Fedra Virtual Monte Carlo. Applications

Transcription

1 Fedra Virtual Monte Carlo. Artem V.Chukanov, Dmitry V.Naumov, Elena A.Naumova, Andrey S.Sheshukov, Svetlana G.Zemskova Opera Internal Note 95 October 24, 2008 Abstract In this document we describe a developed package used for simulation, reconstruction and analysis of OPERA bricks FedraVMC. The developed package is light, flexible and user friendly. We demonstrate various ways to work with it ranging from tracing particles generated by the OPERA OpSim neutrino generator at the primary vertex through the OPERA brick using Geant3, Geant4 or FLUKA, generation of any user defined primary particles like τ, µ, proton, charmed mesons, and others to simulation of cosmic muons background after the brick assembling procedure and alignment of brick emulsion layers. This note covers also issues related to installation and maintainence of the package. The package is an open source software for the OPERA Collaboration members. 1

2 PAGE 2/31 Contents 1 Introduction 3 2 Overview of FedraVMC package The FedraVMC organization FedraVMC Event The FedraVMC maintenence Contact information Running examples Batch and Graphic User Interface (GUI) Simulation of neutrino events Envoking reconstruction Getting online help Generation of cosmic muon background OPERA brick transportation and cosmic muons Simulation: ν event plus remnants of cosmic muons tracks Emulsion brick alignment Introduction to the problem Analysis flow Results Discussion Comparison of Geant3, Geant4 and FLUKA τ decays Charm decays Summary 29 2

3 PAGE 3/31 1 Introduction A search for ν µ ν τ oscillations is not possible without a reliable simulation and reconstruction algorithms. A general scheme for developing the reconstruction algorithms is to confront the reconstruction output with a true information on the input. A detailed simulation of interesting effects gives a solid ground for such an input. ν µ ν τ oscillations would manifest themselves via appearance of τ lepton decaying after some tens of microns in the OPERA brick. The τ lepton can be recognized via its kink decay with a track suddenly changing its direction on a sizeable angle. The tracking accuracy at the level of (0.1 1)µm is the main motivation to use emulsions as the tracking medium. However in real life one meets a lot of effects and problems which should be carefully studied. We mention just a few of them: physics at the primary vertex like: charm production and decay mimicking τ decays, transportation of particles through the OPERA brick: scattering of particles, electromagnetic and hadronic interactions which might break the particle track or hide the true τ by a lot of background hits close to the primary vertex thus loosing the efficiency, mechanics of emulsions: small shifts of emulsion layers and their distortions due to the brick development may result in a false kink structure of a track or in a loss of a true τ decay. It is desirable that reconstruction algorithms can be tuned on simulated events which take into account the above mentioned (and others) effects. Since these effects are related to the OPERA brick it might be useful to use a software focusing just on the brick and ignoring the rest part of the OPERA detector. For such a purpose we developed a light and flexible framework which can be used as simulation reconstruction analysis chain for the OPERA brick. Our package allows also to perform simulation of events in array of emulsion bricks. The software has the following features: Simulation of primary particles: - neutrino events generated in the primary vertex by the OPERA OpSim generator - other charged and neutral particles which a user could choose either in a batch mode, or within GUI and immediately see the result of both simulation and reconstruction. Transportation of particles through the OPERA brick: use of Virtual Monte Carlo allows us to have three transportion engines: - Geant3 [1] 3

4 PAGE 4/31 - Geant4 [2] - FLUKA [3] Developed analysis tools - Generation of cosmic muons background - Study of misalignment of emulsion layers in the OPERA brick User interface - A set of macros is provided as tutorials for a fresh user - Graphical User Interface with intuitive buttons for simulation and reconstruction. The developed package named FedraVMC has not aim to replace simulation and reconstruction of OpSim software. Instead we consider FedraVMC as a complimentary tool which is a fast, flexible and user friendly framework for simulation, reconstruction and analysis of the OPERA emulsion brick. Its advantages include: working interface to Geant3, Geant4 and FLUKA, graphical user interface and interface to FEDRA reconstruction algorithms. The note is organized as follows. In Sec. 2 we overview our package, where we describe its main ingredients, organization and maintenance. In Sec. 3 we describe possible modes of running FedraVMC. Sec. 4 is devoted to description of a special class which simulates the cosmic muon background leaving tracks in the emulsions during the pack s shipment to Gran Sasso. In Sec. 5 we present with some more details an analysis of alignment accuracy of OPERA brick planes using a special cosmic muons exposure. A preliminary comparison of Geant3, Geant4 and FLUKA transportation of particles through the OPERA brick is reported in Sec. 6. Finally, in Sec. 7 we summarize. 4

