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PoS(LC2019)030 . 0 = q m https://pos.sissa.it/ appears which determines κ eigenstate is composite but yet has zero mass for ¯ q q , in agreement with the effective charge determined from measurements 2 κ 4 ∗† / 2 Q − exp ∝ ) 2 Q [email protected] ( s Speaker. Supported in part by the Department of Energy, contract No. DE-AC02-76SF00515. . I review applications of superconformalof algebra, conformal -front symmetry to holography, and spectroscopythe an and traditional extended dynamics. sense form QCD – is the notnor QCD supersymmetrical gluinos. Lagrangian in is However, based its onmal hadronic algebra, eigensolutions reflecting and conform the gluonic underlying to fields conformal a symmetrysuperconformal – representation of algebra not chiral provide of squarks QCD. a superconfor- The unified eigensolutions Regge of of spectroscopy of the , same , and parity anduniversal Regge twist slope. as equal-mass The members pion of the same 4-plet representation with a Light-Front Holography also predicts theα form of the nonperturbative QCD running coupling: universal Regge slopes, hadron massesextended in conformal symmetry the which absence has of a conformallying the invariant mass Higgs action scale even coupling. appears though in an the The underly- the Hamiltonian. result heavy quark Although is mass, conformal the an symmetry supersymmetric is mechanism, strongly which broken to transforms by tetraquarks), to still baryons holds (and andof light, gives heavy-light remarkable and mass double-heavy degeneracies . across the spectrum of the Bjorken sum rule.as One spacelike also and obtains timelike hadronic viable form predictionstransverse factors, for momentum structure tests functions, distributions. of distribution hadron amplitudes, The and dynamicsperconformal combined such algebra approach also of provides light-front insight into holographyfinement. the and origin su- of A the key QCD tool massHamiltonian is scale and and the the color equations dAFF con- of principle motionWhen which while one shows retaining applies the the how conformal dAFF a symmetry procedure mass of to scale the chiral QCD, action. can a appear mass in scale the † ∗ 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). Light Cone 2019 - QCD on16-20 the September light 2019 cone: from hadronsEcole to Polytechnique, heavy Palaiseau, France ions - LC2019 Stanley J. Brodsky Color Confinement and Supersymmetric Properties of Hadron Physics from Light-Front Holography Stanford Linear Accelerator Center, Stanford University, Stanford,E-mail: CA, 94309 PoS(LC2019)030 X × 0 q p ~ 0 · e p , . . S ~ 1 t ) 2 → 1 x m and ≤ − + : the ep 1 i ( 2 ⊥ + i − x x k + k + P i k = ∑ 2 = = i x M + P ≤ Stanley J. Brodsky are conserved. Thus ⊥ P ~ 0 and 0 ], the coherent diffractive The LF wavefunctions of the invariant mass squared 5 ≥ ]. . , as well as and , z 4 i z i i ∞ | , z S k 2 3 P m ]. One also can demonstrate an + + → x z i 9 + + 0 i c . Light-Front wavefunctions encode hadron 2 ⊥ L 0 k k i ; they are thus off-shell in the total P i c ∑ = ∑ / = z + i = k = + ]. z , shadowing and antishadowing of + J P 2 q t ] 10 p function, incorporate the Wilsonfinal lines which and/or involve initialLFWFs. state interactions, Adopted from as anand well illustration C. by as Lorcé B. [ the Pasquini Figure 1: structure and underlie hadronicthe observables Drell-Yan-West Formula such for as elasticform and factors, inelastic structure functions,distribution, generalized etc. parton Observablessuch with as diffractive deep complex inelastic scattering phases, and the Sivers pseudo-T-odd spin correlation ~ µ i = k 0 [ i ], a concept which allows all of the tools and + . They encode the underlying structure of bound ∑ 1 = x i ]. 2 1 are the Fock state projections of the eigensolution H 8 − = [ , Q + + Ψ 7 2 | k = P ⊥ do appear alone as a separate factor in the LFWF; the Position space In addition, 2 P H i τ . 2 = ⊥ M 1 − k i mo- space x − = = r a P i i in the nonrelativistic limit Factorization Theorems Factorization DGLAP, ERBL Evolution DGLAP, x + H t i Transverse density in position ]. When one takes a photograph, the object is observed at a P . The LF 3-momenta ngul 2 Ψ ∑ 0 | a where FFs GPDs = Momentum space Momentum P i 2 n QCD | rbital H H M -particle Fock state. The LFWFs are thus functions of the invariant o is Poincaré invariant; i.e., independent of the observer’s Lorentz frame. Light-Front Wavefunctions Light-Front n underly hadronic observables hadronic underly Ψ c h PDFs

