the entangled 3d structure of qcd

1

The entangled 3D structure of QCD

NFQCD2018, Kyoto, June 12, 2018

[email protected]

Piet Mulders

abstract

YKIS 2018b (Kyoto, 11-15 June 2018): The entangled 3D structure of QCD P.J. Mulders We discuss a new idea to understand the emergence of symmetries in the standard model starting with less than three space dimensions. Even if at this stage it does not upset the present successful phenomenology or make striking predictions , the hope is that it could shed light on the many peculiarities and simplify our understanding of the 3D quark and gluon structure of hadrons at low and high energies.

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  Motivation

(NOT) HAPPY WITH STANDARD MODEL

  In spite of the success of Standard Model!

  Three families, colors, space dimensions!   Left-right (a)symmetry? B-L?   Naturalness? Missing supersymmetry?   Confinement and Collinearity in QCD?

PJM 1601.00300 PJM 1801.03664

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)

[see for instance Kharzeev & Levin (1702.03489)]   hard (short distance) process: partons à partons   emerging partons are pure state(s) à ensemble of hadron states

  Entangled (pure) states |Φ> in 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 both subspaces.

  Maybe both hadrons and partons live in a multipartite Hilbert space !

  Possibly combined with a principle of maximal entanglement (MaxEnt), such as hinted at in Cervera-Lierta, Latorre, Rojo & Rottoli (1703.02989): maximally entangled chiral left/right two-particle states are consistent with QED (gA=0) & electroweak (gV=0), at least if sin ΘW = ½

4

HA⌦H

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  Bell states are maximally entangled (MaxEnt) states: or   They belong to the same class (SLOCC, for us local unitary, local = subspace)

  Symmetry eigenstates are in general entangled

Bipartite entangled states

5

Bell AB

products A-B

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⇢ = |BellihBell| =) ⇢A = 12 (|RihR|+ |LihL|)

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Bell

singlet triplet

aligned generators τ x τ

generators τ x 1 + 1 x τ

|�i = a|RRi+ b|RLi+ c|LRi+ d|LLi<latexit sha1_base64="Y8FOjQHKtbwNbOIb/ejv8u6JSAo=">AAACRnicbZBLSwMxFIXv1Fetr1GXboJFEIQyUwTdCAU3LrqoxT6gM5RMmrahmcyQZIRS+uvcuHbnT3DjQhG3pu0Ua+uFwOE755LkBDFnSjvOq5VZW9/Y3Mpu53Z29/YP7MOjuooSSWiNRDySzQArypmgNc00p81YUhwGnDaCwe3EbzxSqVgkHvQwpn6Ie4J1GcHaoLbte8bVyKv0mSex6HGKbhCewWp1ji5QkKLyLyIzVF5IdVI0T7XtvFNwpoNWhZuKPKRTadsvXiciSUiFJhwr1XKdWPsjLDUjnI5zXqJojMkA92jLSIFDqvzRtIYxOjOkg7qRNEdoNKWLGyMcKjUMA5MMse6rZW8C//Naie5e+yMm4kRTQWYXdROOdIQmnaIOk5RoPjQCE8nMWxHpY4mJNs3nTAnu8pdXRb1YcJ2Ce3+ZLxXTOrJwAqdwDi5cQQnuoAI1IPAEb/ABn9az9W59Wd+zaMZKd47hz2TgB1hor9U=</latexit><latexit sha1_base64="Y8FOjQHKtbwNbOIb/ejv8u6JSAo=">AAACRnicbZBLSwMxFIXv1Fetr1GXboJFEIQyUwTdCAU3LrqoxT6gM5RMmrahmcyQZIRS+uvcuHbnT3DjQhG3pu0Ua+uFwOE755LkBDFnSjvOq5VZW9/Y3Mpu53Z29/YP7MOjuooSSWiNRDySzQArypmgNc00p81YUhwGnDaCwe3EbzxSqVgkHvQwpn6Ie4J1GcHaoLbte8bVyKv0mSex6HGKbhCewWp1ji5QkKLyLyIzVF5IdVI0T7XtvFNwpoNWhZuKPKRTadsvXiciSUiFJhwr1XKdWPsjLDUjnI5zXqJojMkA92jLSIFDqvzRtIYxOjOkg7qRNEdoNKWLGyMcKjUMA5MMse6rZW8C//Naie5e+yMm4kRTQWYXdROOdIQmnaIOk5RoPjQCE8nMWxHpY4mJNs3nTAnu8pdXRb1YcJ2Ce3+ZLxXTOrJwAqdwDi5cQQnuoAI1IPAEb/ABn9az9W59Wd+zaMZKd47hz2TgB1hor9U=</latexit><latexit sha1_base64="Y8FOjQHKtbwNbOIb/ejv8u6JSAo=">AAACRnicbZBLSwMxFIXv1Fetr1GXboJFEIQyUwTdCAU3LrqoxT6gM5RMmrahmcyQZIRS+uvcuHbnT3DjQhG3pu0Ua+uFwOE755LkBDFnSjvOq5VZW9/Y3Mpu53Z29/YP7MOjuooSSWiNRDySzQArypmgNc00p81YUhwGnDaCwe3EbzxSqVgkHvQwpn6Ie4J1GcHaoLbte8bVyKv0mSex6HGKbhCewWp1ji5QkKLyLyIzVF5IdVI0T7XtvFNwpoNWhZuKPKRTadsvXiciSUiFJhwr1XKdWPsjLDUjnI5zXqJojMkA92jLSIFDqvzRtIYxOjOkg7qRNEdoNKWLGyMcKjUMA5MMse6rZW8C//Naie5e+yMm4kRTQWYXdROOdIQmnaIOk5RoPjQCE8nMWxHpY4mJNs3nTAnu8pdXRb1YcJ2Ce3+ZLxXTOrJwAqdwDi5cQQnuoAI1IPAEb/ABn9az9W59Wd+zaMZKd47hz2TgB1hor9U=</latexit><latexit sha1_base64="Y8FOjQHKtbwNbOIb/ejv8u6JSAo=">AAACRnicbZBLSwMxFIXv1Fetr1GXboJFEIQyUwTdCAU3LrqoxT6gM5RMmrahmcyQZIRS+uvcuHbnT3DjQhG3pu0Ua+uFwOE755LkBDFnSjvOq5VZW9/Y3Mpu53Z29/YP7MOjuooSSWiNRDySzQArypmgNc00p81YUhwGnDaCwe3EbzxSqVgkHvQwpn6Ie4J1GcHaoLbte8bVyKv0mSex6HGKbhCewWp1ji5QkKLyLyIzVF5IdVI0T7XtvFNwpoNWhZuKPKRTadsvXiciSUiFJhwr1XKdWPsjLDUjnI5zXqJojMkA92jLSIFDqvzRtIYxOjOkg7qRNEdoNKWLGyMcKjUMA5MMse6rZW8C//Naie5e+yMm4kRTQWYXdROOdIQmnaIOk5RoPjQCE8nMWxHpY4mJNs3nTAnu8pdXRb1YcJ2Ce3+ZLxXTOrJwAqdwDi5cQQnuoAI1IPAEb/ABn9az9W59Wd+zaMZKd47hz2TgB1hor9U=</latexit>

