TOPOLOGY CHANGE AND HADRON PROPERTIES IN COLD DENSE MATTER WCU-Hanyang Project Work in progress with Hyun Kyu Lee and Byung-Yoon Park
Dec 18, 2015
TOPOLOGY CHANGE AND HADRON PROPERTIES IN COLD DENSE MATTER
WCU-Hanyang Project
Work in progress with Hyun Kyu Lee and Byung-Yoon Park
LESSONS FROM CONDENSED MATTER : “EMERGING”(HIDDEN) GAUGE SYMMETRY (HLS)
Neel magnet Broken spin-rotation symmetry
Valence bond solid(VBS) paramagnetBroken lattice-rotation symmetry
Senthil et al, Science 303, 1490 (2004)
Sigma model (skyrmion)
HLS(½-skyrmion)
POWER OF EFFECTIVE FIELD THE-ORY
Both A (Neel magnet) and B (VBS) are captured by the Nonlinear s model + Berry phase.
“Spinon” =order parameter in A ≠ order parameter in B
While the s model describes A and B, the Berry phase playsno role in A but is crucial in B in giving the VBS order, so the phase transition does not involve the same order parameter.“Ginzburg-Landau-Wilson paradigm does not apply here.”
EMERGENT LOCAL SYMMETRY OR HLS
Interplay of the emergent gauge field and the Berry phaseleads to HLS theory between the A phase and the B phase
Skyrmions replaced by 1/2-skyrmions
Skyrmion number ~
CP1
Manifestation in nuclear physics Nuclear tensor forces and (a)symmetry energy Esym in compressed baryonic matter
Analogy (?) to “deconfined Quantum critical phenomenon”
NATURE: ESYM AT
Fit to FOPI/GSI data for p-/p+ ratio → “supersoft” (ESS)
A: “supersoft” Ess
B: all others
Xiao et al, PRL 102 (09) 062502
n > n0 ?
400 MeV/A
Transport model analysis using IBUU04Z. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, PRL 102, 062502 (2009)
Au+Au
“ESS” COULD BE A DISASTER !!??
There could be NO stable neutron stars unless …!!
But Nature is full of neutron stars including the Hulse-Taylor binary pulsar.
If Nature chose the “supersoft” ESS
AVOIDING THE DISASTER
There could be NO stable neutron stars unless …!! But Nature is full of neutron stars including the Hulse-Taylor binary pulsar.
Drastic wayout by D.H. Wen et al, PRL 103, 211102 (09):
Modify Newtonian gravity.
Why not? It could be emergent (E. Verlinde, arXiv:1001.0785).
If Nature chose the “supersoft” ESS
AVOIDING THE DISASTER
There could be NO stable neutron stars unless …!! But Nature is full of neutron stars including the Hulse-Taylor binary pulsar.
Drastic wayout by D.H. Wen et al, PRL 103, 211102 (09):
Modify Newtonian gravity.
Why not? It could be emergent (E. Verlinde, arXiv:1001.0785).
But kaons will not condense, andmake Bethe and Brown very unhappy
If Nature chose the “supersoft” ESS
HOW TO CONCOCT THE ESS
Possible mechanism: medium-scaling tensor forces
, p r
Tensor forces cancel: Exploit medium-enhanced cancelationto describe the C14 dating by J.W. Holt et al, PRL 100, 062501 (08)
Assumed scaling:
C. Xu & B.A. Li, arXiv:0910.4803
APPLY TO ESYM
Esym
n
Fi(n)= 1-ai (n/n0)
a0 =0
a1
a2
a3
am
0=a0 < a1 < a2 <a3 …<am ≈ 0.2
n0
C. Xu & B.A. Li, arXiv:0910.4803
for all density (n)
BUT HALF-SKYRMION (OR DYONIC*) PHASE ENTERS
Described in terms of skyrmions, baryonic matterhas a “phase transition” at ndeconf > n n1/2 > n0 froma skyrmion matter to a ½-skyrmion matter
*Sin, Zahed, R Ismail’s talk
Drastic change
HLS IN DENSE MATTER
Mimic generic features of the Neel-VBS (though with different physics):
Nonlinear sigma model: NLs
Hidden gauge invariance:
Promote to gauge theory with nonabelian gauge field rm : Harada/Yamawaki HLS theory: HLS
NLs model is “gauge-equivalent” to HLS
IN NATURE
xL,R decouple: L,R symmetries “restored” and xL,R and rm arethe relevant degrees of freedom as in the Neel-VBS transition
(a) Nc → → a ≈1 & g ~ 0 : light-quark vector mesons tend to “vector limit” (HG) or “vector manifestation” (Harada-Yamawaki) (b) V(ector)D(ominance) is violated in medium (density & temperature)
H. Georgi, 1990
GEORGI’S “VECTOR MODE”
H. Georgi, 1990
At large Nc , k (1-a) → 0, g ~ 0
• Vector mesons (e.g., r) are light ~ 1/Nc , become degenerate with p in the vector (or VM) limit. Cf: Weinberg’s “mended symmetry.”• Baryons as matter field are massive ~ Nc figuring in terms of two kinds of skyrmions
Supports •A variety of light-quark phenomena, e.g. p mass difference• Heavy-light-quark phenomena, e.g., chiral doubler• Nucleon form factor• Etc etc.
