Topology change, emergent symmetry and compact star matter Yong-Liang Ma Colloquium @ ASU, Dec. 09, 2020. In collaboration with Mannque Rho et al.
Topology change, emergent symmetry
and
compact star matter
Yong-Liang Ma
Colloquium @ ASU, Dec. 09, 2020.
In collaboration with
Mannque Rho et al.
2020/12/09 Colloquium@ASU, UAS. 2
Outline
I. Introduction
II. Topology change and quark-hadron continuity
III.Hidden symmetries of QCD
IV.The pseudoconformal model of dense nuclear matter
V.Predictions of the pseudoconformal model
VI.Summary and discussions
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L. W. Chen, 1506.09057
EoS of nuclear matter at high density is a totally mess and uncharted domain.
IใIntroduction
Lattice QCD?
Low-temperature
terrestrial exp.?
IใIntroduction
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Finite nuclei as well as infinite nuclear matter can be fairly accurately accessed by nuclear EFTs,
pionless or pionful, (sEFT)" anchored on relevant symmetries and invariances along the line of
Weinberg's Folk Theorem.
sEFTs, as befits their premise, are expected to break down at some high density (and low
temperature) relevant to, say, the interior of massive stars.
e.g, In sEFT, the power counting in density is ๐(๐๐น๐). For the normal
nuclear matter, the expansion requires going to ~๐ = 5.
J. W. Holt, M. Rho and W.Weise, 1411.6681
IใIntroduction
Our strategy: Construct โGeneralized" nuclear EFT (GnEFT) while capturing
fully what sEFT successfully does up to ๐๐, can be extrapolated up to a density
where sEFT is presumed to break down.
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IใIntroduction
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Tidal deformability:
ฮ1.4 < 800
ฮ = 300โ230+420 โ ฮ = 190โ120
+390
๐ = 11.9โ1.4+1.4 ๐๐
Pressure: Massive neutron stars:
1.97 ยฑ 0.04 ๐โ Nature, 467(2010),1081.
(2.01 ยฑ 0.04)๐โ Science, 340(2013), 448.
(2.17โ 0.10+ 0.11)๐โ arXiv: 1904.06759.
โค 10๐0
C. Y. Tsang, et al., 1807.06571
IใIntroduction
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Basic new physics considered in our approach
Hidden topology in QCD The microscopic degrees of QCD โ quark and gluon โ enters the system rephrased
using Cheshire Cat Principle
Hidden symmetries of QCD Hidden scale symmetry
Hidden local flavor symmetry
Hidden parity doublet structure of nucleon
IใIntroduction
The former may be verifying the Suzuiki theorem and the latter may be indicating an infrared (IR) fixed point with both the chiral and scale symmetries realized in the NG mode.
GnEFT = sEFT + ฯ and ฯ + scalar meson ๐๐(๐๐๐)
Hidden local symmetry Dilaton/NGB of hidden scale symmetry
Intrinsic in QCD but not visible in the mater-free vacuum.
Get un-hidden by strong nonperturbative nuclear correlations, as nuclear matter is highly compressed.
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YLM & M. Rho, PPNP 20โ;
W. G. Paeng, et al, PRD 17โ.
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๐ฝ ๐ฅ1 ๐ฝ ๐ฅ2 โฏ๐ฝ(0) ๐ธ๐น๐
๐๐๐ก๐โ ๐๐ก ฮ๐<ฮฯ๐ฝ ๐ฅ1 ๐ฝ ๐ฅ2 โฏ๐ฝ(0) ๐๐ถ๐ท
๐ฟ๐ธ๐ถ๐ ๐ผ๐๐ก๐๐๐๐ ๐๐ถ๐ท ๐๐ข๐๐๐ก๐๐ก๐๐๐ ๐
๐๐ , ๐บ2 , โฏ
LECs* Medium modified Vacuum
The density dependence involved is intrinsic of QCD, referred to the IDD.
