3D structure and entanglement of QCD Piet J Mulders - - PowerPoint PPT Presentation

3d structure and entanglement of qcd
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3D structure and entanglement of QCD Piet J Mulders - - PowerPoint PPT Presentation

Argonne National Laboratory, 14 May 2019 3D structure and entanglement of QCD Piet J Mulders p.j.g.mulders@vu.nl <latexit


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SLIDE 1

3D structure and entanglement of QCD

p.j.g.mulders@vu.nl Piet J Mulders Argonne National Laboratory, 14 May 2019

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SLIDE 2

QCD – entangled states and QIT

Parton-hadron duality in hard QCD scattering: PDFs x FFs nucleon is pure state à ensemble of partons (good light-front states) hard (short distance) process: partons à partons emerging partons are pure state(s) à ensemble of hadron states Entangled (pure) states |Φ> in bipartite ( ) space, with a density matrix ρ = |Φ><Φ|, lead to ensembles (non-pure state) in the reduced spaces. EPR bipartite pure state leads to a 50% - 50% ensemble in subspaces Maximal entanglement associated with maximal entropy Tripartite states come in two classes of maximal entangled states. Both hadrons and partons might live in a multipartite space! This requires careful thinking about ‘resolution’ or more fundamental about ‘local’, as well as about ‘TMD’ Multipartite entanglement offers a new perspective to include leptons, quarks, gauge bosons and Higgs field in a more fundamental framework that explains emergence of symmetries in the standard model of particle physics (revival of rishon model).

2

HA ⊗ HB

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HA ⊗ HB ⊗ HC

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SLIDE 3

ENTANGLEMENT OF HADRONS

3

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SLIDE 4

Entanglement in hard processes

A nucleon is an (entangled) pure state (or a spin ensemble) Hard processes serve as entanglement witness (for a hermitean semi-definite operator W) Start with initial state density matrix Split scattering process into Define production part and decay/fragmentation part (specify hadrons/spins) Final state distribution is Entanglement studies via fragmenting (specific hadrons or spin analyzers) ‘Maximal entanglement’ and ‘scattering enhanced entanglement’ (ask me later)

Cervera-Lierta, Latorre, Rojo & Rottoli (1703.02989)

4

ρi = |PihP|

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M(i → f → mf) = M(i → f)M(f → mf)

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ρi = |PihP|

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Rdecay

β0α0

= M ∗

β0→mf (f)Mα0→mf (f)

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Rprod

αβ;α0β0 = M ∗ β→β0(i → f)Mα→α0(i → f)

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ρf = M|PihP|M † Tr(ρi M †M) = ρi Rprod Tr(ρi Rprod)

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Tr(ρfRdecay) = Tr(ρiRprodRdecay) Tr(ρiRprod)

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Tr(ρW) < 0

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SLIDE 5

PDFs are naturally, the ‘momentum ensembles’ upon selecting x = p+/P+ via hard interaction δ(x-xB) Gluons in entangled proton state: partonic entropy

Kharzeev & Levin, 1702.03489; see also 1903.07133 and 1904.11974

Entanglement and distribution functions

5

S(x) = ln(xg(x))

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SLIDE 6

EMERGENCE OF TMDs

Selection/probing through the quark and gluon operators in PDFs and FFs including nonlocal extensions and chiral or directional projections Interesting is probing with something containing color: Wilson loops Diffractive probing see also Tarasov & Venugopalan, 1903.11624

6

ψγ+ψ = ψ†

+ψ+

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F +αF +β

<latexit sha1_base64="wYxjgKpW1fD/lXdwd3iO2/KatM=">AB/nicbZDLSsNAFIYnXmu9RcWVm8EiCEJqDLgiAuK9gLtLGcTCft0MkzEyEgK+ihsXirj1Odz5Nk7TLT1h4GP/5zDOfP7MWdKO863tbS8srq2Xtob25t7+zae/stFSWS0CaJeCQ7PijKmaBNzTSnVhSCH1O2/74elpvP1KpWCTu9SmXghDwQJGQBurbx/ePKRnPeDxCLIcfaoh69sVp+rkwovgFlBhRp9+6s3iEgSUqEJB6W6rhNrLwWpGeE0K/cSRWMgYxjSrkEBIVemp+f4RPjDHAQSfOExrn7eyKFUKlJ6JvOEPRIzdem5n+1bqKDKy9lIk40FWS2KEg41hGeZoEHTFKi+cQAEMnMrZiMQALRJrGyCcGd/IitGpV97xau7uo1GtFHCV0hI7RKXLRJaqjW9RATURQip7RK3qznqwX6936mLUuWcXMAfoj6/MH0YuVWQ=</latexit>

✏α(k)✏β∗(k) = ⇒

Γ[U,U 0] µν(x, pT ; n) = Z d ξ·P d2ξT (2π)3 eip·ξ hP| F nµ(0) U[0,ξ] F nν(ξ) U 0

[ξ,0] |Pi

  • ξ·n=0
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Γαβ( p) Γ0( pT )

