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Mannque Rho CEA Saclay f0 (500) is a Pseudo-Nambu-Goldstone Boson s in Dense Baryonic Matter 2nd APCTP-ECT* Workshop 2015

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

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

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

Solving binding energy puzzle in large Nc QCD Large Nc QCD EB /A ~ Nc LQCD violently at odds with Nature.Puzzle solved with vector mesonsSoliton with p, r, a1 Large Nc~ skyrme modelwith pexperimentCourtesy P. Sutcliffe

BPS matter from of SU(2) vector mesonsCorrections: Coulomb, isospin breaking ..

Parameters: 3 Predicts: Incompressible Fermi liquid, reproduces Bethe-Weiz\acker formulatheoryexpCourtesy Adam et al.

High density Vector manifestation (VM)Wilsonian RG equation for hidden local symmetryhas a fixed point as the quark condensate

Near the VM fixed point (Harada/Yamawaki) together with a1

Toward Weinberg mended symmetriesAdami-Brown proposal forseeing chiral symmetryrestoration 1992

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 -skyrmions (dyons).This topology is robust, could/should andwill be incorporated in effective field theories.

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

skyrmion and -skyrmion are pervasive in all areas of physcsCondensed matterExample: -skyrmions in chiral superconductivityS. Chakravarty, C.S. Hsu 2015-skrmions condense superconductivityHeavy fermion: URu2Si2 (Polar Kerr effect)meronanti-meron

arXiv: 1508.01172;Phys. Rev. rapid communicationAnd also in high-energy physics

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

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 Equally crucial for nuclear dynamics is

In QCD: f0(500) as a dilaton s 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 DI=1/2 rule for K decay and other processes cPT3 fails or has difficulty to explain .

At aIR, in the chiral limit , m Dm =qmm = m Am = 0. s and p are NG bosons.

Dilaton is also pervasive in physicsHiggs as dilaton near ac dilatonic HiggsNF =8, Nc =4.baCosmology, BSM (beyond Standard Model),

In QCD: f0 (500) is a pseudo-NGof spontaneously broken scalar symmetry

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 appearin medium as an emergent symmetry due to strong correlations.

On this possibility, lattice experts do not disagree.

Crewther/Tunstall 2013

Proposal: nuclear dynamics takes place around the IR fixed point.

At the IR fixed point, there is massless dilaton s. In Naturedilaton 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

Impact on nuclear dynamics

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

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

.Departure from IR fixed pointDeviation from chiral limit

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) ( 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) = (n) fs* due to IDD (intrinsic density dependence)

Do (a) RMF with this cbHLS Lagrangian la Walecka or (b) Vlowk RG (renormalization group). I will use (b). Scalar analog to

Finally but not leastHidden local U(1) symmetry: w mesonAbsolutely crucial in nuclear physics, i.e., Walecka-typeRMF theories. In hidden gauge theories, it couples toother 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?

Calculation1. At the scale LM < Lc 4pfp, effective field theory (EFT) Lagrangian eff (N,p, s, r, w ...) is matched to QCD Lagrangian QCD (Gm , q) via correlators, the former in tree order and the latter in Wilsonian OPE. bare Lagrangian2.The bare parameters of 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 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.

Double decimationThere are roughly two RG decimations in nuclear many-body EFT

Decimate from Lc to ~ (2-3) fm-1 or ~ 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.Bogner, Kuo et al, 2003

Main Results i) Where the proton mass comes fromii) Locking of scale symmetry and chiral symmetryEmergence of parity doublingChangeover of EoS from soft to hard Breakdown of hidden local U(2) symmetry Cheshire cat: Massive neutron stars from half-skyrmions without involving quarks.

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

Agrees with skyrmions on crystalTopology changeNo topology change

At odds with Nambu paradigm:

Proton mass arises largely from the spontaneously breaking of chiral symmetry

In finite nuclear systems, fp (pion decay constant) is NOT a direct indicator for chiral symmetry ii) Locking chiral-scale symmetryiii) Emergent parity doubling m0 , a chirally invariant mass, allows parity-doubling for baryons in the presence of pions. It is asymmetry emergent in baryonic matter.

In skyrmion picture, this sets in the half-skyrmion phaseat a density ~ 2n_0. Related to quarkyonic?!

Resembles skyrmion 2-phase structure n = density

iv) VM + topology drastically modify EoS at ~ 2n0

soft-to-hard EoS, e.g., symmetry energy

n=n0n ~ 2n0