Light-Front Holography and Novel Collider Physics

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= 1 − ζ1 ∆ 1 − i∆ 2√ 1 − ζ 2Measily checks that ∑ ni=1 x ′ Press and Media : SLAC National Accelerator Laboratoryi = 1and ∑ ni=1⃗k⊥i ′ = ⃗0 ⊥ . In Eqs. (39) and (40) onChile LHCJanuary 8, 201016π 3ζ 16π δ 1 − x j δ4 ( 1 − ζ )√ E (n→n) (x, ζ,t)Example of LFWF 2representation 1 − ζ j=1j=1n(of) (∏ dx× δ(x i d− 2 ⃗k ⊥ix 1 )ψ(n)( ↑∗ x′n∑i , ⃗k ⊥i ′ , λ ) n)GPDs (n => ↑∑)16π i ψ(n)( 3 δ 1 − x j δ (2) xi ⃗k ⊥j , ⃗k ⊥i , λ i ,1 − ζ1 − ζ H (n→n) (x, ζ,t) −2 n,λ i i=1= ( √ ) 2−n∑∫1 − ζn,λ i= ( √ ) 2−n2M ∑1 − ζE (n→n)(x, ζ,t)1 ∆ 1 − i∆∫2√ E (n→n)(x,∏ n ζ,t)1 − ζ dx i d 2 ⃗k ⊥i= ( √ ) 2−n∑ ∏ n16πdx i d 3 2 ⃗k ⊥i1 − ζ n,λ i i=1 16π 3n,λ i∫16π 3 δLF Holography and QCD20(1 −) (n∑n)∑j=1 x j δ (2) ⃗k ⊥j j=1⃗k ⊥j) (n∑n)∑x j δ (2) ⃗k ⊥ji=1× δ(x (n)( ↑∗j=1x′i , ⃗k ⊥i ′ , λ ) j=1↓ )× δ(x − x i ψ(n)(xi1 )ψ ↑∗ ) ↓ ψ , ⃗k ⊥i , λ i ,re the where arguments the arguments of theof the final-state wavefunction are are given given by byx ′ 1 = x 1 − ζi=116π 3x 1 ′ = x 1 − ζ1 − ζ , ⃗k ⊥1 ′ = ⃗k ⊥1 − 1 − x 11 − ζ , ⃗k ⊥1 ′ = ⃗k ⊥1 − 1 − x 1∆1 − ζ 1 − ζ ⃗ ⊥ for the struck quark,for the struck quark,x i ′ = x xii ′ = x i1 − ζ , 1 − ζ , ⃗k⃗k ⊥i ′ = ⊥i ′ ⃗k = ⃗k ⊥i +⊥i + x x i1i− ζ∆1 − ζ ⃗ ⃗ (41)∆ ⊥ for the spectators i = 2, ..., n.⊥ for the spectators i = 2, ..., n.over all possible combinations of helicities λ iand over all parton numbers nj=1j=1× δ(x − x 1 )ψ(n)( ↑∗ x′i , ⃗k ⊥i ′ , λ ) ↑ )i ψ(n)(xi , ⃗k ⊥i , λ i , (39)16π 3 δ(1 −(n)(x′i , ⃗k ′ ⊥i , λ iDiehl, Hwang, sjb(n)(xi , ⃗k ⊥i , λ i) , (40)One easily checks that ∑ ni=1 xi ′ = 1and ∑ ni=1⃗k⊥i ′ = ⃗0 ⊥ . In Eqs. (39) and (40) one has tosum over all possible combinations of helicities λ iand over all parton numbers n in theFock states. We also imply a sum over all possible ways of numbering Stan theBrodskypartons in then-particle Fock state so that the struck quark has the index i = 1.SLACHOME RESEARCH SCIENTIFIC PROGRAMS
H~Hqq!"#$%&'%()*%+#,%-.+/&"0%1'23%1+0&'2/DIS at !=t=0( x,0,0)' q(x),% q(% x)( x,0,0)' ( q(x),( q(% x)11% 1Form factors (sum rules)~dx H"q#q$ dx)H ( x,!,t)q' F 1 ( t) Dirac f.f.1q$ dx)" E ( x,!,t)# ' F 2 ( t) Pauli f.f.$q( x,!,t)' GA,q(t) ,1$% 1~dx Eq( x,!,t)' GP,q(t)Hq ~ q ~ q, E , H , E ( x,, t)q!Verified using LFWFsDiehl, Hwang, sjbQuark angular momentum (Ji’s sum rule)1q'1% J G =1Jxdx H2 2$% 1" ( x,!,0)& E ( x,!,0)#qqX. Ji, Phy.Rev.Lett.78,610(1997)Chile LHCJanuary 8, 2010LF Holography and QCD21Press and Media : SLAC National Accelerator LaboratoryStan BrodskySLACHOME RESEARCH SCIENTIFIC PROGRAMS
Page 1: Light-Front Holography:A New Approx
Page 4 and 5: Light-Front Holography and Non-Pert
Page 8 and 9: • QCD LagrangianL QCD = − 14g 2
Page 10 and 11: Light-Front Wavefunctions: rigorous
Page 12 and 13: |p,S z >= ∑ Ψ n (x i ,k ⊥i ,λ
Page 14 and 15: te between the struck and spectator
