PYTHIA 6.4 Physics and Manual

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C...Loop over reading and setting parameters/switches.100 READ(*,’(A)’,END=200) PARAMCALL PYGIVE(PARAM)GOTO 100C...Initialize PYTHIA.200 CALL PYINIT(FRAME,BEAM,TARGET,ENERGY)C...Event generation loopDO 300 IEV=1,NEVCALL PYEVNTIF(IEV.LE.NPRT) CALL PYLIST(1)300 CONTINUEC...Print cross sections.CALL PYSTAT(1)ENDand a file indata with the contentsCMS,p,p,14000.1000,3! below follows commands sent to PYGIVEMSEL=0! Mix processes freelyMSUB(102)=1 ! g + g -> h0MSUB(123)=1 ! Z0 + Z0 -> h0MSUB(124)=1 ! W+ + W- -> h0PMAS(25,1)=300. ! Higgs massCKIN(1)=290. ! lower cutoff on massCKIN(2)=310. ! upper cutoff on massMSTP(61)=0 ! no initial-state showersMSTP(71)=0 ! no final-state showersMSTP(81)=0 ! no multiple interactionsMSTP(111)=0 ! no hadronizationHere the text following the exclamation marks is interpreted as a comment by PYGIVE, andthus purely intended to allow better documentation of changes. The main program couldthen be linked to Pythia, to an executable a.out, and run e.g. with a Unix commandlinea.out < indata > outputto produce results on the file output. Here the indata could be changed without requiringa recompilation. Of course, the main program would have to be more realistic, e.g. withevents saved to disk or tape, but the principle should be clear.Further examples of how to use Pythia are available on the Pythia webpage.42
4 Monte Carlo TechniquesQuantum mechanics introduces a concept of randomness in the behaviour of physicalprocesses. The virtue of event generators is that this randomness can be simulated bythe use of Monte Carlo techniques. In the process, the program authors have to use someingenuity to find the most efficient way to simulate an assumed probability distribution.A detailed description of possible techniques would carry us too far, but in this sectionsome of the most frequently used approaches are presented, since they will appear indiscussions in subsequent sections. Further examples may be found e.g. in [Jam80].First of all one assumes the existence of a random number generator. This is a (Fortran)function which, each time it is called, returns a number R in the range between 0and 1, such that the inclusive distribution of numbers R is flat in the range, and such thatdifferent numbers R are uncorrelated. The random number generator that comes withPythia is described at the end of this section, and we defer the discussion until then.4.1 Selection From a DistributionThe situation that is probably most common is that we know a function f(x) which isnon-negative in the allowed x range x min ≤ x ≤ x max . We want to select an x ‘at random’so that the probability in a small interval dx around a given x is proportional to f(x) dx.Here f(x) might be a fragmentation function, a differential cross section, or any of anumber of distributions.One does not have to assume that the integral of f(x) is explicitly normalized to unity:by the Monte Carlo procedure of picking exactly one accepted x value, normalization isimplicit in the final result. Sometimes the integral of f(x) does carry a physics contentof its own, as part of an overall weight factor we want to keep track of. Consider, forinstance, the case when x represents one or several phase-space variables and f(x) adifferential cross section; here the integral has a meaning of total cross section for theprocess studied. The task of a Monte Carlo is then, on the one hand, to generate eventsone at a time, and, on the other hand, to estimate the total cross section. The discussionof this important example is deferred to section 7.4.If it is possible to find a primitive function F (x) which has a known inverse F −1 (x),an x can be found as follows (method 1):∫ xx minf(x) dx = R∫ xmaxx minf(x) dx=⇒ x = F −1 (F (x min ) + R(F (x max ) − F (x min ))) . (2)The statement of the first line is that a fraction R of the total area under f(x) should beto the left of x. However, seldom are functions of interest so nice that the method aboveworks. It is therefore necessary to use more complicated schemes.Special tricks can sometimes be found. Consider e.g. the generation of a Gaussianf(x) = exp(−x 2 ). This function is not integrable, but if we combine it with the sameGaussian distribution of a second variable y, it is possible to transform to polar coordinatesf(x) dx f(y) dy = exp(−x 2 − y 2 ) dx dy = r exp(−r 2 ) dr dϕ , (3)and now the r and ϕ distributions may be easily generated and recombined to yield x.At the same time we get a second number y, which can also be used. For the generationof transverse momenta in fragmentation, this is very convenient, since in fact we want toassign two transverse degrees of freedom.If the maximum of f(x) is known, f(x) ≤ f max in the x range considered, a hit-or-missmethod will always yield the correct answer (method 2):43
