A New Perspectives on QCD Condensates and Dark Energy. Stan Brodsky. Applications of AdS/QCD and Light-Front Holography to Hadron Physics

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1 Applications of AdS/QCD and Light-Front Holography to Hadron Physics A New Perspectives on QCD Condensates and Dark Energy Experimental and Theoretical Challenges to Probing Dark Energy A Workshop sponsored by the France-Stanford Center for Interdisciplinary Studies Stan Brodsky December 2-3, 2010 Stanford University

2 One of the gravest puzzles of theoretical physics DARK ENERGY AND THE COSMOLOGICAL CONSTANT PARADOX A. ZEE Department of Physics, University of California, Santa Barbara, CA 93106, USA Kavil Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA (Ω Λ ) QCD (Ω Λ ) EW Ω Λ = 0.76(expt) (Ω Λ ) QCD < 0 q q 0 > 4 QCD Problem Solved if Quark and Gluon condensates reside within hadrons, not vacuum! R. Shrock, sjb arxiv: [hep- th], Proc. Nat l. Acad. Sci., (in press); ``Condensates in Quantum Chromodynamics and the Cosmological Constant. 2

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4 Light-Front Formalism 4

5 RAPID COMMUNICATI PHYSICAL REVIEW C 82, (R) (2010) New perspectives on the quark condensate Stanley J. Brodsky, 1,2 Craig D. Roberts, 3,4 Robert Shrock, 5 and Peter C. Tandy 6 1 SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA 2 Centre for Particle Physics Phenomenology: CP 3 -Origins, University of Southern Denmark, Odense 5230 M, Denmark 3 Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA 4 Department of Physics, Peking University, Beijing , China 5 C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794, USA 6 Center for Nuclear Research, Department of Physics, Kent State University, Kent, Ohio 44242, USA (Received 25 May 2010; published 18 August 2010) We show that the chiral-limit vacuum quark condensate is qualitatively equivalent to the pseudoscalar meson leptonic decay constant in the sense that they are both obtained as the chiral-limit value of well-defined gaugeinvariant hadron-to-vacuum transition amplitudes that possess a spectral representation in terms of the currentquark mass. Thus, whereas it might sometimes be convenient to imagine otherwise, neither is essentially a constant mass-scale that fills all spacetime. This means, in particular, that the quark condensate can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wave functions. Stanford December 4, 2010 QCD Condensates Stan Brodsky, SLAC 5

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7 Simple physical argument for in-hadron condensate B q b g Roberts, Shrock, Tandy, sjb Gribov pairs q b B-Meson B b q Use Dyson-Schwinger Equation for bound-state quark propagator: find confined condensate <B qq B >not < 0 qq 0 > Stanford December 4, 2010 QCD Condensates Stan Brodsky, SLAC 7

8 Bethe-Salpeter Analysis f H P µ = Z 2 Λ d 4 q 1[ TH (2π) 4 γ 5 γ µ S( P + q))γ H(q; P )S( 1 2 P q))] Maris, Roberts, Tandy f H Meson Decay Constant T H flavor projection operator, Z 2 (Λ), Z 4 (Λ) renormalization constants S(p) dressed quark propagator Γ H (q; P )=F.T. H ψ(x a ) ψ(x b ) 0 Bethe-Salpeter bound-state vertex amplitude. π d γ 5, γ 5 γ µ ū iρ H ζ q q H ζ f H = Z 4 Λ d 4 q 1[ TH (2π) 4 γ 5 S( P + q))γ H(q; P )S( 1 2 P q))] In-Hadron Condensate! iρ π =< 0 qγ 5 q π > f H m 2 H = ρh ζ M H M H = q H m q m 2 π (m q + m q )/f π G-MOR 8

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10 Pion mass and decay constant. Pieter Maris, Craig D. Roberts (Argonne, PHY), Peter C. Tandy (Kent State U.). ANL-PHY-8753-TH-97, KSUCNR , Jul pp. Published in Phys.Lett.B420: ,1998. e-print: nucl-th/ Pi- and K meson Bethe-Salpeter amplitudes. Pieter Maris, Craig D. Roberts (Argonne, PHY). ANL-PHY-8788-TH-97, Aug pp. Published in Phys.Rev.C56: ,1997. e-print: nucl-th/ Concerning the quark condensate. K. Langfeld (Tubingen U.), H. Markum (Vienna, Tech. U.), R. Pullirsch (Regensburg U.), C.D. Roberts (Argonne, PHY & Rostock U.), S.M. Schmidt (Tubingen U. & HGF, Bonn). ANL-PHY TH-2002, MPG-VT-UR , Jan pp. Published in Phys.Rev.C67:065206,2003. e-print: nucl-th/ In-Meson Condensate qq π ζ = f π 0 qγ 5 q π. Valid even for m q 0 f π nonzero Stanford December 4, 2010 QCD Condensates Stan Brodsky, SLAC 10

11 Higher Light-Front Fock State of Pion Simulates DCSB π ū + d - γ 5 γ + Light Front Fock state Analysis f π P + =< 0 qγ 5 γ + q π > π ū + u - ū - d ū γ 5 Instantaneous quark propagator contribution to! derived from higher Fock state iρ π =< 0 qγ 5 q π > δm - ū π - d γ 5 + Higher Fock state acts like mass insertion Roberts, Tandy, Shrock, sjb 11

