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Craig Roberts Physics Division www.phy.anl.gov/theory/staff/cdr.html

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The Physics of Hadrons

Published collaborations in 2010/2011

Adnan BASHIR (U Michoacan);

Stan BRODSKY (SLAC);

Lei CHANG (ANL & PKU);

Huan CHEN (BIHEP);

Ian CLOËT (UW);

Bruno EL-BENNICH (Sao Paulo);

Xiomara GUTIERREZ-GUERRERO (U Michoacan);

Roy HOLT (ANL);

Mikhail IVANOV (Dubna);

Yu-xin LIU (PKU);

Trang NGUYEN (KSU);

Si-xue QIN (PKU);

Hannes ROBERTS (ANL, FZJ, UBerkeley);

Robert SHROCK (Stony Brook);

Peter TANDY (KSU);

David WILSON (ANL)

Students

Early-career

scientists

Craig Roberts

Physics Division

www.phy.anl.gov/theory/staff/cdr.html

Standard Model of Particle Physics

Craig Roberts: The Physics of Hadrons

- With the advent of cosmic ray science and particle accelerators, numerous additional particles were discovered:
- muon (1937), pion (1947), kaon (1947), Roper resonance (1963), …

- By the mid-1960s, it was apparent that not all the particles could be fundamental.
- A new paradigm was necessary.

- Gell-Mann's and Zweig's constituent-quark theory (1964) was a critical step forward.
- Gell-Mann, Nobel Prize 1969: "for his contributions and discoveries concerning the classification of elementary particles and their interactions".

- Over the more than forty intervening years, the theory now called the Standard Model of Particle Physics has passed almost all tests.

Craig Roberts: The Physics of Hadrons

In the early 20th Century, the only matter particles known to exist were the proton, neutron, and electron.

- Politzer, Gross and Wilczek – 1973-1974
- Perturbative Quantum Chromodynamics – QCD
- Nobel Prize (2004):
- "for the discovery of asymptotic freedom in the theory of the strong interaction".

- Worth noting that the character of 96% of the matter in the Universe is completely unknown

Craig Roberts: The Physics of Hadrons

- Strong interaction
- Existence and composition of the vast bulk of visible matter in the Universe:
- proton, neutron
- the forces that form and bind them to form nuclei
- responsible for more than 98% of the visible matter in the Universe

- Existence and composition of the vast bulk of visible matter in the Universe:

Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange

Craig Roberts: The Physics of Hadrons

Two quantum-mechanical constituent-quarks - particle+antiparticle -interacting via a potential, derived from one constituent-gluon exchange

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

Saul Perlmutter, Brian P. Schmidt, Adam G. Riess, Nobel Prize 2011: for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.

Craig Roberts: The Physics of Hadrons

- What is dark energy?
- 1998: A group of scientists had recorded several dozen supernovae, including some so distant that their light had started to travel toward Earth when the universe was only a fraction of its present age.
- Contrary to their expectation, the scientists found that the expansion of the universe is not slowing, but accelerating.

Craig Roberts: The Physics of Hadrons

- Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?
- Quantum chromodynamics, or QCD, is the theory describing the strong nuclear force.
- Carried by gluons, it binds quarks into particles like protons and neutrons.
- Apparently, the tiny subparticles are permanently confined: one can't pull a quark or a gluon from a proton because the strong force gets stronger with distance and snaps them right back inside.

Quantum Chromodynamics

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

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 !

- 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: The Physics of Hadrons

3-gluon vertex

4-gluon vertex

Craig Roberts: The Physics of Hadrons

- 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

Craig Roberts: The Physics of Hadrons

- 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 being 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

5 x10-5

Add 3-gluon self-interaction

gluon

antiscreening

fermion

screening

Craig Roberts: The Physics of Hadrons

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

0.5

0.4

↔

0.3

αs(r)

0.2

0.1

0.002fm

0.02fm

0.2fm

Craig Roberts: The Physics of Hadrons

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

0.5

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 hitherto an empirical fact.

