craig roberts, physics division. problems in theory faced with difficulties in applying fundamental...

The Ins and Outs of Mesons

Craig Roberts, Physics Division

Craig Roberts: (2) The Ins and Outs of Mesons

2

Problems in Theory

Faced with difficulties in applying fundamental theories to the observed Universe, some researchers have called for a change in how theoretical physics is done.

They begin to argue — explicitly — that if a theory is sufficiently elegant and explanatory, it need not be tested experimentally ...

Chief among the “elegance will suffice” advocates are some string theorists and cosmologists …

This is NOT science …

Hadron Physics XIII: 22-27 Mar. 2015 (85pp)

www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535

http://www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535

http://www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535


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Scandal in Academia

“I have no data yet. It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.”

Sherlock Holmes


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Physics is an

empirical science

Hadron Physics XIII: 22-27 Mar. 2015 (85pp)Craig Roberts: (2) The Ins and Outs of Mesons

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It’s not physics unless it can be tested

empirically.


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It’s not proven

unless it’s verified

experimentally.Hadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Jefferson LabHadron Physics XIII: 22-27 Mar. 2015 (85pp)



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Thomas Jefferson National Accelerator Facility (JLab)

Driving distance: Washington DC to JLab ≈ 270km



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1984 … DoE provided initial funding for research, development and design

1987 … Construction begins on Continuous Electron Beam Accelerator Facility (CEBAF) - February 13

1994 … Accelerator reaches design energy of 4 GeV Construction cost in $FY14 ≈ $1-Billion Goal … Write the book about the strongest force

in nature – the force that holds nuclei together – and determine how that force can be explained in terms of the quarks and gluons of quantum chromodynamics (QCD).



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Thomas Jefferson National Accelerator Facility (JLab) One of the primary reasons for building CEBAF/Jlab …

Prediction: at energy-scales greater than some a priori unknown minimum value, Q0, cross-sections and form factors behave as

power = ( number valence-quarks – 1 + Δλ ) Δλ=0,1, depending on whether helicity is conserved

or flipped … prediction of 1/k2 vector-boson exchange

logarithm = distinctive feature & concrete prediction of QCD Initially imagined that Q0 = 1GeV! So, JLab was initially built to reach 4GeV.


Parton model scaling

QCD scaling violations

e.g. S. J. Brodsky and G. R. Farrar, Phys. Rev. Lett. 31, 1153 (1973)


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Thomas Jefferson National Accelerator Facility (JLab) 1994 – 2004

o An enormous number of fascinating experimental results

o Including an empirical demonstration that the distribution of charge and magnetisation within the proton are completely different,

o Suggesting that quark-quark correlations play a crucial role in nucleon structure

But no sign of parton model scaling and certainly not of scaling violations


Particle physics paradigm

Particle physics paradigm


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2004 … Mission Need Agreed on upgrade of CEBAF (JLab's accelerator) to 12GeV

2015 … 12GeV commissioning beams now being delivered to the experimental halls

Final cost of upgrade isapproximately $370-Million

Physics of JLab at 12GeV arXiv:1208.1244 [hep-ex]

QCD and Hadron Physics arXiv:1502.05728


http://arxiv.org/abs/arXiv:1208.1244




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Selected Science Challenges for the coming decade

Search for exotic hadrons – impossible in quark model– Discovery would force dramatic reassessment of the

distinction between the notions of matter fields and force fields

Exploit opportunities provided by new data on hadron 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 contemporray

descriptions of hadron structureHadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Selected Science Challenges for the coming decade

Precision experimental study of valence-quark 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


Discover meaning of confinement and its relationship to DCSB – the Origin of Visible Mass


Dyson-SchwingerEquations

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?

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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



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Significant Progress


Novel understanding of gluon and quarkconfinement and its consequencesis emerging from quantum field theory

Arriving at a clear picture of how hadron masses emerge dynamically in a universe with light quarks

Dynamical Chiral Symmetry Breaking (DCSB) Realistic computations of ground-state hadron wave functions

with a direct connection to QCD are now available Quark-quark correlations are crucial in hadron structure Accumulating empirical evidence in support of this

prediction


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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.”


