Quantum Chromodynamics: The Origin of Mass as We Know it

Quantum Chromodynamics: The Origin of Mass as We Know it
Craig D. Roberts Physics Division Argonne National Laboratory & School of Physics Peking University Transition Region

Argonne National Laboratory
(1) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Argonne National Laboratory
Physics Division ATLAS Tandem Linac: International User Facility for Low Energy Nuclear Physics 37 PhD Scientific Staff Annual Budget: $27million Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Length-Scales of Physics

Physics Division Research sponsored primarily by Department of Energy:
Office of Nuclear Physics Nuclear Hadron Tests of Standard Model Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Physics Division Research sponsored primarily by Department of Energy:
Office of Nuclear Physics Nuclear HADRON Tests of Standard Model Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Hadron Physics “Hadron physics is unique at the cutting edge of modern science because Nature has provided us with just one instance of a fundamental strongly-interacting theory; i.e., Quantum Chromodynamics (QCD). The community of science has never before confronted such a challenge as solving this theory.” Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

NSAC Long Range Plan “A central goal of (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.” (3) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Quarks and Nuclear Physics
Standard Model of Particle Physics: Six quark flavours (4) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Standard Model of Particle Physics: Six quark flavours Real World Normal matter – only two light-quark flavours are active Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Standard Model of Particle Physics: Six quark flavours Real World Normal matter – only two light-quark flavours are active Or, perhaps, three Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Standard Model of Particle Physics: Six quark flavours Real World Normal matter – only two light-quark flavours are active Or, perhaps, three For numerous good reasons, much research also focuses on accessible heavy-quarks Nevertheless, I will focus on the light-quarks; i.e., u & d. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

What is QCD? (5) IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

What is QCD? Relativistic Quantum Gauge Theory:
Interactions mediated by vector boson exchange Vector bosons are perturbatively-massless Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Interactions mediated by vector boson exchange Vector bosons are perturbatively-massless Similar interaction in QED Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Interactions mediated by vector boson exchange Vector bosons are perturbatively-massless Similar interaction in QED Special feature of QCD – gluon self-interactions, which completely change the character of the theory 3-gluon vertex 4-gluon vertex Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

QED cf. QCD? Running coupling

QED cf. QCD? Running coupling
Add 3-gluon self-interaction Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

QED cf. QCD? gluon antiscreening fermion screening
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

QED cf. QCD? 2004 Nobel Prize in Physics : Gross, Politzer and Wilczek
gluon antiscreening fermion screening Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Simple picture - Proton
Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange (7) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Simple picture - Pion Two quantum-mechanical constituent-quarks - particle+antiparticle -interacting via a potential, derived from one constituent-gluon exchange (8) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Modern Miracles in Hadron Physics
proton = three constituent quarks Mproton ≈ 1GeV Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV (9) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

proton = three constituent quarks Mproton ≈ 1GeV Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV pion = constituent quark + constituent antiquark Guess Mpion ≈ ⅔ × Mproton ≈ 700MeV Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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? Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Dichotomy of the pion 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 However: current-algebra (1968) This is impossible in quantum mechanics, for which one always finds: (10) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

NSAC Long Range Plan? What is a constituent quark, a constituent-gluon? (11) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

NSAC Long Range Plan? What is a constituent quark, a constituent-gluon? Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom? Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

NSAC Long Range Plan? What is a constituent quark, a constituent-gluon? Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom? If not, with what should they be replaced? Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

NSAC Long Range Plan? What is a constituent quark, a constituent-gluon? 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? Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

What is the meaning of all this?
If mπ=mρ , then repulsive and attractive forces in the Nucleon-Nucleon potential have the SAME range and there is NO intermediate range attraction. (12) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

If mπ=mρ , then repulsive and attractive forces in the Nucleon-Nucleon potential have the SAME range and there is NO intermediate range attraction. Under these circumstances: Can 12C be stable? Is the deuteron stable; can Big-Bang Nucleosynthesis occur? Many more existential questions … Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