Craig Roberts: The Physics of Hadrons

- 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?

Millennium prize of $1,000,000 for proving that SUc(3) gauge theory is mathematically well-defined, which will necessarily prove or disprove the confinement conjecture, but in the absence of dynamical quarks

Craig Roberts: The Physics of Hadrons

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

Craig Roberts: The Physics of Hadrons

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

- Essentiallynonperturbative
for Q2 < 2 GeV2

- Perhaps?!
- 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: The Physics of Hadrons

The study of nonperturbative QCD is the puriew of …

Craig Roberts: The Physics of Hadrons

Hadron: Any of a class of subatomic particles that are composed of quarks and/or gluons and take part in the strong interaction.

Examples: proton, neutron, & pion.

International Scientific Vocabulary:

hadr- thick, heavy (from Greek hadros thick) + 2on

First Known Use: 1962

Baryon: hadron with half-integer-spin

Meson: hadron with integer-spin

Craig Roberts: The Physics of Hadrons

- Internationally, this is an approximately $1-billion/year effort in experiment and theory, with approximately $375-million/year in the USA.
- Roughly 90% of these funds are spent on experiment
- $1-billion/year is the order of the operating budget of CERN

Craig Roberts: The Physics of Hadrons

“A central goal of (the DOE Office of ) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD.”

Craig Roberts: The Physics of Hadrons

A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's STAR detector

Craig Roberts: The Physics of Hadrons

- USA
- Thomas Jefferson National Accelerator Facility,
Newport News, Virginia

Nature of cold hadronic matter

Upgrade underway

Construction cost $310-million

New generation experiments in 2016

- Relativistic Heavy Ion Collider, Brookhaven National Laboratory,
Long Island, New York

Strong phase transition, 10μs after Big Bang

- Thomas Jefferson National Accelerator Facility,

proton

pion

The structure of matter

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

- 1947 – Pion discovered by Cecil Frank Powell
The beginning of Particle Physics

- Then came
- Disentanglement of confusion
between (1937) muon and pion – similar masses

- Discovery of particles with “strangeness” (e.g., kaon1947-1953)

- Disentanglement of confusion
- Subsequently, a complete spectrum of mesons and baryons
with mass below ≈1 GeV

- 28 states

- Became clear that
pion is “too light”

- hadrons supposed to be heavy, yet …

- Gell-Mann and Ne’eman:
- Eightfold way(1961) – a picture based
- on group theory: SU(3)
- Subsequently, quark model –
- where the u-, d-, s-quarks
- became the basis vectors in the
- fundamental representation
- of SU(3)

- Pion =
- Two quantum-mechanical constituent-quarks - particle+antiparticle -
- interacting via a potential

Craig Roberts: The Physics of Hadrons

IG(JPC)

140 MeV

780 MeV

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

- proton = three constituent quarks
- Mproton ≈ 1GeV
- Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV

- pion = constituent quark + constituent antiquark
- Guess Mpion ≈ ⅔ × Mproton≈ 700MeV

- WRONG . . . . . . . . . . . . . . . . . . . . . . Mpion = 140MeV
- Rho-meson
- Also constituent quark + constituent antiquark
– just pion with spin of one constituent flipped

- Mrho ≈ 770MeV ≈ 2 × Mconstituent−quark
What is “wrong” with the pion?

- Also constituent quark + constituent antiquark

- Rho-meson

Craig Roberts: The Physics of Hadrons

- How does one make an almost massless particle from two massive constituent-quarks?
- Naturally, one could always tune a potential in quantum mechanics so that the ground-state is massless
– but some are still making this mistake

- However:
current-algebra (1968)

- This is impossible in quantum mechanics, for which one always finds:

HIGHLY NONTRIVIAL

Impossible in quantum mechanics

Only possible in asymptotically-free gauge theories

Craig Roberts: The Physics of Hadrons

- The correct understanding of pion observables; e.g. mass, decay constant and form factors, requires an approach to contain a
- well-defined and validchiral limit;
- and an accurate realisation of dynamical chiral symmetry breaking.

