<chapter name="Extra-Dimensional Processes"> <h2>Extra-Dimensional Processes</h2> Scenarios with extra dimensions (ED) allow a multitude of processes. Currently three different categories of processes are implemented. The first involves the production of excited Kaluza Klein states within so-called Randall-Sundrum (RS) scenarios, the second is related to resonance production in TeV-1 sized extra dimensions and the third relates to phenomena from large extra dimensions (LED). Due to the close relation between the LED model and a so-called unparticle model, similar unparticle processes are also kept in this section. <h3>Randall-Sundrum Resonances, production processes</h3> The graviton (G*) and gluon (KKgluon*) resonance states are assigned PDG code 5100039 and 5100021 respectively. The G* processes are described in <ref>Bij01</ref> and the KKgluon* process in <ref>Ask11</ref>. Decays into fermion and boson pairs are handled with the correct angular distributions, while subsequent decays are handled isotropically. <p/> There are two lowest-order processes that together normally should be sufficient for a simulation of <ei>G^*</ei> production. <flag name="ExtraDimensionsG*:all" default="off"> Common switch for the group of lowest-order <ei>G^*</ei> production processes, i.e. the two ones below. </flag> <flag name="ExtraDimensionsG*:gg2G*" default="off"> Scatterings <ei>g g → G^*</ei>. Code 5001. </flag> <flag name="ExtraDimensionsG*:ffbar2G*" default="off"> Scatterings <ei>f fbar → G^*</ei>. Code 5002. </flag> <p/> In addition there are three first-order processes included. These are of less interest, but can be used for dedicated studies of the high-<ei>pT</ei> tail of <ei>G^*</ei> production. As usual, it would be double counting to include the lowest-order and first-order processes simultaneously. Therefore the latter ones are not included with the <code>ExtraDimensionsG*:all = on</code> option. In this set of processes all decay angles are assumed isotropic. <flag name="ExtraDimensionsG*:gg2G*g" default="off"> Scatterings <ei>g g → G^* g</ei>. Code 5003. </flag> <flag name="ExtraDimensionsG*:qg2G*q" default="off"> Scatterings <ei>q g → G^* q</ei>. Code 5004. </flag> <flag name="ExtraDimensionsG*:qqbar2G*g" default="off"> Scatterings <ei>q qbar → G^* g</ei>. Code 5005. </flag> <p/> There is also one process for the production of a gluon resonance. <flag name="ExtraDimensionsG*:qqbar2KKgluon*" default="off"> Scatterings <ei>q qbar → g^*/KKgluon^*</ei>. Code 5006. </flag> <h3>Randall-Sundrum Resonances, parameters</h3> In the above scenario the main free parameters are the masses, which are set as usual. In addition there are the following coupling parameters. The coupling <ei>kappaMG</ei> follows the conventions in <ref>Bij01</ref>, where as the flavour dependent couplings follow the conventions used in <ref>Dav01</ref>. <flag name="ExtraDimensionsG*:SMinBulk" default="off"> Parameter to choose between the two scenarios: <ei>off</ei>, SM on the TeV brane (common <ei>kappaMG</ei> coupling); <ei>on</ei>, SM in the ED bulk (flavour dependent couplings). This parameter is only relevant for the lowest-order graviton (<ei>G*</ei>) processes, where as the first-order processes corresponds to the <ei>off</ei> scenario. </flag> <flag name="ExtraDimensionsG*:VLVL" default="on"> Parameter to specify Z/W coupling scenario: <ei>off</ei>, usual Z/W boson couplings; <ei>on</ei>, coupling only to longitudinal Z/W bosons. In both cases the <ei>GZZ</ei> and <ei>GWW</ei> values are used and this parameter is only relevant