[1] | 1 | <html> |
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| 2 | <head> |
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| 3 | <title>Timelike Showers</title> |
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| 4 | <link rel="stylesheet" type="text/css" href="pythia.css"/> |
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| 5 | <link rel="shortcut icon" href="pythia32.gif"/> |
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| 6 | </head> |
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| 7 | <body> |
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| 8 | |
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| 9 | <h2>Timelike Showers</h2> |
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| 10 | |
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| 11 | The PYTHIA algorithm for timelike final-state showers is based on |
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| 12 | the article [<a href="Bibliography.html" target="page">Sjo05</a>], where a transverse-momentum-ordered |
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| 13 | evolution scheme is introduced, with the extension to fully interleaved |
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| 14 | evolution covered in [<a href="Bibliography.html" target="page">Cor10a</a>]. This algorithm is influenced by |
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| 15 | the previous mass-ordered algorithm in PYTHIA [<a href="Bibliography.html" target="page">Ben87</a>] and by |
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| 16 | the dipole-emission formulation in Ariadne [<a href="Bibliography.html" target="page">Gus86</a>]. From the |
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| 17 | mass-ordered algorithm it inherits a merging procedure for first-order |
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| 18 | gluon-emission matrix elements in essentially all two-body decays |
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| 19 | in the standard model and its minimal supersymmetric extension |
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| 20 | [<a href="Bibliography.html" target="page">Nor01</a>]. |
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| 21 | |
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| 22 | <p/> |
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| 23 | The normal user is not expected to call <code>TimeShower</code> directly, |
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| 24 | but only have it called from <code>Pythia</code>. Some of the parameters |
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| 25 | below, in particular <code>TimeShower:alphaSvalue</code>, would be of |
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| 26 | interest for a tuning exercise, however. |
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| 27 | |
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| 28 | <h3>Main variables</h3> |
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| 29 | |
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| 30 | Often the maximum scale of the FSR shower evolution is understood from the |
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| 31 | context. For instance, in a resonace decay half the resonance mass sets an |
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| 32 | absolute upper limit. For a hard process in a hadronic collision the choice |
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| 33 | is not as unique. Here the <a href="CouplingsAndScales.html" target="page">factorization |
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| 34 | scale</a> has been chosen as the maximum evolution scale. This would be |
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| 35 | the <i>pT</i> for a <i>2 -> 2</i> process, supplemented by mass terms |
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| 36 | for massive outgoing particles. For some special applications we do allow |
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| 37 | an alternative. |
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| 38 | |
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| 39 | <p/><code>mode </code><strong> TimeShower:pTmaxMatch </strong> |
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| 40 | (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/> |
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| 41 | Way in which the maximum shower evolution scale is set to match the |
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| 42 | scale of the hard process itself. |
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| 43 | <br/><code>option </code><strong> 0</strong> : <b>(i)</b> if the final state of the hard process |
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| 44 | (not counting subsequent resonance decays) contains at least one quark |
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| 45 | (<i>u, d, s, c ,b</i>), gluon or photon then <i>pT_max</i> |
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| 46 | is chosen to be the factorization scale for internal processes |
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| 47 | and the <code>scale</code> value for Les Houches input; |
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| 48 | <b>(ii)</b> if not, emissions are allowed to go all the way up to |
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| 49 | the kinematical limit (i.e. to half the dipole mass). |
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| 50 | This option agrees with the corresponding one for |
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| 51 | <a href="SpacelikeShowers.html" target="page">spacelike showers</a>. There the |
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| 52 | reasoning is that in the former set of processes the ISR |
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| 53 | emission of yet another quark, gluon or photon could lead to |
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| 54 | doublecounting, while no such danger exists in the latter case. |
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| 55 | The argument is less compelling for timelike showers, but could |
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| 56 | be a reasonable starting point. |
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| 57 | |
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| 58 | <br/><code>option </code><strong> 1</strong> : always use the factorization scale for an internal |
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| 59 | process and the <code>scale</code> value for Les Houches input, |
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| 60 | i.e. the lower value. This should avoid doublecounting, but |
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| 61 | may leave out some emissions that ought to have been simulated. |
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| 62 | (Also known as wimpy showers.) |
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| 63 | |
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| 64 | <br/><code>option </code><strong> 2</strong> : always allow emissions up to the kinematical limit |
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| 65 | (i.e. to half the dipole mass). This will simulate all possible event |
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| 66 | topologies, but may lead to doublecounting. |
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| 67 | (Also known as power showers.) |
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| 68 | |
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| 69 | <br/><b>Note:</b> These options only apply to the hard interaction. |
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| 70 | Emissions off subsequent multiparton interactions are always constrainted |
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| 71 | to be below the factorization scale of the process itself. They also |
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| 72 | assume you use interleaved evolution, so that FSR is in direct |
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| 73 | competition with ISR for the hardest emission. If you already |
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| 74 | generated a number of ISR partons at low <i>pT</i>, it would not |
