 (d, u, e)

Gv = 0 (d, u, e) “green belt” permitted by M(R) constraints realistic “conventional” nuclear EoS PNJL with vector coupling PNJL without vector coupling quark-nuclear matching region

NEUTRON STAR Equation of State

(2 versions of 2-flavor chiral quark models) 2 flavors (no strangeness)

47

• T. Hell, W. W.
• Phys. Rev.

C90 (2014) 045801

ChEFTPNJL, Gv ⇤ 0.5 G, ⇤d, u, e⌅ ChEFTPNJL, Gv ⇤ 0, ⇤d, u, e⌅ SLy, FKW, polytropes

50 100 200 300 500 1000 2000 1 5 10 20 100 200 ⌅ MeV fm⇥3⇥ P MeV fm⇥3⇥

“green” and “blue”belts permitted by M(R) constraints

Chiral EFT EoS quark-nuclear coexistence (3-flavor PNJL)

Gv = 0.5 G Gv = 0

• T. Hell, W. W.

(2013) preliminary

NEUTRON STAR MATTER Equation of State

In-medium Chiral Effective Field Theory up to 3 loops

(reproducing thermodynamics of normal nuclear matter) coexistence region: Gibbs conditions

n ↔ p + e, µ

3-flavor PNJL model at high densities (incl. strange quarks)

beta equilibrium charge conservation quark-nuclear coexistence occurs (if at all) at baryon densities

ρ > 5 ρ0

48

• T. Hell, W. W.
• Phys. Rev. C90 (2014) 045801

100 1000 1 10 100 1000

P [MeV fm−3] E [MeV fm−3]

8 10 12 14 16 0.5 1 1.5 2 2.5 3

causality causality

Mass [M] Radius [km]

NEUTRON STAR MATTER Equation of State

Further independent analysis of new constraints from n-stars (Chiral EFT EoS and polytrope extrapolation)

• K. Hebeler, J.M. Lattimer, C.J. Pethick, A. Schwenk Astrophys. J. 773 (2013) 11

49