Collaborators: Bao-Jun Cai, Lie-Wen Chen, Chang Xu, Jun Xu, Zhi-Gang Xiao and Gao-Chan Yong

1. Probing High-Density Symmetry Energy with Heavy-Ion Reactions Bao-An Li Collaborators: Bao-Jun Cai, Lie-Wen Chen, Chang Xu, Jun Xu, Zhi-Gang Xiao and Gao-Chan Yong

2. Outline • What is symmetry energy? • Why is it so uncertain especially at high densities? • (e.g., effects of short-range nucleon-nucleon correlation) • How to probe high-density symmetry energy with heavy-ion reactions? • (e.g., near-threshold pion production) • Is there a degeneracy between the high-density EOS and strong-field gravity (e.g., the recently reported detection of a 17 MeV U boson)? neutrons

3. EOS of cold, neutron-rich nucleonic matter symmetry energy Isospin asymmetry δ 12 12 12 Energy per nucleon in symmetric matter 18 18 3 Energy in asymmetric nucleonic matter Symmetric matter ρn=ρp ? ?? density Strangeness The axes of new opportunities Isospin asymmetry ???

4. The multifaceted influence of the isospin dependence of strong interactionand symmetry energy in nuclear physics and astrophysicsJ.M. Lattimer and M. Prakash, Science Vol. 304 (2004) 536-542.A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005). (Effective Field Theory) (QCD) isodiffusion n/p Isospin physics π-/π+ isotransport in isocorrelation Terrestrial Labs isofractionation t/3He K+/K0 isoscaling

5. Characterization of symmetry energy near normal density The physical importance of L In npe matter in the simplest model of neutron stars at ϐ-equilibrium In pure neutron matter at saturation density of nuclear matter Many astrophysical observables, e.g., radii, core-crust transition density, cooling rate, oscillation frequencies and damping rate of isolated neutron stars as well as gravitational waves from deformed pulsars and/or neutron star binaries are sensitive to the density dependence of nuclear symmetry energy.

6. Constraints on Esym(ρ0) and L based on 29 analyses of data Esym(ρ0)≈31.6±2.66 MeV Fiducial values as of Aug. 2013 L≈ 2 Esym(ρ0)=59±16 MeV L=2 Esym(ρ0) if Esym=Esym(ρ0)(ρ/ρ0)2/3 Bao-An Li and Xiao Han, Phys. Lett. B727, 276 (2013).

7. Constraints on Esym(ρ0) and L based on 53 analyses of data Fiducial values as of Oct. 12, 2016 Assuming : (1) Gaussian Distribution of L (2) Democratic principle (i.e., trust everyone) L≈ 2 Esym(ρ0) M. Oertel, M. Hempel, T. Klähn, S. Typel arXiv:1610.03361 [astro-ph.HE]

8. What is the high-density symmetry energy? (Examples of theoretical predictions) Predictions using energy density functionals Predictions using microscopic theories ? BHF Constraints near ρ0 ? ? • M. B. Tsang et al., • Phys. Rev. C86, 015803 (2012) Phys. Rev. C 92, 065802 (2015)

9. What is the high-density symmetry energy? Indications of experiments (model dependent) P. Russotto et al. (ASY-EOS Collaboration), Phys. Rev. C94, 034608 (2016). Z.G. Xiao et al, based on GSI/FOPI data Phys. Rev. Lett. 102, 062502 (2009).

10. Why is the symmetry energy so uncertain?(Besides the different many-body approaches used) • Isospin-dependence of short-range neutron-proton correlation due to the tensor force • Spin-isospin dependence of the 3-body force • Isospin dependence of pairing and clustering at low densities (Valid only at the mean-field level) Keith A. Brueckner, Sidney A. Coon, and Janusz Dabrowski, Phys. Rev. 168, 1184 (1968) Correlation functions Within a simple interacting Fermi gas model Vnp(T0) ? Vnp (T1) fT0 ? fT1 , the tensor force in T0 channel makes them different

11. Dominance of the isosinglet (T=0) interaction Symmetry energy At saturation density Paris potential Self-consistent Green’s function BHF I. Bombaci and U. Lombardo PRC 44, 1892 (1991) PRC68, 064307 (2003)