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| 75 | make sense to have a later FSR shower up to the kinematical for all |
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| 76 | of them. |
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| 77 | |
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| 78 | |
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| 79 | <p/><code>parm </code><strong> TimeShower:pTmaxFudge </strong> |
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| 80 | (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 2.0</code>)<br/> |
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| 81 | In cases where the above <code>pTmaxMatch</code> rules would imply |
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| 82 | that <i>pT_max = pT_factorization</i>, <code>pTmaxFudge</code> |
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| 83 | introduces a multiplicative factor <i>f</i> such that instead |
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| 84 | <i>pT_max = f * pT_factorization</i>. Only applies to the hardest |
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| 85 | interaction in an event, cf. below. It is strongly suggested that |
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| 86 | <i>f = 1</i>, but variations around this default can be useful to |
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| 87 | test this assumption. |
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| 88 | <br/><b>Note:</b>Scales for resonance decays are not affected, but can |
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| 89 | be set separately by <a href="UserHooks.html" target="page">user hooks</a>. |
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| 90 | |
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| 91 | |
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| 92 | <p/><code>parm </code><strong> TimeShower:pTmaxFudgeMPI </strong> |
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| 93 | (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 2.0</code>)<br/> |
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| 94 | A multiplicative factor <i>f</i> such that |
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| 95 | <i>pT_max = f * pT_factorization</i>, as above, but here for the |
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| 96 | non-hardest interactions (when multiparton interactions are allowed). |
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| 97 | |
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| 98 | |
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| 99 | <p/><code>mode </code><strong> TimeShower:pTdampMatch </strong> |
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| 100 | (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/> |
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| 101 | These options only take effect when a process is allowed to radiate up |
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| 102 | to the kinematical limit by the above <code>pTmaxMatch</code> choice, |
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| 103 | and no matrix-element corrections are available. Then, in many processes, |
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| 104 | the fall-off in <i>pT</i> will be too slow by one factor of <i>pT^2</i>. |
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| 105 | That is, while showers have an approximate <i>dpT^2/pT^2</i> shape, often |
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| 106 | it should become more like <i>dpT^2/pT^4</i> at <i>pT</i> values above |
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| 107 | the scale of the hard process. This argument is more obvious for ISR, |
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| 108 | but is taken over unchanged for FSR to have a symmetric description. |
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| 109 | <br/><code>option </code><strong> 0</strong> : emissions go up to the kinematical limit, |
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| 110 | with no special dampening. |
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| 111 | |
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| 112 | <br/><code>option </code><strong> 1</strong> : emissions go up to the kinematical limit, |
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| 113 | but dampened by a factor <i>k^2 Q^2_fac/(pT^2 + k^2 Q^2_fac)</i>, |
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| 114 | where <i>Q_fac</i> is the factorization scale and <i>k</i> is a |
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| 115 | multiplicative fudge factor stored in <code>pTdampFudge</code> below. |
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| 116 | |
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| 117 | <br/><code>option </code><strong> 2</strong> : emissions go up to the kinematical limit, |
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| 118 | but dampened by a factor <i>k^2 Q^2_ren/(pT^2 + k^2 Q^2_ren)</i>, |
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| 119 | where <i>Q_ren</i> is the renormalization scale and <i>k</i> is a |
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| 120 | multiplicative fudge factor stored in <code>pTdampFudge</code> below. |
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| 121 | |
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| 122 | <br/><b>Note:</b> These options only apply to the hard interaction. |
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| 123 | Emissions off subsequent multiparton interactions are always constrainted |
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| 124 | to be below the factorization scale of the process itself. |
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| 125 | |
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| 126 | |
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| 127 | <p/><code>parm </code><strong> TimeShower:pTdampFudge </strong> |
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| 128 | (<code>default = <strong>1.0</strong></code>; <code>minimum = 0.25</code>; <code>maximum = 4.0</code>)<br/> |
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| 129 | In cases 1 and 2 above, where a dampening is imposed at around the |
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| 130 | factorization or renormalization scale, respectively, this allows the |
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| 131 | <i>pT</i> scale of dampening of radiation by a half to be shifted |
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| 132 | by this factor relative to the default <i>Q_fac</i> or <i>Q_ren</i>. |
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| 133 | This number ought to be in the neighbourhood of unity, but variations |
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| 134 | away from this value could do better in some processes. |
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| 135 | |
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| 136 | |
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| 137 | <p/> |
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| 138 | The amount of QCD radiation in the shower is determined by |
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| 139 | <p/><code>parm </code><strong> TimeShower:alphaSvalue </strong> |
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| 140 | (<code>default = <strong>0.1383</strong></code>; <code>minimum = 0.06</code>; <code>maximum = 0.25</code>)<br/> |
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| 141 | The <i>alpha_strong</i> value at scale <i>M_Z^2</i>. The default |
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| 142 | value corresponds to a crude tuning to LEP data, to be improved. |
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| 143 | |
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| 144 | |
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| 145 | <p/> |
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| 146 | The actual value is then regulated by the running to the scale |
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| 147 | <i>pT^2</i>, at which the shower evaluates <i>alpha_strong</i>. |
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| 148 | |
