[1] | 1 | <html> |
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| 2 | <head> |
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| 3 | <title>Diffraction</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>Diffraction</h2> |
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| 10 | |
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| 11 | <h3>Introduction</h3> |
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| 12 | |
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| 13 | Diffraction is not well understood, and several alternative approaches |
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| 14 | have been proposed. Here we follow a fairly conventional Pomeron-based |
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| 15 | one, in the Ingelman-Schlein spirit [<a href="Bibliography.html" target="page">Ing85</a>], |
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| 16 | but integrated to make full use of the standard PYTHIA machinery |
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| 17 | for multiparton interactions, parton showers and hadronization |
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| 18 | [<a href="Bibliography.html" target="page">Nav10,Cor10a</a>]. This is the approach pioneered in the PomPyt |
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| 19 | program by Ingelman and collaborators [<a href="Bibliography.html" target="page">Ing97</a>]. |
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| 20 | |
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| 21 | <p/> |
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| 22 | For ease of use (and of modelling), the Pomeron-specific parts of the |
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| 23 | generation are subdivided into three sets of parameters that are rather |
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| 24 | independent of each other: |
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| 25 | <br/>(i) the total, elastic and diffractive cross sections are |
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| 26 | parametrized as functions of the CM energy, or can be set by the user |
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| 27 | to the desired values, see the |
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| 28 | <a href="TotalCrossSections.html" target="page">Total Cross Sections</a> page; |
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| 29 | <br/>(ii) once it has been decided to have a diffractive process, |
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| 30 | a Pomeron flux parametrization is used to pick the mass of the |
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| 31 | diffractive system(s) and the <i>t</i> of the exchanged Pomeron, |
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| 32 | see below; |
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| 33 | <br/>(iii) a diffractive system of a given mass is classified either |
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| 34 | as low-mass unresolved, which gives a simple low-<i>pT</i> string |
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| 35 | topology, or as high-mass resolved, for which the full machinery of |
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| 36 | multiparton interactions and parton showers are applied, making use of |
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| 37 | <a href="PDFSelection.html" target="page">Pomeron PDFs</a>. |
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| 38 | <br/>The parameters related to multiparton interactions, parton showers |
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| 39 | and hadronization are kept the same as for normal nondiffractive events, |
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| 40 | with only one exception. This may be questioned, especially for the |
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| 41 | multiparton interactions, but we do not believe that there are currently |
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| 42 | enough good diffractive data that would allow detailed separate tunes. |
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| 43 | |
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| 44 | <p/> |
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| 45 | The above subdivision may not represent the way "physics comes about". |
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| 46 | For instance, the total diffractive cross section can be viewed as a |
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| 47 | convolution of a Pomeron flux with a Pomeron-proton total cross section. |
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| 48 | Since neither of the two is known from first principles there will be |
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| 49 | a significant amount of ambiguity in the flux factor. The picture is |
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| 50 | further complicated by the fact that the possibility of simultaneous |
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| 51 | further multiparton interactions ("cut Pomerons") will screen the rate of |
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| 52 | diffractive systems. In the end, our set of parameters refers to the |
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| 53 | effective description that emerges out of these effects, rather than |
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| 54 | to the underlying "bare" parameters. |
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| 55 | |
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| 56 | <p/> |
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| 57 | In the event record the diffractive system in the case of an excited |
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| 58 | proton is denoted <code>p_diffr</code>, code 9902210, whereas |
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| 59 | a central diffractive system is denoted <code>rho_diffr</code>, |
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| 60 | code 9900110. Apart from representing the correct charge and baryon |
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| 61 | numbers, no deeper meaning should be attributed to the names. |
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| 62 | |
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| 63 | <h3>Pomeron flux</h3> |
