PoS(QCDEV2015)003 odd Sivers http://pos.sissa.it/ − T 8 GeV ) provides ideal elec- . 4 ' s √ I will also discuss evidence that the antishad- . ] − µ + µ [ ∗ [email protected] Speaker. owing of nuclear structure functionsarguments is why non-universal; shadowing and i.e., antishadowing flavor phenomena may dependent. betum incompatible I and with will other the momen- also sum present rulesnew for insights the into nuclear the parton distribution hadronQCD functions. mass coupling scale, I in the will the hadron also nonperturbative massperconformal briefly domain algebra spectrum, review predicted leads to the by remarkable functional supersymmetric light-front relations form holography, between of mesons and and the how baryons. su- troproduction kinematics for many novel teststive of domains. QCD in These both include the tests perturbativetions; and of measurements nonperturba- of the the quark QCD flavor running dependence couplingdeep of at inelastic soft the structure scales; function; nuclear measurements measurements structure of of func- thefunction; exclusive diffractive the contributions to identification the of “odderon"features contributions; of tests light-front of holography the asof spectroscopic well open and as and dynamic “meson-nucleon hidden supersymmetry"; charmexotic hadronic the states states production in such the as heavy-quarkquarks. pentaquarks, threshold One tetraquarks domain; can and also and study even theof fundamental octoquarks nuclear production features wavefunctions, containing the of of “color charm QCD transparency" at ofstrangeness hard JLab12 and exclusive such charm" processes, content as and the of the “intrinsic the “hiddenimental proton color" searches wavefunction. for In “dark addition, photons" current at on-going JLabexotic exper- can atom also be of used QED: to produce “true and muonium" detect a long-sought The 12 GeV electron beam energy at Jefferson Laboratory ( ∗ Copyright owned by the author(s) under the terms of the Creative Commons c QCD Evolution 2015 -QCDEV2015- 26-30 May 2015 Jefferson Lab (JLAB), Newport News Virginia, USA Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). Stanley J. Brodsky Novel QCD Phenomena at JLab SLAC National Accelerator Laboratory Stanford University E-mail: PoS(QCDEV2015)003 0” = ]. J 17 odd Sivers measured in ], the “color − ) 2 18 T Q Stanley J. Brodsky , x ( D 2 8 GeV are above the F . / 4 ) 2 ' ]; measurements of diffrac- ], where Lorentz boosts are Q s , via interference with Bethe- ]; verification of the “ 10 x 27 ]; measurements of the QCD √ 0 ( photoproduction and odderon- , 8 13 p [ 0 Fe , γ = 2 26 7 π [ F ] provides ideal kinematics for test- , c W ¯ 1 → ]. One can also study fundamental sX 6 / s p z ]. I will also present arguments why 17 ∗ 7 + → γ ] at CERN will extend electroproduction , t p 6 ]. These include tests of the flavor depen- ∗ exchange) deep inelastic lepton scattering is 25 = , 5 γ ∗ τ γ 28 2 ] and the “intrinsic strangeness and charm" content ]. Finally, I will show how superconformal quantum 19 16 , , in which case boosts are dynamical and can even change t ]. In addition, current on-going experimental searches for 29 asymmetry in 22 s , vs ¯ 21 ]; measurements of exclusive contributions to the ]. s , 11 24 20 , 23 ]; tests of the spectroscopic and dynamic features of light-front holog- [ ] 15 − , ]. µ 4 exchange) and neutral-current ( 14 + , ∗ µ 3 [ , W 2 ] predicts supersymmetric relations between mesons and baryons in QCD [ ]; the identification of “odderon" contributions in 32 12 ], as well as “meson-nucleon supersymmetry" [ 16 The JLab fixed target facility is an important compliment to a high intensity electron-ion col- The ratio of the iron to deuteron nuclear structure functions Jlab12 can also provide ideal electroproduction kinematics for many novel tests of QCD in The new 12 GeV electron beam at Jefferson Laboratory [ I will also discuss in this report the indications that the antishadowing of nuclear structure function [ Heitler amplitude [ shadowing and antishadowing