Full density dependence = IDD + IDDinduced
Lee, Paeng and Rho (2015); Paeng, Kuo, Lee, Ma and Rho (2017)
Harada and Yamawaki, PRD 01โ
Topology enters through IDD
IใIntroduction
IใIntroduction
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Only in terms of hadrons;
Intrinsic density dependence
Enters through the VeV ofdilaton: scale symmetry;
Information from topologychange is considered;
Nucleon mass stays as aconstant after topologychange: parity doublet.
The topology changedensity ๐1/2, parameter.
Density dependence of LECs
Qualitative information from topology change
Quark-Hadron continuity
Cashire Cat
IIใTopology change and quark-hadron continuity
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T. R. Skyrme, 1960
In large ๐๐ limit, baryon in QCD goes to skyrmion. Witten 79โ
Baryonic interactions in all regimes of density, upto that relevant to the core of CSs, can be accessed.
IIใTopology change and quark-hadron continuity
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Winding number =๐
๐Winding number =1
Topology transition
The half-skyrmion phase, characterized by the quark condensate ฮฃ โก ๐๐ vanishing on averagebut locally nonzero with chiral density wave and non-zero pion decay constant.
No phase transition!
IIใTopology change and quark-hadron continuity
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YLM, et al, PRD 13โ, 14โ
๐๐ =1
(2๐ฟ)3 0
2๐ฟ
๐3๐ฅ ๐๐
High density region(small L)๏ผ Quark condensate However Nucleon massvanishes is non-zero
Nucleon mass is not solely from chiral symmetry breaking, it include a chiral invariant part. parity doubling structure.
Agree with Y. Motohiro, et al, Phys.Rev. C92 (2015), 025201
Topology change: Parity doublet structure
IIใTopology change and quark-hadron continuity
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โSymmetry energy is dominated by the tensor forcesโ:
With nuclear correlations
The cusp is associated with the topology change with the emergence ofquasiparticle structure with the half-skyrmions.
Lee, Park and Rho, PRC11โ;Liu, YM and Rho, PRC19.
If this is right, excludes half of the EoS !
n1/2The existence of cusp is model independent.
IIใTopology change and quark-hadron continuity
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p, r N N
G.E. Brown and R. Machleidt 1994 โฆ A. Carbone et al 2013
Going toward to ๐1/2 from below, ๐ธ๐ ๐ฆ๐ to drop and more or less
abruptly turn over at ๐1/2 and then increase beyond ๐1/2. Gives precisely the cusp predicted in crystal; Produced by the emergent VM with ๐๐ โ 0 at ๐ > 25๐0. The only density dependence in the TEMT is through the dilaton
condensate inherited QCD with vacuum change. Cusp structure reflects the NPQCD effect manifested through ฯ . The TF is RG-invariant in both free space and in medium, which
carries the density dependence ONLY through IDD inherited from QCD, NOT nuclear renormalization.
๐1/2 = 2๐0
Same as left for ๐ < ๐1/2
but ๐ ๐โ โ ฮฆ2 for ๐ > ๐1/2.
IIใTopology change and quark-hadron continuity
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The Cheshire Cat
โHow hadrons transform to quarksโ
Baryon charge:
Brown, Goldhaber, Rho 1983Goldstone, Jaffe 1983
IIIใTopology change and quark-hadron continuity
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uud uud pionProton
When the bag radius is shrunk to zero, only the smile of the cat is left with spinning gapless quarks running luminally
Flavor singlet axial charge gA(0) (Lee et al)
IIใTopology change and quark-hadron continuity
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When ๐๐ = 1,
Since ๐3 ๐ 1 = 0 ;
Rule out the skyrmionapproach?
1812.09253 [hep-th]
๐ต๐ = ๐ baryon can be interpreted as quantumHall droplet. An important element in theconstruction is an extended, ๐ + ๐dimensional,meta-stable configuration of the ๐ผโฒ particle.Baryon number is identified with a magneticsymmetry on the ๐ + ๐ sheet.
