[1] | 1 | <chapter name="Hidden Valley Processes"> |
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| 2 | |
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| 3 | <h2>Hidden Valley Processes</h2> |
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| 4 | |
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| 5 | This Hidden Valley (HV) scenario has been developed specifically |
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| 6 | to allow the study of visible consequences of radiation in a |
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| 7 | hidden sector, by recoil effect. A key aspect is therefore that |
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| 8 | the normal timelike showering machinery has been expanded with a |
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| 9 | third kind of radiation, in addition to the QCD and QED ones. |
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| 10 | These three kinds of radiation are fully interleaved, i.e. |
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| 11 | evolution occurs in a common <ei>pT</ei>-ordered sequence. |
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| 12 | The scenario is described in <ref>Car10</ref>. Furthermore |
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| 13 | hadronization in the hidden sector has been implemented. |
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| 14 | Three main scenarios for production into and decay out of the |
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| 15 | hidden sector can be compared, in each case either for an |
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| 16 | Abelian or a non-Abelian gauge group in the HV. For further details |
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| 17 | see <ref>Car11</ref>. |
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| 18 | |
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| 19 | <h3>Particle content and properties</h3> |
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| 20 | |
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| 21 | For simplicity we assume that the HV contains an unbroken <b>SU(N)</b> |
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| 22 | gauge symmetry. This is used in the calculation of production cross |
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| 23 | sections. These could be rescaled by hand for other gauge groups. |
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| 24 | |
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| 25 | <modeopen name="HiddenValley:Ngauge" default="3" min="1"> |
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| 26 | is <b>U(1)</b> for <code>Ngauge = 1</code>, is <b>SU(N)</b> if |
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| 27 | <code>Ngauge > 1</code>. Note that pair production cross sections |
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| 28 | contains a factor of <code>Ngauge</code> for new particles |
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| 29 | in the fundamental representation of this group. |
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| 30 | </modeopen> |
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| 31 | |
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| 32 | <p/> |
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| 33 | A minimal HV particle content has been introduced. Firstly, there is |
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| 34 | a set of 12 particles that mirrors the Standard Model flavour |
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| 35 | structure, and is charged under both the SM and the HV symmetry groups. |
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| 36 | Each new particle couples flavour-diagonally to a corresponding SM |
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| 37 | state, and has the same SM charge and colour, but in addition is in |
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| 38 | the fundamental representation of the HV colour, as follows: |
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| 39 | <br/><code>Dv</code>, identity 4900001, partner to the normal |
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| 40 | <code>d</code> quark; |
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| 41 | <br/><code>Uv</code>, identity 4900002, partner to the normal |
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| 42 | <code>u</code> quark; |
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| 43 | <br/><code>Sv</code>, identity 4900003, partner to the normal |
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| 44 | <code>s</code> quark; |
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| 45 | <br/><code>Cv</code>, identity 4900004, partner to the normal |
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| 46 | <code>c</code> quark; |
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| 47 | <br/><code>Bv</code>, identity 4900005, partner to the normal |
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| 48 | <code>b</code> quark; |
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| 49 | <br/><code>Tv</code>, identity 4900006, partner to the normal |
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| 50 | <code>t</code> quark; |
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| 51 | <br/><code>Ev</code>, identity 4900011, partner to the normal |
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| 52 | <code>e</code> lepton; |
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| 53 | <br/><code>nuEv</code>, identity 4900012, partner to the normal |
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| 54 | <code>nue</code> neutrino; |
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| 55 | <br/><code>MUv</code>, identity 4900013, partner to the normal |
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| 56 | <code>mu</code> lepton; |
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| 57 | <br/><code>nuMUv</code>, identity 4900014, partner to the normal |
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| 58 | <code>numu</code> neutrino; |
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| 59 | <br/><code>TAUv</code>, identity 4900015, partner to the normal |
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| 60 | <code>tau</code> lepton; |
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| 61 | <br/><code>nuTAUv</code>, identity 4900016, partner to the normal |
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| 62 | <code>nutau</code> neutrino. |
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| 63 | <br/>Collectively we will refer to these states as <code>Fv</code>; |