phenomena arefor incompatible nuclear with PDFs. momentum I will and also other brieflyspectrum, review sum new and insights rules the into the effective hadron QCD mass effective scale,obtained charge the from hadron in mass light-front the holography nonperturbative [ domain which have been of the proton wavefunction [ studies to the multi-TeV domainbe where studied. the One studies collisions the of sameand top boost-invariant the light-front quarks, ultrarelativistic wavefunctions of and proton the at electroweak rest-frame the bosons proton on LHeC can the despite very quarks different of kinematics the – proton the at electron fixed scatters light-front time mechanics [ raphy [ lider. The proposed LHeC electron-proton collider [ running coupling (effective charge) in thetive nonperturbative deep domains [ inelastic scattering [ energy-independent real part of Compton amplitude in features of QCD at JLab12 such as the ‘ “hidden color" of nuclear wavefunctions [ “dark photons" at JLab can also“true be muonium" used to produce and detect a long-sought exotic atom of QED: kinematical, not at a fixed “instant" time 2. Is Antishadowing Flavor-Dependent? both the perturbative and nonperturbative domains [ functions is nonuniversal, i.e., flavor dependent [ Novel QCD Phenomena at JLab 1. Introduction ing many aspects quantumElectroproduction chromodynamics (QCD), experiments the in fundamental thethreshold theory JLab12 for of energy producing hadron range open physics. nuclei and of hidden exotic hadronic charm states states, such ascharm including pentaquarks, quarks the tetraquarks, [ and production even “octoquarks" on containing protons and dence of the antishadowing of nuclear structure functions [ Pomeron interference from the transparency" of hard exclusive processes [ particle number. charge-current ( PoS(QCDEV2015)003 2 X at + . of 0 ν 5 . V 0 b j ] is in < x → ]. Since b j 28 ∝ A 8 x ) µ , ,[ 2 7 < interference , Q 1 , 6 channel. This . x et al. t ( n Stanley J. Brodsky 2 F − is ‘shadowed’ by the in the 0 to matrix elements of ) b 2 X destructive ∞ N 0 Q e , x in the nuclear interior → ] description of shadowing ( constructive interference → 2 p b 2 34 N Q F eA , and the Glauber cut gives another located on the front surface of the i a N ], the shadowing of the nuclear structure 6 , 1 Reggeon exchange in the hard subprocess. 0 36 = q 0 , I e 3 35 → 1 Reggeon. Thus antishadowing of nuclear structure eq is a spectator. The interference is destructive since the = sees two beams: the primary virtual photon beam and a I ]. In this case the two-step process involves the contribu- . In effect, the interior nucleon b N ];. 7 N V 8 , , 6 from isospin 7 0 , a scatters intact and stays in the nuclear ground state. The vector 6 a VN N . One can then account for the shape and magnitude of the antishad- → a N . One can account for the magnitude and shape of the observed nuclear ∗ a γ 2 accounts for the Kuti-Weisskopf behavior N , where / where in this case 0 a 1 X . Although the SLAC and NMC deep inelastic lepton scattering data shows both ' VN then interacts inelastically on a second nucleon 1 R → constructively V → α b ] in order to satisfy the momentum sum rule. ]. The phase of the Reggeon amplitude - its “signature factor" – is determined by a N ∗ 33 N 37 γ ∗ . Thus the interior nucleon [ i γ . This two-step process interferes coherently and destructively with the usual one-step DIS b j x X In contrast, antishadowing can be understood as arising from the In fact, these assumptions are wrong in the Gribov-Glauber [ Sum rules for DIS processes are analyzed using the operator product expansion of the for- → b N amplitude diffractive DIS amplitude due to Pomeron exchange has phase the two-step and one-step processes [ Reggeon with owing enhancement of the nuclear structuredomain. function measured However, in the physicsquark of has its antishadowing own is specific coupling flavor to dependent the since each quark and anti- charge conjugation and crossing. Thetudes result interfere is that in this