craig roberts physics division. 1.rocio bermudez (u michoácan); 2.chen chen (anl, iit, ustc);...
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Prospects for the physics of cold, sparse hadrons
Craig Roberts
Physics Division
Prospects for the physics of cold, sparse hadrons (72p)
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Collaborators: 2011-Present1. Rocio BERMUDEZ (U Michoácan);2. Chen CHEN (ANL, IIT, USTC);3. Xiomara GUTIERREZ-GUERRERO (U Michoácan);4. Trang NGUYEN (KSU);5. Khépani Raya (U Michoácan);6. Hannes ROBERTS (ANL, FZJ, UBerkeley);7. Chien-Yeah SENG (UW-Mad)8. Kun-lun WANG (PKU);9. J. Javier COBOS-MARTINEZ (U.Sonora);10. Mario PITSCHMANN (ANL & UW-Mad);11. Si-xue QIN (U. Frankfurt am Main);12. Jorge SEGOVIA (ANL);13. David WILSON (ODU);14. Lei CHANG (FZJ); 15. Ian CLOËT (ANL);16. Bruno EL-BENNICH (São Paulo);
Craig Roberts: U. Frankfurt: 8 July 2013
17. Adnan BASHIR (U Michoácan);18. Stan BRODSKY (SLAC);19. Gastão KREIN (São Paulo)20. Roy HOLT (ANL);21. Mikhail IVANOV (Dubna);22. Yu-xin LIU (PKU);23. Michael RAMSEY-MUSOLF (UW-Mad)24. Alfredo RAYA (U Michoácan);25. Sebastian SCHMIDT (IAS-FZJ & JARA);26. Robert SHROCK (Stony Brook);27. Peter TANDY (KSU);28. Tony THOMAS (U.Adelaide)29. Shaolong WAN (USTC)
StudentsPostdocsAsst. Profs.
Prospects for the physics of cold, sparse hadrons (72p)
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Science Challenges for the coming decade: 2013-2022
Exploit opportunities provided by new data on hadron elastic and transition form factors– Chart infrared evolution of QCD’s coupling and
dressed-masses – Reveal correlations that are key to nucleon structure– Expose the facts or fallacies in modern descriptions of
hadron structure
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Science Challenges for the coming decade: 2013-2022
Precision experimental study of valence region (Bjorken-x > 0.5), and theoretical computation of distribution functions and distribution amplitudes– Computation is critical, parametrisation is inadequate– Without computation, no amount of data will reveal
anything about the theory underlying the phenomena of strong interaction physics
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Overarching Science Challenges for the
coming decade: 2013-2022
Craig Roberts: U. Frankfurt: 8 July 2013
Discover meaning of confinement, and its relationship to DCSB – the origin of visible mass
Prospects for the physics of cold, sparse hadrons (72p)
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What is QCD?Craig Roberts: U. Frankfurt: 8 July 2013
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QCD is a Theory Very likely a self-contained, nonperturbatively renormalisable
and hence well defined Quantum Field TheoryThis is not true of QED – cannot be defined nonperturbatively
No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8000 GeV
Increasingly likely that any extension of the Standard Model will be based on the paradigm established by QCD – Extended Technicolour: electroweak symmetry breaks via a
fermion bilinear operator in a strongly-interacting non-Abelian theory. (Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81)Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
(not an effective theory)
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Contrast: so-called Effective Field Theories
EFTs applicable over a very restricted energy domain; e.g., ChPT known to breakdown for E > 2mπ
Can be used to help explore how features of QCD influence observables
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
QCD appears valid at all energy scales that have been tested so far: no breakdown below
E ≈ 60000 mπ
Cannot be used to test QCD Any mismatch between EF-Theory and experiment owes to an error in the formulation of one or conduct of the other
Can Cannot
Prospects for the physics of cold, sparse hadrons (72p)
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Strong-interaction: QCD
Asymptotically free– Perturbation theory is valid
and accurate tool at large-Q2
– Hence chiral limit is defined Essentially nonperturbative
for Q2 < 2 GeV2
Craig Roberts: U. Frankfurt: 8 July 2013
Nature’s only (now known) example of a truly nonperturbative, fundamental theory A-priori, no idea as to what such a theory can produce
Prospects for the physics of cold, sparse hadrons (72p)
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What is Confinement?