Craig Roberts: The Physics of Hadrons

- Interacting gauge theories, in which it makes sense to speak of massless fermions, have a nonperturbativechiral symmetry
- It is realised in the theory’s spectrum via the appearance of degenerate parity partners
- Perturbative QCD: u- & d- quarks are very light
mu /md≈ 0.5 & md≈ 4MeV

H. Leutwyler, 0911.1416 [hep-ph]

- However, splitting between parity partners is greater-than 100-times this mass-scale; e.g.,

Craig D Roberts

John D Roberts

Craig Roberts: The Physics of Hadrons

- Something is happening in QCD
- some inherent dynamical effect is dramatically changing the pattern by which the Lagrangian’schiral symmetry is expressed

- Qualitatively different from
spontaneous symmetry breaking

aka the Higgs mechanism

- Nothing is added to the theory
- Have only fermions & gauge-bosons
Yet, the mass-operator

generated by the theory

produces a spectrum

with no sign of chiral symmetry

Understand emergent phenomena

- Quark and Gluon Confinement
- No matter how hard one strikes the proton,
- one cannot liberate an individual quark or gluon

Craig Roberts: The Physics of Hadrons

- Dynamical Chiral Symmetry Breaking
Very unnatural pattern of bound state masses;

e.g., Lagrangian (pQCD) quark mass is small but

. . . no degeneracy between JP=+ and JP=− (parity partners)

- Neither of these phenomena is apparent in QCD’s LagrangianYetthey are the dominant determiningcharacteristics of
real-world QCD.

- QCD
– Complex behaviour arises from apparently simple rules.

Craig Roberts: The Physics of Hadrons

Friedman, Kendall, Taylor, Nobel Prize (1990): "for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics"

Craig Roberts: The Physics of Hadrons

- Fermions – two static properties:
proton electric charge = +1; and magnetic moment, μp

- Magnetic Moment discovered by Otto Stern and collaborators in 1933; Stern awarded Nobel Prize (1943): "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton".
- Dirac (1928) – pointlikefermion:
- Stern (1933) –
- Big Hint that Proton is not a point particle
- Proton has constituents
- These are Quarks and Gluons

- Quark discovery via e-p-scattering at SLAC in 1968
- the elementary quanta of QCD

Structurelessfermion, or simply structured fermion, F1=1 & F2=0, so that GE=GM and hence distribution of charge and magnetisation within this fermion are identical

F1 = Dirac form factor

F2 = Pauli form factor

GM = Sachs Magntic form factor

If a nonrelativistic limit exists, this relates to the magnetisation density

GE = Sachs Electric form factor

If a nonrelativistic limit exists, this relates to the charge density

Craig Roberts: The Physics of Hadrons

Electron is a good probe because it is structureless

Electron’s relativistic current is

Proton’s electromagnetic current

Which is correct?

How is the difference to be explained?

Craig Roberts: The Physics of Hadrons

- Data before 1999
- Looks like the structure of the proton is simple

- The properties of JLab (high luminosity) enabled a new technique to be employed.
- First data released in 1999 and paint a VERY DIFFERENT PICTURE

Craig Roberts: The Physics of Hadrons

“A central goal of (the DOE Office of ) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD.”

Craig Roberts: The Physics of Hadrons

- So, what’re the holdups?
They are legion …

- Confinement
- Dynamical chiral symmetry breaking
- A fundamental theory of unprecedented complexity

- QCD defines the difference between nuclear and particle physicists:
- Nuclear physicists try to solve this theory
- Particle physicists run away to a place where tree-level computations are all that’re necessary
– perturbation theory, the last refuge of a scoundrel

- What are the quarks and gluons of QCD?
- Is there such a thing as a constituent quark, a constituent-gluon?
- After all, these are the concepts for which Gell-Mann won the Nobel Prize.

Craig Roberts: The Physics of Hadrons

- Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom?
- If not, with what should they be replaced?
What is the meaning of the NSAC Challenge?