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| 64 | note, however, that they need not be fermions themselves. |
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| 65 | |
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| 66 | <p/> |
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| 67 | In addition the model contains the HV gauge particle, either |
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| 68 | a HV-gluon or a HV-photon, but not both; see <code>Ngauge</code> |
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| 69 | above: |
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| 70 | <br/><code>gv</code>, identity 4900021, is the massless |
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| 71 | gauge boson of the HV <b>SU(N)</b> group; |
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| 72 | <br/><code>gammav</code>, identity 4900022, is the massless |
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| 73 | gauge boson of the HV <b>U(1)</b> group. |
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| 74 | |
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| 75 | <p/> |
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| 76 | Finally, for the basic HV scenario, there is a new massive particle |
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| 77 | with only HV charge sitting in the fundamental representation of the |
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| 78 | HV gauge group: |
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| 79 | <br/><code>qv</code>, identity 4900101. |
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| 80 | |
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| 81 | <p/>The typical scenario would be for pair production of one of the |
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| 82 | states presented first above, e.g. <ei>g g -> Dv Dvbar</ei>. |
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| 83 | Such a <ei>Dv</ei> can radiate gluons and photons like an SM quark, |
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| 84 | but in addition HV-gluons or HV-photons in a similar fashion. |
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| 85 | Eventually the <ei>Dv</ei> will decay like <ei>Dv -> d + qv</ei>. |
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| 86 | The strength of this decay is not set as such, but is implicit in |
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| 87 | your choice of width for the <ei>Dv</ei> state. Thereafter the |
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| 88 | <ei>d</ei> and <ei>qv</ei> can radiate further within their |
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| 89 | respective sectors. The <ei>qv</ei>, <ei>gv</ei> or <ei>gammav</ei> |
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| 90 | are invisible, so their fate need not be considered further. |
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| 91 | |
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| 92 | <p/> |
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| 93 | While not part of the standard scenario, as an alternative there is |
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| 94 | also a kind of <ei>Z'</ei> resonance: |
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| 95 | <br/><code>Zv</code>, identity 4900023, a boson that can couple |
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| 96 | both to pairs of Standard Model fermions and to <ei>qv qvbar</ei> |
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| 97 | pairs. Mass, total width and branching ratios can be set as convenient. |
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| 98 | <br/>This opens up for alternative processes |
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| 99 | <ei>l^+l^-, q qbar -> Zv -> qv qvbar</ei>. |
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| 100 | |
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| 101 | <p/> |
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| 102 | The possibility of a leakage back from the hidden sector will be |
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| 103 | considered in the Hadronization section below. For the <b>U(1)</b> |
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| 104 | case the <ei>gammav</ei> acquires a mass and can decay back to a |
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| 105 | Standard-Model fermion pair, while the <ei>qv</ei> remains invisible. |
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| 106 | The <b>SU(N)</b> alternative remains unbroken, so confinement holds |
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| 107 | and the <ei>gv</ei> is massless. A string like |
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| 108 | <ei>qv - gv - ... - gv - qvbar</ei> can break by the production of |
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| 109 | new <ei>qv - qvbar</ei> pairs, which will produce <ei>qv-qvbar</ei> |
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| 110 | mesons. It would be possible to build a rather sophisticated hidden |
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| 111 | sector by trivial extensions of the HV flavour content. For now, |
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| 112 | however, the <ei>qv</ei> can be duplicated in up to eight copies |
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| 113 | with the same properties except for the flavour charge. These are |
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| 114 | assigned codes 4900101 - 4900108. This gives a total of 64 possible |
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| 115 | lowest-lying mesons. We also include a duplication of that, into two |
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| 116 | multiplets, corrsesponding to the pseudoscalar and vector mesons of |
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| 117 | QCD. For now, again, these are assumed to have the same mass and |
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| 118 | other properties. Only the flavour-diagonal ones can decay back into |
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| 119 | the Standard-Model sector, however, while the rest remains in the |
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| 120 | hidden sector. It is therefore only necessary to distinguish a few |
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| 121 | states: |
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| 122 | <br/><code>pivDiag</code>, identity 4900111, a flavour-diagonal |
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| 123 | HV-meson with spin 0 that can decay back into the Standard-Model sector; |
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| 124 | <br/><code>rhovDiag</code>, identity 4900113, a flavour-diagonal |
