NANJING
UNIVERSITY

Craig Roberts … http://inp.nju.edu.cn/

Grant no. 12135007

Dynamical Diquark
Picture of Baryons

Emergence of Hadron Mass … and Structure➢ Standard Model of Particle Physics has one obvious mass-generating mechanism= Higgs Boson … impacts are critical to evolution of Universe as we know it➢ However, Higgs boson is alone responsible for just ∼ 1% of the visible mass in the Universe➢ Proton mass budget … only 9 MeV/939 MeV is directly from Higgs➢ Evidently, Nature has another very effective
mechanism for producing mass:

Emergent Hadron Mass (EHM)✓ Alone, it produces 94% of the proton’s mass
✓ Remaining 5% is generated by constructive
interference between EHM and Higgs-boson
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
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Emergence of Hadron Mass - Basic Questions➢ What is the origin of EHM?
➢ Does it lie within QCD?
➢ What are the connections with …
– Gluon and quark confinement?
– Dynamical chiral symmetry
breaking (DCSB)?
– Nambu-Goldstone modes = π & K?
➢ What is the role of Higgs inmodulating observable properties ofhadrons?
– Without Higgs mechanism of mass
generation, π and K would beindistinguishable➢ What is and wherefrom mass?
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"Proton and 𝜌-meson mass budgets are practically identical𝜋- and 𝐾-meson mass budgets are essentially/completely different
from those of proton and 𝜌
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Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"Modern Understanding
Grew Slowly from Ancient Origins➢ More than 40 years ago
Dynamical mass generation in continuum quantum chromodynamics,
J.M. Cornwall, Phys. Rev. D 26 (1981) 1453 … ∼ 1070 citations

3-gluon vertex➢ Owing to strong self-interactions, gluon partons ⇒ gluon quasiparticles,
described by a mass function that is large at infrared momenta
4-gluon vertex

1
𝑚𝑔2
Gluon propagator… continuum andlattice QCD agree

Truly mass from nothing
An interacting theory, written interms of massless gluon fields,✓ QCD fact
produces dressed gluon fields thatare characterised by a mass function ✓ Continuum theory andlattice simulations agree
that is large at infrared momenta✓ Empirical verification?
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Modern Understanding
Grew Slowly from Ancient Origins

EHM
means
Gluons are
massive➢ More than 40 years ago

Dynamical mass generation in continuum quantum chromodynamics,
J.M. Cornwall, Phys. Rev. D 26 (1981) 1453 … ∼ 1050 citations

3-gluon vertex➢ Owing to strong self-interactions, gluon partons ⇒ gluon quasiparticles,
described by a mass function that is large at infrared momenta1
𝑚𝑔2

Gluon propagator… continuum andlattice QCD agree

4-gluon vertex

Truly mass from nothing
An interacting theory, written interms of massless gluon fields,✓ QCD fact
produces dressed gluon fields thatare characterised by a mass function ✓ Continuum theory andlattice simulations agree
that is large at infrared momenta✓ Empirical verification?

Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
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This is where we live⇐
What’s happeningout here?!

Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
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W orkshop on Dyson-Schwinger Equations in Modern Mathematics
and Physics (DSEMP2014) Trento, Italy, September 22-26, 2014

Process independent
effective charge = running coupling

Effective charge from lattice QCD, Zhu-Fang Cui, Jin-Li Zhang et al.,NJU-INP 014/19, arXiv:1912.08232 [hep-ph], Chin. Phys. C 44 (2020) 083102/1-10

2064 total downloads➢ Modern theory enables unique QCD analogue of“Gell-Mann – Low”
running charge to be rigorously defined andcalculated➢ Analysis of QCD’s gauge sector
yields a parameter-free prediction➢ N.B. Qualitative change in α̂PI(k) at k ≈ ½ mp
➢ No Landau Pole– “Infrared Slavery” picture – linear potential – is notcorrect explanation of confinement➢ Below 𝑘 ∼ 𝑚
ෝ 0 , interactions become scale
independent, just as they were in the Lagrangian;so, QCD becomes practically conformal again
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"

