## Extra-Dimensional Processes

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.

### Randall-Sundrum Resonances, production processes

The graviton (G*) and gluon (KKgluon*) resonance states are assigned PDG code 5100039 and 5100021 respectively. The G* processes are described in [Bij01] and the KKgluon* process in [Ask11]. Decays into fermion and boson pairs are handled with the correct angular distributions, while subsequent decays are handled isotropically.

There are two lowest-order processes that together normally should be sufficient for a simulation of G^* production.

`flag` ExtraDimensionsG*:all (`default = off`)
Common switch for the group of lowest-order G^* production processes, i.e. the two ones below.

`flag` ExtraDimensionsG*:gg2G* (`default = off`)
Scatterings g g → G^*. Code 5001.

`flag` ExtraDimensionsG*:ffbar2G* (`default = off`)
Scatterings f fbar → G^*. Code 5002.

In addition there are three first-order processes included. These are of less interest, but can be used for dedicated studies of the high-pT tail of G^* 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 `ExtraDimensionsG*:all = on` option. In this set of processes all decay angles are assumed isotropic.

`flag` ExtraDimensionsG*:gg2G*g (`default = off`)
Scatterings g g → G^* g. Code 5003.

`flag` ExtraDimensionsG*:qg2G*q (`default = off`)
Scatterings q g → G^* q. Code 5004.

`flag` ExtraDimensionsG*:qqbar2G*g (`default = off`)
Scatterings q qbar → G^* g. Code 5005.

There is also one process for the production of a gluon resonance.

`flag` ExtraDimensionsG*:qqbar2KKgluon* (`default = off`)
Scatterings q qbar → g^*/KKgluon^*. Code 5006.

### Randall-Sundrum Resonances, parameters

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 kappaMG follows the conventions in [Bij01], where as the flavour dependent couplings follow the conventions used in [Dav01].

`flag` ExtraDimensionsG*:SMinBulk (`default = off`)
Parameter to choose between the two scenarios: off, SM on the TeV brane (common kappaMG coupling); on, SM in the ED bulk (flavour dependent couplings). This parameter is only relevant for the lowest-order graviton (G*) processes, where as the first-order processes corresponds to the off scenario.

`flag` ExtraDimensionsG*:VLVL (`default = on`)
Parameter to specify Z/W coupling scenario: off, usual Z/W boson couplings; on, coupling only to longitudinal Z/W bosons. In both cases the GZZ and GWW values are used and this parameter is only relevant when SMinBulk = on. The formulas for longitudinal bosons should be appropriate up to O(m_V/E_V) corrections.

`parm` ExtraDimensionsG*:kappaMG (`default = 0.054`; `minimum = 0.0`)
dimensionless coupling, which enters quadratically in all on-shell partial widths of the G^*. Is kappa m_G* = sqrt(2) x_1 k / Mbar_Pl, where x_1 = 3.83 is the first zero of the J_1 Bessel function and Mbar_Pl is the modified Planck mass. In width and cross section calculations, kappa is fixed by the on-shell G^* mass and kappaMG, i.e. kappaMG scales with the off-shell G^* mass.

`parm` ExtraDimensionsG*:Gll (`default = 0.0`; `minimum = 0.0`)
Coupling between graviton and leptons.

`parm` ExtraDimensionsG*:Gqq (`default = 0.0`; `minimum = 0.0`)
Coupling between graviton and light quarks.

`parm` ExtraDimensionsG*:Gbb (`default = 0.0`; `minimum = 0.0`)
Coupling between graviton and bottom quark.

`parm` ExtraDimensionsG*:Gtt (`default = 0.001`; `minimum = 0.0`)
Coupling between graviton and top quark.

`parm` ExtraDimensionsG*:Ggg (`default = 0.000013`; `minimum = 0.0`)
Coupling between graviton and gluon.

`parm` ExtraDimensionsG*:Ggmgm (`default = 0.000013`; `minimum = 0.0`)
Coupling between graviton and gamma.

`parm` ExtraDimensionsG*:GZZ (`default = 0.001`; `minimum = 0.0`)
Coupling between graviton and Z boson.

`parm` ExtraDimensionsG*:GWW (`default = 0.001`; `minimum = 0.0`)
Coupling between graviton and W boson.

`parm` ExtraDimensionsG*:Ghh (`default = 0.001`; `minimum = 0.0`)
Coupling between graviton and Higgs bosons.

`parm` ExtraDimensionsG*:KKgqR (`default = -0.2`)
Coupling between KK-gluon and a right-handed light quark.

`parm` ExtraDimensionsG*:KKgqL (`default = -0.2`)
Coupling between KK-gluon and a left-handed light quark.

`parm` ExtraDimensionsG*:KKgbR (`default = -0.2`)
Coupling between KK-gluon and a right-handed bottom quark.