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| 125 | HV-meson with spin 1 that can decay back into the Standard-Model sector; |
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| 126 | <br/><code>pivUp</code>, identity 4900211, an off-diagonal |
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| 127 | HV-meson with spin 0 that is stable and invisible, with an antiparticle |
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| 128 | <code>pivDn</code> with identity -4900211; the particle is |
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| 129 | the one where the code of the flavour is larger than that of the |
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| 130 | antiflavour; |
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| 131 | <br/><code>rhovUp</code>, identity 4900213, an off-diagonal |
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| 132 | HV-meson with spin 1 that is stable and invisible, with an antiparticle |
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| 133 | <code>rhovDn</code> with identity -4900213; again the particle is |
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| 134 | the one where the code of the flavour is larger than that of the |
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| 135 | antiflavour; |
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| 136 | <br/><code>ggv</code>, identity 4900991, is only rarely used, |
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| 137 | to handle cases where it is kinematically impossible to produce an |
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| 138 | HV-meson on shell, and it therefore is assumed to de-excite by the |
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| 139 | emission of invisible <ei>gv-gv </ei> v-glueball bound states. |
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| 140 | |
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| 141 | <p/> |
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| 142 | Only the spin of the HV-gluon or HV-photon is determined unambiguously |
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| 143 | to be unity, for the others you can make your choice. |
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| 144 | |
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| 145 | <modepick name="HiddenValley:spinFv" default="1" min="0" max="2"> |
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| 146 | The spin of the HV partners of the SM fermions, e.g. |
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| 147 | <ei>Dv</ei>, <ei>Uv</ei>, <ei>Ev</ei> and <ei>nuEv</ei>. |
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| 148 | <option value="0">spin 0.</option> |
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| 149 | <option value="1">spin 1/2.</option> |
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| 150 | <option value="2">spin 1.</option> |
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| 151 | </modepick> |
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| 152 | |
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| 153 | <modepick name="HiddenValley:spinqv" default="0" min="0" max="1"> |
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| 154 | The spin of <ei>qv</ei> when the <ei>Fv</ei> (the HV partners of |
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| 155 | the SM fermions) have spin 1/2. (While, if they have spin 0 or 1, |
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| 156 | the <ei>qv</ei> spin is fixed at 1/2.) |
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| 157 | <option value="0">spin 0.</option> |
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| 158 | <option value="1">spin 1.</option> |
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| 159 | </modepick> |
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| 160 | |
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| 161 | <parm name="HiddenValley:kappa" default="1."> |
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| 162 | If the <ei>Fv</ei> have spin 1 then their production |
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| 163 | cross section depends on the presence of ananomalous magnetic dipole |
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| 164 | moment, i.e. of a <ei>kappa</ei> different from unity. For other spins |
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| 165 | this parameter is not used. |
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| 166 | </parm> |
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| 167 | |
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| 168 | <flag name="HiddenValley:doKinMix" default="off"> |
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| 169 | allow kinemtic mixing or not. |
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| 170 | </flag> |
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| 171 | |
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| 172 | <parm name="HiddenValley:kinMix" default="1."> |
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| 173 | strength of kinetic mixing. |
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| 174 | </parm> |
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| 175 | |
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| 176 | <p/> |
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| 177 | You should set the <ei>Fv</ei> and <ei>qv</ei> masses appropriately, |
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| 178 | with the latter smaller than the former two to allow decays. |
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| 179 | When <b>U(1)</b> hadronization is switched on, you need to set the |
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| 180 | <ei>gammav</ei> mass and decay modes. For <b>SU(N)</b> hadronization |
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| 181 | the HV-meson masses should be set to match the <ei>qv</ei> ones. |
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| 182 | The simplest is to assume that <ei>m_qv</ei> defines a constituent |
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| 183 | mass, so that <ei>m_HVmeson = 2 m_qv</ei>. The <ei>hvMesonDiag</ei> |
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| 184 | decay modes also need to be set. |
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| 185 | |
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| 186 | <h3>Production processes</h3> |
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| 187 | |
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| 188 | <flag name="HiddenValley:all" default="off"> |
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| 189 | Common switch for the group of all hard Hidden Valley processes, |
