Confinement contains Condensates Craig Roberts Physics Division Published collaborations: Rocio BERMUDEZ (U Michocan); 2010-present Chen CHEN (ANL, IIT, USTC); Xiomara GUTIERREZ-GUERRERO (U Michocan); Trang NGUYEN (KSU); Si-xue QIN (PKU); Hannes ROBERTS (ANL, FZJ, UBerkeley); Lei CHANG (ANL, FZJ, PKU); Students Huan CHEN (BIHEP); Early-career Ian CLOT (UAdelaide); scientists Bruno EL-BENNICH (So Paulo); David WILSON (ANL); Adnan BASHIR (U Michocan); Stan BRODSKY (SLAC);
Gasto KREIN (So Paulo) Roy HOLT (ANL); Mikhail IVANOV (Dubna); Yu-xin LIU (PKU); Robert SHROCK (Stony Brook); Peter TANDY (KSU) Wholly contained Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 2 Some Relevant References arXiv:1202.2376 Confinement contains condensates Stanley 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 condensates Lei 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: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 3 Confinemen t Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 4
X Confinement Gluon and Quark Confinement Colour singlets No coloured states have yet been observed to reach a detector Empirical fact. However There is no agreed, theoretical definition of light-quark confinement Static-quark confinement is irrelevant to real-world QCD There are no long-lived, very-massive quarks Confinement entails quark-hadron duality; i.e., that all observable consequences of QCD can, in principle, be computed using an hadronic basis. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs
5 Confinement Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured particles & can almost be read from a plot of a states dressed-propagator Gribov (1978); Munczek (1983); Stingl (1984); Cahill (1989); Roberts, Williams & Krein (1992); Tandy (1994); Confined particle Normal particle complex-P2 complex-P2 timelike axis: P2<0 o Real-axis mass-pole splits, moving into pair(s) of complex conjugate poles or branch points o Spectral density no longer positive semidefinite & hence state cannot exist in observable spectrum Craig Roberts: Confinement contains Condensates
SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 6 Dressed-gluon propagator A.C. Aguilar et al., Phys.Rev. D80 (2009) 085018 Gluon propagator satisfies a Dyson-Schwinger Equation Plausible possibilities for the solution DSE and lattice-QCD agree on the result Confined gluon IR-massive but UV-massless mG 2-4 QCD IR-massive but UV-massless, confined gluon perturbative, massless gluon
massive , unconfined gluon Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 7 Qin et al., Phys. Rev. C 84 042202(R) (2011) Rainbow-ladder truncation DSE Studies Phenomenology of gluon Wide-ranging study of & properties Effective coupling Agrees with pQCD in ultraviolet Saturates in infrared (0)/ = 8-15 (mG2)/ = 2-4 Running gluon mass Gluon is massless in ultraviolet
in agreement with pQCD Massive in infrared mG(0) = 0.67-0.81 GeV mG(mG2) = 0.53-0.64 GeV Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 8 Dynamical Chiral Symmetry Breaking Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 9 Dynamical Chiral Symmetry Breaking Strong-interaction: QCD
Confinement Empirical feature Modern theory and lattice-QCD support conjecture that light-quark confinement is a fact associated with violation of reflection positivity; i.e., novel analytic structure for propagators and vertices Still circumstantial, no proof yet of confinement On the other hand, DCSB is a fact in QCD It is the most important mass generating mechanism for visible matter in the Universe. Responsible for approximately 98% of the protons mass. Higgs mechanism is (almost) irrelevant to light-quarks. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 10 Frontiers of Nuclear Science: Theoretical Advances
In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. Craig Roberts: Confinement contains Condensates C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227 SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 11
Frontiers of Nuclear Science: Theoretical Advances In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. Mass from nothing! DSE prediction of DCSB confirmed
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 12 12GeV The Future of JLab Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at Jlab 12GeV: Scanned by 2
Craig Roberts: Confinement contains Condensates elastic & transition form factors. SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 13 Gluon & quark mass-scales mg(0) and M(0) dynamically generated mass scales for gluons and quarks are insensitive to changes in the currentquark mass in the neighbourhood of the physical value Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 14 Persistent Truncation Challenge Craig Roberts: Confinement contains Condensates
SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 15 Persistent challenge in application of DSEs Infinitely many coupled equations: Kernel of the equation for the quark self-energy involves: D(k) dressed-gluon propagatork) dressed-gluon propagator) dressed-gluon propagator (k) dressed-gluon propagatorq,p) dressed-quark) dressed-gluon propagator-gluon vertex each of which satisfies its own DSE, etc Coupling between equations necessitates a truncation Invaluable check on Weak coupling expansion practical truncation produces every diagram in perturbation theory schemes Otherwise useless for the nonperturbative problems in which were interested
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 16 Relationship must be preserved by any truncation Highly nontrivial constraint FAILURE has an extremely high cost loss of any connection with QCD Persistent challenge - truncation scheme Symmetries associated with conservation of vector and axial-vector currents are critical in arriving at a veracious understanding of hadron structure and interactions Example: axial-vector Ward-Takahashi identity Statement of chiral symmetry and the pattern by which its broken in quantum field theory Quark propagator satisfies a
gap equation Axial-Vector vertex Satisfies an inhomogeneous Bethe-Salpeter equation Kernels of these equations are completely different But they must be intimately related Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 17 Persistent challenge - truncation scheme These observations show that symmetries relate the kernel of the gap equation nominally a one-body problem, with that of the Bethe-Salpeter equation considered to be a two-body problem Until 1995/1996 people had quark-antiquark no idea what to do scattering kernel
Equations were truncated, sometimes with good phenomenological results, sometimes with poor results Neither good nor bad could be explained Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 18 Persistent challenge - truncation scheme Happily, that has changed and there are now two nonperturbative & symmetry preserving truncation schemes 1. 2. 1995 H.J. Munczek, Phys. Rev. D 52 (1995) 4736, Dynamical chiral symmetry breaking, Goldstones theorem and the consistency of the
Schwinger-Dyson and Bethe-Salpeter Equations 1996 A. Bender, C.D. Roberts and L. von Smekal, Phys.Lett. B 380 (1996) 7, Goldstone Theorem and Diquark Confinement Beyond Rainbow Ladder Approximation 2009 Lei Chang and C.D. Roberts, Phys. Rev. Lett. 103 (2009) 081601, 0903.5461 [nucl-th], Sketching the Bethe-Salpeter kernel Enables proof of numerous exact results Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 19 Dichotomy of the pion How does one make an almost massless particle from two massive constituent-quarks? Naturally, one could always tune a potential in quantum mechanics so that the ground-state is massless but some are still making this mistake However: current-algebra (1968)
2 m m This is impossible in quantum mechanics, for which one always finds: mbound state mconstituent Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 20 Dichotomy of the pion Goldstone mode and boundstate The correct understanding of pion observables; e.g. mass, decay constant and form factors, requires an approach to contain a well-defined and valid chiral limit; and an accurate realisation of dynamical chiral symmetry breaking. HIGHLY NONTRIVIAL Impossible in quantum mechanics
Only possible in asymptotically-free gauge theories Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 21 Some of many Exact Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 22 Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Pions Goldberger Pions Bethe-Salpeter amplitude-Treiman relation Pseudovector components
necessarily nonzero. Cannot be ignored! Solution of the Bethe-Salpeter equation Dressed-quark propagator Axial-vector Ward-Takahashi identity entails Exact in Chiral QCD Miracle: two body problem solved, almost completely, once solution of one body problem is known Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 23 Dichotomy of the pion Goldstone mode and bound-state
f E(k) dressed-gluon propagatorp22) = B(k) dressed-gluon propagatorp22) Goldstones theorem has a pointwise expression in QCD; Namely, in the chiral limit the wave-function for the twobody 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: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 24 Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Dichotomy of the pion Mass Formula for 0 Mesons
Mass-squared of the pseudscalar hadron Sum of the current-quark masses of the constituents; e.g., pion = mu + md , where is the renormalisation point Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 25 Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Dichotomy of the pion Mass Formula for 0 Mesons Pseudovector projection of the Bethe-Salpeter wave function onto the origin in configuration space Namely, the pseudoscalar mesons leptonic decay constant, which is the strong interaction contribution to the strength of the mesons weak interaction