Γ[U,U 0] (kT ; n) = Z d2ξT (2π)2 eik·ξ hP|U[0,ξ] U 0

[ξ,0] |Pi

  • ξ=ξT
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[ξ−, ξT ]

[0−, 0T ]

[∞, ξT ]

[∞, 0T ]

[−∞, ξT ]

[−∞, 0T ]

[ξ−, ξT ]

[0−, 0T ]

[∞, ξT ]

[∞, 0T ]

[−∞, ξT ]

[−∞, 0T ]

slide-7
SLIDE 7

Gluon TMDs and Wilson loops via GTMDs

7

⌘ ⌘

p = P ∆

2

p0 = P + ∆

2

k + ∆

2

k ∆

2

W

h i∂α

x , U [±] [a,x]

i = ±gU [±]

[a,x]Gα T (x)

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G[+,]αβ(kT , ∆T ) = 16 Z d2z d2b (2π)3 eikT ·zT i∆T ·bT hp0|Gβ

T (x)U [] [x,y]Gα T (y)U [+] [y,x]|pi

  • LF

hP|Pi

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G[+,]αβ(x, kT , ξ, ∆T ) = 4 Z d3z d3b (2π)3 eik·zi∆·b hp0|F nβ(x)U []

[x,y]F nα(y)U [+] [y,x]|pi

  • LF

hP|Pi

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gluonic pole: x=ξ=0 x, y ← → z, b

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T (xT ) =

Z ∞

−∞

dz− U [−]

[0,x]F nα(z−, xT )U [+] [0,x]

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G[⇤](kT , ∆T ) = Z d2z d2b (2π)4 eikT ·zT i∆T ·bT hp0| 1

Nc Tr

  • U [⇤](x, y)
  • |pi
  • LF

hP|Pi

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Basis: Wilson loop GTMD

slide-8
SLIDE 8

Gluon TMDs and Wilson loops via GTMDs

Thus we can use the (off-forward) Wilson loop GTMD, ... to obtain the gluon GTMD at x = 0 as well as the gluon TMD at x = 0

8

G[⇤](kT , ∆T ) = Z d2z d2b (2π)4 eikT ·zT i∆T ·bT hp0| 1

Nc Tr

  • U [⇤](x, y)
  • |pi
  • LF

hP|Pi = αs 2Nc M 2 E(k2

T , ∆2 T , kT ·∆T )

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G[+,−]αβ(kT , ∆T ) = " kα

T kβ T

M 2 − ∆α

T ∆β T

4M 2 − k[α

T ∆β] T

2M 2 # E(k2

T , ∆2 T , kT ·∆T ) ∆→0

= ⇒ kα

T kβ T

M 2 e(k2

T )

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[ξ−, ξT ]

[0−, 0T ]

[∞, ξT ]

[∞, 0T ]

[−∞, ξT ]

[−∞, 0T ]

F αβ = δW[C] δσαβ

slide-9
SLIDE 9

Gluon TMDs in unpolarized hadrons

Wilson loop correlator Gluon (G)TMD at x=ξ=0 There are several gluon TMDs for unpolarized hadrons: Small x behavior of (dipole) gluon TMDs Naively, TMDs behave as 1/x, diverge for x à 0 (or less naively: small x behavior xα with 1 < α < 2)

9

Γαβ( p) Γ0( pT ) Γαβ[U](x, kT ) = x 2 ⇢ −gαβ

T f [U] 1

(x, k2

T ) + kαβ T

M 2 h⊥ [U]

1

(x, k2

T )

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Γ[+,−] (kT ) = 1 2M 2 e[+,−](k2

T )

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x f [+,−]

1

(x, k2

T ) x→0

= ⇒ k2

T

2M 2 e[+,−](k2

T )

<latexit sha1_base64="csF8WP2isD0Oap1/iK1tEkqAmb4=">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</latexit><latexit sha1_base64="csF8WP2isD0Oap1/iK1tEkqAmb4=">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</latexit><latexit sha1_base64="csF8WP2isD0Oap1/iK1tEkqAmb4=">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</latexit><latexit sha1_base64="csF8WP2isD0Oap1/iK1tEkqAmb4=">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</latexit>

x h⊥[+,−]

1

(x, k2

T ) x→0

= ⇒ e[+,−](k2

T )

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G[+,−]αβ(kT , ∆T )

∆→0

= ⇒ kα

T kβ T

M 2 e[+,−](k2

T )

<latexit sha1_base64="2Vp1TJ1YVnXu9bKaRnO24TwDpA=">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</latexit>
slide-10
SLIDE 10

Gluon TMDs in polarized nucleon

Polarized target (vector polarization)

  • Cf. Wilson loop TMDs in polarized nucleon (no TMD for L polarization)

10

Γij[U]

L

(x, kT ) = x 2 ⇢ i✏ij

T SLg[U] 1 (x, k2 T ) + ✏{i T αkj}α T

M 2 SLh⊥ [U]