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| 190 | as listed separately in the following. |
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| 191 | </flag> |
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| 192 | |
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| 193 | <flag name="HiddenValley:gg2DvDvbar" default="off"> |
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| 194 | Pair production <ei>g g -> Dv Dvbar</ei>. |
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| 195 | Code 4901. |
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| 196 | </flag> |
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| 197 | |
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| 198 | <flag name="HiddenValley:gg2UvUvbar" default="off"> |
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| 199 | Pair production <ei>g g -> Uv Uvbar</ei>. |
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| 200 | Code 4902. |
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| 201 | </flag> |
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| 202 | |
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| 203 | <flag name="HiddenValley:gg2SvSvbar" default="off"> |
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| 204 | Pair production <ei>g g -> Sv Svbar</ei>. |
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| 205 | Code 4903. |
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| 206 | </flag> |
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| 207 | |
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| 208 | <flag name="HiddenValley:gg2CvCvbar" default="off"> |
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| 209 | Pair production <ei>g g -> Cv Cvbar</ei>. |
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| 210 | Code 4904. |
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| 211 | </flag> |
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| 212 | |
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| 213 | <flag name="HiddenValley:gg2BvBvbar" default="off"> |
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| 214 | Pair production <ei>g g -> Bv Bvbar</ei>. |
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| 215 | Code 4905. |
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| 216 | </flag> |
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| 217 | |
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| 218 | <flag name="HiddenValley:gg2TvTvbar" default="off"> |
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| 219 | Pair production <ei>g g -> Tv Tvbar</ei>. |
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| 220 | Code 4906. |
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| 221 | </flag> |
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| 222 | |
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| 223 | <flag name="HiddenValley:qqbar2DvDvbar" default="off"> |
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| 224 | Pair production <ei>q qbar -> Dv Dvbar</ei> |
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| 225 | via intermediate gluon. |
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| 226 | Code 4911. |
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| 227 | </flag> |
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| 228 | |
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| 229 | <flag name="HiddenValley:qqbar2UvUvbar" default="off"> |
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| 230 | Pair production <ei>q qbar -> Uv Uvbar</ei> |
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| 231 | via intermediate gluon. |
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| 232 | Code 4912. |
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| 233 | </flag> |
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| 234 | |
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| 235 | <flag name="HiddenValley:qqbar2SvSvbar" default="off"> |
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| 236 | Pair production <ei>q qbar -> Sv Svbar</ei> |
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| 237 | via intermediate gluon. |
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| 238 | Code 4913. |
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| 239 | </flag> |
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| 240 | |
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| 241 | <flag name="HiddenValley:qqbar2CvCvbar" default="off"> |
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| 242 | Pair production <ei>q qbar -> Cv Cvbar</ei> |
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| 243 | via intermediate gluon. |
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| 244 | Code 4914. |
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| 245 | </flag> |
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| 246 | |
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| 247 | <flag name="HiddenValley:qqbar2BvBvbar" default="off"> |
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| 248 | Pair production <ei>q qbar -> Bv Bvbar</ei> |
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| 249 | via intermediate gluon. |
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| 250 | Code 4915. |
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| 251 | </flag> |
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| 252 | |
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| 253 | <flag name="HiddenValley:qqbar2TvTvbar" default="off"> |
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| 254 | Pair production <ei>q qbar -> Tv Tvbar</ei> |
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| 255 | via intermediate gluon. |
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| 256 | Code 4916. |
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| 257 | </flag> |
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| 258 | |
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| 259 | <flag name="HiddenValley:ffbar2DvDvbar" default="off"> |
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| 260 | Pair production <ei>f fbar -> Dv Dvbar</ei> |
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| 261 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 262 | Code 4921. |
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| 263 | </flag> |
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| 264 | |
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| 265 | <flag name="HiddenValley:ffbar2UvUvbar" default="off"> |
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| 266 | Pair production <ei>f fbar -> Uv Uvbar</ei> |
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| 267 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 268 | Code 4922. |