Page 1 and 2: hep-ph/0603175LU TP 06-13FERMILAB-P
Page 4 and 5: Contents1 Introduction 11.1 The Com
Page 6 and 7: 8.6.3 Left-Right Symmetry and Doubl
Page 8 and 9: 13 Particles and Their Decays 38413
Page 10 and 11: another sense, the overall energy f
Page 13 and 14: p ⊥ -ordered parton showers and a
Page 15 and 16: you expect to happen if you do not
Page 17 and 18: The history of the Pythia program i
Page 19 and 20: andom, according to the relative co
Page 21 and 22: Of course, the above ‘resonance
Page 23 and 24: 2.2.1 Matrix elementsMatrix element
Page 25 and 26: analysis strongly suggests the scal
Page 27 and 28: y calling PYEVNW instead of PYEVNT,
Page 29 and 30: charge Casimir operators, N C /C F
Page 31 and 32: 3 Program OverviewThis section cont
Page 33 and 34: Table 2: The main versions of Pythi
Page 35 and 36: • A new master event-generation r
Page 37 and 38: A test program, PYTEST, is included
Page 39 and 40: argument is used with a value that
Page 41 and 42: &XMI(2,240),Q2MI(240),IMISEP(0:240)
Page 43 and 44: original u and u. The parentheses e
Page 45 and 46: C...End of particle and event loops
Page 47 and 48: PMAS(25,1)=300D0CKIN(1)=290D0CKIN(2
Page 49: third the particle-flavour code (wh
Page 53 and 54: different g i ’s, it is possible
Page 55 and 56: The last equality is most easily se
Page 57 and 58: Purpose: to generate a (pseudo)rand
Page 59 and 60: 5 The Event RecordThe event record
Page 61 and 62: Table 4: Gauge boson and other fund
Page 63 and 64: Table 7: Meson codes, part 1.KF Nam
Page 65: Table 10: QCD effective states.KF P
Page 68 and 69: is then required. Normally this mea
Page 70 and 71: quarks. Note that the positions nee
Page 72 and 73: original entries appear with pointe
Page 74 and 75: consistent summary, but then in div
Page 76 and 77: = 3 : a documentation line, defined
Page 78 and 79: 6 The Old Electron-Positron Annihil
Page 80 and 81: 6.1.2 First-order QCD matrix elemen
Page 82 and 83: 6.1.4 Second-order three-jet matrix
Page 84 and 85: evaluated and compared with a param
Page 86 and 87: The angular orientation of a 3- or
Page 88 and 89: these offer unique possibilities to
Page 90 and 91: 6.3.3 Common-block variablesThe sta
Page 92 and 93: 3-jet cross section, so large that
Page 94 and 95: fraction of events containing a rad
Page 96 and 97: ! PYSPHE to work on it (unusual)CAL
Page 98 and 99: Pdflib has been frozen in recent ye
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modelling of γp and γγ events, s
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One can obtain the positron distrib
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7.2 Kinematics and Cross Section fo
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7.3 Resonance ProductionThe simples
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y a factor 1/N C = 1/3. Secondly, t
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This choice certainly is not unique
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The phase-space points tested at in
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spin-1 resonance the expression is,
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probabilities.In some processes, su
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where decay channels are chosen acc
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and for a resonance-antiresonance p
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The Regge formulae above for single
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emnant, but this remnant has a larg
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called direct, our direct×VMD and
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are also covered in other places in
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Table 17: Subprocess codes, part 2.