1L

(x, k2

T )

  • Γij[U]

T

(x, kT ) = x 2 ⇢gij

T ✏kST T

M f ⊥[U]

1T

(x, k2

T ) − i✏ij T kT ·ST

M g[U]

1T (x, k2 T )

− ✏k{i

T Sj} T + ✏ST {i T

kj}

T

4M h1(x, k2

T ) − ✏{i T αkj}αST T

2M 3 h⊥

1T (x, k2 T )

  • Γ0(kT ) =

1 2M 2 ⇢ e(k2

T ) − ✏kST

M eT (k2

T )

  • D Boer, MG Echevarria, PJM, J Zhou, PRL 116 (2016) 122001, ArXiv 1511.03485
  • S. Cotogno, T. van Daal, PJM, JHEP 1711 (2017) 185, ArXiv 1709.07827

‘pomeron’ ‘odderon’

D Boer, S Cotogno, T van Daal, PJM, A. Signori, Y Zhou, JHEP 1610 (2016) 013, ArXiv 1607.01654

Note on bounds: |kT | M |eT (k2

T )| ≤ e(k2 T )

<latexit sha1_base64="SP2Ld+xPXyKFMVTe6cd5tuBLwk=">ACJnicbVDLSgMxFM34rPVdekmWIQKUmaqoBuh4MaNUKEv6IxDJr3ThmYeJBmhDP0aN/6KGxcVEXd+imlnFtp6IHByzrk93gxZ1KZ5pexsrq2vrFZ2Cpu7+zu7ZcODtsySgSFo14JLoekcBZC3FIduLIAEHoeON7qd+Z0nEJFYVONY3ACMgiZzyhRWnJLN7YvCE1tnVF45DbnZJLeT7B9nongNivaeKydZXebA4ZcUtls2rOgZeJlZMytFwS1O7H9EkgFBRTqTsWasnJQIxSiHSdFOJMSEjsgAepqGJADpPM1J/hUK3sR0KfUOG5+nsiJYGU48DTyYCoVz0ZuJ/Xi9R/rWTsjBOFIQ0e8hPOFYRnWG+0wAVXysCaGC6b9iOiS6N6WbLeoSrMWVl0m7VrUuqrWHy3K9ltdRQMfoBFWQha5QHd2hBmohip7RK5qid+PFeDM+jM8sumLkM0foD4zvH8XdpJg=</latexit>

Dominguez, Xiao, Yuan 2011; Hatta, Xiao, Yuan 2016

slide-11
SLIDE 11

Small x physics in terms of TMDs

Dipole gluon TMDs: at small x only two structures for unpolarized and transversely polarized nucleons: pomeron & odderon structure Circularly polarized gluons in transversely polarized nucleons and TMDs in longitudinally polarized nucleons: Naively: TMDs tend to zero for x à 0 (less naively: small x behavior xα with α < 1)

11

x h⊥[+,−]

1

(x, k2

T ) −

→ e[+,−](k2

T )

x f [+,−]

1

(x, k2

T ) −

→ k2

T

2M 2 e[+,−](k2

T )

x f ⊥[+,−]

1T

(x, k2

T ) −

→ k2

T

2M 2 e[+,−]

T

(k2

T )

x h[+,−]

1

(x, k2

T ) −

→ k2

T

2M 2 e[+,−]

T

(k2

T )

x h⊥[+,−]

1T

(x, k2

T ) −

→ e[+,−]

T

(k2

T )

D Boer, S Cotogno, T van Daal, PJM, A. Signori, Y Zhou, JHEP 1610 (2016) 013, ArXiv 1607.01654

slide-12
SLIDE 12

A=208 A=63

0.0 0.2 0.4 0.6 0.8

k (GeV)

0.01 0.02 0.03 0.04

v1

Nuclear measurements of GTMDs

Back to unpolarized GTMDs (at x=ξ=0) Can be complex Odderon (C-odd) contribution in only has odd powers in kT.ΔT and vanishes in the forward limit As bT (FT of ΔT) and zT (FT of kT) involve different scales in a nucleus (nuclear for bT and nucleonic for zT) the odderon part could show up, e.g. in ultra - peripheral pA scattering via azimuthal asymmetries (directed flow) Needs cubic term in CGC action Leads to 1/A1/3 effect

12

G[+,−]αβ(kT , ∆T ) = 2Nc αs h kα

T kβ T − 1 4∆α T ∆β T − 1 2k[α T ∆β] T

i G[⇤](kT , ∆T )

<latexit sha1_base64="Uj8SrbYZcux9Wt/fmTchq41q2Q=">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</latexit>

Hermiticity: G[⇤]∗(kT , ∆T ) = G[⇤](kT , −∆T )

<latexit sha1_base64="lP8HrH8u+0gTHbimLbfQLXBC6Is=">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</latexit>

Time reversal: G[⇤]∗(kT , ∆T ) = G[⇤†](−kT , −∆T )