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| 269 | </flag> |
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| 270 | |
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| 271 | <flag name="HiddenValley:ffbar2SvSvbar" default="off"> |
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| 272 | Pair production <ei>f fbar -> Sv Svbar</ei> |
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| 273 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 274 | Code 4923. |
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| 275 | </flag> |
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| 276 | |
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| 277 | <flag name="HiddenValley:ffbar2CvCvbar" default="off"> |
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| 278 | Pair production <ei>f fbar -> Cv Cvbar</ei> |
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| 279 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 280 | Code 4924. |
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| 281 | </flag> |
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| 282 | |
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| 283 | <flag name="HiddenValley:ffbar2BvBvbar" default="off"> |
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| 284 | Pair production <ei>f fbar -> Bv Bvbar</ei> |
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| 285 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 286 | Code 4925. |
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| 287 | </flag> |
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| 288 | |
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| 289 | <flag name="HiddenValley:ffbar2TvTvbar" default="off"> |
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| 290 | Pair production <ei>f fbar -> Tv Tvbar</ei> |
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| 291 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 292 | Code 4926. |
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| 293 | </flag> |
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| 294 | |
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| 295 | <flag name="HiddenValley:ffbar2EvEvbar" default="off"> |
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| 296 | Pair production <ei>f fbar -> Ev Evbar</ei> |
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| 297 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 298 | Code 4931. |
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| 299 | </flag> |
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| 300 | |
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| 301 | <flag name="HiddenValley:ffbar2nuEvnuEvbar" default="off"> |
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| 302 | Pair production <ei>f fbar -> nuEv nuEvbar</ei> |
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| 303 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 304 | Code 4932. |
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| 305 | </flag> |
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| 306 | |
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| 307 | <flag name="HiddenValley:ffbar2MUvMUvbar" default="off"> |
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| 308 | Pair production <ei>f fbar -> MUv MUvbar</ei> |
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| 309 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 310 | Code 4933. |
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| 311 | </flag> |
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| 312 | |
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| 313 | <flag name="HiddenValley:ffbar2nuMUvnuMUvbar" default="off"> |
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| 314 | Pair production <ei>f fbar -> nuMUv nuMUvbar</ei> |
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| 315 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 316 | Code 4934. |
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| 317 | </flag> |
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| 318 | |
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| 319 | <flag name="HiddenValley:ffbar2TAUvTAUvbar" default="off"> |
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| 320 | Pair production <ei>f fbar -> TAUv TAUvbar</ei> |
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| 321 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 322 | Code 4935. |
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| 323 | </flag> |
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| 324 | |
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| 325 | <flag name="HiddenValley:ffbar2nuTAUvnuTAUvbar" default="off"> |
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| 326 | Pair production <ei>f fbar -> nuTAUv nuTAUvbar</ei> |
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| 327 | via intermediate <ei>gamma*/Z^*</ei>. |
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| 328 | Code 4936. |
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| 329 | </flag> |
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| 330 | |
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| 331 | <flag name="HiddenValley:ffbar2Zv" default="off"> |
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| 332 | Production <ei>f fbar -> Zv</ei> where <ei>Zv</ei> is a generic |
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| 333 | resonace that couples both SM fermion pairs and a <ei>qv qvbar</ei> |
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| 334 | pair. Not part of the framework of the above processes, but as an |
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| 335 | alternative. Code 4941. |
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| 336 | </flag> |
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| 337 | |
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| 338 | <h3>Timelike showers</h3> |
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| 339 | |
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| 340 | One key point of this HV scenario is that radiation off the |
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| 341 | HV-charged particles is allowed. This is done by the standard |
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| 342 | final-state showering machinery. (HV particles are not produced |
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| 343 | in initial-state radiation.) All the (anti)particles <ei>Fv</ei> |
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| 344 | and <ei>qv</ei> have one (negative) unit of HV charge. That is, |
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| 345 | radiation closely mimics the one in QCD. Both QCD, QED and HV |
