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Published collaborations― 2010-Present

Students

Early-career scientists

- Adnan BASHIR (U Michoácan);
- Stan BRODSKY (SLAC);
- Gastão KREIN (São Paulo)
- Roy HOLT (ANL);
- Mikhail IVANOV (Dubna);
- Yu-xin LIU (PKU);
- Michael RAMSEY-MUSOLF (UW-Mad)
- Sebastian SCHMIDT (IAS-FZJ & JARA);
- Robert SHROCK (Stony Brook);
- Peter TANDY (KSU);
- Shaolong WAN (USTC)

Craig Roberts: A New Decade of Hadron Physics (67p)

Rocio BERMUDEZ (U Michoácan);

Chen CHEN (ANL, IIT, USTC);

Xiomara GUTIERREZ-GUERRERO (U Michoácan);

Trang NGUYEN (KSU);

Si-xue QIN (PKU);

Hannes ROBERTS (ANL, FZJ, UBerkeley);

Chien-Yeah SENG (UW-Mad)

Kun-lun WANG (PKU);

Lei CHANG (ANL, FZJ, PKU);

Huan CHEN (BIHEP);

Ian CLOËT (UAdelaide);

Bruno EL-BENNICH (São Paulo);

Mario PITSCHMANN (ANL & UW-Mad);

David WILSON (ANL & ODU);

Science Challenges for the coming decade: 2013-2022

Craig Roberts: A New Decade of Hadron Physics (67p)

- Search for exotic hadrons
- Discovery would force dramatic reassessment of the distinction between the notions of matter fields and force fields
- Exploit opportunities provided by new data on nucleon elastic and transition form factors
- Chart infrared evolution of QCD’s coupling and dressed-masses
- Reveal correlations that are key to nucleon structure
- Expose the facts or fallacies in modern descriptions of nucleon structure

Science Challenges for the coming decade: 2013-2022

Craig Roberts: A New Decade of Hadron Physics (67p)

- Precision experimental study of valence region, and theoretical computation of distribution functions and distribution amplitudes
- Computation is critical
- Without it, no amount of data will reveal anything about the theory underlying the phenomena of strong interaction physics
- Explore and exploit opportunities to use precision-QCD as a probe for physics beyond the Standard Model

Overarching Science Challenges for the coming decade: 2013-2022

Discover meaning of confinement, and its relationship to DCSB – the origin of visible mass

Craig Roberts: A New Decade of Hadron Physics (67p)

What is QCD?

Craig Roberts: A New Decade of Hadron Physics (67p)

QCD is a Theory

(not an effective theory)

Craig Roberts: A New Decade of Hadron Physics (67p)

- Very likely a self-contained, nonperturbativelyrenormalisable and hence well defined Quantum Field Theory

This is not true of QED – cannot be defined nonperturbatively

- No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8000 GeV
- Increasingly likely that any extension of the Standard Model will be based on the paradigm established by QCD
- Extended Technicolour: electroweak symmetry breaks via a fermion bilinear operator in a strongly-interacting non-Abelian theory.

Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity

Contrast: so-called Effective Field Theories

Can

Cannot

- QCD valid at all energy scales that have been tested so far: no breakdown below
- E ≈ 60000 mπ
- Cannot be used to test QCD
- Any mismatch between
- EF-Theory and experiment owes to an error in the formulation of one or conduct of the other

Craig Roberts: A New Decade of Hadron Physics (67p)

EFTs applicable over a very restricted energy domain; e.g., ChPT known to breakdown for E > 2mπ

Can be used to help explore how features of QCD influence observables

Craig Roberts: A New Decade of Hadron Physics (67p)

What is QCD?

Craig Roberts: A New Decade of Hadron Physics (67p)

- Lagrangian of QCD
- G = gluon fields
- Ψ = quark fields
- The key to complexity in QCD … gluon field strength tensor
- Generates gluon self-interactions, whose consequences are quite extraordinary

cf.Quantum Electrodynamics

Craig Roberts: A New Decade of Hadron Physics (67p)

QED is the archetypal gauge field theory

Perturbatively simple

but nonperturbatively undefined

Chracteristic feature:

Light-by-light scattering; i.e.,

photon-photon interaction – leading-order contribution takes

place at order α4. Extremely small probability because α4 ≈10-9 !

