exposing the dressed quark’s masschallenge: understand relationship between parton properties on...
TRANSCRIPT
First Contents Back Conclusion
DCSB & Confinementt
0.5 1. 1.5 2.p
0.1
0.2
0.3
0.4
0.5MHpL
Dressed-quark Mass Function
Exposing the Dressed Quark’s mass
Craig D. [email protected]
Physics Division & School of Physics
Argonne National Laboratory Peking University
http://www.phy.anl.gov/theory/staff/cdr.htmlCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 1/28
First Contents Back Conclusion
Universal Truths
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal Truths
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal TruthsSpectrum of excited states, and 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.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal TruthsSpectrum of excited states, and 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.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal TruthsSpectrum of excited states, and 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 irrelevant to light-quarks.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal TruthsSpectrum of excited states, and 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 irrelevant to light-quarks.
Running of quark mass entails that calculations at even
modest Q2 require a Poincaré-covariant approach.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal TruthsSpectrum of excited states, and 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 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.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal TruthsSpectrum of excited states, and 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 irrelevant to light-quarks.
Challenge: understand relationship between parton properties
on the light-front and rest frame structure of hadrons.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal TruthsSpectrum of excited states, and 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 irrelevant to light-quarks.
Challenge: understand relationship between parton properties
on the light-front and rest frame structure of hadrons. Problem,
e.g., DCSB - an established keystone of low-energy QCD and
the origin of constituent-quark masses - has not yet been
realised in the light-front formulation.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
Universal TruthsSpectrum of excited states, and 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 irrelevant to light-quarks.
Challenge: understand relationship between parton properties
on the light-front and rest frame structure of hadrons. Problem,
e.g., DCSB - an established keystone of low-energy QCD and
the origin of constituent-quark masses - has not yet been
realised in the light-front formulation. Resolution – coherent
contribution from countable infinity of higher Fock-state
components. (Brodsky, Roberts, Shrock, Tandy – in progress.)Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 2/28
First Contents Back Conclusion
QCD’s Challenges
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 3/28
First Contents Back Conclusion
QCD’s Challenges
Quark and Gluon Confinement
No matter how hard one strikes the proton, one
cannot liberate an individual quark or gluon
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 3/28
First Contents Back Conclusion
QCD’s Challenges
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=−
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 3/28
First Contents Back Conclusion
QCD’s Challenges
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=−
Neither of these phenomena is apparent in QCD’s
Lagrangian yet they are the dominant determining
characteristics of real-world QCD.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 3/28
First Contents Back Conclusion
QCD’s ChallengesUnderstand 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=−
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 rulesCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 3/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 4/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
Confinement can be related to the analytic properties of
QCD’s Schwinger functions
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 4/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
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
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 4/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
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.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 4/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
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 – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 4/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
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.
This is a well-posed problem whose solution is an elemental
goal of modern hadron physics.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 4/28
First Contents Back Conclusion
What is the light-quarkLong-Range Potential?
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 5/28
First Contents Back Conclusion
What is the light-quarkLong-Range Potential?
Potential between static (infinitely heavy) quarksmeasured in simulations of lattice-QCD is not relatedin any known way to the light-quark interaction.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 5/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
Through QCD’s Dyson-Schwinger equations (DSEs) the
pointwise behaviour of the β-function determines pattern of
chiral symmetry breaking
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 6/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
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, e.g.,
hadron mass spectrum;
elastic and transition form factors
can be used to chart β-function’s long-range behaviour
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 6/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
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, e.g.,
hadron mass spectrum;
elastic and transition form factors
can be used to chart β-function’s long-range behaviour
E.g.: Extant studies of mesons show that the properties of
hadron excited states are a great deal more sensitive to the
long-range behaviour of β-function than those of the ground
stateCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 6/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
Through 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
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 7/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
Through 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
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 7/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
Through 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
(See nucl-th/9602012 and references thereto)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 7/28
First Contents Back Conclusion
Charting the Interactionbetween light-quarks
Through 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 other hand, at present significant qualitative
advances possible with symmetry-preserving kernel
Ansätze that express important additional
nonperturbative effects – M(p2) – difficult/impossible to
capture in any finite sum of contributionsCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 7/28
First Contents Back Conclusion
Gap EquationGeneral Form
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 8/28
First Contents Back Conclusion
Gap EquationGeneral Form
Σ=
D
γΓS
Sf (p)−1 = Z2 (iγ · p + mbmf ) + Σf (p) ,
Σf (p) = Z1
∫ Λ
qg2Dµν(p − q)
λa
2γµSf (q)
λa
2Γf
ν (q, p),
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 8/28
First Contents Back Conclusion
Gap EquationGeneral Form
Σ=
D
γΓS
Sf (p)−1 = Z2 (iγ · p + mbmf ) + Σf (p) ,
Σf (p) = Z1
∫ Λ
qg2Dµν(p − q)
λa
2γµSf (q)
λa
2Γf
ν (q, p),
Z1,2(ζ2,Λ2) are respectively the vertex and quark wave
function renormalisation constants, with ζ the
renormalisation point
mbm(Λ) is the Lagrangian current-quark bare mass
Dµν(k) is the dressed-gluon propagator
Γfν (q, p) is the dressed-quark-gluon vertex
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 8/28
First Contents Back Conclusion
Gap EquationGeneral Form
Σ=
D
γΓS
Sf (p)−1 = Z2 (iγ · p + mbmf ) + Σf (p) ,
Σf (p) = Z1
∫ Λ
qg2Dµν(p − q)
λa
2γµSf (q)
λa
2Γf
ν (q, p),
Z1,2(ζ2,Λ2) are respectively the vertex and quark wave
function renormalisation constants, with ζ the
renormalisation point
mbm(Λ) is the Lagrangian current-quark bare mass
Dµν(k) is the dressed-gluon propagator
Γfν (q, p) is the dressed-quark-gluon vertex
Suppose one has in-hand the exact form of Γfν (q, p)
What is the associatedSymmetry-preserving Bethe-Salpeter Kernel?