Suppose QCD behaved reasonably →mπ=mρ, then repulsive and attractive forces in the Nucleon-Nucleon potential have the SAME range and there is NO intermediate range attraction.

Craig Roberts: The Physics of Hadrons

Under these circumstances:

- Can 12C be produced, can it be stable?
- Is the deuteron stable; can Big-Bang Nucleosynthesis occur?
(Many more existential questions …)

Probably not … but it wouldn’t matter because we wouldn’t be around to worry about it.

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

- But … QCD’s emergent phenomena can’t be studied using perturbation theory
- So what? Same is true of bound-state problems in quantum mechanics!

- Differences:
- Here relativistic effects are crucial – virtual particles
Quintessence of Relativistic Quantum Field Theory

- Interaction between quarks – the Interquark Potential –
Unknown throughout > 98% of the pion’s/proton’s volume!

- Here relativistic effects are crucial – virtual particles
- Understanding requires ab initio nonperturbative solution of fully-fledged interacting relativistic quantum field theory, something which Mathematics and Theoretical Physics are a long way from achieving.

Craig Roberts: The Physics of Hadrons

The Traditional Approach

– Modelling

– has its problems.

– Spacetime becomes an

hypercubic lattice

– Computational challenge,

many millions of

degrees of freedom

Craig Roberts: The Physics of Hadrons

Lattice-QCD

– Spacetime becomes an

hypercubic lattice

– Computational challenge,

many millions of

degrees of freedom

– Approximately 500 people

worldwide & 20-30 people per

collaboration.

Craig Roberts: The Physics of Hadrons

Lattice-QCD

–

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

- 1994 . . . “As computer technology continues to improve, lattice gauge theory [LGT] will become an increasingly useful means of studying hadronic physics through investigations of discretised quantum chromodynamics [QCD]. . . . .”

Craig Roberts: The Physics of Hadrons

- 1994 . . . “However, it is equally important to develop other complementary nonperturbative methods based on continuum descriptions. In particular, with the advent of new accelerators such as CEBAF (VA) and RHIC (NY), there is a need for the development of approximation techniques and models which bridge the gap between short-distance, perturbative QCD and the extensive amount of low- and intermediate-energy phenomenology in a single covariant framework. . . . ”

Craig Roberts: The Physics of Hadrons

- 1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.”

Craig Roberts: The Physics of Hadrons

- 1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.”
- C. D. Roberts and A. G. Williams, “Dyson-Schwinger equations and their application to hadronic physics,”
Prog. Part. Nucl. Phys. 33, 477 (1994) [arXiv:hep-ph/9403224].

(473 citations)

- Dyson (1949) & Schwinger (1951) . . . One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another.
- Gap equation:
- fermion self energy
- gauge-boson propagator
- fermion-gauge-boson vertex

- Gap equation:
- These are nonperturbative equivalents in quantum field theory of the Lagrange equations of motion.
- Essential in simplifying the general proof of renormalisability of gauge field theories.

Craig Roberts: The Physics of Hadrons

- Approach yields
- Schwinger functions; i.e.,
- propagators and vertices
- Cross-Sections built from
- Schwinger Functions
- Hence, method connects
- observables with long-
- range behaviour of the
- running coupling
- Experiment ↔ Theory
- comparison leads to an
- understanding of long-
- range behaviour of
- strong running-coupling

Craig Roberts: The Physics of Hadrons

- Well suited to Relativistic Quantum Field Theory
- Simplest level: Generating Tool for Perturbation Theory . . . Materially Reduces Model-Dependence … Statement about long-range behaviour of quark-quark interaction
- NonPerturbative, Continuum approach to QCD
- Hadrons as Composites of Quarks and Gluons
- Qualitative and Quantitative Importance of:
- Dynamical Chiral Symmetry Breaking
– Generation of fermion mass from nothing

- Quark & Gluon Confinement
– Coloured objects not detected,

Not detectable?

- Dynamical Chiral Symmetry Breaking

Craig Roberts: The Physics of Hadrons

- QCD is asymptotically-free (2004 Nobel Prize)
- Chiral-limit is well-defined;
i.e., one can truly speak of a massless quark.

