DVCS and exclusive vector meson production in DIS Particle days 08 Christoffer Flensburg (continuing Emil Avsars work) PhD under Leif Lönnblad and Gösta Gustafson (Lund)

Contents The need for Fluctuations How our dipole model accounts for it Comparison with experiments Future plans and ideas

Eikonal cross sections Fluctuations are important in the cascade and interaction!

Dipole model in x-space Initial state dipoles in impact parameter space Can account for fluctuations Easier to account for saturation Easier to account for multiple interactions

Dipole cascades in parameter space Can describe both types of fluctuations: Dipole wavefunctions describes the initial particle in dipoles. The cascade describes the evolution. Collide the two evolved initial states, using

Initial Dipole state Lightcone Dipole Wavefunctions Work in mixed lightcone coordinates: x T, p +, p - Often not well known! Ψ Ψ γ (r 1T, z)

Evolution in Rapidity 1  2 splitting Start from Mueller Dipoles (BFKL) –Emission probability (formula?) Can add effects by modifying the emission probability. (Monte Carlo)

Evolution: Energy conservation Small dipoles ↔ high p T Veto emissions with too high p T –Fewer small Dipoles ↔ Easier Monte Carlo Also check p + and p -

Evolution: Running Coupling Scale set by smallest dipole (right??) ↔ largest p T Handled in Monte Carlo

Evolution: Confinement Large dipoles should be confined –Soft effect Massive force carrier  new emission probability –Supresses emission of large dipoles

Evolution: Saturation The dipole swing, a 2  2 interaction 2 dipoles  N 2  kicks in at high density Swings to smaller dipoles –Small dipole has lower interaction probability So limits growth at high density

Evolution in our model Mueller dipoles in impact parameter space Evolve in rapidity from initial wavefunction: 1 to 2 splitting Energy conservation Running coupling constant Confinement 2 to 2 swing Saturation

Life of a Dipole

Collision in our model Interaction probability Sum over all pairs of dipoles, and unitarise: Average and integrate over b.

Our Model in two slides (2) Starting dipole configuration (wavefunctions) for photons, mesons and protons. Interaction probability for 2 sets of dipoles. Can calculate cross sections!

What xsecs can we calculate? Xsec for any high energy collision where the initial states can be modeled by dipoles. –Total, diffractive, elastic pp –Total γ *p as function of W and Q. –Quasielastic γ *p γ * --> real photons. (DVCS) γ * --> vector mesons.

What do we need? Two parameters in evolution –Λ QCD –Confinement scale r max Dipole Wavefunctions. –Photon WF calculated perturbatively. VMD corrections needed for small Q 2. –Proton and Mesons need to be modeled. –Proton modeled by dipole triangle. –Different meson models are tested.

Proton Wavefunction Triangle of dipoles Size distribution: –Gaussian distribution exp(r 2 /R 2 ) Standard solution. 3 particles in same spot? Wrong elastic/total xsec. Too wide distribution. –Shifted gaussian exp((r-R) 2 /w 2 ) One extra parameter Tuning: w  0 (no/small fluctuations in proton size) Correct elastic/total xsec. Correct t distribution.

Proton results Tuning of evolution and proton parameters. (Note, energy dependence tune independent) (As is large -t xsec)

Photon wavefunction Can be calculated perturbatively –Works fine for high Q 2. –Not so good for low Q 2. Soft corrections: –Confinement. Can reuse r max. No new parameters. –Vector meson resonance. Parametrised enhancment. New parameters. 

Photon results VMD correction in photon WF.

Vector Meson Wavefunction There are models around. We have some information: –Decay rate. –Normalisation. –Long range interaction. DGKP Dosch, Gousset, Kulzinger, Pirner Boosted Gaussian Forshaw, Sandapen, Shaw

Vector Meson Results (rho) Similar results for phi and J/Psi. J/Psi more model dependent.

J/Psi (and other heavy quarks) Vector meson resonance was tuned for light quarks. (mainly) Would need to retune for charm quarks to find reliable J/Psi predictions. –Resonance for much smaller dipoles. Can be done, but would not be that much experimental data left to predict… Don’t bother for now. (maybe later)

Future plans. Exclusive final states.

Problems Need to decide which dipoles interact. Need to decide which dipoles to keep, and which to reabsorb. Need to decide exactly how to reabsorb virtual dipoles.

Example xTxT y Send to FSR.

Summary Fluctuations in cascade and interaction needed. Can be done in an initial state, impact parameter dipole model. Accounts for many other effects. Can be applied to many processes. –Good results Working on final states.

Thank you for your attention. Christoffer Flensburg (continuing Emil Avsars work) PhD under Leif Lönnblad and Gösta Gustafson Particle days 08