entanglement measure: 0 � = 2

p1� Tr(⇢2) = 2|ad� bc| ! 2

pp1p2 1

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Tripartite entangled states

  Two classes of maximally entangled states: (Dur, Vidal, Cirac 2000)

  Beyond tripartites there is an infinite number of classes!

6

|GHZi = 1p2(|RRRi+ |LLLi)

|Wi = 1p3(|LRRi+ |RLRi+ |RRLi)

|Wi =) ⇢AB = 23 |BellihBell|+

13 |RRihRR|

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|GHZi =) ⇢AB =12 (|RRihRR|+ |LLihLL|)

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GHZ

A-B-C

W

BC-A AC-B AB-C GHZ: fragile W: robust

Quarks and leptons as entangled states


  Conjecture is that physically relevant states correspond to MaxEnt tripartite

states with basic product states being simple (CP) and even supersymmetric

7

GHZ colorless

W colored

leptons

γ,Z,W,H

hadrons

quarks

(gluons)

-1/2 1/2

1

Y

I3

-1/2 1/2 I3

1

Y

φL+

φL− φL

0

φR+φR

0

φR−

-1/2 1/2 I3

1

Y

ξL+

ξL− ξL

0

-1/2 1/2

1

Y

I3

ξR+ξR

0

ξR−

A-B-C

PJM 1601.00300, PJM 1801.03664

EMERGENCE OF SPACE-TIME DEPENDENCE

8

PHYSICAL REVIEW VOLUME 159, NUMBER 5 25 JULY 1967

All Possible Symmetries of the 8 Matrix*SiDNEY COLEMAN) AND JEFFREY MANDULAj

Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts(Received 16 March 1967)

We prove a new theorem on the impossibility of combining space-time and internal symmetries in anybut a trivial way. The theorem is an improvement on known results in that it is applicable to infinite-param-eter groups, instead of just to Lie groups. This improvement is gained by using information about the Smatrix; previous investigations used only information about the single-particle spectrum. We define a sym-metry group of the Smatrix as a group of unitary operators which turn one-particle states into one-particlestates, transform many-particle states as if they were tensor products, and commute with the S matrix. LetG be a connected symmetry group of the Smatrix, and let the following five conditions hold: (1) G containsa subgroup locally isomorphic to the Poincare group. (2) For any M&0, there are only a finite number ofone-particle states with mass less than M. (3) Elastic scattering amplitudes are analytic functions of s and t,in some neighborhood of the physical region. (4) The S matrix is nontrivial in the sense that any two one-particle momentum eigenstates scatter (into something), except perhaps at isolated values of s. (5) The gen-erators of G, written as integral operators in momentum space, have distributions for their kernels. Then,we show that G is necessarily locally isomorphic to the direct product of an internal symmetry group andthe Poincard group.