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 8/28
First Contents Back Conclusion
Bound-state DSE
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 9/28
First Contents Back Conclusion
Bound-state DSEBethe-Salpeter Equation
Standard form, familiar from textbooks
[
Γjπ(k; P )
]
tu=
∫
Λ
q
[S(q + P/2)Γjπ(q; P )S(q − P/2)]sr Krs
tu (q, k; P )
K(q, k; P ): Fully-amputated, 2-particle-irreducible,quark-antiquark scattering kernel
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 9/28
First Contents Back Conclusion
Bound-state DSEBethe-Salpeter Equation
Standard form, familiar from textbooks
[
Γjπ(k; P )
]
tu=
∫
Λ
q
[S(q + P/2)Γjπ(q; P )S(q − P/2)]sr Krs
tu (q, k; P )
K(q, k; P ): Fully-amputated, 2-particle-irreducible,quark-antiquark scattering kernel
Compact. Visually appealing. Correct.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 9/28
First Contents Back Conclusion
Bound-state DSEBethe-Salpeter Equation
Standard form, familiar from textbooks
[
Γjπ(k; P )
]
tu=
∫
Λ
q
[S(q + P/2)Γjπ(q; P )S(q − P/2)]sr Krs
tu (q, k; P )
K(q, k; P ): Fully-amputated, 2-particle-irreducible,quark-antiquark scattering kernel
Compact. Visually appealing. Correct.
Blocked progress for more than 60 years.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 9/28
First Contents Back Conclusion
Bethe-Salpeter EquationGeneral FormL. Chang and C. D. Roberts
0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 10/28
First Contents Back Conclusion
Bethe-Salpeter EquationGeneral FormL. Chang and C. D. Roberts
0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601
Equivalent exact form:
Γfg5µ(k;P ) = Z2γ5γµ
−
∫
qg2Dαβ(k − q)
λa
2γαSf (q+)Γfg
5µ(q;P )Sg(q−)λa
2Γg
β(q−, k−)
+
∫
qg2Dαβ(k − q)
λa
2γαSf (q+)
λa
2Λfg
5µβ(k, q;P ),
(Poincaré covariance, hence q± = q ± P/2, etc., without loss of generality.)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 10/28
First Contents Back Conclusion
Bethe-Salpeter EquationGeneral FormL. Chang and C. D. Roberts
0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601
Equivalent exact form:
Γfg5µ(k;P ) = Z2γ5γµ
−
∫
qg2Dαβ(k − q)
λa
2γαSf (q+)Γfg
5µ(q;P )Sg(q−)λa
2Γg
β(q−, k−)
+
∫
qg2Dαβ(k − q)
λa
2γαSf (q+)
λa
2Λfg
5µβ(k, q;P ),
(Poincaré covariance, hence q± = q ± P/2, etc., without loss of generality.)
In this form . . . Λfg5µβ
is completely defined via the dressed-quark self-energy
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 10/28
First Contents Back Conclusion
Bethe-Salpeter KernelL. Chang and C. D. Roberts
0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601
Bethe-Salpeter equation introduced in 1951
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 11/28
First Contents Back Conclusion
Bethe-Salpeter Kernel60 year problemL. Chang and C. D. Roberts
0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601
Bethe-Salpeter equation introduced in 1951
Newly-derived Ward-Takahashi identity
PµΛfg5µβ(k, q;P ) = Γf
β(q+, k+) iγ5 + iγ5 Γgβ(q−, k−)
− i[mf (ζ) + mg(ζ)]Λfg5β(k, q;P ),
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 11/28
First Contents Back Conclusion
Bethe-Salpeter Kernel60 year problemL. Chang and C. D. Roberts
0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601
Bethe-Salpeter equation introduced in 1951
Newly-derived Ward-Takahashi identity
PµΛfg5µβ(k, q;P ) = Γf
β(q+, k+) iγ5 + iγ5 Γgβ(q−, k−)
− i[mf (ζ) + mg(ζ)]Λfg5β(k, q;P ),
For first time: can construct Ansatz for Bethe-Salpeter
kernel consistent with any reasonable quark-gluon vertex
Consistent means - all symmetries preserved!Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 11/28
First Contents Back Conclusion
Bethe-Salpeter Kernel60 year problemL. Chang and C. D. Roberts
0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601
Bethe-Salpeter equation introduced in 1951
Newly-derived Ward-Takahashi identity
PµΛfg5µβ(k, q;P ) = Γf
β(q+, k+) iγ5 + iγ5 Γgβ(q−, k−)
− i[mf (ζ) + mg(ζ)]Λfg5β(k, q;P ),
For first time: can construct Ansatz for Bethe-Salpeter
kernel consistent with any reasonable quark-gluon vertex
Procedure & results to expect . . .see arXiv:1003.5006 [nucl-th]
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 11/28
First Contents Back Conclusion
Mass Splittinga1 – ρ
exp.
mass a1 1230
mass ρ 775
mass-
splitting 455
Splitting known experimentally for more than 35 years.
Hitherto, no explanation.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 12/28
First Contents Back Conclusion
Mass Splittinga1 – ρ
exp. rainbow- one-loop
ladder
mass a1 1230 759 885
mass ρ 775 644 764
mass-
splitting 455 115 121
Systematic, symmetry-preserving, Poincaré-covariant DSE
truncation scheme of nucl-th/9602012.
Never better than ∼ 14
of splitting.
Constructing kernel skeleton-diagram-by-diagram, DCSB
cannot be faithfully expressed: M(p2) is absent!
