Content Introduction Unitarity constraintsˇ Colour Dipole Cascades Saturation, Correlations, and Fluctuations in pp and pA collisions Gösta Gustafson Department of Theoretical Physics Lund University Multiple Partonic Interactions Trieste, 23-27 Nov., 2015 Work in coll. with L. Lönnblad, C. Bierlich and others Colour Dipole Cascades 1 Gösta Gustafson Lund University
Content Introduction Unitarity constraintsˇ Content 1. Introduction. The role of pertubation theory 2. Unitarity constraints. a) Eikonal approximation b) Diffractive excitation 3. BFKL evolution in impact param. space The Dipole Cascade model DIPSY 4. pp scattering /home/shakespeare/people/leif/person 5. pA and AA collisions Colour Dipole Cascades 2 Gösta Gustafson Lund University
Content Introduction Unitarity constraintsˇ 6. Problems with the Glauber or Glauber–Gribov models a) Glauber model and Gribov corrections b) Strikman et al. model c) DIPSY results 7. Conclusions /home/shakespeare/people/leif/person Colour Dipole Cascades 3 Gösta Gustafson Lund University
Content Introduction Unitarity constraintsˇ 1. Introduction DIS at Hera: High parton density at small x grows ∼ 1 / x 1 . 3 Predicted by pert. BFKL pomeron pp coll.: Models based on multiple pert. parton-parton subcollisions very successful at high energies P YTHIA (Sjöstrand–van Zijl 1987) H ERWIG also dominated by semihard subcollisions, although with soft underlying event May be understood from unitarity constraints: CGC: Suppression of partons with k ⊥ < Q 2 s /home/shakespeare/people/leif/person When perturbative physics dominates, can the result be calculated from basic principles, without input pdf’s? Colour Dipole Cascades 4 Gösta Gustafson Lund University
Introductionˆ Unitarity constraints Dipole evolutionˇ 2. Unitarity constraints Saturation most easily described in impact parameter space Rescattering ⇒ convolution in k ⊥ -space → product in b -space 2 {| A el | 2 + � Unitarity ⇒ Optical theorem: Im A el = 1 j | A j | 2 } Re A pp el small ⇒ interaction driven by absorption Rescattering exponentiates in impact param. space: Absorption probability in Born approx. = 2 F ( b ) ⇒ /home/shakespeare/people/leif/person d σ inel / d 2 b = 1 − e − 2 F ( b ) Colour Dipole Cascades 5 Gösta Gustafson Lund University
Introductionˆ Unitarity constraints Dipole evolutionˇ a) Eikonal approximation d σ inel / d 2 b = 1 − e − 2 F ( b ) If NO diffractive excitation: Optical theorem ⇒ Im A el ≡ T ( b ) = 1 − e − F d σ el / d 2 b = T 2 = ( 1 − e − F ) 2 d σ tot / d 2 b = 2 T = 2 ( 1 − e − F ) d σ inel / d 2 b = ( 2 T − T 2 ) = 1 − e − 2 F /home/shakespeare/people/leif/person Colour Dipole Cascades 6 Gösta Gustafson Lund University
Introductionˆ Unitarity constraints Dipole evolutionˇ b) Diffractive excitation Example: A photon in an optically active medium: Righthanded and lefthanded photons move with different velocity; they propagate as particles with different mass. Study a beam of righthanded photons hitting a polarized target, which absorbs photons linearly polarized in the x -direction. The diffractively scattered beam is now a mixture of right- and lefthanded photons. If the righthanded photons have lower mass: The diffractive beam contains also photons excited /home/shakespeare/people/leif/person to a state with higher mass Colour Dipole Cascades 7 Gösta Gustafson Lund University
Introductionˆ Unitarity constraints Dipole evolutionˇ Good–Walker formalism: Projectile with a substructure: Mass eigenstates Ψ k can differ from eigenstates of diffraction Φ n (eigenvalues T n ) Elastic amplitude = � Ψ in | T | Ψ in � d σ el / d 2 b = � T � 2 ⇒ Total diffractive cross section (incl. elastic): d σ diff tot / d 2 b = � k � Ψ in | T | Ψ k �� Ψ k | T | Ψ in � = � T 2 � Diffractive excitation determined by the fluctuations: /home/shakespeare/people/leif/person d σ diff ex / d 2 b = d σ diff − d σ el = � T 2 � − � T � 2 Colour Dipole Cascades 8 Gösta Gustafson Lund University
