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PoS(Confinement2018)040 https://pos.sissa.it/ ∗† [email protected] [email protected] [email protected] [email protected] [email protected] Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). Hans Günter Dosch Institut für Theoretische Physik der Universität,E-mail: Heidelberg, Germany Marina Nielsen Instituto de Física, Universidade de SãoE-mail: Paulo, São Paulo, Brazil Alexandre Deur Thomas Jefferson National Accelerator Facility, Newport News,E-mail: Virginia Stanley J. Brodsky Guy F. de Téramond Universidad de Costa Rica, San José,E-mail: Costa Rica SLAC National Accelerator Laboratory, Stanford University, Stanford,E-mail: California Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra PoS(Confinement2018)040 0 n Q un- κ . The re- 5 1. The matching of + B , in agreement with the L 2 = κ 4 M / 2 L controls the Gaussian fall-off of in the QCD running coupling by Q κ − MS Λ exp ∝ ) 2 Q ( defined at all momenta and a transition scale s α ) 2 Q ( s α appears which determines hadron masses and universal Regge slopes. It κ bound state. The superconformal relations also can be extended to heavy-light quark ¯ q q . The result is an effective coupling 2 bosonic meson and fermionic baryonhadron physics. masses The is pion a eigenstate manifestation isture massless of as for a a massless hidden quarks, despite supersymmetry itsmesons in dynamical and struc- baryons. One alsohadronic obtains form empirically viable factors, predictions structure fordistributions. functions, spacelike and distribution timelike amplitudes, and transverse momentum Speaker. This research was supported by the Department of Energy, contract DE–AC02–76SF00515. SLAC-PUB-17345 derlying hadron masses can be connectedmatching to the the magnitude parameter and slope ofQ the nonperturbative coupling to perturbativewhich QCD separates at perturbative large and nonperturbative dynamics. QCDtraditional is sense not – supersymmetrical in the the QCDgluinos. Lagrangian However, when is one based applies on superconformalof algebra, quark meson, one baryon, and obtains and gluonic a tetraquarks unified as fields, spectroscopy equal-massLF not members resulting Schrödinger of squarks equations the nor match same the 4-plet bound representation.The state The equation predicted obtained Regge from trajectories LF holography. have aand universal orbital slope angular in momentum. both The meson thecompares and principal baryon mesons quantum Regge with number trajectories baryons are with identical when orbital one angular momentum The combined approach of light-frontinto holography the and origin superconformal of algebra color provides confinementdicts insight and Lorentz-invariant light-front the Schrödinger QCD bound mass state scale.quantum equations mechanical Light-front for (LF) Schrödinger QCD, holography analogous equation pre- to fortation the atoms of in the de QED. Alfaro, Awhich Fubini key allows and feature a Furlan is mass (dAFF) parameter the procedure toretaining implemen- for appear the breaking conformal in conformal symmetry the invariance of Hamiltonian the andQCD, action. the a When equations mass one of applies scale motion the while dAFF procedure to chiral also implies a unique form of the soft-wall dilaton which modifies the action of AdS sult is a remarkably simple analytichadronic description of structure quark and confinement, dynamics. as well Thethe as same nonperturbative nonperturbative mass QCD parameter running coupling: effective charge determined from measurements of the Bjorken sum rule. The mass scale † ∗ XIII Quark Confinement and the Hadron31 Spectrum July - - Confinement2018 6 August 2018 Maynooth University, Ireland PoS(Confinement2018)040 ], x 1 to − 2 i ] to i x 2 m to the i 2 ∑ spin and provides ζ and 1 supercon- 4 ¯ light-front q 5 z z κ q P k + + 0 0 k P ] and 2 bound state when ] Eq. (1) with the = [ 9 ¯ q + + q p k .[ c ) / = 1 ) z “soft-wall” modification ( x 2 confines the colored con- 2 ( + ˜ z ) 2 t . 2 κ projection of the ) e ζ = z ? What is the analytic form of ζ ( ( n τ U ? What is the full spectroscopy of ψ ) 2 3 . Quark masses add a term ( q is the ˆ M z identical for both mesons and baryons, S , n and ¯ ]. It is also holographically dual [ ) = ) , , = 8 ) light-front holography 1 ζ is identified with the light-front coordinate q L ] ( 2 S z 6 − / ψ ∝ , S S i 2 2 confining potential for heavy quarkonium in the ) + 2 + r M 1 ζ L L σ ( ( both hard and soft space and the dilaton 2 + U 5 κ n ( 2 + 2 mesons: [ ) + κ 1 ¯ q 4 2 2 q ζ − ζ = 4 ] 2 4 6 2 κ L for at all scales, 4 M ( ) . The color-confining harmonic oscillator contribution ) = Q 1 and the principal quantum number + 2 ( s 2 ζ L 1 spacetime quantized using LF time ( α ζ d + d U is the radial coordinate of light-front (LF) theory, − ] ) 7 h x ]. A key feature is the implementation of the de Alfaro, Fubini and Furlan 4 − , 1 3 ( [ harmonic oscillator contribution to the potential x 2 2 ⊥ b ζ 4 = κ ]. A key consequence for chiral QCD is a Lorentz-invariant single-variable 2 5 is the relative orbital angular momentum of the ζ z In this report, I will review recent insights to the fundamental features of QCD that can be Classical gravity theory based on five-dimensional Anti-de Sitter spacetime AdS Although the foundations of quantum chromodynamics (QCD) were developed 45 years ago [ The L using light-front holography. This specific dilaton is mandated by the dAFF procedure. = nonrelativistic limit. [ obtained using a novel theoretical approach based on in both angular momentum the QCD running coupling hadrons in QCD, including tetraquarks, pentaquarks, gluonia,fundamental and frame-independent other nonperturbative exotic wavefunctions states? of What theunderly are the hadronic dynamical observables eigenstates such which as structurequarks functions and and gluons form produced factors? in Howproduce collisions do the remain the final-state confined off-shell hadrons? and What hadronize isexist at the without