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 12/28
First Contents Back Conclusion
Mass Splittinga1 – ρ
exp. rainbow- one-loop Ball-Chiu
ladder consistent
mass a1 1230 759 885 1066
mass ρ 775 644 764 924
mass-
splitting 455 115 121 142
New nonperturbative, symmetry-preserving
Poincaré-covariant Bethe-Salpeter equation formulation of
arXiv:0903.5461 [nucl-th]
Ball-Chiu Ansatz for quark-gluon vertex
ΓBCµ (k, p) = . . . + (k + p)µ
B(k)−B(p)k2−p2
Some effects of DCSB built into vertex
Explains π – σ splitting but not this problemCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 12/28
First Contents Back Conclusion
Mass Splittinga1 – ρChang & Roberts arXiv:1003.5006 [nucl-th]
exp. rainbow- one-loop Ball-Chiu Ball-Chiu plus
ladder consistent anom. cm mom.
mass a1 1230 759 885 1066 1230
mass ρ 775 644 764 924 745
mass-
splitting 455 115 121 142 485
New nonperturbative, symmetry-preserving
Poincaré-covariant Bethe-Salpeter equation formulation of
arXiv:0903.5461 [nucl-th]
Ball-Chiu augmented by quark anomalous chromomagnetic
moment term: Γµ(k, p) = ΓBCµ + σµν(k − p)ν
B(k)−B(p)k2−p2
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 12/28
First Contents Back Conclusion
Mass Splittinga1 – ρChang & Roberts arXiv:1003.5006 [nucl-th]
exp. rainbow- one-loop Ball-Chiu Ball-Chiu plus
ladder consistent anom. cm mom.
mass a1 1230 759 885 1066 1230
mass ρ 775 644 764 924 745
mass-
splitting 455 115 121 142 485
New nonperturbative, symmetry-preserving
Poincaré-covariant Bethe-Salpeter equation formulation of
arXiv:0903.5461 [nucl-th]
DCSB is the answer. Subtle interplay between competing
effects, which can only now be explicated
Promise of first reliable prediction of light-quark meson
spectrum, including the so-called hybrid and exotic states.Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 12/28
First Contents Back Conclusion
Frontiers of Nuclear Science:A Long Range Plan (2007)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 13/28
First Contents Back Conclusion
Frontiers of Nuclear Science:Theoretical Advances
Σ=
D
γΓS
Gap Equation
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 13/28
First Contents Back Conclusion
Frontiers of Nuclear Science:Theoretical Advances
Σ=
D
γΓS
Gap Equation
S(p) =Z(p2)
iγ · p + M(p2)
0 1 2 3
p [GeV]
0
0.1
0.2
0.3
0.4
M(p
) [G
eV] m = 0 (Chiral limit)
m = 30 MeVm = 70 MeV
effect of gluon cloudRapid acquisition of mass is
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 13/28
First Contents Back Conclusion
Frontiers of Nuclear Science:Theoretical Advances
S(p) =Z(p2)
iγ · p + M(p2)
0 1 2 3
p [GeV]
0
0.1
0.2
0.3
0.4
M(p
) [G
eV]
m=0 (Chiral limit)30 MeV70 MeV
Lattice QCD confirms DSE prediction of DCSB
Mass from nothing.
In QCD a quark’s effective massdepends on its momentum. Thefunction describing this can becalculated and is depicted here.Numerical simulations of latticeQCD (data, at two different baremasses) have confirmed modelpredictions (solid curves) that thevast bulk of the constituent massof a light quark comes from acloud of gluons that are draggedalong by the quark as itpropagates. In this way, a quarkthat appears to be absolutelymassless at high energies(m = 0, red curve) acquires alarge constituent mass at lowenergies.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 13/28
First Contents Back Conclusion
Frontiers of Nuclear Science:Theoretical Advances
S(p) =Z(p2)
iγ · p + M(p2)
0 1 2 3
p [GeV]
0
0.1
0.2
0.3
0.4
M(p
) [G
eV]
m=0 (Chiral limit)30 MeV70 MeV
for DSE-predictedHint of support in Lattice-QCD results
confinement signal
Mass from nothing.
In QCD a quark’s effective massdepends on its momentum. Thefunction describing this can becalculated and is depicted here.Numerical simulations of latticeQCD (data, at two different baremasses) have confirmed modelpredictions (solid curves) that thevast bulk of the constituent massof a light quark comes from acloud of gluons that are draggedalong by the quark as itpropagates. In this way, a quarkthat appears to be absolutelymassless at high energies(m = 0, red curve) acquires alarge constituent mass at lowenergies.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 13/28
First Contents Back Conclusion
Frontiers of Nuclear Science:Theoretical Advances
S(p) =Z(p2)
iγ · p + M(p2)
0 1 2 3
p [GeV]
0
0.1
0.2
0.3
0.4
M(p
) [G
eV]
m=0 (Chiral limit)30 MeV70 MeV
for DSE-predictedHint of support in Lattice-QCD results
confinement signal
Mass from nothing.
In QCD a quark’s effective massdepends on its momentum. Thefunction describing this can becalculated and is depicted here.Numerical simulations of latticeQCD (data, at two different baremasses) have confirmed modelpredictions (solid curves) that thevast bulk of the constituent massof a light quark comes from acloud of gluons that are draggedalong by the quark as itpropagates. In this way, a quarkthat appears to be absolutelymassless at high energies(m = 0, red curve) acquires alarge constituent mass at lowenergies.
