1. Mannque Rho CEA Saclay “f 0 (500)” is a Pseudo-Nambu-Goldstone “f 0 (500)” is a Pseudo-Nambu-Goldstone Boson  in Dense Baryonic Matter Boson  in Dense Baryonic Matter 2 nd APCTP-ECT* Workshop 2015

2. A Brief History: Conceiving “RAON” Problem: Where the proton mass comes from?  From Higgs mechanism: perhaps ~ 1%?  From Nambu mechanism: perhaps ~ 30%? So where is ~ 70% from? Find the answer in dense matter …

3. References References My talk is based on 1. H.K. Lee, W.-G. Paeng, MR, arXiv:1508.05210 2. W.-G. Paeng, T.T.S. Kuo, H.K. Lee, MR, arXiv:1508.05210 Anchored on ideas by a. M. Harada, K. Yamawaki, Phys. Rept. 381 (2003) 1 “HLS, vector manifestation” b. R.J. Crewther, L.C. Tunstall, Phys. Rev. 91 (2015) 3 “QCD IR fixed point, chiral-scale symmetry” c. S. Weinberg, Phys. Rev. Lett. 65 (1990) 1177; Salamfest (1994) “Mended symmetries”

4. Symmetries and topology in dense matter Symmetries and topology in dense matter  Chiral symmetry (intrinsic):   1. low-energy theorems, chiral Lagrangian, nuclear  PT.  2. nucleon as a skyrmion from  field.  SU(2) hidden local symmetry (HLS):  ‘,  ”  ’’’   a 1, a 1 ’, a 1 “, …  1. Infinite tower of vector mesons  BPS skyrmion  2. approaching chiral symmetry restoration with  m   0 “vector manifestation (VM) fixed point” 

5. Solving binding energy puzzle in la Solving binding energy puzzle in large N c QCD Large N c QCD  E B /A ~ N c  QCD violently at odds with Nature. Puzzle solved with vector mesons Soliton with  a 1 Large N c ~ skyrme model with  experiment Courtesy P. Sutcliffe

6. BPS matter from ∞ of SU(2) vector mesons Corrections: Coulomb, isospin breaking.. Parameters: 3 Predicts: Incompressible Fermi liquid, reproduces Bethe-Weiz\”acker formula theory exp Courtesy Adam et al.

7. High density  Vector manifestation (VM) Wilsonian RG equation for hidden local symmetry has a fixed point as the quark condensate Near the VM fixed point (Harada/Yamawaki) together with a 1 Toward Weinberg “mended symmetries” Adami-Brown proposal for “seeing” chiral symmetry restoration 1992

8. Power of Topology Skyrmion\instanton crystal 1. In large N c QCD, nuclear matter at large density is a crystal, with instantons or skyrmions 2. At “high” density n >n 0, skyrmions (instantons) fractionize to ½-skyrmions (dyons). This topology is robust, could/should and will be incorporated in effective field theories.

9.  At density n 1/2 ~ (2-3)n 0, baryon number 1 skyrmions franctionize into half-skyrmions (similarly in condensed matter) skyrmions half-skyrmions Half-skyrmions emerge

10. skyrmion and ½- skyrmion are pervasive in all areas of physcs skyrmion and ½- skyrmion are pervasive in all areas of physcs Condensed matter Example: ½-skyrmions in chiral superconductivity S. Chakravarty, C.S. Hsu 2015 ½-skrmions condense  superconductivity Heavy fermion: URu 2 Si 2 (Polar Kerr effect) meron anti-meron

12. arXiv: 1508.01172; Phys. Rev. rapid communication And also in high-energy physics