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| 64 | |
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| 65 | As already mentioned above, the total diffractive cross section is fixed |
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| 66 | by a default energy-dependent parametrization or by the user, see the |
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| 67 | <a href="TotalCrossSections.html" target="page">Total Cross Sections</a> page. |
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| 68 | Therefore we do not attribute any significance to the absolute |
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| 69 | normalization of the Pomeron flux. The choice of Pomeron flux model |
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| 70 | still will decide on the mass spectrum of diffractive states and the |
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| 71 | <i>t</i> spectrum of the Pomeron exchange. |
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| 72 | |
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| 73 | <p/><code>mode </code><strong> Diffraction:PomFlux </strong> |
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| 74 | (<code>default = <strong>1</strong></code>; <code>minimum = 1</code>; <code>maximum = 5</code>)<br/> |
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| 75 | Parametrization of the Pomeron flux <i>f_Pom/p( x_Pom, t)</i>. |
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| 76 | <br/><code>option </code><strong> 1</strong> : Schuler and Sjöstrand [<a href="Bibliography.html" target="page">Sch94</a>]: based on a |
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| 77 | critical Pomeron, giving a mass spectrum roughly like <i>dm^2/m^2</i>; |
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| 78 | a mass-dependent exponential <i>t</i> slope that reduces the rate |
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| 79 | of low-mass states; partly compensated by a very-low-mass (resonance region) |
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| 80 | enhancement. Is currently the only one that contains a separate |
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| 81 | <i>t</i> spectrum for double diffraction (along with MBR) and |
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| 82 | separate parameters for pion beams. |
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| 83 | <br/><code>option </code><strong> 2</strong> : Bruni and Ingelman [<a href="Bibliography.html" target="page">Bru93</a>]: also a critical |
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| 84 | Pomeron giving close to <i>dm^2/m^2</i>, with a <i>t</i> distribution |
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| 85 | the sum of two exponentials. The original model only covers single |
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| 86 | diffraction, but is here expanded by analogy to double and central |
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| 87 | diffraction. |
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| 88 | <br/><code>option </code><strong> 3</strong> : a conventional Pomeron description, in the RapGap |
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| 89 | manual [<a href="Bibliography.html" target="page">Jun95</a>] attributed to Berger et al. and Streng |
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| 90 | [<a href="Bibliography.html" target="page">Ber87a</a>], but there (and here) with values updated to a |
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| 91 | supercritical Pomeron with <i>epsilon > 0</i> (see below), |
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| 92 | which gives a stronger peaking towards low-mass diffractive states, |
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| 93 | and with a mass-dependent (the <i>alpha'</i> below) exponential |
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| 94 | <i>t</i> slope. The original model only covers single diffraction, |
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| 95 | but is here expanded by analogy to double and central diffraction. |
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| 96 | |
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| 97 | <br/><code>option </code><strong> 4</strong> : a conventional Pomeron description, attributed to |
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| 98 | Donnachie and Landshoff [<a href="Bibliography.html" target="page">Don84</a>], again with supercritical Pomeron, |
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| 99 | with the same two parameters as option 3 above, but this time with a |
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| 100 | power-law <i>t</i> distribution. The original model only covers single |
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| 101 | diffraction, but is here expanded by analogy to double and central |
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| 102 | diffraction. |
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| 103 | <br/><code>option </code><strong> 5</strong> : the MBR (Minimum Bias Rockefeller) simulation of |
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| 104 | (anti)proton-proton interactions [<a href="Bibliography.html" target="page">Cie12</a>]. The event |
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| 105 | generation follows a renormalized-Regge-theory model, sucessfully tested |
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| 106 | using CDF data. The simulation includes single and double diffraction, |
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| 107 | as well as the central diffractive (double-Pomeron exchange) process (106). |
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| 108 | Only <i>p p</i>, <i>pbar p</i> and <i>p pbar</i> beam combinations |
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| 109 | are allowed for this option. Several parameters of this model are listed |
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| 110 | below. |
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| 111 | |
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| 112 | |
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| 113 | <p/> |
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| 114 | In options 3 and 4 above, the Pomeron Regge trajectory is |
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| 115 | parametrized as |