If mπ=mρ , then repulsive and attractive forces in the Nucleon-Nucleon potential have the SAME range and there is NO intermediate range attraction. Under these circumstances: Can 12C 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, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

QCD’s Challenges Quark and Gluon Confinement
No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon (12) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon 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) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon 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 Lagrangian Yet they are the dominant determining characteristics of real-world QCD. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

QCD’s Challenges Understand emergent phenomena
Quark and Gluon Confinement No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon 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 Lagrangian Yet they are the dominant determining characteristics of real-world QCD. QCD – Complex behaviour arises from apparently simple rules. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Why don’t we just stop talking & solve the problem?
Emergent phenomena can’t be studied using perturbation theory (13) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Emergent phenomena can’t be studied using perturbation theory So what? Same is true of bound-state problems in quantum mechanics! Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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! Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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! Understanding requires ab initio nonperturbative solution of fully-fledged interacting relativistic quantum field theory Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Universal Truths Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising properties amongst its QCD constituents. (14) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Universal Truths Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising 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. (14) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Universal Truths Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising 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 calculations at even modest Q2 require a Poincaré-covariant approach. Covariance requires existence of quark orbital angular momentum in hadron's rest-frame wave function. (14) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Universal Truths Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising 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 calculations at even modest Q2 require a Poincaré-covariant approach. Covariance requires 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, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

How can we tackle the SM’s Strongly-interacting piece?

The Traditional Approach – Modelling Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

The Traditional Approach – Modelling – has its problems. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Lattice-QCD – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Lattice-QCD – – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom – Approximately 500 people worldwide & people per collaboration. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

A Compromise? Dyson-Schwinger Equations

“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] ” (15) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

“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 ” (15) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

“Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.” (15) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

“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/ ]. (473 citations) (15) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

A Compromise? DSEs Dyson (1949) & Schwinger (1951) One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another. (16) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

A Compromise? DSEs 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 (16) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

A Compromise? DSEs 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 These are nonperturbative equivalents in quantum field theory to the Lagrange equations of motion. Essential in simplifying the general proof of renormalisability of gauge field theories. (16) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Dyson-Schwinger Equations
Well suited to Relativistic Quantum Field Theory Simplest level: Generating Tool for Perturbation Theory Materially Reduces Model-Dependence 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? (17) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Dyson-Schwinger Equations
Well suited to Relativistic Quantum Field Theory Simplest level: Generating Tool for Perturbation Theory Materially Reduces Model-Dependence 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? In doing this, arrive at understanding of long- range behaviour of strong running-coupling 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 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Mass from Nothing?! Perturbation Theory
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 nonperturbatively impossible in QED. (18) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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 nonperturbatively impossible in QED. Dressed-quark propagator: Weak coupling expansion of gap equation yields every diagram in perturbation theory In perturbation theory: Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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 nonperturbatively impossible in QED. 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 Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Dynamical (Spontaneous) Chiral Symmetry Breaking
The 2008 Nobel Prize in Physics was divided, one half awarded to Yoichiro Nambu "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics" (21a) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Mass from Nothing?! Nonperturbative DSEs
Gap equation is a nonlinear integral equation Modern computers enable it to be solved, self-consistently, with ease In the last ten years, we have learnt a great deal about the nature of its kernel What do the self-consistent, nonperturbative solutions tell us? (19) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Frontiers of Nuclear Science: Theoretical Advances
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. (20) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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. Hint of lattice-QCD support for DSE prediction of violation of reflection positivity Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

12GeV The Future of JLab 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, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Dichotomy of the pion Building on the concepts and theory that produces the features that have been described, one can derive numerous exact results in QCD. (21) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