/ R GTMDs out z can appear at a vertex in a renormalizable theory. This leads to new rigorous direction, in contrast to ordinary Wick helicity. Only one power of orbital = ab + ) = z ) TMFFs Charges z i i t L λ b rks ,

i ) = i , the time along the light-front [ + ⊥ c τ i , k 0 ~ i

/ rema , 1

R i z b

i TMDs , instead of energy = k

x TMSDs z x , = i ( + are conserved at every vertex, essential covariant kinematical constraints. The LF spins i ( ral + i P x i reduces to ordinary time H n t b x

( =1

⊥ n Longitudinal R n i n i n i − τ i Ψ k Diffractive DIS from FSI = ~ x Gene mentum 0 i momentum space momentum P + ∑ Transverse density in Hadronic LFWFs are defined at fixed One of the most important theoretical tool in high energy physics is Dirac’s light-front time x Transverse = = form factors Sivers, fromT-odd lensing = Weak transition transition Weak − ⊥ hadrons LF time appear in the LF Fock states, with selection rules for the spinimportant dependence property of of scattering quantum amplitudes applied [ toof hadrons: every the LF anomalous Fock gravitomagnetic state moment of a hadron vanishes at angular momentum are quantized in the P fixed light-front (LF) time. Similarly,a Compton hadron scattering are and measurements of deep-inelastic hadronphysics lepton at structure scattering fixed at on fixed LF time. Unlike ordinary “instant time” of the QCD LF Hamiltonian dissociation of high energy hadrons into jets [ of the constituents in the Thus the constituent transverse momenta light-front analog of rotational invariance. Only positive mass squared of the constituents in the Fock state. For a two-particle Fock state: insights of Schrödinger’s nonrelativisticbe quantum applied mechanics to and relativistic the physics Hamiltonian [ formalism to transverse momenta are always always coupled to the longitudinal LF momentum fractions τ Supersymmetric Properties of QCD and Light-Front Holography 1. Introduction states in quantum field theory and underlieHadronic virtually LFWFs every can observable in also hadron be physics. measured See directly Fig. by the Ashery method [ P LFWFs are also off-shell in ~ PoS(LC2019)030 ], ]. ], ∝ LF 1 i ] to i 18 15 x 0 | ]: the 21 12 ; i.e., i y integration of ]. This feature − k Stanley J. Brodsky 11 of the renormalized ], the “hidden color” larger than measured. 13 mechanism, the heavy MS ] and zero cosmological 42 ¯ Λ Q 10 ], nontrivial vacuum struc- Q 0 [ 18 → = g i LF 0 | µν , but they tend to be maximal at minimal − i T | k ]. The DGLAP evolution of structure func- ∑ LF 16 0 h 6= − 2 along the light-front, the light-front vacuum P . . In fact, in the holographic LFWFs where color is c i 2 x / z asymmetry of non-valence sea-quark distributions [ M 0 fixed-pole”) contributions in the Compton amplitude + ) t x = ( ¯ = q J + 6= x ) x ( q ], the loop integrals and picking up the pole contributions. However, there is an 14 k 4 d R ]. In addition, LF perturbation theory has the special property of “history”: One ]. 17 20 ], such as the “color transparency” of hard exclusive reactions [ , 2 . Thus, in contradiction to the usual splitting i 19 2 ⊥ k + In general, one can reproduce the LF Hamiltonian results from covariant Feynman-Lagrangian The LF zero modes correspond to a constant scalar background with zero energy and three- If one sets the quark masses to zero in the Lagrangian of (QCD), The LFWFs of bound states are off-shell in There are many other important physics properties which become explicit using the light-front 2 i Hadronic Mass Scale m theory and the Bethe-Salpeter formalism for bound states by first performingimportant the exception: in the case of vacuum loops, there are “circle at infinity ” contributions [ perturbative theory generates thetransmutation” nonperturbative solution QCD is mass problematic since scale;pendent, the whereas however, perturbative hadron this scale masses “dimensional is cannot depend -schemethe on QCD de- a mass scale theoretical reflects convention. the It presenceHowever, is of such often quark condensates and argued lead gluon that condensates to in a theIn cosmological QCD fact, vacuum constant state. up a factor to of LFture 10 zero does modes, not appear such in asmass QCD the of if the Higgs one QCD background light-front defines field (LF) thewhere Hamiltonian. [ vacuum the In state time fact, variable as in is Dirac’s the boost the eigenstate invariant time “front of form” lowest invariant [ constant [ This Higgs LF zeroYukawa mode couplings. (the LF analog of the Higgs VEV ) gives mass tothe fermions 4-dimensional via their momentum. In the case of theis Higgs replaced theory, the by traditional a Higgs “zero vacuum mode”, expectation in value the (VEV) LF theory, analogous to a classical Stark or Zeeman field [ off-shellness; i.e., minimal invariant mass of minimal off-shellness of theLFWFs LFWFs haveq also maximal underlie support intrinsic when heavy all quark of Fock the states [ constituents have the same rapidity and the local two-photon “seagull”from (“ LF instantaneous quark exchange interactionstions [ and the ERBL evolution oftonian distribution theory amplitudes [ are most easily derived using LF Hamil- no hadronic mass scale is evident.of Thus the a fundamental question and for other QCD hadrons. is the origin It of is the often mass stated that the mass scale does not need to computeonly the the numerator LF of denominator changes any from perturbative one LF computation amplitude to more another. than once,2. since Color Confinement, Extended Conformal Covariance, and the Origin of the confined, the LFWFs of hadrons have fast Gaussian fall-off in invariant mass [ formalism [ Supersymmetric Properties of QCD and Light-Front Holography have the highest momentum fractions of nuclear eigenstates [ is both causal and frame-independent; one thus has PoS(LC2019)030 ] 23 theory, 4 φ g ] have shown . 0 contributions 2 24 Stanley J. Brodsky = µ is the LF orbital an- k | z L | is not determined and serves max ) ζ κ = ( L ψ The convergence of theoretical methods for 2 is in analogy to the non-relativistic M = ψ )] Figure 2: generating a model ofnamics with hadron color spectroscopy confinement and andpersymmetric meson-baryon dy- relations. su- 2 ζ ( 0 can be systematically reduced to a differential ]. De Téramond, Dosch, and I [ U 2 0 can at best only predict ratios of masses such as 3 = + ; however, after a redefinition of the time variable, q ) = 2 2 m x q 2 1 L 4 2 m 4 = κ ζ z i 4 : ⌥ − 1 2 1 ζ 1 ( = ) ) =1 n i Unique Unique g z ) ( ( ⇤ ⇣ L + ⇥ ⇥ of the action ( into the Hamiltonian of a conformal theory without affecting the 2 2 +