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Table 25: Subprocess codes, part 10
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8.2 QCD ProcessesObviously most pro
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1. if MSEL = 4 - 8 then the flavour
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into the cross section. However, cu
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Uncertainties come from a number of
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If you are only concerned with stan
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for MSTP(14) = 1 and the VMD part o
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vertex. MSTP(66) offer some alterna
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calculation is preferred. Some caut
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contains a full two-Higgs-multiplet
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8.5.2 Heavy Standard Model HiggsISU
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parton-distribution-function approa
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The advantage of the explicit pair
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handed neutrinos. The Higgs fields
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former and ŝ for the latter. To ma
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mode is therefore tt, if kinematica
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through a vector-dominance mechanis
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where α a = ga/4π.2The phenomenol
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has two scalar partners, one associ
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above. To obtain proper linking wit
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or (ii) the masses of the first- an
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mSUGRA model input parameters shoul
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stable. If this is not the case, MW
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is no a priori generic prediction f
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tools exist. Therefore the producti
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’gamma/lepton’ machinery. There
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numerical precision may suffer; if
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call, e.g. at the end of the run, o
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on so as to give the full (paramete
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MSEL = 10) (ISUB = 19, 20, 22, 23,
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CKIN(7), CKIN(8) : (D = −10., 10.
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For two resonances that are identic
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= 1 : you should set couplings for
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or GVMD; we will use both interchan
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MSTP(17) : (D = 4) possibility of a
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h 0 and H 0 . It is mainly intended
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correct only in the Standard Model
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for three technicolors, based on sc
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esponsibility on you.Note 2: when P
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= 1 : the recommended standard for
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where a reconnection is actually ma
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MSTP(145) : (D = 0) choice of polar
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PARP(32) : (D = 2.0) special K fact
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PARP(121) : (D = 1.) the maxima obt
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Q2 : the momentum transfer scale Q
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1-PARU(136) corresponding to the sa
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cot θ 3 .ITCM(5) : (D = 0) presenc
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are SUGRA, SSMSSM and VISAJE, locat
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IMSS(22) : (D = 0) Read-in of SLHA
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it is the constant of proportionali
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k = 1 : only possibility.ISUB = 13,
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number is obtained as a by-product
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vanishing if no splitting is needed
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CALL PYINIT(’CMS’,’p’,’pb
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C...Histograms.CALL PYBOOK(1,’dn_
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Of course, the separation of which
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does imply an infinite total cross
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Pythia. The solution adopted here
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est strategy would vary, depending
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tered during the course of the run,
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NPRUP entries of the XSECUP, XERRUP
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should be denoted by using the valu
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more information than is provided b
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9.9.3 An exampleTo exemplify the ab
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DOUBLE PRECISION EBMUP,XSECUP,XERRU
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momenta and masses can be reconstru
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quantity, the effect of such events
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9.10 Interfaces to Other Generators
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= 2 : assign the interference contr
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value before the routine is called.