Craig Roberts: U. Frankfurt: 8 July 2013
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Light quarks & Confinement
A unit area placed midway between the quarks and perpendicular to the line connecting them intercepts a constant number of field lines, independent of the distance between the quarks. This leads to a constant force between the quarks – and a large force at that, equal to about 16 metric tons.”
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Folklore … Hall-D Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes.
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Light quarks & Confinement
Problem: 16 tonnes of force makes a lot of pions.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Light quarks & Confinement
Problem: 16 tonnes of force makes a lot of pions.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Light quarks & Confinement In the presence of
light quarks, pair creation seems to occur non-localized and instantaneously
No flux tube in a theory with light-quarks.
Flux-tube is not the correct paradigm for confinement in hadron physics
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
G. Bali et al., PoS LAT2005 (2006) 308
Prospects for the physics of cold, sparse hadrons (72p)
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QFT Paradigm: – Confinement is expressed through a dramatic
change in the analytic structure of propagators for coloured states
– It can almost be read from a plot of the dressed-propagator for a coloured state
Confinement
complex-P2 complex-P2
o Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularitieso State described by rapidly damped wave & hence state cannot exist in observable spectrum
Normal particle Confined particle
Craig Roberts: U. Frankfurt: 8 July 2013
timelike axis: P2<0
s ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fm
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Light quarks & Confinement
In the study of hadrons, attention should turn from potential models toward the continuum bound-state problem in quantum field theory
Such approaches offer the possibility of posing simultaneously the questions – What is confinement?– What is dynamical chiral symmetry breaking?– How are they related?
Is it possible that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a mass-scale in QCD, can have different origins and fates?
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Dynamical Chiral Symmetry Breaking
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Dynamical Chiral Symmetry BreakingDCSB is a fact in QCD
– Dynamical, not spontaneous• Add nothing to QCD , no Higgs field, nothing! • Effect achieved purely through the quark+gluon dynamics.
– It’s the most important mass generating mechanism for visible matter in the Universe. • Responsible for ≈98% of the proton’s mass.• Higgs mechanism is (almost) irrelevant to light-quarks.
– Just like gluons and quarks, and for the same reasons, condensates are confined within hadrons. • There are no vacuum condensates.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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“Orthodox Vacuum”
Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,
containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
u
u
ud
u ud
du
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Background Worth noting that nonzero vacuum expectation values of local
operators in QCD—the so-called vacuum condensates—are phenomenological parameters, which were introduced at a time of limited computational resources in order to assist with the theoretical estimation of essentially nonperturbative strong-interaction matrix elements.
A universality of these condensates was assumed, namely, that the properties of all hadrons could be expanded in terms of the same condensates. While this helps to retard proliferation, there are nevertheless infinitely many of them.
As qualities associated with an unmeasurable state (the vacuum), such condensates do not admit direct measurement. Practitioners have attempted to assign values to them via an internally consistent treatment of many separate empirical observables.
However, only one, the so-called quark condensate, is attributed a value with any confidence.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Confinement contains
condensatesCraig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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“Orthodox Vacuum”
Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,
containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
u
u
ud
u ud
du
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New Paradigm
Vacuum = hadronic fluctuations but no condensates
Hadrons = complex, interacting systemswithin which perturbative behaviour is restricted to just 2% of the interior
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
u
u
ud
u ud
du
“EMPTY space may really be empty. Though quantum theory suggests that a vacuum should be fizzing with particle activity, it turns out that this paradoxical picture of nothingness may not be needed. A calmer view of the vacuum would also help resolve a nagging inconsistency with dark energy, the elusive force thought to be speeding up the expansion of the universe.”
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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“Void that is truly empty solves dark energy puzzle”Rachel Courtland, New Scientist 4th Sept. 2010
Cosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1046
Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model
4620
4
103
8
HG QCDNscondensateQCD
Paradigm shift:In-Hadron Condensates
Prospects for the physics of cold, sparse hadrons (72p)
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Relevant References arXiv:1202.2376, Phys. Rev. C 85 (2012) 065202
Confinement contains condensatesStanley J. Brodsky, Craig D. Roberts, Robert Shrock, Peter C. Tandy
arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(RapCom), Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. Tandy
arXiv:1005.4610 [nucl-th], Phys. Rev. C82 (2010) 022201(RapCom.) New perspectives on the quark condensate, Brodsky, Roberts, Shrock, Tandy
arXiv:0905.1151 [hep-th], PNAS 108, 45 (2011) Condensates in Quantum Chromodynamics and the Cosmological Constant , Brodsky and Shrock,
hep-th/0012253 The Quantum vacuum and the cosmological constant problem, Svend Erik Rugh and Henrik Zinkernagel.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
DCSB
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Mass from nothing!