What is QCD?

- Relativistic Quantum Gauge Field Theory:
- Interactions mediated by vector boson exchange
- Vector bosons are perturbatively-massless
- Similar interaction in QED
- Special feature of QCD – gluon self-interactions

3-gluon vertex

4-gluon vertex

Craig Roberts: A New Decade of Hadron Physics (67p)

What is QCD?

3-gluon vertex

4-gluon vertex

Craig Roberts: A New Decade of Hadron Physics (67p)

- Novel feature of QCD
- Tree-level interactions between gauge-bosons
- O(αs) cross-section cf. O(αem4) in QED
- One might guess that this

is going to have a big impact

- Elucidating part of that impact is the origin

of the 2004 Nobel Prize to Politzer,

and Gross & Wilczek

Running couplings

Craig Roberts: A New Decade of Hadron Physics (67p)

- Quantum gauge-field theories are all typified by the feature that Nothing is Constant
- Distribution of charge and mass, the number of particles, etc., indeed, all the things that quantum mechanics holds fixed, depend upon the wavelength of the tool used to measure them
- particle number is not conserved in quantum field theory
- Couplings and masses are renormalised via processes involving virtual-particles. Such effects make these quantities depend on the energy scale at which one observes them

QED cf. QCD?

5 x10-5

Add 3-gluon self-interaction

gluon

antiscreening

fermion

screening

Craig Roberts: A New Decade of Hadron Physics (67p)

- 2004 Nobel Prize in Physics : Politzer, Gross and Wilczek

What is QCD?

0.5

0.4

↔

0.3

αs(r)

0.2

0.1

0.002fm

0.02fm

0.2fm

Craig Roberts: A New Decade of Hadron Physics (67p)

This momentum-dependent coupling

translates into a coupling that

depends strongly on separation.

Namely, the interaction between quarks, between gluons, and between quarks and gluons grows rapidly with separation

Coupling is hugeat separations r = 0.2fm ≈ ⅟₄ rproton

Confinement in QCD

0.4

0.3

αs(r)

0.2

0.1

0.002fm

0.02fm

0.2fm

- The Confinement Hypothesis:
- Colour-charged particles cannot be isolated and therefore cannot be directly observed. They clump together in colour-neutral bound-states
- This is an empirical fact.

Craig Roberts: A New Decade of Hadron Physics (67p)

- A peculiar circumstance; viz., an interaction that becomes stronger as the participants try to separate
- If coupling grows so strongly with separation, then
- perhaps it is unbounded?
- perhaps it would require an infinite amount of energy in order to extract a quark or gluon from the interior of a hadron?

- What we know unambiguously …
- Is that we know too little!

What is the interaction throughout more than 98% of the proton’s volume?

Craig Roberts: A New Decade of Hadron Physics (67p)

Strong-interaction: QCD

- Nature’sonly example of truly nonperturbative,
- fundamental theory
- A-priori, no idea as to what such a theory
- can produce

Craig Roberts: A New Decade of Hadron Physics (67p)

- Asymptotically free
- Perturbation theory is valid and accurate tool at large-Q2
- Hence chiral limit is defined
- Essentiallynonperturbative

for Q2 < 2 GeV2

What is Confinement?

Craig Roberts: A New Decade of Hadron Physics (67p)

Light quarks & Confinement

- Folklore

“The color field lines between a quark and an anti-quark form flux tubes.

Craig Roberts: A New Decade of Hadron Physics (67p)

A unit area placed midway between the quarks and perpendicular to the line connecting them intercepts a constant number of field lines, independent of the distance between the quarks.

This leads to a constant force between the quarks – and a large force at that, equal to about 16 metric tons.”

Hall-DConceptual-DR(5)

Light quarks & Confinement

Craig Roberts: A New Decade of Hadron Physics (67p)

- Problem:

16 tonnes of force

makes a lot of pions.

Light quarks & Confinement

Craig Roberts: A New Decade of Hadron Physics (67p)

Problem:

16 tonnes of force

makes a lot of pions.

G. Bali et al., PoS LAT2005 (2006) 308

Light quarks & ConfinementCraig Roberts: A New Decade of Hadron Physics (67p)

In the presence of light quarks, pair creation seems to occur non-localized and instantaneously

No flux tube in a theory with light-quarks.