nature the causing of amplitude huge the level contributions QCD to to vacuum the – can cosmological vacuum constant? condensates LF potential for light quarks becomes the usual the quarks are massless? Why are Regge slopes The potential has the unique form [ where are the quark and antiquark LFL momentum fractions, field theory in physical 3 potential (2) can then be derived using AdS stituent quarks. The eigenvalues of this equation (dAFF) procedure for breakingin conformal the invariance Hamiltonian which and allows theaction a equations [ mass of parameter motion, to while retaining appear the conformal symmetry of the there are fundamental and profound questions whichthe are dynamical not mechanism fully for understood. color For confinement example, whichas what prevents is asymptotic quarks states? and gluons What from appearing isand what the is origin the of color the confining QCD dynamics which mass can scale produce which a gives massless the pion proton its mass, formal algebra Schrödinger bound-state equation the LF Hamiltonian. See Fig. a geometrical representation of conformal symmetry [ Color Confinement and HadronStanley Physics J. from Brodsky Light-Front Holography and Superconformal Algebra 1. Profound Questions for Hadron Physics of its action, where the fifthζ coordinate of AdS space ˜ PoS(Confinement2018)040 , i ]. ]. ] ¯ q 10 ¯ 17 20 q , , ][ in the where , 2 16 19 qq are then b κ [ coupling , H | , 4 n / L 5 2 15 + 18 . The Regge Q [ , H a − n 0 and e 14 + ) Q , GeV 1 n 0 ) ( s 13 s 53 / . , α 1 0 ]. ( at the amplitude level. 12 composite diquark [ = 21 ∝ ) = C H ) κ 2 ¯ 3 b Q H ( → s ¯ q + α provide the LF wave functions q a ]. ) H 1 with equal weight so that there 2 ⊥ 23 k + → , at all scales for any choice of renor- , asymmetries [ B x − ) quark and a ( 22 L ¯ e 2 L Q , C + Q n Q e ( ( ψ s and α σ B L with the QCD coupling [ . A crucial difference with the meson equation 2 2 ˜ z B 2 baryons are also degenerate in mass with L κ e i ] qq [ q | ]. One can also predict the distributions of higher Fock states 20 are represented as a 3 i ] . The meson and baryon Regge trajectories in are irrelevant to QCD, only ratios of masses can be predicted by M qq 0 is massless for massless quarks, despite its dynamical structure [ L q | = is not a fixed parameter – the only parameters entering the light-front = S GeV κ L mesons and the = i L ¯ q are predicted to be identical, consistent with observed hadron spectroscopy. q = | with intrinsic heavy quarks with their L i n ¯ Q 1. This equality of bosonic meson and fermionic baryon masses is a manifestation 1 replaces and − + n with the pQCD coupling then determines B uudQ bound state. The eigensolutions of Eq. (1) | 0 B L ¯ q L Q q ]. Thus the total angular momentum of the quark-scalar diquark proton is carried by the Quark counting rules for hadron form factors and other hard exclusive amplitudes are also a The running coupling of QCD is predicted to have the form Remarkably, a similar LF Schrodinger equation is predicted for baryons by superconformal 3 = is the number of valence constituent fields (the leading twist ) of a meson (n=2), baryon (n=3 ), [ ] with relative orbital angular momentum M H z n tetraquark (n=4), gluonium (n=2,3), or pentaquark (n=5). [ property of these nonperturbative solutions.content One of can mesons, thus baryons, use tetraquarks,falloff counting of and the rules exclusive gluonium. annihilation to cross identify For sections for the example, field the asymptotic power-law nonperturbative domain. This isdefined derived by using the LF conformally holography breaking dilaton The by matching identifying of the the AdS magnitudepoint and derivative of this nonperturbative prediction at its inflection Superconformal algebra predicts that thebaryons resulting have generalized a parton universal structure distributions [ ofsuch mesons as and The pion with of a hidden supersymmetrybaryon in wave hadron function physics. has two Superconformal components algebra with also predicts that each slopes in identical when one comparesL the mesons and baryons spectra with orbital angular momentum is equal probability forJ the quark to havequark’s spin orbital angular parallel momentum. and This antiparallelLagrangian. is a to The novel the realization total of thetetraquarks. baryon chiral spin symmetry Thus of the another QCD into remarkable “4-plet” consequence supersymmetric is representations. thedynamics organization using Solving of this for the LF relativisticdynamics formalism hadron in hadron is nonrelativistic spectrum Schrödinger spectroscopy analogous theory. and to solving for atomic hadron spectroscopy and malization scheme. We have alsotogether used with effective BFKL, nonperturbative ERBL LF and holographictribution DGLAP wave amplitudes evolution functions, and equations, hard to predict exclusive structure amplitudes functions, beyond dis- the transition scale 11 Color Confinement and HadronStanley Physics J. from Brodsky Light-Front Holography and Superconformal Algebra provide a surprisingly accurate representation of meson spectroscopy for as a is that underlying hadron structure and dynamics in thethe nonperturbative conversion domain, of as well the as hadronization, off-shellSince constituent the quarks units to of the mass mesons holographic predictions are the quarkModel. masses predicted by the Higgs mechanism in the Standard algebra where the baryons QCD; thus the value of PoS(Confinement2018)040 Dis- . 0 = i 0 | conservation, z LF J H ], and one predicts 26 0 conformal series. The = terms in the pQCD series into β ]. Thus in the front form, QCD β The convergence of theoret- 25 0 [ ] which shows how a mass scale can = 5 LF i Figure 1: ical methods forhadron generating spectroscopy a and model dynamicscolor of confinement with and meson-baryonpersymmetric su- relations. 0 ] and it reduces to the Gell Mann-Low scale | 32 µν ]. T | 3 27 ]. 0 h 24 1 2 = z i ⌥ 1 2 1 = ) ) =1 n i Unique Unique g z ) ( ( ⇤ ⇣ L ⇥ ⇥ of the action ( 2 2 +

