Mannque Rho CEA Saclay

1. “f0 (500)” is a Pseudo-Nambu-Goldstone Boson s in Dense Baryonic Matter Mannque Rho CEA Saclay 2nd 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 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 • Chiral symmetry (intrinsic): p • 1. low-energy theorems, chiral Lagrangian, nuclear cPT. • 2. nucleon as a skyrmion from p field. • SU(2) hidden local symmetry (HLS): r, r‘, r”, r’’’ ... • a1, a1’, a1“, … • 1.Infinite tower of vector mesons  BPS skyrmion • 2. approaching chiral symmetry restoration with • mr  0 “vector manifestation (VM) fixed point”

5. Solving binding energy puzzle in large Nc QCD Courtesy P. Sutcliffe Large NcQCD  EB /A ~ Nc LQCD violently at odds with Nature. Puzzle solved with vector mesons experiment Soliton with p, r, a1 Large Nc~ skyrme model with p

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

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 a1 Adami-Brown proposal for “seeing” chiral symmetry restoration 1992 Toward Weinberg “mended symmetries”

8. Power of Topology Skyrmion\instanton crystal 1. In large Nc QCD, nuclear matter at large density is a crystal, with instantons or skyrmions 2. At “high” density n >n0, skyrmions (instantons) fractionize to ½-skyrmions (dyons). This topology is robust, could/should and will be incorporated in effective field theories.

9. Half-skyrmions emerge • At density n1/2 ~ (2-3)n0 , baryon number 1 • skyrmions franctionize into half-skyrmions • (similarly in condensed matter) half-skyrmions skyrmions

10. 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 meron ½-skrmions condense  superconductivity Heavy fermion: URu2Si2 (Polar Kerr effect) anti-meron

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

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

15. Equally crucial for nuclear dynamics is • Scale (or conformal) symmetry: “s” (dilaton) • 1. QCD infra-red (IR) fixed point at gs~ O(1) for Nc = NF =3. • 2. s (dilaton) emerges as a scalar (pseudo) NG • (Nambu-Goldstone) boson  f0(500) in PDB. • 3. s joins p to form a multiplet of NG excitations: “dilaton • limit (DL) fixed point” • Mended symmetries: p, s, r, a1 • 1. NG bosons and vector fields obey the Weinberg • collinear current algebra • 2. At VM+DL fixed point, mp = ms = mr = ma1 0

16. In QCD: f0(500) as a dilaton s Crewther-Tunstall (CT) Theory: QCD IR fixed point At aIR, in the chiral limit , mDm =qmm= mAm = 0. s and p are NG bosons. Potential breakthrough in particle physics. Could solve some long-standing unsolved problems in particle physics. It elegantly explains DI=1/2 rule for K decay and other processes cPT3 fails or has difficulty to explain .

17. Dilaton is also pervasive in physics Cosmology, BSM (beyond Standard Model), … b NF =8, Nc =4. Higgs as dilaton near ac  “dilatonic Higgs” a

18. In QCD: f0 (500) is a pseudo-NGof spontaneously broken scalar symmetry Crewther/Tunstall 2013 No lattice calculations have found the IR fixed point for NF =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.

19. Impact on nuclear dynamics • Proposal: nuclear dynamics takes place around • the IR fixed point. • At the IR fixed point, there is massless dilaton s. In Nature • dilaton mass is  Da=(aIR – as), explicit breaking, and • mq , 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” cPTs • with power counting

20. 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 NF < 8, a high order numerical stochastic perturbation calculation (i.e., with Padé approximant) ”voted for” an IR fixed point for two-flavor (NF =2) QCD. Horsley et al, arXiv:1309.4311

21. And anomalies figure … • Trace anomaly: s, glueball • Together with the quark mass, breaks scale (or • conformal) symmetry explicitly. Gives mass to the • dilaton f0 (500). A highly subtle business due to • Freund-Nambu theorem:“scale symmetry cannot • be spontaneously broken without explicit breaking” • EFT • . Deviation from chiral limit Departure from IR fixed point

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

23. Finally but not leastHidden local U(1) symmetry: w 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 (r, w). But in nuclear matter, it must break down. How badly?

24. Calculation • 1. At the scale LM < Lc 4pfp, effective field theory (EFT) Lagrangian ℒeff (N,p, s, r, w ...) is matched to QCD Lagrangian ℒQCD (Gm , q) via correlators, the former in tree order and the latter in Wilsonian OPE. “bare” Lagrangian • 2.The “bare” parameters of ℒeffinherit 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 Vlowk – 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 Bogner, Kuo et al, 2003 • There are roughly two RG decimations in • nuclear many-body EFT • Decimate from Lcto ~ (2-3) fm-1or ~ 400 MeV • up to which accurate NN scattering data are available, • say, Elab ≤ 350 MeV. Call it Ldata. Yields VlowK • Decimate from Ldata to Fermi surface scale LFS using • VlowK operative up to Elab. This derives Fermi liquid • fixed point theory valid for nuclear matter.

26. Main Results • i) Where the proton mass comes from • ii) Locking of scale symmetry and chiral symmetry • Emergence of parity doubling • Changeover of EoS from soft to hard • Breakdown of hidden local U(2) symmetry • “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 No topology change Topology change

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

30. ii) Locking chiral-scale symmetry  In finite nuclear systems, fp(pion decay constant) is NOTa direct indicator for chiral symmetry iii) Emergent parity doubling m0 , 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 ~ 2n0 •  soft-to-hard EoS, e.g., symmetry energy Topology effect and VM (g 0) effect suppress r tensor making the p tensor dominate  p0 condensed crystal. n=n0 n=0 n ~ 2n0

33. Symmetry Energy n1/2 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 Kim et al 2015 Tidal deformability parameter l 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

37. vi) Dense matter engenders U(2) symmetry (r, w) breakdown at n >~ 2n0. Suppose local U(2) symmetry held, with w meson scaling with rà la VM, then nuclear matter would collapse for n > ~ (2-3) n0 CBELSA/TABS Experiments?

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