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| 116 | <br/><i> |
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| 117 | alpha(t) = 1 + epsilon + alpha' t |
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| 118 | </i><br/> |
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| 119 | The <i>epsilon</i> and <i>alpha'</i> parameters can be set |
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| 120 | separately: |
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| 121 | |
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| 122 | <p/><code>parm </code><strong> Diffraction:PomFluxEpsilon </strong> |
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| 123 | (<code>default = <strong>0.085</strong></code>; <code>minimum = 0.02</code>; <code>maximum = 0.15</code>)<br/> |
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| 124 | The Pomeron trajectory intercept <i>epsilon</i> above. For technical |
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| 125 | reasons <i>epsilon > 0</i> is necessary in the current implementation. |
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| 126 | |
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| 127 | <p/><code>parm </code><strong> Diffraction:PomFluxAlphaPrime </strong> |
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| 128 | (<code>default = <strong>0.25</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 0.4</code>)<br/> |
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| 129 | The Pomeron trajectory slope <i>alpha'</i> above. |
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| 130 | |
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| 131 | <p/> |
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| 132 | When option 5 is selected, the following parameters of the MBR model |
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| 133 | [<a href="Bibliography.html" target="page">Cie12</a>] are used: |
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| 134 | |
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| 135 | <p/><code>parm </code><strong> Diffraction:MBRepsilon </strong> |
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| 136 | (<code>default = <strong>0.104</strong></code>; <code>minimum = 0.02</code>; <code>maximum = 0.15</code>)<br/> |
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| 137 | <p/><code>parm </code><strong> Diffraction:MBRalpha </strong> |
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| 138 | (<code>default = <strong>0.25</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 0.4</code>)<br/> |
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| 139 | the parameters of the Pomeron trajectory. |
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| 140 | |
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| 141 | <p/><code>parm </code><strong> Diffraction:MBRbeta0 </strong> |
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| 142 | (<code>default = <strong>6.566</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 10.0</code>)<br/> |
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| 143 | <p/><code>parm </code><strong> Diffraction:MBRsigma0 </strong> |
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| 144 | (<code>default = <strong>2.82</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 5.0</code>)<br/> |
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| 145 | the Pomeron-proton coupling, and the total Pomeron-proton cross section. |
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| 146 | |
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| 147 | <p/><code>parm </code><strong> Diffraction:MBRm2Min </strong> |
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| 148 | (<code>default = <strong>1.5</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 3.0</code>)<br/> |
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| 149 | the lowest value of the mass squared of the dissociated system. |
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| 150 | |
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| 151 | <p/><code>parm </code><strong> Diffraction:MBRdyminSDflux </strong> |
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| 152 | (<code>default = <strong>2.3</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 5.0</code>)<br/> |
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| 153 | <p/><code>parm </code><strong> Diffraction:MBRdyminDDflux </strong> |
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| 154 | (<code>default = <strong>2.3</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 5.0</code>)<br/> |
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| 155 | <p/><code>parm </code><strong> Diffraction:MBRdyminCDflux </strong> |
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| 156 | (<code>default = <strong>2.3</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 5.0</code>)<br/> |
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| 157 | the minimum width of the rapidity gap used in the calculation of |
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| 158 | <i>Ngap(s)</i> (flux renormalization). |
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| 159 | |
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| 160 | <p/><code>parm </code><strong> Diffraction:MBRdyminSD </strong> |
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| 161 | (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 5.0</code>)<br/> |
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| 162 | <p/><code>parm </code><strong> Diffraction:MBRdyminDD </strong> |
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| 163 | (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 5.0</code>)<br/> |
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| 164 | <p/><code>parm </code><strong> Diffraction:MBRdyminCD </strong> |
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| 165 | (<code>default = <strong>2.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 5.0</code>)<br/> |
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| 166 | the minimum width of the rapidity gap used in the calculation of cross |
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| 167 | sections, i.e. the parameter <i>dy_S</i>, which suppresses the cross |
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| 168 | section at low <i>dy</i> (non-diffractive region). |
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| 169 | |
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| 170 | <p/><code>parm </code><strong> Diffraction:MBRdyminSigSD </strong> |