Craig Roberts: U. Frankfurt: 8 July 2013
C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227 In QCD, all “constants” of
quantum mechanics are actually strongly momentum dependent: couplings, number density, mass, etc.
So, a quark’s mass depends on its momentum.
Mass function can be calculated and is depicted here.
Continuum- and Lattice-QCD are in agreement: the vast bulk of the light-quark mass comes from a cloud of gluons, dragged along by the quark as it propagates.
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Enigma of MassCraig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Pion’s Goldberger-Treiman relation
Prospects for the physics of cold, sparse hadrons (72p)
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Pion’s Bethe-Salpeter amplitudeSolution of the Bethe-Salpeter equation
Dressed-quark propagator
Axial-vector Ward-Takahashi identity entails
Pseudovector componentsnecessarily nonzero.
Cannot be ignored!
Exact inChiral QCD
Craig Roberts: U. Frankfurt: 8 July 2013
Miracle: two body problem solved, almost completely, once solution of one body problem is known
Maris, Roberts and Tandynucl-th/9707003, Phys.Lett. B420 (1998) 267-273
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Dichotomy of the pionGoldstone mode and bound-state
Goldstone’s theorem has a pointwise expression in QCD;
Namely, in the chiral limit the wave-function for the two-body bound-state Goldstone mode is intimately connected with, and almost completely specified by, the fully-dressed one-body propagator of its characteristic constituent • The one-body momentum is equated with the relative
momentum of the two-body system
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
fπ Eπ(p2) = B(p2)
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Enigma of mass
The quark level Goldberger-Treiman relation shows that DCSB has a very deep and far reaching impact on physics within the strong interaction sector of the Standard Model; viz.,
Goldstone's theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in the pseudoscalar channel.
This emphasises that Goldstone's theorem has a pointwise expression in QCD
Hence, pion properties are an almost direct measure of the dressed-quark mass function.
Thus, enigmatically, the properties of the massless pion are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
fπ Eπ(p2) = B(p2)
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In QCD, Gluons, too, become massive
Not just quarks … Gluons also have a
gap equation …1/k2 behaviour signals essential singularity in the running coupling:
Impossible to reach in perturbation theory
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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422 )(
kkm
g
gg
)( 2k
const
e
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Parton structure of
hadronsCraig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Valence quarks
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Deep inelastic scattering
Quark discovery experiment at SLAC (1966-1978, Nobel Prize in 1990)
Completely different to elastic scattering– Blow the target to pieces instead of keeping only
those events where it remains intact. Cross-section is interpreted as a measurement of
the momentum-fraction probability distribution for quarks and gluons within the target hadron: q(x), g(x)
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Probability that a quark/gluon within the target will carry a fraction x of the bound-state’s light-front momentumDistribution Functions of the Nucleon and Pion in the
Valence Region, Roy J. Holt and Craig D. Roberts, arXiv:1002.4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991-3044
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Parton Structure of Hadrons
Valence-quark structure of hadrons– Definitive of a hadron – it’s how we tell a proton from
a neutron– Expresses charge; flavour; baryon number; and other
Poincaré-invariant macroscopic quantum numbers– Via evolution, determines background at LHC
Sea-quark distributions– Flavour content, asymmetry, intrinsic: yes or no?