- NB. This is nonperturbativelyimpossible in QED.

- Chiral-limit is well-defined;
- Dressed-quark propagator:
- Weak coupling expansion of
gap equation yields every diagram in perturbation theory

- In perturbation theory:
If m=0, then M(p2)=0

Start with no mass,

Always have no mass.

Craig D Roberts

John D Roberts

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

The 2008Nobel Prize in Physics was divided, one half awarded to YoichiroNambu

"for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"

Craig Roberts: The Physics of Hadrons

In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.

Mass from nothing!

DSE prediction of DCSB confirmed

Craig Roberts: The Physics of Hadrons

In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.

Jlab 12GeV: Scanned by 2<Q2<9 GeV2

elastic & transition form factors.

Craig Roberts: The Physics of Hadrons

Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.

Craig Roberts: The Physics of Hadrons

- Hadron spectrum, and elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron'scharacterising properties amongst its QCD constituents.
- Dynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe.
Higgs mechanism is (almost) irrelevant to light-quarks.

- Running of quark mass entails that hadron physics calculations at even modest Q2 require a Poincaré-covariant approach.
Covariance + M(p2) require existence of quark orbital angular momentum in hadron's rest-frame wave function.

- Confinement is expressed through a violent change of the propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator.
It is intimately connected with DCSB.

?

Craig Roberts: The Physics of Hadrons

- Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum)
“The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.”

“The advent of quantum field theory made consideration of the cosmological constant obligatory not optional.”

Michael Turner, “Dark Energy and the New Cosmology”

Craig Roberts: The Physics of Hadrons

- The only possible covariant form for the energy of the (quantum) vacuum; viz.,
is mathematically equivalent to the cosmological constant.

“It is a perfect fluid and precisely spatially uniform”

“Vacuum energy is almost the perfect candidate for dark energy.”

Enormous and even greater contribution from Higgs VEV!

Mass-scale generated by

spacetime-independent

condensate

“The biggest embarrassment in theoretical physics.”

Craig Roberts: The Physics of Hadrons

- QCD vacuum contribution
- If chiral symmetry breaking is expressed in a nonzero expectation value of the quark bilinear, then the energy difference between the symmetric and broken phases is of order
MQCD≈0.3GeV

- One obtains therefrom:

- If chiral symmetry breaking is expressed in a nonzero expectation value of the quark bilinear, then the energy difference between the symmetric and broken phases is of order

Craig Roberts: The Physics of Hadrons

- Quantum Healing Central:
- “KSU physics professor [Peter Tandy] publishes groundbreaking research on inconsistency in Einstein theory.”

- Paranormal Psychic Forums:
- “Now Stanley Brodsky of the SLAC National
Accelerator Laboratory in Menlo Park,

California, and colleagues have found a way

to get rid of the discrepancy. “People have

just been taking it on faith that this quark

condensate is present throughout the

vacuum,” says Brodsky.

- “Now Stanley Brodsky of the SLAC National

Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201

Brodsky and Shrock, PNAS 108, 45 (2011)

Chang, Roberts, Tandy, arXiv:1109.2903 [nucl-th]

QCD

Craig Roberts: The Physics of Hadrons

- Resolution
- Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime.
- So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example,
in their Bethe-Salpeter or

light-front wavefunctions.

- GMOR
cf.

Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201

Brodsky and Shrock, PNAS 108, 45 (2011)

Chang, Roberts, Tandy, arXiv:1109.2903 [nucl-th]

And |π> →|0>

matrix elements

Craig Roberts: The Physics of Hadrons

- Resolution
- Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime.
- So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example,
in their Bethe-Salpeter or

light-front wavefunctions.

