Prospects at ILC A gold place for QCD in the perturbative Regge - PowerPoint PPT Presentation

Prospects at ILC A gold place for QCD in the perturbative Regge limit Samuel Wallon 1 1 Laboratoire de Physique Théorique Université Paris Sud Orsay Blois 2007, DESY, Hamburg 1 / 54

Outline QCD in the Regge limit: theoretical status 1 LL BFKL Pomeron k T factorization LL BFKL Pomeron: limitations Higher order corrections Non-linear regime and saturation Onium-onium scattering as a gold plated experiment: γ ( ∗ ) γ ( ∗ ) at colliders Inclusive and Exclusive tests of BFKL dynamics 2 Hadron-hadron colliders HERA Total cross-section at LEP Onium-onium scattering at ILC collider 3 Sources of photons ILC project cost ILC collider Detectors at ILC γ ∗ γ ∗ → hadrons total cross-section γ ∗ γ ∗ exclusive processes 2 / 54

Outline QCD in the Regge limit: theoretical status 1 LL BFKL Pomeron k T factorization LL BFKL Pomeron: limitations Higher order corrections Non-linear regime and saturation Onium-onium scattering as a gold plated experiment: γ ( ∗ ) γ ( ∗ ) at colliders Inclusive and Exclusive tests of BFKL dynamics 2 Hadron-hadron colliders HERA Total cross-section at LEP Onium-onium scattering at ILC collider 3 Sources of photons ILC project cost ILC collider Detectors at ILC γ ∗ γ ∗ → hadrons total cross-section γ ∗ γ ∗ exclusive processes 3 / 54

QCD in the Regge limit LL BFKL Pomeron: basics At high energy s ≫ − t , consider the elastic scattering amplitude of two IR safe t probes. ↓ M 2 1 ≫ Λ 2 impact factor QCD s → ← vacuum quantum number M 2 2 ≫ Λ 2 impact factor QCD Small values of α S (perturbation theory applies due to hard scales) can be n ( α S ln s ) n series compensated by large ln s enhancements. ⇒ resummation of P (Balitski, Fadin, Kuraev, Lipatov) 0 1 0 1 B C B C B C B C + + + · · · + + · · · + B C B C B C B C @ A @ A ∼ α S ln s ∼ ( α S ln s ) 2 ∼ 1 4 / 54

QCD in the Regge limit LL BFKL Pomeron: basics this results in the effective BFKL ladder, called Leading Log hard Pomeron. reggeon = "dressed gluon" gluon effective vertex one gets, using optical theorem σ tot ∼ s α P ( 0 ) − 1 with α P ( 0 ) − 1 = C α S C > 0 ⇒ Froissart bound violated at perturbative order equivalent approach at large N c : dipole model (Nikolaev, Zakharov; Mueller) based on perturbation theory on the light-cone equivalence between BFKL and dipole model proven at the level of diagrams (Chen, Mueller) and at the level of amplitude (Navelet, S.W.) 5 / 54

Outline QCD in the Regge limit: theoretical status 1 LL BFKL Pomeron k T factorization LL BFKL Pomeron: limitations Higher order corrections Non-linear regime and saturation Onium-onium scattering as a gold plated experiment: γ ( ∗ ) γ ( ∗ ) at colliders Inclusive and Exclusive tests of BFKL dynamics 2 Hadron-hadron colliders HERA Total cross-section at LEP Onium-onium scattering at ILC collider 3 Sources of photons ILC project cost ILC collider Detectors at ILC γ ∗ γ ∗ → hadrons total cross-section γ ∗ γ ∗ exclusive processes 6 / 54

QCD in the Regge limit k T factorization: illustration for γ ∗ γ ∗ → γ ∗ γ ∗ case Use Sudakov decomposition k = α p 1 + β p 2 + k ⊥ and write d 4 k = s 2 d α d β d 2 k ⊥ rearrange integrations in the large s limit: α k ≪ α quarks d β γ ∗ R ⇒ set α k = 0 and β ր r − k k α ց γ ∗ R d α ⇒ set β k = 0 and β k ≪ β quarks ⇒ impact representation note: k = Eucl. ↔ k ⊥ = Mink. d 2 k Z ( 2 π ) 4 k 2 ( r − k ) 2 J γ ∗ → γ ∗ ( k , r − k ) J γ ∗ → γ ∗ ( − k , − r + k ) M = is 7 / 54

Outline QCD in the Regge limit: theoretical status 1 LL BFKL Pomeron k T factorization LL BFKL Pomeron: limitations Higher order corrections Non-linear regime and saturation Onium-onium scattering as a gold plated experiment: γ ( ∗ ) γ ( ∗ ) at colliders Inclusive and Exclusive tests of BFKL dynamics 2 Hadron-hadron colliders HERA Total cross-section at LEP Onium-onium scattering at ILC collider 3 Sources of photons ILC project cost ILC collider Detectors at ILC γ ∗ γ ∗ → hadrons total cross-section γ ∗ γ ∗ exclusive processes 8 / 54

QCD in the Regge limit LL BFKL Pomeron: limitations how to fix the scale s 0 which enters in ln s / s 0 resummation? α S is fixed at LL how to implement running and scale? energy-momentum is not conserved in BFKL approach note that this remains at any order: NLL, NNLL, ... in the usual collinear renormalisation group approach (à la DGLAP), this is naturally implemented in the usual renormalisation group approach (vanishing of the first moment of splitting function): technically, from the very beginning, one starts with non local matrix elements. The energy-momentum tensor corresponds to its first moment, which is protected by radiative corrections 9 / 54