case, the two-step and one-step ampli- meson system shadowing from this mechanism [ function measured in deep inelastic lepton-nucleusof colisions two-step is and due one-step to the processes.diffractive deep In inelastic the scattering two-stepnucleus: process, (DDIS) the on incoming a current nucleon first produces factor of front-surface nucleon tion to diffractive DIS function, unlike Pomeron-dominated shadowing, is predicted tothe be weights flavor dependent of [ quark flavors aresured different, the in antishadowing the of charged the current nuclearthe structure DIS SLAC function NuTeV mea- and reaction can NMC differ neutraltagging from the current the flavor reaction. of antishadowing the measured This struck in quark novel in physics the could be tested at JLab-12 by local operators such as theother energy-momentum distributions tensor. can then The be moments evaluated as of overlaps the of structure the target function hadron’s and light-front wavefunction ward virtual Compton amplitude, assuming it reduces in the limit the secondary vector hadronic system 3. Is the Momentum Sum Rule Valid for Nuclear Structure Functions? shadowing and antishadowing, the NuTeV measurement of the charged current reaction Novel QCD Phenomena at JLab illustrated in fig. does not appear to show antishadowing.direct This contradiction important to observation the by usual Scheinbein assumptionof that the the nuclear nuclear structure light-front function wavefunction measures andthe the usual is square assumption thus that independent the of nuclear theeach modifications other probe. of [ shadowing It and is antishadowing also must contradicts balance and shadowing. In the Gribov-Glauber theory [ small PoS(QCDEV2015)003 c X → b . The N ¯ c and high c 2 + Q V . For example, 2 Stanley J. Brodsky on a nuclear target. A ∗ γ → A ∗ γ ] is directly sensitive to the rescat- ]. 12 ] which do not affect the moments. 45 42 the lepton-quark scattering, give non-trivial produced by the diffractive DIS interaction ]. These “lensing" corrections survive when OPE analysis. V 11 . However, the propagation of the vector system ∞ after 2 4 Q → / 2 are characterized by a longer LF time which scales as ] to the measured parton distribution functions (PDF), Q -odd Sivers effect [ X ]. The phases of the resulting DIS amplitude and OPE 44 T , 41 → , 43 b scales as 1 N 40 A , + ∗ γ V 39 , → 38 A ∗ γ are large since the vector gluon couplings grow with energy. Part of the phase can For example, the pseudo- 2 . 2 Q the lepton interacts with the struck quark. Because of the rescattering dynamics, the ) p and + 2 q after . Thus the leading-twist multi-nucleon processes that produce shadowing and antishadowing W 2 It is useful to think of electron-proton collisions at JLab in terms of the collision of the virtual Diffractive DIS is leading-twist and is the essential component of the two-step amplitude It should be emphasized that shadowing in deep inelastic lepton scattering on a nucleus in- However, final-state interactions which occur The Glauber propagation of the vector system can then exchange a minimally off-shell gluon with a quark of the proton target, in analogy to = ( and Proton Structure Functions c W produced by the diffractive DIS interaction on the front face and its inelastic interaction with the 2 / a real or virtual photonor emitted by ¯ the electron can readily couple to charm quark pairs photon structure function with the proton structure function, as illustrated in fig. 4. Representing Inelastic Lepton-Proton Scattering as a Collision of Virtual Photon which causes shadowing and antishadowing ofthe the nuclear momentum PDF. and It is other important sumremain to rules valid analyze when derived whether these from dynamical theOPE rescattering OPE is corrections derived expansion assuming to in that the the terms nuclear LFtual time of PDF Compton separation are local amplitude between included. the operators virtual The photons in the forward vir- volves the nucleons at orThis near geometrical the bias front is surface