<latexit sha1_base64="hBKz10bnLOrMPBhja4pf2xfSGMk=">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</latexit>

G[⇤](kT , ∆T )

<latexit sha1_base64="dOx8WRc98obzcPWOZd5dLVFu8=">ACAXicbVDLSsNAFJ3UV62vqBvBzWARKkhJqDLoIuK/QFSQyT6bQdOpmEmYlYQt34K25cKOLWv3Dn3zhts9DWAxcO59zLvfcEMaNSWda3kVtYXFpeya8W1tY3NrfM7Z2mjBKBSQNHLBLtAEnCKCcNRUj7VgQFAaMtILB5dhv3RMhacTrahgTL0Q9TrsUI6Ul39y7vksd9yJ68EalgV8/dq8IU8ivH/lm0SpbE8B5YmekCDLUfPL7UQ4CQlXmCEpHduKlZcioShmZFRwE0lihAeoRxNOQqJ9NLJByN4qJUO7EZCF1dwov6eSFEo5TAMdGeIVF/OemPxP89JVPfcSymPE0U4ni7qJgyqCI7jgB0qCFZsqAnCgupbIe4jgbDSoRV0CPbsy/OkWSnbJ+XK7WmxWsniyIN9cABKwAZnoApuQA0AaP4Bm8gjfjyXgx3o2PaWvOyGZ2wR8Ynz8jSJX9</latexit>

Directed flow v1(k) for p Cu and p Pb scattering using CGC

D Boer, PJM, E. Petreska, JHEP 1807 (2018) 140, ArXiv 1805.05219

slide-13
SLIDE 13

ENTANGLEMENT OF PARTONS?

13

slide-14
SLIDE 14

Fragmentation

Fragmentation also leads to an ensemble that (within the constraints such as charge, flavor, spin) appears to maximize entropy.

14

Possibly explains success of statistical hadronization model not due to thermalization by collisions note presence of (> 5 fm) Conjecture: Entanglement of partons! Involving color as well as space-time freedom!

Mass (GeV)

0.5 1 1.5 2 2.5 3 3.5 4

+1) J /(2 y /d N d

7 −

10

6 −

10

5 −

10

4 −

10

3 −

10

2 −

10

1 −

10 1 10

2

10

3

10 Data, ALICE Statistical Hadronization total (after decays) primordial

=2.76 TeV

NN

s Pb-Pb

0-10% centrality

+

π

+

K p φ Λ

  • Ξ
  • Ω

d He

3

H

Λ 3

He

4

  • FIG. 2. Mass dependence of hadron yields compared with

predictions of the statistical hadronization model. Only par- ticles, no anti-particles, are included and the yields are di- vided by the spin degeneracy factor (2J + 1). Data are from the ALICE collaboration for central Pb–Pb collisions at the

  • LHC. For the statistical hadronization approach, plotted are

the “total” yields, including all contributions from high-mass resonances (for the Λ hyperon, the contribution from the elec- tromagnetic decay Σ0 → Λγ, which cannot be resolved ex- perimentally, is also included), and the (“primordial”) yields prior to strong and electromagnetic decays. For more details see text.

3 ΛH

<latexit sha1_base64="9AvY2M7X9AhVmdQFEgoQacdXfc=">AB/XicbVDLSsNAFJ3UV62v+Ni5CRbBVUlaQZcFN124qGAf0MQwmUzaoTOZMDMRawj+ihsXirj1P9z5N07bLT1wMDhnHu4d06QUCKVbX8bpZXVtfWN8mZla3tnd8/cP+hKngqEO4hTLvoBlJiSGHcURT3E4EhCyjuBeOrqd+7x0ISHt+qSYI9BocxiQiCSku+eZTldw3fvdaJELos4A9ZK/fNql2zZ7CWiVOQKijQ9s0vN+QoZThWiEIpB46dKC+DQhFEcV5xU4kTiMZwiAeaxpBh6Wz63PrVCuhFXGhX6ysmfo7kUEm5YQFepJBNZKL3lT8zxukKr0MhInqcIxmi+KUmopbk2rsEIiMFJ0oglEguhbLTSCAiKlC6voEpzFLy+Tbr3mNGr1m/Nqs17UQbH4AScAQdcgCZogTboAQewTN4BW/Gk/FivBsf89GSUWQOwR8Ynz+O7ZU+</latexit>

A Andronic, P Braun-Munzinger, K Redlich, J Stachel, 1710.09425 F Berges, S Floerchinger, R Venugopalan, NPA 982 (2019) 819

slide-15
SLIDE 15

Statistical model for hadronization

15

  • Fig. 1 Above: fitted vs. measured midrapidity densities in pp colli-

sions at √s = 200 GeV. Below: residual distributions

proton-proton scattering electron-positron annihilation

F Becattini, P Castorina, J Manninen and H Satz, EPJ C 56 (2008) 493 F Becattini, P Castorina, A Milov and H Satz, EPJ C 66 (2010) 377

slide-16
SLIDE 16

Statistical model for hadronization

Precise details of model not so relevant

16

  • Fig. 4 Comparison between measured and fit multiplicities of long-lived hadronic species in e+e− collisions at √s = 91.25 GeV. Left: statistical

hadronization model with one temperature. Right: Hawking–Unruh radiation model

F Becattini, P Castorina, J Manninen and H Satz, EPJ C 56 (2008) 493

slide-17
SLIDE 17

EMERGENT GAUGE SYMMETRIES

17

slide-18
SLIDE 18

entanglement of quarks and leptons (another perspective)

