High-energy QCD and Wilson lines I. Balitsky JLAB & ODU LANL - PowerPoint PPT Presentation

High-energy QCD and Wilson lines I. Balitsky JLAB & ODU LANL Nuclear Theory Seminar 13 March 2014 LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Outline 1 Introduction: BFKL pomeron in hign-energy pQCD Regge limit in QCD. Perturbative QCD at high energies. BFKL and collider physics 2 High-energy scattering and Wilson lines High-energy scattering and Wilson lines. Evolution equation for color dipoles. Light-ray vs Wilson-line operator expansion. Leading order: BK equation. 3 NLO high-energy amplitudes Conformal composite dipoles and NLO BK kernel in N = 4 . NLO amplitude in N = 4 SYM Photon impact factor. NLO BK kernel in QCD. rcBK. NLO hierarchy of Wilson-lines evolution. Conclusions LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Light-ray operators Heisenberg uncertainty principle: ∆ x = � p = � c E LHC: E=7 → 14 TeV ⇔ distances ∼ 10 − 18 cm (Planck scale is 10 − 33 cm - a long way to go!) old stuff: p � � mesons L arge protons H adron C ollider new particle p To separate a “new physics signal” from the “old” background one needs to understand the behavior of QCD cross sections at large energies LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Strong interactions at asymptotic energies: Froissart bound Regge limit: E ≫ everything else E →∞ � Causality ln 2 E ≤ σ tot Froissart, 1962 ⇒ Unitarity Long-standing problem - not explained in any quantum field theory (or string theory) in 50 years! Experiment: σ tot ∼ s 0 . 08 ( s ≡ 4 E 2 c . m . ). Numerically close to ln 2 E . LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Deep inelastic scattering in QCD D q ( x B ) → D q ( x B , Q 2 ) - “scaling violations” DGLAP evolution (LLA( Q 2 ) � 1 Q d dQD q ( x , Q 2 ) = dx ′ K DGLAP ( x , x ′ ) D q ( x ′ , Q 2 ) x Dokshitzer, Gribov, Lipatov, Altarelli, Parisi, 1972-77 K DGLAP = α s ( Q ) K LO + α 2 s ( Q ) K NLO + α 3 s ( Q ) K NNLO ... The DGLAP equation sums up logs of Q 2 m 2 N α s ln Q 2 � n � � D q ( x , Q 2 ) = a n ( x ) + α s b n ( x ) + α 2 � � s c n ( x ) + ... m 2 N n 0 ∼ 1 GeV 2 describes all the experimental data on DIS! One fit at low Q 2 LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Deep inelastic scattering at small x B Regge limit in DIS: E ≫ Q ≡ x B ≪ 1 DGLAP evolution ≡ Q 2 evolution HERA data for xD g ( x ) Q d dQD g ( x B , Q 2 ) = K DGLAP D g ( x B , Q 2 ) Q2 = 20 GeV 2 Q2 = 200 GeV2 Not really a theory - needs the x -dependence of the input xG(x,Q 2) at Q 2 0 ∼ 1 GeV 2 Q2= 5 GeV2 10-4 10-3 -2 10-1 x 10 LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Deep inelastic scattering at small x B Regge limit in DIS: E ≫ Q ≡ x B ≪ 1 DGLAP evolution ≡ Q 2 evolution HERA data for xD g ( x ) Q d dQD g ( x B , Q 2 ) = K DGLAP D g ( x B , Q 2 ) Q2 = 20 GeV 2 Q2 = 200 GeV2 Not really a theory - needs the x -dependence of the input xG(x,Q 2) at Q 2 0 ∼ 1 GeV 2 Q2= 5 GeV2 BFKL evolution ≡ x B evolution (Balitsky, Fadin, Kuraev, Lipatov, 1975-78) 10-4 10-3 -2 10-1 x 10 d D g ( x B , Q 2 ) = K BFKL D g ( x B , Q 2 ) dx B Theory, but with problems LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

In pQCD: Leading Log Approximation ⇒ BFKL pomeron s = ( p A + p B ) 2 ≃ 4 E 2 Leading Log Approximation (LLA(x)): α s ≪ 1 , α s ln s ∼ 1 p A p B LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

In pQCD: Leading Log Approximation ⇒ BFKL pomeron s = ( p A + p B ) 2 ≃ 4 E 2 Leading Log Approximation (LLA(x)): α s ≪ 1 , α s ln s ∼ 1 p A The sum of gluon ladder diagrams gives σ tot ∼ s 12 α s π ln 2 BFKL pomeron p B Numerically: for DIS at HERA σ ∼ s 0 . 3 = x − 0 . 3 B - qualitatively OK LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

In pQCD: Leading Log Approximation ⇒ BFKL pomeron s = ( p A + p B ) 2 ≃ 4 E 2 Leading Log Approximation (LLA(x)): α s ≪ 1 , α s ln s ∼ 1 p A The sum of gluon ladder diagrams gives σ tot ∼ s 12 α s π ln 2 BFKL pomeron p B Numerically: for DIS at HERA σ ∼ s 0 . 3 = x − 0 . 3 B - qualitatively OK LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