P. Maris, C.D. Roberts & P.C. Tandy nucl-th/9707003
Dichotomy of the pion Building on the concepts and theory that produces the features that have been described, one can derive numerous exact results in QCD. One of them explains the peculiar nature of the pion’s mass; i.e., it’s relationship to the Lagrangian current-quark mass m(ς): (21) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Dichotomy of the pion What are the constants of
P. Maris, C.D. Roberts & P.C. Tandy nucl-th/ Dichotomy of the pion Building on the concepts and theory that produces the features that have been described, one can derive numerous exact results in QCD. One of them explains the peculiar nature of the pion’s mass; i.e., it’s relationship to the Lagrangian current-quark mass m(ς): This is the promised, peculiar, non-quantum-mechanical relationship. What are the constants of proportionality, physically? (21) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Gell-Mann – Oakes – Renner Relation (1968)

Pion’s leptonic decay constant, mass-dimensioned observable which describes rate of process π+→μ+ν Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Pion’s leptonic decay constant, mass-dimensioned observable which describes rate of process π+→μ+ν Vacuum quark condensate (22) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Pion’s leptonic decay constant, mass-dimensioned observable which describes rate of process π+→μ+ν Vacuum quark condensate With the GMOR, without the authors’ intention, began the story of vacuum condensates Through the intervening years it became commonplace to believe that condensates are “REAL”; Namely, spacetime-independent mass-dimensioned vacuum expectation values, which have measurable consequences. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Universal “Truths” Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities (23) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Universal “Truths” Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities Wikipedia: ( “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.” (23) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Universal Misapprehensions
Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities Then they couple to gravity in general relativity and make an enormous contribution to the cosmological constant Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities Then they couple to gravity in general relativity and make an enormous contribution to the cosmological constant Experimentally, the answer is Ωcosm. const. = 0.76 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities Then they couple to gravity in general relativity and make an enormous contribution to the cosmological constant Experimentally, the answer is Ωcosm. const. = 0.76 This appalling mismatch is a bit of a problem. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Paradigm shift: In-Hadron Condensates
B Resolution Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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. Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) (24) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

B Resolution Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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) QCD Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

B Resolution Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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 fπ and ρπ Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

B Resolution Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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 fπ and ρπ And Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

B Resolution Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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 fπ and ρπ And Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) Chiral limit Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

“Void that is truly empty solves dark energy puzzle” Rachel Courtland, New Scientist 4th Sept. 2010 “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.” Cosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1045 Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Nature of the Pion: QCD’s Goldstone Mode

Nature of the Pion: QCD’s Goldstone Mode
2 → many or infinitely many Nature and number of constituents depends on the wavelength of the probe Constituent- quarks are replaced by the dressed-quarks and –gluons of QCD Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Charting the interaction between light-quarks
We’ve covered Dynamical Chiral Symmetry Breaking in detail. It’s the origin of 98% of all the visible matter in the Universe What about confinement, the other and probably most fundamental of the emergent phenomena? (26) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Confinement can be related to the analytic properties of QCD's Schwinger functions. Question of light-quark confinement can be translated into the challenge of charting the infrared behavior of QCD's universal β-function This function may depend on the scheme chosen to renormalise the quantum field theory but it is unique within a given scheme. Of course, the behaviour of the β-function on the perturbative domain is well known. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