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| 346 | radiation are interleaved in one common sequence of decreasing |
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| 347 | emission <ei>pT</ei> scales. Each radiation kind defines a set of |
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| 348 | dipoles, usually spanned between a radiating parton and its recoil |
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| 349 | partner, such that the invariant mass of the pair is not changed |
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| 350 | when a radiation occurs. This need not follow from trivial colour |
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| 351 | assignments, but is often obvious. For instance, in a decay |
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| 352 | <ei>Qv -> q + qv</ei> the QCD dipole is between the <ei>q</ei> and |
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| 353 | the hole after <ei>Qv</ei>, but <ei>qv</ei> becomes the recoiler |
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| 354 | should a radiation occur, while the role of <ei>q</ei> and <ei>qv</ei> |
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| 355 | is reversed for HV radiation. |
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| 356 | |
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| 357 | <p/>This also includes matrix-element corrections for a number |
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| 358 | of decay processes, with colour, spin and mass effects included |
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| 359 | <ref>Nor01</ref>. They were calculated within the context of the |
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| 360 | particle content of the MSSM, however, which does not include spin 1 |
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| 361 | particles with unit colour charge. In such cases spin 0 is assumed |
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| 362 | instead. By experience, the main effects come from mass and colour |
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| 363 | flow anyway, so this is not a bad approximation. (Furthermore the |
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| 364 | MSSM formulae allow for <ei>gamma_5</ei> factors from wave |
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| 365 | functions or vertices; these are even less important.) |
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| 366 | |
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| 367 | <p/>An emitted <ei>gv</ei> can branch in its turn, |
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| 368 | <ei>gv -> gv + gv</ei>. This radiation may affect momenta |
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| 369 | in the visible sector by recoil effect, but this is a minor |
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| 370 | effect relative to the primary emission of the <ei>gv</ei>. |
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| 371 | |
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| 372 | <flag name="HiddenValley:FSR" default="off"> |
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| 373 | switch on final-state shower of <ei>gv</ei> or <ei>gammav</ei> |
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| 374 | in a HV production process. |
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| 375 | </flag> |
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| 376 | |
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| 377 | <parm name="HiddenValley:alphaFSR" default="0.1" min="0.0"> |
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| 378 | fixed alpha scale of <ei>gv/gammav</ei> emission; corresponds to |
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| 379 | <ei>alpha_strong</ei> of QCD or <ei>alpha_em</ei> of QED. For |
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| 380 | shower branchings such as <ei>Dv -> Dv + gv</ei> the coupling is |
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| 381 | multiplied by <ei>C_F = (N^2 - 1) / (2 * N)</ei> for an |
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| 382 | <b>SU(N)</b> group and for <ei>gv -> gv + gv</ei> by <ei>N</ei>. |
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| 383 | </parm> |
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| 384 | |
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| 385 | <parm name="HiddenValley:pTminFSR" default="0.4" min="0.1"> |
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| 386 | lowest allowed <ei>pT</ei> of emission. Chosen with same default |
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| 387 | as in normal QCD showers. |
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| 388 | </parm> |
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| 389 | |
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| 390 | <h3>Hadronization</h3> |
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| 391 | |
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| 392 | By default the HV particles with no Standard Model couplings |
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| 393 | are not visible. Their presence can only be deduced by the |
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| 394 | observation of missing (transverse) momentum in the event as a |
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| 395 | whole. In the current implementation it is possible to simulate |
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| 396 | two different scenarios where activity can leak back from the |
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| 397 | hidden sector. |
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| 398 | |
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| 399 | <p/> |
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| 400 | The first possibility is relevant for the <b>U(1)</b> scenario. |
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| 401 | The <b>U(1)</b> group may be broken, so that the <ei>gammav</ei> |
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| 402 | acquires a mass. Furthermore, the <ei>gammav</ei> may have a |
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| 403 | small mixing angle with the normal photon, or with some <ei>Z'</ei> |
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| 404 | state or other mediator, and may thus decay back into Standard |
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| 405 | Model particles. The <ei>qv</ei> still escapes undetected; |
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| 406 | recall that there is no confinement in the <b>U(1)</b> option. |
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| 407 | |