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 26 Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Dichotomy of the pion Mass Formula for 0 Mesons Pseudoscalar projection of the Bethe-Salpeter wave function onto the origin in configuration space Namely, a pseudoscalar analogue of the mesons leptonic decay constant Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 27
Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Dichotomy of the pion Mass Formula for 0 Mesons Consider the case of light quarks; namely, mq 0 If chiral symmetry is dynamically broken, then fH5 fH50 0 H5 < q-bar q> / fH50 0 both of which are independent of mq The so-called vacuum quark condensate. More later about this. Hence, one arrives at the corollary Gell-Mann, Oakes, Renner relation 2 m m
1968 Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 28 Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Dichotomy of the pion Mass Formula for 0 Mesons Consider a different case; namely, one quark mass fixed and the other becoming very large, so that mq /mQ << 1 Then Provides fH5 1/m 1/mH5 QCD proof of potential model result
H5 1/m mH5 and one arrives at mH5 1/m mQ Ivanov, Kalinovsky, Roberts Phys. Rev. D 60, 034018 (1999) [17 pages] Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 29 Dynamical Chiral Symmetry Breaking Vacuum Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs
30 Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Dichotomy of the pion Mass Formula for 0 Mesons Consider the case of light quarks; namely, mq 0 We now have sufficient information If chiral symmetry is dynamically broken, then to address whatvacuum The so-called f f 0 the question of just quark condensate. More < q-bar q> / f 0 is this so-called vacuum quark) dressed-gluon propagator
later about this. both of which are independent of m condensate. Gell-Mann, Oakes, Renner relation H5 0 H5 H5 0 H5 q Hence, one arrives at the corollary 2 m m
1968 Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 31 Spontaneous(Dynamical) Chiral Symmetry Breaking The 2008 Nobel Prize in Physics was divided, one half awarded to Yoichiro Nambu "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics" Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 32
Nambu Jona-Lasinio Model Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961) 345358 Dynamical Model Of Elementary Particles Based On An Analogy With Superconductivity. II Y. Nambu, G. Jona-Lasinio, Phys.Rev. 124 (1961) 246-254 Treats a chirally-invariant four-fermion Lagrangian & solves the gap equation in Hartree-Fock approximation (analogous to rainbow truncation) Possibility of dynamical generation of nucleon mass is elucidated Essentially inequivalent vacuum states are identified (Wigner and Nambu states) & demonstration that there are infinitely many, degenerate but distinct Nambu vacua, related by a chiral rotation Nontrivial Vacuum is Born
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 33 Gell-Mann Oakes Renner Behavior of current divergences under SU(3) x SU(3). Relation Murray Gell-Mann, R.J. Oakes , B. Renner Phys.Rev. 175 (1968) 2195-2199 This paper derives a relation between m2 and the expectation-value < |uu0|u>, where uo is an operator that is linear in the putative Hamiltonians explicit chiral-symmetry breaking term NB. QCDs current-quarks were not yet invented, so u0 was not expressed in terms of current-quark fields PCAC-hypothesis (partial conservation of axial current) is used in the derivation Subsequently, the concepts of soft-pion theory Operator expectation values do not change as t=m2 t=0
to take < |uu0|u> < 0|uu0|u0> in-pion in-vacuum Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 34 Gell-Mann Oakes Renner Behavior of current divergences under SU(3) x SU(3). Relation Murray Gell-Mann, R.J. Oakes , B. Renner Phys.Rev. 175 (1968) 2195-2199 PCAC hypothesis; viz., pion field dominates the divergence of Zhou Guangzhao the axial-vector current Born 1929 Changsha, Hunan province Soft-pion theorem Commutator is chiral rotation Therefore, isolates explicit
chiral-symmetry breaking term in the putative Hamiltonian In QCD, this is m qq and one therefore has Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 35 Gell-Mann Oakes Renner Relation - (0.25GeV)3 Theoretical physics at its best. But no one is thinking about how properly to consider or define what will come to be called the