when <ei>SMinBulk = on</ei>. The formulas for longitudinal bosons should be appropriate up to <ei>O(m_V/E_V)</ei> corrections. </flag> <parm name="ExtraDimensionsG*:kappaMG" default="0.054" min="0.0"> dimensionless coupling, which enters quadratically in all on-shell partial widths of the <ei>G^*</ei>. Is <ei>kappa m_G* = sqrt(2) x_1 k / Mbar_Pl</ei>, where <ei>x_1 = 3.83</ei> is the first zero of the <ei>J_1</ei> Bessel function and <ei>Mbar_Pl</ei> is the modified Planck mass. In width and cross section calculations, <ei>kappa</ei> is fixed by the on-shell <ei>G^*</ei> mass and <ei>kappaMG</ei>, i.e. <ei>kappaMG</ei> scales with the off-shell <ei>G^*</ei> mass. </parm> <parm name="ExtraDimensionsG*:Gll" default="0.0" min="0.0"> Coupling between graviton and leptons. </parm> <parm name="ExtraDimensionsG*:Gqq" default="0.0" min="0.0"> Coupling between graviton and light quarks. </parm> <parm name="ExtraDimensionsG*:Gbb" default="0.0" min="0.0"> Coupling between graviton and bottom quark. </parm> <parm name="ExtraDimensionsG*:Gtt" default="0.001" min="0.0"> Coupling between graviton and top quark. </parm> <parm name="ExtraDimensionsG*:Ggg" default="0.000013" min="0.0"> Coupling between graviton and gluon. </parm> <parm name="ExtraDimensionsG*:Ggmgm" default="0.000013" min="0.0"> Coupling between graviton and gamma. </parm> <parm name="ExtraDimensionsG*:GZZ" default="0.001" min="0.0"> Coupling between graviton and Z boson. </parm> <parm name="ExtraDimensionsG*:GWW" default="0.001" min="0.0"> Coupling between graviton and W boson. </parm> <parm name="ExtraDimensionsG*:Ghh" default="0.001" min="0.0"> Coupling between graviton and Higgs bosons. </parm> <parm name="ExtraDimensionsG*:KKgqR" default="-0.2"> Coupling between KK-gluon and a right-handed light quark. </parm> <parm name="ExtraDimensionsG*:KKgqL" default="-0.2"> Coupling between KK-gluon and a left-handed light quark. </parm> <parm name="ExtraDimensionsG*:KKgbR" default="-0.2"> Coupling between KK-gluon and a right-handed bottom quark. </parm> <parm name="ExtraDimensionsG*:KKgbL" default="1.0"> Coupling between KK-gluon and a left-handed bottom quark. </parm> <parm name="ExtraDimensionsG*:KKgtR" default="4.0"> Coupling between KK-gluon and a right-handed top quark. </parm> <parm name="ExtraDimensionsG*:KKgtL" default="1.0"> Coupling between KK-gluon and a left-handed top quark. </parm> <modepick name="ExtraDimensionsG*:KKintMode" default="0" min="0" max="2"> Choice of full <ei>g^*/KK-gluon^*</ei> structure or not in relevant processes. <option value="0">full <ei>g^*/KK-gluon^*</ei> structure, with interference included.</option> <option value="1">only pure <ei>gluon_{SM}</ei> contribution.</option> <option value="2">only pure <ei>gluon_{KK}</ei> contribution.</option> </modepick> <h3>TeV^-1 Sized Extra Dimension, production processes</h3> This section contains a processes involving the production of electroweak KK gauge bosons, i.e. <ei>gamma_{KK}/Z_{KK}</ei>, in one TeV^-1 sized extra dimension. The process is described in <ref>Bel10</ref> and allows for individual final states to be specified. <flag name="ExtraDimensionsTEV:ffbar2ddbar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → d dbar </ei>, Code 5061. </flag> <flag name="ExtraDimensionsTEV:ffbar2uubar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → u ubar </ei>, Code 5062. </flag> <flag name="ExtraDimensionsTEV:ffbar2ssbar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → s sbar </ei>, Code 5063. </flag> <flag name="ExtraDimensionsTEV:ffbar2ccbar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → c cbar </ei>, Code 5064. </flag> <flag name="ExtraDimensionsTEV:ffbar2bbbar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → b bbar </ei>, Code 5065. </flag> <flag name="ExtraDimensionsTEV:ffbar2ttbar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → t tbar </ei>, Code 5066. </flag> <flag name="ExtraDimensionsTEV:ffbar2e+e-" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → e+ e- </ei>, Code 5071. </flag> <flag name="ExtraDimensionsTEV:ffbar2nuenuebar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → nue nuebar </ei>, Code 5072. </flag> <flag name="ExtraDimensionsTEV:ffbar2mu+mu-" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → mu+ mu- </ei>, Code 5073. </flag> <flag name="ExtraDimensionsTEV:ffbar2numunumubar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → numu numubar </ei>, Code 5074. </flag> <flag name="ExtraDimensionsTEV:ffbar2tau+tau-" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → tau+ tau- </ei>, Code 5075. </flag> <flag name="ExtraDimensionsTEV:ffbar2nutaunutaubar" default="off"> Scatterings <ei>f fbar → (gamma_{KK}/Z_{KK}) → nutau nutaubar </ei>, Code 5076. </flag> <h3>TeV^-1 Sized Extra Dimension, parameters</h3> Irrespective of the parameter options used, the particle produced, <ei>gamma_{KK}/Z_{KK}</ei>, will always be assigned code 5000023. <modepick name="ExtraDimensionsTEV:gmZmode" default="3" min="0" max="5"> Choice of full <ei>gamma_{KK}/Z_{KK}</ei> structure or not in relevant processes. <option value="0">full <ei>gamma_{SM}/Z_{SM}</ei> structure, with interference included.</option> <option value="1">only pure <ei>gamma_{SM}</ei> contribution.</option> <option value="2">only pure <ei>Z_{SM}</ei> contribution.</option> <option value="3">full <ei>gamma_{KK}/Z_{KK}</ei> structure, with interference included.</option> <option value="4">only pure <ei>gamma_{KK}</ei> contribution, with SM interference included.</option> <option value="5">only pure <ei>Z_{KK}</ei> contribution, with SM interference included.</option> </modepick> <parm name="ExtraDimensionsTEV:nMax" default="10" min="1" max="100"> The number of included KK excitations. </parm> <parm name="ExtraDimensionsTEV:mStar" default="4000.0" min="1000.0"> The KK mass <ei>m^*</ei>, given by the inverse of the single extra dimension radius. </parm> <h3>Large Extra Dimensions, production processes</h3> The LED graviton, where the KK-modes normally are summed and do not give rise to phenomena individually, is assigned PDG code 5000039. The graviton emission and virtual graviton exchange processes use the same implementation as the corresponding unparticle processes, which are all described in <ref>Ask10</ref>. It is also possible to generate monojet events from scalar graviton emission as described in <ref>Azu05</ref>, by turning on the option <ei>GravScalar</ei>. <p/> <ei>Note:</ei> As discussed in <ref>Ask09</ref>, for the graviton or unparticle emission processes the underlying Breit-Wigner mass distribution should be matched to the graviton mass spectrum in order to achieve an optimal MC efficiency. <p/> The following lowest order graviton emission processes are available. <flag name="ExtraDimensionsLED:monojet" default="off"> Common switch for the group of lowest-order <ei>G jet</ei> emission processes, i.e. the three ones below. </flag> <flag name="ExtraDimensionsLED:gg2Gg" default="off"> Scatterings <ei>g g → G g</ei>. Code 5021. </flag> <flag name="ExtraDimensionsLED:qg2Gq" default="off"> Scatterings <ei>q g → G q</ei>. Code 5022. </flag> <flag