Flux-tube is not the correct paradigm for confinement in hadron physics

Confinement

Confined particle

Normal particle

complex-P2

complex-P2

timelike axis: P2<0

s ≈ 1/Im(m) ≈ 1/2ΛQCD≈ ½fm

- Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities
- State described by rapidly damped wave & hence state cannot exist in observable spectrum

Craig Roberts: A New Decade of Hadron Physics (67p)

- QFT Paradigm:
- Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured states
- It can almost be read from a plot of the dressed-propagator for a coloured state

Light quarks & Confinement

Craig Roberts: A New Decade of Hadron Physics (67p)

- In the study of hadrons, attention should turn from potential models toward the continuum bound-state problem in quantum field theory
- Such approaches offer the possibility of posing simultaneously the questions
- What is confinement?
- What is dynamical chiral symmetry breaking?
- How are they related?

Is it possible that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a mass-scale in QCD, can have different origins and fates?

Dynamical ChiralSymmetry Breaking

Craig Roberts: A New Decade of Hadron Physics (67p)

Dynamical ChiralSymmetry Breaking

Craig Roberts: A New Decade of Hadron Physics (67p)

- DCSB is a fact in QCD
- Dynamical, not spontaneous
- Add nothing to QCD , no Higgs field, nothing!
- Effect achieved purely through the dynamics of gluons and quarks.
- It’s the most important mass generating mechanism for visible matter in the Universe.
- Responsible for approximately 98% of the proton’s mass.
- Higgs mechanism is (almost) irrelevant to light-quarks.

DCSB

C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50

M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227

- In QCD, all “constants” of quantum mechanics are actually strongly momentum dependent: couplings, number density, mass, etc.
- So, a quark’s mass depends on its momentum.
- Mass function can be calculated and is depicted here.
- Continuum- and Lattice-QCD

Mass from nothing!

- are in agreement: the vast bulk of the light-quark mass comes from a cloud of gluons, dragged along by the quark as it propagates.

Craig Roberts: A New Decade of Hadron Physics (67p)

Where does the mass come from?

αS23

Just one of the terms that are summed in a solution of the rainbow-ladder gap equation

Craig Roberts: A New Decade of Hadron Physics (67p)

Deceptively simply picture

Corresponds to the sum of a countable infinity of diagrams.

NB. QED has 12,672 α5 diagrams

Impossible to compute this in perturbation theory.

The standard algebraic manipulation

tools are just inadequate

In QCD, Gluons, too, become massive

Craig Roberts: A New Decade of Hadron Physics (67p)

Not just quarks …

Gluons also have a gap equation …

1/k2behaviour signals essential singularity in the running coupling:

Impossible to reach in perturbation theory

Spectroscopy

Craig Roberts: A New Decade of Hadron Physics (67p)

Exotic Mesons

Craig Roberts: A New Decade of Hadron Physics (67p)

Quantum mechanics is very restrictive.

Systems constituted solely from a particle and its antiparticle are only permitted to have a limited set of quantum numbers

JPC = 0-+, 0++, 1--, 1+-, 1++, 2-+, 2++, 2--, …

Exotic mesons – states whose quantum numbers cannot be supported by quantum mechanical quark-antiquark systems; e.g., JPC = 0--, 0+-, 1-+, 2+-, …

Hybrid mesons – states with quark-model quantum numbers but a non-quark-model decay pattern.

Both systems are suspected to possess “constituent gluon” content, which translates into a statement that they are expected to have a large overlap with interpolating fields that explicitly contain gluon fields.

Meson Spectroscopy

Craig Roberts: A New Decade of Hadron Physics (67p)

- Exotics and hybrids are truly novel states
- They’re not matter as we know it
- In possessing valence glue, such states confound the distinction between matter fields and force carriers
- But they’re only exotic in a quantum mechanics based on constituent-quark degrees-of-freedom
- They’re natural in strongly-coupled quantum field theory, far from the nonrelativistic (potential model) limit
- No symmetry forbids exotics

QCD interaction promotes them

So they very probably exist!

Lattice Spectra ― Prediction of exotics

Craig Roberts: A New Decade of Hadron Physics (67p)

A spectrum of normal mesons, which simultaneously produces states with “exotic” quantum numbers

Lattice Spectra- Problem

Baryons

Craig Roberts: A New Decade of Hadron Physics (67p)

Masses of known states are wrong.