Any nontrivial answers are essentially nonperturbative features of QCD
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Parton Structure of Hadrons Light front provides a link with quantum mechanics
– If a probability interpretation is ever valid, then it’s in the infinite-momentum frame
Enormous amount of intuitively expressive information about hadrons & processes involving them is encoded in – Parton distribution functions – Generalised parton distribution functions – Transverse-momentum-dependent parton distribution
functions Information will be revealed by the measurement of
these functions – so long as they can be calculatedSuccess of programme demands very close collaboration between experiment and theory
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Parton Structure of Hadrons
Need for calculation is emphasised by Saga of pion’s valence-quark distribution:o 1989: uv
π ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD;
o 2001: DSE- QCD predictsuv
π ~ (1-x)2 argues that distribution inferred from data can’t be correct;
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
37
Parton Structure of Hadrons
Need for calculation is emphasised by Saga of pion’s valence-quark distribution:o 1989: uv
π ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD;
o 2001: DSE- QCD predicts uv
π ~ (1-x)2 argues that distribution inferred from data can’t be correct;
o 2010: NLO reanalysis including soft-gluon resummation, inferred distribution agrees with DSE and QCD
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Prospects for the physics of cold, sparse hadrons (72p)
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Exact expression in QCD for the pion’s valence-quark parton distribution amplitude
Expression is Poincaré invariant but a probability interpretation is only valid in the light-front frame because only therein does one have particle-number conservation.
Probability that a valence-quark or antiquark carries a fraction x=k+ / P+
of the pion’s light-front momentum { n2=0, n.P = -mπ}
Pion’s valence-quark Distribution Amplitude
Craig Roberts: U. Frankfurt: 8 July 2013
Pion’s Bethe-Salpeter wave function
Whenever a nonrelativistic limit is realistic, this would correspond to the Schroedinger wave function.
Prospects for the physics of cold, sparse hadrons (72p)
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Moments method is ideal for φπ(x):
entails
Contact interaction(1/k2)ν , ν=0Straightforward exercise to show∫0
1 dx xm φπ(x) = fπ 1/(1+m) , hence φπ(x)= fπ Θ(x)Θ(1-x)
Pion’s valence-quark Distribution Amplitude
Craig Roberts: U. Frankfurt: 8 July 2013
Pion’s Bethe-Salpeter wave function
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Pion’s valence-quark Distribution Amplitude
The distribution amplitude φπ(x) is actually dependent on the momentum-scale at which a particular interaction takes place; viz., φπ(x)= φπ(x,Q)
One may show in general that φπ(x) has an expansion in terms of Gegenbauer–α=3/2 polynomials:
Only even terms contribute because the neutral pion is an eigenstate of charge conjugation, so φπ(x)=φπ(1-x)
Evolution, analogous to that of the parton distribution functions, is encoded in the coefficients an(Q)
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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Pion’s valence-quark Distribution Amplitude
However, practically, in reconstructing φπ(x) from its moments, it is better to use Gegenbauer–α polynomials and then rebuild the Gegenbauer–α=3/2 expansion from that.– Better means – far more rapid convergence because
Gegenbauer–α=3/2 is only accurate near ΛQCD/Q=0.– One nontrivial Gegenbauer–α polynomial provides converged
reconstruction cf. more than SEVEN Gegenbauer–α=3/2 polynomials
Results have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available.– xα (1-x)α, with α=0.3
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].
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Pion’s valence-quark Distribution Amplitude
Both kernels agree: marked broadening of φπ(x), which owes to DCSB
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Asymptoticφπ(x)=6 x (1-x)
RL
DB
This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.
Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result
Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].
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Pion’s valence-quark Distribution Amplitude
Both kernels agree: marked broadening of φπ(x), which owes to DCSB
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Asymptotic
RL
DB
This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.
Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result
These computations are the first to directly expose DCSB – pointwise – on the light-front; i.e., in the infinite momentum frame.
Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].
44Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Established a one-to-one connection between DCSB and the pointwise form of the pion’s wave function.
Dilation measures the rate at which dressed-quark approaches the asymptotic bare-parton limit
Experiments at JLab12 can empirically verify the behaviour of M(p), and hence chart the IR limit of QCD
C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50
Dilation of pion’s wave function is measurable in
pion’s electromagnetic form factor at JLab12
A-rated: E12-06-10
Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark
Distribution Amplitude
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Lattice comparisonPion’s valence-quark PDA
Employ the generalised-Gegenbauer method described previously (and in Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]).