vacuum quark condensate So long as the condensate is just a mass-dimensioned constant, which approximates another well-defined matrix element, there is no problem. Problem arises if one over-interprets this number, which textbooks have been doing for a VERY LONG TIME. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 36 Note of Warning Chiral Magnetism (or Magnetohadrochironics) A. Casher and L. Susskind, Phys. Rev. D9 (1974) 436 These authors argue that dynamical chiralsymmetry breaking can be realised as a
property of hadrons, instead of via a nontrivial vacuum exterior to the measurable degrees of freedom Craig Roberts: Confinement contains Condensates The essential ingredient required for a spontaneous symmetry breakdown in a composite system is the existence of a divergent number of constituents DIS provided evidence for divergent sea of low-momentum partons parton model. SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 37 QCD Sum Rules QCD and Resonance Physics. Sum Rules. M.A. Shifman, A.I. Vainshtein, and V.I. Zakharov Nucl.Phys. B147 (1979) 385-447; citations: 3713 Introduction of the gluon vacuum condensate
and development of sum rules relating properties of low-lying hadronic states to vacuum condensates Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 38 QCD Sum Rules QCD and Resonance Physics. Sum Rules. M.A. Shifman, A.I. Vainshtein, and V.I. Zakharov Nucl.Phys. B147 (1979) 385-447; citations: 3781 Introduction of the gluon vacuum condensate and development of sum rules relating properties of low-lying hadronic states to vacuum condensates At this point (1979), the cat was out of the bag: a physical reality was seriously attributed to a plethora of vacuum condensates
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 39 quark condensate 1960-1980 Instantons in non-perturbative QCD vacuum, MA Shifman, AI Vainshtein - Nuclear Physics B, 1980 Instanton density in a theory with massless quarks, MA Shifman, AI Vainshtein - Nuclear Physics B, 1980 Exotic new quarks and dynamical symmetry breaking, WJ Marciano - Physical Review D, 1980 The pion in QCD J Finger, JE Mandula - Physics Letters B, 1980 NoREFERENCES references toTO thisTHIS phrase before
19801980 7330+ PHRASE SINCE Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 40 Universal Conventions Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum) The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a nonperturbative vacuum state, characterized by many nonvanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs
41 QCD 0 | qq | 0 1973-1974 How should one approach this problem, understand it, within Quantum ChromoDynamics? 1) Are the quark and gluon condensates theoretically welldefined? 2) Is there a physical meaning to this quantity or is it merely just a mass-dimensioned parameter in a theoretical computation procedure? Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 42 QCD 0 | qq | 0 1973-1974
Why does it matter? Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 43 Dark Energy Two pieces of evidence for an accelerating universe 1) Observations of type Ia supernovae the rate of expansion of the Universe is growing 2) Measurements of the composition of the Universe point to a missing energy component with negative pressure: CMB anisotropy measurements indicate that the Universe is at 0 = 1 0.04. In a flat Universe, the matter density and energy density must sum to the critical density. However, matter only contributes about of the critical density, M = 0.33 0.04. Craig Roberts: Confinement contains Condensates Thus, of the critical density
is missing. SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 44 Dark Energy In order to have escaped detection, the missing energy must be smoothly distributed. In order not to interfere with the formation of structure (by inhibiting the growth of density perturbations) the energy density in this component must change more slowly than matter (so that it was subdominant in the past). Accelerated expansion can be accommodated in General Relativity through the Cosmological Constant, . Contemporary Einstein introduced the repulsive effect ofmean: the cosmological cosmological observations constant in order
to balance gravity of matter so the attractive obs 12 4 universe (10 HeGeV ) discarded it that a static promptly was possible. 8the Gexpansion of the Universe. after the discovery of Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 45 Dark Energy
The advent of quantum field theory made consideration of the cosmological constant obligatory not optional. Michael Turner, Dark Energy and the New Cosmology The only possible covariant form for the energy of the (quantum) vacuum; viz., is mathematically equivalent to the cosmological constant. It is a perfect fluid and precisely spatially uniform Vacuum energy is almost the perfect candidate for dark energy. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 46 Dark Energy Enormous and even greater contribution from Higgs VEV!