↑ ↑
Scanned by Q2 ∈ [2,9] GeV2 Baryon Elastic and Transition Form FactorsCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 13/28
First Contents Back Conclusion
Goldberger-Treiman for pionMaris, Roberts, Tandynucl-th/9707003
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 14/28
First Contents Back Conclusion
Goldberger-Treiman for pionMaris, Roberts, Tandynucl-th/9707003
• Pseudoscalar Bethe-Salpeter amplitude
Γπj (k;P ) = τπj
γ5
[
iEπ(k;P ) + γ · PF π(k;P )
+ γ · k k · P Gπ(k;P ) + σµν kµPν Hπ(k;P )]
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 14/28
First Contents Back Conclusion
Goldberger-Treiman for pionMaris, Roberts, Tandynucl-th/9707003
• Pseudoscalar Bethe-Salpeter amplitude
Γπj (k;P ) = τπj
γ5
[
iEπ(k;P ) + γ · PF π(k;P )
+ γ · k k · P Gπ(k;P ) + σµν kµPν Hπ(k;P )]
• Dressed-quark Propagator: S(p) =1
iγ · pA(p2) + B(p2)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 14/28
First Contents Back Conclusion
Goldberger-Treiman for pionMaris, Roberts, Tandynucl-th/9707003
• Pseudoscalar Bethe-Salpeter amplitude
Γπj (k;P ) = τπj
γ5
[
iEπ(k;P ) + γ · PF π(k;P )
+ γ · k k · P Gπ(k;P ) + σµν kµPν Hπ(k;P )]
• Dressed-quark Propagator: S(p) =1
iγ · pA(p2) + B(p2)• Axial-vector Ward-Takahashi identity
⇒ fπEπ(k;P = 0) = B(p2)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 14/28
First Contents Back Conclusion
Goldberger-Treiman for pionMaris, Roberts, Tandynucl-th/9707003
• Pseudoscalar Bethe-Salpeter amplitude
Γπj (k;P ) = τπj
γ5
[
iEπ(k;P ) + γ · PF π(k;P )
+ γ · k k · P Gπ(k;P ) + σµν kµPν Hπ(k;P )]
• Dressed-quark Propagator: S(p) =1
iγ · pA(p2) + B(p2)• Axial-vector Ward-Takahashi identity
⇒ fπEπ(k;P = 0) = B(p2)
FR(k; 0) + 2 fπFπ(k; 0) = A(k2)
GR(k; 0) + 2 fπGπ(k; 0) = 2A′(k2)
HR(k; 0) + 2 fπHπ(k; 0) = 0
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 14/28
First Contents Back Conclusion
Goldberger-Treiman for pionMaris, Roberts, Tandynucl-th/9707003
Pseudovectorcomponentsnecessarilynonzero
• Pseudoscalar Bethe-Salpeter amplitude
Γπj (k;P ) = τπj
γ5
[
iEπ(k;P ) + γ · PF π(k;P )
+ γ · k k · P Gπ(k;P ) + σµν kµPν Hπ(k;P )]
• Dressed-quark Propagator: S(p) =1
iγ · pA(p2) + B(p2)• Axial-vector Ward-Takahashi identity
⇒ fπEπ(k;P = 0) = B(p2)
FR(k; 0) + 2 fπFπ(k; 0) = A(k2)
GR(k; 0) + 2 fπGπ(k; 0) = 2A′(k2)
HR(k; 0) + 2 fπHπ(k; 0) = 0
Exact in
Chiral QCD
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 14/28
First Contents Back Conclusion
GT for pion– QCD and F em
π (Q2)Maris, Robertsnucl-th/9804062
What does this mean for observables?
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 15/28
First Contents Back Conclusion
GT for pion– QCD and F em
π (Q2)Maris, Robertsnucl-th/9804062
What does this mean for observables?
0.0 5.0 10.0 15.0q
2 (GeV
2)
0.00
0.10
0.20
0.30
0.40
q2 Fπ(
q2 ) (G
eV2 )
Only Eπ −> 1/Q4
Including Fπ −> 1/Q2
0.19
0.12
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 15/28
First Contents Back Conclusion
GT for pion– QCD and F em
π (Q2)Maris, Robertsnucl-th/9804062
What does this mean for observables?
0.0 5.0 10.0 15.0q
2 (GeV
2)
0.00
0.10
0.20
0.30
0.40
q2 Fπ(
q2 ) (G
eV2 )
Only Eπ −> 1/Q4
Including Fπ −> 1/Q2
0.19
0.12
(
Q
2
)2
= 2GeV2
⇒ Q2 = 8GeV2
Pseudovector components dominate ultraviolet behaviour of
electromagnetic form factorCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 15/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 16/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude can’t depend on relative
momentum
⇒ General Form Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 16/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude can’t depend on relative
momentum
⇒ General Form Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Solve chiral-limit gap and Bethe-Salpeter equations
P 2 = 0 : MQ = 0.40 , Eπ = 0.98 ,Fπ
MQ
= 0.50
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 16/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude can’t depend on relative
momentum
⇒ General Form Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Solve chiral-limit gap and Bethe-Salpeter equations
P 2 = 0 : MQ = 0.40 , Eπ = 0.98 ,Fπ
MQ
= 0.50
Origin of pseudovector component: Eπ drives Fπ
RHS Bethe-Salpeter equation:
γµS(k + P/2)iγ5EπS(k − P/2)γµ
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 16/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude can’t depend on relative
momentum
⇒ General Form Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Solve chiral-limit gap and Bethe-Salpeter equations
P 2 = 0 : MQ = 0.40 , Eπ = 0.98 ,Fπ
MQ
= 0.50
Origin of pseudovector component: Eπ drives Fπ
RHS Bethe-Salpeter equation:
γµS(k + P/2)iγ5EπS(k − P/2)γµ
Has pseudovector component
∼ Eπ[σS(k+)σV (k−) + σS(k−)σV (k+)]
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 16/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude can’t depend on relative
momentum
⇒ General Form Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Solve chiral-limit gap and Bethe-Salpeter equations
P 2 = 0 : MQ = 0.40 , Eπ = 0.98 ,Fπ
MQ
= 0.50
Origin of pseudovector component: Eπ drives Fπ
RHS Bethe-Salpeter equation:
γµS(k + P/2)iγ5EπS(k − P/2)γµ
Hence Fπ on LHS is forced to be nonzero
because Eπ on RHS is nonzero owing to DCSB
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 16/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude: General Form
Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 17/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude: General Form
Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Asymptotic form of electromagnetic pion form factor
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 17/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude: General Form
Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Asymptotic form of electromagnetic pion form factor
E2π-term ⇒ F em
π E(Q2) ∼M2
Q2, photon(Q)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 17/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude: General Form
Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Asymptotic form of electromagnetic pion form factor
E2π-term ⇒ F em
π E(Q2) ∼M2
Q2, photon(Q)
EπFπ-term.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 17/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude: General Form
Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Asymptotic form of electromagnetic pion form factor
E2π-term ⇒ F em
π E(Q2) ∼M2
Q2, photon(Q)
EπFπ-term. Breit Frame:
pion(P = (0, 0, −Q/2, iQ/2))
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 17/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude: General Form
Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Asymptotic form of electromagnetic pion form factor
E2π-term ⇒ F em
π E(Q2) ∼M2
Q2, photon(Q)
EπFπ-term. Breit Frame:
pion(P = (0, 0, −Q/2, iQ/2))
F emπ EF (Q2) ∼ 2 Sγ · (P + Q)FπSγ4SEπ
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 17/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude: General Form
Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Asymptotic form of electromagnetic pion form factor
E2π-term ⇒ F em
π E(Q2) ∼M2
Q2, photon(Q)
EπFπ-term. Breit Frame:
pion(P = (0, 0, −Q/2, iQ/2))
F emπ EF (Q2) ∼ 2 Sγ · (P + Q)FπSγ4SEπ
⇒ F emπ EF (Q2) ∝
Q2
M2Q
Fπ
Eπ
× E2π−term = constant!