2 + 2 z Conformal Symmetry i Confinement Potential! Confinement Light-Front Holography q z ζ d M M κ S . M L d te 2 ⇥ 9 = = age P Light-Front Schrödinger equation + b =1 bound states for ⇥ ⇥ 1) − n i ) )= ) ) [ z g ]. ¯ ⇣ Sta x q ⇤ S a term proportional to the dilation operator and/or the special conformal ( ( ( q

S 21 ζ V V = ⇤ + ck ) H is the radial variable of the front form and , + o z z p q (1 ⇣ + + 2007 ( F ) S S x Scale can appear in Hamiltonian and EQM EQM and in Hamiltonian appear can Scale L 20-24, ]. This 2 ( 22 x 2 2 ugust U A , 2 h 2 d d idge without affecting conformal invariance of invariance conformal without affecting action! = = = d d Cambr  , + 11 QCD − z z p 2 ing 2 Explor J eac J 1 L 2 +2 ( 4 ⇣ 2 4 x ⇣ 2 1 4 z 2 ⊥ 2  b  2 2 + ⇣ Single variable d )= e = d ⇣ Front Schrödinger Equation Schrödinger -Front Light ( 2 and other dimensionless quantities. The work of de Alfaro, Fubini, and Furlan (dAFF) [ = U ζ ⇥ ) p z AdS/QCD AdS/QCD ( The same principle of “extended conformal invariance” can be applied to relativistic quantum The LF equation for It is conventional to measure hadron masses in MeV units; however, QCD has no knowledge of m ' / e de Alfaro, Fubini, Furlan: Furlan: Fubini, Alfaro, de Fubini, Rabinovici: Rabinovici: Fubini, Soft-Wall Model ρ • • field theory using light-front (LF) quantization [ as a holding parameter– only ratios of eigen-masses are predicted. radial Schrödinger equation for bound states such as positronium in QCD. See fig. m which are not given bying a distinction between light-front the Hamiltonian vacuum Fock structureHamiltonian space of theory analysis. conventional [ Feynman-Lagrangian theory There and is LF thus an interest- provides a novel solution for the originintroduce of a the nonzero hadron mass mass scale scale inconformal QCD. They invariance of showed that the one action. can Theadd essential to step of the this Hamiltonian “extended conformaloperator. invariance” is In to the case ofa one-dimensional confining quantum harmonic mechanics, oscillator the potential resulting Hamiltonian acquires that a mass gap and a fundamentalprocedure color to confinement light-front scale (LF) also Hamiltonian appear theory when in one extends physical the 3+1 dAFF . gular momentum [ units such as electron-volts. Thus QCD at the action remains conformal. The newtime time between variable the has constituents finite in range, a consistent confining theory. with The the mass finite scale LF Supersymmetric Properties of QCD and Light-Front Holography the Feynman loop integration which do notof appear LF unambiguously Hamiltonian from the perturbation vacuum theory. loopthese diagrams non-pole For contributions example, cause in vacuum scalar amplitudes field to theories have “zero such mode” as equation in a single LF radial variable where PoS(LC2019)030 , = 25 L pseu- . One ¯ 2 q ) q µ confining i k controlling r of the front i s σ ∑ ζ meson bound may be found and the orbital . This identifi- Λ ¯ contribution to q 5 n q = ( 2 Stanley J. Brodsky m 2 i 0. Thus light-front x + 2 ⊥ M k = The mesonic spectrum i for all q . ∑ ) ) m ] for form factors at large L λ 2 , + 17 J ⊥ , k + , 0 for in agreement with the effective ] which replaces the usual VEV 31 x n ( . 2 ( = ) 18 2 M κ 1 in the LF Hamiltonian, where π κ 4 ψ 4 / ) m − ] to a Gaussian functional form for the 2 1 Light-Front Holography S Q 25 − ) = + − n with the LF radial coordinate S L , z ( and introduces a specific modification of the L + 2 ( exp ζ 2 κ L ( 2 . Color confinement is then a consequence of the ∝ ] formula for form factors in AdS M 2 2 4 ) + κ is massless: , which determines the mass scale of hadrons and κ 2 30 2 also leads [ ) κ Q ζ 0 5 ( 4 s . The resulting prediction from AdS/QCD is the single 2 κ α = z 2 with the light-front Hamiltonian theory also automatically L κ , where are the LF spins. The application of dAFF thus leads to a 5 + ) = ζ e 2 = z ζ S ]. J space with LF Hamiltonian theory in 3+1 dimensions and the ( , , where again the action remains conformal. 