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| 408 | <p/> |
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| 409 | In order to enable this machinery two commands are necessary, |
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| 410 | <code>4900022:m0 = ...</code> to set the <ei>gammav</ei> mass |
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| 411 | to the desired value, and <code>4900022:onMode = on</code> to enable |
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| 412 | <ei>gammav</ei> decays. The default <ei>gammav</ei> decay |
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| 413 | table contains all Standard Model fermion-antifermion pairs, |
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| 414 | except top, with branching ratios in proportion to their coupling |
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| 415 | to the photon, whenever the production channel is allowed by |
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| 416 | kinematics. This table could easily be tailored to more specific |
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| 417 | models and needs. For instance, for a mass below 1 - 2 GeV, it |
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| 418 | would make sense to construct a table of exclusive hadronic decay |
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| 419 | channels rather than go the way via a hadronizing quark pair. |
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| 420 | |
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| 421 | <p/> |
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| 422 | The <ei>gammav</ei> are expected to decay so rapidly that no |
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| 423 | secondary vertex will be detectable. However, it is possible to |
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| 424 | set <code>4900022:tau0</code> to a finite lifetime (in mm) that |
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| 425 | will be used to create separated secondary vertices. |
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| 426 | |
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| 427 | <p/> |
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| 428 | The second, more interesting, possibility is relevant for the |
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| 429 | <b>SU(N)</b> scenarios. Here the gauge group remains unbroken, i.e. |
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| 430 | <ei>gv</ei> is massless, and the partons are confined. Like in |
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| 431 | QCD, the HV-partons can therefore be arranged in one single |
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| 432 | HV-colour-ordered chain, with a <ei>qv</ei> in one end, a |
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| 433 | <ei>qvbar</ei> in the other, and a varying number of |
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| 434 | <ei>gv</ei> in between. Each event will only contain (at most) |
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| 435 | one such string, (i) since perturbative branchings |
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| 436 | <ei>gv -> qv qvbar</ei> have been neglected, as is a reasonable |
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| 437 | approximation for QCD, and (ii) since HV-colours are assigned in the |
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| 438 | <ei>N_C -> infinity</ei> limit, just like in the handling of |
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| 439 | string fragmentation in QCD. The HV-string can then fragment by the |
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| 440 | nonperturbative creation of <ei>qv qvbar</ei> pairs, leading to |
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| 441 | the formation of HV-mesons along the string, each with its |
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| 442 | <ei>qv</ei> from one vertex and its <ei>qvbar</ei> from |
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| 443 | the neighbouring one. |
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| 444 | |
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| 445 | <p/> |
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| 446 | Since, so far, we have only assumed there to be one <ei>qv</ei> |
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| 447 | species, all produced <ei>qv qvbar</ei> HV-mesons are of the |
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| 448 | same flavour-diagonal species. Such an HV-meson can decay back to |
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| 449 | the normal sector, typically by whatever mediator particle allowed |
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| 450 | production in the first place. In this framework the full energy put |
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| 451 | into the HV sector will leak back to the normal one. To allow more |
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| 452 | flexibility, an ad hoc possibility of <ei>n_Flav</ei> different |
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| 453 | <ei>qv</ei> species is introduced. For now they are all assumed |
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| 454 | to have the same mass and other properties, but distinguished by |
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| 455 | some flavour-like property. Only the flavour-diagonal ones can decay, |
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| 456 | meaning that only a fraction (approximately) <ei>1/n_Flav</ei> of the |
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| 457 | HV-energy leaks back, while the rest remains in the hidden sector. |
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| 458 | |
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| 459 | <p/> |
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| 460 | This scenario contains more parameters than the first one, for the |
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| 461 | <b>U(1)</b> group. They can be subdivided into two sets. One is |
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| 462 | related to particle properties, both for <ei>qv</ei> and for the |
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| 463 | two different kinds of HV-mesons, here labelled 4900111 and 4900113 |
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| 464 | for the diagonal ones, and +-4900211 and +-4900213 for the |
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| 465 | off-diagonal ones. It makes sense to set the HV-meson masses to be |
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| 466 | twice the <ei>qv</ei> one, as in a simple constituent mass context. |