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 17/28
First Contents Back Conclusion
GT for pion– Contact Interaction
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
Bethe-Salpeter amplitude: General Form
Γπ(P ) = iγ5Eπ(P ) +1
MQ
γ · PFπ(P )
Asymptotic form of electromagnetic pion form factor
E2π-term ⇒ F em
π E(Q2) ∼M2
Q2, photon(Q)
EπFπ-term. Breit Frame:
pion(P = (0, 0, −Q/2, iQ/2))
F emπ EF (Q2) ∼ 2 Sγ · (P + Q)FπSγ4SEπ
⇒ F emπ EF (Q2) ∝
Q2
M2Q
Fπ
Eπ
× E2π−term = constant!
This behaviour dominates for Q2 & M2Q
Eπ
Fπ
> 0.8 GeV2
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 17/28
First Contents Back Conclusion
Computation : ElasticPion Form Factor
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
DSE prediction: M(p2); i.e., interaction1
|x − y|2
cf. M(p2) = Constant; i.e., interaction δ4(x − y)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 18/28
First Contents Back Conclusion
Computation : ElasticPion Form Factor
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
DSE prediction: M(p2); i.e., interaction1
|x − y|2
cf. M(p2) = Constant; i.e., interaction δ4(x − y)
Single mass-scale parameterin both studies
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 18/28
First Contents Back Conclusion
Computation : ElasticPion Form Factor
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
DSE prediction: M(p2); i.e., interaction1
|x − y|2
cf. M(p2) = Constant; i.e., interaction δ4(x − y)
Single mass-scale parameterin both studies
Same predictions forQ2 = 0 properties
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 18/28
First Contents Back Conclusion
Computation : ElasticPion Form Factor
Guttierez, Bashir, Cloët, Roberts:arXiv:1002.1968 [nucl-th]
DSE prediction: M(p2); i.e., interaction1
|x − y|2
cf. M(p2) = Constant; i.e., interaction δ4(x − y)
0 2 4 6Q
2 [GeV
2]
0
0.1
0.2
0.3
0.4
0.5
Q2 F
π(Q2 )
[GeV
2 ]
Maris-Tandy-2000
VMD ρ pole
CERN ’80s
JLab, 2001
JLab at 12 GeV
pert. QCD
JLab, 2006b
JLab, 2006a
NJL Model
Single mass-scale parameterin both studies
Same predictions forQ2 = 0 properties
Disagreement > 20%for Q2 > M2
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 18/28
First Contents Back Conclusion
Ratio – Kaon/Pionu-valence distribution
Trang: PhD Thesis (Kent State U.)Trang, Tandy, Bashir, Roberts, in progressHolt & Roberts: arXiv:1002.4666 [nucl-th]
0 0.2 0.4 0.6 0.8 1x
0
0.2
0.4
0.6
0.8
1
1.2
uk / u
π at q = 5 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (E
0, F
0)
uK
/ uπ at q = 5 GeV (E
0, F
0)
Evolved uk, u
π Pade fits at q
0 = 0.57 GeV to q = 5 GeVdata: Badier, et al. , Phys. Lett. B 93 (1980) 354
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 19/28
First Contents Back Conclusion
Ratio – Kaon/Pionu-valence distribution
Trang: PhD Thesis (Kent State U.)Trang, Tandy, Bashir, Roberts, in progressHolt & Roberts: arXiv:1002.4666 [nucl-th]
0 0.2 0.4 0.6 0.8 1x
0
0.2
0.4
0.6
0.8
1
1.2
uk / u
π at q = 5 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (E
0, F
0)
uK
/ uπ at q = 5 GeV (E
0, F
0)
Evolved uk, u
π Pade fits at q
0 = 0.57 GeV to q = 5 GeVdata: Badier, et al. , Phys. Lett. B 93 (1980) 354DSE–result obtained
using interaction that
predicted Fπ(Q2)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 19/28
First Contents Back Conclusion
Ratio – Kaon/Pionu-valence distribution
Trang: PhD Thesis (Kent State U.)Trang, Tandy, Bashir, Roberts, in progressHolt & Roberts: arXiv:1002.4666 [nucl-th]
0 0.2 0.4 0.6 0.8 1x
0
0.2
0.4
0.6
0.8
1
1.2
uk / u
π at q = 5 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (E
0, F
0)
uK
/ uπ at q = 5 GeV (E
0, F
0)
Evolved uk, u
π Pade fits at q
0 = 0.57 GeV to q = 5 GeVdata: Badier, et al. , Phys. Lett. B 93 (1980) 354DSE–result obtained
using interaction that
predicted Fπ(Q2)
Influence of M(p2)
felt strongly for x > 0.5
QCD-M(p2) ⇒
prediction:
uπ,K(x) ∝ (1 − x)2
at resolving-scale
Q0 = 0.6 GeV
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 19/28
First Contents Back Conclusion
Ratio – Kaon/Pionu-valence distribution
Trang: PhD Thesis (Kent State U.)Trang, Tandy, Bashir, Roberts, in progressHolt & Roberts: arXiv:1002.4666 [nucl-th]
0 0.2 0.4 0.6 0.8 1x
0
0.2
0.4
0.6
0.8
1
1.2
uk / u
π at q = 5 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (E
0, F
0)
uK
/ uπ at q = 5 GeV (E
0, F
0)
Evolved uk, u
π Pade fits at q
0 = 0.57 GeV to q = 5 GeVdata: Badier, et al. , Phys. Lett. B 93 (1980) 354DSE–result obtained
using interaction that
predicted Fπ(Q2)
Influence of M(p2)
felt strongly for x > 0.5
QCD-M(p2) ⇒