BFKL vs HERA data F 2 ( x B , Q 2 ) = c ( Q 2 ) x − λ ( Q 2 ) B M.Hentschinski, A. Sabio Vera and C. Salas, 2010 LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

DGLAP vs BFKL in particle production Collinear factorization (LLA( Q 2 )): � 1 σ pp → X = dx 1 dx 2 D g ( x 1 , m X ) D g ( x 2 , m X ) σ gg → X 0 x 1 X α s ln m 2 � n , s = 14TeV s � sum of the logs ln X ∼ 1 X m 2 m 2 x 2 N LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

DGLAP vs BFKL in particle production Collinear factorization (LLA( Q 2 )): � 1 σ pp → X = dx 1 dx 2 D g ( x 1 , m X ) D g ( x 2 , m X ) σ gg → X 0 x 1 X α s ln m 2 � n , s = 14TeV s � sum of the logs ln X ∼ 1 X m 2 m 2 x 2 N LLA(x): k T -factorization � dk ⊥ 1 dk ⊥ 2 g ( k ⊥ 1 , x A ) g ( k ⊥ σ pp → X = 2 , x B ) σ gg → X ln m 2 � n , � - sum of the logs α s ln x i N ∼ 1 X m 2 Much less understood theoretically. LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

DGLAP vs BFKL in particle production Collinear factorization (LLA( Q 2 )): � 1 σ pp → X = dx 1 dx 2 D g ( x 1 , m X ) D g ( x 2 , m X ) σ gg → X 0 x 1 X α s ln m 2 � n , s = 14TeV s � sum of the logs ln X ∼ 1 X m 2 m 2 x 2 N LLA(x): k T -factorization � dk ⊥ 1 dk ⊥ 2 g ( k ⊥ 1 , x A ) g ( k ⊥ σ pp → X = 2 , x B ) σ gg → X ln m 2 � n , � - sum of the logs α s ln x i N ∼ 1 X m 2 Much less understood theoretically. For Higgs production in the central rapidity region x 1 . 2 ∼ m H √ s ≃ 0 . 01 and we know from DIS experiments that at such x B the DGLAP formalism works pretty well ⇒ no need for BFKL resummation LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

DGLAP vs BFKL in particle production Collinear factorization (LLA( Q 2 )): � 1 σ pp → X = dx 1 dx 2 D g ( x 1 , m X ) D g ( x 2 , m X ) σ gg → X 0 x 1 X α s ln m 2 � n , s = 14TeV � s X ∼ 1 sum of the logs X ln m 2 m 2 x 2 N LLA(x): k T -factorization � dk ⊥ 1 dk ⊥ 2 g ( k ⊥ 1 , x A ) g ( k ⊥ σ pp → X = 2 , x B ) σ gg → X ln m 2 � n , � N ∼ 1 - sum of the logs α s ln x i X m 2 Much less understood theoretically. For m X ∼ 10 GeV (like ¯ bb pair or mini-jet) collinear factorization does not seem to work well ⇒ some kind of BFKL resummation is needed. LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Uses of BFKL: MHV amplitudes in N = 4 SYM MHV gluon amplitudes ⇔ light-like Wilson-loop polygons Alday, Maldacena (at large α s N c ) Checked up to 6 gluons/2 loops (Korchemsky et. al). LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Uses of BFKL: MHV amplitudes in N = 4 SYM MHV gluon amplitudes ⇔ light-like Wilson-loop polygons Alday, Maldacena (at large α s N c ) Checked up to 6 gluons/2 loops (Korchemsky et. al). BDS ansatz: ln A MHV = IR terms + F n , F n = Γ cusp ( angles ) + ( F 1 ) n + R n ) BFKL in multi-Regge region ⇒ asymptotics of remainder function R n (Lipatov et a)l LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Uses of BFKL: Anomalous dimensions of twist-2 operators Structure functions of DIS are determined by matrix elements of twist-2 operators O ( j ) G = F µ 1 ξ D µ 2 ... D µ j − 2 F ξ µ j G = γ ( j ) ( α s ) µ 2 d d µ 2 O ( j ) O ( j ) G 4 π BFKL gives asymptotics of γ ( j ) at j → 1 in all orders in α s � α s � n � � C ( n ) LO BFKL + α s C ( n ) � γ ( j ) = NLO BFKL j − 1 n Checked by explicit calculation of Feynman diagrams.up to 3 loops in QCD and N = 4 SYM. (Janik et al) Integrablility of spin chains corresponding to evolution of N = 4 SYM operators ⇒ γ ( j ) in 5 loops agrees with BFKL (Janik et al). For all order of pert. theory: Y-system of equations (Gromov, Kazakov, Viera). Hopefully agrees with BFKL. LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63

Towards the high-energy QCD σ total BFKL Froissart bound 2 ln s π ln 2 violates σ tot ∼ s 12 α s r e Froissart bound σ tot ≤ ln 2 s w s n a e u r T ⇒ pre-asymptotic behav- ior. Applicability of BFKL pomeron Born Term s True asymptotics as E → ∞ = ? Possible approaches: s ln n s Sum all logs α m Reduce high-energy QCD to 2 + 1 effective theory LANL Nuclear Theory Seminar 13 March 2014 I. Balitsky (JLAB & ODU) High-energy QCD and Wilson lines / 63