not –matrix built elements the into of the nucleons local frame-independent facing currents. nuclear the Thusantishadowing LFWFs incoming the appear used dynamical lepton to to phenomena invalidate beam. the evaluate of sum the leading-twistin rules shadowing the for and leading-twist nuclear analysis PDFs. of The deeply same virtual complications Compton occur scattering matrix elements reflect the real phasetion of defines the the stable “static" target contribution hadron’s [ wavefunction. This approxima- be associated with a Wilson line as an augmented LFWF [ nucleons in the nuclear interior in a nucleus are evidently not present in the transverse momentum distributions, etc. The resultingthe momentum, properties spin of and the other hadron’s sum light-front rules wavefunction. reflect both on the front face and its inelastic interaction with the nucleons in the nuclear interior 1 Novel QCD Phenomena at JLab (LFWF), the hadronic eigensolutionfor of hadronic the form LF factors Hamiltonian, [ as in the Drell-Yan-West formulae contributions to deep inelastic scattering processes at leading twist and survive attering high of the struck quark. Similarly,gluon diffractive deep after inelastic the scattering quark involves has the exchange been of struck a by the lepton [ occurs DDIS amplitude acquires arescattering complex corrections phase lead from to Pomeron nontrivialthey and involve “dynamical" physics Regge contributions aspects exchange; of to thus the the scattering final-state measured process itself PDFs; [ i.e., V W PoS(QCDEV2015)003 q . l f f - s e e r s o r e 2 e e e e e e h y k d d n n plane n - e a l o o t m i i h e h n F a r ¯ n e h h h h l h E b q i o i e i n l w t t r e q e a t t t t t l a s c t r t o D t b t e a l r w o t i t , a l r a o n d n n u u f t c a a n P t r i u y u y h b o r n o n e r a B l , the n q e l a 3 v f d c e i u e h , t m p r o l r e c X f p i r n w a e e t 0 e b n h n D s a n h Stanley J. Brodsky 2 e ) e a o l e e - o r r n p t h t a t o i d , a e w r a i d s F . r i ff t a g h n o i e t t → o s a t s n i i n p s o t o d n b i x o r r n n o b n n l c n u o d a e t i F a d ep c e s a e o W n u a ], one can understand the l Stan Brodsky t r o n m i t f o
h u d l i h , i D s r t a h e o d r t l o 47 d o r o n c t t , l t t ) . n t e . In the case of the LHeC, the i t V a d e P t a c l c n s c b V o h p s fi s e g o m s e n h d e s i e t e a i n h i d a e − scattering does not appear to show ) e w s l e e n e t g e e c t τ C a e t g a c r i g 2 u e i T e a X l o i c + f c g a A s d o t s G r e n ν u a n can be used to understand the pro- τ , d n y u a i h m i r z e i l t g y u u i a d i i e l 2 s m s p t t p c a → s 3 ( a 5 o r → . a a r t r n r u N s . n d u s f a t l A t n p e y F v d s u e s D GeV t ∗ µ s ]. m 2 3 n a o t u t t Quark Specific? Quark a e collisions will tend to be aligned with the a n V i e p t γ e d t e e s t e a e p y 28 D F c s e p n e h e h 5 d y h u l s r h n ∗ o s i a .[ t n S flux tube will be controlled both by the flavor t / s t x u > t g g m γ t e P T q d e l a r e d I t ¯ e r r a a q i e u n fi ! i r a t a = f q l c t 5 c l v V t description, where the dynamics of the collision is u a e u et al r F d r p o t 2 s a s d i D a e a e e ) o o r ( s i s S 2 l a i o d h - 0 t W a s e s F r i N d t m e I S F e T i e r t p ( s t e e . Thus electron-proton collisions provide an important 1 , ν = of the virtual photon with the flux tube between the I Q d o r c SLAC/NMC data SLAC/NMC t h s 2 n u u h e - o o d c p 3 z a e e D c D q h t i s Q a e q i n a C n A r - b ]. This physics is obscured if one utilizes the conventional F D T o a N t n t e s h h e s i n V P n e + -pair production: s u r o r s r a ν 46 t a t a s r M r τ o 0 Tests of Novel QCD at Jlab o and ¯ e . s f r y ) e h t r i y e e q t p o e t d e e n g s B q t l s t o N v f t x d Is Anti-Shadowing T g = h s s t p n n b e c V b t o n n c / n m a n f e a i e e i t i i + u r i n l a e o o c n l n s a e t Extrapolations from NuTeV from Extrapolations y T q o o o i h i t C d fi t i t m ( ( a