prediction:
uπ,K(x) ∝ (1 − x)2
at resolving-scale
Q0 = 0.6 GeV
uπ,K(x = 1) invariant under DGLAP-evolution
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 19/28
First Contents Back Conclusion
Ratio – Kaon/Pionu-valence distribution
Trang: PhD Thesis (Kent State U.)Trang, Tandy, Bashir, Roberts, in progressHolt & Roberts: arXiv:1002.4666 [nucl-th]
0 0.2 0.4 0.6 0.8 1x
0
0.2
0.4
0.6
0.8
1
1.2
uk / u
π at q = 5 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (Full BSE)
uK
/ uπ at q
0 = 0.57 GeV (E
0, F
0)
uK
/ uπ at q = 5 GeV (E
0, F
0)
Evolved uk, u
π Pade fits at q
0 = 0.57 GeV to q = 5 GeVdata: Badier, et al. , Phys. Lett. B 93 (1980) 354DSE–result obtained
using interaction that
predicted Fπ(Q2)
Influence of M(p2)
felt strongly for x > 0.5
QCD-M(p2) ⇒
prediction:
uπ,K(x) ∝ (1 − x)2
at resolving-scale
Q0 = 0.6 GeV
uπ,K(x = 1) invariant under DGLAP-evolution
Accessible at Upgraded JLab & Electron-Ion ColliderCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 19/28
First Contents Back Conclusion
Unifying Studyof Mesons and Baryons
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 20/28
First Contents Back Conclusion
Unifying Studyof Mesons and Baryons
How does one incorporate dressed-quark mass function,
M(p2), in study of baryons? Behaviour of M(p2) is es-
sentially a quantum field theoretical effect.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 20/28
First Contents Back Conclusion
Unifying Studyof Mesons and Baryons
How does one incorporate dressed-quark mass function,
M(p2), in study of baryons? Behaviour of M(p2) is es-
sentially a quantum field theoretical effect.
In quantum field theory a nucleon appears as a pole in a six-
point quark Green function.
Residue is proportional to nucleon’s Faddeev amplitude
Poincaré covariant Faddeev equation sums all possible
exchanges and interactions that can take place between
three dressed-quarks
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 20/28
First Contents Back Conclusion
Unifying Studyof Mesons and Baryons
How does one incorporate dressed-quark mass function,
M(p2), in study of baryons? Behaviour of M(p2) is es-
sentially a quantum field theoretical effect.
In quantum field theory a nucleon appears as a pole in a six-
point quark Green function.
Residue is proportional to nucleon’s Faddeev amplitude
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 quark-quark (diquark) correlations in the
colour-3̄ (antitriplet) channelCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 20/28
First Contents Back Conclusion
Faddeev equationR. T. Cahill et al. Austral. J. Phys. 42 (1989) 129
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 21/28
First Contents Back Conclusion
Faddeev equationR. T. Cahill et al. Austral. J. Phys. 42 (1989) 129
=aΨ
P
pq
pd Γb
Γ−a
pd
pq
bΨP
q
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 21/28
First Contents Back Conclusion
Faddeev equationR. T. Cahill et al. Austral. J. Phys. 42 (1989) 129
=aΨ
P
pq
pd Γb
Γ−a
pd
pq
bΨP
q
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 . . . In Nucleon’s Rest
Frame Amplitude has . . . s−, p− & d−wave correlations
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 21/28
First Contents Back Conclusion
Nucleon-Photon Vertex
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 22/28
First Contents Back Conclusion
Nucleon-Photon Vertex
M. Oettel, M. Pichowskyand L. von Smekal, nu-th/9909082
6 terms . . .constructed systematically . . . current conserved automatically
for on-shell nucleons described by Faddeev Amplitude
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 22/28
First Contents Back Conclusion
Nucleon-Photon Vertex
M. Oettel, M. Pichowskyand L. von Smekal, nu-th/9909082
6 terms . . .constructed systematically . . . current conserved automatically
for on-shell nucleons described by Faddeev Amplitude
i
iΨ ΨPf
f
P
Q i
iΨ ΨPf
f
P
Q
i
iΨ ΨPPf
f
Q
Γ−
Γ
scalaraxial vector
i
iΨ ΨPf
f
P
Q
µ
i
i
X
Ψ ΨPf
f
Q
P Γ−
µi
i
X−
Ψ ΨPf
f
P
Q
ΓCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 22/28
First Contents Back Conclusion
µnGE(Q2)
GM(Q2)
Cloët, Roberts et al.– arXiv:0710.2059 [nucl-th]– arXiv:0710.5746 [nucl-th]– arXiv:0804.3118 [nucl-th]– arXiv:0812.0416 [nucl-th] – Survey of nucleon EM form factors
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 23/28
First Contents Back Conclusion
µnGE(Q2)
GM(Q2)
Cloët, Roberts et al.– arXiv:0710.2059 [nucl-th]– arXiv:0710.5746 [nucl-th]– arXiv:0804.3118 [nucl-th]– arXiv:0812.0416 [nucl-th] – Survey of nucleon EM form factors