Introductionˆ Unitarity constraints Dipole evolutionˇ Scattering against a fluctuating target Total diffractive excitation: d σ tot . diffr . exc . / d 2 b = � T 2 � p , t − � T � 2 p , t d σ el / d 2 b = � T � 2 p , t Averageing over target states before squaring ⇒ the probability for an elastic interaction for the target. Subtract σ el → single diffr. excit.: d σ SD , p / d 2 b � � T � 2 t � p − � T � 2 = p , t d σ SD , t / d 2 b � � T � 2 p � t − � T � 2 = p , t /home/shakespeare/people/leif/person � T 2 � p , t − � � T � 2 d σ DD / d 2 b t � p − � � T � 2 p � t + � T � 2 = p , t . Colour Dipole Cascades 9 Gösta Gustafson Lund University
Introductionˆ Unitarity constraints Dipole evolutionˇ Relation Good–Walker vs triple-pomeron Diffractive excitation in pp coll. commonly described by Mueller’s triple-pomeron formalism proj. Stochastic nature of the y 1 = ln M 2 BFKL cascade ⇒ X Good–Walker and Triple-pomeron describe the same dynamics y 2 = ln s / M 2 ( PL B718 (2013) 1054 ) X target But: Saturation is easier treated in the Good–Walker formalism; /home/shakespeare/people/leif/person in particular for collisions with nuclei Colour Dipole Cascades 10 Gösta Gustafson Lund University
Unitarity constraintsˆ Dipole evolution DIPSY pp resultsˇ 3. BFKL evolution in impact param. space a) Mueller’s Dipol model: LL BFKL evolution in transverse coordinate space Gluon emission: dipole splits in two dipoles: Q 1 1 1 3 r 12 y r 01 2 2 x r 02 ¯ 0 0 0 Q r 2 Emission probability: d P ¯ α 2 π d 2 r 2 dy = 01 /home/shakespeare/people/leif/person r 2 02 r 2 12 Colour Dipole Cascades 11 Gösta Gustafson Lund University
Unitarity constraintsˆ Dipole evolution DIPSY pp resultsˇ Dipole-dipole scattering Single gluon exhange ⇒ Colour reconnection between projectile and target Born amplitude: 3 1 j f ij = α 2 i 2 ln 2 � � r 13 r 24 s 4 2 r 14 r 23 BFKL stochastic process with independent subcollisions: /home/shakespeare/people/leif/person Multiple subcollisions handled in eikonal approximation Colour Dipole Cascades 12 Gösta Gustafson Lund University
Unitarity constraintsˆ Dipole evolution DIPSY pp resultsˇ b) The Lund cascade model, DIPSY (E. Avsar, GG, L. Lönnblad, Ch. Flensburg) Based on Mueller’s dipole model in transverse space Includes also: ◮ Important non-leading effects in BFKL evol. (most essential rel. to energy cons. and running α s ) ◮ Saturation from pomeron loops in the evolution (Not included by Mueller or in BK) ◮ Confinement ⇒ t -channel unitarity ◮ MC DIPSY; includes also fluctuations and correlations ◮ Applicable to collisions between electrons, protons, /home/shakespeare/people/leif/person and nuclei Colour Dipole Cascades 13 Gösta Gustafson Lund University
Unitarity constraintsˆ Dipole evolution DIPSY pp resultsˇ Saturation within evolution Multiple interactions ⇒ colour loops ∼ pomeron loops proj. targ. y Gluon scattering is colour suppressed cf to gluon emission ⇒ Loop formation related to identical colours. /home/shakespeare/people/leif/person Multiple interaction in one frame ⇒ colour loop within evolution in another frame Colour Dipole Cascades 14 Gösta Gustafson Lund University
Unitarity constraintsˆ Dipole evolution DIPSY pp resultsˇ Colour loop formation in a different frame Same colour ⇒ quadrupole May be better described by recoupled smaller dipoles r ¯ r ¯ r r ⇒ smaller cross section: fixed resolution ⇒ effective 2 → 1 and 2 → 0 transitions Is a form of colour reconnection Not included in Mueller’s model or in BK equation /home/shakespeare/people/leif/person Colour Dipole Cascades 15 Gösta Gustafson Lund University
Dipole evolutionˆ DIPSY pp results Collisions with nucleiˇ 4. pp scattering DIPSY results Total and elastic cross sections σ tot and σ el d σ/ dt 10000 UA4 1000 Tevatron MC 100 LHC 10 1 546GeV (x100) 0.1 630GeV (x10) 0.01 0.001 1.8TeV 0.0001 14TeV (x0.1) 1e-05 0 0.5 1 1.5 2 -t (GeV 2 ) /home/shakespeare/people/leif/person Colour Dipole Cascades 16 Gösta Gustafson Lund University
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