This is a well-posed problem whose solution is an elemental goal of modern hadron physics. The answer provides QCD’s running coupling. Confinement can be related to the analytic properties of QCD's Schwinger functions. Question of light-quark confinement can be translated into the challenge of charting the infrared behavior of QCD's universal β-function This function may depend on the scheme chosen to renormalise the quantum field theory but it is unique within a given scheme. Of course, the behaviour of the β-function on the perturbative domain is well known. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking. DSEs connect β-function to experimental observables. Hence, comparison between computations and observations of Hadron mass spectrum Elastic and transition form factors can be used to chart β-function’s long-range behaviour. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking. DSEs connect β-function to experimental observables. Hence, comparison between computations and observations of Hadron mass spectrum Elastic and transition form factors can be used to chart β-function’s long-range behaviour. Extant studies of mesons show that the properties of hadron excited states are a great deal more sensitive to the long-range behaviour of the β-function than those of the ground states. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking. DSEs connect β-function to experimental observables. Hence, comparison between computations and observations can be used to chart β-function’s long-range behaviour. To realise this goal, a nonperturbative symmetry-preserving DSE truncation is necessary: Steady quantitative progress is being made with a scheme that is systematically improvable (Bender, Roberts, von Smekal – nucl-th/ ) Leading-order is called the rainbow-ladder truncation. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Can’t walk beyond the rainbow, but must leap! Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking. DSEs connect β-function to experimental observables. Hence, comparison between computations and observations can be used to chart β-function’s long-range behaviour. To realise this goal, a nonperturbative symmetry-preserving DSE truncation is necessary: On the other hand, at significant qualitative advances are possible with symmetry-preserving kernel Ansätze that express important additional nonperturbative effects – M(p2) – difficult/impossible to capture in any finite sum of contributions. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Gap Equation General Form