5 PAGE 5/31 2 Overview of FedraVMC package FedraVMC stands for FEDRA Virtual Monte Carlo which is a package of C++ libraries. The package is based on ROOT VMC [5] which provides the interfaces to well known transportation engines: Geant3, Geant4 and FLUKA. The advantage of using VMC interface is that one defines the detector geometry and properties via ROOT TGeo classes [4] and the concrete transport engine is defined at the run-time of user application. Therefore one can simulate a registration of events making use of different transport engines within exactly the same user code. FedraVMC simulates neutrino interactions in the OPERA bricks and transport the particles through the OPERA brick material using one the available transportation software: Geant3, Geant4 and FLUKA. Also FedraVMC is interfaced to FEDRA [6] package which enables us to reconstruct the simulated event. Finally we develop various analysis modules within the FedraVMC framework. The package was tested with Geant3, Geant4 and FLUKA. 2.1 The FedraVMC organization In Fig. 1 we display the FedraVMC package organization. Figure 1: FedraVMC packages organization 5

6 PAGE 6/31 Simulation Inputs: - Reads output from OpSim HBOOK ntuples with primary vertices - User defined primary particles (leptons, hadrons, whatever...) - A generic interface to any other generator can be implemented Transportation engine can be defined at the run time: - Geant3 - Geant4 - FLUKA In general these transportation engines are not identical. While they are expected to describe in a similar way the electromagnetic interactions they drastically differ for hadronic interactions, implemented decays and sets of supported particles. In Sec. 6 we attempt to compare these engines for the OPERA brick. Saving simulation output: - to FedraVMC Root Event (see Sec. 2.2) - to FEDRA couples format converted from FedraVMC event Reconstruction: - Envokes FEDRA reconstruction routines to reconstruct FEDRA native events converted on fly from the FedraVMC Root Event - User can play with reconstruction parameters ONLINE: re-reconstruct the same event with new parameters, etc Background - We have developed a special class which simulates the cosmic muon background (see Sec. 4). 2.2 FedraVMC Event FedraVMC stores its output in the Root TTree object with VMCEvent objects as entries. The schematic view of VMCEvent object is given in Fig. 2. The VMCEvent is a container of three objects as show in a piece of code below: class VMCEvent: public TObject { <skip> private: <skip> VMCEventHeader *fheader; TObjArray *fdetresponse; TObjArray *ftracks; 6

7 PAGE 7/31 VMCEvent VMCEventHeader array of TGeoTrack array of DetectorResponce frun fn fpdg fenergy fw2 Run number Event number Beam particle PDG code Beam particle energy Event W2 fbrickid fplates fnumofplates ftotalenergyreleased factiveplates Number of brick Array of plates with hits Number of plates with hits Total energy release in brick list of names of active plates fq2 fnu fxbj Event Q2 Event nu Event Xbj array of EMCPlate fybj fposx fposy ftaudecayx ftaudecayy Event Ybj Beam particle position.x Beam particle position.y Tau decay position.x Tau decay position.x fplateid ftotalenergyreleased fhits fnumofhits ID number of this plate Total energy released in this plate Array of hits in this plate Number of hits in this plate ftaudecayz Tau decay position.z array of EMCHit fenergyreleased Total energy released in this hit ftrkmomentum Momentum of track which left this hit ftrkmass Mass of particle which left this hit ftrkid ID number of track which left this hit fpdg PDG code of particle which left this hit fhit1 Track hit begin 3D position fhit2 Track end begin 3D position Figure 2: Structure of VMCEvent class in FedraVMC where VMCEventHeader is the object which stores some basic information about event: class VMCEventHeader: public TObject { <skip> private: <skip> Int_t frun; // Run number Int_t fn; // event number Int_t fpdg; // Beam particle PDG code Double_t fenergy; // Beam particle energy Double_t fw2; // Event W2 Double_t fq2; // Event Q2 Double_t fnu; // Event nu Double_t fxbj; // Event xbj 7