e c e a a o t t r l e a s N g s c h d G o i e l f r A f i u i c r . h h e e ! s e o u m t r e u c a t c s p t h . As Bjorken, Goldhaber and I have discussed [ s L e n l n e r r P s 2 o s o h c r s r o φ n F c e a S o u r o r o s u h e s h e t e i t e f f d t u c ) o a t s t a u r t o r ! e d i e i Scheinbein, Yu, Keppel,Scheinbein, Yu, Morfin, Olness, Owens No anti-shadowing in deep inelastic neutrino ! scattering inelastic in deep anti-shadowing No D e h s > h t v l : F s a o n e d r d c e s t - t h o t d n e 2 s - a a n e a r e P a i m 2 n o c w i D t s w e h l a t h T v r u d s h QCD Evolution QCDEvolution a i e c e e o e o c t e g t a l JLab, May 26,2015JLab, m h P t Q a t n ) r t r a . t e i d e d a c h t e 2 pair and the photon virtuality t Comparison of nuclear structure functions measured in charge and neutral current deep inelastic o i s h r s e r 6 p a a u o r a f , c l t h u ¯ l a w t q t t e n t t e χ diquark of the proton. Maximum multiplicity occurs when the flux tubes are aligned at the a g o 4 n n p e o r d o q m t i c n s d e a i e d n x e e s h t c o e 1 o c i The collision of structure functions illustrated in fig. a e i qq e l d ( e d t F s y u s a n r d r r h l n c 1 h r f n c o i t r w b i t n g e i ( e u p a e t u e e virtual photon can first coupleand to then top emit quark a pairs Higgs which particle, can etc. exchange [ a minimally off-shell gluon of the laboratory to study the physics underlying ridge phenomena in QCD. Coulomb exchange in Bethe-Heitler “infinite momentum frame" attributed solely to the proton’s parton distribution function. electron scattering plane. The properties of the Figure 1: lepton scattering. The NuTeV chargedantishadowing. current The measurement compilation is from Scheinbein duction of high multiplicity eventsgluonic in flux electron-proton tube collisions connecting as the due to the interactions of the occurrence of the “ridge" phenomena producedspective: at high RHIC multiplicity in events proton-proton caused collisionsover by from all this the rapidities per- activations of on the bothcreated colliding the by flux trigger the tubes side will virtual and extend photonhadronic away is final side. aligned state with In produced the the in electron case high-multiplicity scattering of plane. Thus the ridge of the Novel QCD Phenomena at JLab and same azimuthal angle e a u - t p u t a v r . , o s ) r s b 1 e d m ff h e e e e c f n n o O s t n o n n i p u l e . l n s n a e e d 4 Q r h ; o a e n o c i g . f q d c d u e r o y r t i e n x u
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p ? C = ( p ions 2 φ 2 ]. Stanley J. Brodsky W x, k proton or proton 52 ( , ame 51 p,A f
. The rate is enhanced at diquark-antidiquark struc- c s B. Features of the produc- C 3 ! ¯ 3 p at JLab-12 is above the open C and ¯ ], in analogy to nuclear-bound γ x ider ider c E 55 p ]. This analysis of multi-scale pro- l ⇥ ]. The electroproduction of the M 48 ] the 3 [ 2 . It is also advantageous to utilize the 2 50 ¯ c , Collider + b j c p co x x 2 - 49 q + = 2 q ¯ ˆ q s M ! 6 can also be electroproduced near threshold in ex- = > ], as illustrated in fig. ) (A). When one is close to threshold, 2 ¯ u ) 3 53 om the e om the p , ¯ , cu c 2 ? f + | [ pair is multiple-connected to the valence quarks of the pro- ) q ¯ c p c 0 x, k = ( X ( ) 3872 ( s ⇤ 2 ] or a meson-meson molecule [ 0 → 2 q X Electron-Ion Colliders: Electron-Ion ! p , (
is the relative velocity of the ∗ e’ ⇤ γ 54 v Virtual Photon-Ion like photon virtuality, virtuality, photon like -quark-interchange amplitude for a typical open charm exclusive channel - is illustrated in fig. u ) ]. The strong attractive color binding of the diquark-antidiquark model gives Perspective Perspective cdu 57 , where ( e s c , 2 Front-surfacedynamics: shadowing/antishadowing Λ v , diagrams where the various primary flavors 56 ) 2 ) q q plane aligned with lepton scattering planeq q plane ~ cos aligned with lepton scattering ¯ cu ψ ( / Interactions at an electron-ion collider viewed as the collision of a photon structure function (real 0 J ¯ D M variable space The available CM energy Tetraquarks such as the + → p p ∗ M quarkonium [ ( ton become dominant. The multi-connected diagramswhich are dominates the basis the for charm intrinsic charm structureFermi [ motion function of at a nuclear large target.old The cross because section of for open the charm Coulombic isthreshold further gluonic by enhanced interactions near the thresh- between Sudakov-Sakharov-Sommerfeld the scale effect of due order to multi-gluoncesses exchange uses at BLM/PMC the renormalization scale soft was setting observed with [ a substantial cross section at Cornell close to threshold [ tion cross section canantidiquark be bound used state to [ analyze the composition of themaximal tetraquark binding. as As a Hwang, 3 Lebed, and I have shown [ clusive reactions such as Figure 2: or virtual) with a proton or nuclear structure function. 5. Charm Production at Jab12 Novel QCD Phenomena at JLab γ charm threshold. The PoS(QCDEV2015)003 " + " > " ψπ trans- / J nS are more ] Diquark Diquark ¯ - NN cuudd | c cc pentaquark [¯ ¯ u> A → p > ¯ + cu c Lebed, Hwang, sjb c and ¯ + Z | X(3872) ⇡ Diquark State? vs Molecular ! approach New decays to hadronic c Lebed, Hwang, sjb ]. Stanley J. Brodsky 0 elastic scattering. 2 0 decays
¯ cuudd p Ψ | + on a deuteron target decay begins to occur ⇡ pp " ’ vs J/ + c > ! Ψ Z u ) → C. It is even possible to ¯ q> ¯ size C ¯ d c u c - 3 3 See ref. [ l ] ¯ cq ¯ . p d c - c u (3872) + l | [¯ u ψ d u diquark Model diquark C p / - X ¯ 3 ] C C ¯ J c c ¯ 3 3 cu ¯ ccuududd ! Production at Threshold ([ decay compared to | decays + p c Ψ is illustrated. (B) Contribution to the 9 GeV + ⇤ Z . c π Diquark Anti Diquark ! 0 ’ vs J/ Λ 11 ¯ Ψ antidiquark. The ψ D > tetraquark to a pion plus charmonium state if + c C Formation of charmonium at large separation: of charmonium at large Formation ⇤ Dominance of overlap with large Dominance Z ) 3 ¯ → → p d ] lab ¯ ¯ c p + c d is illustrated in fig E ∗ c Z cu [ Tetraquark Tetraquark γ octoquark can account for the strong c ( Dominance of Dominance Λ + c > ] 7 Z D. The electroproduction of a charmed n 0 3 ] with eight quarks ¯ D 4 [ ! ]. (C) Exclusive electroproduction of a ] 2 n → 0 . Since this occurs primarily when the diquark and antidiquark ¯ c ¯ D ccuuduud diquark and a [ D | + ⇤ ) ∗ C π will also be at relatively large separation. Thus the 0 γ 3 c ] D c ) ¯ cu cuudd ⇤ [ n ](¯ and ¯ 0 cud quarkonium state than the more compact n ( ¯ c 0 ) D c c c ψ ⇤ cu at low relative velocity at low relative ) (¯ 0 Charm Factory! Charm cu d u (¯ D u ¯ c u ¯ c u 0 d D +[ quark interchange quark interchange c ! ⇤ overlap to form the ¯ p . The existence of the d ⇤ e ! ] c c and u d Λ ⇤ 58 ] and , (A) Open charm can be electroproduced or photoproduced at JLab12. The quark-interchange n ⇤ u ⇤ 0 3 p D JLab JLab 12 GeV: A ¯ D [ Open Charm ProductionOpen Charm at Threshold Create pentaquark on deuteron on deuteron pentaquark Create Open Charm ProductionOpen Charm at Threshold → D on a deuteron target. (D) Modelit for is the a decay bound of the state composed of a when the match the size of the pion, the Figure 3: amplitude for a typical open charm exclusive channel exclusive electroproduction of a tetraquark [ likely to form the larger size pentaquark on a aelectroproduce deuteron an target “octoquark" bound state [ Novel QCD Phenomena at JLab ture can account for the observeddecay. dominance of The the mechanism is illustrated in fig. e verse spin correlation observed atSee the ref. charm [ threshold in polarized PoS(QCDEV2015)003 ] ]. ], 30 16 29 . The c / z ]. These + 62 [ t 0 space, and the = p 5 τ ρ Stanley J. Brodsky bound-state eigen- with the light-front space with the spe- can be derived [ in the light-front in- ]. The supercharges → ¯ z q 5 2 J q meson gives excellent p 32 ζ ∗ 4 ρ γ κ . and internal orbital angular 4 n of the ) ⊥ k , . The equation predicts that the pion x ) ( 2 ρ / S ψ + electroproduction L ρ + ] have shown that a mass gap and a fundamen- n ( 59 8 . The result is a single-variable frame-independent 