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| 149 | <p/><code>mode </code><strong> TimeShower:alphaSorder </strong> |
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| 150 | (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 2</code>)<br/> |
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| 151 | Order at which <i>alpha_strong</i> runs, |
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| 152 | <br/><code>option </code><strong> 0</strong> : zeroth order, i.e. <i>alpha_strong</i> is kept |
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| 153 | fixed. |
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| 154 | <br/><code>option </code><strong> 1</strong> : first order, which is the normal value. |
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| 155 | <br/><code>option </code><strong> 2</strong> : second order. Since other parts of the code do |
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| 156 | not go to second order there is no strong reason to use this option, |
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| 157 | but there is also nothing wrong with it. |
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| 158 | |
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| 159 | |
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| 160 | <p/> |
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| 161 | QED radiation is regulated by the <i>alpha_electromagnetic</i> |
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| 162 | value at the <i>pT^2</i> scale of a branching. |
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| 163 | |
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| 164 | <p/><code>mode </code><strong> TimeShower:alphaEMorder </strong> |
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| 165 | (<code>default = <strong>1</strong></code>; <code>minimum = -1</code>; <code>maximum = 1</code>)<br/> |
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| 166 | The running of <i>alpha_em</i>. |
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| 167 | <br/><code>option </code><strong> 1</strong> : first-order running, constrained to agree with |
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| 168 | <code>StandardModel:alphaEMmZ</code> at the <i>Z^0</i> mass. |
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| 169 | |
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| 170 | <br/><code>option </code><strong> 0</strong> : zeroth order, i.e. <i>alpha_em</i> is kept |
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| 171 | fixed at its value at vanishing momentum transfer. |
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| 172 | <br/><code>option </code><strong> -1</strong> : zeroth order, i.e. <i>alpha_em</i> is kept |
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| 173 | fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value |
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| 174 | at the <i>Z^0</i> mass. |
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| 175 | |
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| 176 | |
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| 177 | |
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| 178 | <p/> |
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| 179 | The natural scale for couplings, and PDFs for dipoles stretching out |
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| 180 | to the beam remnants, is <i>pT^2</i>. To explore uncertainties it |
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| 181 | is possibly to vary around this value, however, in analogy with what |
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| 182 | can be done for <a href="CouplingsAndScales.html" target="page">hard processes</a>. |
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| 183 | |
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| 184 | <p/><code>parm </code><strong> TimeShower:renormMultFac </strong> |
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| 185 | (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)<br/> |
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| 186 | The default <i>pT^2</i> renormalization scale is multiplied by |
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| 187 | this prefactor. For QCD this is equivalent to a change of |
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| 188 | <i>Lambda^2</i> in the opposite direction, i.e. to a change of |
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| 189 | <i>alpha_strong(M_Z^2)</i> (except that flavour thresholds |
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| 190 | remain at fixed scales). |
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| 191 | |
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| 192 | |
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| 193 | <p/><code>parm </code><strong> TimeShower:factorMultFac </strong> |
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| 194 | (<code>default = <strong>1.</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 10.</code>)<br/> |
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| 195 | The default <i>pT^2</i> factorization scale is multiplied by |
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| 196 | this prefactor. |
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| 197 | |
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| 198 | |
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| 199 | <p/> |
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| 200 | The rate of radiation if divergent in the <i>pT -> 0</i> limit. Here, |
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| 201 | however, perturbation theory is expected to break down. Therefore an |
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| 202 | effective <i>pT_min</i> cutoff parameter is introduced, below which |
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| 203 | no emissions are allowed. The cutoff may be different for QCD and QED |
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| 204 | radiation off quarks, and is mainly a technical parameter for QED |
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| 205 | radiation off leptons. |
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| 206 | |
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| 207 | <p/><code>parm </code><strong> TimeShower:pTmin </strong> |
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| 208 | (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.0</code>)<br/> |
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| 209 | Parton shower cut-off <i>pT</i> for QCD emissions. |
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| 210 | |
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| 211 | |
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| 212 | <p/><code>parm </code><strong> TimeShower:pTminChgQ </strong> |
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| 213 | (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 2.0</code>)<br/> |
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| 214 | Parton shower cut-off <i>pT</i> for photon coupling to coloured particle. |
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| 215 | |
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| 216 | |
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| 217 | <p/><code>parm </code><strong> TimeShower:pTminChgL </strong> |
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| 218 | (<code>default = <strong>0.0005</strong></code>; <code>minimum = 0.0001</code>; <code>maximum = 2.0</code>)<br/> |
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| 219 | Parton shower cut-off <i>pT</i> for pure QED branchings. |
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| 220 | Assumed smaller than (or equal to) <code>pTminChgQ</code>. |
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| 221 | |
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| 222 | |
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| 223 | <p/> |
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| 224 | Shower branchings <i>gamma -> f fbar</i>, where <i>f</i> is a |
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| 225 | quark or lepton, in part compete with the hard processes involving |
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| 226 | <i>gamma^*/Z^0</i> production. In order to avoid overlap it makes |