I. INTRODUCTIONlNT&L a few years ago, most physicists believedthat the exact or approximate symmetry groups

of the world were (locally) isomorphic to direct productsof the Poincare group and compact Lie groups. Thisworld-view changed drastically with the publication ofthe first papers on SU(6)'; these raised. the dazzlingpossibility of a relativistic symmetry group which wasnot simply such a direct product. Unfortunately, allattempts to And such a group came to disastrous ends,and the situation was finally settled by the discovery ofa set of theorems' which showed that, for a wide classof Lie groups, any group which contained the Poincaregroup and admitted supermultiplets containing finitenumbers of particles was necessarily a direct product.However, although these theorems served their

polemic purposes, they are in many ways displeasing:Their statements involve many unnatural and artificialassumptions, typically concerning the normality of thetranslation subgroup. Even worse, they are restrictedto Lie groups —this despite the fact that in6nite-parameter groups have been proposed in the literature.The theories based on these groups were destroyed notby general theorems but by particular arguments.Typically, these arguments showed that these groupsdo not allow scattering except in the forward and back-ward directions. ' Thus, if one accepts the usual dogmaon the analyticity of scattering amplitudes, they allowno scattering at all.The purpose of this paper is to tie up these loose ends.

We prove the following theorem: Let G be a connected

*Work supported in part by the U. S. Air Force Ofhce ofScientific Research under Contract AF49 (638)—1380.t Alfred P. Sloan Research Fellow.$ National Science Foundation Postdoctoral Fellow.' B. Sakita, Phys. Rev. 136, B1756 (1964); F. Gursey and L.

Radicati, Phys. Rev. Letters 13, 299 (1964).2 S. Coleman, Phys. Rev. 138, 81262 (1965);S.Weinberg, ibid.

139, 8597 (1965); L. Michel and 8. Sakita, Ann. Inst. HenriPoincare 2, 167 (1965).

3 T. F. Jordan, Phys. Rev. 140, B766 (1965).

symmetry group of the S matrix, which contains thePoincare group and which puts a finite number ofparticles in a supermultiplet. Let the S matrix be non-trivial and let elastic scattering amplitudes be analyticfunctions of s and t in some neighborhood of the physicalregion. Finally, let the generators of G be representableas integral operators in momentum space, with kernelsthat are distributions. Then 0 is locally isomorphic tothe direct product of the Poincare group and an in-ternal symmetry group. (This is a loose statement ofthe theorem; a more precise one follows below. )We believe that all of the assumptions in this theorem

are physical, except for the last one, which, althoughweak, is ugly. We hope that it can be eliminated withsuKciently careful analysis; to date we have beenunable to do so.We emphasize that our theorem has application only

to groups which are symmetries of the S matrix. There-fore it has nothing to say about symmetry groups arisingfrom the saturation of current commutators; thesegroups generate symmetries of form factors only.The remainder of this section contains a precise state-

ment of the theorem and some remarks about its impli-cations. Section II contains the proof. Although attimes this attains mathematical levels of obscurity, wemake no claim for corresponding standards of rigor.

A. Statement of the Theorem

We begin by briefly reviewing some of the funda-mental definitions of scattering theory. The Hilbertspace of scattering theory, K, is an infinite direct sumof subspaces,

X=K"'Q+BC&'&Q+

X&"' is called the n-particle subspace. It is a subspace(determined by the generalized exclusion principle) ofthe direct product of e Hilbert spaces, each isomorphicto R&'&. The S matrix S is a unitary operator on K.A unitary operator U on X is said to be a symmetry125i

9

  Hilbert space   Supercharges

  For boson and fermion fields

  Implement symmetries via constraints F ... and a nontrivial vacuum (not everything is for free!)

10

[a, a†] = 1, {b, b†} = 1{(a†)n|0i, b†|0i}

Basic symmetries including SUSY

Q†ik = bi a

†k and Qik = b†iak

a†kQik�! b†i a†k

Q†ik � b†i hamiltonian/number operators (i=j, k=l)

& unitary rotations

{Q†ik, Qjl} = 1

2 �ij{a†l , ak}+

12 �kl[b

†i , bj ]

' =1p2!

