Craig Roberts Physics Division

A New Decadeof Hadron Physics

Craig Roberts

Physics Division

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

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Published collaborations― 2010-Present

1. Rocio BERMUDEZ (U Michoácan);2. Chen CHEN (ANL, IIT, USTC);3. Xiomara GUTIERREZ-GUERRERO (U Michoácan);4. Trang NGUYEN (KSU);5. Si-xue QIN (PKU);6. Hannes ROBERTS (ANL, FZJ, UBerkeley);7. Chien-Yeah SENG (UW-Mad)8. Kun-lun WANG (PKU);9. Lei CHANG (ANL, FZJ, PKU); 10. Huan CHEN (BIHEP);11. Ian CLOËT (UAdelaide);12. Bruno EL-BENNICH (São Paulo);13. Mario PITSCHMANN (ANL & UW-Mad);14. David WILSON (ANL & ODU);

Physics Division Seminar: 26 Nov 12

15. Adnan BASHIR (U Michoácan);16. Stan BRODSKY (SLAC);17. Gastão KREIN (São Paulo)18. Roy HOLT (ANL);19. Mikhail IVANOV (Dubna);20. Yu-xin LIU (PKU);21. Michael RAMSEY-MUSOLF (UW-Mad)22. Sebastian SCHMIDT (IAS-FZJ & JARA);23. Robert SHROCK (Stony Brook);24. Peter TANDY (KSU);25. Shaolong WAN (USTC)

StudentsEarly-career scientists


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Science Challenges for the coming decade: 2013-2022

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 structurePhysics Division Seminar: 26 Nov 12


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Science Challenges for the coming decade: 2013-2022

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



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Overarching Science Challenges for the

coming decade: 2013-2022


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


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What is QCD?Physics Division Seminar: 26 Nov 12

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QCD is a Theory Very likely a self-contained, nonperturbatively renormalisable

and hence well defined Quantum Field TheoryThis 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



(not an effective theory)

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Contrast: so-called Effective Field Theories

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



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

Can Cannot

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Quantum Chromodynami

cs

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What is QCD?

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



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

cf.Quantum Electrodynamics



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

What is QCD?


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3-gluon vertex

4-gluon vertex


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What is QCD?

Novel feature of QCD– Tree-level interactions between gauge-bosons– O(αs) cross-section cf. O(αem

4) in QED

One might guess that this is going to have a big impact

Elucidating part of that impact is the originof the 2004 Nobel Prize to Politzer, and Gross & Wilczek



3-gluon vertex

4-gluon vertex

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Running couplings

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?


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2004 Nobel Prize in Physics : Politzer, Gross and Wilczek

e

QED

mQQ

ln321

)(

QNQ

f

QCD

ln)233(

6)( fermionscreening

gluonantiscreening


Add 3-gluon self-interaction5 x10-5

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What is QCD? 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 huge at separations r = 0.2fm ≈ ⅟₄ rproton



↔

0.002fm 0.02fm 0.2fm

αs (r)

0.1

0.2

0.3

0.4

0.5

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Confinement in QCD 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?



0.002fm 0.02fm 0.2fm

αs (r)

0.1

0.2

0.3

0.4

0.5

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.

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

The Problem with QCD



Perhaps?!What we know

unambiguously …Is that we know too little!


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Strong-interaction: QCD

Asymptotically free– Perturbation theory is valid

and accurate tool at large-Q2

– Hence chiral limit is defined Essentially nonperturbative

for Q2 < 2 GeV2


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


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What is Confinement?


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Light quarks & Confinement

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-D Conceptual-DR(5)



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

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Problem: 16 tonnes of force makes a lot of pions.



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Problem: 16 tonnes of force makes a lot of pions.



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Light quarks & Confinement 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



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

http://inspirebeta.net/record/694488?ln=en



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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

Confinement

complex-P2 complex-P2

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

Normal particle Confined particle


timelike axis: P2<0

s ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fm

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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?



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Dynamical Chiral Symmetry Breaking




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Dynamical Chiral Symmetry Breaking

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.Physics Division Seminar: 26 Nov 12


DCSB

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Mass from nothing!


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






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

Where does the mass come from?

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



αS23

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In QCD, Gluons, too, become massive

Not just quarks … Gluons also have a

gap equation …1/k2 behaviour signals essential singularity in the running coupling:

Impossible to reach in perturbation theory



22

422 )(

kkm

g

gg

)( 2kconst

e

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SpectroscopyPhysics Division Seminar: 26 Nov 12


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Exotic Mesons 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.