Folklore … Hall-D Conceptual Design Report(5) “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


Confinement QFT Paradigm: – Confinement is expressed through a dramatic

change in the analytic structure of propagators for coloured states

– It can be read from a plot of the dressed-propagator for a coloured state


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Normal particleConfined particle

σ ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fm

Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or qualitatively analogous structures chracterised by a dynamically generated mass-scale)

Propagation described by rapidly damped wave & hence state cannot exist in observable spectrum


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Plane wave propagation Feynman propagator for

a fermion describes a Plane Wave

A fermion begins to propagate

It can proceed a long way before undergoing any qualitative changes


meson

meson

meson

meson

Baryon


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Quark Fragmentation A quark begins to

propagate But after each “step” of

length σ, on average, an interaction occurs, so that the quark loses its identity, sharing it with other partons

Finally, a cloud of partons is produced, which coalesces into colour-singlet final states


meson

meson

meson

meson

Baryon

σConfinement is a dynamical phenomenon!


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Quark Gap EquationHadron Physics XIII: 22-27 Mar. 2015 (85pp)

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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 throughquark+gluon dynamics.

– It’s the most important mass generating mechanism for visible matter in the Universe. • Responsible for ≈98% of the proton’s mass.• Higgs mechanism is (almost) irrelevant to light-quarks.

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Just one of the terms that are summed in a solution of the simplest, reasonable truncation of QCD’s 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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Persistent Challenge



Truncation

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Infinitely many coupled equations:Kernel of the equation for the quark self-energy involves:– Dμν(k) – dressed-gluon propagator– Γν(q,p) – dressed-quark-gluon vertex

each of which satisfies its own DSE, etc… Coupling between equations necessitates a truncation

– Weak coupling expansion ⇒ produces every diagram in perturbation theory

– Otherwise useless for the nonperturbative problems in which we’re interested

Persistent challenge in application of DSEs


Invaluable check on practical truncation schemes

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Ward-Green-

Takahashi Identities


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Persistent challenge- truncation scheme

Symmetries associated with conservation of vector and axial-vector currents are critical in arriving at a veracious understanding of hadron structure and interactions

Example: axial-vector Ward-Green-Takahashi identity– Statement of chiral symmetry and the pattern by which it’s broken in

quantum field theory


Axial-Vector vertex Satisfies an inhomogeneous Bethe-Salpeter equation

Quark propagator satisfies a gap equation

Kernels of these equations are completely differentBut they must be intimately related

Relationship must be preserved by any truncationHighly nontrivial constraintFAILURE has an extremely high cost

– loss of any connection with QCD

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Transverse Ward-Green-

Takahashi IdentitiesHadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Longitudinal WGT identity expresses properties of the divergence of the vertex

Transverse identities relate to its curl (as Faraday’s law of induction involves an electric field)


The last two terms in each identity arise in computing the momentum space expression of a nonlocal axial-vector/vector vertex, whose definition involves a gauge-field-dependent line integral

But … practical progress can be made without knowing their precise forms

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These observations show that symmetries relate the kernel of the gap equation – nominally a one-body problem, with that of the Bethe-Salpeter equation – considered to be a two-body problem

Until 1995/1996 people had no idea what to do

Equations were truncated,sometimes with goodphenomenological results,sometimes with poor results

Neither good nor badcould be explained


quark-antiquark scattering kernel

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Happily, that changed, and there is now at least one systematic, nonperturbative and symmetry preserving truncation scheme– H.J. Munczek, Phys. Rev. D 52 (1995) 4736, Dynamical chiral symmetry

breaking, Goldstone’s theorem and the consistency of the Schwinger-Dyson and Bethe-Salpeter Equations

– A. Bender, C.D. Roberts and L. von Smekal, Phys.Lett. B 380 (1996) 7, Goldstone Theorem and Diquark Confinement Beyond Rainbow Ladder Approximation









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Cutting scheme

The procedure generates a Bethe-Salpeter kernel from the kernel of any gap equation whose diagrammatic content is known– That this is possible and

achievable systematically is necessary and sufficient to prove some exact results in QCD


The procedure also enables the formulation of practical phenomenological models that can be used to illustrate the exact results and provide predictions for experiment with readily quantifiable errors.