14. Skyrmions on crystal predict Skyrmions on crystal predict. This topology change involves NO symmetry change

15.  Scale (or conformal) symmetry: “  ” (dilaton) 1. QCD infra-red (IR) fixed point at g s ~ O(1) for N c = N F =3. 2.  dilaton) emerges as a scalar (pseudo) NG (Nambu-Goldstone) boson  f 0 (500) in PDB. 3.  joins  to form a multiplet of NG excitations: “dilaton limit (DL) fixed point”  Mended symmetries:  a 1 1. NG bosons and vector fields obey the Weinberg collinear current algebra 2. At VM+DL fixed point, m  = m  = m  = m a1  0 Equally crucial for nuclear dynamics is Equally crucial for nuclear dynamics is

16.  In QCD: f 0 (500) as a dilaton  Crewther-Tunstall (CT) Theory: QCD IR fixed point Potential breakthrough in particle physics. Could solve some long-standing unsolved problems in particle physics. It elegantly explains  I=1/2 rule for K decay and other processes  PT 3 fails or has difficulty to explain. At  IR, in the chiral limit    D      =    A   0.  and  are NG bosons.

17. Dilaton is also pervasive in physics Dilaton is also pervasive in physics Higgs as dilaton near  c  “dilatonic Higgs” N F =8, N c =4.   Cosmology, BSM (beyond Standard Model), …

18. In QCD: f 0 (500) is a pseudo-NG of spontaneously broken scalar symmetry No lattice calculations have found the IR fixed point for N F =3. Whether It exists in Nature is a controversy among lattice experts. My claim: even if absent in matter-free space, it could appear in medium as an emergent symmetry due to strong correlations. On this possibility, lattice experts do not disagree. Crewther/Tunstall 2013

19. Proposal: nuclear dynamics takes place around the IR fixed point. At the IR fixed point, there is massless dilaton  In Nature dilaton mass is   (  IR –  s ), explicit breaking, and  m q, current quark mass. The two effects are connected to each other.  inseparable locking of chiral symmetry and scale symmetry. Gives rise to “chiral-scalar perturbation theory”  PT  with power counting Impact on nuclear dynamics

20. There is a support for the QCD IR fixed point at very high order perturbation There is a support for the QCD IR fixed point at very high order perturbation Although IR fixed point is so far seen in lattice calculations only only for N F < 8, a high order numerical stochastic perturbation calculation (i.e., with Padé approximant) ”voted for” an IR fixed point for two-flavor (N F =2) QCD. Horsley et al, arXiv:1309.4311

21. And anomalies figure …  Trace anomaly:  glueball  Together with the quark mass, breaks scale (or conformal) symmetry explicitly. Gives mass to the dilaton f 0 (500). A highly subtle business due to Freund-Nambu theorem: “scale symmetry cannot be spontaneously broken without explicit breaking” EFT. Departure from IR fixed point Deviation from chiral limit

22. How it enters in nuclear dynamics … What figures is “conformalon”  with decay constant f    Use  n in HLS Lagrangian to make it scale-invariant and put scale symmetry breaking potential V(  ) (à la CT). Incorporate nucleons as skyrmions and/or explicit local fields. Call it  bHLS Lagrangian. Breakings of chiral symmetry and scale symmetry get locked to each other. In baryonic matter, all hadron masses slide in medium with f   (n) = <  n)  f   due to IDD (intrinsic density dependence) Do (a) RMF with this  bHLS Lagrangian à la Walecka or (b) V lowk RG (renormalization group). I will use (b). Scalar analog to

23. Finally but not least Hidden local U(1) symmetry:  meson Absolutely crucial in nuclear physics, i.e., Walecka-type RMF theories. In hidden gauge theories, it couples to other fields via “anomaly” term (Chern-Simons in 5D). In the vacuum, U(2) symmetry holds well for (  But in nuclear matter, it must break down. How badly?