Worse: level ordering of known states is wrong.

Expt: + + -

Lattice: + - +

Just like constituent-quark model and for similar reasons – namely, DCSB is suppressed by too-large current-quark masses

Exotics exist but not, perhaps, in a universe with our light-quarks?

Hadron Spectra ― Prediction of exotics

DSE

Lattice

Craig Roberts: A New Decade of Hadron Physics (67p)

Difficult to avoid “exotics” in strong-coupling quantum field theory

Meson Spectroscopy

Craig Roberts: A New Decade of Hadron Physics (67p)

- Theory:
- Expected mass domain predicted by models, and continuum- and lattice-QCD
- That domain is accessible to
- JLab at 12 GeV (GluEx in Hall-D, dedicated to mesons. Also experiments to search for baryonic hybrids.)
- GSI (PANDA) : antiproton-proton annihilation in charmonium region (2017-)
- BES-III: electron-positron annihilation in charmonium region & also decays to light quark bound states
- However, need information on transition form factors, decay channels and widths

Anomalies

Functional integral measure

Action integral of the theory’s classical Lagrangian

Flavour-diagonal chiral transformations

Ψ(x) → exp(iα(x) γ5 If) Ψ(x)

Craig Roberts: A New Decade of Hadron Physics (67p)

Understanding origin of anomalies is straightforward

Quantum field theories are defined via a functional integral

Z[J,ξ] = ∫D(AΨ) Exp(-S[A,Ψ] + ∫d4x [A(x)J(x) + ξ ―(x)Ψ(x) + Ψ―(x)ξ(x) ])

If Action is invariant under a particular local transformation, then the classical theory possesses an associated conserved current.

Anomalies arise when the measure is not invariant under that local transformation:

Meson Spectroscopy

Craig Roberts: A New Decade of Hadron Physics (67p)

- Anomalies:
- fascinating feature of quantum field theory
- currents conserved classically, but whose conservation law is badly broken after second quantisation
- Two anomalies in QCD are readily probed by experiment
- Abelian anomaly, via γγ decays of light neutral pseudoscalars
- Provides access to light-quark mass ratio 2 ms /(mu+md)
- non-Abelian anomaly via η-η'mixing
- Both are intimately & inextricably linked with DCSB

Quantitative understanding ofη-η'mixing gives access to strength of topological fluctuations in QCD

Meson Spectroscopy- fπ0, η, η' are order parameters for DCSB!

Vacuum polarisation, measuring overlap of topological charge with matter sector

Craig Roberts: A New Decade of Hadron Physics (67p)

- Strength of matrix element for π0, η, η' →γγ is inversely proportional to the mesons’ weak decay constant:

M ~ 1/fπ0, η, η'

On the other hand, for “normal” systems,

M ~ f2π0, η, η' /mπ0, η, η'; i.e., pattern completely reversed

& matrix element vanishes in chiral limit!

- non-Abelian anomaly connects DCSB rigorously with essentially topological features of QCD:
- Quantitative understanding ofη-η'mixing gives access to strength of topological

fluctuations in QCD

Hadron Structure

Craig Roberts: A New Decade of Hadron Physics (67p)

Structure of Hadrons

Craig Roberts: A New Decade of Hadron Physics (67p)

- Elastic form factors
- Provide vital information about the structure and composition of the most basic elements of nuclear physics.
- They are a measurable and physical manifestation of the nature of the hadrons' constituents and the dynamics that binds them together.
- Accurate form factor data are driving paradigmatic shifts in our pictures of hadrons and their structure; e.g.,
- role of orbital angular momentum and nonpointlikediquark correlations
- scale at which p-QCD effects become evident
- strangeness content
- meson-cloud effects
- etc.

Austral. J. Phys. 42 (1989) 129-145

Structure of HadronsSUc(3):

Craig Roberts: A New Decade of Hadron Physics (67p)

- Dynamical chiral symmetry breaking (DCSB)

– has enormous impact on meson properties.

- Must be included in description

and prediction of baryon properties.

- DCSB is essentially a quantum field theoretical effect.