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| 227 | sense to correlate the maximum <i>gamma</i> mass allowed in showers |
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| 228 | with the minumum <i>gamma^*/Z^0</i> mass allowed in hard processes. |
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| 229 | In addition, the shower contribution only contains the pure |
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| 230 | <i>gamma^*</i> contribution, i.e. not the <i>Z^0</i> part, so |
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| 231 | the mass spectrum above 50 GeV or so would not be well described. |
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| 232 | |
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| 233 | <p/><code>parm </code><strong> TimeShower:mMaxGamma </strong> |
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| 234 | (<code>default = <strong>10.0</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 50.0</code>)<br/> |
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| 235 | Maximum invariant mass allowed for the created fermion pair in a |
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| 236 | <i>gamma -> f fbar</i> branching in the shower. |
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| 237 | |
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| 238 | |
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| 239 | <h3>Interleaved evolution</h3> |
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| 240 | |
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| 241 | Multiparton interactions (MPI) and initial-state showers (ISR) are |
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| 242 | always interleaved, as follows. Starting from the hard interaction, |
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| 243 | the complete event is constructed by a set of steps. In each step |
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| 244 | the <i>pT</i> scale of the previous step is used as starting scale |
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| 245 | for a downwards evolution. The MPI and ISR components each make |
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| 246 | their respective Monte Carlo choices for the next lower <i>pT</i> |
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| 247 | value. The one with larger <i>pT</i> is allowed to carry out its |
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| 248 | proposed action, thereby modifying the conditions for the next steps. |
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| 249 | This is relevant since the two components compete for the energy |
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| 250 | contained in the beam remnants: both an interaction and an emission |
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| 251 | take avay some of the energy, leaving less for the future. The end |
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| 252 | result is a combined chain of decreasing <i>pT</i> values, where |
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| 253 | ones associated with new interactions and ones with new emissions |
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| 254 | are interleaved. |
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| 255 | |
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| 256 | <p/> |
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| 257 | There is no corresponding requirement for final-state radiation (FSR) |
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| 258 | to be interleaved. Such an FSR emission does not compete directly for |
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| 259 | beam energy (but see below), and also can be viewed as occuring after |
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| 260 | the other two components in some kind of time sense. Interleaving is |
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| 261 | allowed, however, since it can be argued that a high-<i>pT</i> FSR |
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| 262 | occurs on shorter time scales than a low-<i>pT</i> MPI, say. |
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| 263 | Backwards evolution of ISR is also an example that physical time |
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| 264 | is not the only possible ordering principle, but that one can work |
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| 265 | with conditional probabilities: given the partonic picture at a |
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| 266 | specific <i>pT</i> resolution scale, what possibilities are open |
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| 267 | for a modified picture at a slightly lower <i>pT</i> scale, either |
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| 268 | by MPI, ISR or FSR? Complete interleaving of the three components also |
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| 269 | offers advantages if one aims at matching to higher-order matrix |
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| 270 | elements above some given scale. |
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| 271 | |
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| 272 | <p/><code>flag </code><strong> TimeShower:interleave </strong> |
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| 273 | (<code>default = <strong>on</strong></code>)<br/> |
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| 274 | If on, final-state emissions are interleaved in the same |
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| 275 | decreasing-<i>pT</i> chain as multiparton interactions and initial-state |
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| 276 | emissions. If off, final-state emissions are only addressed after the |
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| 277 | multiparton interactions and initial-state radiation have been considered. |
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| 278 | |
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| 279 | |
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| 280 | <p/> |
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| 281 | As an aside, it should be noted that such interleaving does not affect |
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| 282 | showering in resonance decays, such as a <i>Z^0</i>. These decays are |
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| 283 | only introduced after the production process has been considered in full, |
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| 284 | and the subsequent FSR is carried out inside the resonance, with |
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| 285 | preserved resonance mass. |
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| 286 | |
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| 287 | <p/> |
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| 288 | One aspect of FSR for a hard process in hadron collisions is that often |
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| 289 | colour diples are formed between a scattered parton and a beam remnant, |
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| 290 | or rather the hole left behind by an incoming partons. If such holes |
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| 291 | are allowed as dipole ends and take the recoil when the scattered parton |
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| 292 | undergoes a branching then this translates into the need to take some |
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| 293 | amount of remnant energy also in the case of FSR, i.e. the roles of |
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| 294 | ISR and FSR are not completely decoupled. The energy taken away is |
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| 295 | bokkept by increasing the <i>x</i> value assigned to the incoming |
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| 296 | scattering parton, and a reweighting factor |
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| 297 | <i>x_new f(x_new, pT^2) / x_old f(x_old, pT^2)</i> |
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| 298 | in the emission probability ensures that not unphysically large |