8 PAGE 8/31 (...continued) Double_t fybj; // Event ybj Double_t fposx; // Beam particle position.x() Double_t fposy; // Beam particle position.y() Double_t fposz; // Beam particle position.z() Double_t ftaudecayx; // Tau lepton decay position.x() Double_t ftaudecayy; // Tau lepton decay position.y() Double_t ftaudecayz; // Tau lepton decay position.z() The fdetresponse variable in VMCEvent is a collection of DetectorResponse objects class DetectorResponse: public TObject { <skip> private: // brick id number Int_t fbrickid; // information on hits left by a track in plates TObjArray *fplates; // number of hits Int_t fnumofplates; // total amount of energy released in the brick Float_t ftotalenergyreleased; // list of names of already active plates map <Int_t, Int_t> factiveplates; Each element of TObjArray *fplates contains the most basic elements VMCHit which is a simulation hit in the OPERA brick with the following redundant information saved: class VMCHit: public TObject { <skip> private: <skip> // amount of energy released at given position Float_t fenergyreleased; // mass of the particle which left this hit Float_t ftrkmass; // id number of track which left this hit Int_t ftrkid; 8

9 PAGE 9/31 // PDG code of the particle which left this hit Int_t fpdg; // track hit begin 3D position TVector3 fhit1; // track hit end 3D position TVector3 fhit2; // momentum of the track which left this hit TVector3 ftrkmomentum; (...continued) 9

10 PAGE 10/ The FedraVMC maintenence Developers access subversion repository for the most up-to-date versions of the code. Often releases are available from (see in Fig. 3). Figure 3: Visit The webpage contains useful information also on: Release Notes Installation How to run Html Class Documentation Today current version is tagged as v2r Contact information The authors can be contacted via s: Artem V.Chukanov Dmitry V.Naumov Elena A.Naumova Andrey S.Sheshukov Svetlana G.Zemskova zemskova s g@rambler.ru 10

11 PAGE 11/31 3 Running examples 3.1 Batch and Graphic User Interface (GUI) When the package is built one can find the executable VMCSim in the bin directory. It can be run as a batch job:./bin/vmcsim -b or as GUI:./bin/VMCSim A help on the command line arguments can be obtained with:./bin/vmcsim --opt Let us give some examples. A batch job with Geant4 transportation engine with 100 events to generate can be done with a command:./bin/vmcsim -b --events=100 --setup=g4config.c In order to run VMCSim with Geant3 use: --setup=g3config.c Similarly VMCSim with FLUKA can be run as./bin/vmcsim --setup=flconfig.c Let us consider in some details a GUI example. Run it with:./bin/vmcsim An application will be launched and you may see something like shown in Fig

12 PAGE 12/31 Figure 4: FedraVMC GUI 3.2 Simulation of neutrino events One can click on Get previosly generated vertex button which means to select events generated by the OpSim simulation on the level of the primary vertex only (without tracing the primary vertex particles through the detector). After clicking Execute event one may see something like shown in Fig. 5 where an example of ν τ n pτ QEL simulation is presented. There are clearly visible proton track (in red) and the τ track (drawn in black) emerging from the primary vertex. Then the τ decays into µ and two neutrinos. Let us note that the considered example of ν τ n pτ QEL event is just for illustration purpose and the reader should not draw his/her conclusions on any inefficiency appearing in the reconstruction stage in what follows. Let us make a small comment concerning τ lepton production and decay. As it is implemented in the OpSim software the τ lepton does not experience any interaction withing the OPERA brick material decaying just according to its lifetime. This might be a resonable approximation while it needs to be validated. For this reason we have a special option which allows one to track the τ lepton by the tracking engine (Geant3, Geant4 or FLUKA). Let us note that Geant3 does not decay the τ lepton if an external decayer is not envoked, Geant4 decays τ lepton in a very approximate way (with wrong momenta of outgoing particles in leptonic channels and ignoring V A structure of the currents for hadronic channels, while FLUKA seems to do this work properly (see Sec. 6). We add a possibility to visualize the τ trajectory in the GUI mode and let 12

13 PAGE 13/31 the reconstruction programm to reconstruct it. Figure 5: FedraVMC GUI. ν τ n pτ QEL simulation. 13

14 PAGE 14/31 If one clicks on the tab chits then a picture with simulated hits left in the emulsion layers will appear similar to that in Fig. 6. Figure 6: FedraVMC GUI. ν τ n pτ QEL simulation. Hits in the emulsion layers 14