12. Uncertainty of the tensor force at short distance Takaharu Otsuka et al., PRL 95, 232502 (2005); PRL 97, 162501 (2006) Cut-off=0.7 fm for nuclear structure studies Gogny+tensor Gogny

13. Can the symmetry energy become negative at high densities? Yes, it happens when the tensor force due to ρ exchange in the T=0 channel dominates At high densities, the energy of pure neutron matter can be lower than symmetric matter leading to negative symmetry energy Potential part of the symmetry energy RMF Example: proton fractions with interactions/models leading to negative symmetry energy VMB M. Kutschera et al., Acta Physica Polonica B37 (2006) with tensor force Tensor force and/or 3-body force can make Esym negative at high densities Affecting the threshold of hyperon formation, kaon condensation, etc 3-body force effects in Gogny or Skyrme HF Super-Soft

14. What are Short Range Correlations (SRC) in nuclei ? (Eli Piasetzky) K 1 SRC ~RN LRC ~RA K 1 > KF , K 2 > KF K 2 2N-SRC ~1 fm 1.f kF ~ 250 MeV/c High momentum tail: 300-600 MeV/c 1.5 KF - 3 KF 1.7f 1.7f 1.8 fm o = 0.16 GeV/fm3 Nucleons In momentum space: A pair with large relative momentum between the nucleons and small CM momentum.

15. Tensor force induced (1) high-momentum tail in nucleon momentum distribution and (2) isospin dependence of SRC Theory of Nuclear matter H.A. Bethe Ann. Rev. Nucl. Part. Sci., 21, 93-244 (1971) Fermi Sphere

16. Phenomenological nucleon momentum distribution n(k) including SRC effects guided by microscopic theories and experimental findings The n(k) is not directly measurable, but some of its features are observable. B.J. Cai and B.A. Li, PRC92, 011601(R) (2015); PRC93, 014619 (2016). Isospin-dependent depletion of Fermi sea Isospin-dependent high momentum tail • All parameters are fixed by • Jlab data: HMT in SNM=25%, 1.5% in PNM, • Contact C for SNM from deuteron wavefunction • (3) Contact C in PNM from microscopic theories All parameters are assumed to have a linear dependence on isospin asymmetry as indicated by SCGF and BHF calculations

17. The high-momentum tail in deuteron scales as 1/K4 O. Hen, L. B. Weinstein, E. Piasetzky, G. A. Miller, M. M. Sargsian and Y. Sagi, PRC92, 045205 (2015). VMB calculations VMB calculations Ultracold 6Li and 40K Ultracold 6Li and 40K =k/kF K’=K/KF Stewart et al. PRL 104, 235301 (2010) Kuhnle et al. PRL 105, 070402 (2010)

18. EOS and contact C of pure neutron matter B.J. Cai and B.A. Li, PRC92, 011601(R) (2015). density The contact C of PNM is derived from its EOS Using Tan’s adiabatic sweep theorem n(k)=C/K4 S. Tan, Annals of Physics 323 (2008) 2971-2986

19. Modified Gogny Hartree-Fock energy density functional incorporating SRC-induced high momentum tail in the single nucleon momentum distribution Two-body force Kinetic Three-body force Momentum-dependent potential energy due to finite-range interaction SRC-induced HMT in the single-nucleon momentum distribution affects both the kinetic energy and the momentum-dependent part of the potential energy Bao-Jun Cai and Bao-An Li (2016)

20. Readjusting model parameters to reproduce the same saturation properties of nuclear matter as well as Esym(ρ0)=31.6 MeV and L(ρ0)=58.9 MeV Consequence: Symmetry energy gets softened at both low and high densities The isospin-dependent part of the incompressibility at ρ0 agrees better with data Data: MDI+HMT-exp: -492 MDI+FFG: -370

21. Promising Probes of the Esym(ρ) in Nuclear Reactions • Correlations of multi-observableare important • (2) Detecting neutrons simultaneously with charged particles is critical B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008)

22. Symmetry energy and single nucleon potential MDI used in theIBUU04 transport model The x parameter is introduced to mimic various predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions. It is the coefficient of the 3-body force term stiff ρ soft Default: Gogny force Density ρ/ρ0 Potential energy density Single nucleon potential within the HF approach using a modified Gogny force: C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, 034611 (2003). B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614; NPA 735, 563 (2004).