Page 16 and 17: Calculation of Form Factors in Equa
Page 18 and 19: Light-Front QCD Features and Phenom
Page 22 and 23: J=0 Fixed pole in real and virtual
Page 24 and 25: Applications of AdS/CFT to QCDChang
Page 26 and 27: Conformal Theories are invariant un
Page 28 and 29: Conformal Behavior of QCD in Infrar
Page 30 and 31: IR Conformal Window for QCD• Dyso
Page 32 and 33: Scale Transformations• Isomorphis
Page 34 and 35: Press and Media : SLAC National Acc
Page 36 and 37: Press and Media : SLAC National Acc
Page 39 and 40: Light-Front Holography:Map AdS/CFT
Page 41 and 42: AdS/CFT• Use mapping of conformal
Page 43 and 44: Let Φ(z) = z 3/2 φ(z)AdS Schrodin
Page 45 and 46: Φ(z)3242Φ(z)01-22-20078721A1800 1
Page 47 and 48: • Erlich, Karch, Katz, Son, Steph
Page 49 and 50: Quark separationincreases with L645
Page 51 and 52: Higher Spin Bosonic Modes SW• Eff
Page 53 and 54: igenvaluesM 2 = 2κ 2 (2n + 2L + S)
Page 55 and 56: Propagation of external perturbatio
Page 57 and 58: Current Matrix Elements in AdS Spac
Page 59 and 60: • Analytical continuation to time
Page 61 and 62: Note: Analytical Form of Hadronic F
Page 63 and 64: Holographic Model Light-Front for Q
Page 65 and 66: • Electromagnetic form-factor in
Page 67 and 68: Gravitational Form Factor in AdS sp
Page 69 and 70: H QEDHQCDLFQCD Meson Spectrum(H 0 L
Page 71 and 72:
• Find (L = |M|)M 2 =dζφ ∗ (
Page 73 and 74:
Example: Pion LFWF• Two parton LF
Page 75 and 76:
Prediction from AdS/CFT: Meson LFWF
Page 77 and 78:
Example: Evaluation of QCD Matrix E
Page 79 and 80:
Second Moment of Pion Distribution
Page 81 and 82:
2 Fermionic Modes• Baryons Spectr
Page 83 and 84:
BaryonsHolographic Light-Front Inte
Page 85 and 86:
• Note: in the Weyl representatio
Page 87 and 88:
Non-Conformal Extension of Algebrai
Page 89 and 90:
indebted to B. Metsch and H. Petry
Page 91 and 92:
Space-Like Dirac Proton Form Factor
Page 93 and 94:
• Scaling behavior for large Q 2
Page 95 and 96:
String TheoryGoal: First Approximan
Page 97 and 98:
More generally, consider a meson in
Page 99 and 100:
New Perspectives for QCD from AdS/C
Page 101 and 102:
Running Coupling from Light-Front H
Page 103 and 104:
• β-functiond! seff/dlog(Q 2 )0-
Page 105 and 106:
Applications of NonperturbativeRunn
Page 107 and 108:
Final-State Interactions ProducePse
Page 109 and 110:
Formation of Relativistic Anti-Hydr
Page 111 and 112:
Features of LF T-Matrix Formalism
Page 113 and 114:
Chiral Symmetry Breaking in AdS/QCD
Page 115 and 116:
Light-Front(Front Form)Formalism
Page 117 and 118:
5[iE π (q; P ) + γ · P F π (q;
Page 119 and 120:
Quark and Gluon condensates reside
Page 121 and 122:
Features of AdS/QCD LF Holography
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Light-Front Holography and Novel Collider Physics

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