`parm` ExtraDimensionsG*:KKgbL (`default = 1.0`)
Coupling between KK-gluon and a left-handed bottom quark.

`parm` ExtraDimensionsG*:KKgtR (`default = 4.0`)
Coupling between KK-gluon and a right-handed top quark.

`parm` ExtraDimensionsG*:KKgtL (`default = 1.0`)
Coupling between KK-gluon and a left-handed top quark.

`mode` ExtraDimensionsG*:KKintMode (`default = 0`; `minimum = 0`; `maximum = 2`)
Choice of full g^*/KK-gluon^* structure or not in relevant processes.
`option` 0 : full g^*/KK-gluon^* structure, with interference included.
`option` 1 : only pure gluon_{SM} contribution.
`option` 2 : only pure gluon_{KK} contribution.

### TeV^-1 Sized Extra Dimension, production processes

This section contains a processes involving the production of electroweak KK gauge bosons, i.e. gamma_{KK}/Z_{KK}, in one TeV^-1 sized extra dimension. The process is described in [Bel10] and allows for individual final states to be specified.

`flag` ExtraDimensionsTEV:ffbar2ddbar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → d dbar , Code 5061.

`flag` ExtraDimensionsTEV:ffbar2uubar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → u ubar , Code 5062.

`flag` ExtraDimensionsTEV:ffbar2ssbar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → s sbar , Code 5063.

`flag` ExtraDimensionsTEV:ffbar2ccbar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → c cbar , Code 5064.

`flag` ExtraDimensionsTEV:ffbar2bbbar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → b bbar , Code 5065.

`flag` ExtraDimensionsTEV:ffbar2ttbar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → t tbar , Code 5066.

`flag` ExtraDimensionsTEV:ffbar2e+e- (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → e+ e- , Code 5071.

`flag` ExtraDimensionsTEV:ffbar2nuenuebar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → nue nuebar , Code 5072.

`flag` ExtraDimensionsTEV:ffbar2mu+mu- (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → mu+ mu- , Code 5073.

`flag` ExtraDimensionsTEV:ffbar2numunumubar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → numu numubar , Code 5074.

`flag` ExtraDimensionsTEV:ffbar2tau+tau- (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → tau+ tau- , Code 5075.

`flag` ExtraDimensionsTEV:ffbar2nutaunutaubar (`default = off`)
Scatterings f fbar → (gamma_{KK}/Z_{KK}) → nutau nutaubar , Code 5076.

### TeV^-1 Sized Extra Dimension, parameters

Irrespective of the parameter options used, the particle produced, gamma_{KK}/Z_{KK}, will always be assigned code 5000023.

`mode` ExtraDimensionsTEV:gmZmode (`default = 3`; `minimum = 0`; `maximum = 5`)
Choice of full gamma_{KK}/Z_{KK} structure or not in relevant processes.
`option` 0 : full gamma_{SM}/Z_{SM} structure, with interference included.
`option` 1 : only pure gamma_{SM} contribution.
`option` 2 : only pure Z_{SM} contribution.
`option` 3 : full gamma_{KK}/Z_{KK} structure, with interference included.
`option` 4 : only pure gamma_{KK} contribution, with SM interference included.
`option` 5 : only pure Z_{KK} contribution, with SM interference included.

`parm` ExtraDimensionsTEV:nMax (`default = 10`; `minimum = 1`; `maximum = 100`)
The number of included KK excitations.

`parm` ExtraDimensionsTEV:mStar (`default = 4000.0`; `minimum = 1000.0`)
The KK mass m^*, given by the inverse of the single extra dimension radius.

### Large Extra Dimensions, production processes

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 [Ask10]. It is also possible to generate monojet events from scalar graviton emission as described in [Azu05], by turning on the option GravScalar.

Note: As discussed in [Ask09], 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.

The following lowest order graviton emission processes are available.

`flag` ExtraDimensionsLED:monojet (`default = off`)
Common switch for the group of lowest-order G jet emission processes, i.e. the three ones below.

`flag` ExtraDimensionsLED:gg2Gg (`default = off`)
Scatterings g g → G g. Code 5021.

`flag` ExtraDimensionsLED:qg2Gq (`default = off`)
Scatterings q g → G q. Code 5022.

`flag` ExtraDimensionsLED:qqbar2Gg (`default = off`)
Scatterings q qbar → G g. Code 5023.

`flag` ExtraDimensionsLED:ffbar2GZ (`default = off`)
Scatterings f fbar → G Z. Code 5024.

`flag` ExtraDimensionsLED:ffbar2Ggamma (`default = off`)
Scatterings f fbar → G gamma. This process corresponds to the photon limit of the G Z process, as described in [Ask09]. Code 5025.