name="ExtraDimensionsLED:qqbar2Gg" default="off"> Scatterings <ei>q qbar → G g</ei>. Code 5023. </flag> <flag name="ExtraDimensionsLED:ffbar2GZ" default="off"> Scatterings <ei>f fbar → G Z</ei>. Code 5024. </flag> <flag name="ExtraDimensionsLED:ffbar2Ggamma" default="off"> Scatterings <ei>f fbar → G gamma</ei>. This process corresponds to the photon limit of the <ei>G Z</ei> process, as described in <ref>Ask09</ref>. Code 5025. </flag> <p/> The following LED processes with virtual graviton exchange are available. <flag name="ExtraDimensionsLED:ffbar2gammagamma" default="off"> Scatterings <ei>f fbar → (LED G*) → gamma gamma</ei>. If the graviton contribution is zero, the results corresponds to the SM contribution, i.e. equivalent to <code>PromptPhoton:ffbar2gammagamma</code>. Code 5026. </flag> <flag name="ExtraDimensionsLED:gg2gammagamma" default="off"> Scatterings <ei>g g → (LED G*) → gamma gamma</ei>. Code 5027. </flag> <flag name="ExtraDimensionsLED:ffbar2llbar" default="off"> Scatterings <ei>f fbar → (LED G*) → l l </ei>, where <ei>l</ei> is a charged lepton. If the graviton contribution is zero, the results corresponds to the SM contribution, i.e. similar to <code>WeakSingleBoson:ffbar2gmZ</code>. Does not include t-channel amplitude relevant for e^+e^- to e^+e^- and no K-factor is used. Code 5028. </flag> <flag name="ExtraDimensionsLED:gg2llbar" default="off"> Scatterings <ei>g g → (LED G*) → l l</ei>. Code 5029. </flag> <p/> Dijet production including graviton exchange is also available, using the same effective theory approach as the LED G exchange processes above or including more detailed amplitudes in accordance with <ref>Fra11</ref>. In case of the latter, the value of <ei>LambdaT</ei> is used as the value of the cut-off scale <ei>Lambda</ei>. For this reason the dijet processes only relates to the LED model and no unparticle versions are available. The processes are grouped together like their <ei>HardQCD</ei> equivalents and should therefore converge to the same results in the limit of an insignificant graviton contribution. <p/> <ei>Warning:</ei> These LED dijets processes are still being validated. <flag name="ExtraDimensionsLED:dijets" default="off"> Common switch for the group of lowest-order <ei>jet jet</ei> production processes with graviton exchange, i.e. the six ones below. </flag> <flag name="ExtraDimensionsLED:gg2DJgg" default="off"> Scatterings <ei>g g → (LED G*) → g g</ei>. Code 5030. </flag> <flag name="ExtraDimensionsLED:gg2DJqqbar" default="off"> Scatterings <ei>g g → (LED G*) → q qbar</ei>. Number of outgoing flavours specified by <ei>nQuarkNew</ei> parameter below. Code 5031. </flag> <flag name="ExtraDimensionsLED:qg2DJqg" default="off"> Scatterings <ei>q g → (LED G*) → q g</ei> and <ei>qbar g → (LED G*) → qbar g</ei>. Code 5032. </flag> <flag name="ExtraDimensionsLED:qq2DJqq" default="off"> Scatterings <ei>q q(bar)' → (LED G*) → q q(bar)'</ei>. Including <ei>q</ei> and <ei>qbar</ei> of same or different flavours, but the outgoing flavours equals the incoming ones. Code 5033. </flag> <flag name="ExtraDimensionsLED:qqbar2DJgg" default="off"> Scatterings <ei>q qbar → (LED G*) → g g</ei>. Code 5034. </flag> <flag name="ExtraDimensionsLED:qqbar2DJqqbarNew" default="off"> Scatterings <ei>q qbar → (LED G*) → q' qbar'</ei>. Number of outgoing flavours specified by <ei>nQuarkNew</ei> parameter below. Code 5035. </flag> <h3>Large Extra Dimensions, parameters</h3> <flag name="ExtraDimensionsLED:GravScalar" default="off"> Allow the monojet processes to produce scalar graviton emission instead of the default tensor