Lepton Pair Production Generator For CMS.

1. The XII-th International School-Seminar Lepton Pair Production Generator For CMS. • The Actual Problems of Microworld Physics Y. Dydyshka*, V. Yermolchyk* *National Center of Particle and High Energy Physics of the Belarusian State University (Minsk, Belarus) 2013

2. CMS: Compact Muon Solenoid • is a powerfull muon detection system • known (Z0,W±,Upsilon) and unknown (Z‘,G) particles have decay modes with muons • resultsof measurements are so precise, that advanced theoretical tools are needed to predict or reproduce them

3. Monte-Carlo Generator • is a stochastic simulation tool. • is not an Integrator (value of integral is a byproduct, main product – events) • any observable can be investigated (filling histograms, density-plots etc.) • any cuts can be applied • error estimate is reliable and stable • easy for parallelization

4. Importance Sampling • to flatten a peak – change variable: • in tree-level amplitude all peaks are due to propagators • Can we parametrize phase-space by invariant variables, which appear in propogators?

5. Cutting lines • changing of variables is as simple, as taking integrals with δ-functions: • problem now reduces to « generalized unitarity » integrals • now all (intermediate and final) particles are « on-shell » • what about « simple unitarity »?

6. Optical Theorem • squared amplitude is imaginary part of multi-loop diagram

7. Loop Contraction • we are going to integrate loop-by-loop

8. Reconstruction • one-loop sub-diagrams can be used for reconstruction of the momentum, running in the loop • external legs are used to determine reference frame and axes directions • boosts and rotations can easily be performed by operators from Clifford-algebra

9. Cuts and Limits • for each “propagator” variable there are limits, which must be determined • they depend on inner-loop masses and outer-loop variables • limits can be modified by applying user cuts • we adopt interval arithmetic package for doing this job

10. LePaProGen • is generator for Drell-Yan process:p+p-→ γ,Z→ μ+μ- • for “charged-current” Drell-Yan:p+p-→ W + → μ+ν • with one-loop electroweak corrections • with exact hard QED Bremsstrahlung contribution: p+p-→ l+l- + γ • QCD and double-Bremsstrahlung are in development:p+p-→ l+l- + γ/g + γ/g

11. LePaProGen Interfaces • can be Pythia8 plug-in; • Les Houches Accord (LHA) event format; • HepMC output format; • LHAPDF interface for parton density functions; • variety of renormalization schemes; • POWHEG-like matching (in preparation).

12. Some plots: pseudo-rapidity

13. Some plots: transverse momentum

14. Some plots: pair invariant mass

15. Some plots: correction δ=Δσ/σ M, GeV

16. Conclusions • proposed method of generation and reconstruction is proved to be efficient (event acceptance ratio ~3%) • all necessary interfaces for inclusion into CMS analysis infrastructure next steps: • comparison against other existing codes (HORACE, POLRAD etc.) • matching with parton shower MCs

17. Thank you!