spirals of chiral & spin dw in dense qcd in b · chiral spirals in 3+1-d at b ≠ 0 ! spiral is...
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Spirals of Chiral & Spin DW in Dense QCD in B !
Vivian de la Incera!University of Texas at El Paso!
Collaborators: Efrain. J. Ferrer and Angel C. Sanchez arXiv:1205.4492!
2!
Key Observations!• Large Nc QCD (good to describe nonperturbative effects
"" "" "" "" "" "of QCD: meson parameters, parton distributions)
Large Nc Limit: gs2Nc = constant!
‘tHoo$’74, Wi,en’79
• Vacuum Gluon and Quark Contributions
gs2 Nc ~ 1 gs
2 ~ 1/Nc
• Finite Density Screening effects ~ μ2/Nc!
only important at very high density
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
3!
μ
ΛQCD ~ !
Large NC : Gluon Propagator unaffected by quarks (same as in confined vacuum). Gribov-Zwanziger propagator:!!
Valid in the Coulomb gauge and for ! p≤ ΛQCD
McLerran & Pisarski, NPA’07; Kojo, et al NPA’10!
perturba=ve
Quarkyonic Matter!Relevant at high density & large Nc , where screening effects are negligible !!!Bulk Properties: perturbative!Excitations at the Fermi surface: confined !
!
mD << "QCD << µ
✕
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
4!
Dimensional Reduction at B=0!
Can neglect p⊥ in the quark propagator, because in the !patch at the Fermi surface p⊥< ΛQCD << µ and !
then,!
4D QCD in Coulomb gauge reduces to 1+1 D QCD in axial gauge Az=0!
Shuster & Son, ‘99!Kojo et al, ‘10!Sp
irals o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
5!
Effective 1+1 D Theory at B=0!Chiral rotation!
Chiral Spirals!
=
Chiral !condensate!
=
Kojo, et.al NPA’10!
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
6!
Condensates!At B = 0
Contributions of opposite spins cancel out!
Inverting the chiral rotation !
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
7!
A New Needed Ingredient: Nonzero B!
Landau levels!
Possible realization of QCS:!Heavy ion collision experiments & neutron stars !Both environments typically have very strong magnetic fields,
!
B " #QCD
2
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
8!
SD Eq. at B ≠ 0 in Confining Potential!
Gribov-Zwansiger propagator:!
CF=(Nc2 -1)/2Nc ! σ! ~! ΛQCD
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
9!
SD Eq. at B ≠ 0 in Confining Potential!Sp
irals o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
Gribov-Zwansiger propagator:!
CF=(Nc2 -1)/2Nc ! σ! ~! ΛQCD
10!
Patch on the z-axis: Dimensional Reduction!Assume qB (ΛQCD)2 !
!
"
One equation for each LL in the patch. The LLs become flavors l
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
Only one spin contributes to the lowest LL!
!
"(l) = #(+) + #($)(I $%l0)
11!
Efffective (1+1)-D Theory at B≠0!Assume qB (ΛQCD)2 !
1+1-D theory with lmax flavors
!
"
zero Landau level!
!
"0
=#0$
0
%
& '
(
) *
!
"l=#
l$
#l%
&
' (
)
* +
higher Landau levels l>0!
lmax
= [!2/ 2eB]
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
12!
Quarkyonic Chiral Spirals at B≠0!Chiral rotation!
Kojo, et.al NPA’10!
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
13!
Spirals at B ≠ 0 !
Ferrer, V.I, and Sanchez, arXiv:1205.4492!
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
P and T broken. Rotational sym. explicitly broken by B, translational symmetry spontaneously broken by the spirals!
14!
Chiral Spirals in 3+1-D at B ≠ 0 !
Spiral is formed by chiral and electric dipole condensates!
Spiral is formed by pion and magnetic moment condensates!
Ferrer, V.I, and Sanchez, arXiv:1205.4492!Sp
irals o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
Generation of Parallel & Inhomogeneous Electric and Magnetic fields!
15!
Condensates!At B ≠ 0
The LLL makes it nonzero!!!
and
Spira
ls o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
16!
Outlook!Sp
irals o
f Ch
iral & S
pin
DW in
Den
se Q
CD in
B!
Preliminary Findings:!Ferrer, VI, and Sanchez, in prep.!In the equatorial patch the contribution is very similar to the case at B=0 since the LLs are very close to each other. Only one type of quarkyonic spiral in this patch.!
Equatorial Patch!
Has B anything else hidden in the drawer?!
Galilo & Nedelko ’11 !In a strong magnetic field the gluon field configuration that minimize the action does not support confinement of quarks !
Miransky & Shovkovy ’02 !In a strong magnetic the confining scale is smaller! (for Nc< Nc
thr)! λQCD< ΛQCD !!
Findings at μ=0:!
Can B increase the screening by modifying mD?!
Quarkyonic!
μ >> ∧QCD
17
Graph, courtesy of T. Kojo!
Can B increase the screening by modifying mD?!
Quarkyonic!
μ >> ∧QCD
18 B Λ2
QCD !~!