QCD vacuum contribution If chiral symmetry breaking is expressed in a nonzero expectation value of the quark bilinear, then the energy difference between the symmetric and broken phases is of order Mass-scale generated by MQCD0.3 GeV One obtains therefrom: Craig Roberts: Confinement contains Condensates QCD 46 10 obs
spacetime-independent condensate The biggest embarrassment in theoretical physics. SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 47 Resolution? Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives 48 QCD 0 | qq | 0
1973-1974 Are the condensates real? Is there a physical meaning to the vacuum quark condensate (and others)? Or is it merely just a mass-dimensioned parameter in a theoretical computation procedure? Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 49 What is measurable? S. Weinberg, Physica 96A (1979) Elements of truth in this perspective Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs
50 Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Dichotomy of the pion Mass Formula for 0 Mesons Consider the case of light quarks; namely, mq 0 We now have sufficient information If chiral symmetry is dynamically broken, then to address whatvacuum The so-called f f 0 the question of just quark condensate. More < q-bar q> / f 0 is this so-called vacuum quark) dressed-gluon propagator
later about this. both of which are independent of m condensate. Gell-Mann, Oakes, Renner relation H5 0 H5 H5 0 H5 q Hence, one arrives at the corollary 2 m m
1968 Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 51 In-meson condensate Maris & Roberts nucl-th/9708029 Pseudoscalar projection of pions Bethe-Salpeter wavefunction onto the origin in configuration space: |PS(k) dressed-gluon propagator0)| or the pseudoscalar pion-to-vacuum matrix element Rigorously defined in QCD gauge-independent, cutoffindependent, etc. For arbitrary current-quark masses For any pseudoscalar meson Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 52
In-meson condensate Maris & Roberts nucl-th/9708029 Pseudovector projection of pions Bethe-Salpeter wavefunction onto the origin in configuration space: |AV(k) dressed-gluon propagator0)| or the pseudoscalar pion-to-vacuum matrix element or the pions leptonic decay constant Rigorously defined in QCD gauge-independent, cutoffindependent, etc. For arbitrary current-quark masses For any pseudoscalar meson Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 53 In-meson condensate Maris & Roberts nucl-th/9708029 Define
Then, using the pion Goldberger-Treiman relations (equivalence of 1- and 2-body problems), one derives, in the chiral limit Chiral limit (0; ) qq 0 Namely, the so-called vacuum quark condensate |PS(k) dressed-gluon propagator0)|*|AV(k) dressed-gluon propagator0)| is the chiral-limit value of the in-pion condensate The in-pion condensate is the only well-defined function of current-quark mass in QCD that is smoothly connected to the vacuum quark condensate. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 54 There is only one condensate Langeld, Roberts et al. nucl-th/0301024, Phys.Rev. C67 (2003) 065206
I. Casher Banks formula: Density of eigenvalues of Dirac operator II. Constant in the Operator Product Expansion: III. Trace of the dressed-quark propagator: Algebraic proof that these are all the same. So, no matter how one chooses to calculate it, one is always calculating the same thing; viz., |PS(k) dressed-gluon propagator0)|*|AV(k) dressed-gluon propagator0)|
m0 Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 55 Paradigm shift: In-Hadron Condensates Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011) Resolution Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, condensates do not exist as spacetime-independent mass-scales that fill all spacetime. So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. GMOR cf.