23. Formation of neutron-star matter in terrestrial nuclear laboratories Li Ou and Bao-An Li, Physical Review C84, 064605 (2011) Highly-magnetized, high-density, isospin-asymmetric matter formed in heavy-ion reactions *1.44 1013 G

24. Isospin fractionation in heavy-ion reactions low(high)density region is more neutron-rich withstiff(soft)symmetry energy Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701

25. Pion ratio probe of symmetry energyat supra-normal densities GC Coefficients2

26. Probing the symmetry energy at supra-saturation densities Symmetry energy Stiff Central density density π-/ π+ probe of dense matter Soft Esym Stiff Esym n/p ? n/p ratio at supra-normal densities

27. Probing the symmetry energy at high densities • π -/π + in heavy-ion collisions • Neutron-proton differential flow & n/p ratio in heavy-ion coll. • Neutrino flux of supernova explosions • Strength and frequency of gravitational waves Where does the Esym information get in, get out or get lost in pion production? *1 Isospin fractionation, i.e., the nn/pp ratio at high density is determined by the Esym(ρ) *2 The isovector potential for Delta resonance is completely unknown *5.Pion mean-field (dispersion relation), S and/or P wave and their isospin dependence are poorly known, existing studies are inconclusive. How does the pion mean-field affect the Delta production threshold? Other final state interactions? NN NΔ 3. How to define the isospin asymmetry of the N+Δ matter? 4. The lifetime of Δ controls the effects of its mean field on pions N+π

28. U0(Δ) is 0-30 MeV deeper than U0(N) at ρ0 from e+A, π+A and γ+A scattering, but nothing is known about the U1(Δ)

29. Bao-Jun Cai, F. J. Fattoyev, Bao-An Li and W.G. Newton, PRC 92, 015802 (2015). Xρ=1

30. In the pi-N molecule model, assuming pions have no mean-field,the Delta isovector potential is linked to the nucleon isovector potential Bao-An Li, PRL88, 192701 (2002) and NPA 365 (2002) To study effects of the completely unknown Delta isovector potential, multiply the above with a Delta-probing-factor:

32. Delta isovector potential has NO effect on the high-energy spectrum!

33. In-medium Delta width, H. Lenske et al. Delta lifetime and mass distribution in Au+Au collisions at b=0 WHY? High-mass Delta produced in energetic collisions decays too quickly to feel any mean-field effect! Only long-lived low mass Deltas have the time to feel mean-field effects.

34. Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities A super-soft nuclear symmetry energy is favored by the FOPI data!!! Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, Phys. Rev. Lett. 102 (2009) 062502 W. Reisdorf et al. NPA781 (2007) 459 Data: Calculations: IQMD and IBUU04

35. A challenge: how can neutron stars be stable with a super-soft symmetry energy?If the symmetry energy is too soft, then a mechanical instability will occur when dP/dρ is negative, neutron stars will then all collapse while they do exist in nature TOV equation: a condition at hydrodynamical equilibrium Gravity Nuclear pressure For npe matter P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002)) dP/dρ<0 if E’sym is big and negative (super-soft)

36. Neutron stars as a natural testing ground of fundamental forces • Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century, Committee on the Physics of the Universe, National Research Council • • What is the dark matter? • • What is the nature of the dark energy? • • How did the universe begin? • • What is gravity? Does Einstein’s GR have a limit? • • Are there additional spacetime dimensions? • • What are the masses of the neutrinos, and how have • they shaped the evolution of the universe? • • How do cosmic accelerators work and what are they • accelerating? • • Are protons unstable? • • Are there new states of matter at exceedingly high • density and temperature? • • How were the elements from iron to uranium made? • • Is a new theory of matter and light needed at the • highest energies? gravity weak E&M Strong force