5 + 2 ) = 28 0 U z z ζ ( 4 L = φ κ e n = ( . Again, only ratios of masses and decay constants are predicted. z ) J 2 contribution to the LFKE as arising in the Higgs theory from the coupling ζ ( ]. with the identical slope 4 2 with the LF radial coordinate x m U L with z 35 , z S 34 , ]. In fact, The Drell-Yan-West formulae for electromagnetic and gravitational form max 33 29 , = 32 S of each quark to the background zero-mode Higgs field [ , ] have also shown how the parameter metric – the “dilaton” z bound states is thus described as Regge trajectories in both the radial variable The form of the dilaton modifying AdS The correspondence of AdS Remarkably, the pion Even more remarkably, the identical LF color-confining potential and the same LF equation The eigenvalues for the meson spectrum are Nonzero quark masses appear in the “LF kinetic energy” (LFKE) L m 5 ¯ 27 q q , × x m can identify the the cation also provides a nonperturbative derivation of scaling laws [ of the standard time “instant form”.potential for In heavy the quarkonium heavy [ quark limit, one recovers the usual form in physical 3+1 spacetimesuch is as called elastic “light-front and holography”. transitionfunctions form Exclusive [ hadron factors amplitudes, are given in terms of convolutions of light-front wave- 3. The QCD Running Coupling at all Scales nonperturbative QCD running coupling: charge determined from measurements of26 the Bjorken sum rule. Deur, de Teramond, and I [ identification of the fifth dimensional AdS coordinate factors is identical to the Polchinski-Strassler [ Regge slopes in the zero quark mass limit, can be connected to the mass scale of angular momentum the LF Hamiltonian – the square of the invariant mass of the constituents: momentum transfer. Additional references andin reviews refs. of [ variable LF Schrödinger Equation in of motion are obtained usingthe Maldacena’s fifth five coordinate dimension anti-deSitter space when one identifies Supersymmetric Properties of QCD and Light-Front Holography AdS The holographic identification of AdS light-front potential introduces the spin-dependent constant term 2 color-confining LF potential max holography explains another fundamental questiondoscalar in bound hadron state physics can – emerge, despite how theate a pion’s both zero composite the mass structure. mass The spectrum eigensolutions andstate. gener- the light front wavefunctions PoS(LC2019)030 ]. 08 . 36 0 [ from s ]. The 2 ± Q √ 37 87 . in the QCD 0 scheme. The = MS 0 Λ Stanley J. Brodsky MS Q superconformal alge- ] we have applied the 36 ] of ]. 53 Sublimated below 1 GeV Sublimated 42 , over a wide range of ) QCD coupling at all scales, IR Fixed Point Fixed at allQCD coupling scales, IR 52 Comparison of the matched nonperturba- 2 , Q ( s 51 α ], which satisfies all the requirements of AdS/QCD dilaton captures the higher twist corrections to effective charges for Q < 1 GeV effective charges to the higher twist corrections captures dilaton AdS/QCD ], a rigorous scale-setting method for gauge 40 Figure 4: tive QCD from LF holographyprediction and with perturbative experiment. QCD annihilation: the thrust (T) and C-parameter 39 ]. In a recent paper [ , − e 41 38 . 5 + 0 e MS Q sjb Λ GeV defined at all momenta. GeV GeV MS scheme 0 limit [ ) 007 . 2 0 017 019 . . 10 ± 0 Q 0 → ( ± ± s 513 . C Q (GeV) Deur, de Tèramond, de Deur, α Prediction: 332 N 339 . =0 .  at all scales. The GeV Fit to Bj + DHG Sum Rules:Sum DHG + FittoBj =0 =0 ]. ) which underlies the 08 of the running coupling depends dynamically on the virtuality of the 2 Perturbative QCD 0 () . PerturbativeQCD MS MS 0 25 5-Loop 2 (AsymptoticFreedom) Experiment: Q ⇤ κ ⇤ ( ± Q 1 0 g s Q 87 1 . α perturbative − =0 Transition scale Q Transition – both its value and its slope – then determines a scale Non Holographic QCD 0 2 (QuarkConfinement) NonperturbativeQCD 2  ) Q , consistent with both LF holography and pQCD [ Q is predicted by pQCD. The matching of the high and low momentum transfer 4 2 2 for starting for 0 All-ScaleQCDCoupling ) Evolution Q Q 2 e ( 1 DGLAP and ERBL and DGLAP Use Q Use Q underlying hadron masses can thus be connected to the parameter g ( 1 α -1 κ