+ 2 z Conformal Symmetry i Conﬁnement Potential! Conﬁnement Light-Front Holography q z M M S . M L at each vertex [ te 2 ⇥ 9 = = age z P + b =1 ⇥ ⇥ 1) n i ) )= L ) ) z g ⇣ Sta x ⇤ S ( ( (

S ζ V V = ⇤ + ck ) + o z z p q (1 ⇣ + + ]. A primary problem for perturbative QCD analyses is how to set the renor- 2007 ( F S S x Scale can appear in Hamiltonian and EQM EQM and in Hamiltonian appear can Scale L 20-24, 2 ( 2 2 ugust U A , 2 h 2 d d idge without affecting conformal invariance of invariance conformal without affecting action! = = 31 = d d Cambr  , + QCD z z , p 2 ing 2 Explor J eac J L 2 +2 4 ⇣ 30 2 4 , ⇣ 2 1 4 z 2  29  2 , 2 + ⇣ Single variable d )= e d ⇣ 28 Front Schrödinger Equation Schrödinger -Front Light ( appears which determines universal Regge slopes and hadron masses in the absence of the = U ⇥ ) κ z AdS/QCD AdS/QCD ( Conformal symmetry also leads to a rigorous way to eliminate the renormalization scale am- In Dirac’s front form, the vacuum state is the state of lowest invariant mass Light-front perturbation theory has many important simplifications for computing scattering In the following sections I will discuss these points in detail. Conformal symmetry is an underlying symmetry of QCD. If one sets the quark masses to zero A key tool is the remarkable observation of dAFF [ ' e de Alfaro, Fubini, Furlan: Furlan: Fubini, Alfaro, de Fubini, Rabinovici: Rabinovici: Fubini, Soft-Wall Model • • PMC generalizes the BLM procedure to all orders [ the running coupling. The resulting pQCD series then matches the malization scale of the QCDfor running physical coupling observables. in order The toway Principle achieve to precise of set fixed-order the Maximal predictions renormalization Conformalitying scales (PMC) the order-by-order ambiguities provides for associated a any with systematic perturbative theresulting QCD conventional predictions renormalization process, are scale-setting eliminat- procedure. independent of The renormalization the group invariance. choice of The renormalizationquark scales flavors scheme, of are set a the order-by-order by QCD requirement absorbing couplings of the nonconformal and the effective number of biguity [ zero contribution to the cosmological constant [ appear in the Hamiltonian andsymmetry the of equations the of action. motion When ofscale one a applies theory the while dAFF retaining procedureHiggs the to coupling. conformal chiral light-front QCD, a mass amplitudes perturbatively, including explicit unitarity, recursion relations, overall 2. Conformal Invariance of QCD and the Principle of Maximum Conformality in the QCD Lagrangian, theIn theory effect, has the no classical evident chiral mass QCD scale, theory and is it conformal. is manifestly scale invariant. Color Confinement and HadronStanley Physics J. from Brodsky Light-Front Holography and Superconformal Algebra and limits on the change in connected vacuum diagrams do not appear,effects so associated with the vacuum are contained in the hadron wavefunctions [ PoS(Confinement2018)040 ] 35 , 34 ]. In the , and other 26 33 p , m / 27 ρ ]. The Higgs LF m 36 of the renormalized MS Λ is both causal and frame- LF ], where the time variable is i 9 0 | function vanishes. Specifically, it a term proportional to the dilation ] provides a novel solution for the function. The resulting relation is 5 β H β to fulfill the algebra of the of the generators of the 0 limit. The divergent renormalon series does not 4 ] and zero cosmological constant [ K 25 → C 0 [ N = LF i 0 | µν ], which was originally derived for conformal theory, provides a T larger than measured. Nontrivial vacuum structure does not appear | 33 0 0 can at best only predict ratios of masses such as 42 h = q along the light-front, the light-front vacuum m c / z + t ] has no energy-momentum density, so it also gives zero contribution to the cosmo- = 36 and the special conformal operator + D x into the Hamiltonian of a conformal theory without affecting the conformal invariance of κ The remarkable work of de Alfaro, Fubini, and Furlan [ The Crewther relation [ A fundamental question for QCD is the origin of the mass of the proton and other hadrons conformal group. In theacquires case a of confining harmonic one-dimensional oscillator quantum potential; however, mechanics, afterthe a action the redefinition remains resulting of conformal. the Hamiltonian time variable, the time zero mode [ origin of the hadron mass scalescale in QCD. dAFF have shownthe that one action. can introduce The a essential nonzerooperator step mass is to add to the Hamiltonian logical constant. in QCD if oneLF defines Hamiltonian. the vacuum In state fact, as in the Dirac’s eigenstate boost of invariant “front lowest form” invariant [ mass of the QCD when the quark masses are zero. It is often stated that the mass scale appear. The PMC satisfies renormalizationconditions derived group from invariance the and renormalization all group.retical of It uncertainty the for thus pQCD other systematically predictions eliminates self-consistency and a increasesbeyond major the the theo- sensitivity Standard of Model. experiment to new physics relates these observables forindependent physical of QCD the with choice of nonzero on the the renormalization choice of scheme the atalso initial any scale connect finite is other order, negligible. and physical Similar theconvention-independent observables scale-fixed precision dependence at “commensurate tests of scale their QCD. relations” physical momentum scales, thus providing new 3. The Origin of the QCD Mass Scale and de Alfaro, Fubini and Furlan Procedure perturbative theory generates thetransmutation” nonperturbative solution QCD is mass problematic since scale;pendent, the however, whereas perturbative hadron this