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| 467 | Furthermore the <ei>hvMesonDiag</ei> decay modes need to be set up. |
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| 468 | Like with the |
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| 469 | <ei>gammav</ei> in the <b>U(1)</b> option, the default decay table |
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| 470 | is based on the branching ratios of an off-shell photon. |
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| 471 | |
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| 472 | <p/> |
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| 473 | The second set are fragmentation parameters that extend or replace |
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| 474 | the ones used in normal string fragmentation. Some of them are not |
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| 475 | encoded in the same way as normally, however, but rather scale as |
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| 476 | the <ei>qv</ei> mass is changed, so as to keep a sensible default |
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| 477 | behaviour. This does not mean that deviations from this set should |
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| 478 | not be explored, or that other scaling rules could be prefered |
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| 479 | within alternative scenarios. These parameters are as follows. |
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| 480 | |
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| 481 | <flag name="HiddenValley:fragment" default="off"> |
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| 482 | switch on string fragmentation of the HV partonic system. |
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| 483 | Only relevant for <b>SU(N)</b> scenarios. |
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| 484 | </flag> |
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| 485 | |
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| 486 | <modeopen name="HiddenValley:nFlav" default="1" min="1" max="8"> |
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| 487 | number of different flavours assumed to exist in the hadronization |
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| 488 | description, leading to approximately <ei>1/n_Flav</ei> of the |
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| 489 | produced HV-mesons being flavour-diagonal and capable to decay back |
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| 490 | to Standard Model particles. |
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| 491 | </modeopen> |
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| 492 | |
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| 493 | <parm name="HiddenValley:probVector" default="0.75" min="0." max="1."> |
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| 494 | fraction of HV-mesons that are assigned spin 1 (vector), with the |
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| 495 | remainder spin 0 (pseudoscalar). Assuming the <ei>qv</ei> have |
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| 496 | spin <ei>1/2</ei> and the mass splitting is small, spin counting |
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| 497 | predicts that <ei>3/4</ei> of the mesons should have spin 1. |
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| 498 | </modeopen> |
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| 499 | |
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| 500 | <parm name="HiddenValley:aLund" default="0.3" min="0.0" max="2.0"> |
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| 501 | The <ei>a</ei> parameter of the Lund symmetric fragmentation function. |
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| 502 | See the normal <aloc href="Fragmentation">fragmentation |
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| 503 | function</aloc> description for the shape of this function.</parm> |
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| 504 | |
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| 505 | <parm name="HiddenValley:bmqv2" default="0.8" min="0.2" max="2.0"> |
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| 506 | The <ei>b</ei> parameter of the Lund symmetric fragmentation function, |
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| 507 | multiplied by the square of the <ei>qv</ei> mass. This scaling ensures |
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| 508 | that the fragmentation function keeps the same shape when the |
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| 509 | <ei>qv</ei> mass is changed (neglecting transverse momenta). |
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| 510 | </parm> |
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| 511 | |
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| 512 | <parm name="HiddenValley:rFactqv" default="1.0" min="0.0" max="2.0"> |
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| 513 | <ei>r_qv</ei>, i.e. the Bowler correction factor to the Lund symmetric |
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| 514 | fragmentation function, which could be made weaker or stronger than |
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| 515 | its natural value. |
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| 516 | </parm> |
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| 517 | |
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| 518 | <parm name="HiddenValley:sigmamqv" default="0.5" min="0.0"> |
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| 519 | the width <ei>sigma</ei> of transverse momenta in the HV fragmentation |
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| 520 | process, normalized to the <ei>qv</ei> mass. This ensures that |
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| 521 | <ei>sigma</ei> scales proportionately to <ei>m_qv</ei>. |
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| 522 | See the normal <aloc href="Fragmentation">fragmentation |
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| 523 | <ei>pT</ei></aloc> description for conventions for factors of 2. |
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| 524 | </parm> |
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| 525 | |
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| 526 | </chapter> |
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| 527 | |
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| 528 | <!-- Copyright (C) 2012 Torbjorn Sjostrand --> |
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| 529 | |
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