Standard model: symmetry pattern: SU(3) x [SU(2) x U(1)] but … complex

right-left, particle-antiparticle color families

Emergence? Conjecture: at the basis of this pattern are entangled triplets of supersymmetric fields

18

eL

eR uR

dR dL

uL

uL

dL

uR

dR

νR

νL eL

eR

uR

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uL

Z, γ

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W +

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W −

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Y

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I3

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Q

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A x B x C

φ2L

  • 1/2

1/2 1

Y I3

φ1L

φ1R

+

φ2R φ3L

+

φ3R

Q

ξ2L

  • 1/2

1/2 1

Y I3

ξ1L

ξ1R

+

ξ2R ξ3L

+

ξ3R

Q

slide-19
SLIDE 19

Hilbert space (0D field theory) Supercharges For boson and fermion fields Implement symmetries via constraints F ... and a nontrivial vacuum (not everything is for free!)

19

[a, a†] = 1, {b, b†} = 1

{(a†)n|0i, b†|0i} Q†

ik = bi a† k and Qik = b† iak

a†

k Qik

− → b†

i

a†

k Q†

ik

← − b†

i hamiltonian/number operators (i=j, k=l) & unitary rotations

{Q†

ik, Qjl} = 1 2 δij{a† l , ak} + 1 2 δkl[b† i, bj]

ϕ = 1 √ 2ω

  • a + a†

and ξ = 1 √ 2

  • b + b†

iD = i∂ + gA

[Q, ϕ] = ξ {Q, ξ} = {Q, [Q, ϕ]} = F = iDϕ [Q, F] = [Q, {Q, ξ}] = iDξ

Single (free) field

unitary rotations

Q = √ω(a†b − b†a)

F = [ϕ, H] = iDϕ = i ˙ ϕ

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φ(t) = T exp ✓ −i Z t ds·D ◆ φ

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Emergent symmetries in a SUSY setting

slide-20
SLIDE 20

Real/Majorana: (Wess-Zumino) Fields Generators Internal Space-time & multipartite setting H P+, P- K, SU(3)

20

φ ξ and hφi = 1

φR/L ξR/L and hφRi = hφLi = 1/ p 2

U(1)R x U(1)L x SU(3)

Emerging symmetries and space-time

slide-21
SLIDE 21

Real/Majorana: (Wess-Zumino à gauge theory) 1D: Fields Generators Space-time & Internal H P+, P- K, SU(3) Z(2) H, P, K SU(3)

21

φ ξ and hφi = 1

φR/L ξR/L and hφRi = hφLi = 1/ p 2

φS φP Aa

3

ψ

P(1,1) x SU(3) iDσψi = i∂σψi + g0 X

a=1,...8

Aa

σ(Ta)i jψj

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Emerging symmetries and space-time

slide-22
SLIDE 22

Real/Majorana: (Wess-Zumino à gauge theory) 1D: 3D: Fields Generators Space-time & Internal H P+, P- K, SU(3) Z(2) H, P, K SU(3) = [SO(3),SU(2)xU(1)] Z(3) H, P, K, J SU(2)xU(1)

22

φS Aa

k

ψ φ ξ and hφi = 1

φR/L ξR/L and hφRi = hφLi = 1/ p 2

φS φP Aa

3

ψ

P(1,3) x SU(2) x U(1) iDσψi = i∂σψi + g0 X

a=1,...8

Aa

σ(Ta)i jψj

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iDµψi = i∂µψi + g X

a=1,2,3,8

Aa

µ(Ta)i jψj

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Emerging symmetries and space-time

slide-23
SLIDE 23

Real/Majorana: (Wess-Zumino à gauge theory) 1D: 3D: and .... in order to match space-time and field symmetries and respect Coleman-Mandula Fields Generators Space-time & Internal H P+, P- K, SU(3) Z(2) H, P, K SU(3) = [SO(3),SU(2)xU(1)] Z(3) H, P, K, J SU(2)xU(1) A(4)

23

± −

→ nµ

α

γσ =  nσ

+

→ γµ =  ¯ σµ σµ

  • φS

Aa

k

ψ φ ξ and hφi = 1

φR/L ξR/L and hφRi = hφLi = 1/ p 2

φS φP Aa

3

ψ

P(1,3) x SU(2) x U(1) iDσψi = i∂σψi + g0 X

a=1,...8

Aa

σ(Ta)i jψj

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iDµψi = i∂µψi + g X

a=1,2,3,8

Aa

µ(Ta)i jψj

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Emerging symmetries and space-time

slide-24
SLIDE 24

DYNAMICS

24

slide-25
SLIDE 25

Dynamics

Right-Left symmetry Supersymmetry (Wess-Zumino structure) Bosons: Fermions: Wess-Zumino in 1+1 dim including potential and vev determining symmetry Pseudoscalar fields (θ) à gauge fields ... + masses through symmetry breaking Link to gravity (?) via constraint