�a+ a†

�and ⇠ =

1p2

�b+ b†

�

iD = i@ + gA

[Q,'] = ⇠ {Q, ⇠} = {Q, [Q,']} = F = iD'

[Q,F ] = [Q, {Q, ⇠}] = iD⇠

Single (free) field

unitary rotations

Q =p!(a†b� b†a) F = [', H]

= iD' = i'̇<latexit sha1_base64="yHUlR16Pxx+tm5nF1ZECSi1enfQ=">AAACGnicbVDNS8MwHE39nPWr6tFLcDg8yGjHQD0MBorsOMG6QVtGmqVbWPpBkg5G2f/hxX/FiwcVb+LF/8Z060E3HwRe3vs9kt/zE0aFNM1vbWV1bX1js7Slb+/s7u0bB4cPIk45JjaOWcy7PhKE0YjYkkpGugknKPQZ6fij69zvjAkXNI7u5SQhXogGEQ0oRlJJPaN2CysN6LhjxJMhPW95UHddvQIbkN4UYs7dfiyLq94zymbVnAEuE6sgZVCg3TM+VRynIYkkZkgIxzIT6WWIS4oZmepuKkiC8AgNiKNohEIivGy22xSeKqUPg5irE0k4U38nMhQKMQl9NRkiORSLXi7+5zmpDC69jEZJKkmE5w8FKYMyhnlRsE85wZJNFEGYU/VXiIeIIyxVnXkJ1uLKy8SuVa+q1l293KwXbZTAMTgBZ8ACF6AJWqANbIDBI3gGr+BNe9JetHftYz66ohWZI/AH2tcPJsKd+w==</latexit><latexit sha1_base64="yHUlR16Pxx+tm5nF1ZECSi1enfQ=">AAACGnicbVDNS8MwHE39nPWr6tFLcDg8yGjHQD0MBorsOMG6QVtGmqVbWPpBkg5G2f/hxX/FiwcVb+LF/8Z060E3HwRe3vs9kt/zE0aFNM1vbWV1bX1js7Slb+/s7u0bB4cPIk45JjaOWcy7PhKE0YjYkkpGugknKPQZ6fij69zvjAkXNI7u5SQhXogGEQ0oRlJJPaN2CysN6LhjxJMhPW95UHddvQIbkN4UYs7dfiyLq94zymbVnAEuE6sgZVCg3TM+VRynIYkkZkgIxzIT6WWIS4oZmepuKkiC8AgNiKNohEIivGy22xSeKqUPg5irE0k4U38nMhQKMQl9NRkiORSLXi7+5zmpDC69jEZJKkmE5w8FKYMyhnlRsE85wZJNFEGYU/VXiIeIIyxVnXkJ1uLKy8SuVa+q1l293KwXbZTAMTgBZ8ACF6AJWqANbIDBI3gGr+BNe9JetHftYz66ohWZI/AH2tcPJsKd+w==</latexit><latexit sha1_base64="yHUlR16Pxx+tm5nF1ZECSi1enfQ=">AAACGnicbVDNS8MwHE39nPWr6tFLcDg8yGjHQD0MBorsOMG6QVtGmqVbWPpBkg5G2f/hxX/FiwcVb+LF/8Z060E3HwRe3vs9kt/zE0aFNM1vbWV1bX1js7Slb+/s7u0bB4cPIk45JjaOWcy7PhKE0YjYkkpGugknKPQZ6fij69zvjAkXNI7u5SQhXogGEQ0oRlJJPaN2CysN6LhjxJMhPW95UHddvQIbkN4UYs7dfiyLq94zymbVnAEuE6sgZVCg3TM+VRynIYkkZkgIxzIT6WWIS4oZmepuKkiC8AgNiKNohEIivGy22xSeKqUPg5irE0k4U38nMhQKMQl9NRkiORSLXi7+5zmpDC69jEZJKkmE5w8FKYMyhnlRsE85wZJNFEGYU/VXiIeIIyxVnXkJ1uLKy8SuVa+q1l293KwXbZTAMTgBZ8ACF6AJWqANbIDBI3gGr+BNe9JetHftYz66ohWZI/AH2tcPJsKd+w==</latexit><latexit sha1_base64="yHUlR16Pxx+tm5nF1ZECSi1enfQ=">AAACGnicbVDNS8MwHE39nPWr6tFLcDg8yGjHQD0MBorsOMG6QVtGmqVbWPpBkg5G2f/hxX/FiwcVb+LF/8Z060E3HwRe3vs9kt/zE0aFNM1vbWV1bX1js7Slb+/s7u0bB4cPIk45JjaOWcy7PhKE0YjYkkpGugknKPQZ6fij69zvjAkXNI7u5SQhXogGEQ0oRlJJPaN2CysN6LhjxJMhPW95UHddvQIbkN4UYs7dfiyLq94zymbVnAEuE6sgZVCg3TM+VRynIYkkZkgIxzIT6WWIS4oZmepuKkiC8AgNiKNohEIivGy22xSeKqUPg5irE0k4U38nMhQKMQl9NRkiORSLXi7+5zmpDC69jEZJKkmE5w8FKYMyhnlRsE85wZJNFEGYU/VXiIeIIyxVnXkJ1uLKy8SuVa+q1l293KwXbZTAMTgBZ8ACF6AJWqANbIDBI3gGr+BNe9JetHftYz66ohWZI/AH2tcPJsKd+w==</latexit>