QCD Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 56 Paradigm shift: In-Hadron Condensates Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011) Resolution Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, condensates do not exist as spacetime-independent mass-scales that fill all spacetime. So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. No qualitative difference between f and
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 57 Paradigm shift: In-Hadron Condensates Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011) Resolution Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, condensates do not exist as spacetime-independent mass-scales that fill all spacetime. So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. Chiral limit No qualitative difference 0
( 0 ; ) q q between f and And Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 58 Topological charge of vacuum
Wikipedia: Instanton effects are important in understanding the formation of condensates in the vacuum of quantum chromodynamics (QCD) Wikipedia: The difference between the mass of the and that of the ' is larger than the quark model can naturally explain. This -' puzzle is resolved by instantons. Claimed that some lattice simulations demonstrate nontrivial topological structures in QCD vacuum Now illustrate new paradigm perspective Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 59 Bhagwat, Chang, Liu, Roberts, Tandy Phys.Rev. C76 (2007) 045203 Charge-neutral pseudoscalar mesons
AVWTI QCD mass formulae for all pseudoscalar mesons, including those which are charge-neutral Consider the limit of a U(Nf)-symmetric mass matrix, then this Algebraic result. formula yields: Very different than Qualitatively requiring QCDs the same as f, vacuum to possess a property of nontrivial topological the boundstructure state Topological charge density: Q(x) = i(s/4) trC F F Plainly, the mass splitting is nonzero in the chiral limit so long as 0 viz., so long as the topological content of the is nonzero! Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs
60 Bhagwat, Chang, Liu, Roberts, Tandy Phys.Rev. C76 (2007) 045203 Topology and the condensate Exact result in QCD, algebraic proof: chiral condensate = in-pion condensate the the zeroth moment of a mixed vacuum polarisation connecting topological charge with the pseudoscalar quark operator Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 61 GMOR Relation
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 62 Expanding the concept of in-hadron condensates Lei Chang, Craig D. Roberts and Peter C. Tandy arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R) GMOR Relation Valuable to highlight the precise form of the Gell-MannOakes Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175 (1968) 2195 o m is the pions mass o Hsbsb is that part of the hadronic Hamiltonian density which explicitly breaks chiral symmetry. Crucial to observe that the operator expectation value in this equation is evaluated between pion states. Moreover, the virtual low-energy limit expressed in the equation is purely formal. It does not describe an achievable empirical situation.
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 63 Expanding the concept of in-hadron condensates Lei Chang, Craig D. Roberts and Peter C. Tandy arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R) GMOR Relation In terms of QCD quantities, GMOR relation entails o mud = mu + md the current-quark masses o S (0) is the pions scalar form factor at zero momentum transfer, Q2=0 RHS is proportional to the pion -term Consequently, using the connection between the -term and the Feynman-Hellmann theorem, GMOR relation is actually the statement Craig Roberts: Confinement contains Condensates
SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 64 Expanding the concept of in-hadron condensates Lei Chang, Craig D. Roberts and Peter C. Tandy arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R) GMOR Relation Using Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273 it follows that This equation is valid for any values of mu,d, including the neighbourhood of the chiral limit, wherein Craig Roberts: Confinement contains Condensates
SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 65 Expanding the concept of in-hadron condensates Lei Chang, Craig D. Roberts and Peter C. Tandy arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R) GMOR Relation Consequently, in the neighbourhood of the chiral limit This is a QCD derivation of the commonly recognised form of the GMOR relation. Neither PCAC nor soft-pion theorems were employed in the analysis. Nature of each factor in the expression is abundantly clear; viz., chiral limit values of matrix elements that explicitly involve the hadron. Craig Roberts: Confinement contains Condensates
SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 66 Expanding the Concept Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 67 Expanding the concept of in-hadron condensates Lei Chang, Craig D. Roberts and Peter C. Tandy arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R) In-Hadron Condensates Plainly, the in-pseudoscalar-meson condensate can be represented through the pseudoscalar mesons scalar form factor at zero momentum transfer Q2 = 0.
