In the future high energy physics experiments, the question of properly
matching the phenomenological programs that describe different parts of the
physics processes (such as hard scattering, hadronization, decay of resonances,
detector response, etc.) is very important. In the past, FORTAN common blocks
filled with lists of objects (particles, strings, clusters, etc.) of defined
properties, origins and descendants were in use. Similar structures are now
envisaged, for future programs, to be written in languages such as C++ or Java.
  From the physics point of view such an approach is not correct, since this
kind of data structures impose certain approximations on the physics content.
In the present paper, we will explore their limits, using examples from the
physics of W's, tau's and the Higgs boson, still to be discovered.Comment: latex 10 pages, including 10 attachments in postscript forma

Was, Z.

English

arXiv

In the future high energy physics experiments, the question of properly matching the phenomenological programs that describe different parts of the physics processes (such as hard scattering, hadronization, decay of resonances, detector response, etc.) is very important. In the past, FORTAN common blocks filled with lists of objects (particles, strings, clusters, etc.) of defined properties, origins and descendants were in use. Similar structures are now envisaged, for future programs, to be written in languages such as C++ or Java. From the physics point of view such an approach is not correct, since this kind of data structures impose certain approximations on the physics content. In the present paper, we will explore their limits, using examples from the physics of W's, tau's and the Higgs boson, still to be discovered.In the future high energy physics experiments, the question of properly matching the phenomenological programs that describe different parts of the physics processes (such as hard scattering, hadronization, decay of resonances, detector response, etc.) is very important. In the past, FORTAN common blocks filled with lists of objects (particles, strings, clusters, etc.) of defined properties, origins and descendants were in use. Similar structures are now envisaged, for future programs, to be written in languages such as C++ or Java. From the physics point of view such an approach is not correct, since this kind of data structures impose certain approximations on the physics content. In the present paper, we will explore their limits, using examples from the physics of W's, tau's and the Higgs boson, still to be discovered

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CERN-TH/2002-061March 2002Spin polarizationand the Einstein–Podolsky–Rosen paradoxin the Monte Carlo event records ∗Z. Wa¸sa,baInstitute of Nuclear PhysicsKawiory 26a, 30-055 Cracow, Poland.bCERN, Theory Division, CH-1211 Geneva 23, Switzerland.e-mail: Zbigniew.Was@cern.chAbstractIn the future high energy physics experiments, the question of properly matchingthe phenomenological programs that describe different parts of the physics processes(such as hard scattering, hadronization, decay of resonances, detector response, etc.)is very important. In the past, FORTAN common blocks filled with lists of objects(particles, strings, clusters, etc.) of defined properties, origins and descendants werein use. Similar structures are now envisaged, for future programs, to be written inlanguages such as C++ or Java. From the physics point of view such an approach isnot correct, since this kind of data structures impose certain approximations on thephysics content. In the present paper, we will explore their limits, using examplesfrom the physics of W ’s, τ ’s and the Higgs boson, still to be discovered.Presented at CPP2001 on Automatic Calculation for Future CollidersTokyo Metropolitan Univ., 28–30 November 2001.CERN-TH/2002-061March 2002∗ This work is partly supported by the Polish State Committee for Scientific Research (KBN) grantNo. 