g

10

0 1

g1

(Q)/ 0.4 0.2 0.8 0.6 α π Prediction from LF Holography and pQCD α  )  2 2 Q p ( 2 ⇡ 1  Another advance in LF holography is the application [ One can measure the running QCD Reverse Dimensional Transmutation! s g =2 = ↵ ⌘ p ⇢ m m magnitude and derivative of the perturbativeperturbative and coupling non- are matched at the scale Figure 3: for the running coupling underlying quark and gluon subprocess and thus the specific kinematics of each event [ This matching connects the perturbative scale mass scale running coupling by matching its predictedThe nonperturbative result form is to an the effective coupling perturbative QCD regime. The renormalization scale determination of the renormalization scalethe for Principle event of Maximum shape Conformality distributions (PMC) can [ be obtained by using Invariance, including renormalization-schemetency with independence Abelian and theory consis- in the to the non-perturbative scale hadron mass scale. From Ref. [ theories, an all-orders extension of the BLM method [ 4. Superconformal Algebra and Supersymmetric Hadron Spectroscopy regimes of Supersymmetric Properties of QCD and Light-Front Holography the evolution of the perturbative QCDcoupling coupling. The high momentum transfer dependence of the event shapes for electron-positron annihilation measured at a single annihilation energy PMC to two classic event shapes measured in GeV which sets theconnection interface can between be perturbative done and for nonperturbative any hadron choice dynamics. of renormalization This scheme, such as the (C). The application of PMCa scale-setting wide determines range the of running coupling to high precision over PoS(LC2019)030 , 51 with its 1 and M ! 2 5 ! 11 L ] and a ! $ † B See Refs. [ ! + 7 2 Q L . , $ 1 Ψ , 4 ! meson Regge tra- ! Q 5 2 quarks to a [ + $ 2 M , ω B C ! (with parallel / 3 2 L / L , the analog of 4 $ and anomalous 1 f ρ !! !! " 3 , ! !! # K , + ! = ) 4 1 2 Stanley J. Brodsky a = 2 baryon trajectory. Super- % ω $ ψ 3 2 M Q $ ∆ L H 3 + , ( % !! " 2 Ω !! # 2 1 2 2 , Q , originally discovered $ 3 F 1 LF wavefunctions in / Ρ 3 " 1 with equal probability, 2 = ! → 3 2 2 = f " 1 ! # $ + L , Q J 2 B superpartner trajectories a GeV L ! , for each baryon, corresponding 2 Ω " 0 B # , ⇢ Ρ ± Comparison of the 0 and M L Ψ 2 1 0 6 5 4 3 = Dosch, de Teramond, sjb Dosch, Teramond, de L ], a nonconformal Hamiltonian with a ]. 48 (21) ect of superpartner baryon with conformal algebra predicts the degeneracyson of and the me- baryon trajectorieswith if internal one orbital identifies a angular meson momentum Figure 6: jectory with the 52 ,thus 2 ↵ m superconformal algebra 1 2 . . Candidates 6 9 e + 1. This property of the baryon LFWFs is the analog + to the LF kinetic . The partners of =1 ] C + L 2 i i ¯ 3 qq P 0 x [ m 2matrix: , ]. The conformal Hamiltonian operator and the special ! B ,J ⇥ ! )operate C =1 .Opencirclesrepresent , n i and ¯ 3 47 ¯ } =0 q ee uu ,L 17 ]. The overlap of the T =0 ! L T † P P '$ &% I ) R - , 49 = . B I,J L B 2 + +1) (with anti-parallel quark and baryon spins) have equal Fock state †

m , = Ψ B R − + L +1 T V . The 4-plet contains two entries B ( bound states, baryons ψ L B B − p

5 ¯ ~ ( q · , E B T q σ ~ M

,L ,L + e e connects quarks and anti- + ee ee m { B B Baryon Baryon † λ

12 '$ &% '$ &% ]. The baryonic eigensolutions correspond to bound states of 3 - diquark cluster; the tetraquarks in the 4-plet are bound states of diquarks and = R +1) 53 ) − B qq (1260), respectively. † , B ) and the Hamiltonian ( 1 ] mesons, baryons and tetraquarks are also hadronic states L Ψ R 1 a L ( 20 +1 52 = , plus two bosonic wave functions, namely the meson 2X2 Hadronic Multiplets 2X2Hadronic + , B 2 Pauli matrix representation called . As shown by Fubini and Rabinovici, [ B M ]. Mesons are ] Equal Weight: L=0,L=1 EqualWeight: B ]

The 4-plet representation of mass- † L ¯ C q

60 × u e ,L ( 3 q 24 S ]. This ansatz extends the predictions for the hadron spectrum to a “4-plet” – consist- [¯ , , M M ! ] that the natural way to include light quark masses in the S Meson Superconformal Algebra . These states can be arranged as a 2 ! '$ &% (980) and Proton: |u[ud]> Quark + ScalarQuark+ DiquarkProton:|u[ud]> and 48 [ C 51 0 T 3 is one unit higher than that of the positive- (leading-twist) 11 q 2 (1233) have the quantum numbers f +

Bosons, Fermions with Mass! Equal † / B B 1 R

LF Schrödinger Equations for both baryons and mesons can be derived from superconformal