DSE-Faddeev Equation prediction
]2 [GeV2Q
n M/G
n EG nµ
0.0
0.2
0.4
0.6
0.8
RCQM - MillerGPD - DiehlKelly fit
n
MGalster fit/Kelly Gq(qq) Faddeev&DSE
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
B. Wojtsekhowski, Jefferson Lab E02-013 Collaboration, in preparation.
Figure courtesy S. RiordanCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 23/28
First Contents Back Conclusion
µnGE(Q2)
GM(Q2)
Cloët, Roberts et al.– arXiv:0710.2059 [nucl-th]– arXiv:0710.5746 [nucl-th]– arXiv:0804.3118 [nucl-th]– arXiv:0812.0416 [nucl-th] – Survey of nucleon EM form factors
DSE-Faddeev Equation prediction
Red solid curve
]2 [GeV2Q
n M/G
n EG nµ
0.0
0.2
0.4
0.6
0.8
RCQM - MillerGPD - DiehlKelly fit
n
MGalster fit/Kelly Gq(qq) Faddeev&DSE
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
B. Wojtsekhowski, Jefferson Lab E02-013 Collaboration, in preparation.
Figure courtesy S. RiordanCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 23/28
First Contents Back Conclusion
µnGE(Q2)
GM(Q2)
Cloët, Roberts et al.– arXiv:0710.2059 [nucl-th]– arXiv:0710.5746 [nucl-th]– arXiv:0804.3118 [nucl-th]– arXiv:0812.0416 [nucl-th] – Survey of nucleon EM form factors
DSE-Faddeev Equation prediction
Red solid curve
]2 [GeV2Q
n M/G
n EG nµ
0.0
0.2
0.4
0.6
0.8
RCQM - MillerGPD - DiehlKelly fit
n
MGalster fit/Kelly Gq(qq) Faddeev&DSE
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
B. Wojtsekhowski, Jefferson Lab E02-013 Collaboration, in preparation.
Figure courtesy S. Riordan
This evolution
very sensitive
to momentum
-dependence
dressed-quark
propagator
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 23/28
First Contents Back Conclusion
GnM(Q2)
µnGD(Q2)
Cloët, Roberts et al.– arXiv:0710.2059 [nucl-th]– arXiv:0710.5746 [nucl-th]– arXiv:0804.3118 [nucl-th]– arXiv:0812.0416 [nucl-th] – Survey of nucleon EM form factors
)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 24/28
First Contents Back Conclusion
GnM(Q2)
µnGD(Q2)
Cloët, Roberts et al.– arXiv:0710.2059 [nucl-th]– arXiv:0710.5746 [nucl-th]– arXiv:0804.3118 [nucl-th]– arXiv:0812.0416 [nucl-th] – Survey of nucleon EM form factors
DSE-Faddeev Equation prediction
2009-12-23 15:36:10 )2
(GeV2
Q
2 4 6 8 10 12 14
DG
nµ/
MnG
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Solid - Kelly
Dotted - Alberico et al.
Squares - CLAS12 anticipated
Green - Previous world data.
Red - J.Lachniet et al.
Blue, dashed - Cloet et al.
Anticipated error bars show
systematic uncertainty.
Jefferson Lab E12-07-104, 12GeV Proposal.
Gilfoyle, Brooks, Hafidi for CLAS CollaborationCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 24/28
First Contents Back Conclusion
GnM(Q2)
µnGD(Q2)
Cloët, Roberts et al.– arXiv:0710.2059 [nucl-th]– arXiv:0710.5746 [nucl-th]– arXiv:0804.3118 [nucl-th]– arXiv:0812.0416 [nucl-th] – Survey of nucleon EM form factors
DSE-Faddeev Equation prediction
Blue long-dashed curve
2009-12-23 15:36:10 )2
(GeV2
Q
2 4 6 8 10 12 14
DG
nµ/
MnG
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Solid - Kelly
Dotted - Alberico et al.
Squares - CLAS12 anticipated
Green - Previous world data.
Red - J.Lachniet et al.
Blue, dashed - Cloet et al.
Anticipated error bars show
systematic uncertainty.
Jefferson Lab E12-07-104, 12GeV Proposal.
Gilfoyle, Brooks, Hafidi for CLAS CollaborationCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 24/28
First Contents Back Conclusion
GnM(Q2)
µnGD(Q2)
Cloët, Roberts et al.– arXiv:0710.2059 [nucl-th]– arXiv:0710.5746 [nucl-th]– arXiv:0804.3118 [nucl-th]– arXiv:0812.0416 [nucl-th] – Survey of nucleon EM form factors
DSE-Faddeev Equation prediction
Blue long-dashed curve
2009-12-23 15:36:10 )2
(GeV2
Q
2 4 6 8 10 12 14
DG
nµ/
MnG
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Solid - Kelly
Dotted - Alberico et al.
Squares - CLAS12 anticipated
Green - Previous world data.
Red - J.Lachniet et al.
Blue, dashed - Cloet et al.
Anticipated error bars show
systematic uncertainty.
Jefferson Lab E12-07-104, 12GeV Proposal.