Leading-order:rainbow- ladder truncation

dressed propagators

bare vertices

Modified skeleton expansion in which the propagators are fully-dressed but the vertices are constructed term-by-term

gap eq.

BS kernel

In gap eq., add1-loop vertex correction

Then BS kernel has3 new terms at this order

Bethe-Salpeter EquationBound-State DSE

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.


38Hadron Physics XIII: 22-27 Mar. 2015 (85pp)


Bethe-Salpeter EquationGeneral Form

Equivalent exact bound-state equation but in this form 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)

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Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601






Ward-Takahashi IdentityBethe-Salpeter Kernel

Now, for first time, it’s possible to formulate an Ansatz for Bethe-Salpeter kernel given any form for the dressed-quark-gluon vertex by using this identity

This enables the identification and elucidation of a wide range of novel consequences of DCSB

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Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601

iγ5 iγ5






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Gluons, too, have a gap equation

Pinch-technique + background field method … reordering of diagrammatic summations in the self-energy – Πμν – ensures that subclusters are individually transverse and gluon-loop and ghost-loop contributions are separately transverse

STIs → WGTIs Enables systematic analysis and evaluation of truncations and

straightforward comparison of results with those of lQCD


Non-perturbative comparison of QCD effective charges, A.C. Aguilar, D. Binosi, J. Papavassiliou and J. Rodriguez-Quintero, Phys. Rev. D80 (2009) 085018


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RGI Running Interaction Input to the DSE analysis

= lQCD result for the ghost dressing function at a given renormalisation scale, ζ

Solve ghost gap equation self-consistently such that αS(ζ) reproduces lQCD result

Gluon-ghost vertex in ghost gap equation is computed from its own DSE in the one-loop dressed approximation.

Continuum- and lattice-QCD solutions agree on solution for the gluon self energy


(kd ̂ 2)= α(ζ) (kΔ̂ 2; ζ)

Bridging a gap between continuum-QCD and ab initio predictions of hadron observables, D. Binosi, L. Chang, J.Papavassiliou, C.D. Roberts, arXiv:1412.4782 [nucl-th], Phys. Lett. B742 (2015) 183-188

http://inspirehep.net/record/1334528?ln=en



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In QCD: Gluons alsobecome massive! Running gluon mass

Gluons are cannibals – a particle species whose members become massive by eating each other!


22

422 )(

kkm

g

gg

Power-law suppressed in ultraviolet, so invisible in perturbation theory

Gluon mass-squared function

Interaction model for the gap equation, S.-x.Qin, L.Chang, Y-x.Liu, C.D.Roberts and D. J. Wilson, arXiv:1108.0603 [nucl-th], Phys. Rev. C 84 (2011) 042202(R) [5 pages]

Bridging a gap between continuum-QCD and ab initio predictions of hadron observables, D. Binosi, L. Chang, J.Papavassiliou, C.D. Roberts, arXiv:1412.4782 [nucl-th], Phys. Lett. B742 (2015) 183-188




http://link.aps.org/doi/10.1103/PhysRevC.84.042202







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Massive Gauge Bosons! Gauge boson cannibalism

… a new physics frontier … within the Standard Model Asymptotic freedom means

… ultraviolet behaviour of QCD is controllable Dynamically generated masses for gluons and quarks means

that QCD dynamically generates its own infrared cutoffs– Gluons and quarks with

wavelength λ > 2/mass ≈ 1 fm decouple from the dynamics … Confinement?!