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| 299 | <i>x_new</i> values are reached. Usually such <i>x</i> changes are |
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| 300 | small, and they can be viewed as a higher-order effect beyond the |
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| 301 | accuracy of the leading-log initial-state showers. |
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| 302 | |
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| 303 | <p/> |
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| 304 | This choice is not unique, however. As an alternative, if nothing else |
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| 305 | useful for cross-checks, one could imagine that the FSR is completely |
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| 306 | decoupled from the ISR and beam remnants. |
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| 307 | |
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| 308 | <p/><code>flag </code><strong> TimeShower:allowBeamRecoil </strong> |
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| 309 | (<code>default = <strong>on</strong></code>)<br/> |
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| 310 | If on, the final-state shower is allowed to borrow energy from |
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| 311 | the beam remnants as described above, thereby changing the mass of the |
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| 312 | scattering subsystem. If off, the partons in the scattering subsystem |
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| 313 | are constrained to borrow energy from each other, such that the total |
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| 314 | four-momentum of the system is preserved. This flag has no effect |
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| 315 | on resonance decays, where the shower always preserves the resonance |
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| 316 | mass, cf. the comment above about showers for resonances never being |
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| 317 | interleaved. |
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| 318 | |
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| 319 | |
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| 320 | <p/><code>flag </code><strong> TimeShower:dampenBeamRecoil </strong> |
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| 321 | (<code>default = <strong>on</strong></code>)<br/> |
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| 322 | When beam recoil is allowed there is still some ambiguity how far |
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| 323 | into the beam end of the dipole that emission should be allowed. |
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| 324 | It is dampened in the beam region, but probably not enough. |
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| 325 | When on an additional suppression factor |
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| 326 | <i>4 pT2_hard / (4 pT2_hard + m2)</i> is multiplied on to the |
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| 327 | emission probability. Here <i>pT_hard</i> is the transverse momentum |
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| 328 | of the radiating parton and <i>m</i> the off-shell mass it acquires |
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| 329 | by the branching, <i>m2 = pT2/(z(1-z))</i>. Note that |
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| 330 | <i>m2 = 4 pT2_hard</i> is the kinematical limit for a scattering |
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| 331 | at 90 degrees without beam recoil. |
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| 332 | |
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| 333 | |
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| 334 | <h3>Global recoil</h3> |
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| 335 | |
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| 336 | The final-state algorithm is based on dipole-style recoils, where |
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| 337 | one single parton takes the full recoil of a branching. This is unlike |
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| 338 | the initial-state algorithm, where the complete already-existing |
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| 339 | final state shares the recoil of each new emission. As an alternative, |
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| 340 | also the final-state algorithm contains an option where the recoil |
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| 341 | is shared between all partons in the final state. Thus the radiation |
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| 342 | pattern is unrelated to colour correlations. This is especially |
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| 343 | convenient for some matching algorithms, like MC@NLO, where a full |
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| 344 | analytic knowledge of the shower radiation pattern is needed to avoid |
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| 345 | doublecountning. (The <i>pT</i>-ordered shower is described in |
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| 346 | [<a href="Bibliography.html" target="page">Sjo05</a>], and the corrections for massive radiator and recoiler |
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| 347 | in [<a href="Bibliography.html" target="page">Nor01</a>].) |
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| 348 | |
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| 349 | <p/> |
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| 350 | Technically, the radiation pattern is most conveniently represented |
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| 351 | in the rest frame of the final state of the hard subprocess. Then, for |
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| 352 | each parton at a time, the rest of the final state can be viewed as |
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| 353 | a single effective parton. This "parton" has a fixed invariant mass |
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| 354 | during the emission process, and takes the recoil without any changed |
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| 355 | direction of motion. The momenta of the individual new recoilers are |
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| 356 | then obtained by a simple common boost of the original ones. |
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| 357 | |
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| 358 | <p/> |
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| 359 | This alternative approach will miss out on the colour coherence |
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| 360 | phenomena. Specifically, with the whole subcollision mass as "dipole" |
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| 361 | mass, the phase space for subsequent emissions is larger than for |
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| 362 | the normal dipole algorithm. The phase space difference grows as |
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| 363 | more and more gluons are created, and thus leads to a way too steep |
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| 364 | multiplication of soft gluons. Therefore the main application is |
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| 365 | for the first one or few emissions of the shower, where a potential |
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| 366 | overestimate of the emission rate is to be corrected for anyway, |
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| 367 | by matching to the relevant matrix elements. Thereafter, subsequent |
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| 368 | emissions should be handled as before, i.e. with dipoles spanned |
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| 369 | between nearby partons. Furthermore, only the first (hardest) |
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| 370 | subcollision is handled with global recoils, since subsequent MPI's |
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| 371 | would not be subject to matrix element corrections anyway. |