, a feature of the underlying conformal symmetry of chiral QCD. The conformal group has spin-0 or spin-1 = C . ¯ algebra [ anti-diquarks. The quark-diquark baryons have two amplitudes 3 a feature of “quarkquark chirality and baryon invariance”. spins) and Theprobability – proton a Fock feature state oforbital component “quark angular chirality momentum invariance”. in Thus thethe the nonperturbative proton’s domain. are spin Predictions discussed is in for carriedthe Ref. the by Drell-Yan-West formula [ static quark is properties required to of have a non-zero Pauli form factor conformal operators can be represented as anticommutators of Pauli matrices ing of mass-degenerate quark-antiquark mesons,tetraquarks, quark-diquark as baryons, shown in and fig. diquark-antidiquark degenerate hadronic states predictedmal by algebra superconfor- [ are quark – antidiquarkare bound diquark-antidiquark states bound and states. tetraquarks metric The ladder supersym- operator K mass scale and universal confinement can then be obtained by shifting to internal orbital angular momentum lower component Figure 5: diquark clusters of the same color. bra an elegant 2 of the eigensolution of the Dirac-Coulomb equation which has both an upper component Supersymmetric Properties of QCD and Light-Front Holography by Haag, Lopuszanski, and Sohnius [ the dAFF procedure. In effect,algebra one [ has obtained generalized supercharges of the superconformal evaluated using the modified wave functions. This prescription leads to + The supersymmetric quadruplet 2 B

m (1320) and the (1235) and the ; 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. the nonzero quark masses for thevalue squared hadron masses of is then given by the expectation and add the additionalenergy. term of The the resulting invariant LFproviding mass a wave relativistically function invariant is form for then the modified hadronic by wave functions. the The factor e