Dμν(k) – dressed-gluon propagator Γν(q,p) – dressed-quark-gluon vertex Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Bethe-Salpeter Equation Bound-State DSE
K(q,k;P) – fully amputated, two-particle irreducible, quark-antiquark scattering kernel Textbook material. Compact. Visually appealing. Correct (28) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Bethe-Salpeter Equation Bound-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. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Bethe-Salpeter Equation General Form
Lei Chang and C.D. Roberts [nucl-th] Phys. Rev. Lett. 103 (2009) 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) (29) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Ward-Takahashi Identity Bethe-Salpeter Kernel
Lei Chang and C.D. Roberts [nucl-th] Phys. Rev. Lett. 103 (2009) iγ5 iγ5 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 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Ward-Takahashi Identity Bethe-Salpeter Kernel
Lei Chang and C.D. Roberts [nucl-th] Phys. Rev. Lett. 103 (2009) iγ5 iγ5 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 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Dressed-quark anomalous magnetic moments
Schwinger’s result for QED: (30) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Schwinger’s result for QED: pQCD: two diagrams (a) is QED-like (b) is only possible in QCD – involves 3-gluon vertex Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Interaction term that describes magnetic-moment coupling to gauge field Straightforward to show that it mixes left ↔ right Thus, explicitly violates chiral symmetry (31) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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’s e.m. current γμF1 does cannot mix with σμνqνF2 No Gordon Identity Hence massless fermions cannot not possess a measurable chromo- or electro-magnetic moment Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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’s e.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? Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Lei Chang, Yu-Xin Liu and Craig D. Roberts arXiv: [nucl-th] Dressed-quark anomalous magnetic moments DCSB Three strongly-dressed and essentially- nonperturbative contributions to dressed-quark-gluon vertex: (32) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Lei Chang, Yu-Xin Liu and Craig D. Roberts arXiv: [nucl-th] Dressed-quark anomalous magnetic moments DCSB Three strongly-dressed and essentially- nonperturbative contributions to dressed-quark-gluon vertex: Ball-Chiu term Vanishes if no DCSB Appearance driven by STI Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Lei Chang, Yu-Xin Liu and Craig D. Roberts arXiv: [nucl-th] Dressed-quark anomalous magnetic moments DCSB Three strongly-dressed and essentially- nonperturbative contributions to dressed-quark-gluon vertex: 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, Kizilersu et al. hep-ph/ Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Lei Chang, Yu-Xin Liu and Craig D. Roberts arXiv: [nucl-th] Dressed-quark anomalous magnetic moments DCSB Three strongly-dressed and essentially- nonperturbative contributions to dressed-quark-gluon vertex: 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, Kizilersu et al. hep-ph/ Role and importance is Novel discovery Essential to recover pQCD Constructive interference with Γ5 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Lei Chang, Yu-Xin Liu and Craig D. Roberts arXiv: [nucl-th] Dressed-quark anomalous magnetic moments 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 (33) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Lei Chang, Yu-Xin Liu and Craig D. Roberts arXiv: [nucl-th] Dressed-quark anomalous magnetic moments 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 AEM is opposite in sign but of roughly equal magnitude as ACM Potentially important for transition form factors, etc. Muon g-2 ? ME κACM κAEM Full vertex 0.44 -0.22 0.45 Rainbow-ladder 0.35 0.048 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Dressed Vertex & Meson Spectrum
Experiment Rainbow-ladder One-loop corrected Ball-Chiu Full vertex a1 1230 ρ 770 Mass splitting 455 Splitting known experimentally for more than 35 years Hitherto, no explanation (34) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Experiment Rainbow-ladder One-loop corrected Ball-Chiu Full vertex a1 1230 759 885 ρ 770 644 764 Mass splitting 455 115 121 Splitting known experimentally for more than 35 years Hitherto, no explanation Systematic symmetry-preserving, Poincaré-covariant DSE truncation scheme of nucl-th/ Never better than ∼ ⅟₄ of splitting Constructing kernel skeleton-diagram-by-diagram, DCSB cannot be faithfully expressed: Full impact of M(p2) cannot be realised! Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Experiment Rainbow-ladder One-loop corrected Ball-Chiu Full vertex a1 1230 759 885 1066 ρ 770 644 764 924 Mass splitting 455 115 121 142 Fully consistent treatment of Ball-Chiu vertex Retain λ3 – term but ignore Γ4 & Γ5 Some effects of DCSB built into vertex & Bethe-Salpeter kernel Big impact on σ – π complex But, clearly, not the complete answer. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Experiment Rainbow-ladder One-loop corrected Ball-Chiu Full vertex a1 1230 759 885 1066 ρ 770 644 764 924 745 Mass splitting 455 115 121 142 485 Fully consistent treatment of Ball-Chiu vertex Retain λ3 – term but ignore Γ4 & Γ5 Some effects of DCSB built into vertex & Bethe-Salpeter kernel Big impact on σ – π complex But, clearly, not the complete answer. Fully-consistent treatment of complete vertex Ansatz Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Experiment Rainbow-ladder One-loop corrected Ball-Chiu Full vertex a1 1230 759 885 1066 ρ 770 644 764 924 745 Mass splitting 455 115 121 142 485 Fully-consistent treatment of complete vertex Ansatz Subtle interplay between competing effects, which can only now be explicated Promise of first reliable prediction of light-quark hadron spectrum, including the so-called hybrid and exotic states. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Pion’s Goldberger -Treiman relation
Maris, Roberts and Tandy nucl-th/ Pion’s Goldberger -Treiman relation Pion’s Bethe-Salpeter amplitude Dressed-quark propagator (35) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Maris, Roberts and Tandy nucl-th/ Pion’s Goldberger -Treiman relation Pion’s Bethe-Salpeter amplitude Dressed-quark propagator Axial-vector Ward-Takahashi identity entails Exact in Chiral QCD Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Maris, Roberts and Tandy nucl-th/ Pion’s Goldberger -Treiman relation Pion’s Bethe-Salpeter amplitude Dressed-quark propagator Axial-vector Ward-Takahashi identity entails Pseudovector components necessarily nonzero. Cannot be ignored! Exact in Chiral QCD Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Pion’s GT relation Implications for observables?
Maris and Roberts nucl-th/ Pion’s GT relation Implications for observables? (36) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Pion’s GT relation Implications for observables?
Maris and Roberts nucl-th/ Pion’s GT relation Implications for observables? Pseudovector components dominate in ultraviolet: (Q/2)2 = 2 GeV2 pQCD point for M(p2) → pQCD at Q2 = 8GeV2 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Pion’s GT relation Pion’s Bethe-Salpeter amplitude
Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s GT relation Pion’s Bethe-Salpeter amplitude Dressed-quark propagator (37) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Pion’s GT relation Contact interaction
Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s GT relation Contact interaction Pion’s Bethe-Salpeter amplitude Dressed-quark propagator Bethe-Salpeter amplitude can’t depend on relative momentum; propagator can’t be momentum-dependent MQ Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s GT relation Contact interaction Pion’s Bethe-Salpeter amplitude Dressed-quark propagator Bethe-Salpeter amplitude can’t depend on relative momentum; propagator can’t be momentum-dependent Solved gap and Bethe-Salpeter equations P2=0: MQ=0.4GeV, Eπ=0.098, Fπ=0.5MQ MQ Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s GT relation Contact interaction Pion’s Bethe-Salpeter amplitude Dressed-quark propagator Bethe-Salpeter amplitude can’t depend on relative momentum; propagator can’t be momentum-dependent Solved gap and Bethe-Salpeter equations P2=0: MQ=0.4GeV, Eπ=0.098, Fπ=0.5MQ MQ Nonzero and significant Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s GT relation Contact interaction Pion’s Bethe-Salpeter amplitude Dressed-quark propagator Asymptotic form of Fπ(Q2) Eπ2(P)→ Fπem(Q2) = MQ2/Q2 MQ For 20+ years it was imagined that contact-interaction produced a result that’s indistinguishable From pQCD counting rule Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s GT relation Contact interaction Pion’s Bethe-Salpeter amplitude Dressed-quark propagator Asymptotic form of Fπ(Q2) Eπ2(P)→ Fπem(Q2) = MQ2/Q2 Eπ(P) Fπ(P) – cross-term → Fπem(Q2) = (Q2/MQ2) * [Eπ(P)/Fπ(P)] * Eπ2(P)-term = CONSTANT! MQ For 20+ years it was imagined that contact-interaction produced a result that’s indistinguishable From pQCD counting rule Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Pion’s Electromagnetic Form Factor
Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s Electromagnetic Form Factor QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2 cf. contact-interaction: produces M(p2)=constant (38) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s Electromagnetic Form Factor QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2 cf. contact-interaction: produces M(p2)=constant Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Guttierez, Bashir, Cloët, Roberts arXiv: [nucl-th] Pion’s Electromagnetic Form Factor QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2 cf. contact-interaction: produces M(p2)=constant Single mass parameter in both studies Same predictions for Q2=0 observables Disagreement >20% for Q2>MQ2 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

