Mannque Rho CEA Saclay

Nuclear tensor forces and a signal forNuclear tensor forces and a signal forscalescale-chiral symmetry in nuclei-chiral symmetry in nuclei

2nd APCTP-ECT* Workshop 2015

What I would propose to work out at RAON

Monday’s talkMonday’s talk:

a) Start with scale-invariant hidden local symmetry with dilaton and pions coupled to matter fields and subject to explicit symmetry breaking away from the IR fixed point and current quark masses. The degrees of freedom are the nucleons (N), the hidden gauge mesons and a multiplet of pNG and ‘s.b) The effective Lagrangian is matched via correlators to QCD at the matching scale M from which the EFT picks up IDD (intrinsic density dependence) from QCD condensates.c) Nuclear dynamics is described by “double decimation” RG flows from M, the first decimation leading to Vlowk endowed with IDD and the second to what corresponds to Fermi-liquid fixed point approach to many body problem.d) Monday’s talk was focused on dense matter, n > n0 .

This talkThis talk

I will focus on processes near nuclear matter,in particular connected to nuclear tensor forces.

I will then propose how to “see” the manifestation – i.e., a signal – of scale-chiral symmetry of QCD in nuclear medium. Perhaps in RAON-type physics!(?)

Debate between Gerry Brown and Steven Weinbergin early 1990’s.

To go from soft-pion scale up to higher scale

At E ≈ 0 , Soft pion/current algebra applies:

Notice An Invariance:

This is a “redundancy” , exploit it to gauge the symmetry to “hidden local symmetry (HLS)” à la Harada and Yamawaki.

Provides potentially powerful tool to go toward the vector meson scale.

Write

Brown-Weinberg debateBrown-Weinberg debateOn EFT in nuclear physicsOn EFT in nuclear physics

Brown (espousing HLS): “the meson is essential in nuclear physics”. Weinberg (espousing standard ChPT): “the is not needed, its effect can be incorporated in counter terms involving pions only”

Weinberg’s “mended symmetry”acknowledges Brown’s thesis

One vector meson:

Georgi et al. 1999

Something deep aboutSomething deep aboutHLS is involved in the debateHLS is involved in the debate

Approaching QCD with effective fields involves Infinite towers of vector mesons as hidden gauge fields

Moose construction by

Two vector mesons …

Many (K=) vector mesons in “open moose”:

where

And take continuum limit with K = , →0 : → 5D YM

o Chiral symmetry in 4D is elevated to a local gauge symmetry in 5D. It also comesfrom string theory, e.g., Sakai and Sugimoto 2003.

So at some mass scale, vector mesons must appear.But the question is: Is any of them essential in nuclearphysics? The answer is most likely YES.

Tensor forces: Tensor forces: An old problem with a new twistAn old problem with a new twist

N N

What scale-chiral symmetry predicts What scale-chiral symmetry predicts for nuclear tensor forces for nuclear tensor forces

IDD (intrinsic density dependence), representing matching ofEFT and QCD, in the “bare” parameters of the EFT Lagrangianreflects the vacuum change in nuclear matter.

Crucial ingredient: Crucial ingredient: chiral symmetry locked to scale symmetry chiral symmetry locked to scale symmetry

At IR, in the chiral limitD= A0. (“dialon”) and (pseudo) NG bosons

f f

Dilaton condensate provides IDD’s to EFT Lagrangian

Crewther and Tunstall 2013

2-phase baryon structure via topology

n = density

Consequence on the nucleon mass

“Emergent” parity-doublet symmetry for nucleons: m* = m0 +

n1/2

m0 (0.6 – 0.8) mN

Y.L. Ma et al 2013

IDDs drastically modify tensor forcesIDDs drastically modify tensor forces

For density n n1/2 :

n=n0

n=2n0

n=0

The pion tensor is protected by chiral symmetry, so only the tensor is affected by density.

n1/2

For density n < n1/2 :

IDD

Net tensor decreases Net tensor increases

Impact on EoSImpact on EoS

For matter with excess of neutrons (i.e., neutron star)the “symmetry energy” Esym plays a dominant role.

EEsymsym by closure approximationby closure approximationG.E. Brown and R. Machleidt

n=n0

n > n1/2

n=0

Decreasing tensor Increasing tensor

Esym is dominated by tensor forces

n1/2

cusp

EEsymsym from half-skyrmion matter from half-skyrmion matter

The Esym calculated with the IDDs extracted from the topology change matches the Esym given bythe order 1/Nc (rotational quantized) skyrmion energy.This supports the robustness of using the topologychange for the IDDs.

H.K. Lee, B.Y. Park, R. 2010

n1/2

EEsymsym in in VVlowklowkPaeng, Kuo, Lee, R

Surprising things happen in Finite nuclei and nuclear matterFinite nuclei and nuclear matter

Use “Double decimation”Use “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, 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.

Fluctuate around Fermi surface; Many body technique

Bogner, Kuo et al, arXiv:nucl-th/0305035

VVlowklowk - RG approach- RG approach

Kuo, Brown, Holt, Schwenk et al

Tensor forces are notrenormalized !!

Observation but no proof

Tom Kuo 2013

Non-renormalization of the tensor forceIn deuteron

Tom Kuo 2013

In second decimation

Ring diagram summationÀ la Kuo et al.

Monopole matrix element

Evolution of single-particle energy

Tensor forces in shell evolutionTensor forces in shell evolution In exotic nucleiIn exotic nuclei T. Otsuka 05

Tensor forces are important in complex nuclei

“Vbare”=“Vlowk”=“VQbox”

ConclusionConclusion

In light as well as complex nuclei at low density

involving no IDD, i.e., .

I take one step further and assume that the remains zero independently of the IDD.This means that tensor forces with IDD’s for varying densities are non-renormalized.

How to “see” IDDHow to “see” IDD

Tensor forces are “scale-independent” at any density, i.e., fixed-point quantity.

If one can dial the density, then tensor forces will offer a pristine signal for IDD free of renormalization.

Zero-in on processes probing tensor forces.

An “evidence”:An “evidence”: C14 dating probes scaling C14 dating probes scaling

J.W. Holt et al, PRL 100, 062501 (08)

n=0

n=n0

Caveat? Many-body forces Caveat? Many-body forces

(a) (b) (c)

The long lifetime of C14 has also been explained by 3-body forces without IDD (Holt and Weise 2010, Maris et al 2011…).

Way out: The contact 3-body force (c) is of the same mass-scale as IDD. In medium with HLS, it is encoded in the IDD. With exchange, the contact term should be negligible.

What are the observables in RIB physics thatWhat are the observables in RIB physics thatcan zero-in -- like in the C14 case – on tensor can zero-in -- like in the C14 case – on tensor forces acting in varying density regimes?forces acting in varying density regimes?

If feasible, it will give a pristine signal if one If feasible, it will give a pristine signal if one can reach a density regime can reach a density regime nn1/21/2 ~ 2n ~ 2n0.0.