In quantum field theory

- Meson appears as pole in four-point quark-antiquark Green function

→ Bethe-Salpeter Equation

- Nucleon appears as a pole in a six-point quark Green function

→ Faddeev Equation.

- Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks
- Tractable equation is based on the observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel

Austral. J. Phys. 42 (1989) 129-145

Faddeev Equationquark exchange

ensures Pauli statistics

quark

diquark

composed of strongly-dressed quarks bound by dressed-gluons

Craig Roberts: A New Decade of Hadron Physics (67p)

- Linear, Homogeneous Matrix equation
- Yields wave function (Poincaré Covariant FaddeevAmplitude) thatdescribes quark-diquark relative motion within the nucleon
- Scalar and Axial-Vector Diquarks . . .
- Both have “correct” parity and “right” masses
- In Nucleon’s Rest Frame Amplitude has

s−, p− & d−wave correlations

Faddeev Equation

quark-quark scattering matrix

- a pole approximation is used to arrive at the Faddeev-equation

Craig Roberts: A New Decade of Hadron Physics (67p)

Why should a pole approximation produce reliable results?

Calculation of diquark masses in QCD

R.T. Cahill, C.D. Roberts and J. Praschifka

Phys.Rev. D36 (1987) 2804

DiquarksCraig Roberts: A New Decade of Hadron Physics (67p)

- Consider the rainbow-gap and ladder-Bethe-Salpeter equations
- In this symmetry-preserving truncation, colour-antitriplet quark-quark correlations (diquarks) are described by a very similar homogeneous Bethe-Salpeter equation
- Only difference is factor of ½
- Hence, an interaction that describes mesons also generates diquark correlations in the colour-antitriplet channel

SU(2)isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles.

Structure of HadronsCraig Roberts: A New Decade of Hadron Physics (67p)

Remarks

- Diquark correlations are not inserted by hand

Such correlations are a dynamical consequence of strong-coupling in QCD

- The same mechanism that produces an almost masslesspion from two dynamically-massive quarks;

i.e., DCSB, forces a strong correlation between two quarks in colour-antitriplet channels within a baryon

– an indirect consequence of Pauli-Gürsey symmetry

- Diquark correlations are not pointlike
- Typically, r0+ ~ rπ & r1+ ~ rρ(actually 10% larger)
- They have soft form factors

Flavor separation of proton form factors

Q4F2q/k

Cates, de Jager,

Riordan, Wojtsekhowski,

PRL 106 (2011) 252003

Q4 F1q

Craig Roberts: A New Decade of Hadron Physics (67p)

Very different behavior for u & d quarks

Means apparent scaling in proton F2/F1 is purely accidental

Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36

Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205

Diquark correlations!u

d

=Q2/M2

- Doubly-represented u-quark is predominantly linked with harder
- 0+diquark contributions
- Interference produces zero in Dirac form factor of d-quark in proton
- Location of the zero depends on the relative probability of finding
- 1+ & 0+diquarks in proton
- Correlated, e.g., with valence d/u ratio at x=1

Craig Roberts: A New Decade of Hadron Physics (67p)

- Poincaré covariant Faddeev equation
- Predicts scalar and axial-vector diquarks
- Proton's singly-represented d-quark more likely to be struck in association with 1+diquark than with 0+
- form factor contributions involving

1+diquark are softer

Structure of Hadrons

Craig Roberts: A New Decade of Hadron Physics (67p)

- Nucleon to resonance transition form factors
- Critical extension to elastic form factors and promising tool in probing for valence-glue in baryons
- Meson excited states and nucleon resonances are more sensitive to long-range effects in QCD than are the properties of ground states

… analogous to exotics and hybrids

- N→ Δ

Indications emerging that diquark correlations can explain the (unnaturally) rapid fall-off exhibited by the magnetic form factor which dominates the description of this spin-flip transition.