The QCD Running Coupling,
A. Deur, S. J. Brodsky and G. F. de Teramond, Prog. Part. Nucl. Phys. 90 (2016) 1-74
Process independent strong running coupling
Daniele Binosi et al., arXiv:1612.04835 [nucl-th], Phys. Rev. D 96 (2017) 054026/1-7
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EHM Basics➢ Absent Higgs boson couplings, the Lagrangian of QCD is scale invariant➢ Yet …
Three
– Massless gluons become massive
pillars– A momentum-dependent charge is producedof ehM– Massless quarks become massive➢ EHM is expressed in
EVERY strong interaction observable➢ Challenge to Theory =Elucidate all observable consequences of these phenomena
and highlight the paths to measuring them
➢ Challenge to Experiment =Test the theory predictions so thatthe boundaries of the Standard Model can finally be drawn
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EHM as the Driver ofClustering within hadrons
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Exposing & Charting EHM➢ Proton was discovered 100 years ago
It is stable; hence, an ideal target in experiments➢ But just as studying the hydrogen atom ground state didn’t give us QED,
focusing on the ground state of only one form of hadron matter will not solve QCD➢ New era is dawningHigh energy + high luminosity⇒ science can move beyond the monomaniacal focus on the proton➢ Precision studies of the structure of– Nature’s most fundamental Nambu-Goldstone bosons (𝜋 & K) will become possible– Baryon excited states✓Baryons are the most fundamental three-body systems in Nature✓If we don’t understand how QCD, a Poincaré-invariant quantum field theory, builds
each of the baryons in the complete spectrum, then we don't understand Nature.
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
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Nucleon mass from a covariant three-quark Faddeev equation
G. Eichmann et al., Phys. Rev. Lett. 104 (2010) 201601

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Structure of Baryons➢ Poincaré covariant Faddeev equation sums all possible exchanges and interactions that cantake place between three dressed-quarks➢ Direct solution of Faddeev equation using rainbow-ladder truncation is now possible, but
numerical challenges remain

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Structure of Baryons
Solution delivers
Poincaré-covariant
proton wave function➢ Poincaré covariant Faddeev equation sums all possible exchanges and interactions that cantake place between three dressed-quarks➢ Direct solution of Faddeev equation using rainbow-ladder truncation is now possible, but
numerical challenges remain➢ For many/most applications, diquark approximation to quark+quark scattering kernel is used
➢ Prediction: owing to EHM phenomena, strong diquark correlations exist within baryons– proton and neutron … both scalar and axial-vector diquarks are present✓ CSM prediction =presence of
axialvector (AV)diquark correlation in
the proton✓ AV Responsible for ≈40% of proton charge
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
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Diquarks - Facts➢ Theory predicts experimental observables thatwould constitute unambiguous measurable
signals for the presence of diquark correlations.
➢ Some connect with spectroscopy of exotics✓ tetraquarks and pentaquarks➢ Numerous observables connected with structureof conventional hadrons, e.g.
✓ existence of zeros in d-quark contribution to
proton Dirac and Pauli form factors✓ 𝑄 2 -dependence of nucleon-to-resonancetransition form factors✓ 𝑥-dependence of proton structure functions✓ deep inelastic scattering on nuclear targets(nDIS) … proton production described bydirect knockout of diquarks, which
subsequently form into new protons
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
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Nucleon Electroweak
Form Factors and PionNucleon Coupling➢ Symmetry preserving current for realistic
nucleon = quark + nonpointlike diquark➢ Probe strikes➢ Quark – (1)➢ Diquark elastic – (2)➢ Diquark transition – (3)➢ Quark in-flight – (4)➢ Seagull terms – (5) & (6)➢ Guarantees PCAC and all related
identities➢ Parameter-free predictions

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Nucleon axial form factor: 𝐺𝐴 (𝑄 2 )✓ Parameter-free continuum
quark+diquark prediction comparedwith up-to-date lattice result✓ Mean 𝜒 2 = 0.27
✓ 𝑄 2 reach of continuum prediction isunlimited✓ Now have results to 10 GeV 2✓ “Precision” lattice result is constrained
to the small 𝑄 2 -window shown✓ Contribution dissection:

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Large 𝑄 2 Nucleon Axial Form Factor➢ Parameter-free CSM predictions to 𝑄2 = 10 𝑚𝑝2➢ One other calculation, viz. LCSRs using different models for
proton DA ... Only available on 𝑄2 > 1 𝑚𝑝2➢ CSM prediction agrees with available data: small & large 𝑄2➢ Large 𝑄2 data from CLAS [K. Park et al., Phys. Rev. C 85
(2012) 035208], threshold pion electroproduction, extends
𝑄2 ≈ 5 𝑚𝑝2✓ This technique could be used to reach higher 𝑄2✓ Regarding oft-used dipole Ansatz,✓ Fair representation of GA(x) on x ∈ [0, 3] = fitting
domain✓ But outside fitted domain, quality of approximation
deteriorates quickly✓ dipole overestimates true result by 56% at x = 10
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Large 𝑄 2 Nucleon Axial Form Factor➢ Light-front transverse density profiles➢ Omitting axialvector diquarks✓ magnitude of the d quark contribution to
GA is just 10% of that from the u quark✓ d quark is also much more localized𝑟𝐴⊥𝑑 ≈ 0.5 𝑟𝐴⊥𝑢
➢ Working with realistic axialvector diquark
fraction✓ d and u quark transverse profiles arequite similar𝑟𝐴⊥𝑑 ≈ 0.9 𝑟𝐴⊥𝑢
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Proton Spin Structure➢ Flavour separation of proton axial charge➢ d-quark receives large contribution fromprobe+quark in presence of axialvector diquark𝑑+ +𝑔𝐴o 𝑔𝑢 =0 &1 −0.32 2𝐴𝑑+ only𝑔𝐴
0o 𝑔𝑢 =−0.054(13)𝐴

Probability that scalar diquark only picture of
proton is consistent with data = 1/7,100,000

𝑑
+ &1+
𝑔𝐴
0
➢ Experiment: 𝑔𝑢 =−0.27 4 ⇐ strong pointer to importance of AV correlation𝐴➢ Hadron scale: 𝑔𝐴𝑢 + 𝑔𝐴𝑑 (+𝑔𝐴𝑠 = 0) = 0.65 2 ⇒ quarks carry 65% of the proton spin

➢ Poincaré-covariant proton wave function: remaining 35% lodged with quark+diquark
orbital angular momentum➢ Extended to entire octet of ground-state baryons: dressed-quarks carry 50(7)% of proton
spin at hadron scale
Contact interaction analysis of octet baryon axialvector and pseudoscalar form factors,
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"Peng Cheng (程鹏), Fernando E. Serna, Zhao-Qian Yao (姚照千) et al., NJU-INP 063/22,
e-Print: 2207.13811 [hep-ph], Phys. Rev. D 106,(2022) 054031
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Baryon Structure➢ Poincaré covariance ⇒ irrespective of quark model assignments 𝑛2𝑠+1 ℓ𝐽 ,every hadron contains orbital angular momentum, e.g.,– 𝜋 contains two S-wave components and two P-wave components– Few systems are simply radial excitations of another➢ No separation of 𝐽 into 𝐿 + 𝑆 is Poincaré invariant– Consequently, e.g., negative parity states are not simply orbital angular momentum
excitations of positive parity ground states➢ In quantum field theory, there is no direct connection between parity and orbital angularmomentum– Parity is a Poincaré invariant quantum number– 𝐿 is not Poincaré invariant = value depends on the observer’s frame of reference➢ QCD structure of hadrons – mesons and baryons – is far richer than can be produced byquark models, relativized or not✓ Baryons are the most fundamental three-body systems in Nature✓ If we don’t understand how QCD, a Poincaré-invariant quantum field theory, builds eachof the baryons in the complete spectrum, then we don't understand Nature.
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𝟑±
Composition of low-lying J=𝟐 𝚫-baryons➢ Poincaré-covariant quark+diquark Faddeev equation
3 3±⇒ insights into the structure of four lightest= (2 , 2 ) baryon multiplets.
➢ Prediction: Whilst these systems can contain isovector-axialvector 1,1+ and isovector-

𝐼, 𝐽𝑃

vector (1,1− ) diquarks, one may neglect the latter and still arrive at a reliable description.
3 3+➢ (2 , 2 ) are the simpler systems &features bear some resemblance
to quark model pictures– Most prominent rest-frame
orbital angular momentum
component is 𝑆-wave–

Δ 1232

3+
mainly 𝑆-wave.
2

3+
mainly 𝑆-wave,
2

Δ 1600
but significant 𝐷-wave.