2 ) x κ 4 appears; it sets the confinement and the hadron mass − space provides a geometrical representation of the con- is consistent with the Belle data for the photon-to-pion 1 κ ( 5 ) ) = x x S bound states, a “Light-Front Schrödinger Equation" [ 2 ⊥ , b ¯ − L q , ] to effective QCD light-front equations for both mesons and q 1 = n ( ( x 2 64 2 ζ , p M π 17 f , ∝ , where one identifies the fifth dimension coordinate 63 where ]. The prediction for the LFWF ) 2 0 is massless at zero quark mass, The Regge spectra of the pseudoscalar z x ζ 2 61 ( 1 mesons are predicted correctly, with equal slope in the principal quantum κ = π + φ S = e S = L . The same light-front equation for mesons of arbitrary spin . The five-dimensional AdS = L ζ n and the internal orbital angular momentum. The predicted nonperturbative pion dis- (A). Only one mass parameter 5 n mesons and their valence LF wavefunctions are the eigensolutions of a frame-independent ¯ q Thus the combination of light-front dynamics, its holographic mapping to AdS One of the most fundamental problems in quantum chromodynamics is to understand the ori- q 0 and vector = number tribution amplitude S eigenstate The bound state equation, the Light-Frontvalues Schrödinger for massless Equation. quarks are The mesonic predictions for the observed features of diffractive baryons by using the generalized supercharges of superconformal algebra [ scale in the chiral limit, asHolography" well not as only the predicts length meson scalenamics: which and light-front underlies baryon hadron wavefunctions, spectroscopy vector structure. successfully, meson “Light-Front factors, but electroproduction, and also distribution valence hadron amplitudes, structure dy- form functions. The LF Schrödinger Equations for baryons and mesons transition form factor [ relativistic equation of motionanalogous for to the nonrelativisticFront radial Schrödinger Schrödinger Equation equation incorporates in colordynamical quantum confinement features and mechanics. other of essential hadron The spectroscopic physics, Light- Regge and trajectories including with a the same massless slope pionmomentum in for the radial zero quantum quark number massfrom and the holographic linear mapping ofcific the dilaton “soft-wall profile model" modification ofcoordinate AdS dAFF procedure provides new insightturbative into QCD the coupling, physics and underlying the color QCD confinement, mass the scale. nonper- A comprehensive review is given in ref. [ results can be extended [ connect the baryon and mesonmanner: spectra each and meson their has internal Regge angularSee trajectories momentum fig. to one each unit other higher than in its a superpartner remarkable baryon. formal group. It is holographically dual to 3+1 spacetime using light-front time gin of the mass scaleFor which example, controls if the one range setsin of the the color Higgs QCD confinement couplings Lagrangian, and of andhave the quarks the a theory to hadronic finite is mass. zero, spectrum. conformal then de at Teramond, no the Dosch, mass classical and parameter level. I appears [ Nevertheless, hadrons Novel QCD Phenomena at JLab 6. Color Confinement and Supersymmetry in Hadron Physics from LF Holography tal color confinement scale canthe be formalism derived of from de a Alfaro, conformallyresulting Fubini covariant light-front action and potential when Furlan has to one a light-front extends uniquevariant Hamiltonian form impact theory. of variable a Remarkably, harmonic the oscillator derivation of the confining LF Schrodinger Equation is outlined in fig. PoS(QCDEV2015)003 . 2 ⇥ − 1 ) b ) 1 ( (B). x ( − ⇤ 2 ⇥ ⇥ x 5 ) b b ) M = mesons ( ) x = 1 (1 L ) x ⇤ ¯ QCD ⇥ q x b ⇥ 2 ⇥ q b = ) = ζ ) 1 (1 ) = x x, QCD z (1 x = ( ⇥ ( B ⇥ 0 b ⇥ z z z x ⇤ L ) ]. The dilaton holographically = x, z (1 = ( ( 0 5 x ⇤ ⇥ z z z which is defined z 66 c Stanley J. Brodsky for is equivalent to 3 2 / , where ⇥ ) P k =0 2 b 2 ⇥ z 2 0 ζ , ) z b + ) + ζ ) q 0 Q 0 ( 4 x P < + x ( k ⇤ ⇥ P κ 1 t b ) m s g + 2 = 2 ) 1 (1 α = ) x Azimuthal Basis Azimuthal QCD Q Q = 0 x ⇥ ⇥ potential! ( ) b s + ln P ⌅ + ) (1 = x, k d z P (1 = ( b d ( 0 x = , ⇥ z z z x ⇤ ed Confining AdS/QCD Sums an # diagrams infinite = ⇤ trajectory is shown in fig. = Coupled Fock states + ( = i ∆ P Fix x ⇧ ⇥ u 2 ) 2 ]. ⇣ and retarded interactions retarded and / ( Effective two-particle equation Eliminate Fockhigher states 31