VD VIOLATION IN NUCLEON FORM FACTOR
Iachello, Jackson & Lande, 1973 Brown, Weise, R., 1986Bijker & Iachello, 2004
+ (1-z/2)z + (1-z/2)
Cf: VD → z=2 Phenomenology: z ≈ 1
HLS: z =
g g
HLS4D
“Core” &Cheshire Cat
Holography
I. Zahed
“a” goes to 1: Vector dominance a la Sakurai violated in medium!!!
V = , r r’,r”, …r
HLS5D
APPEARANCE OF FRACTIONIZED SKYRMIONS
skyrmion
half-skyrmion
Simulate dense matter by putting skyrmions in FCC crystals and squeeze them: ½-skyrmions in CC appear at n1/2
B.Y. Park et al,1999
skyrmions Half-skyrmions
ALSO IN HQCD: “DYONIC SALT”
Increasing density
Instantons: FCC
½ instantons(dyons): BCC
Sin, Zahed, R., Phys. Lett. B689, 23 (2010)
Dyons are bound by ~ 180 MeV.
“PHASE”STRUCTURE
Sigma model
HLS model
The ½-skyrmion phase at n n1/2 is characterized by
Rough estimate: n1/2 ~ (1.3 – 2) n0
n1/2ndeconf
i.e. “vector mode”
WHAT DOES THE ½-SKYRMION PHASE DO TO ESYM ?
Symmetry energy 1/N∼ c
Isospin rotation
Collective-quantize the (neutron) skyrmion matterI. Klebanov, 1985
Moment of inertia
HOW TO UNDERSTAND THE CUSP AT IN “STANDARD”NUCLEAR PHYSICS?
In-medium scaling
n1/2
H.K. Lee, B.Y. Park, R. 2010
ASSUMPTIONS 1. Skyrmion number Q is conserved, a baryon can be considered as a bound pair (B ~ 100-200 MeV) of 2 half-skyrmions in the half-skyrmion phase.2. Half-baryons interact via exchange of pions and vector mesons, giving a meaning to “effective nuclear forces.”3. Quasiparticle description with effective masses and coupling constants makes sense.
Scaling in density
TENSOR FORCES ARE DRASTICALLY MODIFIED IN THE ½-SKYRMION PHASE
For density n n1/2 :
n=n0
n=2n0
n=0+p r
Above n1/2, the r tensor gets “killed,” enabling the pions (p0’s) to condense → pionic crystal in dense neutron matter ( e.g., Pandharipande and Smith 74).
Decreasing tensor Increasing tensor
n1/2
For density n < n1/2 :
“standard” nuclear physics
,
½-skyrmion vs. scaling
Scaling prediction
This prediction could be checked or falsified atFAIR or even RIB (e.g., KoRIA) machines
½-skyrmion
APPLICATION: STRANGE GOINGS-ON IN COMPRESSED MATTER
Insert anti-kaon in half-skyrmion matter
Skyrmion-1/2-skyrmion background
Ignore kaon back-reaction onto (half-)skyrmion matter
J.I. Kim, B.Y. Park, R. 2009
ANALOGY TO “MAGNETIC SPIRALS” WITH SPIN → ISOSPIN?
Pfleiderer & Rosche,Nature, 17 June 2010
Chiral magnetic spiralsDzyaloshinsky-Moriya interaction
ppnK-
“Challenging problem” !
pp
n
K-
1.5 fm
rN(0) = 9r0
rNav= 3r0
1.2 fm
MeV20,MeV108 E
MeV25,MeV6169 EExp.
DB th -ex ~ 60 MeV
Chiral restoration ?
Relativistic effect ?
Y. Akaishi 2010
“MYSTERIOUS” ATTRACTION IN ½-SKYRMION MATTER
△B ~ 50-60 MeV
Is this what Akaishiand Yamazaki need for dense kaonic matter ?
DB
DEDONFINED QUANTUM CRITICAL?
ss Crystal
Density
Sigmamodel
Sigmamodel
½-skyrmions
n1/2 ~ (1.3-2)n0
“superqualiton”
Hong, Zahed, R. (99)
CONCLUSION
If the ½-skyrmion phase (in 4D) or the ½-instanton (or dyonic-salt) phase (in 5D) is present at a density not far above n0 , drastic effects are expected for a variety of low-temperature nuclear processes, in particular, in the EOS crucial for compact stars.
So what is the real “doorway” to higher-density phase(s)?