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• PYSGQC : normal QCD processes,
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afterwards.)MINT(17), MINT(18) : fl
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= 0 : normal initialization.= 1 : i
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agrees with the Bjorken definition,
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action; used to find what is left f
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VINT(319) : photon flux factor in P
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COMMON/PYINT4/MWID(500),WIDS(500,5)
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Purpose: to store information on to
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10 Initial- and Final-State Radiati
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for the original parton a. On the o
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180 ◦ and therefore the emission
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anching activity of the gluon. (Wit
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anching of both the q and the q, in
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10.2.5 Other final-state shower asp
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wide selection of generic colour an
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e a function of the transverse mome
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That way we hope to achieve the mos
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step by step one moves ‘backwards
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in hadronic interactions, with the
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happens it is almost always for one
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need be.The scheme presented above
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with the new PYPTIS one. The advant
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of the system.)CALL PYPTFS(NPART,IP
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Note:a few non-standard options hav
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g → gg and reduced angle for g
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(MSTP(42) = 2) and MSTJ(46) = 3).PA
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= 3 : the k ⊥ of the anomalous/GV
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to the cut implied by PARP(65).PARP
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outlines where the intermediate and
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11.1.4 Primordial k ⊥It is custom
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mended first to read this section,
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In general, there is quite a strong
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• Scatterings of the gg → gg ty
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where the denominator comes from th
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hard processes in pp or pp collisio
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proton net flavour content, and ene
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can be used here, from sharing the
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There is also the matter of a lower
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The program needs to know the assum
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Λ FSR scale: PARJ(81) = 0.14D0;Bea
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‘correct’ total cross section.M
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generated with the new model (in PY
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e attached to the remnant, PARP(80)
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Determine physical PT2MAX and PT2MI
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COMMON/PYCTAG/NCT, MCT(4000,2)Purpo
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string is assumed to have no transv
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Only two baryon multiplets are incl
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Additional parameters include the r
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or the q one, ‘left-right symmetr
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are changed, some retuning should b
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end in the initial stages of the st
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The fact that the hadron should be
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(including the one between the two
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the ratio of rescaled jet momentum
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duly randomized, but properly it wo
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Other models include a simplified i
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The negative sign is exactly what w
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13 Particles and Their DecaysPartic
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multiplet m 0 kpseudoscalars and ve
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toIn Dalitz decays, π 0 or η →
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fragmentation description. This doe
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14 The Fragmentation and Decay Prog
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Initially the partons must be given
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SUBROUTINE PYZDIS(KFL1,KFL3,PR,Z) :
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MSTU(4) : (D = 4000) number of line
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full. Is reset at each PYEXEC call.
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= 4 : transverse momenta are compen
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included in the event. If the showe
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allowed to shower, is 0 if no pair
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an independent gluon jet generated
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• Increase PARJ(1) by about a fac
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With five possible flavours for q 1
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LFN :is intended for the program au
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where both KTAB1 and KTAB3 are know
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a fourth generation is small.Remark
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code it is possible to define chann
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to be borne out by comparisons with
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CALL PYEXEC! particles decay, excep
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15 Event Study and Analysis Routine
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it can be further specified to +z a
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= 8 : KF code (K(I,2)) for a remain
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15.2 Event ShapesIn this section we
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To find the thrust value and axis t
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Hence rapidity, azimuthal angle and
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as a starting point for the iterati
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may be performed in E rather than i
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Here n = ∑ j n j is the total mul
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MSTU(63) and PARU(61) - PARU(63). I
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H40 : H 4 /H 0 .Remark: the number
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V(I,2) - V(I,5) = statistical error
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PYTHRU, PYCLUS and PYCELL.= 1 : sto
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MSTU(53)).PARU(57) : (D = 3.2) maxi
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Purpose: to dump the contents of ex
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References[Abb87]A. Abbasabadi and
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[Bai83] R. Baier and R. Rückl, Z.
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[Bra64] S. Brandt, Ch. Peyrou, R. S
Page 470 and 471:
[Djo97] A. Djouadi, J. Kalinowski a
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[Gie04]S. Gieseke, A. Ribon, M.H. S
Page 474 and 475:
[Ing80] G. Ingelman and T. Sjöstra
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[Lan00] K. Lane, T. Rador and E. Ei
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[OPA91] OPAL Collaboration, M.Z. Ak
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[Sjö92][Sjö92a][Sjö92b]T. Sjöst
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Appendix A: Subprocess Summary Tabl
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No. Subprocess No. SubprocessNo. Su
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Appendix B: Index of Subprograms an
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PYK function 429PYKCUT subroutine 1
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