�(t) = T exp

✓�i

Z t

0ds·D

◆�

<latexit sha1_base64="gHAow6RrvlGQLDk56QEW+s91T5g=">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</latexit><latexit sha1_base64="gHAow6RrvlGQLDk56QEW+s91T5g=">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</latexit><latexit sha1_base64="gHAow6RrvlGQLDk56QEW+s91T5g=">AAACK3icbVDLSgMxFM34tr6qLt0Ei1AXlhkR1IUg6MKlglWhqSWTudMGM5khuSOWoR/kxl8RxIWKW//DTO3C14HA4Zx7uLknzJS06Puv3tj4xOTU9MxsZW5+YXGpurxyYdPcCGiKVKXmKuQWlNTQRIkKrjIDPAkVXIY3R6V/eQvGylSfYz+DdsK7WsZScHRSp3rEsp6s4yY9oCzh2BNc0XMGdxlTEGN9SzKpseNfI41swUSU4uCYGdnt4WaZpBWHTrXmN/wh6F8SjEiNjHDaqT6xKBV5AhqF4ta2Aj/DdsENSqFgUGG5hYyLG96FlqOaJ2DbxfDYAd1wSkTj1LinkQ7V74mCJ9b2k9BNlgfZ314p/ue1coz32oXUWY6gxdeiOFcUU1o2RyNpQKDqO8KFke6vVPS44QJdv2UJwe+T/5LmdmO/EZzt1A53Rm3MkDWyTuokILvkkJyQU9IkgtyTR/JCXr0H79l7896/Rse8UWaV/ID38QkZG6XP</latexit><latexit sha1_base64="gHAow6RrvlGQLDk56QEW+s91T5g=">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</latexit>

Basic starting point

  Right-Left symmetry Supersymmetry (Wess-Zumino structure)

  Bosons:

  Fermions:

  Space-time structure via covariant derivatives and supercharges   Different ‘kinds’ of particles correspond to SLOCC equivalence classes where the

fun starts in tripartite space with the following basis:

11

�p2 = ei⇡/4�R + e�i⇡/4�L

= �S + i�P<latexit sha1_base64="Qak3/AbPlhjBaeXRRbE8U/U/+GM=">AAACN3icbVBLSwMxGMzWV11fqx69BIsiiHW3FPQiFLx4EKmPPqBbSzZN29DswyQrlGX/lRf/hje9eFDEq//A7HYPtXUgMJmZj+QbJ2BUSNN81XJz8wuLS/llfWV1bX3D2NyqCz/kmNSwz3zedJAgjHqkJqlkpBlwglyHkYYzPE/8xiPhgvrenRwFpO2ivkd7FCOppI5xZQcDaosHLqNSDPfPILmPqB3Q43KcOJ0beJhIR5PaJdRtO8mmt1uVoCmr6nrHKJhFMwWcJVZGCiBDtWO82F0fhy7xJGZIiJZlBrIdIS4pZiTW7VCQAOEh6pOWoh5yiWhH6d4x3FNKF/Z8ro4nYapOTkTIFWLkOirpIjkQ014i/ue1Qtk7bUfUC0JJPDx+qBcyKH2YlAi7lBMs2UgRhDlVf4V4gDjCUlWdlGBNrzxL6qWiZRat63KhUsrqyIMdsAsOgAVOQAVcgCqoAQyewBv4AJ/as/aufWnf42hOy2a2wR9oP78k96jl</latexit><latexit sha1_base64="Qak3/AbPlhjBaeXRRbE8U/U/+GM=">AAACN3icbVBLSwMxGMzWV11fqx69BIsiiHW3FPQiFLx4EKmPPqBbSzZN29DswyQrlGX/lRf/hje9eFDEq//A7HYPtXUgMJmZj+QbJ2BUSNN81XJz8wuLS/llfWV1bX3D2NyqCz/kmNSwz3zedJAgjHqkJqlkpBlwglyHkYYzPE/8xiPhgvrenRwFpO2ivkd7FCOppI5xZQcDaosHLqNSDPfPILmPqB3Q43KcOJ0beJhIR5PaJdRtO8mmt1uVoCmr6nrHKJhFMwWcJVZGCiBDtWO82F0fhy7xJGZIiJZlBrIdIS4pZiTW7VCQAOEh6pOWoh5yiWhH6d4x3FNKF/Z8ro4nYapOTkTIFWLkOirpIjkQ014i/ue1Qtk7bUfUC0JJPDx+qBcyKH2YlAi7lBMs2UgRhDlVf4V4gDjCUlWdlGBNrzxL6qWiZRat63KhUsrqyIMdsAsOgAVOQAVcgCqoAQyewBv4AJ/as/aufWnf42hOy2a2wR9oP78k96jl</latexit><latexit sha1_base64="Qak3/AbPlhjBaeXRRbE8U/U/+GM=">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</latexit><latexit sha1_base64="Qak3/AbPlhjBaeXRRbE8U/U/+GM=">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</latexit>