hadron mass spectrum is to leave the LF potential unchanged as a first approximation 2.4 Inclusion of quark masses and comparison with experiment the the for these states are the on which the symmetry generators ( component spinor wavefunction Figure 1: quarks, full circles antiquarks.multiplet. The tetraquark Notice has that thefunction the same of mass LF a as angular baryon its momentum baryon of partner in the the negative-chirality component wave PoS(LC2019)030 ) n ]. 1 is a 59 ( the + ] , i L meson ¯ c cq diquark 56 ]. [ c + | ω , can be set / 54 n qq ( 53 κ ρ 2 κ space, and the 4 ]. 1 have the same 5 Stanley J. Brodsky 50 + ) = B , where the L i L ] , n = ( cq [ 2 identified by SELEX and c M . The value of | spin-0 or spin-1 ) M 6 L C ¯ 3 3520 ( 1 orbital excitation of the + ccd = Ξ L quarks to a C for mesons and ) double-charm tetraquark. In fact, the mass of with its superpartner baryon or tetraquark with L i ] M ¯ + q 7 ¯ L c n ( ][ 2 cq κ [ | 4 ]. The effective supersymmetric properties of QCD can be ) = 58 [ L -baryon trajectory is shown in Fig. ) , n ∆ ]. ( 2 2 / 54 3415 M 3 ( cc = Ξ J ]. The existence of both components is also necessary to generate the pseudo- 29 ) and also the mass of the ) matches the mass of the double-charm baryon 1 ) 1. Superconformal algebra thus predicts that mesons with = − mass; however, only ratios of masses are predicted. L M ( 3525 ρ 0 c are identical. The predicted meson, baryon and tetraquark masses coincide if one identifies a ( L c h The combination of light-front dynamics, its holographic mapping to AdS Thus one predicts supersymmetric hadron spectroscopy – bosons and fermions with the same The predictions from light-front holography and superconformal algebra have been extended The combination of light-front holography with superconformal algebra thus leads to the novel The predicted spectrum, L h = B ++ dAFF procedure provide new insights, not only into the physics underlying color confinement, but 1 cluster; the tetraquarks in the 4-plet are bound states of diquarks and anti-diquarks. 6. Summary mass and twist- not onlyalso identical supersymmetric masses relations for between their thebaryonic eigenfunctions– bosonic eigensolutions their correspond and to light-front fermionic bound wavefunctions. states hadron of The eigenvalues, 3 but for baryons, is remarkably consistent withand observed hadronic spectroscopy. The Regge-slopes in meson with internal orbital angular momentum L 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 on radial slope. universal and For linear orbital example, Regge quantum thescalar trajectories diquark, numbers, mass is but of predicted to the with be lightest an identical double-charm to increased the baryon value mass of for the the a tetraquark candidate the to mesons, baryons, and tetraquarks with strange, charm and bottom quarks in refs. [ 5. Supersymmetric Hadron Spectroscopy for Heavy Quarks 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 mass as the baryons in theRegge supermultiplet. trajectory with An the example of theby mass the degeneracy of the used to identify the structure of the heavy quark mesons, baryons and tetraquark states [ T-odd Sivers single-spin asymmetry in deep inelastic lepton-nucleon scattering [ Supersymmetric Properties of QCD and Light-Front Holography magnetic moment [ PoS(LC2019)030 , 35 and internal n ]. A new method Stanley J. Brodsky ], uses the eigenso- 64 ]. Empirically viable 65 61 ]. One can also observe 62 is a tetraquark [ ] T 67 in the radial quantum number where 8 T π → on nuclei and thus