24. Calculation Calculation  1. At the scale      4  f , effective field theory (EFT) Lagrangian ℒ eff ( N,  ) is matched to QCD Lagrangian ℒ QCD ( G   q) via correlators, the former in tree order and the latter in Wilsonian OPE.  “bare” Lagrangian  2.The “bare” parameters of ℒ eff inherit from QCD, dependence on nonperturbative properties of QCD, ie, quark condensate, gluon condensate etc. which encode properties of the vacuum change by density etc.  IDD (intrinsic density dependence)  3. Nuclear dynamics is done by “double decimation” RG analysis, the first to obtain the Stony Brook V lowk – which encodes the intrinsic density dependence (IDD) inherited from QCD (alias “BR scaling”) -- and the second to do the Fermi-liquid fixed point (or sophisticated many-body) calculation.

25. Double decimation There are roughly two RG decimations in nuclear many-body EFT a) Decimate from    to ~ (2-3) fm -1 or ~ 400 MeV up to which accurate NN scattering data are available, say, E lab ≤ 350 MeV. Call it  data. Yields V lowK b) Decimate from  data to Fermi surface scale  FS using V lowK operative up to E lab. This derives Fermi liquid fixed point theory valid for nuclear matter. Bogner, Kuo et al, 2003

26. Main Results i) Where the proton mass comes from ii) Locking of scale symmetry and chiral symmetry iii)Emergence of parity doubling iv)Changeover of EoS from soft to hard v)Breakdown of hidden local U(2) symmetry vi)“Cheshire cat”: Massive neutron stars from half-skyrmions without involving quarks.

27. i) Where does the proton mass come from?  It comes mostly, if not all, from dilaton condensation, only little from spontaneous breaking of scale symmetry. As  The proton mass can vanish only when both the quark condensate and the dilaton condensate vanish

28. Agrees with skyrmions on crystal Topology change No topology change

29. At odds with “Nambu paradigm”: “Proton mass ‘arises largely’ from the spontaneously breaking of chiral symmetry …”

30.  In finite nuclear systems, f   (pion decay constant) is NOT a direct indicator for chiral symmetry ii) Locking chiral-scale symmetry iii) Emergent parity doubling m 0, a “chirally invariant” mass, allows parity-doubling for baryons in the presence of pions. It is a symmetry emergent in baryonic matter. In skyrmion picture, this sets in the half-skyrmion phase at a density ~ 2n_0. Related to “quarkyonic”?!

31. Resembles skyrmion 2-phase structure n = density

32. iv) VM + topology drastically modify EoS at ~ 2n 0 iv) VM + topology drastically modify EoS at ~ 2n 0  soft-to-hard EoS, e.g., symmetry energy n=n 0 n ~ 2n 0 n=0 Topology effect and VM (g  0) effect suppress  tensor making the  tensor dominate   0 condensed crystal.

33. n 1/2 Symmetry Energy More in detail on this in Friday talk.

34. v) EoS for massive stars “softer” in nuclear matter, “harder” in neutron matter

35. Massive stars

36. Gravity wave: aLIGO & aVIRGO Tidal deformability parameter Gravitational waves from coalescing binary neutron stars carry signal for tidal distortion of stars, sensitive to EoS. Claim is that can be accurately measured! 1 1.5 2 Kim et al 2015

37. vi) Dense matter engenders vi) Dense matter engenders U(2) symmetry (  breakdown at n >~ 2n 0  Suppose local U(2) symmetry held, with  meson scaling with  à la VM, then nuclear matter would collapse for n > ~ (2-3) n 0 CBELSA/TABS Experiments?

38. vi “Cheshire Cat” phenomenon … vi “Cheshire Cat” phenomenon … Conclusion: Smooth changeover from baryons to quarks via skyrmion-to-half-skyrmion transition without symmetry change up to deconfinement as density increases Likely related to baryon-to-quarkionic transition of Fukushima and Kojo 2015. Suggest: approach to deconfinement via “un-fermionic- liquid” as in condensed matter  RAON, FAIR, …

39. Thanks for attention

40. gluons quarkss Total Exp Flavor singlet Axial charge skyrmion MIT bag