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| 171 | (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 5.0</code>)<br/> |
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| 172 | <p/><code>parm </code><strong> Diffraction:MBRdyminSigDD </strong> |
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| 173 | (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 5.0</code>)<br/> |
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| 174 | <p/><code>parm </code><strong> Diffraction:MBRdyminSigCD </strong> |
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| 175 | (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.001</code>; <code>maximum = 5.0</code>)<br/> |
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| 176 | the parameter <i>sigma_S</i>, used for the cross section suppression at |
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| 177 | low <i>dy</i> (non-diffractive region). |
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| 178 | |
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| 179 | <h3>Separation into low and high masses</h3> |
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| 180 | |
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| 181 | Preferably one would want to have a perturbative picture of the |
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| 182 | dynamics of Pomeron-proton collisions, like multiparton interactions |
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| 183 | provide for proton-proton ones. However, while PYTHIA by default |
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| 184 | will only allow collisions with a CM energy above 10 GeV, the |
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| 185 | mass spectrum of diffractive systems will stretch to down to |
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| 186 | the order of 1.2 GeV. It would not be feasible to attempt a |
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| 187 | perturbative description there. Therefore we do offer a simpler |
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| 188 | low-mass description, with only longitudinally stretched strings, |
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| 189 | with a gradual switch-over to the perturbative picture for higher |
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| 190 | masses. The probability for the latter picture is parametrized as |
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| 191 | <br/><i> |
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| 192 | P_pert = P_max ( 1 - exp( (m_diffr - m_min) / m_width ) ) |
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| 193 | </i><br/> |
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| 194 | which vanishes for the diffractive system mass |
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| 195 | <i>m_diffr < m_min</i>, and is <i>1 - 1/e = 0.632</i> for |
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| 196 | <i>m_diffr = m_min + m_width</i>, assuming <i>P_max = 1</i>. |
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| 197 | |
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| 198 | <p/><code>parm </code><strong> Diffraction:mMinPert </strong> |
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| 199 | (<code>default = <strong>10.</strong></code>; <code>minimum = 5.</code>)<br/> |
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| 200 | The abovementioned threshold mass <i>m_min</i> for phasing in a |
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| 201 | perturbative treatment. If you put this parameter to be bigger than |
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| 202 | the CM energy then there will be no perturbative description at all, |
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| 203 | but only the older low-<i>pt</i> description. |
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| 204 | |
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| 205 | |
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| 206 | <p/><code>parm </code><strong> Diffraction:mWidthPert </strong> |
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| 207 | (<code>default = <strong>10.</strong></code>; <code>minimum = 0.</code>)<br/> |
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| 208 | The abovementioned threshold width <i>m_width.</i> |
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| 209 | |
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| 210 | |
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| 211 | <p/><code>parm </code><strong> Diffraction:probMaxPert </strong> |
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| 212 | (<code>default = <strong>1.</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)<br/> |
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| 213 | The abovementioned maximum probability <i>P_max.</i>. Would |
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| 214 | normally be assumed to be unity, but a somewhat lower value could |
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| 215 | be used to represent a small nonperturbative component also at |
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| 216 | high diffractive masses. |
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| 217 | |
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| 218 | |
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| 219 | <h3>Low-mass diffraction</h3> |
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| 220 | |
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| 221 | When an incoming hadron beam is diffractively excited, it is modeled |
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| 222 | as if either a valence quark or a gluon is kicked out from the hadron. |
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| 223 | In the former case this produces a simple string to the leftover |
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| 224 | remnant, in the latter it gives a hairpin arrangement where a string |
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| 225 | is stretched from one quark in the remnant, via the gluon, back to the |
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| 226 | rest of the remnant. The latter ought to dominate at higher mass of |
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| 227 | the diffractive system. Therefore an approximate behaviour like |