⇠p2 =

⇠R

�i ⇠L

�

<latexit sha1_base64="v6/RjONpSe5OlxdtgsBUeJ86fnI=">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</latexit><latexit sha1_base64="v6/RjONpSe5OlxdtgsBUeJ86fnI=">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</latexit><latexit sha1_base64="v6/RjONpSe5OlxdtgsBUeJ86fnI=">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</latexit><latexit sha1_base64="v6/RjONpSe5OlxdtgsBUeJ86fnI=">AAACM3icbVBNSyQxEE37tTrr6ugevQSHBQ/u0D0IelkQvIh4UHFUmDRDOlM9E0yn26RaHJr+T178Ix4E2YMiXv0PZsY++PUg8PLqVSX1okxJi75/701MTk3P/Jidq/2c/7WwWF9aPrFpbgS0RapScxZxC0pqaKNEBWeZAZ5ECk6j851R/fQSjJWpPsZhBmHC+1rGUnB0Ure+x64ksxcGi1ZJ/1GmIMYOi6AvdcGN4cOyECV1pu4RZYz+lWx9dNmnDHSvcjAj+wMMu/WG3/THoF9JUJEGqXDQrd+yXiryBDQKxa3tBH6GoRuKUigoayy3kHFxzvvQcVTzBGxYjHcu6R+n9GicGnc00rH6vqPgibXDJHLOhOPAfq6NxO9qnRzjrbCQOssRtHh7KM4VxZSOAqQ9aUCgGjrChZHur1QMuOECXcw1F0LweeWv5KTVDPxmcLjR2G5VccySFbJK1khANsk22SUHpE0EuSZ35IE8ejfef+/Je36zTnhVz2/yAd7LK5EFq2s=</latexit>

-1/2 1/2

1

Y

I3

-1/2 1/2 I3

1

Y

φL+

φL− φL

0

φR+φR

0

φR−

-1/2 1/2 I3

1

Y

ξL+

ξL− ξL

0

-1/2 1/2

1

Y

I3

ξR+ξR

0

ξR−

  Real/Majorana:  

(Wess-Zumino)

Fields Generators Space-time & Internal

  H   P+, P- K, SU(3)

12

Emerging symmetries & space-time

� ⇠ and h�i = 1�R/L ⇠R/L and h�Ri = h�Li = 1/

p2

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


(Wess-Zumino à gauge theory)   1D:


  H   P+, P- K, SU(3)

Z(2)   H, P, K SU(3)

13


iD��i = i@��

i + g0X

a=1,...8

Aa�(Ta)

ij�

j


p2

�S �P Aa3

P(1,1) x SU(3)



  3D:


  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)

14


iD��i = i@��

i + g0X

a=1,...8

Aa�(Ta)

ij�

j

iDµ�i = i@µ�

i + gX

a=1,2,3,8

Aaµ(Ta)

ij�

j

�S Aak


p2

�S �P Aa3

P(3,1) x SU(2) x U(1)



  3D:

  and ....

in order to match space-time and field symmetries and respect Coleman-Mandula


  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)

15


n�± �! nµ

↵ �� =

0 n�

�n�+ 0

��! �µ =

0 �̄µ

�µ 0

�

iD��i = i@��

i + g0X

a=1,...8

Aa�(Ta)

ij�

j

iDµ�i = i@µ�

i + gX

a=1,2,3,8

Aaµ(Ta)

ij�

j

�S Aak


p2

�S �P Aa3

P(3,1) x SU(2) x U(1)

FERMIONS AND BOSONS AS TRIPARTITE STATES

16

Quarks and leptons as entangled states


  Conjecture is that physically relevant states correspond to MaxEnt tripartite

states with basic product states being simple and even supersymmetric.