one. The scalar option is according to the processes described in <ref>Azu05</ref> and includes two coupling constants below. </flag> <modeopen name="ExtraDimensionsLED:n" default="2" min="1"> Number of extra dimensions. </modeopen> <parm name="ExtraDimensionsLED:MD" default="2000." min="100.0"> Fundamental scale of gravity in <ei>D = 4 + n</ei> dimensions. </parm> <parm name="ExtraDimensionsLED:LambdaT" default="2000." min="100.0"> Ultraviolet cutoff parameter for the virtual graviton exchange processes. </parm> <modepick name="ExtraDimensionsLED:NegInt" default="0" min="0" max="1"> Allows to change sign of the interference terms in the graviton exchange processes, common in connection to using the <ei>Hewett</ei> convention <ref>Hew99</ref>. <option value="0">1</option> <option value="1">-1</option> </modepick> <modepick name="ExtraDimensionsLED:CutOffMode" default="0" min="0" max="3"> Options for when the hard scale of the process (e.g. <ei>sHat</ei>) approaches or exceed the scale of validity of the low energy effective theory (e.g. <ei>M_D</ei>). <ei>Note:</ei> Option 1 only concerns the graviton emission processes and the form factor is currently not available for the scalar graviton processes. <option value="0">Do nothing, i.e. all values of <ei>sHat</ei> contribute. </option> <option value="1">Truncate contributing <ei>sHat</ei> region (<ref>Ask09</ref>).</option> <option value="2">Form factor, using <ei>mu = renormScale2</ei> .</option> <option value="3">Form factor, using <ei>mu = E_jet</ei>.</option> </modepick> <parm name="ExtraDimensionsLED:t" default="1." min="0.001"> Form factor parameter. </parm> <parm name="ExtraDimensionsLED:g" default="1.0" min="0.0"> Coupling related to scalar graviton emission. </parm> <parm name="ExtraDimensionsLED:c" default="1.0" min="0.0"> Coupling related to scalar graviton emission. </parm> <modeopen name="ExtraDimensionsLED:nQuarkNew" default="3" min="0" max="5"> Number of allowed outgoing new quark flavours in the above <ei>q qbar → (LED G*) → q' qbar'</ei> and <ei>g g → (LED G*) → q' qbar'</ei> processes. Similar to <ei>HardQCD:nQuarkNew</ei> for the QCD processes. </modeopen> <modeopen name="ExtraDimensionsLED:opMode" default="0" min="0" max="1"> Options to specify <ei>S</ei> function for LED dijet amplitudes. <option value="0">Use detailed amplitude, as described in <ref>Fra11</ref>. </option> <option value="1">Use conventional <ei>LambdaT</ei> parametrization, like the other LED processes.</option> </modeopen> <h3>Unparticles, production processes</h3> As mentioned above, the similar unparticle and graviton processes share the same implementations. The unparticle processes, however, only use the dedicated unparticle parameters below. The unparticle is also assigned the PDG code 5000039 and is therefore called <ei>Graviton</ei> in the event record. The graviton and unparticle emission as well as virtual graviton and unparticle exchange processes are described in <ref>Ask10</ref>. <p/> <ei>Note:</ei> As discussed in <ref>Ask09</ref>, for the graviton or unparticle emission processes the underlying Breit-Wigner mass distribution should be matched to the graviton mass spectrum in order to achieve an optimal MC efficiency. <p/> The following unparticle emission processes are available. <flag name="ExtraDimensionsUnpart:monojet" default="off"> Common switch for the group of lowest-order <ei>U jet</ei> emission processes, i.e. the three ones below. </flag> <flag name="ExtraDimensionsUnpart:gg2Ug" default="off"> Scatterings <ei>g g → U g</ei>. Code 5045. </flag> <flag