How does that affect observables?– It will have an impact in

any continuum study– Must play a role in gluon saturation ...

In fact, perhaps it’s a harbinger of gluon saturation?Hadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Top down & Bottom up

Top-down approach – ab initio computation of the interaction via direct analysis of the gauge-sector gap equations

Bottom-up scheme – infer interaction by fitting data within a well-defined truncation of the matter sector DSEs that are relevant to bound-state properties.

Serendipitous collaboration, conceived at one-week ECT* Workshop on DSEs in Mathematics and Physics, has united these two approaches


Bridging a gap between continuum-QCD & ab initio predictions of hadron observables D. Binosi (Italy), L. Chang (Australia), J. Papavassiliou (Spain), C. D. Roberts (US), arXiv:1412.4782 [nucl-th] , Phys. Lett. B 742 (2015) 183

Top-down result = gauge-sector prediction

– Interaction predicted by modern analyses of QCD's gauge sector coincides with that required to describe ground-state observables using the sophisticated matter-sector ANL-PKU DSE truncation

“Maris-Tandy” interaction. Developed at ANL & KSU in 1997-1998. More-than 600 citations – but quantitative disagreement with gauge-sector solution.

Modern kernels and interaction, developed at ANL and Peking U.One parameter, fitted to ground-state properties without reference to gauge-sector studies. Modern top-down and bottom-up results agree within 3% !






46








Modern kernels and interaction, developed at ANL and Peking U.

One parameter, fitted to ground-state properties without reference to gauge-sector studies. Modern top-down and bottom-up results agree within 3% !






47








Modern kernels and interaction, developed at ANL and Peking U.

One parameter, fitted to ground-state properties without reference to gauge-sector studies. Modern top-down and bottom-up results agree within 3% !


Significant steps towardparameter-free prediction

of hadron properties




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Enigma of MassHadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Symmetry preserving analyses in continuum

QCDHadron Physics XIII: 22-27 Mar. 2015 (85pp)Craig Roberts: (2) The Ins and Outs of Mesons

Pion’s Goldberger-Treiman relation


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Pion’s Bethe-Salpeter amplitudeSolution of the Bethe-Salpeter equation

Dressed-quark propagator

Axial-vector Ward-Takahashi identity entails

Owing to DCSB& Exact inChiral QCD


Miracle: two body problem solved, almost completely, once solution of one body problem is known

Maris, Roberts and Tandynucl-th/9707003, Phys.Lett. B420 (1998) 267-273

B(k2)



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The most fundamental expression of

Goldstone’s Theorem and DCSB


fπ Eπ(p2) = B(p2)

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Enigma of mass

The quark level Goldberger-Treiman relation shows that DCSB has a very deep and far reaching impact on physics within the strong interaction sector of the Standard Model; viz.,

Goldstone's theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in the pseudoscalar channel.

This emphasises that Goldstone's theorem has a pointwise expression in QCD

Hence, pion properties are an almost direct measure of the dressed-quark mass function.

Thus, enigmatically, the properties of the massless pion are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe.


fπ Eπ(p2) = B(p2)This identity is why the pion is massless in the chiral limit

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Dynamical Chiral Symmetry Breaking

Vacuum Condensates?Hadron Physics XIII: 22-27 Mar. 2015 (85pp)Craig Roberts: (2) The Ins and Outs of Mesons

Universal Conventions

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.”


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http://en.wikipedia.org/wiki/QCD_vacuum

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“Orthodox Vacuum” Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,

containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!


u

u

ud

u ud

du


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However, just like gluons and quarks, and for the same reasons:Condensates are confined within hadrons. There are no vacuum condensates.

Historically, DCSB has come to be associated with the presumed existence of spacetime-independent condensates that permeate the Universe.