BaBar Anomaly γ* γ → π0 QCD-based DSE prediction: D(x-y) =
H.L.L. Roberts, C.D. Roberts, Bashir, Guttierez, Tandy arXiv: [nucl-th] BaBar Anomaly γ* γ → π0 QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2 cf. contact-interaction: produces M(p2)=constant (39) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

H.L.L. Roberts, C.D. Roberts, Bashir, Guttierez, Tandy arXiv: [nucl-th] BaBar Anomaly γ* γ → π0 QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2 cf. contact-interaction: produces M(p2)=constant pQCD Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

H.L.L. Roberts, C.D. Roberts, Bashir, Guttierez, Tandy arXiv: [nucl-th] BaBar Anomaly γ* γ → π0 QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2 cf. contact-interaction: produces M(p2)=constant No fully-self-consistent treatment of the pion can reproduce the BaBar data. All produce monotonically- increasing concave functions. BaBar data not a true measure of γ* γ → π0 Likely source of error is misidentification of π0 π0 events where 2nd π0 isn’t seen. pQCD Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Unifying Baryons and Mesons
M(p2) – effects have enormous impact on meson properties. Must be included in description and prediction of baryon properties. (40) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

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. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

R.T. Cahill et al., Austral. J. Phys. 42 (1989) Unifying Baryons and Mesons 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 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Faddeev Equation Linear, Homogeneous Matrix equation
R.T. Cahill et al., Austral. J. Phys. 42 (1989) Faddeev Equation quark Linear, Homogeneous Matrix equation diquark (41) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

R.T. Cahill et al., Austral. J. Phys. 42 (1989) Faddeev Equation quark exchange ensures Pauli statistics quark Linear, Homogeneous Matrix equation Yields wave function (Poincaré Covariant Faddeev Amplitude) that describes quark-diquark relative motion within the nucleon diquark Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

R.T. Cahill et al., Austral. J. Phys. 42 (1989) Faddeev Equation quark exchange ensures Pauli statistics quark Linear, Homogeneous Matrix equation Yields 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 correlations diquark Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Spectrum of some known u- & d-quark baryons
H.L.L. Roberts, L. Chang and C.D. Roberts arXiv: [nucl-th] H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts arXiv: [nucl-th] Spectrum of some known u- & d-quark baryons Mesons & Diquarks m0+ m1+ m0- m1- mπ mρ mσ ma1 0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23 (42) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

H.L.L. Roberts, L. Chang and C.D. Roberts arXiv: [nucl-th] H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts arXiv: [nucl-th] Spectrum of some known u- & d-quark baryons Mesons & Diquarks Cahill, Roberts, Praschifka: Phys.Rev. D36 (1987) 2804 Proof of mass ordering: diquark-mJ+ > meson-mJ- m0+ m1+ m0- m1- mπ mρ mσ ma1 0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

H.L.L. Roberts, L. Chang and C.D. Roberts arXiv: [nucl-th] H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts arXiv: [nucl-th] Spectrum of some known u- & d-quark baryons Mesons & Diquarks Cahill, Roberts, Praschifka: Phys.Rev. D36 (1987) 2804 Proof of mass ordering: diquark-mJ+ > meson-mJ- m0+ m1+ m0- m1- mπ mρ mσ ma1 0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23 Baryons: ground-states and 1st radial exciations mN mN* mN(⅟₂) mN*(⅟₂-) mΔ mΔ* mΔ(3⁄₂-) mΔ*(3⁄₂-) DSE 1.05 1.73 1.86 2.09 1.33 1.85 1.98 2.16 EBAC 1.76 1.80 1.39 Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

H.L.L. Roberts, L. Chang and C.D. Roberts arXiv: [nucl-th] H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts arXiv: [nucl-th] Spectrum of some known u- & d-quark baryons Mesons & Diquarks Cahill, Roberts, Praschifka: Phys.Rev. D36 (1987) 2804 Proof of mass ordering: diquark-mJ+ > meson-mJ- m0+ m1+ m0- m1- mπ mρ mσ ma1 0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23 Baryons: ground-states and 1st radial exciations mN mN* mN(⅟₂) mN*(⅟₂-) mΔ mΔ* mΔ(3⁄₂-) mΔ*(3⁄₂-) DSE 1.05 1.73 1.86 2.09 1.33 1.85 1.98 2.16 EBAC 1.76 1.80 1.39 mean-|relative-error| = 2%-Agreement DSE dressed-quark-core masses cf. Excited Baryon Analysis Center (JLab) bare masses is significant ’cause no attempt was made to ensure this. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