12 Determinations of the vacuum Gluon Condensate < 0 α s π G 2 0 > [GeV 4 ] ± from τ decay ± from τ decay. Davier et al. Geshkenbein, Ioffe, Zyablyuk ± from charmonium sum rules 1.32 m, GeV b) Ioffe, Zyablyuk Consistent with zero vacuum condensate G 2, GeV Stanford December 4, 2010 QCD Condensates Stan Brodsky, SLAC 12

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14 Quark and Gluon condensates reside within hadrons, not vacuum Casher and Susskind Maris, Roberts, Tandy Shrock and sjb Bound-State Dyson Schwinger Equations AdS/QCD Analogous to finite size superconductor Implications for cosmological constant -- Eliminates 45 orders of magnitude conflict R. Shrock, sjb ArXiv: Stanford December 4, 2010 QCD Condensates Stan Brodsky, SLAC 14

15 One of the gravest puzzles of theoretical physics DARK ENERGY AND THE COSMOLOGICAL CONSTANT PARADOX A. ZEE Department of Physics, University of California, Santa Barbara, CA 93106, USA Kavil Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA (Ω Λ ) QCD (Ω Λ ) EW Ω Λ = 0.76(expt) (Ω Λ ) QCD < 0 q q 0 > 4 QCD Problem Solved if Quark and Gluon condensates reside within hadrons, not vacuum! R. Shrock, sjb arxiv: [hep- th], Proc. Nat l. Acad. Sci., (in press); ``Condensates in Quantum Chromodynamics and the Cosmological Constant. 15

16 P.A.M Dirac, Rev. Mod. Phys. 21, 392 (1949) Evolve in ordinary time Dirac s Amazing Idea: The Front Form Evolve in light-front time! σ = ct z τ = t + z/c Instant Form Front Form Plessas: Point Form Stanford December 4, 2010 QCD Condensates Stan Brodsky, SLAC 16

17 Each element of flash photograph illuminated at same Light Front time τ = t + z/c Evolve in LF time P = i d dτ Causal, Trivial Vacuum zero!!

18 Light-Front Wavefunctions: rigorous representation of composite systems in quantum field theory x = k+ P + = k0 + k 3 P 0 + P 3 Fixed τ = t + z/c x i P +, x i P + k i P +, P Process Independent Direct Link to QCD Lagrangian! Ψ n (x i, k i, λ i ) ni x i = 1 Invariant under boosts! Independent of P Plus momenta conserved; all Causal, Trivial Vacuum k + 0 ni k i = 0 zero!!

19 a e = g e 2 2 = α 2π Wick Theorem Feynman diagram = sum n! instant-form time-ordered diagrams Peking University October 27, 2010 Applications of Light-Front Holography Stan Brodsky 19 SLAC

20 Wick Theorem Drell, sjb a e = g e 2 2 = α 2π Feynman diagram = one front-form time-ordered diagram! Also P observer frame (Weinberg) Choose q + =0 Peking University October 27, 2010 Applications of Light-Front Holography Stan Brodsky 20 SLAC

21 Calculation of Form Factors in Equal-Time Theory Instant Form Need vacuum-induced currents Calculation of Form Factors in Light-Front Theory Front Form Peking University October 27, 2010 Absent zero for forq + q + = 00 zero!! Complete Answer No vacuum graphs Applications of Light-Front Holography Stan Brodsky 21 SLAC

22 F 2 (q 2 ) 2M e j 1 2 Drell, sjb = [dx][d 2 k ] a j [ 1 q L ψ a (x i, k i, λ i ) ψa(x i, k i, λ i ) + 1 q R ψ a (x i, k i, λ i ) ψa(x i, k i, λ i ) ] k i = k i x i q k j = k j + (1 x j )q q R,L = q x ± iq y - Must have l z = ±1 to have nonzero F 2 (q 2 ) Peking University October 27, 2010 Nonzero Proton Anomalous Moment --> Nonzero orbital quark angular momentum Applications of Light-Front Holography Stan Brodsky 22 SLAC

23 Anomalous gravitomagnetic moment B(0) Terayev, Okun, et al: B(0) Must vanish because of Equivalence Theorem graviton sum over constituents - Hwang, Schmidt, sjb; Holstein et al B(0) = 0 Each Fock State Peking University October 27, 2010 Applications of Light-Front Holography Stan Brodsky 23 SLAC

24 LF(3+1) AdS 5 de Teramond, sjb ψ(x, b ) φ(z) ζ = x(1 x) b 2 z x b (1 x) ψ(x, ζ) = x(1 x)ζ 1/2 φ(ζ) Light Front Holography: Unique mapping derived from equality of LF and AdS formula for current matrix elements Stanford December 4, 2010 QCD Condensates Stan Brodsky, SLAC 24

25 One of the gravest puzzles of theoretical physics DARK ENERGY AND THE COSMOLOGICAL CONSTANT PARADOX A. ZEE Department of Physics, University of California, Santa Barbara, CA 93106, USA Kavil Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA (Ω Λ ) QCD (Ω Λ ) EW Ω Λ = 0.76(expt) (Ω Λ ) QCD < 0 q q 0 > 4 QCD Problem Solved if Quark and Gluon condensates reside within hadrons, not vacuum! R. Shrock, sjb arxiv: [hep- th], Proc. Nat l. Acad. Sci., (in press); ``Condensates in Quantum Chromodynamics and the Cosmological Constant. 25

26 Applications of AdS/QCD and Light-Front Holography to Hadron Physics Experimental and Theoretical Challenges to Probing Dark Energy A Workshop sponsored by the France-Stanford Center for Interdisciplinary Studies December 2-3, 2010 Stanford University Stan Brodsky