The following LED processes with virtual graviton exchange are available.

`flag` ExtraDimensionsLED:ffbar2gammagamma (`default = off`)
Scatterings f fbar → (LED G*) → gamma gamma. If the graviton contribution is zero, the results corresponds to the SM contribution, i.e. equivalent to `PromptPhoton:ffbar2gammagamma`. Code 5026.

`flag` ExtraDimensionsLED:gg2gammagamma (`default = off`)
Scatterings g g → (LED G*) → gamma gamma. Code 5027.

`flag` ExtraDimensionsLED:ffbar2llbar (`default = off`)
Scatterings f fbar → (LED G*) → l l , where l is a charged lepton. If the graviton contribution is zero, the results corresponds to the SM contribution, i.e. similar to `WeakSingleBoson:ffbar2gmZ`. Does not include t-channel amplitude relevant for e^+e^- to e^+e^- and no K-factor is used. Code 5028.

`flag` ExtraDimensionsLED:gg2llbar (`default = off`)
Scatterings g g → (LED G*) → l l. Code 5029.

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 [Fra11]. In case of the latter, the value of LambdaT is used as the value of the cut-off scale Lambda. 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 HardQCD equivalents and should therefore converge to the same results in the limit of an insignificant graviton contribution.

Warning: These LED dijets processes are still being validated.

`flag` ExtraDimensionsLED:dijets (`default = off`)
Common switch for the group of lowest-order jet jet production processes with graviton exchange, i.e. the six ones below.

`flag` ExtraDimensionsLED:gg2DJgg (`default = off`)
Scatterings g g → (LED G*) → g g. Code 5030.

`flag` ExtraDimensionsLED:gg2DJqqbar (`default = off`)
Scatterings g g → (LED G*) → q qbar. Number of outgoing flavours specified by nQuarkNew parameter below. Code 5031.

`flag` ExtraDimensionsLED:qg2DJqg (`default = off`)
Scatterings q g → (LED G*) → q g and qbar g → (LED G*) → qbar g. Code 5032.

`flag` ExtraDimensionsLED:qq2DJqq (`default = off`)
Scatterings q q(bar)' → (LED G*) → q q(bar)'. Including q and qbar of same or different flavours, but the outgoing flavours equals the incoming ones. Code 5033.

`flag` ExtraDimensionsLED:qqbar2DJgg (`default = off`)
Scatterings q qbar → (LED G*) → g g. Code 5034.

`flag` ExtraDimensionsLED:qqbar2DJqqbarNew (`default = off`)
Scatterings q qbar → (LED G*) → q' qbar'. Number of outgoing flavours specified by nQuarkNew parameter below. Code 5035.

### Large Extra Dimensions, parameters

`flag` 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 [Azu05] and includes two coupling constants below.

`mode` ExtraDimensionsLED:n (`default = 2`; `minimum = 1`)
Number of extra dimensions.

`parm` ExtraDimensionsLED:MD (`default = 2000.`; `minimum = 100.0`)
Fundamental scale of gravity in D = 4 + n dimensions.

`parm` ExtraDimensionsLED:LambdaT (`default = 2000.`; `minimum = 100.0`)
Ultraviolet cutoff parameter for the virtual graviton exchange processes.

`mode` ExtraDimensionsLED:NegInt (`default = 0`; `minimum = 0`; `maximum = 1`)
Allows to change sign of the interference terms in the graviton exchange processes, common in connection to using the Hewett convention [Hew99].
`option` 0 : 1
`option` 1 : -1

`mode` ExtraDimensionsLED:CutOffMode (`default = 0`; `minimum = 0`; `maximum = 3`)
Options for when the hard scale of the process (e.g. sHat) approaches or exceed the scale of validity of the low energy effective theory (e.g. M_D). Note: Option 1 only concerns the graviton emission processes and the form factor is currently not available for the scalar graviton processes.
`option` 0 : Do nothing, i.e. all values of sHat contribute.
`option` 1 : Truncate contributing sHat region ([Ask09]).
`option` 2 : Form factor, using mu = renormScale2 .
`option` 3 : Form factor, using mu = E_jet.

`parm` ExtraDimensionsLED:t (`default = 1.`; `minimum = 0.001`)
Form factor parameter.

`parm` ExtraDimensionsLED:g (`default = 1.0`; `minimum = 0.0`)
Coupling related to scalar graviton emission.

`parm` ExtraDimensionsLED:c (`default = 1.0`; `minimum = 0.0`)
Coupling related to scalar graviton emission.