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| 228 | <br/><i> |
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| 229 | P_q / P_g = N / m^p |
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| 230 | </i><br/> |
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| 231 | is assumed. |
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| 232 | |
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| 233 | <p/><code>parm </code><strong> Diffraction:pickQuarkNorm </strong> |
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| 234 | (<code>default = <strong>5.0</strong></code>; <code>minimum = 0.</code>)<br/> |
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| 235 | The abovementioned normalization <i>N</i> for the relative quark |
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| 236 | rate in diffractive systems. |
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| 237 | |
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| 238 | |
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| 239 | <p/><code>parm </code><strong> Diffraction:pickQuarkPower </strong> |
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| 240 | (<code>default = <strong>1.0</strong></code>)<br/> |
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| 241 | The abovementioned mass-dependence power <i>p</i> for the relative |
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| 242 | quark rate in diffractive systems. |
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| 243 | |
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| 244 | |
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| 245 | <p/> |
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| 246 | When a gluon is kicked out from the hadron, the longitudinal momentum |
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| 247 | sharing between the the two remnant partons is determined by the |
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| 248 | same parameters as above. It is plausible that the primordial |
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| 249 | <i>kT</i> may be lower than in perturbative processes, however: |
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| 250 | |
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| 251 | <p/><code>parm </code><strong> Diffraction:primKTwidth </strong> |
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| 252 | (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.</code>)<br/> |
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| 253 | The width of Gaussian distributions in <i>p_x</i> and <i>p_y</i> |
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| 254 | separately that is assigned as a primordial <i>kT</i> to the two |
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| 255 | beam remnants when a gluon is kicked out of a diffractive system. |
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| 256 | |
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| 257 | |
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| 258 | <p/><code>parm </code><strong> Diffraction:largeMassSuppress </strong> |
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| 259 | (<code>default = <strong>2.</strong></code>; <code>minimum = 0.</code>)<br/> |
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| 260 | The choice of longitudinal and transverse structure of a diffractive |
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| 261 | beam remnant for a kicked-out gluon implies a remnant mass |
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| 262 | <i>m_rem</i> distribution (i.e. quark plus diquark invariant mass |
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| 263 | for a baryon beam) that knows no bounds. A suppression like |
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| 264 | <i>(1 - m_rem^2 / m_diff^2)^p</i> is therefore introduced, where |
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| 265 | <i>p</i> is the <code>diffLargeMassSuppress</code> parameter. |
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| 266 | |
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| 267 | |
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| 268 | <h3>High-mass diffraction</h3> |
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| 269 | |
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| 270 | The perturbative description need to use parton densities of the |
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| 271 | Pomeron. The options are described in the page on |
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| 272 | <a href="PDFSelection.html" target="page">PDF Selection</a>. The standard |
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| 273 | perturbative multiparton interactions framework then provides |
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| 274 | cross sections for parton-parton interactions. In order to |
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| 275 | turn these cross section into probabilities one also needs an |
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| 276 | ansatz for the Pomeron-proton total cross section. In the literature |
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| 277 | one often finds low numbers for this, of the order of 2 mb. |
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| 278 | These, if taken at face value, would give way too much activity |
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| 279 | per event. There are ways to tame this, e.g. by a larger <i>pT0</i> |
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| 280 | than in the normal pp framework. Actually, there are many reasons |
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| 281 | to use a completely different set of parameters for MPI in |
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| 282 | diffraction than in pp collisions, especially with respect to the |
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| 283 | impact-parameter picture, see below. A lower number in some frameworks |
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| 284 | could alternatively be regarded as a consequence of screening, with |
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| 285 | a larger "bare" number. |
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| 286 | |
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| 287 | <p/> |
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| 288 | For now, however, an attempt at the most general solution would |