scale masses “dimensional is cannot renormalization-schememeasure depend de- hadron on masses a in theoretical MeV convention. units;volts. however, It QCD Thus is has no conventional QCD to knowledge at ofdimensionless quantities. units such It as is electron- often arguedand that gluon the condensates QCD in mass the scale QCDical reflects vacuum constant the state. a presence However, of factor such quark of condensates lead 10 to a cosmolog- independent; one thus has case of the Higgs theory,“zero the mode” traditional in Higgs the vacuum LF expectation theory, value analogous (VEV) to is a replaced classical Stark by or a Zeeman field [ remarkable connection between two observables when the Color Confinement and HadronStanley Physics J. from Brodsky Light-Front Holography and Superconformal Algebra setting procedure for Abelian QED in the connects the non-singlet Adlerinelastic function electron to scattering the at Bjorken leading sum twist. rule coefficient The for “Generalized polarized Crewther deep- Relation" [ PoS(Confinement2018)040 , | ¯ – q z is = q L ) 47 ) ) = | S 2 2 2 , z Q ] have ] have ]. The Q Q ( L ( 6 ( and in- 1 1 s max 15 g 38 g α , ) provides ζ α α = 5 max 14 L , = . This dilaton 2 ˜ 13 z L 2 , κ underlying hadron + 12 ] for form factors at κ e 41 = , ) ˜ z 40 ( φ e can be used as a starting point controlling the evolution of the 08 GeV which sets the interface . . This identification “light-front 5 s 5 0 ]. This connection can be done for Λ ± 17 87 . is holographically dual to gauge theory 0 5 with the LF radial coordinate = z 0 scheme, The mass scale in the QCD running coupling by matching its Q in the LF Hamiltonian, where ) MS MS 1 5 Λ metric – the “dilaton” − S 5 is the radial variable of the front form and ) . Deur, de Téramond, and Brodsky [ + . x 2 3 L ( − 2 ]. This is in analogy to the non-relativistic radial Schrödinger 1 κ ( 2 x 2 ⊥ b , which determines the mass scale of hadrons and Regge slopes in with the light-front Hamiltonian theory automatically introduces an κ ], anti-deSitter space in five space-time dimensions (AdS = ] formula for form factors in AdS 5 8 2 39 ζ are the LF spins. The resulting holographic prediction is the single variable ]. , in agreement with the effective charge determined from measurements [ z 0 can be systematically reduced to Eq. (1), a differential equation in a single S 46 2 = ]. ; where , + κ z . The same procedure can be applied to relativistic quantum field theory using q ζ 4 37 2 45 L / m , ζ 2 4 = Q z 44 κ when one identifies the fifth coordinate ˜ J , − 5 43 , defined at all momenta. See Fig. with ) ] of the Bjorken sum rule. See Fig. exp z 42 2 The identification of AdS Remarkably, the identical LF potential and the same LF equation of motion are obtained As noted by Maldacena [ The application of dAFF then leads in fact to a color-confining LF harmonic oscillator poten- ) S 49 0 Q , ( ( s s predicted by pQCD. The matchingboth of its the value and high its and slope low –between momentum then perturbative determines transfer and a regimes nonperturbative scale of hadron dynamics [ bound states for is the LF orbital angular momentum [ large momentum transfer. Additional referencesrefs. and [ reviews of LF Holography may be found in troduces a specific modificationalso of leads the to AdS a Gaussian functionalα form of the nonperturbative QCD running coupling: perturbative QCD coupling. The high momentum transfer dependence of the coupling predicted nonperturbative form to the perturbative QCDα regime. The result is an effective coupling LF radial variable 48 the zero quark mass limit, can be connected to the mass scale shown that a mass gapthe and dAFF a procedure fundamental to color LF Hamiltonian confinement theory scale in also physical appear 3+1 when spacetime. one The extends LF equation for equation for bound states such ascausal, positronium frame-independent in light-front QCD. Hamiltonian Thus formalism inunique – the the form case confining of LF QCD(3+1) potential –LF has using quantization the the [ a geometrical representation of thefor conformal a group. conformal theory Thus suchquantized AdS as using chiral light-front QCD. time, In Dirac’s fact frontand transition AdS form. form factors Exclusive are hadron given in amplitudes, terms such of convolutions as of elastic light-front wavefunctions [ holography” also provides a nonperturbative derivation of scaling laws [ from AdS also shown how the parameter any choice of renormalization scheme, such asmasses the can thus be connected to the parameter extra spin-dependent constant term 2 max 4. Light-Front Holography tial, where again the action remains conformal. In fact, de Téramond, Dosch, and Brodsky [ Color Confinement and HadronStanley Physics J. from Brodsky Light-Front Holography and Superconformal Algebra light-front Drell-Yan-West formulae for electromagnetic and gravitationalto form the factors Polchinski-Strassler is [ identical PoS(Confinement2018)040 , is 1. 14 ) , = 0 13 S = , GeV GeV + L with the 5- 12 017 019 10 L GeV . . 0 0 = 2 ± ± = J 007 Q (GeV) . κ , 0 Prediction: J 339 332 4 contribution to . 0 . GeV ± / . Color confine- to the pion mass 2 MS scheme 2 =0 2 =0 x = 08 m 2 0 Perturbative QCD (asymptotic freedom) . 513 Q κ . confining potential PerturbativeQCD 0 n MS bound states is thus MS κ 5-Loop ( since ⇤ Experiment: See Refs. [ ⇤ r − ± ¯ 2 =0 q 0 . Fit to Bj + DHG Sum Rules:SumDHG + FittoBj ρ  Q σ q ) 87 1 − . 2 perturbative . The synthesis of holo- − which is analogous to the Q exp . The eigenvalues for the ) =0 Transition scale Q Transition ( Non ) Holographic QCD 0 1 1 1 (the number of nodes in the 1 = g Q n 2 − 2 α π −  Q / S 4 J s of each quark to the background ( α + 2 e Connecting the nonperturbative run- m κ -1 L