`mode` ExtraDimensionsLED:nQuarkNew (`default = 3`; `minimum = 0`; `maximum = 5`)
Number of allowed outgoing new quark flavours in the above q qbar → (LED G*) → q' qbar' and g g → (LED G*) → q' qbar' processes. Similar to HardQCD:nQuarkNew for the QCD processes.

`mode` ExtraDimensionsLED:opMode (`default = 0`; `minimum = 0`; `maximum = 1`)
Options to specify S function for LED dijet amplitudes.
`option` 0 : Use detailed amplitude, as described in [Fra11].
`option` 1 : Use conventional LambdaT parametrization, like the other LED processes.

### Unparticles, production processes

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 Graviton in the event record. The graviton and unparticle emission as well as virtual graviton and unparticle exchange processes are described in [Ask10].

Note: As discussed in [Ask09], 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.

The following unparticle emission processes are available.

`flag` ExtraDimensionsUnpart:monojet (`default = off`)
Common switch for the group of lowest-order U jet emission processes, i.e. the three ones below.

`flag` ExtraDimensionsUnpart:gg2Ug (`default = off`)
Scatterings g g → U g. Code 5045.

`flag` ExtraDimensionsUnpart:qg2Uq (`default = off`)
Scatterings q g → U q. Code 5046.

`flag` ExtraDimensionsUnpart:qqbar2Ug (`default = off`)
Scatterings q qbar → U g. Code 5047.

`flag` ExtraDimensionsUnpart:ffbar2UZ (`default = off`)
Scatterings f fbar → U Z. Code 5041.

`flag` ExtraDimensionsUnpart:ffbar2Ugamma (`default = off`)
Scatterings f fbar → U gamma. This process corresponds to the photon limit of the U Z process, as described in [Ask09]. Code 5042.

The following processes with virtual unparticle exchange are available.

`flag` ExtraDimensionsUnpart:ffbar2gammagamma (`default = off`)
Scatterings f fbar → (U*) → gamma gamma. If the unparticle contribution is zero in the spin-2 case, the results corresponds to the SM contribution, i.e. equivalent to `PromptPhoton:ffbar2gammagamma`. Code 5043.

`flag` ExtraDimensionsUnpart:gg2gammagamma (`default = off`)
Scatterings g g → (U*) → gamma gamma. Code 5044.

`flag` ExtraDimensionsUnpart:ffbar2llbar (`default = off`)
Scatterings f fbar → (U*) → l lbar , where l is a charged lepton. If the unparticle contribution is zero, the results corresponds to the SM contribution, i.e. similar to `WeakSingleBoson:ffbar2gmZ`. Does not include t-channel amplitude relevant for e^+e^- to e^+e^- and no K-factor is used. Code 5048.

`flag` ExtraDimensionsUnpart:gg2llbar (`default = off`)
Scatterings g g → (U*) → l lbar. Code 5049.

### Unparticles, parameters

`mode` ExtraDimensionsUnpart:spinU (`default = 2`; `minimum = 0`; `maximum = 2`)
Unparticle spin.

`parm` ExtraDimensionsUnpart:dU (`default = 1.4`; `minimum = 1.0`)
Scale dimension parameter.

`parm` ExtraDimensionsUnpart:LambdaU (`default = 2000.`; `minimum = 100.0`)
Unparticle renormalization scale.

`parm` ExtraDimensionsUnpart:lambda (`default = 1.0`; `minimum = 0.0`)
Unparticle coupling to the SM fields.

`parm` ExtraDimensionsUnpart:ratio (`default = 1.0`; `minimum = 1.0`; `maximum = 1.0`)
Ratio, lambda'/lambda, between the two possible coupling constants of the spin-2 ME. Warning: A ratio value different from one give rise to an IR divergence which makes the event generation very slow, so this values is fixed to ratio = 1 for the moment.

`mode` ExtraDimensionsUnpart:CutOffMode (`default = 0`; `minimum = 0`; `maximum = 1`)
Options for when the hard scale of the process (e.g. sHat) approaches or exceed the scale of validity of the low energy effective theory (Lambda_U). This mode only concerns the unparticle emission processes.
`option` 0 : Do nothing, i.e. all values of sHat contribute.
`option` 1 : Truncate contributing sHat region ([Ask09]).

`mode` ExtraDimensionsUnpart:gXX (`default = 0`; `minimum = 0`; `maximum = 2`)
Chiral unparticle couplings, gXX = gLL = gRR. Only relevant for lepton production from spin-1 unparticle exchange.
`option` 0 : 1
`option` 1 : -1
`option` 2 : 0

`mode` ExtraDimensionsUnpart:gXY (`default = 0`; `minimum = 0`; `maximum = 2`)
Chiral unparticle couplings, gXY = gLR = gRL. Only relevant for lepton production from spin-1 unparticle exchange.
`option` 0 : 1
`option` 1 : -1
`option` 2 : 0