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| 289 | carry too far, and instead we patch up the problem by using a |
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| 290 | larger Pomeron-proton total cross section, such that average |
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| 291 | activity makes more sense. This should be viewed as the main |
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| 292 | tunable parameter in the description of high-mass diffraction. |
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| 293 | It is to be fitted to diffractive event-shape data such as the average |
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| 294 | charged multiplicity. It would be very closely tied to the choice of |
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| 295 | Pomeron PDF; we remind that some of these add up to less than unit |
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| 296 | momentum sum in the Pomeron, a choice that also affect the value |
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| 297 | one ends up with. Furthermore, like with hadronic cross sections, |
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| 298 | it is quite plausible that the Pomeron-proton cross section increases |
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| 299 | with energy, so we have allowed for a powerlike dependence on the |
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| 300 | diffractive mass. |
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| 301 | |
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| 302 | <p/><code>parm </code><strong> Diffraction:sigmaRefPomP </strong> |
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| 303 | (<code>default = <strong>10.</strong></code>; <code>minimum = 2.</code>; <code>maximum = 40.</code>)<br/> |
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| 304 | The assumed Pomeron-proton effective cross section, as used for |
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| 305 | multiparton interactions in diffractive systems. If this cross section |
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| 306 | is made to depend on the mass of the diffractive system then the above |
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| 307 | value refers to the cross section at the reference scale, and |
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| 308 | <br/><i> |
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| 309 | sigma_PomP(m) = sigma_PomP(m_ref) * (m / m_ref)^p |
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| 310 | </i><br/> |
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| 311 | where <i>m</i> is the mass of the diffractive system, <i>m_ref</i> |
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| 312 | is the reference mass scale <code>Diffraction:mRefPomP</code> below and |
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| 313 | <i>p</i> is the mass-dependence power <code>Diffraction:mPowPomP</code>. |
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| 314 | Note that a larger cross section value gives less MPI activity per event. |
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| 315 | There is no point in making the cross section too big, however, since |
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| 316 | then <i>pT0</i> will be adjusted downwards to ensure that the |
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| 317 | integrated perturbative cross section stays above this assumed total |
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| 318 | cross section. (The requirement of at least one perturbative interaction |
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| 319 | per event.) |
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| 320 | |
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| 321 | |
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| 322 | <p/><code>parm </code><strong> Diffraction:mRefPomP </strong> |
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| 323 | (<code>default = <strong>100.0</strong></code>; <code>minimum = 1.</code>)<br/> |
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| 324 | The <i>mRef</i> reference mass scale introduced above. |
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| 325 | |
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| 326 | |
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| 327 | <p/><code>parm </code><strong> Diffraction:mPowPomP </strong> |
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| 328 | (<code>default = <strong>0.0</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 0.5</code>)<br/> |
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| 329 | The <i>p</i> mass rescaling pace introduced above. |
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| 330 | |
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| 331 | |
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| 332 | <p/> |
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| 333 | Also note that, even for a fixed CM energy of events, the diffractive |
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| 334 | subsystem will range from the abovementioned threshold mass |
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| 335 | <i>m_min</i> to the full CM energy, with a variation of parameters |
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| 336 | such as <i>pT0</i> along this mass range. Therefore multiparton |
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| 337 | interactions are initialized for a few different diffractive masses, |
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| 338 | currently five, and all relevant parameters are interpolated between |
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| 339 | them to obtain the behaviour at a specific diffractive mass. |
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| 340 | Furthermore, <i>A B ->X B</i> and <i>A B ->A X</i> are |
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| 341 | initialized separately, to allow for different beams or PDF's on the |
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| 342 | two sides. These two aspects mean that initialization of MPI is |
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| 343 | appreciably slower when perturbative high-mass diffraction is allowed. |
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| 344 | |