( 1 0

(Q)/ 0.8 0.6 0.4 0.2 π α 2 × ) κ 2 x m 2 Q with the same slope 4 All-Scale QCD Coupling All-ScaleQCD ( ⇡ . One can identify the 1 . The pion distribution amplitude has the s g 2 L + ) ↵ 2 ⊥ . Remarkably, the pion 2 ] ) k µ i 2 ζ p 4 loop QCD prediction for the effectiveBjorken charge of sum the rule Figure 3: ning coupling 16 ζ i contribution to the LF Hamiltonian – the square ( κ The mesonic spectrum of meson bound states. Nonzero quark masses ap- ∑ i . ] U ¯ 6 q ) 2 q 2 m = ( ) = , / 2 x 2 + 2 S 2 ⊥ Q ζ 47 k ( [ + 0, it gives a negative contribution i M U L for all ∑ 2 = 10 ) 4 + predicted / J 2 n λ GeV Q Q (GeV) ( , from the 2 2 54 e . ⊥ ) κ 2 κ k = 4 , where =0 , 4 ⇥ Q /  x / ζ ( ) 2 ( 1 Q g Q ( M ) = α Deur, de Teramond, sjb Teramond, de Deur, 0. The LF potential contains a term 2 n ψ − AdS s ] which replaces the usual VEV of the standard time “instant form”. The , ]. In the heavy quark limit, one recovers the usual in the nonperturbative domain, which then evolves by ERBL evolution to ]. 1 L = (2007) 36 7 ) ( 18 q 2 x [ / exp F3 m 2 M pseudoscalar pion bound state can emerge, despite its composite structure. − = Q ¯ 1 q ; they do not factor as functions of ( 2 q π x 0 for / (pQCD) world data JLab CLAS Hall A/CLAS OPAL s / / / / / M g1 g1 g1 g1 p 2 α = Modified AdS AdS GDH limit Lattice QCD (2004) Sublimated gluons below 1 GeV Sublimated z 2 π  ∝ -1 + m e ) 10 0 1 Comparison of the nonperturbative run-