Structure of Hadrons

LF QM with M(p2)

- DSE – M=constant

DSE – M(p2)

CLAS Np (2009)

CLAS p+p-p (2011)

CLASp+p-p (2012)

CLAS12 projected

Craig Roberts: A New Decade of Hadron Physics (67p)

- Nucleon to resonance transition form factors
- Critical extension to elastic form factors and promising tool in probing for valence-glue in baryons
- Meson excited states and nucleon resonances are more sensitive to long-range effects in QCD than are the properties of ground states

… analogous to exotics and hybrids

- N→ P11(1440) “Roper”
- First zero crossing measured in

any nucleon form factor

or transition amplitude

- Appearance of zero has eliminated

numerous proposals for explaining

Roper resonance

Structure of Hadrons

Craig Roberts: A New Decade of Hadron Physics (67p)

- During last five years, the Excited Baryon Analysis Center, directed by Harry Lee, resolved a fifty-year puzzle by demonstrating conclusively that the Roper resonance is the proton's first radial excitation
- its lower-than-expected mass owes to a dressed-quark core shielded by a dense cloud of pions and other mesons.

(Decadal Report on Nuclear Physics: Exploring the Heart of Matter)

- Breakthrough enabled by both new analysis tools and new high quality data.
- This Experiment/Theory collaboration

holds lessons for GlueX and future baryon analyses

Parton Structure of Hadrons

Valence quarks

The rest is “sea” and glue

- Understanding hadron structure means charting and computing the distribution of this matter and energy within the hadron

Craig Roberts: A New Decade of Hadron Physics (67p)

Within the nucleon, valence quarks are the source of everything. They’re what a person means when stating “The nucleon contains three-quarks”

However, as one employs probes that increasingly resolve the smallest longitudinal or transverse length scales within a rapidly moving proton, then the glue comes to dominate so that, quite probably, no memory of the valence quark structure permeates to this level

Parton Structure of Hadrons

- Is there strangeness in the proton?
- Is the number of anti-u quarks the
- same as the number of anti-d quarks?

Craig Roberts: A New Decade of Hadron Physics (67p)

- Valence-quark structure of hadrons
- Definitive of a hadron – it’s how we tell a proton from a neutron
- Expresses charge; flavour; baryon number; and other Poincaré-invariant macroscopic quantum numbers
- Via evolution (a well-defined procedure for taking measurements at one energy and evolving them to higher energies) valence quark structure determines background at LHC
- Sea-quark distributions
- Can’t alter hadronic state
- But can possess nontrivial f+f-bar content and asymmetry
- Former and any nontrivial structure in the latter are both essentially nonperturbative features of QCD

Parton Structure of Hadrons

Craig Roberts: A New Decade of Hadron Physics (67p)

- Light front provides a link with quantum mechanics
- If a probability interpretation is ever valid, it’s in the infinite-momentum frame (quantisation on the light front)
- Enormous amount of intuitively expressive information about hadrons & processes involving them is encoded in
- Parton distribution functions (PDFs)
- Generalised PDFs
- Transverse-momentum-dependent PDFs
- Information will be revealed by the measurement of these functions

– so long as they can be calculated

Success of programme demands very close collaboration between experiment and theory

Parton Structure of Hadrons

Craig Roberts: A New Decade of Hadron Physics (67p)

- Need for QCD–connected calculation is emphasised by saga of pion’s valence-quark distribution:
- E615 (1989): uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD

Models of the Pion’svalence-quark distributions

Pion

Craig Roberts: A New Decade of Hadron Physics (67p)

- (1−x)β with β=0 (i.e., a constant – any fraction is equally probable! )
- AdS/QCD models using light-front holography
- Nambu–Jona-Lasinio models, when a translationally invariant regularization is used
- (1−x)β with β=1
- Nambu–Jona-Lasinio NJL models with a hard cutoff
- Duality arguments produced by some theorists
- (1−x)β with 0<β<2
- Relativistic constituent-quark models, with power-law depending on the form of model wave function
- (1−x)β with 1<β<2
- Instanton-based models, all of which have incorrect large-k2behaviour

Models of the Pion’svalence-quark distributions

Pion

Completely unsatisfactory.

Impossible to suggest that there’s even qualitative agreement!

Craig Roberts: A New Decade of Hadron Physics (67p)

- (1−x)β with β=0 (i.e., a constant – any fraction is equally probable! )
- AdS/QCD models using light-front holography
- Nambu–Jona-Lasinio models, when a translationally invariant regularization is used
- (1−x)β with β=1
- Nambu–Jona-Lasinio NJL models with a hard cutoff
- Duality arguments produced by some theorists
- (1−x)β with 0<β<2
- Relativistic constituent-quark models, depending on the form of model wave function
- (1−x)β with 1<β<2
- Instanton-based models

DSE prediction of the Pion’svalence-quark distributions

Pion

Craig Roberts: A New Decade of Hadron Physics (67p)

Consider a theory in which quarks scatter via a vector-boson exchange interaction whosek2>>μG2behaviour is(1/k2)β,

Then at a resolving scale Q0

uπ(x;Q0) ~ (1-x)2β

namely, the large-x behaviour of the quark distribution function is a direct measure of the momentum-dependence of the underlying interaction.