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| 372 | |
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| 373 | <p/> |
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| 374 | In order for the mid-shower switch from global to local recoils |
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| 375 | to work, colours are traced and bookkept just as for normal showers; |
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| 376 | it is only that this information is not used in those steps where |
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| 377 | a global recoil is requested. (Thus, e.g., a gluon is still bookkept |
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| 378 | as one colour and one anticolour dipole end, with half the charge |
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| 379 | each, but with global recoil those two ends radiate identically.) |
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| 380 | |
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| 381 | <p/><code>flag </code><strong> TimeShower:globalRecoil </strong> |
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| 382 | (<code>default = <strong>off</strong></code>)<br/> |
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| 383 | Alternative approach as above, where all final-state particles share |
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| 384 | the recoil of an emission. |
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| 385 | <br/>If off, then use the standard dipole-recoil approach. |
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| 386 | <br/>If on, use the alternative global recoil, but only for the first |
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| 387 | interaction, and only while the number of particles in the final state |
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| 388 | is at most <code>TimeShower:nMaxGlobalRecoil</code> before the |
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| 389 | branching. |
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| 390 | |
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| 391 | |
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| 392 | <p/><code>mode </code><strong> TimeShower:nMaxGlobalRecoil </strong> |
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| 393 | (<code>default = <strong>2</strong></code>; <code>minimum = 1</code>)<br/> |
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| 394 | Represents the maximum number of particles in the final state for which |
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| 395 | the next final-state emission can be performed with the global recoil |
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| 396 | strategy. This number counts all particles, whether they are |
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| 397 | allowed to radiate or not, e.g. also <i>Z^0</i>. Also partons |
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| 398 | created by initial-state radiation emissions counts towards this sum, |
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| 399 | as part of the interleaved evolution. Without interleaved evolution |
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| 400 | this option would not make sense, since then a varying and large |
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| 401 | number of partons could already have been created by the initial-state |
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| 402 | radiation before the first final-state one, and then there is not |
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| 403 | likely to be any matrix elements available for matching. |
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| 404 | |
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| 405 | |
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| 406 | <p/> |
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| 407 | The global-recoil machinery does not work well with rescattering in the |
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| 408 | MPI machinery, since then the recoiling system is not uniquely defined. |
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| 409 | <code>MultipartonInteractions:allowRescatter = off</code> by default, |
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| 410 | so this is not a main issue. If both options are switched on, |
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| 411 | rescattering will only be allowed to kick in after the global recoil |
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| 412 | has ceased to be active, i.e. once the <code>nMaxGlobalRecoil</code> |
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| 413 | limit has been exceeded. This should not be a major conflict, |
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| 414 | since rescattering is mainly of interest at later stages of the |
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| 415 | downwards <i>pT</i> evolution. |
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| 416 | |
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| 417 | <p/> |
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| 418 | Further, it is strongly recommended to set |
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| 419 | <code>TimeShower:MEcorrections = off</code> (not default!), i.e. not |
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| 420 | to correct the emission probability to the internal matrix elements. |
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| 421 | The internal ME options do not cover any cases relevant for a multibody |
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| 422 | recoiler anyway, so no guarantees are given what prescription would |
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| 423 | come to be used. Instead, without ME corrections, a process-independent |
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| 424 | emission rate is obtained, and <a href="UserHooks.html" target="page">user hooks</a> |
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| 425 | can provide the desired process-specific rejection factors. |
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| 426 | |
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| 427 | <h3>Radiation off octet onium states</h3> |
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| 428 | |
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| 429 | In the current implementation, charmonium and bottomonium production |
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| 430 | can proceed either through colour singlet or colour octet mechanisms, |
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| 431 | both of them implemented in terms of <i>2 -> 2</i> hard processes |
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| 432 | such as <i>g g -> (onium) g</i>. |
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| 433 | In the former case the state does not radiate and the onium therefore |
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| 434 | is produced in isolation, up to normal underlying-event activity. In |
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| 435 | the latter case the situation is not so clear, but it is sensible to |
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| 436 | assume that a shower can evolve. (Assuming, of course, that the |
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| 437 | transverse momentum of the onium state is sufficiently high that |
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| 438 | radiation is of relevance.) |
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| 439 | |
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| 440 | <p/> |
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| 441 | There could be two parts to such a shower. Firstly a gluon (or even a |
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| 442 | quark, though less likely) produced in a hard <i>2 -> 2</i> process |
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| 443 | can undergo showering into many gluons, whereof one branches into the |
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| 444 | heavy-quark pair. Secondly, once the pair has been produced, each quark |