Using an exact mass formula for scalar mesons, one proves the in-scalar-meson condensate can be represented in precisely the same way. By analogy, and with appeal to demonstrable results of heavy-quark symmetry, the Q2 = 0 values of vector- and pseudovector-meson scalar form factors also determine the in-hadron condensates in these cases. This expression for the concept of in-hadron quark condensates is readily extended to the case of baryons. Via the Q2 = 0 value of any hadrons scalar form factor, one can extract the value for a quark condensate in that hadron which is a reasonable and realistic measure of dynamical chiral symmetry breaking. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 68 Hadron Charges Hadron Form factor matrix elements Scalar charge of a hadron is an intrinsic property of
that hadron no more a property of the vacuum than the hadrons electric charge, axial charge, tensor charge, etc. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 69 Confinemen Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 70 Confinement Contains Condensates S.J. Brodsky, C.D. Roberts, R. Shrock and P.C. Tandy arXiv:1202.2376 [nucl-th] Confinement Confinement is essential to the validity of the notion of in-hadron
condensates. Confinement makes it impossible to construct gluon or quark quasiparticle operators that are nonperturbatively valid. So, although one can define a perturbative (bare) vacuum for QCD, it is impossible to rigorously define a ground state for QCD upon a foundation of gluon and quark quasiparticle operators. Likewise, it is impossible to construct an interacting vacuum a BCS-like trial state and hence DCSB in QCD cannot rigorously be expressed via a spacetime-independent coherent state built upon the ground state of perturbative QCD. Whilst this does not prevent one from following this path to build practical models for use in hadron physics phenomenology, it does invalidate any claim that theoretical artifices in such models are empirical. Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 71 Paradigm shift: In-Hadron Condensates Void that is truly empty
solves dark energy puzzle Rachel Courtland, New Scientist 4th Sept. 2010 EMPTY space may really be empty. Though quantum theory suggests that a 4 vacuum should be fizzing with particle activity, it turns out that this paradoxical QCD 46 picture of nothingness may not be needed. A calmer view of the vacuum would QCD condensates 8 GN
10 2 also help resolve a nagging inconsistency with dark energy, the elusive force 3H 0 thought to be speeding up the expansion of the universe. Cosmological Constant: Putting QCD condensates back) dressed-gluon propagator into hadrons reduces the mismatch between experiment and theory by a factor of 1046 Possibly by far more, if technicolour-lik) dressed-gluon propagatore theories are the correct paradigm for extending the Standard Model Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 72 This is not the end
Craig Roberts: Confinement contains Condensates SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 73 Simulations with is not observable static quarks Strongly reminiscent of mean-field bag model Mean-field picture of gauge-field action g pictures of the nucleon, popular in 80s. Gauge configurations are instanton-like, and instantons have nothing to do with confinement. What is the dynamically generated confinement length-scale in this
simulation? This is not related in any known way to the length-scale imposed on the simulation by choosing a value of the string tension. Infinitely heavy quarks, repositioned by hand. Natural size of system constituted from infinitely heavy quarks is radius=0 [ r ~ ln MQ/MQ ] Therefore, no dynamical information present. What is hadron spectrum associated with this simulation? There are no quarks, so is there a quark-hadron duality? The latter is critical to the new condensate paradigm. Provide simulation results with realistic quark masses, then one can test the new perspective on condensates present pictures quite likely Craig Roberts: Confinement contains Condensates represent features of hadron interiors. SP, 7-8/05/12: Perspectives in Non-P QCD - 74pgs 74