17

GHZ colorless

W colored

leptons

γ,Z,W,H

hadrons

quarks

(gluons)

-1/2 1/2

1

Y

I3

-1/2 1/2 I3

1

Y

φL+

φL− φL

0

φR+φR

0

φR−

-1/2 1/2 I3

1

Y

ξL+

ξL− ξL

0

-1/2 1/2

1

Y

I3

ξR+ξR

0

ξR−

A-B-C

PJM 1601.00300, PJM 1801.03664



  For symmetry considerations we employ SU(3) and SU(2) x U(1) subgroups (I, U, V) in

intermediate classes   For space-time embedding we employ A(4) symmetry: three singlets and three triplets

18




13 |RRihRR|




GHZ

A-B-C

W

BC-A U, YU

AC-B V, YV

AB-C I, YI

GHZ: I, U, and V symmetry states W: I, U, or V symmetry states

Fermionic excitations: 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)

19

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



  For symmetry considerations we employ SU(3) and SU(2) x U(1) subgroups (I, U, V) in

intermediate classes   For space-time embedding we employ A(4) symmetry: three singlets and three triplets

20




13 |RRihRR|




GHZ 3D, c=1

A-B-C

W 1D, color

BC-A Ib=U, YU

AC-B Ig=V, YV

AB-C Ir=I, YI

GHZ: I, U, and V symmetry states W: I, U, or V symmetry states

S(3), SO(3) and SU(3) in tripartite space

Relevant symmetry in tripartite space is S(3), SO(3), and SU(3)   Example: a 3D harmonic oscillator: states |nxnynz> or |nrlm> or |n>

  3D HO is separable, has rotational [SO(3)] and more [SU(3)] symmetry. Symmetry eigenstates (involving ABC) are in general entangled states.

  Bosons (R or L) Fermions (R/L)

21

HA⌦H

B⌦H

C

3*

E

-1/2-3/2

+3/2+1/2

+5/21

3 1

E

-1/2-3/2

+3/2+1/2

+7/2+5/2 3

1

6 10

level degeneracy (nx, ny, nz) SO(3) (nr`) SU(3) (n)0 1 (0,0,0) 0s 1

1 3 (1,0,0), . . . 0p 3

2 6 (2,0,0), (1,1,0), . . . 1s � 0d 6

3 10 (3,0,0), (2,1,0), (1,1,1), . . . 1p � 0f 10

4 15 . . . 2s � 1d � 0g 15s<latexit sha1_base64="B65fW0AmKajVrBDkpXlxR2XNCTw=">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</latexit><latexit sha1_base64="B65fW0AmKajVrBDkpXlxR2XNCTw=">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</latexit><latexit sha1_base64="B65fW0AmKajVrBDkpXlxR2XNCTw=">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</latexit><latexit sha1_base64="B65fW0AmKajVrBDkpXlxR2XNCTw=">AAADsXicbVJdb9MwFE0bPkb46uCRF4uWKZWqKk63weMkXnhjaOs21JTgOG4b1XEi25koIb+Pd974N9y4YXQZtizde+45xzfOjXKeKO15vztd+979Bw/3HjmPnzx99ry3/+JCZYWkbEoznsmriCjGE8GmOtGcXeWSkTTi7DJav6/rl9dMqiQT53qTs3lKliJZJJRogML9zs8gYstElJpEBSeyKukP2JRWDmfXjKMDFLMlE0wSuoFk4Irw20iEGzjfhwNA0NlHdzI0BRkwzg14Nt1iQSFiJuvmkIBCEDjBqs4cD0gYHbjeCPYQEk/V7jt8bOjAQRM4LjbEEVB4nGlVX+LlLcnESHxAj2uJ30hAi9tarCDLcl5A5sUtn2PjU1+L6z7dyV8jvzEyjrjlmO84Lm47ltirjOdhTTwyxRuhv9MKjndMlm2ToypUg39vGDAR3/y3sNf3xp5Z6G6Am6BvNes07P0K4owWKROacqLUDHu5npdE6oRyVjlBoVhO6Jos2QxCQVKm5qWZuAq9ASRGi0zCERoZdFdRklSpTRoBMyV6pdq1GvxfbVboxbt5mYi80EzQ7UWLgiOdoXp8UZxIRjXfQECoTKBXRFcEhlPDkDvwCLj9yXeDC3+MvTH+dNg/8Zvn2LNeWa8t18LWW+vE+mCdWlOLdsfd8+68+8We2J/tr3a0pXY7jealdWvZ6z+BVQly</latexit>

Fermionic excitations: electroweak identification

22

eL

eR

uR

uR

uR

dR

dR

dRdL dL

dLuL

uL

uL

uL

uL

uL

dL

dL

dLuR

uRuR

dR

dR

dR

⌫R

⌫LeL

eRY g

Y b

Ib3

Ig3 Qg

Qb

Qr

Ir3 = 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)

Standard model particle content

23

Y

+1

-1

I3

uR

eR−

eL+

dL

νR eR+

dL

uR

eL−

dR

uL

dR

uL

ν L

-1/2 +1/2 W +γZ 0W −

H 0

A multipartite classification can give a natural explanation for the electroweak symmetry structure in the standard model