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Meson Spectroscopy

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) limitNo symmetry forbids exotics

QCD interaction promotes themSo they very probably exist!



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Lattice Spectra ― Prediction

of exotics A spectrum of normal mesons,

which simultaneously produces states with “exotic” quantum numbers



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Lattice Spectra- Problem

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?



Baryons

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Hadron Spectra ― Prediction

of exotics

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



DSE

Lattice

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Meson Spectroscopy 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



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Anomalies 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:



Functional integral measure Action integral of the theory’s classical

Lagrangian

Flavour-diagonal chiral transformations

Ψ(x) → exp(i α(x) γ5 If ) Ψ(x)

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Meson SpectroscopyAnomalies:

– 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



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Meson Spectroscopy 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 ~ f2

π0, 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 of η-η' mixing gives access to

strength of topological fluctuations in QCD



fπ0, η, η' are order parameters for DCSB!

Vacuum polarisation, measuring overlap of topological charge with matter sector

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

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Hadron StructurePhysics Division Seminar: 26 Nov 12


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Structure of Hadrons 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 nonpointlike diquark

correlations– scale at which p-QCD effects become evident– strangeness content– meson-cloud effects– etc.




Structure of Hadrons 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

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R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145


6333 SUc(3):



Faddeev Equation

Linear, Homogeneous Matrix equationYields wave function (Poincaré Covariant Faddeev Amplitude)

that describes 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 correlations45

diquark

quark

quark exchangeensures Pauli statistics

composed of strongly-dressed quarks bound by dressed-gluons


R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145


Why should a pole approximation produce reliable results?

Faddeev Equation



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

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

Diquarks



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Calculation of diquark masses in QCDR.T. Cahill, C.D. Roberts and J. PraschifkaPhys.Rev. D36 (1987) 2804





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Structure of Hadrons

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 massless pion 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



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


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Flavor separation of proton form factors

Very different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental


Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) 252003

Q4F2q/k

Q4 F1q


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Diquark correlations!

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


Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205

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

d

u

=Q2/M2

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Structure of HadronsNucleon 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→ ΔIndications 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.



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Structure of HadronsNucleon 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 eliminatednumerous proposals for explainingRoper resonance



CLAS12 projected

CLAS N (2009)

CLAS p (2011)

CLAS p (2012)

LF QM with M(p2) DSE – M=constant DSE – M(p2)

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Structure of HadronsDuring 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



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Parton Structure of Hadrons

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



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

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Parton Structure of Hadrons 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



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

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Parton Structure of Hadrons 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 calculatedSuccess of programme demands very close collaboration between experiment and theory



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Parton Structure of Hadrons Need for QCD–connected calculation is emphasised by

saga of pion’s valence-quark distribution:o E615 (1989): uv

π ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD



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Models of the Pion’s valence-quark distributions

(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-k2 behaviour



Pion

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Models of the Pion’s valence-quark distributions

(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



Pion

Completely unsatisfactory. Impossible to suggest that there’s even qualitative agreement!

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DSE prediction of the Pion’s valence-quark distributions

Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k2>>μG

2 behaviour 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 QCD uπ(x;Q0) ~ (1-x)2



Pion

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Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k2>mG

2 behaviour 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 QCD uπ(x;Q0) ~ (1-x)2

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

DSE prediction of the Pion’s valence-quark distributions



Pion

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Parton Structure of Hadrons Need for calculation is emphasised by Saga of pion’s

valence-quark distribution:o E615 (1989): uv

π ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD;

o 2001: DSE predicts uv

π ~ (1-x)2 Argues that distribution inferred from data can’t be correct;

o 2010: NLO reanalysis, including soft-gluon resummation. Inferred distribution agrees with DSE-QCD



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uK(x)/uπ(x) 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



Value of ratio at x=1 is a fixed point of the evolution equationsHence, it’s a very strong test of nonperturbative dynamics

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

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]




http://link.aps.org/doi/10.1103/PhysRevC.83.062201





64Beyo

nd S

M



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Beyond the Standard Model

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 muon g-2 and dark

matter puzzles– plausible masses are accessible to nonp-QCD machines



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Theory

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



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Future Clay Mathematics Institute

Prove confinement in pure-gauge QCDPrize: $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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