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Lattice-QCD => one nontrivial moment:
<(2x-1)2> = 0.27 ± 0.04 Legend
• Solid = DB (Best) DSE• Dashed = RL DSE• Dotted (black) = 6 x (1-x)• Dot-dashed = midpoint
lattice; and the yellow shading exhibits band allowed by lattice errors
φπ~ xα (1-x)α
α=0.35+0.32 = 0.67- 0.24 = 0.11
DB α=0.31 but 10% a2<0RL α=0.29 and 0% a2
V. Braun et al., PRD 74 (2006) 074501
Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]
46
Lattice comparisonPion’s valence-quark PDA
Establishes that contemporary DSE- and lattice-QCD computations, at the same scale, agree on the pointwise form of the pion's PDA, φπ(x).
This unification of DSE- and lattice-QCD results expresses a deeper equivalence between them, expressed, in particular, via the common behaviour they predict for the dressed-quark mass-function, which is both – a definitive signature of dynamical chiral symmetry breaking – and the origin of the distribution amplitude's dilation.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]
47
When is asymptotic PDA valid?
Under leading-order evolution, the PDA remains broad to Q2>100 GeV2
Feature signals persistence of the influence of dynamical chiral symmetry breaking.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Consequently, the asymptotic distribution, φπ
asy(x), is a poor approximation to the pion's PDA at all such scales that are either currently accessible or foreseeable in experiments on pion elastic and transition form factors.
Thus, related expectations based on φπasy(x) should be revised.
asymptotic
4 GeV2
100 GeV2
Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]
48
When is asymptotic PDA valid?
φπasy(x) can only be a
good approximation to the pion's PDA when it is accurate to write
uvπ (x) ≈ δ(x)
for the pion's valence-quark distribution function.
This is far from valid at currently accessible scales
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Q2=27 GeV2
This is not δ(x)!
Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]
Prospects for the physics of cold, sparse hadrons (72p)
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Elastic Scattering
Craig Roberts: U. Frankfurt: 8 July 2013
50Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Charged pion elastic form factor
P. Maris & P.C. Tandy, Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q2>4GeV2, so prediction ends!
Algorithm developed for pion PDA overcomes this obstacle
Solves the practical problem of continuing from Euclidean metric formulation to Minkowski space
Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th]
51Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Charged pion elastic form factor
Improved DSE interaction kernel, based on DSE and lattice-QCD studies of gluon sectorS.-x. Qin, L. Chang et al. Phys.Rev. C84 (2011) 042202(R)
New prediction in better agreement with available data than old DSE result
Prediction extends from Q2=0 to arbitrarily large Q2, without interruption, unifying both domains
DSE 2000 … Breakdown here
Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th]
52Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Charged pion elastic form factor
Unlimited domain of validity emphasised in this figure
Depict prediction on domain 0<Q2<20GeV2 but have computed the result to Q2=100GeV2.
If it were necessary, reliable results could readily be obtained at even higher values.
DSE 2013
Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th]
53Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Charged pion elastic form factor
Predict a maximum at 6-GeV2, which lies within domain that is accessible to JLab12
Difficult, however, to distinguish DSE prediction from Amendolia-1986 monopole
What about comparison with perturbative QCD?
Amendolia et al.
DSE 2013
ρ-meson pole VMD
maximum
A-rated: E12-06-10
Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th]
54Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Charged pion elastic form factor Prediction of pQCD
obtained when the pion valence-quark PDA has the form appropriate to the scale accessible in modern experiments is markedly different from the result obtained using the asymptotic PDA
Near agreement between the pertinent perturbative QCD prediction and DSE-2013 prediction is striking.
DSE 2013
pQCD obtained with φπasy(x)
pQCD obtained with φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment
15%
Single DSE interaction kernel, determined fully by just one parameter and preserving the one-loop renormalisation group behaviour of QCD, has unified the Fπ(Q2) and φπ(x) (and numerous other quantities)
Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th]
55Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Charged pion elastic form factor Leading-order, leading-twist
QCD prediction, obtained with φπ(x) evaluated at a scale appropriate to the experiment underestimates DSE-2013 prediction by merely an approximately uniform 15%.
Small mismatch is explained by a combination of higher-order, higher-twist corrections & and shortcomings in the rainbow-ladder truncation.
DSE 2013
pQCD obtained with φπasy(x)
pQCD obtained φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment
15%
Hence, one should expect dominance of hard contributions to the pion form factor for Q2>8GeV2.