25

ξ √ 2 =  ξR −i ξL

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φ √ 2 = eiπ/4φR + e−iπ/4φL = φS + iφP = χ eiθ

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0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.5 1.0 1.5 2.0

V (χ, θ) θ = π/3 θ = π/4 θ = 0 θ = π/6 θ = π/2

χ

λ

  • χ2 cos2(2θ) − 1
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V (φ) = 1

8M 2

4φ2

Sφ2 P + (1 − φ2 S + φ2 P )2

= 1

8M 2

χ4 sin2(2θ) + (χ2 cos(2θ) − 1)2

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φ†∂σφ = 1

2 χT Dσχ

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SO(3) symmetry via vev

slide-26
SLIDE 26

26

FERMIONS AND BOSONS AS TRIPARTITE STATES

slide-27
SLIDE 27

Bell states are maximally entangled (MaxEnt) states in product space :

  • r

They belong to the same class (SLOCC, for us local unitary, local = subspace) Symmetry eigenstates can be aligned or entangled

Bipartite entangled states

27

ρ = |BellihBell| = ) ρA = 1

2 (|RihR| + |LihL|)

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Bell

singlet triplet aligned

generators τ x τ generators τ x 1 + 1 x τ entanglement measure: |Φi = a|RRi + b|RLi + c|LRi + d|LLi = pp1|a1b1i + pp2|a2b2i

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(Schmidt decomp.) 0 ≤ ∆ = p 2(1 − Tr(ρ2)) = 2|ad − bc| → 2√p1p2 ≤ 1

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HA ⊗ HB

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|RRi + eiϕ|LLi

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|RLi + eiϕ|LRi

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Bell

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SU(2)

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A × B

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slide-28
SLIDE 28

Tripartite entangled chiral states

Two classes of maximally entangled tripartite ABC states: (Dur, Vidal, Cirac 2000) Beyond tripartites there is an infinite number of classes!

28

|GHZi =

1 √ 2(|RRRi + |LLLi)

|Wi =

1 √ 3(|LRRi + |RLRi + |RRLi)

GHZ: fragile ρAB = 1

2 (|RRihRR| + |LLihLL|)

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ρAB = 2

3|BellihBell| + 1 3|RRihRR|

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W: robust

GHZ

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W

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3D, c = 1

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1D, c = 3

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I = Ir, YI

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V = Ig, YV

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U = Ib, YU

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Z(2) × Z(3) ⊂ A(4) ⊂ SO(3) ⊂ SU(3)

<latexit sha1_base64="hWdhvFreQKsQUs/KjE1bm+YNdaM=">ACPnicbZBNT8JAEIa3fiJ+oR69NBITvJAWSPSI8eJNDBaItCHbZYENu2zOzWShl/mxd/gzaMXDxrj1aNbwETBN9nkzTMz2ZnXjzhTYFnPxtLyuraemYju7m1vbOb29tvqDCWhDok5KFs+VhRzgLqANOW5GkWPicNv3hRVpv3lGpWBjcwCinsD9gPUYwaBRJ+e4wg/vk9tC6WTsAhNU/YCyBir2FYUpOS9U5kj9aqGp7qQo28nlraI1kblo7JnJo5lqndyT2w1JLGgAhGOl2rYVgZdgCYxwOs6saIRJkPcp21tA6wX9ZLJ+WPzWJOu2QulfgGYE/p7IsFCqZHwdafAMFDztRT+V2vH0DvzEhZEMdCATD/qxdyE0EyzNLtMUgJ8pA0mkuldTLAEhPQiach2PMnL5pGqWiXi6XrSr5amsWRQYfoCBWQjU5RFV2iGnIQ/oBb2hd+PReDU+jM9p65IxmzlAf2R8fQO38a9U</latexit>

AB-C

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BC-A

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AC-B

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A-B-C

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slide-29
SLIDE 29

Leptons

GHZ class, has same symmetry as basis (in particular chirality) Using note that is LU equivalent to and the aligned GHZ states can be SO(3) multiplets (living in 3D) identified with leptons (cf HO) Embedding symmetry A(4) has three singlet representations: families This gives tri-bimaximal family – electroweak mixing [slightly different from the way

  • btained by Fritsch & Xing, or Harrison, Perkins & Scott]

29

|GHZi =

1 √ 2(|RRRi + |LLLi)