3+
Δ 1600may fairly be viewed
2
3+
as radial excitation of Δ 1232 2

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𝟑±
Composition of low-lying J=𝟐 𝚫-baryons➢ Poincaré-covariant quark+diquark Faddeev equation
3 3±⇒ insights into the structure of four lightest= (2 , 2 ) baryon multiplets.
➢ Prediction: Whilst these systems can contain isovector-axialvector 1,1+ and isovector-

𝐼, 𝐽𝑃

vector (1,1− ) diquarks, one may neglect the latter and still arrive at a reliable description.
3 3−➢ (2 , 2 ) states are more complex
3−−
Δ 1700 2 mainly 𝑃-wave.
3– Δ 1940
doesn’t look much2
3−
like Δ 1700 2 radial excitation

3−

Δ 1940 2 mainly 𝑆-wave!
Unlike quark model– Rest-frame wave function of3−
Δ 1700is predominantly
2
𝑃-wave– but Δ 19403−
is largely 𝑆-wave
2

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𝟑±
Composition of low-lying J=𝟐 𝚫-baryons➢ Poincaré-covariant quark+diquark Faddeev equation
3electroexcitation
3±
Large
momentumtransfer
resonance𝑃⇒ insights into the structure of four lightest 𝐼, 𝐽 = (2 , 2 ) baryon multiplets.
experiments can test these predictions; so, will shedlight+
➢ Prediction: Whilst these systems can contain isovector-axialvector 1,1 and isovectoron−thenatureemergent
hadronmass.
vector (1,1
) diquarks,
oneofmayneglect thelatter andstill arrive at a reliable description.

3 3−➢ (2 , 2 ) states are more complex
3−−
Δ 1700 2 mainly 𝑃-wave.
3– Δ 1940
doesn’t look much2
3−
like Δ 1700 2 radial excitation

3−

Δ 1940 2 mainly 𝑆-wave!
Unlike quark model– Rest-frame wave function of3−
Δ 1700is predominantly
2
𝑃-wave– but Δ 19403−
is largely 𝑆-wave
2

Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"Rest-frame angular momentum decompositions
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Proton and pion distribution functions in counterpoint
Proton and pion distribution functions in counterpoint, Ya Lu (陆亚) et al.,NJU-INP 056/22, e-Print: 2203.00753 [hep-ph], Phys. Lett. B 830 (2022) 137130➢ Symmetry-preserving analyses using continuum Schwinger
function methods (CSMs) deliver hadron scale DFs thatagree with QCD constraints➢ Valence-quark degrees-of-freedom carry all hadron’s
momentum at 𝜁𝐻 :dilation➢ Diquark correlations in proton, induced by EHM⇒ 𝑢𝑉 (𝑥) ≠ 2𝑑𝑉 𝑥➢ Proton and pion valence-quark DFs have markedly
different behaviour– 𝑢𝜋 (𝑥; 𝜁𝐻 ) is Nature’s most dilated DF
i. “Obvious” because 1 − 𝑥 2 vs. 1 − 𝑥 3 behaviour& preservation of this unit difference under evolution
ii. Also “hidden” = strong EHM-induced broadeningu in proton
d in protonu in pion
dilation

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Proton and pion distribution functions in counterpoint– glue and sea➢ CSM prediction for glue-in-pion DF confirmed by recent lQCD
simulation[Regarding the distribution of glue in the pion, Lei Chang (常雷) and Craig D Roberts, e-Print:
2106.08451 [hep-ph], Chin. Phys. Lett. 38 (8) (2021) 081101/1-6]➢ Glue-in-π DF possess significantly more support on the valence
domain 𝑥 ≥ 0.2 than the glue-in-p DF➢ Sea-in-π DF possess significantly more support on the valence
domain than sea-in-p DFs.
➢ s and c sea DFs are commensurate in size with those of the lightquark sea DFs➢ For s-and c-quarks, too, the pion DFs possess significantly greater
support on the valence domain than the kindred proton DFs.
➢ These outcomes are measurable expressions of EHM
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Diquarks & Deep Inelastic Scattering➢ The ratio of neutron and proton structure functions atlarge 𝑥 is keen discriminator between competing
pictures of proton structure➢ Example:– Only scalar diquark in the proton (no axial-vector):

lim

𝐹2𝑛 𝑥

𝑝
𝑥→1 𝐹2 𝑥

1=4– No correlations in the proton wave function (SU(4)spin-flavour) lim

𝐹2𝑛 𝑥

𝑝
𝑥→1 𝐹2 𝑥

2=3➢ Experiments have been trying to deliver reliable dataon this ratio for fifty years!
➢ MARATHON – a more-than ten-year effort, using a
tritium target at JLab, has delivered precise results