- No qualitative difference
betweenfπand ρπ

- Both are equivalent
order parameters for DCSB

Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201

Brodsky and Shrock, PNAS 108, 45 (2011)

Chang, Roberts, Tandy, arXiv:1109.2903 [nucl-th]

Chiral limit

One of ONLY TWO expressions related to the condensate that are

rigorously defined in QCD for nonzero current-quark mass

Craig Roberts: The Physics of Hadrons

- Resolution
- Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime.
- So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example,
in their Bethe-Salpeter or

light-front wavefunctions.

- No qualitative difference
between fπand ρπ

- And

“Void that is truly empty solves dark energy puzzle”

Rachel Courtland, New Scientist 4th Sept. 2010

- Cosmological Constant:
- Putting QCD condensates back into hadrons reduces the
- mismatch between experiment and theory by a factor of 1046
- Possibly by far more, if technicolour-like theories are the correct
- paradigm for extending the Standard Model

Craig Roberts: The Physics of Hadrons

“EMPTY space may really be empty. Though quantum theory suggests that a vacuum should be fizzing with particle activity, it turns out that this paradoxical picture of nothingness may not be needed. A calmer view of the vacuum would also help resolve a nagging inconsistency with dark energy, the elusive force thought to be speeding up the expansion of the universe.”

Craig Roberts: The Physics of Hadrons

- Dμν(k) – dressed-gluon propagator
- Γν(q,p) – dressed-quark-gluon vertex
- Suppose one has in hand – from anywhere – the exact form of the dressed-quark-gluon vertex
What is the associated symmetry-

preserving Bethe-Salpeter kernel?!

Craig Roberts: The Physics of Hadrons

- K(q,k;P) – fully amputated, two-particle irreducible,
quark-antiquark scattering kernel

- Textbook material.
- Compact. Visually appealing. Correct
Blocked progress for more than 60 years.

Lei Chang and C.D. Roberts

0903.5461 [nucl-th]

Phys. Rev. Lett. 103 (2009) 081601

Craig Roberts: The Physics of Hadrons

- Equivalent exact bound-state equation but in thisform K(q,k;P) → Λ(q,k;P), which is completely determined by dressed-quark self-energy
- Enables derivation of a Ward-Takahashi identity for Λ(q,k;P)
- Now, for first time, by using this identity, it’s possible to formulate Ansatz for Bethe-Salpeter kernel given anyform for dressed-quark-gluon vertex
- This enables the identification and elucidation of a wide range of novel consequences of DCSB

Craig Roberts: The Physics of Hadrons

- Schwinger’s result for QED:
- pQCD: two diagrams
- (a) is QED-like
- (b) is only possible in QCD – involves 3-gluon vertex

- Analyse (a) and (b)
- (b) vanishes identically: the 3-gluon vertex does not contribute to a quark’s anomalous chromomag. moment at leading-order
- (a) Produces a finite result: “ – ⅙ αs/2π ”
~ (– ⅙) QED-result

- But, in QED and QCD, the anomalous chromo- and electro-magnetic moments vanish identically in the chiral limit!

Craig Roberts: The Physics of Hadrons

- Interaction term that describes magnetic-moment coupling to gauge field
- Straightforward to show that it mixes left ↔ right
- Thus, explicitly violates chiral symmetry

- Follows that in fermion’se.m. current
γμF1 does cannot mix with σμνqνF2

No Gordon Identity

- Hence massless fermions cannot not possess a measurable chromo- or electro-magnetic moment

- But what if the chiral symmetry is dynamically broken, strongly, as it is in QCD?

L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]

Phys. Rev. Lett. 106 (2011) 072001

DCSB

- Ball-Chiu term
- Vanishes if no DCSB
- Appearance driven by STI

- Anom. chrom. mag. mom.
- contribution to vertex
- Similar properties to BC term
- Strength commensurate with lattice-QCD
- Skullerud, Bowman, Kizilersuet al.
- hep-ph/0303176

- Role and importance is
- Novel discovery
- Essential to recover pQCD
- Constructive interference with Γ5

Craig Roberts: The Physics of Hadrons

- Three strongly-dressed and essentially-
nonperturbative contributions to dressed-quark-gluon vertex:

L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]