Analytic, deﬁned at all scales, IR Fixed Point Fixed Analytic, deﬁned at all scales, IR

0.6 0.4 0.2 0.8 s

x (Q)/ at infinite = ( ) ' π ) e x ] of the effective charge Q φ ( ⇥ The eigensolutions of the LF Schrödinger equation generate both the mass spectrum and the s − 49 , 1 ective charges for Q < 1 GeV efective charges to the higher twist corrections captures dilaton AdS/QCD ( squared which exactly cancels the positivepotential. contributions from Thus the light-front LF holography kinetic explainshow energy another a and fundamental zero confining question mass in hadron physics – pear in the “LF kinetic energy” (LFKE) light front wave functions described as Regge trajectories in both theradial principal wavefunction) quantum and number the orbital angular momentum massless: hyperfine spin-spin splitting interaction in atoms.However, This in term the vanishes case for of the the pion with ment is a consequence of the light-front potential x meson spectrum are the LFKE as arising in thezero-mode Higgs Higgs theory field from [ the coupling resulting nonperturbative hadronic LF wavefunctions are Gaussianmass functions of squared the parton invariant dependence of the Bjorken sum rule. “LF Schrödinger equation” in graphic QCD and conformal quantum mechanics is illustrated in Fig. form for heavy quarkonium [ Figure 2: 48 ning coupling by light front holography with measurements [ of the invariant mass of the constituents: Color Confinement and HadronStanley Physics J. from Brodsky Light-Front Holography and Superconformal Algebra PoS(Confinement2018)040 ) 1 L + . As + B } n † L 1. This ( , -baryon S 2 , B ∆ + , a feature κ S L (with anti- L 4 { 2 2 / − / 3 2 Pauli matrix ψ 1 and ) = . = × L L = + , J n Ψ ( K 2 V − p ~ M · E and σ ~ + . The 4-plet contains two } m 4 † Q = , ]. The predicted meson, baryon − Q { Ψ 54 superconformal algebra 2 / 1. Superconformal algebra thus pre- 1 , with the same confinement potential − 2 = ]. In effect, one has obtained extended z M 2 4 H κ L , + 3 = e ]. This ansatz extends the predictions for the are identical. The extension of the supercon- B L 52 L , 7 ]. The predicted spectrum, 51 and meson Regge trajectory with the is not a fixed parameter, since only ratios of masses n 53 for nucleons, is remarkably consistent with observed κ ω ) / 1 and a lower component ρ (with parallel quark and baryon spins) and diquark cluster; they each have two amplitudes + + + L ], a nonconformal Hamiltonian with a mass scale can then be Ψ ψ , the supersymmetric analog of the dAFF procedure. When ex- qq + 1 have the same mass as the baryons in the supermultiplet. An 51 ]. K n + ( ω 55 2 B √ κ L . The value of 4 + ]. Remarkably, the predicted meson equation is identical to the LF with the soft-wall dilaton 5 = 4 5 Q , M ) = 3 L L → , n Q ( spin-0 or spin-1 2 C ]. The superconformal group in one dimension has an elegant 2 M ¯ 3 50 for each baryon, corresponding to internal orbital angular momentum ± Ψ The combination of superconformal algebra and light-front dynamics thus leads to the novel Bound-state LF Schrödinger equations for both baryons and mesons can be derived from su- Another advance in LF hadron physics is the application of with its superpartner baryon or tetraquark with quarks to a M C prediction that hadron physics has supersymmetricThe properties excitation in spectra both spectroscopy of andlie relativistic dynamics. on light-quark linear meson, Regge baryon trajectoriesDetailed with and predictions identical for tetraquark slopes the bound inspectrum tetraquark states are the spectroscopy presented all radial in and Ref. and comparisons [ orbital with quantum the numbers. observed hadron parallel quark and baryon spins) haveby equal quark Fock orbital state angular probability; momentum thus in theerties the proton’s nonperturbative of spin domain. is the carried Predictions nucleons for are thefor discussed static mesons prop- in and Ref. [ hadronic spectroscopy: The Regge-slopes in and tetraquark masses coincide ifL one identifies a meson withdicts internal that orbital mesons angular with momentum are predicted by QCD. formal structure to include the spin-spin interaction is described [ example of the mass degeneracy of the perconformal algebra [ Schrödinger equation with theLF same holography confinement from potential AdS and spin term that was derived from of the underlying conformal symmetry of chiraland QCD, originally Sohnius discovered [ by Haag, Lopuszanski, representation. The conformal Hamiltonianrepresented as operator anticommutators and of the fermionic generators special conformal operator canobtained be by shifting tended to hadron physics in the lightand front baryons this procedure and leads a to zero universalrepresentations confinement mass of for pion mesons the superconformal in algebra the [ chiral limit [ property of the baryon LFWFswhich is has the both an analog upper of component the eigensolution of the Dirac-Coulomb equation and spin term. See3 Eqs. (1) and (2).with have The equal baryonic Fock eigensolutions correspond statethe to probability proton’s Fock bound – state states a components of feature of “quark chirality invariance”. For example, hadron spectrum to a “4-plet”diquark – baryon, consisting and of a a diquark-antidiquark mass-degenerate tetraquark, quark-antiquark as meson, shown a in quark- Fig. Color Confinement and HadronStanley Physics J. from Brodsky Light-Front Holography and Superconformal Algebra 5. Superconformal Algebra and Supersymmetric Hadron Spectroscopy shown by Fubini and Rabinovici, [ entries trajectory is shown in Fig. PoS(Confinement2018)040 C ]. and ]. 11 ) , 2 57 ∆ ]. The Q 10 2 me- ( 56 identified / 2 , 3 ) F ω 1 LF wave- 1 / ]. ! = 55 2 5 ! 11 4 ! ρ = $ J , B ! 7 2 L L 3 3520 $ ( , 4 ! ! 5 2 $ M , + ccd ! 3 2 L 4 $ Ξ f !! !! " 3 , , where the composite ! !! # 1 orbital excitation of 0 and , ! 4 1 2 i a % ] $ 3 2 = = $ 3 , % cq See Refs. [ !! " 2 Ω !! # 1 2 L [ L , . $ 3 c Ρ 1 | " 2 double-charm tetraquark. In ! 3 2 2 f " 1 ! + # $ , i with its superpartner baryon 2 B ] superpartner trajectories a GeV Comparison of the ¯ ! L q M ¯ 2 c Ω " 0 # , L = ⇢ Ρ ][ M 4 3 2 1 0 6 5 M cq Dosch, de Teramond, sjb Dosch, Teramond, de [ L | son Regge trajectory withbaryon the trajectory. Superconformalbra alge- predicts the degeneracy ofand the baryon meson trajectories if onemeson identifies with a internal orbitalmentum angular mo- Figure 5: with . For more details, see Refs. [ ) 8 ]. 3415 ( 55 cc (21) Ξ ect of ,thus 2 ↵ m 1 2 . . Candidates 9 e + to the LF kinetic . The partners of =1 ] diquark cluster; the tetraquarks in the 4-plet are bound states of C + 2 i i ¯ 3 qq P 0 ]. The existence of both components is also necessary to generate x [ m 2matrix: , ! B ,J qq ⇥ ! )operate C =1 .Opencirclesrepresent , 38 n i ) and also the mass of the ¯ 3 ¯ matches the mass of the double-charm baryon } =0 q ee uu ,L 17 T bound states, baryons =0 ! T † P P ) ) '$ &% I ) R - ¯ , Tetraquark q 1 = B q I,J L B 2 +1) †