15 PAGE 15/ Envoking reconstruction Setting up a flag Reconstruct will reconstruct the event on fly and display the result in the tab chits as can be seen from Fig. 7. One can observe base tracks in terms of the FEDRA package superimposed by the reconstructed tracks. In this particular example one can note that the muon track was nicely reconstructed while τ lepton and proton left not reconstructed. The τ was not reconstructed because the FEDRA with its default settings 1 accepts the track with at least three segments while in our example τ lepton left only two segments. The proton track was not reconstructed because it was too curved. Obviously one does not pretend to reconstruct the τ track by a default algorithm because in most cases it is very short. Nevertheless for illustration purposes we show how this track can be reconstructed by FEDRA algorithm. Figure 7: FedraVMC GUI. ν τ n pτ QEL reconstruction. Shown base tracks in terms of the FEDRA package superimposed by the reconstructed tracks. 1 Actually there are no default settings and a user must tune the parameters for his/her own analysis. We note it here just as an illustrtation of a possibility to modify the parameters from GUI on fly 15

16 PAGE 16/31 Let us play with the reconstruction parameters and decrease the number of required segments from three to two (see Tab Reconstruction options ). As soon as we modify the parameters the event is reconstructed again and now the τ lepton track is reconstructed as can be seen from Fig. 8. Figure 8: FedraVMC GUI. ν τ n pτ QEL reconstruction. Shown base tracks in terms of the FEDRA package superimposed by the reconstructed tracks. τ lepton track is reconstructed due to lowering nsegmin parameter from three to two (for illustration purpose only). 16

17 PAGE 17/ Getting online help Running./bin/VMCSim --opt you will see on the screen currently available options:... Description of supported flags -b flag is for the batch processing. --events=n set up number of events n to simulate --seed=n set up the seed init number. Put a large and unique number if you want a new sequence --emin=emin set up the minimum kinetic energy [in GeV] to simulate --emax=emax set up the maximum kinetic energy [in GeV] to simulate --tmin=thetamin set up the minimum zenith angle [in deg] to simulate --tmax=thetamax set up the maximum zenith angle [in deg] to simulate --run=n set up the run number --setup= set up the Transporter: Geant4 (g4config.c), Geant3(g3Config.C), FLUKA(flConfig.C) via the corresponding config file --gener= set up the Generator to use: OperaHbook, PromptTracks Exit... FEDRA VMC completed. 17

18 PAGE 18/31 4 Generation of cosmic muon background 4.1 OPERA brick transportation and cosmic muons The cosmic muons extensively hit the emulsions during the pack s shippment to Gran Sasso thus producing the background tracks in OPERA emulsion. At Gran Sasso the OPERA bricks are assembled exchanging emulsion layers order from top to bottom and alternating with lead plates. This assembling procedure is known to breakdown the straight tracks left by muons. FedraVMC contains a special class which was developed to simulate the cosmic muon background. In its current implementation the algorithm consists of the following steps: it assumes that muons leave straight line tracks in the emulsions (no transportation engine used). exchange emulsion layers from top to bottom and add the lead layers. user can define random shifts of emulsions planes during the OPERA brick assembling procedure. In one of the next releases of FedraVMC will have an improved version of the background simulation: propagate muons with user defined spectrum through the OPERA brick (without lead as correct for the transportation mode) and save the output emulsion segments user defined three dimensional volume of OPERA brick in which the cosmic muon background is to be simulated 4.2 Simulation: ν event plus remnants of cosmic muons tracks A result of such a preliminary simulation is shown in Fig. 9. On the top plot the simulated ν τ n τp τ µ ν τ ν µ event is shown. Bottom plot of the same figure displays the reconstructed by FEDRA tracks superimposed by the cosmic muons background segments simulated by our algorithm. 18

19 PAGE 19/ x x Figure 9: Simulated ν τ n τp event is shown on the top plot. The same event reconstructed by FEDRA and superimposed by the cosmic muons background segments simulated by our algorithm is shown in the bottom plot. 19