ξ2L

  • 1/2

1/2 1

Y I3

ξ1L

ξ1R

+

ξ2R ξ3L

+

ξ3R

Q

ν L

  • 1/2

1/2 1 Y I3

eL

eR

+

ν R eL

+

eR

Q

tI ⊗ tU ⊗ tV

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tI ⊗ tI ⊗ tI

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UTB = WUQ = 1 √ 3 2 4 1 1 1 ω2 1 ω ω 1 ω2 3 5 1 √ 2 2 4 1 −i 1 1 i 3 5 = 2 4 p 2/3 p 1/3 − p 1/6 p 1/3 − p 1/2 − p 1/6 p 1/3 p 1/2 3 5

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I⊗3

3

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tI ≡ (I, YI)

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slide-30
SLIDE 30

Quarks

For W-class chirality is more complex again employ SU(3) and SU(2) x U(1) subgroups (I, U, V) in bipartite classes à A(4) symmetry: three singlets and three triplets Construct SU(3) root diagram to see all GHZ- and W-states

30

|GHZi =

1 √ 2(|RRRi + |LLLi)

|Wi =

1 √ 3(|LRRi + |RLRi + |RRLi)

AC-B

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GHZ

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W

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AB-C

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BC-A

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A-B-C

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SU(3)

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I, YI

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U, YU

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V, YV

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tr

I ⊗ tg I ⊗ tb I

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tI ⊗ tU ⊗ tV

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AC-B

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GHZ

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W

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3D, c = 1

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1D, c = 3

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AB-C

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BC-A

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I = Ir, YI

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V = Ig, YV

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U = Ib, YU

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A-B-C

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SU(3)

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slide-31
SLIDE 31

222 223 312 332 123 323 131 333 221 112 212 231 111 113 331 131 123 333 331 212 323 332 113 231 312 223 111 112 221 222

I3 U3 V3

I3=1/2 I3=1/2 V3=1/2 U3=1/2 U3=1/2 V3=1/2

(fermionic) root diagram: tripartite entanglement

Tripartite states (R: 1 2 3 & L: 1 2 3) Aligned (RRR, LLL): GHZ states I, U, and V allowed SO(3) à asymptotic/space Three A(4) singlets Mingled (RRL, RLL): W-states I, U, or V allowed non-asymptotic Three A(4) triplets (color)

31

V⊗3

3

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U⊗3

3

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I⊗3

3

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slide-32
SLIDE 32

(fermionic) root diagram: electroweak identification

32

eL

eR uR uR uR

dR dR dR dL dL dL

uL uL uL

uL uL uL

dL dL dL

uR uR uR

dR dR dR

νR

νL

eL

eR

Y g

Y b

Ib

3

Ig

3

Qg

Qb Qr

Ir

3 = I3

Y r = Y Tripartite states (R: 1 2 3 & L: 1 2 3) Aligned (RRR, LLL): LEPTONS I, U, and V allowed SO(3) à asymptotic/space Three A(4) singlets Mingled (RRL, RLL): QUARKS I, U, or V allowed non-asymptotic Three A(4) triplets (color) Resembles the rishon model

Harari & Seiberg 1982, Shupe 1979

slide-33
SLIDE 33

Entanglement offers new perspective quarks and leptons

Standard model: beautifully symmetric: SU(3) x SU(2) x U(1) but … complex:

right-left, particle-antiparticle color families

Emergence ... ... in a tripartite Hilbert space SU(2) x U(1) in SU(3) à sin ΘW = ½ Weinberg 1972 triality Z(3) ... reflected in family structure & color PJM, PLB 787 (2018) 193

33

eL

eR uR uR uR

dR dR dR dL dL dL

uL uL uL

uL uL uL

dL dL dL

uR uR uR

dR dR dR

νR

νL

eL

eR

Y g

Y b

Ib

3

Ig

3

Qg

Qb Qr

Ir

3 = I3

Y r = Y

eL

eR uR

dR dL

uL

uL

dL

uR

dR

νR

νL eL

eR

uR

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uL

Z, γ

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W +

<latexit sha1_base64="fGfKP1E4sAUWRlZWthwAkZ5WJIQ=">AB6nicbVDLSgNBEOyNrxhfUY9eBoMgCGE3CuY8OIxonlAsobZSW8yZHZ2mZkVQsgnePGgiFe/yJt/4yTZgyYWNBRV3XR3BYng2rjut5NbW9/Y3MpvF3Z29/YPiodHTR2nimGDxSJW7YBqFxiw3AjsJ0opFEgsBWMbmZ+6wmV5rF8MOME/YgOJA85o8ZK963Hi16x5JbdOcgq8TJSgz1XvGr249ZGqE0TFCtO56bGH9CleFM4LTQTUmlI3oADuWShqh9ifzU6fkzCp9EsbKljRkrv6emNBI63EU2M6ImqFe9mbif14nNWHVn3CZpAYlWywKU0FMTGZ/kz5XyIwYW0KZ4vZWwoZUWZsOgUbgrf8ipVsreZblyd1WqVbM48nACp3AOHlxDW6hDg1gMIBneIU3RzgvzrvzsWjNOdnMfyB8/kDzQqNcg=</latexit>

