PHOTOS MC Event Generator Simulating QED radiative correction in decays 徐庆君 Xu Qingjun 杭州师范大学理学院 Collaboration with Z.Was 中国高能物理学会第十次会议， 2010 年 4 月 19 日，南昌

MC Event Generator, 徐庆君 2 Outline Recent Development of PHOTOS MC Introduction PHOTOS MC Event Generator Summary and Outlook

MC Event Generator, 徐庆君 3 Introduction Theory σ,Γ, Br and Distributions Very Important!! Tell the experiment where to go Events written in 4-momentum MC Simulation with detector effects MC Events in 4-momentum Exp. Compare Phenomenology TheoryExp. = Or not!! Conclusion: MC Integration Further discussions

MC Event Generator, 徐庆君 4 Introduction: MC Integration vs. Simulation For an integral: MC Integration MC Simulation Use approximationInstead of, following steps of MC Integration, events are saved for future use Calculate weight Events are accepted ifW is the maximum weight, Otherwise we reject them. Statistical error Rejection density

MC Event Generator, 徐庆君 5 Introduction MC Event Generator QCDQED New Physics PHOTOS MC Event Generator PHOTOS is used to simulate QED effects in decays It is widely used (LEP. LHC, DESY, KEK, SLAC, BEPC, BELLE, BARBAR) and has 300+ citations PHOTOS can be combined with other main process generators Process independent kernel is used in PHOTOS Systematic error needs to be controlled process by process

MC Event Generator, 徐庆君 6 PHOTOS MC: simulate QED effects Using Feynman rules, calculate Calculate virtual QED corrections Calculate soft and collinear photon contribution ++ free of IR and collinear divergences = Calculate non-collinear photon contribution, add corrections of virtual and real photon together, we get one-loop level result Normal way to study QED radiative correction (1 +)+ non-collinea r

MC Event Generator, 徐庆君 7 PHOTOS MC: simulate QED effects PHOTOS MC simulates hard photon emission from final states A process independent kernel is used instead of exact matrix element, it satisfies: in soft and collinear limits, Lim = =remaining part+ Phase space is exact, factorized into Born level Amplitude and phase space Process independent kernel and exact phase space Events (suppose to be events with and without hard photon) Events with hard photon Affects the precision

MC Event Generator, 徐庆君 8 PHOTOS MC : study the precision How to increase the precision (important for exp. systematic error ) Write it into two parts, one is same as the kernel in PHOTOS, another is remaining part (it is small normally). The remaining part is process dependent and decide the precision of PHOTOS Compareresults using Consist, OK Not consist, Should the remaining part be considered at two-loop order? Calculate QED corrections, implement it into PHOTOS Study the amplitude of hard photon emission help to build other generators 1.Increase the precision of PHOTOS 2. find the similarity of processes in different theory framework (QCD, QED, Scalar QED) Study the underlying theory

MC Event Generator, 徐庆君 9 Status of PHOTOS MC Original references QED, Scalar QED decay processes in PHOTOS At this moment PHOTOS kernel is a very good approximation. Multi-photon emission can be simulated. G. Nanava, Qingjun Xu and Z. Was, arXiv: [hep-ph] Qingjun Xu and Z. Was, arXiv: [hep-ph] At work decay

MC Event Generator, 徐庆君 10 Recent Development: Consider For precision measurement of g-2

MC Event Generator, 徐庆君 11 Recent Development: Similar factor in QCD Amplitude Similar to Scalar QED kernel Born level amplitude

MC Event Generator, 徐庆君 12 Recent Development:, fraction of events with,hard photons

MC Event Generator, 徐庆君 13 Recent Development: Conclusion: for the integration and invariant mass distribution, not well for the angular distribution!! agrees with the scalar QED kernel very well Compare complete amplitude with the kernel Differences in some range of phase space Numerical results are consistent with POKAHARA MC Event Generator

MC Event Generator, 徐庆君 14 Recent Development: Following approximations in Eur.Phys.J.C64 (2009)47-54, neglecting diagrams with photons emission from hadronic and weak blocks For precison measurement of pipi scatering lengths Part of diagrams

MC Event Generator, 徐庆君 15 Recent Development:

MC Event Generator, 徐庆君 16 Recent Development:

MC Event Generator, 徐庆君 17 Recent Development: Implement QED correction to PHOTOS MC, compare it with Coulomb correction used by CERN NA48 (K meson experiment) Solid line: Coulomb correction Dashed line: QED correction Difference of Coulomb correction and QED correction

MC Event Generator, 徐庆君 18 Recent Development: Compare result from analytical expression for hard photon with result from PHOTOS kernel Ratios of result from PHOTOS to results using soft-photon and hard-photon expression for hard photon emission., where we set varies from Note that Conclusion: the agreement is good for hard photon expression Differences in harder photon energy range can be seen Next step: photon emission from hadronic blocks will be considered!!

MC Event Generator, 徐庆君 19 Recent development: Precise measurement of decay (no numerical results) form factor and CKM mixing angle Helpful for simulating B → D e ν(γ), D → pi (K) e ν(γ) For B exp. and BESIII Consider at low energy neglected Rewrite it into three gauge invariant parts Collinear singularity Soft and collinear singularities No singularity, dropped by previous references

MC Event Generator, 徐庆君 20 Summary and Outlook PHOTOS is a widely used MC event generator which simulates QED radiative correction in decays Controlling the precision is necessary and important process at work, simulating B and D meson semileptonic decays Future work: D, J/Ψ, Ψ(2s) semileptonic decays If you have a new idea and/or find something very interesting, it is better to simulate your process and send the code to the experimentalist directly. Exchange Idea and Code Exchange Idea

MC Event Generator, 徐庆君 21