20 PAGE 20/31 5 Emulsion brick alignment The content of this section is also mostly for illustrative purposes of the analyses which can be done within FedraVMC framework. We plan to release soon a special note devoted to the estimation of time needed for the OPERA brick exposure in order to achieve the required alignment accuracy using the simulated fluxes of cosmics (µ, e, γ) by M.Sioli[7]. In what follows we present a somewhat simplified approach which nevertheless is useful for qualitative and quantitative estimates. 5.1 Introduction to the problem Assembling of the OPERA brick necessarely introduces misalignments of emulsion layers as shown schematically in Fig. 10. Obviously these misalignments must be taken into account for reconstruction of tracks, their momenta, vertices etc. FEDRA package provides algorithms for alignment procedure. It describes shifts and rotations of OPERA brick planes using 2D affine transformations: ( x y ) ( a11 a = 12 a 21 a 22 )( x y ) ( b1 + b 2 ) (1) Figure 10: Schematic view of misalignment. Left: ideally aligned OPERA brick and a track made of base tracks. Middle: Exagerated shifts of the planes. Right: Basetracks recorded if one assumes an ideally aligned OPERA brick (as shown in the left panel), while in reality planes experienced shifts (as shown in the middle panel). Alignment of the OPERA brick planes can be done using: 20

21 PAGE 21/31 X-rays marks [8] Exposure of extracted OPERA brick to atmospheric muons. 5.2 Analysis flow In this section we apply FedraVMC package to study an alignment accuracy which can be achieved with help of cosmic muons. The analysis scheme is as follows: 1. Define 1 1 cm 2 surface on the top of the brick which will be hitted by muons. We do not introduce any shifts and rotations of OPERA brick planes. Therefore the spread in shifts and rotations obtained after FE- DRA attempts to align the OPERA brick planes will give us the expected accuracy. We study in this note the accuracy in shifts b 1, b 2 and ignore rotations. 2. Generate N µ tracks with given energy E µ, zenith angle Θ µ and isotropic azimith angle φ µ and transform these tracks into FEDRA base tracks objects 3. Align OPERA brick planes using generated FEDRA base tracks objects with help of FEDRA alignment methods and save b 1, b 2 into the output. 4. Repeat steps 2-3 about five hundred times in order to collect the statistics. As an example in left panel of Fig. 11 we display a simulation of GeV muons passing through the OPERA brick, while the right panel shows a reconstruction of left tracks with FEDRA. Figure 11: Left: FedraVMC simulation of 1000 muons passing through the OPERA brick. Right: FEDRA reconstruction of the event from left picture. 21

22 PAGE 22/ Results The results of our analysis are reported below. First we show a three dimensional picture of alignment offsets for vertical 10 GeV muons in Fig. 12. One can conclude that b 1 and b 2 are within something like µm. Also clearly seen is that widths of b 1 and b 2 distributions increase for bottom layers compared to that for top. This feature is even more apparent if we display one dimensional distributions for various groups of layers (we groupped 10 planes together from top to bottom and last 6 plates at the bottom ). In Figs. 13,14 we show distributions of b 1 and b 2 for various slices in z-axis and integral over z for 50 and 250 muons with 10 GeV energy and vertical inclination respectively. Since FEDRA makes alignment between two neighbouring plates, the value to study is relative plates shifts: b i 1 bi 1 1 and b i 2 bi 1 2. Also one can see that the alignment becomes more accurate for larger number of muons used for the aligning procedure. Plate N Y off, micrometers X off , micrometers Figure 12: Shifts in microns b 1 (x-axis), and b 2 (y-axis) for all OPERA brick planes (z-axis). Vertical 10 GeV muons come from the top of the picture. In Fig. 15 we display gaussian σ of b 1 and b 2 distributions for muons with E µ = 10 GeV and vertical inclination as a function of number of muons. One can conclude from these plots that the alignment accuracy strongly depends on the 22

23 PAGE 23/31 X offset for 50 tracks Y offset for 50 tracks Hist2_50_px Entries 8250 Mean RMS X off, micrometers 1-Hist2_50_py Entries 8250 Mean RMS Y off, micrometers Figure 13: Distributions of b 1 (top) and b 2 (bottom) for various slices in z-axis and integral over z for 50 muons with 10 GeV energy and vertical inclination. number of muons passed through the OPERA brick in the interval N µ [1, 100] still improving at N µ > 100. Also the accuracy would improve with rise of the muon energy because less energetic muons have more quaking tracks due to the multiple scattering. 5.4 Discussion Let us summarize the results of our preliminary study. 1. The alignment accuracy of about 1µm can be reached with muons with 1 GeV energy only collecting about 100 muon tracks (see Fig. 15). However the cosmic muons at Gran-Sasso site have a spectrum which has to be taken into account. Also it is important that the real cosmics run will collect not only muons but also electrons and γs. 2. One should take into account that increase in the exposure time while giving better alignment accuracy will add inefficiency in reconstruction of neutrino events. This loss of efficiency must be studied. 23