Nevertheless, the normalisation of the form factor is fixed by a pion wave-function whose dilation with respect to φπ
asy(x) is a definitive signature of DCSB
Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th]
Prospects for the physics of cold, sparse hadrons (72p)
Baryon Structure Dynamical chiral symmetry breaking (DCSB)
– has enormous impact on meson properties. Must be included in description
and prediction of baryon properties. DCSB is essentially a quantum field theoretical effect.
In quantum field theory Meson appears as pole in four-point quark-antiquark Green function
→ Bethe-Salpeter Equation Nucleon appears as a pole in a six-point quark Green function
→ Faddeev Equation. Poincaré covariant Faddeev equation sums all possible exchanges and
interactions that can take place between three dressed-quarks Tractable equation is based on the observation that an interaction
which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel
Craig Roberts: U. Frankfurt: 8 July 2013 56
R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145
6333 SUc(3):
57
Baryon Structure
Remarks Diquark correlations are not inserted by hand
Such correlations are a dynamical consequence of strong-coupling in QCD
The same mechanism that produces an almost massless pion from two dynamically-massive quarks; i.e., DCSB, forces a strong correlation between two quarks in colour-antitriplet channels within a baryon – an indirect consequence of Pauli-Gürsey symmetry
Diquark correlations are not pointlike– Typically, r0+ ~ rπ & r1+ ~ rρ
(actually 10% larger)– They have soft form factors
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
SU(2) isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles.
Faddeev Equation
58
Structure of Hadrons Elastic form factors
– Provide vital information about the structure and composition of the most basic elements of nuclear physics.
– They are a measurable and physical manifestation of the nature of the hadrons' constituents and the dynamics that binds them together.
Accurate form factor data are driving paradigmatic shifts in our pictures of hadrons and their structure; e.g., – role of orbital angular momentum and nonpointlike diquark
correlations– scale at which p-QCD effects become evident– strangeness content– meson-cloud effects– etc.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
59
Jlab Highlights
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
)(
)(
2
2
QG
QG
pM
pEp
http://www.jlab.org/highlights/phys.html
Distribution of charge is different from distribution of magnetisation
Prospects for the physics of cold, sparse hadrons (72p)
60
Photon-nucleon current
Composite nucleon must interact with photon via nontrivial current constrained by Ward-Green-Takahashi identities
DSE → BSE → Faddeev equation plus current → nucleon form factors
Vertex must contain the dressed-quark anomalous magnetic moment
Oettel, Pichowsky, SmekalEur.Phys.J. A8 (2000) 251-281
Craig Roberts: U. Frankfurt: 8 July 2013
L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]Phys. Rev. Lett. 106 (2011) 072001
In a realistic calculation, the last three diagrams represent 8-dimensional integrals, which can be evaluated using Monte-Carlo techniques
Prospects for the physics of cold, sparse hadrons (72p)
61
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]
)(
)(
2
2
QG
QG
pM
pEp
Highlights again the critical importance of DCSB in explanation of real-world observables.
DSE result Dec 08
DSE result – including the anomalous magnetic moment distribution
Craig Roberts: U. Frankfurt: 8 July 2013
L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]Phys. Rev. Lett. 106 (2011) 072001
Prospects for the physics of cold, sparse hadrons (72p)
Visible Impacts of DCSB
62Craig Roberts: U. Frankfurt: 8 July 2013
Apparently small changes in M(p) within the domain 1<p(GeV)<3have striking effect on the proton’s electric form factor
The possible existence and location of the zero is determined by behaviour of Q2F2
p(Q2) Like the pion’s PDA, Q2F2
p(Q2) measures the rate at which dress-ed-quarks become parton-like: F2
p=0 for bare quark-partons Therefore, GE
p can’t be zero on the bare-parton domain
I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv: 1304.0855 [nucl-th]
Prospects for the physics of cold, sparse hadrons (72p)
Visible Impacts of DCSB
63Craig Roberts: U. Frankfurt: 8 July 2013
Follows that the possible existence and location
of a zero in the ratio of proton elastic form factors
[μpGEp(Q2)/GMp(Q2)] are a direct measure of the nature of the quark-quark interaction in the Standard Model.