negate the validity of the momentum − A e same slope ∗ + γ e ] and its nonperturbative strange quark sea [ → A 63 ∗ γ for mesons, baryons, and tetraquarks. L ], prevent the application of the operator product expansion to the virtual 66 I thank Cédric Lorcé for hosting LC2019 at Ecole Polytechnique. The physics results pre- We have also shown that the Gribov-Glauber processes, which arise from leading-twist diffrac- One can also observe features of superconformal symmetry in the spectroscopy and dynam- ]. The combination of light-front holography with superconformal algebra leads to the novel sum rule for deep inelastic nuclear structure functions. [ for solving nonperturbative QCD “Basis Light-Front Quantization” (BLFQ) [ sented here are based on collaborations anddre discussions with Deur, many Guy collaborators, de including Téramond, Alexan- HansMatin Günter Dosch, Mojaza, Cédric Lorcé, Kelly Chueng Chiu, Ji,Miller, Leonardo Peter Jennifer Di Lepage, Giustino, Rittenhouse West, Stan Bo-Qiang Głazek,Arkady Ma, Trawinski, Peter Fred Sheng-Quan Lowdon, Goldhaber, Wang, Xing-Gang Robert Philip Wu, Shrock, and Mannheim, Marina Ivan Jerry Nielsen. Schmidt, Compton scattering amplitude 7. Acknowledgements tive deep inelastic scattering on nucleonsstructure and underly functions the [ shadowing and antishadowing of nuclear predictions for spacelike and timelike hadronic form factors,tudes, structure and functions, transverse distribution ampli- momentum distributions havefeatures also of been superconformal obtained symmetry [ in the spectroscopybaryons. and dynamics LF of heavy-light holography mesons gives and namics, a and the remarkable hadronic first LFWFs. approximation Onesuch also to as obtains hadron viable spacelike spectroscopy predictions and for and timelike testsand hadronic dy- of form transverse hadron dynamics factors, momentum structure distributions. functions,from distribution In LF amplitudes, recent Holography to papers, incorporate we non-valence haveto higher Fock extended compute states the other and physics LFWFs DGLAP observables. evolution derived inthe This valence order quarks includes in detailed the predictions proton [ for the spin structure of lutions of a color-confining approximation torather QCD than (such the as plane-wave LF basis holography) used as in the DLCQ, basis functions, thus incorporating the full dynamics of QCD. prediction that hadron physics has supersymmetricThe properties QCD in Lagrangian both is spectroscopy not andfundamental supersymmetrical; dynamics. 4-plet however supersymmetric its representation of hadronic superconformal eigensolutions algebra,lying conform reflecting conformal the to symmetry under- a of semi-classical QCDSchrödinger for equations” massless derived from quarks. LF The holography resulting incorporatetroscopic color “Light-Front and confinement dynamical and features other spec- of hadronand physics, including linear a Regge massless pion trajectories for with zero quark the mass 60 Supersymmetric Properties of QCD and Light-Front Holography also the nonperturbative QCD coupling and the QCD mass scale. Reviews are given in Refs. [ orbital angular momentum ics of heavy-light mesonsbetween and mesons, baryons. baryons, and tetraquarks This ofsentation the approach of same predicts superconformal parity algebra. as novel members One supersymmetric of canfactors relations the in test same exclusive the 4-plet reactions similarities repre- such of as their wavefunctions and form PoS(LC2019)030 Stanley J. 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