Bosonic excitations: electroweak and strong

  Looking for physical bosonic degrees of freedom depends on S(3) symmetric vacuum structure in tripartite space and the introduction of locality (3D or 1D) and remaining gauge freedom. Leptonic sector

  3D electroweak symmetry breaking is SU(2) x U(1) à U(1)QED with usual relations in SM and some new ones such as MH

2 = 2MZ2 and sin ΘW = ½

(Weinberg 1972) and Yukawa coupling to top quark being 1   QCD sector

  Resembles XQCD1+1 (analogous to Kaplan 1306.5818), while dynamics governed by via Wilson loop

24

iD��i = i@��

i + g0X

a=1,...8

Aa�(Ta)

ij�

j

iDµ� = i@µ�+g

2

✓ 3X

i=1

W iµ�i +Bµ�8

◆�

= i@µ�+gp2

�W+

µ I� +W�µ I+

��+

�gW 0

µI3 +g

2p3BµY

��

W [C] = exp

✓�ig

I

CdsµAµ(s)

◆gF⌧� = �W [C]/��⌧�

GENERAL IMPLICATIONS

25

Emergence in the Standard Model

  Basic degrees of freedom can also be described in less dimensions while the extension of 1+1 à 1+3 proceeds via tripartite entanglement.   Advantageous for convergence: d[φ] = (d-2)/2 à 0, d[ξ] = (d-1)/2 à½, naturalness, … [see Stojkovic – 1406.2696]   Consequences in looking at higher order corrections for e.g. g-2 ? Supersymmetry included, but invisible in 3D !   Gravity also emerges in 1D à 3D.

  A natural framework to look at family structure and symmetries of standard model as emergent phenomena   e.g. tribimaximal mixing for leptons

  Tripartite space for quarks naturally has color dual to space/electroweak.   explains why color naturally is decoupled from electroweak interactions   color invisible in 3D: local gauge invariance! No asymptotic quarks or gluons!   global color remains visible in 3D via color factors such as N vs 1/N, f x D (distribution x fragmentation)

  Gravity also emerges in 1D to 3D transition

26

IMPLICATIONS FOR QCD

27

Emergence in QCD

  Natural arena for light-front approach with a ‘preferred’ space direction: quantization of good fields, dominating the OPE at high energies, these are asymptotic (free) fields (Kogut & Soper):

  Natural role for Wilson loops generating (gluon) TMDs (1805.05219), process dependence linked to global color flow from initial to final states

  Possible new ways to look at color-kinematic duality, soft collinear effective theory (SCET) via embedding in the entanglement schemes

28

12�

��+ and g↵µT Aaµ

F↵� =�W [C]

��↵�

0

ξΤ

-

Emergence of hadrons in QCD

  Include hadrons: construct color singlets in tripartite space (naively make three-particle baryonic states) and use local invariance for the 3D embedding. This is analogous to choosing the appropriate basis of quantum states in multipartite space [cf ontological basis of ‘t Hooft – 1405.1548]

  Example: a 3D harmonic oscillator: states |nxnynz> or |nrlm> or |n>

  Compare the well-known NRQM classification of baryons

29

N configuration SU(6) ⇥ O(3) multiplets

0 (0s)3 [56, 0+]1 (0s)2(1p) (56, 1�) [70, 1�]2 (0s)2(2s) (56, 0+) [70, 0+]

(0s)2(2d) (56, 2+) [70, 2+](0s)(1p)2 [56, 0+] [56, 2+] (70, 0+) (70, 1+) (70, 2+) [20, 1+]

level degeneracy (nx, ny, nz) SO(3) (nr`) SU(3) (n)0 1 (0,0,0) 0s 1

1 3 (1,0,0), . . . 0p 3

2 6 (2,0,0), (1,1,0), . . . 1s � 0d 6

3 10 (3,0,0), (2,1,0), (1,1,1), . . . 1p � 0f 10

4 15 . . . 2s � 1d � 0g 15s<latexit sha1_base64="B65fW0AmKajVrBDkpXlxR2XNCTw=">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</latexit><latexit sha1_base64="B65fW0AmKajVrBDkpXlxR2XNCTw=">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</latexit><latexit sha1_base64="B65fW0AmKajVrBDkpXlxR2XNCTw=">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</latexit><latexit sha1_base64="B65fW0AmKajVrBDkpXlxR2XNCTw=">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</latexit>

Concluding remarks

  Conjecture: quarks, leptons and hadrons in multipartite spaces   Starts with a simple (even supersymmetric basis) which at tripartite level

enables embedding of known standard model symmetries

  May provide an embedding of all ways to look at QCD, e.g. valence vs current, chiral dynamics, SCET, ...

30

GHZ colorless

W colored

leptons

γ,Z,W,H

hadrons

quarks

(gluons)

the entangled 3d structure of qcd

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