0+ only

D. Abrams, et al., Measurement of the Nucleon Fn2/Fp2 Structure
Function Ratio by the Jefferson Lab MARATHON Tritium/Helium-3 Deep
Inelastic Scattering Experiment – arXiv:2104.05850 [hep-ex],
Phys. Rev. Lett. (2022) in press.
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Neutron/Proton structure function ratio➢ Ratio 1+ /0+ diquarks in proton wave function

is measure of EHM➢ Structure function ratio is clear window onto𝑑𝑉 (𝑥)/𝑢𝑉 (𝑥)✓ CSM prediction =presence of axialvector diquark
correlation in the
proton✓ Responsible for ≈40% of proton charge

U 𝑥; 𝜁 = 𝑢 𝑥; 𝜁 + 𝑢ത 𝑥; 𝜁 , D x; 𝜁 = 𝑑 𝑥; 𝜁 + 𝑑ҧ 𝑥; 𝜁
Σ 𝑥; 𝜁 = 𝑠 𝑥; 𝜁 + 𝑠ҧ 𝑥; 𝜁 + 𝑐 𝑥; 𝜁 + 𝑐 ҧ 𝑥; 𝜁Sea quark dominanceon x<0.2➢ Comparison with MARATHON data𝑝

[D. Abrams, et al., Measurement of Nucleon 𝐹2𝑛 /𝐹2 Structure Function Ratio
by the Jefferson Lab MARATHON Tritium/Helium-3 Deep Inelastic Scattering
Experiment – arXiv:2104.05850 [hep-ex], Phys. Rev. Lett. (2022) in press]

Valence quark dominance on x>0.2➢ Agreement with modern data on entire x-domain –parameter-free prediction
🎆 Valence quark ratio in the proton, Zhu-Fang Cui, (崔著钫), Fei Gao (高飞), Daniele Binosi, Lei
Chang (常雷), Craig D. Roberts and Sebastian M. Schmidt, NJU-INP 049/21, e-print: 2108.11493[hep-ph], Chin. Phys. Lett. Express 39 (04) (2022) 041401/1-5: Express Letter
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Probability that scalar diquark only models of nucleon
might be consistent with available data is 1/141,000
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Expanding array of parameter-free predictions, including➢ Transition form factors: γ∗ + p → Δ(1232), Δ(1600), Ya Lu, Chen Chen, Zhu-Fang Cui, Craig D Roberts, Sebastian M Schmidt,
Jorge Segovia and Hong Shi Zong, arXiv:1904.03205 [nucl-th], Phys. Rev. D 100 (2019) 034001/1-13– Predictions confirmed in recent months following analysis of large-Q2 CLAS data
➢ Nucleon-to-Roper electromagnetic transition form factors at large-Q2, Chen Chen et al., arXiv:1811.08440 [nucl-th], Phys. Rev.
D 99 (2019) 034013/1-13➢ Nucleon elastic form factors at accessible large spacelike momenta, Zhu-Fang Cui et al., NJU-INP 017/20, arXiv:2003.11655[hep-ph], Phys. Rev. D 102 (2020) 014043/1-14➢ Dynamical diquarks in the γ*p → N(1535)1/2− transition, Khépani Raya et al., NJU-INP 046/21, arXiv:2108.02306 [hep-ph],Eur. Phys. J. A 57 (2021) 266/1-16➢ Revealing pion and kaon structure via generalised parton distributions, Khépani Raya et al., NJU-INP 051/21, e-Print:
2109.11686 [hep-ph], Chin. Phys. C 46 (01) (2022) 013107/1-22➢ Proton and pion distribution functions in counterpoint, Ya Lu (陆亚) et al., NJU-INP 056/22, e-Print: 2203.00753 [hep-ph], Phys.
Lett. B 830 (2022) 137130/1-7

Validate the EHM paradigm & consequent appearance of diquark clusters

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Grant no. 12135007

Emergent Hadron Mass
➢ QCD is unique amongst known fundamental theories of natural phenomena– Degrees-of-freedom used to express the scale-free Lagrangian are not directly observable– Massless gauge bosons become massive, with no “human” interference– Gluon mass ensures a stable, infrared completion of the theory through appearance of arunning coupling that saturates at infrared momenta, being everywhere finite– Massless fermions become massive, producing• Massive baryons and simultaneously Massless mesons➢ Emergent features of QCD are expressed in every strong interaction observable➢ They can also be revealed via
EHM interference with Nature’s other known source of mass = Higgs➢ High energy and high luminosity facilities are the key to validating these concepts
proving QCD to be 1st well-defined four-dimensional quantum field theory ever contemplated➢ This may open doors that lead far beyond the Standard Model
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Grant no. 12135007