IR diffusion along the BFKL ladder: (for t-channel gluons, k 2 ∼ − k 2 T ) at fixed α S : gaussian diffusion of k T : cigar-like picture (Bartels, Lotter) the more s increases, the larger is the broadness: Q 2 define l = ln (fixed from the probes) Λ 2 QCD and l ′ = ln k 2 ( k 2 =virtuality of an arbitrary exchanged gluon along the chain) Λ 2 then the typical width of the cigar is given by a diffusion picture: ∆ t ′ ∼ √ α S Y QCD ⇒ non-perturbative domain (NP) touched when ∆ t ′ ∼ √ α S Y ∼ t t’ t’ t’ (a) "banana" (b) asymptotic configuration t t t t t t NP NP NP y y y using a simple running implementation tell that the border of the cigare touches NP for Y ∼ b QCD t 3 ( b = 11 / 12 ) while the center of the cigar approaches NP when Y ∼ bt 2 ("banana structure") A more involved treatment of LL BFKL with running coupling (Ciafaloni, Colferai, Salam, Sasto) showed that the cigare is “swallowed” by NP in the middle of the ladder: one faces tunneling when Y ∼ t ! ⇒ IR safety doubtless 10 / 54

Outline QCD in the Regge limit: theoretical status 1 LL BFKL Pomeron k T factorization LL BFKL Pomeron: limitations Higher order corrections Non-linear regime and saturation Onium-onium scattering as a gold plated experiment: γ ( ∗ ) γ ( ∗ ) at colliders Inclusive and Exclusive tests of BFKL dynamics 2 Hadron-hadron colliders HERA Total cross-section at LEP Onium-onium scattering at ILC collider 3 Sources of photons ILC project cost ILC collider Detectors at ILC γ ∗ γ ∗ → hadrons total cross-section γ ∗ γ ∗ exclusive processes 11 / 54

QCD in the Regge limit Higher order corrections Higher order corrections to BFKL kernel are known at NLL order (Lipatov Fadin; Camici, Ciafaloni), now for arbitrary impact parameter n ( α S ln s ) n resummation α S P impact factors are known in some cases at NLL γ ∗ → γ ∗ at t = 0 (Bartels, Colferai, Gieseke, Kyrieleis, Qiao) forward jet production (Bartels, Colferai, Vacca) γ ∗ → ρ in forward limit (Ivanov, Kotsky, Papa) ⇒ this leads to very large corrections with respect to LL rem: the main part of these corrections can be obtained from a physical principle, based on a kinematical constraint along the gluon ladder (which is subleading with respect to LL BFKL (Kwiecinski) However it is rather unclear whether this has anything to do with NLL correction: in principle this constraint would be satisfied when including LL+NLL+NNLL+NNNLL+.... Such a constraint is more related to in the mproved collinear resummed approach (see bellow) for which the vanishing of the first moment of the splitting function is natural. These perturbative instabilities means that an improved scheme is desirable 12 / 54

either use a physical motivation to fix the scale of the coupling running should be implemented at NLL scale is fixed starting from NNLL it has been suggested to use BLM scheme in order to fix the scale: cf γ ∗ γ ∗ → X total cross-section (Brodsky, Fadin, Lipatov, Kim, Pivovarov) and γ ∗ γ ∗ → ρρ exclusive process (Enberg, Pire, Szymanowski, S.W; Ivanov,Papa) either one uses a resummed approach inspired by compatibility with usual renormalization group approach (Salam; Ciafaloni, Colferai): in γ ∗ ( Q 1 ) γ ∗ ( Q 2 ) takes care of full DGLAP LL Q 1 ≫ Q 2 takes care of full anti-DGLAP LL Q 1 ≪ Q 2 fixes the relation between rapidity Y and s is a symmetric way compatible with DGLAP evolution implement running of α S back to the infrared diffusion problem, such a scheme enlarge the validity of perturbative QCD. simplified version (Khoze, Martin, Ryskin, Stirling) at fixed α S ! γ − 1 / 2 e ω Y d ω d γ k 2 1 Z Z k 3 k ′ 3 2 π i 2 π i k ′ 2 ω − ω ( γ ) at LL is replaced by simply performing 1 1 ω − ω ( γ ) ⇒ ω − ω ( γ, ω ) d ω ⇒ pole: one then solves ω = ω ( γ, ω ) d γ at large Y approximation ⇒ Saddle point in γ takes into account the main NLL corrections (within 7 % accuracy) 13 / 54

Outline QCD in the Regge limit: theoretical status 1 LL BFKL Pomeron k T factorization LL BFKL Pomeron: limitations Higher order corrections Non-linear regime and saturation Onium-onium scattering as a gold plated experiment: γ ( ∗ ) γ ( ∗ ) at colliders Inclusive and Exclusive tests of BFKL dynamics 2 Hadron-hadron colliders HERA Total cross-section at LEP Onium-onium scattering at ILC collider 3 Sources of photons ILC project cost ILC collider Detectors at ILC γ ∗ γ ∗ → hadrons total cross-section γ ∗ γ ∗ exclusive processes 14 / 54