name="ExtraDimensionsUnpart:qg2Uq" default="off"> Scatterings <ei>q g → U q</ei>. Code 5046. </flag> <flag name="ExtraDimensionsUnpart:qqbar2Ug" default="off"> Scatterings <ei>q qbar → U g</ei>. Code 5047. </flag> <flag name="ExtraDimensionsUnpart:ffbar2UZ" default="off"> Scatterings <ei>f fbar → U Z</ei>. Code 5041. </flag> <flag name="ExtraDimensionsUnpart:ffbar2Ugamma" default="off"> Scatterings <ei>f fbar → U gamma</ei>. This process corresponds to the photon limit of the <ei>U Z</ei> process, as described in <ref>Ask09</ref>. Code 5042. </flag> <p/> The following processes with virtual unparticle exchange are available. <flag name="ExtraDimensionsUnpart:ffbar2gammagamma" default="off"> Scatterings <ei>f fbar → (U*) → gamma gamma</ei>. If the unparticle contribution is zero in the spin-2 case, the results corresponds to the SM contribution, i.e. equivalent to <code>PromptPhoton:ffbar2gammagamma</code>. Code 5043. </flag> <flag name="ExtraDimensionsUnpart:gg2gammagamma" default="off"> Scatterings <ei>g g → (U*) → gamma gamma</ei>. Code 5044. </flag> <flag name="ExtraDimensionsUnpart:ffbar2llbar" default="off"> Scatterings <ei>f fbar → (U*) → l lbar </ei>, where <ei>l</ei> is a charged lepton. If the unparticle contribution is zero, the results corresponds to the SM contribution, i.e. similar to <code>WeakSingleBoson:ffbar2gmZ</code>. Does not include t-channel amplitude relevant for e^+e^- to e^+e^- and no K-factor is used. Code 5048. </flag> <flag name="ExtraDimensionsUnpart:gg2llbar" default="off"> Scatterings <ei>g g → (U*) → l lbar</ei>. Code 5049. </flag> <h3>Unparticles, parameters</h3> <modeopen name="ExtraDimensionsUnpart:spinU" default="2" min="0" max="2"> Unparticle spin. </modeopen> <parm name="ExtraDimensionsUnpart:dU" default="1.4" min="1.0"> Scale dimension parameter. </parm> <parm name="ExtraDimensionsUnpart:LambdaU" default="2000." min="100.0"> Unparticle renormalization scale. </parm> <parm name="ExtraDimensionsUnpart:lambda" default="1.0" min="0.0"> Unparticle coupling to the SM fields. </parm> <parm name="ExtraDimensionsUnpart:ratio" default="1.0" min="1.0" max="1.0"> Ratio, <ei>lambda'/lambda</ei>, between the two possible coupling constants of the spin-2 ME. <b>Warning:</b> A <ei>ratio</ei> value different from one give rise to an IR divergence which makes the event generation very slow, so this values is fixed to <ei>ratio = 1</ei> for the moment. </parm> <modepick name="ExtraDimensionsUnpart:CutOffMode" default="0" min="0" max="1"> Options for when the hard scale of the process (e.g. <ei>sHat</ei>) approaches or exceed the scale of validity of the low energy effective theory (<ei>Lambda_U</ei>). This mode only concerns the unparticle emission processes. <option value="0">Do nothing, i.e. all values of <ei>sHat</ei> contribute.</option> <option value="1">Truncate contributing <ei>sHat</ei> region (<ref>Ask09</ref>).</option> </modepick> <modepick name="ExtraDimensionsUnpart:gXX" default="0" min="0" max="2"> Chiral unparticle couplings, <ei>gXX = gLL = gRR</ei>. Only relevant for lepton production from spin-1 unparticle exchange. <option value="0">1</option> <option value="1">-1</option> <option value="2">0</option> </modepick> <modepick name="ExtraDimensionsUnpart:gXY" default="0" min="0" max="2"> Chiral unparticle couplings, <ei>gXY = gLR = gRL</ei>. Only relevant for lepton production from spin-1 unparticle exchange. <option value="0">1</option> <option value="1">-1</option> <option value="2">0</option> </modepick> </chapter> <!-- Copyright (C) 2014 Torbjorn Sjostrand -->