connects quarks and anti- m = , = B R + 3525 L +1 T B ( † λ ( L L B B

( c ( R , B T 0 c h M

,L ,L e e h + ee ee { B B Baryon Baryon

12 '$ &% '$ &% - +1) ++ ) B (1260), respectively. † spin-0 or spin-1 B ) and the Hamiltonian ( 1 ] mesons, baryons and tetraquarks are also hadronic states L R 1 a L ]. Mesons are The 4-plet representation of mass- ( 20 C +1 = , plus two bosonic wave functions, namely the meson 2X2Multiplets Hadronic + 6 ¯ 3 B B M Equal Weight: L=0,L=1 EqualWeight: B ]

L ¯ C q

u e ,L ( 3 q [¯ ( the 1 M M ! ] that the natural way to include light quark masses in the Meson Superconformal Algebra . These states can be arranged as a 2 ! '$ &% (980) and Proton: |u[ud]> Quark + ScalarQuark+ Proton:|u[ud]> Diquark and C i 0 T 3 is one unit higher than that of the positive-chirality (leading-twist) 11 q ¯ c (1233) have the quantum numbers f +

Bosons, Fermions with Mass! Equal † B c Thus one predicts supersymmetric hadron spectroscopy – bosons and fermions with the same The predictions from light-front holography and superconformal algebra have been extended is a scalar diquark, is predicted to be identical to the mass of the B | R