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| 445 | can radiate further gluons. This latter kind of emission could easily |
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| 446 | break up a semibound quark pair, but might also create a new semibound |
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| 447 | state where before an unbound pair existed, and to some approximation |
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| 448 | these two effects should balance in the onium production rate. |
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| 449 | The showering "off an onium state" as implemented here therefore should |
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| 450 | not be viewed as an accurate description of the emission history |
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| 451 | step by step, but rather as an effective approach to ensure that the |
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| 452 | octet onium produced "in the hard process" is embedded in a realistic |
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| 453 | amount of jet activity. |
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| 454 | Of course both the isolated singlet and embedded octet are likely to |
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| 455 | be extremes, but hopefully the mix of the two will strike a reasonable |
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| 456 | balance. However, it is possible that some part of the octet production |
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| 457 | occurs in channels where it should not be accompanied by (hard) radiation. |
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| 458 | Therefore reducing the fraction of octet onium states allowed to radiate |
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| 459 | is a valid variation to explore uncertainties. |
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| 460 | |
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| 461 | <p/> |
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| 462 | If an octet onium state is chosen to radiate, the simulation of branchings |
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| 463 | is based on the assumption that the full radiation is provided by an |
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| 464 | incoherent sum of radiation off the quark and off the antiquark of the |
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| 465 | onium state. Thus the splitting kernel is taken to be the normal |
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| 466 | <i>q -> q g</i> one, multiplied by a factor of two. Obviously this is |
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| 467 | a simplification of a more complex picture, averaging over factors pulling |
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| 468 | in different directions. Firstly, radiation off a gluon ought |
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| 469 | to be enhanced by a factor 9/4 relative to a quark rather than the 2 |
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| 470 | now used, but this is a minor difference. Secondly, our use of the |
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| 471 | <i>q -> q g</i> branching kernel is roughly equivalent to always |
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| 472 | following the harder gluon in a <i>g -> g g</i> branching. This could |
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| 473 | give us a bias towards producing too hard onia. A soft gluon would have |
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| 474 | little phase space to branch into a heavy-quark pair however, so the |
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| 475 | bias may not be as big as it would seem at first glance. Thirdly, |
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| 476 | once the gluon has branched into a quark pair, each quark carries roughly |
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| 477 | only half of the onium energy. The maximum energy per emitted gluon should |
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| 478 | then be roughly half the onium energy rather than the full, as it is now. |
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| 479 | Thereby the energy of radiated gluons is exaggerated, i.e. onia become too |
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| 480 | soft. So the second and the third points tend to cancel each other. |
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| 481 | |
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| 482 | <p/> |
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| 483 | Finally, note that the lower cutoff scale of the shower evolution depends |
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| 484 | on the onium mass rather than on the quark mass, as it should be. Gluons |
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| 485 | below the octet-onium scale should only be part of the octet-to-singlet |
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| 486 | transition. |
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| 487 | |
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| 488 | <p/><code>parm </code><strong> TimeShower:octetOniumFraction </strong> |
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| 489 | (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)<br/> |
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| 490 | Allow colour-octet charmonium and bottomonium states to radiate gluons. |
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| 491 | 0 means that no octet-onium states radiate, 1 that all do, with possibility |
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| 492 | to interpolate between these two extremes. |
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| 493 | |
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| 494 | |
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| 495 | <p/><code>parm </code><strong> TimeShower:octetOniumColFac </strong> |
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| 496 | (<code>default = <strong>2.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 4.</code>)<br/> |
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| 497 | The colour factor used used in the splitting kernel for those octet onium |
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| 498 | states that are allowed to radiate, normalized to the <i>q -> q g</i> |
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| 499 | splitting kernel. Thus the default corresponds to twice the radiation |
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| 500 | off a quark. The physically preferred range would be between 1 and 9/4. |
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| 501 | |
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| 502 | |
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| 503 | <h3>Further variables</h3> |
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| 504 | |
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| 505 | There are several possibilities you can use to switch on or off selected |
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| 506 | branching types in the shower, or in other respects simplify the shower. |
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| 507 | These should normally not be touched. Their main function is for |
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| 508 | cross-checks. |
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| 509 | |
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| 510 | <p/><code>flag </code><strong> TimeShower:QCDshower </strong> |
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| 511 | (<code>default = <strong>on</strong></code>)<br/> |
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| 512 | Allow a QCD shower, i.e. branchings <i>q -> q g</i>, <i>g -> g g</i> |
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| 513 | and <i>g -> q qbar</i>; on/off = true/false. |
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| 514 | |
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| 515 | |
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| 516 | <p/><code>mode </code><strong> TimeShower:nGluonToQuark </strong> |
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| 517 | (<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)<br/> |