24 PAGE 24/31 X offset for 250 tracks Y offset for 250 tracks Hist2_250_px Entries 8250 Mean RMS X off, micrometers 1-Hist2_250_py Entries 8250 Mean RMS Y off, micrometers Figure 14: Distributions of b 1 (top) and b 2 (bottom) for various slices in z-axis and integral over z for 250 muons with 10 GeV energy and vertical inclination. 3. We plan to report about a more complete study in a separate note. 24

25 PAGE 25/31 X off, micrometers N tracks Y off, micrometers N tracks Figure 15: Gaussian σ of b 1 (top) and b 2 (bottom) distributions for muons with energy E µ = 10 GeV, and vertical inclination as a function of number of muons (x axis). 25

26 PAGE 26/31 6 Comparison of Geant3, Geant4 and FLUKA This section is in a very preliminary form. We plan to continue this study in a separate note. For the illustrative purpose we show below two examples considered with help of Geant3, Geant4 and FLUKA: τ and D + s decays. 6.1 τ decays The τ lepton with 5 GeV energy enters the OPERA brick and Geant3, Geant4 and FLUKA subsequently propagate this particle. In Fig. 16 we display three examples of simulation of τ lepton propagation through the OPERA brick. One can notice that Geant3 propagates τ until its decay and no decay products appear 2, Geant4 decays τ and traces µ, ν τ, ν µ seemingly reasonable (while in the Geant4 source code we find a statement that the neutrino energies are not correct), FLUKA shows a more complicated picture of τ π π 0 with π 0 γγ. 6.2 Charm decays Charmed particles are a source of dangerous background to the τ lepton appearance. We tried to simulate D + s meson propagation through the OPERA brick using the available engines. We find that both Geant3 and Geant4 can not decay this particle, while FLUKA does as displayed in Fig. 17. We find this as an important argument to use different transportation engines. 2 because an external decayer like Pythia needs to be envoked 26

27 PAGE 27/ x x x Figure 16: Simulation of τ lepton propagation through the OPERA brick with help of Geant3 (Top), Geant4 (Middle) and FLUKA (Bottom). 27

28 PAGE 28/ x Figure 17: Simulation of D + s K + K + K meson propagation through the OPERA brick with help of FLUKA. 28

29 PAGE 29/31 7 Summary We report about a package of C++ classes which is a flexible framework for simulation/reconstruction/analysis and visualization of various phenomena in OPERA brick like: neutrino interactions, propagation of any user defined particles, simulation of cosmic background, alignment procedure. The package might be a usefull tool for members of OPERA Collaboration. We welcome any feedback, comments, critical remarks, suggestions. 29

30 PAGE 30/31 Acknowledgements We have a great pleasure to thank our colleagues Yu.Gornushkin, I.Krelo, A.Olchevski, V.Tereshchenko, V.Tioukov for numerous discussions, help and support. We also thank M.Sioli for sharing his calculations of cosmics fluxes with us, which will be used in forthcoming publication. 30

31 PAGE 31/31 References [1] [2] NIM A 506 (2003), ; [3] A. Ferrari, P.R. Sala, A. Fassó, and J. Ranft, FLUKA: a multi-particle transport code, CERN (2005), INFN/TC 05/11, SLAC-R-773; A. Fassó, A. Ferrari, S. Roesler, P.R. Sala, G. Battistoni, F. Cerutti, E. Gadioli, M.V. Garzelli, F. Ballarini, A. Ottolenghi, A. Empl and J. Ranft, The physics models of FLUKA: status and recent developments, Computing in High Energy and Nuclear Physics 2003 Conference (CHEP2003), La Jolla, CA, USA, March 24-28, 2003, (paper MOMT005) econf C (2003), arxiv:hep-ph/ ; [4] [5] [6] (password protected) [7] private communication [8] 31