๐ฑ๐ถ๐ท๐ธ = ๐๐ถ๐ท๐ธ๐น๐๐นฮทโฒ/๐๐
IIใTopology change and quark-hadron continuity
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Consists of free 2-dim quarks, charge
๐, and subject to a chiral bag BC
along the radial ๐ฅ-direction.
Leaks most quantum numbers.
Annulus of radius ๐ and clouded by an ๐โฒ-
field with a monodromy of 2๐.
The bag radius is immaterial thanks to CCP.
A current transverse to the smile is shown to appear. Hall current.
YLM, Nowak, Rho & Zahed, 1907.00958
IIIใHidden symmetries of QCD
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๐ ๐ฅ = ฮพ๐ฟ โ ๐ฅ โ(๐ฅ)โ ฮพ๐ โ
Redundancy in the decomposition
โ(๐ฅ) โ ๐๐(2)๐ฟ+๐ ร ๐(1)๐ฟ+๐
ฯ meson ฯ meson
The idea -- that is totally different from what one could call โstandardโ in nuclear community -is that ฯ (and ฯ, in a different way) is โhidden gauge fieldโ.Bando, et al 89; Harada & Yamawaki, 03
Rho and omega mesons play an important role in our formalism of compact star structure
It captures extremely well certain strong interaction dynamics even at tree order.
IIIใHidden symmetries of QCD
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Suzuki Theorem๏ผ
Proposition: Hidden local symmetry can emerge in nuclear dynamics with the vector meson mass driven to
zero at the vector manifestation fixed point by high density. Indeed in SUSY QCD, Komargodski, JHEP
1102, 019 (2011).
This theorem holds for rho if there is a sense of massless rho at some parameter space. The HLS with the
redundancy elevated to gauge theory, treated ร la Wilsonian RG, has (Harada & Yamawaki,01โ) a fixed point
at ๐๐ = 0. The KSRF relation ๐๐2 โ ๐๐
2๐๐2 holds to all loop orders, hence at the fixed point, called vector
manifestation (VM) fixed point, there โemergesโ a gauge field.
IIIใHidden symmetries of QCD
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๐๐(2)๐ฟร ๐๐(2)๐ linear sigma model
๐๐ฟ๐๐ =1
2๐๐ ๐๐๐ ๐๐๐โ -
๐2
2๐๐(๐ ๐โ ) -
ฮป
4(๐๐(๐ ๐โ ))2
K. Yamawaki, 2015
Proposition: Baryonic matter can be driven by increasing density from Nambu-Goldstone mode in scale-chiral symmetry to the dilaton-limit fixed point in pseudo-conformal mode.
Scale invariantLOSS
Scale noninvariant
IIIใHidden symmetries of QCD
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๐0(500) is a pNGB arising from (noted ๐๐0 โ ๐๐พ). The SB of SS associated + an explicit breaking of SI.
Assumption: There is an Nonperturbative IR fixed point in the running QCD coupling constant ฮฑ๐ .
EB of SI: Departure of ฮฑ๐ from IRFP + current quark mass.
Crewther and Tunstall , PRD91, 034016
Provides an approach to include scalar meson in ChPT.
IIIใHidden symmetries of QCD
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Beane and Klock, PLB, 94โ Paeng, Lee, Rho and Sasaki, 12โ
Proposition: Moving toward to the dilaton-limit fixed point, the fundamental constants in scale-chiral symmetry get transformed as ๐๐ โ ๐ฯ, ๐๐ด โ ๐๐ฃ๐ โ 1, and the ๐ meson decouples while the ฯ remains coupled, breaking the flavor ๐(2) symmetry.
ฯ decouples, HFS emerges.
Chiral inv. mass
๐ โ 0
IIIใHidden symmetries of QCD
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Paeng, Lee, Rho and Sasaki, PRD 13โ.
Emergent from parameter dialing from RMF:
Parity doubling emerges via an interplay between ฯโN coupling -- with ๐(2) symmetry strongly broken -- and the dilaton condensate.
In the MF of bsHLS, the TEMT is given solely by the dilaton condensate.