] cq . by SELEX and a tetraquark candidate the diquarks and anti-diquarks. In the case of a nucleon, the overlap of the mass and twist. Thefermionic members hadron of eigenvalues, but the alsotheir 4-plet supersymmetric not light-front relations only wavefunctions. between have their identical The eigenfunctions masses baryonic – for eigensolutions the correspond bosonic to and bound states of 3 [ the fact, the mass of the quarks to a functions in the Drell-Yan-West formula is required toanomalous have a magnetic non-zero moment Pauli [ form factor the pseudo-T-odd Sivers single-spin asymmetry in deep inelastic lepton-nucleon scattering [ Figure 4: degenerate hadronic states predictedmal by algebra superconfor- [ Although conformal symmetry is stronglysupersymmetric broken mechanism, by the which heavy transforms quarkinto mesons each mass, other, the to still holds basic baryons and underlying givesspectrum (and remarkable of connections baryons light, and heavy-light to and mass double-heavy degeneracy tetraquarks) hadrons. acrossmeson, the The baryon entire excitation spectra and of tetraquark the heavy boundwith quark states identical continue slopes to in lie thethe slope. on radial For universal and example, linear orbital the Regge mass quantum of trajectories numbers, the but lightest double-charm with baryon an increased value for are quark – antidiquarkare bound diquark-antidiquark states bound and states. tetraquarks metric The ladder supersym- operator diquark clusters of the same color representation. to mesons, baryons, and tetraquarks with strange, charm and bottom quarks in Refs. [ Color Conﬁnement and HadronStanley Physics J. from Brodsky Light-Front Holography and Superconformal Algebra 6. Supersymmetric Hadron Spectroscopy for Heavy Quarks effective supersymmetric properties ofquark QCD mesons, can baryons and be tetraquark used states [ to identify the structure of the heavy evaluated using the modiﬁed wave functions. This prescription leads to + The supersymmetric quadruplet 2 B

m (1320) and the (1235) and the nucleon; it has quantum numbers 2 1 b a According to this analysis, the lowest-lying light-quark tetraquark is a partner of We have argued in [ and the tetraquark It is interesting to note that in Ref. [ 9 B within the same multiplet. energy. The resulting LFproviding a wave relativistically function invariant is form for thenthe nonzero the modified quark hadronic masses by wave for functions. the thevalue squared The factor hadron e masses of is then given by the expectation hadron mass spectrum is toand leave add the the LF additional potential term unchanged of as the a first invariant mass approximation for these states are the 2.4 Inclusion of quark masses and comparison with experiment on which the symmetry generators ( the the function of a baryon component spinor wavefunction Figure 1: quarks, full circles antiquarks.multiplet. The tetraquark Notice has that the the same mass LF as angular its momentum baryon of partner in the the negative-chirality component wave PoS(Confinement2018)040 ]. is a and 59 5 , T 20 ]. where 45 T π → ] using the extended − 50 e + e and internal orbital angular mo- space, has provided new insights, ]. The combination of light-front n 5 55 , ]. One can thus use counting rules to 11 23 , 22 9 ], one obtains a unified spectroscopy of meson, 51 . The set of “Light-front Schrödinger equations” pre- 3 × ], match the bound-state equation obtained from AdS 3 ], uses the eigensolutions of a color-confining approxima- 4 , ∼ 3 58 ¯ 3 in the radial quantum number representation same slope C ) 3 1. Their LF wavefunctions, the eigensolutions of the LF Schrödinger equations, ( ]. Quark counting rules for hadron form factors and other hard exclusive amplitudes + SU B 23 L for mesons, baryons, and tetraquarks. In fact, the meson and baryon Regge trajectories L = M L The light-front holographic approach, with the constraints imposed by the superconformal al- The combination of conformal symmetry, light-front dynamics, the dAFF procedure (confor- The QCD Lagrangian is not supersymmetrical; it is based on quark and gluonic fields, not One can also observe featuresheavy-light of as superconformal well symmetry as in double-heavy mesons thefield and spectroscopy theory baryons and with [ dynamics superconformal of has algebra supersymmetric thus properties leads in to bothof the spectroscopy their novel and wavefunctions prediction and dynamics. form that One factors hadron can in physics test exclusive reactions theare such similarities also as a property of theseidentify nonperturbative the solutions field [ content ofthus mesons, gives baryons, a remarkably tetraquarks, simple and analytictive gluonium. description hadronic of structure Light-front quark and holography confinement, dynamics. as well as nonperturba- gebraic structure, predicts novel supersymmetric relations between mesons,of baryons, the and tetraquarks same parity aspirically members viable of predictions the same for 4-plet spacelikedistribution representation and amplitudes, of and timelike superconformal transverse hadronic algebra. momentum form distributions Em- factors, have also structure been functions, obtained [ tion to QCD (such as LFin holography) DLCQ, as thus the incorporating basis the functions, full rather dynamics than of the QCD. plane-wave basis used not only into the physics underlying color confinement,QCD but coupling also and into the the form QCD of mass the scale. nonperturbative A comprehensive review is given in Ref. [ dAFF procedure of Fubini and Rabinovici [ dicted from superconformal algebra [ LF holography. They incorporate color confinementical and features other of essential spectroscopic hadron and physics,trajectories dynam- including with a the massless pionmentum for zero quark massand and spectra linear are Regge identical whentum one compares mesons withhave baryons the same with underlying orbital universal angular form.Light-Front momen- A Quantization” new (BLFQ) method [ for solving nonperturbative QCD “Basis tetraquark [ mal quantum mechanics) and its holographic embedding in AdS baryon, and tetraquarks as equal-massunderlying members conformal of symmetry the of same semi-classicaldynamics underlying 4-plet QCD the representation, for supersymmetric massless reflecting connection quarks of the fundamental mesons, as baryons well and as tetraquarks from the the color 7. Summary squarks nor gluinos. 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