I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv: 1304.0855 [nucl-th]
Prospects for the physics of cold, sparse hadrons (72p)
64
Flavor separation of proton form factors
Very different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental
Craig Roberts: U. Frankfurt: 8 July 2013
Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) 252003
Q4F2q/k
Q4 F1q
Prospects for the physics of cold, sparse hadrons (72p)
65
Diquark correlations!
Poincaré covariant Faddeev equation – Predicts scalar and axial-vector
diquarks Proton's singly-represented d-quark
more likely to be struck in association with 1+ diquark than with 0+
– form factor contributions involving 1+ diquark are softer
Craig Roberts: U. Frankfurt: 8 July 2013
Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205
Doubly-represented u-quark is predominantly linked with harder 0+ diquark contributions
Interference produces zero in Dirac form factor of d-quark in proton– Location of the zero depends on the relative probability of finding
1+ & 0+ diquarks in proton– Correlated, e.g., with valence d/u ratio at x=1
d
u
=Q2/M2
66
Neutron Structure Function at high-x
Valence-quark distributions at x=1– Fixed point under DGLAP evolution– Strong discriminator between theories
Algebraic formula
– P1p,s = contribution to the proton's charge arising from diagrams
with a scalar diquark component in both the initial and final state
– P1p,a = kindred axial-vector diquark contribution
– P1p,m = contribution to the proton's charge arising from diagrams
with a different diquark component in the initial and final state.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
Measures relative strength of axial-vector/scalar diquarks in proton
Prospects for the physics of cold, sparse hadrons (72p)
67
Neutron StructureFunction at high-x
Craig Roberts: U. Frankfurt: 8 July 2013
d/u=1/2
SU(6) symmetry
pQCD, uncorrelated Ψ
0+ qq only, d/u=0
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)
d/u=0.28
DSE: “realistic”
Distribution of neutron’s momentum amongst quarks on the valence-quark domain
DSE: “contact”d/u=0.18
Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501
x>0.9
Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
Prospects for the physics of cold, sparse hadrons (72p)
68
Neutron StructureFunction at high-x
SU(6) symmetry
pQCD, uncorrelated Ψ
0+ qq only
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)
DSE: “realistic”
Distribution of neutron’s momentum amongst quarks on the valence-quark domainCraig Roberts: U. Frankfurt: 8 July 2013
DSE: “contact”
Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501
x>0.9
Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
NB. d/u|x=1= 0 means there are
no valence d-quarks in the proton!
JLab12 can resolve this conundrum
Prospects for the physics of cold, sparse hadrons (72p)
69
Neutron StructureFunction at high-x
“While it is quite hazardous to extrapolate from our limited xB range all the way to xB = 1, these results appear to disfavor models of the proton with d/u=0 at xB = 1”
Craig Roberts: U. Frankfurt: 8 July 2013
Short Range Correlations and the EMC Effect, L.B. Weinstein et al., Phys.Rev.Lett. 106 (2011) 052301, arXiv:1009.5666 [hep-ph]
Figure courtesy of D.W. Higinbotham
Observation: EMC effect measured in electron DIS at 0.35 < xB < 0.7, is linearly related to the Short Range Correlation (SRC) scale factor obtained from electron inclusive scattering at xB > 1.
70
Theory Lattice-QCD
– Significant progress in the last five years
– This must continue Bound-state problem in
continuum quantum field theory– Significant progress, too– This must continue
First Sino-Americas School & Workshop on the Continuum Bound-State Problem, Hefei, China. 22-26/Oct./2013
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
71Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
Epilogue
72
Epilogue The Physics of Hadrons is Unique:
– Confronting a fundamental theory in which the elementary degrees-of-freedom are intangible and only composites reach detectors
Confinement in real-world is NOT understood DCSB is crucial to any understanding of hadron
phenomena
They must have a common origin Experimental and theoretical study of the Bound-
state problem in continuum QCD promises to provide many more insights and answers.
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
73
This is not the end
Craig Roberts: U. Frankfurt: 8 July 2013
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74
Table of Contents
I. IntroductionII. Pion valence-quark distributionIII. Pion valence-quark parton distribution amplitudeIV. Charged pion elastic form factorV. Baryon StructureVI. Nucleon form factorsVII. Nucleon structure functions at large-xVIII.Epilogue
Craig Roberts: U. Frankfurt: 8 July 2013
Prospects for the physics of cold, sparse hadrons (72p)
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