H.L.L. Roberts, L. Chang and C.D. Roberts arXiv: [nucl-th] H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts arXiv: [nucl-th] Spectrum of some known u- & d-quark baryons Mesons & Diquarks Cahill, Roberts, Praschifka: Phys.Rev. D36 (1987) 2804 Proof of mass ordering: diquark-mJ+ > meson-mJ- m0+ m1+ m0- m1- mπ mρ mσ ma1 0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23 1st radial Excitation of N(1535)? Baryons: ground-states and 1st radial exciations mN mN* mN(⅟₂) mN*(⅟₂-) mΔ mΔ* mΔ(3⁄₂-) mΔ*(3⁄₂-) DSE 1.05 1.73 1.86 2.09 1.33 1.85 1.98 2.16 EBAC 1.76 1.80 1.39 mean-|relative-error| = 2%-Agreement DSE dressed-quark-core masses cf. Excited Baryon Analysis Center (JLab) bare masses is significant ’cause no attempt was made to ensure this. Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Nucleon Elastic Form Factors
I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th] Nucleon Elastic Form Factors Photon-baryon vertex Oettel, Pichowsky and von Smekal, nucl-th/ Form factors reveal how the observable properties of the nucleon – charge and magnetisation – are shared amongst its constituents (43) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Nucleon Elastic Form Factors
I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th] Nucleon Elastic Form Factors Photon-baryon vertex Oettel, Pichowsky and von Smekal, 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, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

S. Riordan et al., arXiv:1008.1738 [nucl-ex]
I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th] New JLab data: S. Riordan et al., arXiv: [nucl-ex] (44) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

DSE-prediction This evolution is very sensitive to momentum-dependence
I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th] New JLab data: S. Riordan et al., arXiv: [nucl-ex] DSE-prediction This evolution is very sensitive to momentum-dependence of dressed-quark propagator Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th] New JLab data: S. Riordan et al., arXiv: [nucl-ex] (45) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th] New JLab data: S. Riordan et al., arXiv: [nucl-ex] Brooks, Bodek, Budd, Arrington fit to data: hep-ex/ Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Location of zero DSE-prediction measures relative strength of scalar
I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th] New JLab data: S. Riordan et al., arXiv: [nucl-ex] DSE-prediction Location of zero measures relative strength of scalar and axial-vector qq-correlations Brooks, Bodek, Budd, Arrington fit to data: hep-ex/ Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Neutron Structure Function at high x
I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th] Neutron Structure Function at high x SU(6) symmetry Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments Reviews: S. Brodsky et al. NP B441 (1995) W. Melnitchouk & A.W.Thomas PL B377 (1996) 11 N. Isgur, PRD 59 (1999) R.J. Holt & C.D. Roberts RMP (2010) pQCD DSE: 0+ & 1+ qq 0+ qq only (46) Distribution of neutron’s momentum amongst quarks on the valence-quark domain Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Epilogue Dynamical chiral symmetry breaking (DCSB) – mass from nothing for 98% of visible matter – is a reality Expressed in M(p2), with observable signals in experiment Confinement is almost Certainly the origin of DCSB (47) Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Epilogue Dynamical chiral symmetry breaking (DCSB) – mass from nothing for 98% of visible matter – is a reality Expressed in M(p2), with observable signals in experiment Poincaré covariance Crucial in description of contemporary data Confinement is almost Certainly the origin of DCSB Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Epilogue Dynamical chiral symmetry breaking (DCSB) – mass from nothing for 98% of visible matter – is a reality Expressed in M(p2), with observable signals in experiment Poincaré covariance Crucial in description of contemporary data Fully-self-consistent treatment of an interaction Essential if experimental data is truly to be understood. Confinement is almost Certainly the origin of DCSB Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Epilogue Dynamical chiral symmetry breaking (DCSB) – mass from nothing for 98% of visible matter – is a reality Expressed in M(p2), with observable signals in experiment Poincaré covariance Crucial in description of contemporary data Fully-self-consistent treatment of an interaction Essential if experimental data is truly to be understood. Dyson-Schwinger equations: single framework, with IR model-input turned to advantage, “almost unique in providing unambiguous path from a defined interaction → Confinement & DCSB → Masses → radii → form factors → distribution functions → etc.” Confinement is almost Certainly the origin of DCSB McLerran & Pisarski arXiv: [hep-ph] Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It IIT Physics Colloquium: 7 Oct 2010

Quantum Chromodynamics: The Origin of Mass as We Know it

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Quantum Chromodynamics: The Origin of Mass as We Know it

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