Emergent Hadron Mass
➢ QCD is unique amongst known fundamental theories of natural phenomena– Degrees-of-freedom used to express the scale-free Lagrangian are not directly observable– Massless gauge bosons become massive, with no “human” interference– Gluon mass ensures a stable, infrared completion of the theory through appearance of arunning coupling that saturates at infrared momenta, being everywhere finite– Massless fermions become massive, producing• Massive baryons and simultaneously Massless mesons➢ Emergent features of QCD are expressed in every strong interaction observable
𝑁𝑎𝑡𝑢𝑟𝑒➢ They can also be revealed via
EHM interference with Nature’s other known source of mass = Higgs➢ High energy and high luminosity facilities are the key to validating these concepts
proving QCD to be 1st well-defined four-dimensional quantum field theory ever contemplated➢ This may open doors that lead far beyond the Standard Model

L=?

There are theories of many things,
But is there a theory of everything?

Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
35

Clustering as a Window on the Hierarchical Structure of Quantum Systems(35)

Thankyou
L𝑁𝑎𝑡𝑢𝑟𝑒 = ?
There are theories of many things,
But is there a theory of everything?
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"

Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"

Clustering as a Window on the Hierarchical 37
Structure of Quantum Systems (35)Valence quark ratio in the proton, Zhu-Fang Cui (崔著钫), Fei Gao (高飞), Daniele Binosi, Lei Chang (常雷), C. D. Roberts and S. M. Schmidt,
NJU-INP 049/21, e-print: 2108.11493 [hep-ph], Chin. Phys. Lett.
Express 39 (04) (2022) 041401/1-5: Express Letter

MARATHON EXPERIMENT- Schlessinger point method➢ New mathematical method for interpolationand extrapolation of data
– based on continued-fraction representationof functions, augmented by statisticalsampling➢ Delivers model-independent prediction for all
ratios– No reference to models or physics theories➢ Provides benchmark against which all picturesof nucleon structure can be measured➢ Probability that scalar diquark only models of
nucleon might be consistent with available
data is 1/141,000
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
38

Clustering as a Window on the Hierarchical Structure of Quantum Systems(35)

Proton valence-quark DFs: Continuum cf. Lattice➢ Owing to difficulties in handling so-called
disconnected contributions, the calculation ofindividual proton valence DFs using lattice-regularised
QCD (lQCD) is problematic➢ lQCD results are typically only available for isovector
distributions, from which disconnected contributions
vanish in the continuum limit.
➢ Comparison of isovector distributions
𝑢𝑝 𝑥; 𝜁3 − 𝑑𝑝 𝑥; 𝜁3➢ Completely different approaches; yet good
agreement, especially since refinements of both
calculations may be anticipated.

✓ Continuum: Proton and pion distribution functions incounterpoint, Ya Lu (陆亚) et al., NJU-INP 056/22, e-Print:
2203.00753 [hep-ph]✓ Lattice: Nucleon Isovector Unpolarized Parton
Distribution in the Physical-Continuum Limit, H.-W. Lin etal., arXiv:2011.14971 [hep-lat]

Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"
39

Clustering as a Window on the Hierarchical Structure of Quantum Systems(35)

Asymmetry of antimatter in the proton➢ Pauli blocking: gluon splitting produces𝑑 + 𝑑ҧ in preference to 𝑢 + 𝑢ത➢ Comparison with SeaQuest data
[J. Dove, et al., The asymmetry of antimatter in the proton, Nature 590(7847) (2021) 561–565.]➢ Gottfried sum rule

✓ Most recent result from global fits [CT18]:
0.110(80)✓ Proton and pion distribution functions in counterpoint, Ya Lu (陆亚), Lei Chang (常雷), Khépani Raya,
Craig D. Roberts and José Rodríguez-Quintero, NJU-INP 056/22, e-Print: 2203.00753 [hep-ph], Phys.
Lett. B 830 (2022) 137130/1-7✓ Parton distributions of light quarks and antiquarks in the proton, Lei Chang (常雷), Fei Gao (高飞) andCraig D. Roberts, NJU-INP 055/22, e-Print: 2201.07870 [hep-ph], Phys. Lett. B 829 (2022) 137078/1-7
Craig Roberts: cdroberts@nju.edu.cn 419 "Dynamical Diquark Picture of Baryons"40

Clustering as a Window on the Hierarchical Structure of Quantum Systems(35)