Gilfoyle, Brooks, Hafidi for CLAS Collaboration
Sensitivity to
M(p2) means
experiments probe
IR behaviour
of strong running
coupling
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 24/28
First Contents Back Conclusion
Some current12 GeV-related projects
Elucidate signals of M(p2) in Q2-evolution of nucleon elastic andtransition form factors; viz.,
N → ∆
N →P11(1440)
(M. Bhagwat, I. Cloët, H. Roberts)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 25/28
First Contents Back Conclusion
Some current12 GeV-related projects
Elucidate signals of M(p2) in Q2-evolution of nucleon elastic andtransition form factors; viz.,
N → ∆
N →P11(1440)
(M. Bhagwat, I. Cloët, H. Roberts)
Elucidate effects of DCSB in
light-quark meson spectrum, including so-called hybrids andexotics, using Poincaré-covariant symmetry-preservingBethe-Salpeter equation (L. Chang, arXiv:0903.5461 [nucl-th])
hadron valence-quark distribution functions (A. Bashir,P.C. Tandy)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 25/28
First Contents Back Conclusion
Some current12 GeV-related projects
Elucidate signals of M(p2) in Q2-evolution of nucleon elastic andtransition form factors; viz.,
N → ∆
N →P11(1440)
(M. Bhagwat, I. Cloët, H. Roberts)
Elucidate effects of DCSB in
light-quark meson spectrum, including so-called hybrids andexotics, using Poincaré-covariant symmetry-preservingBethe-Salpeter equation (L. Chang, arXiv:0903.5461 [nucl-th])
hadron valence-quark distribution functions (A. Bashir,P.C. Tandy)
Incorporate “resonant contributions” (pion cloud) in kernels ofbound-state equations (e.g., arXiv:0802.1948 [nucl-th] &arXiv:0811.2018 [nucl-th]; and C.S. Fischer et al.)
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 25/28
First Contents Back Conclusion
Epilogue
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
EpilogueDCSB exists in QCD.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
EpilogueDCSB exists in QCD.
It is manifest in dressed propagators and
vertices
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
EpilogueDCSB exists in QCD.
It is manifest in dressed propagators and
vertices
It predicts, amongst other things, that
light current-quarks become heavy
constituent-quarks: 4 → 400 MeV
pseudoscalar mesons are unnaturally
light: mρ = 770 cf. mπ = 140 MeV
pseudoscalar mesons couple unnaturally
strongly to light-quarks: gπq̄q ≈ 4.3
pseudscalar mesons couple unnaturally
strongly to the lightest baryons
gπN̄N ≈ 12.8 ≈ 3gπq̄q
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
Epilogue
DCSB impacts dramatically upon observables
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
Epilogue
DCSB impacts dramatically upon observables
Spectrum; e.g., splittings: σ–π & a1–ρ
Elastic and Transition Form Factors
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
Epilogue
DCSB impacts dramatically upon observables
Spectrum; e.g., splittings: σ–π & a1–ρ
Elastic and Transition Form FactorsBut M(p2) is an essentially quantum field theoretical effect
Exposing & elucidating its effect in hadron physics requires
nonperturbative, symmetry preserving framework; i.e.,
Poincaré covariance, chiral and e.m. current conservation, etc.
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
Epilogue
DCSB impacts dramatically upon observables
Spectrum; e.g., splittings: σ–π & a1–ρ
Elastic and Transition Form FactorsBut M(p2) is an essentially quantum field theoretical effect
Exposing & elucidating its effect in hadron physics requires
nonperturbative, symmetry preserving framework; i.e.,
Poincaré covariance, chiral and e.m. current conservation, etc.
DSEs provide such a framework.
Studies underway will identify observable signals of M(p2),
the most important mass-generating mechanism for visible
matter in the Universe
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
Epilogue
DCSB impacts dramatically upon observables
Spectrum; e.g., splittings: σ–π & a1–ρ
Elastic and Transition Form FactorsBut M(p2) is an essentially quantum field theoretical effect
Exposing & elucidating its effect in hadron physics requires
nonperturbative, symmetry preserving framework; i.e.,
Poincaré covariance, chiral and e.m. current conservation, etc.
DSEs provide such a framework.
Studies underway will identify observable signals of M(p2),
the most important mass-generating mechanism for visible
matter in the Universe
DSEs: Tool enabling insight to be drawn from experiment
into long-range piece of interaction between light-quarksCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 26/28
First Contents Back Conclusion
Epilogue
Now is an exciting time . . .
Positioned to unify phenomena as apparently disparate as
Hadron spectrum
Elastic and transition form factors, from small- to large-Q2
Parton distribution functions
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 27/28
First Contents Back Conclusion
Epilogue
0 1 2 3
p [GeV]
0
0.1
0.2
0.3
0.4
M(p
) [G
eV] m = 0 (Chiral limit)
m = 30 MeVm = 70 MeV
effect of gluon cloudRapid acquisition of mass is
Now is an exciting time . . .
Positioned to unify phenomena as apparently disparate as
Hadron spectrum
Elastic and transition form factors, from small- to large-Q2
Parton distribution functions
Key: an understanding of both the fundamental origin of nuclear
mass and the far-reaching consequences of the mechanism
responsible; namely, Dynamical Chiral Symmetry BreakingCraig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 27/28
First Contents Back Conclusion
Contents
1. Universal Truths
2. QCD’s Challenges
3. Charting the Interaction
4. Bound-state DSE
5. BSE – General Form
6. a1 – ρ
7. Frontiers of Nuclear Science
8. Goldberger-Treiman for pion
9. GT – Contact Interaction
10. Computation: Fπ(Q2)
11. Kaon/Pion u-valence distribution
12. Unifying Meson & Nucleon
13. Faddeev equation
14. Nucleon-Photon Vertex
15.µnGE (Q2)
GM (Q2)
16.Gn
M (Q2)
µnGD(Q2)
17. Current Projects
Craig Roberts – Exposing the Dressed Quark’s mass4th Workshop on Exclusive Reactions at High Momentum Transfer, 18-21 May 2010 . . . 27 – p. 28/28