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Confinement contains

condensatesHadron Physics XIII: 22-27 Mar. 2015 (85pp)


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GMOR Relation



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GMOR Relation Valuable to highlight the precise form of the Gell-Mann–

Oakes–Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175 (1968) 2195

o mπ is the pion’s mass o Hχsb is that part of the hadronic Hamiltonian density which

explicitly breaks chiral symmetry. The operator expectation value in this equation is evaluated

between pion states. Un-approximated form of the GMOR relation doesn’t make

any reference to a vacuum condensateHadron Physics XIII: 22-27 Mar. 2015 (85pp)

Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)






http://prc.aps.org/abstract/PRC/v85/i1/e012201



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GMOR is synonymous with “Vacuum Quark

Condensate”Hadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Concept of in-hadron

condensatesHadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Gell-Mann Oakes Renner Relation

Demonstrated algebraically that the so-called Gell-Mann – Oakes – Renner relation is the following statement

Namely, the mass of the pion is completely determined by the pion’s scalar form factor at zero momentum transfer Q2 = 0. viz., by the pion’s scalar charge


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Hadron Charges

Matrix elements associated with hadron form factors Scalar charge of a hadron is an intrinsic property of

that hadron … no more a property of the vacuum than the hadron’s electric charge, axial charge, tensor charge, etc. …


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“Orthodox Vacuum” Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,

containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!


u

u

ud

u ud

du

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New Paradigm Vacuum = perturbative hadronic fluctuations

but no nonperturbative condensates Hadrons = complex, interacting systems

within which perturbative behaviour is restricted to just 2% of the interior


u

u

ud

u ud

du

“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.”


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“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

experiment*103

8 4620

4

HG QCDNscondensateQCD

Paradigm shift:In-Hadron Condensates

“The biggest embarrassment in

theoretical physics.”

http://www.newscientist.com/article/mg19325911.700-dark-energy-seeking-the-heart-of-darkness.html

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Parton structure of

hadronsHadron Physics XIII: 22-27 Mar. 2015 (85pp)


Valence quarks

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Parton Structure of Hadrons

Valence-quark structure of hadrons– Definitive of a hadron.

After all, it’s how we distinguish a proton from a neutron– Expresses charge; flavour; baryon number; and other Poincaré-

invariant macroscopic quantum numbers– Via evolution, determines background at LHC

Foreseeable future will bring precision experimental study of (far) 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


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Why light-front?Hadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Light-front Quantisation Hamiltonian formulation of quantum field theory.

– Fields are specified on a particular initial surface: Light front x+ = x0 + x3 = 0


Using LF quantisation: quantum mechanics-like wave

functions can be defined; quantum-mechanics-like

expectation values can be defined and evaluated

Parton distributions are correlation functions at equal LF-time x+ ; namely, within the initial surface x+ = 0, and can thus be expressed directly in terms of ground state LF wavefunctions

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Pion’s Wave FunctionHadron Physics XIII: 22-27 Mar. 2015 (85pp)


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Pion’s valence-quark Distribution Amplitude

Following a workshop in Caraguatatuba (2012), methods were developed that enable direct computation of the pion’s light-front wave function

φπ(x) = twist-two parton distribution amplitude = projection of the pion’s Poincaré-covariant wave-function onto the light-front

Results have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available.

xα (1-x)α, with α≈0.5Hadron Physics XIII: 22-27 Mar. 2015 (85pp)


Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].




http://prl.aps.org/abstract/PRL/v110/i13/e132001







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Both kernels agree: marked broadening of φπ(x), which owes to DCSB


Asymptotic

RL

DB

This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.

Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result












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Both kernels agree: marked broadening of φπ(x), which owes to DCSB


Asymptotic

RL

DB

This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.

Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result


These computations are the first and only to directly expose DCSB – pointwise – on the light-front; i.e., in the infinite momentum frame.