5P03B09320, and the European Commission 5th framework contract HPRN-CT-2000-00149.Home page: http://wasm.home.cern.ch/wasm/At present, intensive studies are being performed to design future software architec-tures for experiments on proton proton colliders, such as the Tevatron [1] or the LHC [2,3]and high energy e+e− linear colliders such as JLC [4], NLC [5] or TESLA [6].One of the important ingredients in such designs is the data structure for storing theMonte Carlo events. It is generally accepted that the data structures based on objectssuch as particles, clusters, strings, etc. with properties such as tracks, momenta, colour,spin, mass, etc. and on the relations explaining the origins and descendants of the objectsis the most convenient one. This is the case at present [7], and it is also envisaged for thefuture, see [8]. At the same time such a picture is in conflict with the basic principles ofquantum mechanics. Einstein{Rosen{Podolsky paradox is an example of such phenomena.A general problem is that the quantum state of a multiparticle system cannot (at least inprinciple) be represented as a statistical combination of the states dened by the productsof the pure quantum states of the individual particles. It is thus of the utmost importanceto examine whether the approximation enforced by the data structure is purely academic,or if it rather represents a real diculty, which may aect the interpretation of the futuredata.It would not be a serious problem if the predictions of the Standard Model used inthe interpretation of the future data could be provided by a single program, black box,without any need of analysing its parts. Then anything that would be measured beyondthe prediction of such a hypothetical Monte Carlo program1 would be interpreted as \newphysics". Agreement, on the other hand, would constitute conrmation of the StandardModel, as it is understood at present (and proper functioning of the detector as well).Because of the complexity of the problem, Monte Carlo predictions need to be dealtwith by programs describing: the action of the detector and of the analysis, on theexperimental side, and various eects, such as those from hard processes, hadronization,decay of resonances, etc., on the theoretical side. Every part is inevitably calculatedwith some approximation and, as a consequence, some systematic errors aect thesepredictions.In the following, we will omit these complex issues from the discussion. We will limitourselves to the question of spin eects, more precisely to the consequences of approxima-tions used in combining production and decays of the intermediate states. As exampleswe will use eects in the production of pairs of  -leptons and W -bosons2.I advocate here that spin eects are non-treatable in the scheme where properties areattributed to individual particles only, in spite of the fact that it is the very method weused in KORALZ [9] { the program widely used at LEP for the simulation of  -lepton pairproduction and decay, including spin and QED bremssstrahlung eects. As described inref. [9] the algorithm of spin generation for any individual event was consisting of thefollowing steps:1. An event consisting of a pair of  leptons, bremsstrahlung photons, etc., was gener-1As experimental data are always obtained with imperfect detectors, cuts, inefficiencies, etc. theoreti-cal predictions must be convoluted with the experimental effects. Monte Carlo simulation techniques arethe only tools, for the time being, able to complete the task.2For the sake of convenience, I will use as examples theoretical calculations I was involved in myself.1ated.2. Helicity states for both + and − were generated. At this point, an approximationwith respect to quantum mechanisc was introduced.3. Information on these helicty states, including the denition of quantization frames,i.e. the relation between  ’s rest frame and laboratory frame, was then transmittedto TAUOLA [10{12], the package for the generation of  -lepton decays.4. Finally TAUOLA performed decays of 100% polarized  ’s, and the event in the HEPEVTcommon block was completed. It was not considered necessary to store the informa-tion about spin degrees of freedom; however, it proved convenient, for applicationsthat rely on the approximate spin picture.At LEP, in (nearly) all cases, such an approach was sucient. Thanks to the ultrarel-ativistic nature of  -leptons (mτmZ)2  1, missing eects were in most cases negligible.Let us note, however, that it was not always the case. Thanks to the excellent perfor-mance of the LEP detectors it was necessary to revisit the complete spin eects [13] andindeed the eects turned out to be measurable [14,15]. Even more important was the caseof complete spin eects in the measurement of the  -lepton lifetime, using the method ofimpact parameter sum (see e.g. [16]). In that case, terms missing in KORALZ were not atall suppressed by the mass factors. Fortunately we could recall the solution of KORALB[17, 18], which was always serving as a backup solution for the spin treatment in KORALZ.KORALB relies on the full spin density matrix, but includes rst order bremsstrahlung cor-rections only; it also misses electroweak corrections, necessary in high precision studies ofLEP.We conclude that the solution for the spin treatment of  leptons at LEP was optimal.On one side, a convenient picture of particles with properties, origins and descendantscould be used and, on the other, a complete full spin solution was available, if necessary.Let us now turn to another example of the spin eect, this time in the process, whichcan be a source of a background. Let us consider a semi-realistic observable of invariantmass distribution for pairs of s-flavoured jets, and its background from the four-jet processin the e+e− annihilation into four quarks (ccss jets) at the 350 GeV centre-of-mass energy,with the veto cut on c-jets forcing them into directions close to the beam pipe. We willnot discuss details of the study, which is presented in ref. [19]. We will simply recall somenumerical results from that paper. In g. 1, thin line represents the result of the completeCC-433 matrix element. Not only the expected peak of Z-boson is clearly visible, but thereis another one, at high energies as well. If we reduce the matrix element to the simple caseof CC-03, where the double resonant WW -pair production is kept only (thick line), theZ resonance disappears, but the second peak remains visible. In g. 2 we investigate theorigin of the second peak even further. We compare the CC-03 (distribution identical tothat in the previous gure) with the case when transverse spin correlations are switched3At the Born level there are in total 43 diagrams for the charge current mediated e+e− → cs¯c¯sprocess. This number is reduced to 3 if only the doubly W -resonant diagrams are taken.2o. The dierence is enormous. Not only is the peak at high energies reduced by a factorof 4, but also a huge shoulder of the distribution forms at lower invariant masses. There isno question, if an observable like ours was used in a search for new particles, that the lackof proper spin eects in the code simulating the background could lead to diculties indata analysis and even to the temporary \discovery" of non{existing resonance for smallexperimental samples.100 200 30000:5  10 41:0  10 41:5  10 42:0  10 4Mss[GeV]ddMss[pb]CC-43CC-03Figure 1: The ddMss¯ dierential distribution of the invariant mass of the \visible" ssjet pair. Veto cut on cc jets is applied. The centre-of-mass energy is 350 GeV. Matrixelement of type CC-03 (thick line) and type CC-43 (thin line). For details, see the textand ref. [19].Is this example really worrisome? Probably not. At the future high energy experi-ments, data will be collected in sucient quantities, all Monte Carlo programs will usethe matrix elements for the combined production and decay of the W -pairs with no ap-proximations. Already now the physics of the W -pair production is well established andthe separation between production and decay is neither necessary (all its decay channelscan be described by the same matrix element) nor convenient; eects due to the structureof the W propagator make the separation into production and decay complicated.Let us now turn to another example of the spin implementation algorithm. It is takenfrom ref. [20]. The algorithm, essentially that of KORALZ, was adopted to work with anyMonte Carlo program providing the production of  -leptons. If the generated events are3100 200 30001  10 42  10 43  10 44  10 4Mss[GeV]ddMss[pb]no-spinspin onFigure 2: The ddMss¯ dierential distribution of the invariant mass of the \visible" ss jetpair. Veto cut on cc jets is applied. The centre-of-mass energy is 350 GeV. Matrix elementof type CC-03: no spin correlation (thin line), of type CC-03: with spin correlationsswitched on (thick line). For details, see the text and ref. [19].stored in the format