Proposition: Going toward the DLFP with the ฯdecoupling from the nucleons, the paritydoubling emerges and ๐๐
โ โ ฯ โ โ ๐0 .Consequently the TEMT in medium in ๐๐๐๐ค ๐๐ ๐บtheory is a function of only ๐0 which isindependent of density. This leads to the``pseudo-conformal" sound velocity ๐ฃ๐
2 โ 1/3 incompact stars
IVใThe pseudoconformal model of dense nuclear matter
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Only in terms of hadrons;
Intrinsic density dependence
Enters through the VeV ofdilaton: scale symmetry;
Information from topologychange is considered;
Nucleon mass stays as aconstant after topologychange: parity doublet.
The topology changedensity ๐1/2, parameter.
Density dependence of LECs
Qualitative information from topology change
Quark-Hadron continuity
Cashire Cat
IIIใHidden symmetries of QCD
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In GNEFT, the TEMT is given solely by the dilaton condensate.
Going toward the DLFP with the ฯ decoupling from the nucleons, the parity doubling
emerges and ๐๐โ โ ฯ โ โ ๐0. Consequently the TEMT in medium is a function of
only ๐0which is independent of density. This leads to the ``pseudo-conformal" sound
velocity ๐ฃ๐ 2 โ 1/3in compact stars
IVใThe pseudoconformal model of dense nuclear matter
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Hadron properties have different scales in ๐ < ๐๐/๐ and ๐ > ๐๐/๐
Different scaling behavior: ฮฆ๐ฐ and ฮฆ๐ฐ๐ฐ
Implement topology transition to EoS
ฮฆ๐ฐ: Predictions agree with the nuclear
matter at low density.
ฮฆ๐ฐ๐ฐ: Density independent.
Imbed the quanlitative conclusion to bsHLS
Calculate ๐ฝ๐๐๐ ๐
EoS for nuclear matter with IDD
IDD
DDinducedBeyond mean field
S.K. Bogner, T.T.S. Kuo, A. Schwenk, Phys. Rep. 386 (2003) .
IVใThe pseudoconformal model of dense nuclear matter
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Fitted function
PC Prediction
IVใThe pseudoconformal model of dense nuclear matter
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YLM & M. Rho, 2006.14173 v1
Agrees with the empirical values of the nuclear matter properties quite well.
IVใThe pseudoconformal model of dense nuclear matter
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Trace of energy-momentum tensor is not zero but a density independent constant at โฅ 2๐0;
When โฅ 2๐0๏ผthe sound velocity โ 1/ 3 -- conformal sound velocity.
A feature NOT shared by ANY other models or theories in the field
Low density relevant to NSs
IVใThe pseudoconformal model of dense nuclear matter
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Standard
Scenario
S. Reddy et al, 2018
We are disagreeing!
Very high densityPQCD applicable
VใPredictions of the pseudoconformal model
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Accommodate massive star โฅ ๐. ๐ ๐ด๐๐๐๐๐
GW data: ๐ฆ๐.๐, ๐น๐.๐ โฏ reflect the EoS for ๐ < ๐๐๐ ,below the topology change, and hence do not directlycontrol the massive stars of > ๐๐ด๐๐๐๐๐.
VใPredictions of the pseudoconformal model
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๐๐/๐ is constrained as ~(๐ โ ๐ )๐๐Agree with the constraints
VใPredictions of the pseudoconformal model
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YLM & M. Rho, 2006.14173
We do NOT agree
VใPredictions of the pseudoconformal model
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Estimate the location of ๐๐/๐using GWs emitted from BNS merger
VIใ Summary and discussions
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Hidden symmetriesHidden topology
PCM for DM ๐๐๐
โ 0; ๐ฃ๐ โ 1/ 3
Stand for the test fromboth nuclear physicsand astrophysics
Accommodates
massive NSs upto 2.23๐๐ ๐๐๐๐.
Quark-hadron continuity/CCP
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Is this pseudo-conformal structureat odds with Nature?
Not with whatโs measured (or known)up to now
Constraint to: 2.0๐0 โค ๐1
2
< 4.0 ๐0
VIใ Summary and discussions