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Features of Ground-state PDAs

A diverse array of studies since Caraguatatuba (2012) have shown that ground-state meson PDAs are broad, concave functions

Camel-humped distributions – popular for many years – are physically unreasonable because they correspond to bound-state amplitudes that disfavour equal momentum partitioning between valence-quark degrees of freedom


Concave function: no line segment lies above any point on the graph

arXiv:1301.0324 [nucl-th], arXiv:1306.2645 [nucl-th], arXiv:1311.1390 [nucl-th], arXiv:1405.0289 [nucl-th], arXiv:1406:3353 [nucl-th]

















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Hard Exclusive Processes& PDAs

In the theory of strong interactions, the cross-sections for many hard exclusive hadronic reactions can be expressed in terms of the PDAs of the hadrons involved

Example: pseudoscalar-meson elastic electromagnetic form factor

o αS(Q2) is the strong running coupling, o φπ(u) is the meson’s twist-two valence-quark PDAo fP is the meson's leptonic decay constant


It was promised that JLab would verify this fundamental prediction


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Pion electromagnetic form factor

In 2001 – seven years after beginning operations, Jefferson Lab provided the first high precision pion electroproduction data for Fπ between Q2 values of 0.6 and 1.6 (GeV/c)2.


2006 & 2007 – new result, at Q2=2.45 (GeV/c)2

Authors of the publications stated: “still far from the transition to the Q2 region where the pion looks like a simple quark-antiquark pair” disappointment and surprise

Result imagined by many to be QCD prediction

JLab Data

Evaluated with φπ = 6x(1-x)

lQCD only provides access to this small domain, already well-mapped by experiments


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Pion electromagnetic form factor

Year 2000 prediction for Fπ(Q2) – P.Maris & P.C. Tandy,

Phys.Rev. C62 (2000) 055204

Problem … used brute-force computational method … unable to compute for Q2>4GeV2



JLab Data

Shape of prediction suggested to many that one might never see parton model scaling and QCD scaling violations

Factor of three discrepancy



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Pion electromagnetic form factor Plans were made and an

experiment approved that use the higher-energy electron beam at the 12 GeV Upgrade at Jefferson Lab.

The Upgrade will allow an extension of the Fπ measurement up to a value of Q2 of about 6 (GeV/c)2, which will probe the pion at double the resolution.


Projected JLab reach

Will there be any hint of a trend toward the asymptotic pQCD prediction?




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New AlgorithmNew Insights



81



Pion electromagnetic form factor Solution – Part 1

– Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD


Real QCD prediction – obtained with realistic, computed PDA


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Pion electromagnetic form factor Solution – Part 1

– Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD

Solution – Part 2– Algorithm used to

compute the PDA can also be employed to compute Fπ(Q2) directly, to arbitrarily large Q2


Real QCD prediction – obtained with realistic, computed PDA

Predictions: JLab will see maximum Experiments to 8GeV2 will see

parton model scaling and QCD scaling violations for the first time in a hadron form factor

Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013)

maximum

Agreement within 15%








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Implications

Verify the theory of factorisation in hard exclusive processes, with dominance of hard contributions to the pion form factor for Q2>8GeV2.

Notwithstanding that, normalisation of Fπ(Q2) is fixed by a pion wave-function whose dilation with respect to φπ

asy(x)=6x(1-x) is a definitive signature of DCSB– Empirical measurement of the strength of DCSB in the

Standard Model – the origin of visible mass Close the book on a story that began thirty-five years ago Paves the way for a dramatic reassessment of pictures of

proton & neutron structure, which is already well underway


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Epilogue


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Epilogue DCSB →equivalence between quark 1-body and pseudoscalar 2-body problem– Complete understanding of pion … no model dependence …

the dressed-quark mass function is known– Hence, continuum-QCD theory is on the threshold of a

complete picture of the pion’s light-front valence-quark wave function

In parallel, continuum-QCD is providing predictions of the light-front structure of other light-quark hadrons

Near-term Aim– Unified QCD-based and quantum mechanical picture of the light-

quark meson sector of the Standard Model Developments in baryon sector

are equally dramatic: e.g.,


is understood

I.C. Cloët, C.D. Roberts, A.W. Thomas:arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803









craig roberts, physics division. problems in theory faced with difficulties in applying fundamental...

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