of a HEPEVT common block, then the algorithm consisting of thefollowing basic steps can be used:1. Search for  -leptons in a HEPEVT common block (lled by any MC program).2. Check what the origin of {lepton is: Z; γ; W; h; H or eventually, 2 → 2{bodyprocess such as: e+e−; (uu); (d d) → +−.3. For the 2→ 2{body process of  -pair production, it is sometimes possible to calcu-late the  polarization as a function of the invariant mass of the {lepton pair andangle between the directions of {leptons and incoming eective beams (in the restframe of  -pair).4. If in addition to the  -leptons, photons or partons (gluons, quarks, etc.) are storedin HEPEVT common block, one needs to dene the \eective incoming beams".5. From such an information one can generate  helicity states and dene the relationbetween the  rest frame and the laboratory frame.6. The  decay is generated with the help of a program such as TAUOLA.47. Finally the entire event stored in a HEPEVT common block is appended with the ’s decay products.8. Optionally the nal-state bremsstrahlung (emission from  -leptons) can be gener-ated using PHOTOS [21, 22].As we can see in gs. 3 and 4, all leading spin eects are nicely reproduced by theabove set of programs. A more complete discussion can be found in ref. [20].Nevt(arbitrary units)2E=ps0:25 0:50 0:75 1:00aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaNevt(arbitrary units)Fast-FastSlow-SlowFast-SlowSlow-FastFigure 3: Basic properties of the spin eects in the case of  -leptons produced from Z=γintermediate state. The eects of  polarization are in the left-hand side plot. We cansee the slope of the  energy slopes calculated in the Z boson rest frame. The eects ofthe spin correlations are in the right-hand side plot. See ref. [20] for details.The Monte Carlo PHOTOS, is another example of a program that uses a HEPEVT com-mon block as a data structure. Its role is to generate, whenever suitable, bremsstrahlungphotons in the decays of particles, resonances or sometimes from other intermediatecharged states. The program was developped starting from the careful downgrading of thematrix element MUSTRAAL Monte Carlo [23], more precisely its part describing the decayof a Z to a pair of leptons. Then, the algorithm was extended to work for the decay of\any" particle or resonance. By construction it is limited to leading logarithmic (ll) ap-proximation with proper soft-photon angular distributions only. Thanks to comparisonswith codes based on matrix elements, PHOTOS was checked to performed better than ll inthe following cases:  → eγ,  → γ, Z → +−γ(γ), gg → ttγ(γ).5P(cos )cos ps =MZ  3GeVps =MZps =MZ+ 3GeV 1:0  0:5 0:0 0:5 1:0 1:0 0:50:00:51:0P(cos )cos ps =MZ  3GeVps =MZps =MZ+ 3GeV 1:0  0:5 0:0 0:5 1:0 1:0 0:50:00:51:0Figure 4: Angular dependence of the  polarization produced through Z=γ intermediatestate at energies close to the Z mass from u flavour (left side) and d flavour (right side).See ref. [20] for details.In the special case of a hypothetical (scalar or pseudoscalar) Higgs boson decayh → +−, it is possible to dene the full spin density matrix for the pair of  -leptons,independently of the Higgs boson production mechanism. The previously discussed algo-rithm of the spin implementation was extended (ref. [24]) to include the full spin eects inthat case. As we can see in g. 5, the program reproduces the eects of the Higgs paritycorrectly for the + − acollinearity calculated in the rest frame of the Higgs boson anddecay chain h→ +−;  → τ [25]. When some detector smearings are introduced,see g. 6, the eect becomes less visible. In this example, the Higgs-strahlung productionmechanism at 350 GeV centre-of-mass energy was generated with the help of PYTHIA [26];see ref. [24] for details of the study.SummaryWe can conclude that, in none of the discussed cases was it necessary to store spindegrees of freedom in the event records. In fact, storing such information in an approx-imate way as an attribute of particles would not lead to the correct solutions anyway.The general principle was shown of how to construct an interface that can calculate therelevant multiparticle density matrix from the kinematical information stored in the eventrecord. A backup solution was always necessary.Another solution relies on algorithms where decays and productions