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| 345 | <p/> |
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| 346 | Diffraction tends to be peripheral, i.e. occur at intermediate impact |
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| 347 | parameter for the two protons. That aspect is implicit in the selection |
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| 348 | of diffractive cross section. For the simulation of the Pomeron-proton |
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| 349 | subcollision it is the impact-parameter distribution of that particular |
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| 350 | subsystem that should rather be modelled. That is, it also involves |
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| 351 | the transverse coordinate space of a Pomeron wavefunction. The outcome |
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| 352 | of the convolution therefore could be a different shape than for |
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| 353 | nondiffractive events. For simplicity we allow the same kind of |
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| 354 | options as for nondiffractive events, except that the |
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| 355 | <code>bProfile = 4</code> option for now is not implemented. |
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| 356 | |
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| 357 | <p/><code>mode </code><strong> Diffraction:bProfile </strong> |
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| 358 | (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 3</code>)<br/> |
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| 359 | Choice of impact parameter profile for the incoming hadron beams. |
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| 360 | <br/><code>option </code><strong> 0</strong> : no impact parameter dependence at all. |
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| 361 | <br/><code>option </code><strong> 1</strong> : a simple Gaussian matter distribution; |
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| 362 | no free parameters. |
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| 363 | <br/><code>option </code><strong> 2</strong> : a double Gaussian matter distribution, |
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| 364 | with the two free parameters <i>coreRadius</i> and |
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| 365 | <i>coreFraction</i>. |
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| 366 | <br/><code>option </code><strong> 3</strong> : an overlap function, i.e. the convolution of |
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| 367 | the matter distributions of the two incoming hadrons, of the form |
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| 368 | <i>exp(- b^expPow)</i>, where <i>expPow</i> is a free |
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| 369 | parameter. |
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| 370 | |
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| 371 | |
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| 372 | <p/><code>parm </code><strong> Diffraction:coreRadius </strong> |
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| 373 | (<code>default = <strong>0.4</strong></code>; <code>minimum = 0.1</code>; <code>maximum = 1.</code>)<br/> |
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| 374 | When assuming a double Gaussian matter profile, <i>bProfile = 2</i>, |
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| 375 | the inner core is assumed to have a radius that is a factor |
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| 376 | <i>coreRadius</i> smaller than the rest. |
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| 377 | |
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| 378 | |
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| 379 | <p/><code>parm </code><strong> Diffraction:coreFraction </strong> |
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| 380 | (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.</code>)<br/> |
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| 381 | When assuming a double Gaussian matter profile, <i>bProfile = 2</i>, |
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| 382 | the inner core is assumed to have a fraction <i>coreFraction</i> |
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| 383 | of the matter content of the hadron. |
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| 384 | |
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| 385 | |
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| 386 | <p/><code>parm </code><strong> Diffraction:expPow </strong> |
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| 387 | (<code>default = <strong>1.</strong></code>; <code>minimum = 0.4</code>; <code>maximum = 10.</code>)<br/> |
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| 388 | When <i>bProfile = 3</i> it gives the power of the assumed overlap |
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| 389 | shape <i>exp(- b^expPow)</i>. Default corresponds to a simple |
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| 390 | exponential drop, which is not too dissimilar from the overlap |
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| 391 | obtained with the standard double Gaussian parameters. For |
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| 392 | <i>expPow = 2</i> we reduce to the simple Gaussian, <i>bProfile = 1</i>, |
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| 393 | and for <i>expPow -> infinity</i> to no impact parameter dependence |
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| 394 | at all, <i>bProfile = 0</i>. For small <i>expPow</i> the program |
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| 395 | becomes slow and unstable, so the min limit must be respected. |
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| 396 | |
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| 397 | |
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| 398 | </body> |
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| 399 | </html> |
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| 400 | |
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| 401 | <!-- Copyright (C) 2012 Torbjorn Sjostrand --> |
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