37. Gravity-EOS Degeneracy in massive neutron stars Strong-field gravity: GR or Modified Gravity? ? gravity GR+[Modified Gravity] Action S=Sgravity+Smatter ======== Massive neutron stars Matter+[Dark Matter]+[Dark Energy] EOS ? Contents and stiffness of the EOS of super-dense matter? For high-density neutron-rich nucleonic matter, the most uncertain part of the EOS is the nuclear symmetry energy

38. An example of EOS-Gravity degeneracy Simon DeDeo, Dimitrios Psaltis Phys. Rev. Lett. 90 (2003) 141101 Dimitrios Psaltis, Living Reviews in Relativity, 11, 9 (2008) • Neutron stars are among the densest • objects with the strongest gravity • General Relativity (GR) may break down at • strong-field limit and there is no fundamental • reason to choose Einstein’s GR over alternative • gravity theories • Need at least 2 observables to break the • degeneracy Uncertain range of EOS Stiff EOS: V. R. Pandharipande, Nucl. Phys. A 174, 641 (1971). Soft EOS: R. B. Wiringa, V. Fiks, and A. Fabrocini, Phys. Rev. C38, 1010 (1988) Scalar-Tensor theory with quadratic coupling:

39. Physics origin of the Yukawa term In grand unification theories, conventional gravity has to be modified due to either geometrical effects of extra space-time dimensions at short length, a new boson or the 5th force String theorists have published TONS of papers on the extra space-time dimensions N. Arkani-Hamed et al., Phys Lett. B 429, 263–272 (1998); J.C. Long et al., Nature 421, 922 (2003); C.D. Hoyle, Nature 421, 899 (2003) Yukawa potential due to the exchange of a new boson proposed in the super-symmetric extension of the Standard Model of the Grand Unification Theory, or the fifth force In terms of the gravitational potential Yasunori Fujii, Nature 234, 5-7 (1971); G.W. Gibbons and B.F. Whiting, Nature291, 636 - 638 (1981) The neutral spin-1 gauge boson U is a candidate, it is light and weakly interacting, Pierre Fayet, PLB675, 267 (2009), C. Boehm, D. Hooper, J. Silk, M. Casse and J. Paul, PRL, 92, 101301 (2004).

40. Upper limits on the strength α and range λ of the Yukawa term Torsion balance M.I. Krivoruchenko et al., PRD 79, 125023 (2009) E.G. Adelberger et al., PRL 98, 131104 (2007) D.J. Kapner et al., PRL 98, 021101 (2007) Serge Reynaud et al., Int. J. Mod. Phys. A20, 2294 (2005)

41. Supersoft Symmetry Energy Encountering Non-Newtonian Gravity in Neutron Stars De-Hua Wen, Bao-An Li and Lie-Wen Chen, Phys. Rev. Lett. 103, 211102 (2009) With an EOS including the Yukawa contribution

42. The rise, fall and reappearing of the 5th force --- evidence of a new (U) boson of 17 MeV

43. Supporting theories---- nothing seems to be wrong with a U-boson of 17 MeV

46. Summary • The study on nuclear symmetry energy and its astrophysical impacts is Exciting! • Symmetry energy at supra-saturation densities is the most uncertain part of the EOS of dense neutron-rich nucleonic matter • Symmetry energy has significant effects on terrestrial experiments and astrophysical observables

47. May the 5th Force be with You! Symmetry Energy or Hard Soft? Dark Matter or Modified Gravity?

48. Momentum and density dependence of the symmetry potential Usym,1 SLY4 used in AMD+JAM M*n < M*p M*n > M*p • Symmetry potential is uncertain at high density/momentum • Isospin effects are expected to stronger at low energies where Usym is larger • Most models and nucleon-A scattering indicate a Usym sign inversion at high momentum R. Chen et al., PRC 85, 024305 (2012).

49. Momentum dependence of the isoscalar and isovector (symmetry) potential at normal densityconstrained by nucleon-nucleus scattering data Physics Letters B743 (2015) 408 Non-relativistic X.H. Li et al., from analyzing 2249 sets of nucleon-A scattering data relativistic

50. Constraining the energy dependence of symmetry potential at saturation density RMF Isovector optical potential from nucleon-nucleus scattering J. W. Holt, N. Kaiser, G. A. Miller Phys. Rev. C 93, 064603 (2016)