of some interme-6diate states are embodied in the monolithic program individually tailored to the process.This is a good approach in cases such as production and decay of () (WW ) (ZZ) in-termediate states. It may be reasonable as well for the case of tt production and decay,even though at least 6-body nal states will have to be generated in single steps. Sucha solution may pose problems if production and decay of pairs of new particles carryingspin will be discovered, especially if a multitude of decay channels, each described by adistinct model, would have to be combined.We think that non-factorizability of the spin density matrices into properties of indi-vidual particles is important, and should be borne in mind in the discussions of futurestandards for event records, and redesigned software for high energy physics.3:02 3:03 3:04 3:05 3:06 3:070:0  1040:5  1041:0  1041:5  1042:0  1042:5  1043:0  1043:08 3:09 3:10 3:11 3:12 3:13 3:140  1041  1042  1043  104Figure 5: The +− acollinearity distribution (angle ) in the Higgs boson rest frame.Parts of the distribution close to the end of the spectrum;  ∼  are shown. The thickline denotes the case of the scalar Higgs boson and the thin line the pseudoscalar one.AcknowledgementsThe inspiring atmosphere at the ECFA-DESY workshop in Cracow and CPP Tokyowas essential to the performance of this work. The author is specially grateful to M.Ronan for a discussion.References[1] M. Carena et al., “Report on the Tevatron Higgs Working Group”, hep-ph/0010338.[2] CMS Collaboration, “Technical Proposal”, CERN/LHCC/94-38.73:02 3:03 3:04 3:05 3:06 3:070:0  1040:5  1041:0  1041:5  1042:0  1042:5  1043:0  1043:08 3:09 3:10 3:11 3:12 3:13 3:140  1041  1042  1043  104Figure 6: The +− acollinearity distribution (angle ) in the scalar Higgs boson recon-structed rest frame. Parts of the distribution close to the end of the spectrum;  ∼ are shown. The thick line denotes the case when all spin eects are included, while onlylongitudinal spin correlations are taken for the thin line.[3] ATLAS Collaboration, “ATLAS Detector and Physics Performance: Technical De-sign Report”, CERN/LHCC/99-15.[4] ACFA Linear Collider Working Group Collaboration, “Particle physics experimentsat JLC”, hep-ph/0109166.[5] NLC Collaboration, “2001 Report on the Next Linear Collider: A Report submittedto Snowmass 2001”, SLAC-R-571.[6] F. Richard, J. Schneider, D. Trines, and A. Wagner, “TESLA Technical DesignReport Part I: Executive Summary”, hep-ph/0106314.[7] Particle Data Group Collaboration, C. Caso et al., Eur. Phys. J. C3 (1998) 1.[8] E. Boos et al., hep-ph/0109068.[9] S. Jadach, B. F. L. Ward, and Z. Was, Comput. Phys. Commun. 79 (1994) 503.[10] S. Jadach, Z. Was, R. Decker, and J. H. Ku¨hn, Comput. Phys. Commun. 76 (1993)361.[11] M. Je_zabek, Z. Was, S. Jadach, and J. H. Ku¨hn, Comput. Phys. Commun. 70 (1992)69.8[12] S. Jadach, J. H. Ku¨hn, and Z. Was, Comput. Phys. Commun. 64 (1990) 275.[13] F. Sanchez and Z. Was, Phys. Lett. B351 (1995) 562{568.[14] DELPHI Collaboration, P. Abreu et al., Phys. Lett. B404 (1997) 194{206.[15] ALEPH Collaboration, R. Barate et al., Phys. Lett. B405 (1997) 191{201.[16] I. Ferrante, Nucl. Phys. Proc. Suppl. 40 (1995) 299{309.[17] S. Jadach and Z. Was, Comput. Phys. Commun. 36 (1985) 191.[18] S. Jadach and Z. Was, Acta Phys. Polon. B15 (1984) 1151, Erratum: B16 (1985)483.[19] T. Ishikawa, Y. Kurihara, M. Skrzypek, and Z. Was, Eur. Phys. J. C4 (1998) 75{84,hep-ph/9702249.[20] T. Pierzcha la, E. Richter-Was, Z. Was, and M. Worek, Acta Phys. Polon. B32 (2001)1277{1296, hep-ph/0101311.[21] E. Barberio, B. van Eijk, and Z. Was, Comput. Phys. Commun. 66 (1991) 115.[22] E. Barberio and Z. Was, Comput. Phys. Commun. 79 (1994) 291{308.[23] F. A. Berends, R. Kleiss, and S. Jadach, Comput. Phys. Commun. 29 (1983) 185.[24] Z. Was and M. Worek, hep-ph/0202007.[25] M. Kramer, J. H. Ku¨hn, M. L. Stong, and P. M. Zerwas, Z. Phys. C64 (1994) 21{30,hep-ph/9404280.[26] T. Sjo¨strand et al., Comput. Phys. Commun. 135 (2001) 238.9100 200 30000:5  10 41:0  10 41:5  10 42:0  10 4Mss[GeV]ddMss[pb]CC-43CC-03100 200 30001  10 42  10 43  10 44  10 4Mss[GeV]ddMss[pb]no-spinspin on

Spin polarization and the Einstein--Podolsky--Rosen paradox in the Monte Carlo event records

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