0 to reduce the dynamics to a single variable 2 . The comparison between the meson and 5 is the fifth coordinate of AdS = z q M 1) ) m k with its superpartner baryon with > 9 )= for , including its spin-J dependence, is derived from the x, ) where S ( M ⇣ ) , x ζ ( L 2 ( 2 LF | ⊥ − z + to an effective two-body eigenvalue equation for k 1
2 2 U ( ⇤ κ of the interpolating operators for the meson and baryon x > 2 ) L + B e ( ⇣ M Ψ M L | ( 2 2 = + U = M ) 3 > = + k D D = +2 > 2 x, ( M 2 | Ψ L | L 2 ⇣ ) 4 LF ⇣ Regge trajectory with the spin-3 4 LF LF QC + QE 4 ] H LF kinetic energy 2 I LF ω ¯ AdS/QCD: / q 1 LF H = e q H ρ H V ] has emphasized, the QCD running coupling can be defined at all momentum τ )= + ]. The light-front harmonic oscillator confinement potential + + ⇣ 65 2 59 ) 2 ( 2 x ⇣ Light-Front QCD m d U d 0 LF + (1 2 Semiclassical first approximation to QCD H x k ( [ ⇥ Derivation of the Effective Light-Front Schrödinger Equation from QCD. As in QED, one reduces QCD . See ref. [ L ζ is conjugate to the As Grunberg [ 2 ⊥ b ) from measurements of the Bjorken sumsatisfy rule. At asymptotic high freedom, momentum transfer, obey suchrelated the “effective charges" to usual each pQCD other renormalization without group scale equations, ambiguity by and commensurate can scale be relations [ soft-wall AdS/QCD model with the dilaton a linear confining potential for heavy quarks in the instant form [ derived from superconformal algebra are shownbaryon in masses fig. of the Superconformal algebra predicts the meson andson baryon with masses are internal identical orbital if angular oneNotice identifies momentum that a the me- twist superpartners are the same.partners Superconformal are identical, algebra and also thus predicts theyfactors. have that These identical features the dynamics, can such LFWFs be their of tested elastic for the and spacelike transition super- form form factors at JLab12. 7. The QCD Coupling at all Scales scales from a perturbatively calculable observable, such as the coupling bound state equation. The confining potential Figure 4: the LF Heisenberg equation by systematically eliminating higher Fock states.x One utilizes the LF radial variable dual to Novel QCD Phenomena at JLab PoS(QCDEV2015)003 ) 2 Q with ( 1 s g M with its 2 α L 10 4 M / 1 ! 2 L 2 5 ! 11 GeV Q Q (GeV) ! $ meson Regge 54 e B . ! 7 2 L = . This matching $ ω =0 , ⇥ 0 . The magnitude / 4 ! / ! 5 2 ) ) 2. The meson and Stanley J. Brodsky Q ρ 2 $ Q / M , ( ! Q 1 3 2 L ( Deur, de Teramond, sjb Teramond, de Deur, 4 $ f 1 AdS s ± !! !! " 3 , ! !! # s , g ! 4 1 2 1 a α (2007) % = $ 3 2 z $ / 3 , J F3 % !! " 2 Ω !! # 1 2 , $ 3 Ρ " 2 ! 3 2 2 f " 1 ! (pQCD) world data JLab CLAS Hall A/CLAS # $ OPAL , / / / / / 2 g1 g1 g1 g1 2 are the baryon quark-diquark LFWFs superpartner trajectories a Modified AdS AdS GDH limit Lattice QCD (2004) Sublimated gluons below 1 GeV Sublimated z GeV 2 ! ± which underlies the hadron mass scale. 2 -1 Ω + " 0 # ψ , 10 e
1 0 Analytic, defined at all scales, IR Fixed Point Fixed Analytic, defined at all scales, IR
κ
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0.8 0.6 0.4 0.2 M s (Q)/ = 1 0 6 5 4 3 2 ]. (B). Comparison of the ' ) e Dosch, de Teramond, sjb Dosch, Teramond, de Q ( ⇥ 64 s , ective charges for Q < 1 GeV efective charges to the higher twist corrections captures dilaton AdS/QCD ]. 17 Running Coupling Running from Light-Front AdS/QCD Holography and , 17 10 , 63 63 22 11 sjb 11 ! G G ]. GeV G GeV κ J 67 + J
024 016 . .
2 See ref. [ J 0 0 2 S=1/2, P=+ S=1/2, . M 2 ± ± M Same Same 10 both chiralities chiralities both 1 = See refs. [ M = ! . 339 341 J − . = . + +1 Expt: J 1 to the nonpertubative scale Q (GeV)
B Deur, de Tèramond, de Deur,