W −

<latexit sha1_base64="cu7qEDk4hinwDr2TwO7WV5ypohk=">AB6nicbVDLSgNBEOyNrxhfUY9eBoPgxbAbBXMePEY0TwgWcPspDcZMju7zMwKIeQTvHhQxKtf5M2/cZLsQRMLGoqbrq7gkRwbVz328mtrW9sbuW3Czu7e/sHxcOjpo5TxbDBYhGrdkA1Ci6xYbgR2E4U0igQ2ApGNzO/9YRK81g+mHGCfkQHkoecUWOl+9bjRa9YcsvuHGSVeBkpQYZ6r/jV7csjVAaJqjWHc9NjD+hynAmcFrophoTykZ0gB1LJY1Q+5P5qVNyZpU+CWNlSxoyV39PTGik9TgKbGdEzVAvezPxP6+TmrDqT7hMUoOSLRaFqSAmJrO/SZ8rZEaMLaFMcXsrYUOqKDM2nYINwVt+eZU0K2Xvsly5uyrVqlkceTiBUzgHD6hBrdQhwYwGMAzvMKbI5wX5935WLTmnGzmGP7A+fwB0BKNdA=</latexit>

Y

<latexit sha1_base64="M6y0AWDRBL2tYspDI78r4dby4SY=">AB6HicbVDLTgJBEOzF+IL9ehlIjHxRHbRI4kXjxCIg8DGzI79MLI7OxmZtaEL7AiweN8eonefNvHGAPClbSaWqO91dQSK4Nq7eQ2Nre2d/K7hb39g8Oj4vFJS8epYthksYhVJ6AaBZfYNwI7CQKaRQIbAfj27nfkKleSzvzSRBP6JDyUPOqLFS46FfLldwGyTryMlCBDvV/86g1ilkYoDRNU67nJsafUmU4Ezgr9FKNCWVjOsSupZJGqP3p4tAZubDKgISxsiUNWai/J6Y0noSBbYzomakV725+J/XTU1Y9adcJqlByZaLwlQE5P512TAFTIjJpZQpri9lbARVZQZm03BhuCtvrxOWpWyd1WuNK5LtWoWRx7O4BwuwYMbqMEd1KEJDBCe4RXenEfnxXl3PpatOSebOYU/cD5/ALWJjNc=</latexit>

I3

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Q

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slide-34
SLIDE 34

Bosons

Boson fields appear as Higgs field and in covariant derivatives: Depending on implementation: Gauge fields linked to symmetry generators More or less like SM starting with Need for radiative corrections

34

φ √ 2 = χ eiθ

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φ†∂σφ = 1 2χT Dσχ

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iDσψi = i∂σψi + g0 X

a=1,...8

Aa

σ(Ta)i jψj

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iDµψi = i∂µψi + g X

a=1,2,3,8

Aa

µ(Ta)i jψj

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AC-B

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AB-C

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BC-A

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A-B-C

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quarks

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leptons

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H

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gluons

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γ, Z,W

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gluons

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γ, Z,W

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gluons

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γ, Z,W

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gluons

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γ, Z,W

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sin θW = 1/2

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MZ √ 2 = MH = Mtop/ √ 2

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3D 1D

PJM, PLB 787 (2018) 193

slide-35
SLIDE 35

Entanglement and 3D composites (preliminary)

Strong Interactions: resembles XQCD1+1 (analogous to Kaplan 1306.5818), while dynamics governed via Wilson loop (including freezing of color at small x/high energies) Elementary constituents only involve entanglement in discrete R/L and 1,2,3 degrees of freedom; composites involve entanglement in the continuous space-time freedom

35

W[C] = exp ✓ −ig I

C

dsµAµ(s) ◆

gFτσ = δW[C]/δστσ

AC-B

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AB-C

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BC-A

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A-B-C

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quarks

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leptons

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H

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gluons

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γ, Z,W

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gluons

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γ, Z,W

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gluons

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γ, Z,W

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gluons

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γ, Z,W

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γ, Z,W

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e+e−

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hadrons

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Quark-entangled states form hadrons that are global SU(3) color singlets appearing in 3D (more or less following the rules of the NRQM) valence – current quarks (ontological basis choice) More on QCD: collinearity and TMD light-front dominance, OPE jets, SCET AdS/CFT color-kinematic dualities

ξ

Τ

slide-36
SLIDE 36

Concluding remarks

Entanglement of hadrons: PDFs Simplifications of gluon TMDs at small x: linearly polarized gluon distributions in unpolarized and transversely polarized nucleons dominate

  • ver circularly polarized distributions.

Wilson loop matrix elements crucial in low x domain. Access to C-odd matrix elements via nuclear density profiles Fragmentation linked to entanglement of partons Emergent gauge symmetries Use of supercharges and emergence of space-time symmetries Classes of tripartite entanglement: GHZ and W Leptons and quarks in different classes with different implementations of basic symmetries

36