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| 518 | Number of allowed quark flavours in <i>g -> q qbar</i> branchings |
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| 519 | (phase space permitting). A change to 4 would exclude |
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| 520 | <i>g -> b bbar</i>, etc. |
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| 521 | |
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| 522 | |
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| 523 | <p/><code>flag </code><strong> TimeShower:QEDshowerByQ </strong> |
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| 524 | (<code>default = <strong>on</strong></code>)<br/> |
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| 525 | Allow quarks to radiate photons, i.e. branchings <i>q -> q gamma</i>; |
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| 526 | on/off = true/false. |
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| 527 | |
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| 528 | |
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| 529 | <p/><code>flag </code><strong> TimeShower:QEDshowerByL </strong> |
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| 530 | (<code>default = <strong>on</strong></code>)<br/> |
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| 531 | Allow leptons to radiate photons, i.e. branchings <i>l -> l gamma</i>; |
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| 532 | on/off = true/false. |
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| 533 | |
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| 534 | |
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| 535 | <p/><code>flag </code><strong> TimeShower:QEDshowerByGamma </strong> |
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| 536 | (<code>default = <strong>on</strong></code>)<br/> |
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| 537 | Allow photons to branch into lepton or quark pairs, i.e. branchings |
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| 538 | <i>gamma -> l+ l-</i> and <i>gamma -> q qbar</i>; |
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| 539 | on/off = true/false. |
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| 540 | |
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| 541 | |
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| 542 | <p/><code>mode </code><strong> TimeShower:nGammaToQuark </strong> |
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| 543 | (<code>default = <strong>5</strong></code>; <code>minimum = 0</code>; <code>maximum = 5</code>)<br/> |
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| 544 | Number of allowed quark flavours in <i>gamma -> q qbar</i> branchings |
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| 545 | (phase space permitting). A change to 4 would exclude |
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| 546 | <i>g -> b bbar</i>, etc. |
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| 547 | |
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| 548 | |
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| 549 | <p/><code>mode </code><strong> TimeShower:nGammaToLepton </strong> |
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| 550 | (<code>default = <strong>3</strong></code>; <code>minimum = 0</code>; <code>maximum = 3</code>)<br/> |
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| 551 | Number of allowed lepton flavours in <i>gamma -> l+ l-</i> branchings |
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| 552 | (phase space permitting). A change to 2 would exclude |
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| 553 | <i>gamma -> tau+ tau-</i>, and a change to 1 also |
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| 554 | <i>gamma -> mu+ mu-</i>. |
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| 555 | |
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| 556 | |
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| 557 | <p/><code>flag </code><strong> TimeShower:MEcorrections </strong> |
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| 558 | (<code>default = <strong>on</strong></code>)<br/> |
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| 559 | Use of matrix element corrections where available; on/off = true/false. |
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| 560 | |
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| 561 | |
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| 562 | <p/><code>flag </code><strong> TimeShower:MEafterFirst </strong> |
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| 563 | (<code>default = <strong>on</strong></code>)<br/> |
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| 564 | Use of matrix element corrections also after the first emission, |
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| 565 | for dipole ends of the same system that did not yet radiate. |
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| 566 | Only has a meaning if <code>MEcorrections</code> above is |
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| 567 | switched on. |
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| 568 | |
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| 569 | |
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| 570 | <p/><code>flag </code><strong> TimeShower:phiPolAsym </strong> |
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| 571 | (<code>default = <strong>on</strong></code>)<br/> |
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| 572 | Azimuthal asymmetry induced by gluon polarization; on/off = true/false. |
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| 573 | |
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| 574 | |
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| 575 | <p/><code>flag </code><strong> TimeShower:recoilToColoured </strong> |
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| 576 | (<code>default = <strong>on</strong></code>)<br/> |
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| 577 | In the decays of coloured resonances, say <i>t -> b W</i>, it is not |
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| 578 | possible to set up dipoles with matched colours. Originally the |
---|
| 579 | <i>b</i> radiator therefore has <i>W</i> as recoiler, and that |
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| 580 | choice is unique. Once a gluon has been radiated, however, it is |
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| 581 | possible either to have the unmatched colour (inherited by the gluon) |
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| 582 | still recoiling against the <i>W</i> (<code>off</code>), or else |
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| 583 | let it recoil against the <i>b</i> also for this dipole |
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| 584 | (<code>on</code>). Before version 8.160 the former was the only |
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| 585 | possibility, which could give unphysical radiation patterns. It is |
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| 586 | kept as an option to check backwards compatibility. The same issue |
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| 587 | exists for QED radiation, but obviously is less significant. Consider |
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| 588 | the example <i>W -> e nu</i>, where originally the <i>nu</i> |
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| 589 | takes the recoil. In the old (<code>off</code>) scheme the <i>nu</i> |
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| 590 | would remain recoiler, while in the new (<code>on</code>) instead |
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| 591 | each newly emitted photon becomes the new recoiler. |
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| 592 | |
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| 593 | |
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| 594 | </body> |
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| 595 | </html> |
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| 596 | |
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| 597 | <!-- Copyright (C) 2012 Torbjorn Sjostrand --> |
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