Mannque Rho CEA Saclay

“ “ff00 (500)” (500)” is a Pseudo-Nambu-Goldstone is a Pseudo-Nambu-Goldstone

Boson Boson in Dense Baryonic Matterin 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 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 matterSymmetries 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): ‘, ”’’’ a1, a1’, a1“, … 1. Infinite tower of vector mesons BPS skyrmion 2. approaching chiral symmetry restoration with m 0 “vector manifestation (VM) fixed point”

Solving binding energy puzzle in laSolving binding energy puzzle in large Nc QCD

Large Nc QCD EB /A ~ Nc QCD violently at odds with Nature.Puzzle solved with vector mesons

Soliton with a1

Large Nc~ skyrme modelwith

experiment

Courtesy P. Sutcliffe

BPS matter from ∞ of SU(2) vector mesons

Corrections: Coulomb, isospin breaking ..

Parameters: 3

Predicts: Incompressible Fermi liquid, reproduces Bethe-Weiz\”acker formula

theory

expCourtesy Adam et al.

High density High density Vector manifestation (VM) 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 symmetries”

Adami-Brown proposal for“seeing” 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 ½-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-skyrmions

Half-skyrmions emerge

skyrmion and ½-skyrmion and ½-skyrmion are skyrmion are pervasive in all areas of physcs 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: URu2Si2

(Polar Kerr effect)

meron

anti-meron

arXiv: 1508.01172;Phys. Rev. rapid communication

And also in high-energy physicsAnd also in high-energy physics

Skyrmions on crystal predictSkyrmions on crystal predict

. This topology change involves NO symmetry change

Scale (or conformal) symmetry: “” (dilaton)

1. QCD infra-red (IR) fixed point at gs~ O(1) for Nc = NF =3.

2. dilaton) emerges as a scalar (pseudo) NG (Nambu-Goldstone) boson f0(500) in PDB. 3. joins to form a multiplet of NG excitations: “dilaton limit (DL) fixed point” Mended symmetries: a1

1. NG bosons and vector fields obey the Weinberg collinear current algebra

2. At VM+DL fixed point, m = m = m = ma1 0

Equally crucial for nuclear dynamics isEqually crucial for nuclear dynamics is

In QCD: f0(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 PT3 fails or has difficulty to explain .

At IR, in the chiral limitD= A0. and are NG bosons.

Dilaton is also pervasive in physicsDilaton is also pervasive in physics

Higgs as dilaton near c

“dilatonic Higgs”

NF =8, Nc =4.

Cosmology, 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 In Naturedilaton mass is (IR – s), 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” PT with power counting

Impact on nuclear dynamics

There is aThere is a support for the QCD IR fixed point support for the QCD IR fixed point at very high order perturbation at very high order perturbation

Although IR fixed point is so far seen in lattice calculations onlyonly 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

And anomalies figure … Trace anomaly: 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 point

Deviation from chiral limit

How it enters in nuclear dynamics …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) Vlowk RG (renormalization group). I will use (b).

Scalar analog to

Finally but not leastHidden local U(1) symmetry: meson

Absolutely 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 (But in nuclear matter, it must break down. How badly?

CalculationCalculation

1. At the scale 4f, effective field theory (EFT) Lagrangian ℒeff (N,) is matched to QCD Lagrangian ℒQCD (Gq) via correlators, the former in tree order and the latter in Wilsonian OPE. “bare” Lagrangian 2.The “bare” parameters of ℒeff 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 decimationDouble 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, Elab ≤ 350 MeV. Call it data. Yields VlowK

b) Decimate from data to Fermi surface scale FS using VlowK operative up to Elab. This derives Fermi liquid fixed point theory valid for nuclear matter.

Bogner, Kuo et al, 2003

Main Results Main Results

i) Where the proton mass comes fromii) Locking of scale symmetry and chiral symmetryiii)Emergence of parity doublingiv)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.

i) Where does the proton mass come from? 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 crystal

Topology change No topology change

At odds with “Nambu paradigm”:

“Proton mass ‘arises largely’ from the spontaneously breaking of chiral symmetry …”

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 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 ~ 2niv) VM + topology drastically modify EoS at ~ 2n00

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

n=n0

n ~ 2n0

n=0

Topology effect and VM (g 0) effect suppress tensormaking the tensor dominate 0 condensed crystal.

n1/2

Symmetry EnergySymmetry Energy

More in detail on this in Friday talk.

v) EoS for massive stars

“softer” in nuclear matter, “harder” in neutron matter

Massive stars

Gravity waveGravity wave: aLIGO & aVIRGO: aLIGO & aVIRGO

Tidal deformability parameter

Gravitational waves from coalescing binary neutron starscarry signal for tidal distortion of stars, sensitive to EoS.Claim is that can be accurately measured!

1

1.5

2

Kim et al 2015

vi) Dense matter engendersvi) Dense matter engendersU(2) symmetry (breakdown at n >~ 2n0

Suppose local U(2) symmetry held, with mesonscaling with à la VM, then nuclearmatter would collapse for n > ~ (2-3) n0

CBELSA/TABSExperiments?

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, …

Thanks for attention

0.0

0.5

-0.5

1.0

-1.00.5 1.0 1.50.0

R (fm )

Fra c tio n Sp in

gluons

quarkss

Total

Exp

Flavor singletAxial charge

skyrmionMITbag