Phys. Rev. Lett. 106 (2011) 072001

- Formulated and solved general
- Bethe-Salpeter equation
- Obtained dressed
- electromagnetic vertex
- Confined quarks
- don’t have a mass-shell
- Can’t unambiguously define
- magnetic moments
- But can define
- magnetic moment distribution

Factor of 10

magnification

- AEM is opposite in sign but of
- roughly equal magnitude
- as ACM

Craig Roberts: The Physics of Hadrons

L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]

Phys. Rev. Lett. 106 (2011) 072001

- Formulated and solved general
- Bethe-Salpeter equation
- Obtained dressed
- electromagnetic vertex
- Confined quarks
- don’t have a mass-shell
- Can’t unambiguously define
- magnetic moments
- But can define
- magnetic moment distribution

Factor of 10

magnification

Contemporary theoretical estimates:

1 – 10 x 10-10

Largest value reduces discrepancy expt.↔theory from 3.3σ to below 2σ.

- Potentially important for elastic and transition form factors, etc.
- Significantly, also quite possibly for muong-2 – via Box diagram,
- which is not constrained by extant data.

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

R.T. Cahill et al.,

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

rqq≈ rπ

Craig Roberts: The Physics of Hadrons

- M(p2) – effects have enormous impact on meson properties.
- Must be included in description and prediction of baryon properties.

- M(p2) 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 founded on observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel

R.T. Cahill et al.,

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

quark exchange

ensures Pauli statistics

quark

diquark

Craig Roberts: The Physics of Hadrons

- 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

I.C. Cloëtet al.

arXiv:0812.0416 [nucl-th]

- “Survey of nucleon electromagnetic form factors”
- – unification of meson and baryon observables; and prediction of nucleon elastic form factors to
- 15 GeV2

Craig Roberts: The Physics of Hadrons

- Photon-baryon vertex
Oettel, Pichowskyand von Smekal, nucl-th/9909082

I.C. Cloët, C.D. Roberts, et al.

arXiv:0812.0416 [nucl-th]

I.C. Cloët, C.D. Roberts, et al.

In progress

- DSE result Dec 08

- DSE result
- – including the
- anomalous
- magnetic
- moment distribution

- Highlights again the
- critical importance of
- DCSB in explanation of
- real-world observables.

Craig Roberts: The Physics of Hadrons

Proton plus proton-like resonances

Does this ratio pass through zero?

Craig Roberts: The Physics of Hadrons

DSE studies indicate that the proton has a very rich internal structure

The JLab data, obtained using the polarisaton transfer method, are an accurate indication of the behaviour of this ratio

The pre-1999 data (Rosenbluth) receive large corrections from so-called 2-photon exchange contributions

I.C. Cloët, C.D. Roberts, et al.

arXiv:0812.0416 [nucl-th]

I.C. Cloët, C.D. Roberts, et al.

In progress

- Does this ratio pass through zero?
- DSE studies say YES, with a zero crossing at 8GeV2, as a consequence of strong correlations within the nucleon
- Experiments at the upgraded JLab facility will provide the answer

Linear fit to data ⇒ zero at 8GeV2

[1,1] Padé fit ⇒ zero at 10GeV2

- In the meantime, the DSE studies will be refined

Craig Roberts: The Physics of Hadrons

Craig Roberts: The Physics of Hadrons

Standard Model’s truly Nonperturbative Challenge

– Just what is the interaction that produces the pion, proton, indeed, all hadrons?

- Physics is an experimental science; and there’s
- an international experimental programme …
- Goal to understand …
- how the interactions between dressed–quarks
and –gluons create ground & excited hadrons;

- how these interactions emerge from QCD

- how the interactions between dressed–quarks

Craig Roberts: The Physics of Hadrons

- No single approach is yet able to provide a unified description of all hadron phenomena
- E.g., intelligent reaction theory will long be necessary as bridge between experiment and QCD-based theory

- Nevertheless, DSEs today provide an insightful connection between QCD and experiment:
- DCSB explained & developing a perspective on confinement

Craig Roberts: The Physics of Hadrons