In QCD, β=1 and hence

QCDuπ(x;Q0) ~ (1-x)2

DSE prediction of the Pion’svalence-quark distributions

Pion

Completely unambigous!

Direct connection between experiment and theory, empowering both as tools of discovery.

Craig Roberts: A New Decade of Hadron Physics (67p)

Consider a theory in which quarks scatter via a vector-boson exchange interaction whosek2>mG2behaviour is(1/k2)β,

Then at a resolving scale Q0

uπ(x;Q0) ~ (1-x)2β

namely, the large-x behaviour of the quark distribution function is a direct measure of the momentum-dependence of the underlying interaction.

In QCD, β=1 and hence

QCDuπ(x;Q0) ~ (1-x)2

Parton Structure of Hadrons

Craig Roberts: A New Decade of Hadron Physics (67p)

- Need for calculation is emphasised by Saga of pion’s valence-quark distribution:
- E615 (1989): uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD;
- 2001: DSE predicts

uvπ ~ (1-x)2

Argues that distribution

inferred from data

can’t be correct;

- 2010: NLO reanalysis, including

soft-gluon resummation.

Inferred distribution agrees

with DSE-QCD

Trang, Bashir, Roberts & Tandy,“Pion and kaon valence-quark parton distribution functions,” arXiv:1102.2448 [nucl-th],Phys. Rev. C 83, 062201(R) (2011) [5 pages]

uK(x)/uπ(x)Value of ratio at x=0 will approach “1” under evolution to higher resolving scales. This is a feature of perturbative dynamics

Using DSEs in QCD, one derives that the x=1 value is

≈ (fπ/fK)2 (Mu /Ms)4 = 0.3

Value of ratio at x=1 is a fixed point of the evolution equations

Hence, it’s a very strong test of nonperturbative dynamics

Craig Roberts: A New Decade of Hadron Physics (67p)

Drell-Yan experiments at CERN (1980 & 1983) provide the only extant measurement of this ratio

DSE result in complete accord with the (old) measurement

New Drell-Yan experiments are capable of validating this comparison

It should be done so that complete understanding can be claimed

Beyond SM

Craig Roberts: A New Decade of Hadron Physics (67p)

Beyond the Standard Model

Craig Roberts: A New Decade of Hadron Physics (67p)

- High precision electroweak measurements
- Any observed and confirmed discrepancy with Standard Model reveals New Physics
- Precise null results place hard lower bounds on the scale at which new physics might begin to have an impact
- Experiment and theory bounds on nucleon strangeness content place tight limits on dark-matter – hadron cross-sections
- Sensitive dark photon searches
- dark photon is possible contributor to muong-2 and dark matter puzzles
- plausible masses are accessible to nonp-QCD machines

Theory

Craig Roberts: A New Decade of Hadron Physics (67p)

- Lattice-QCD
- Significant progress in the

last five years

- This must continue
- Bound-state problem in

continuum quantum field theory

- Significant progress, too
- Must also continue
- Completed and planned experiments will deliver the pieces of the puzzle that is QCD.

Theory must be developed to explain how they fit together

Future

Craig Roberts: A New Decade of Hadron Physics (67p)

- Clay Mathematics Institute

Prove confinement in pure-gauge QCD

Prize: $1-million

That’s about all this easy problem is worth

- In the real world, all readily accessible matter is defined by light quarks

Confinement in this world is certainly an immeasurably more complicated phenomenon

- Hadron physics is unique:
- Confronting a fundamental theory in which the elementary degrees-of-freedom are intangible and only composites reach detectors
- Hadron physics must deploy a diverse array of experimental and theoretical probes and tools in order to define and solve the problems of confinement and its relationship with DCSB
- These are two of the most important challenges in fundamental Science; and hadron physics provides the means to solve them

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