Extra-Dimensional Processes

Scenarios with extra dimensions allow a multitude of processes. Currently two different categories of processes are implemented. The first involves the production of an excited graviton state G^* within a Randall-Sundrum (RS) scenario, the second phenomena from large extra dimensions (LED). Due to the close relation between the LED model and a so-called unparticle model, unparticle processes are also kept in this section.

Randall-Sundrum Resonances, production processes

The Graviton resonance state is assigned PDG code 5100039. Decays into fermion, gluon and photon pairs are handled with the correct angular distributions, while other decay channels currently 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.

Randall-Sundrum Resonances, parameters

In the above scenario the main free parameter is the G^* mass, which is set as usual. In addition there is one further parameter.

parm  ExtraDimensionsG*:kappaMG   (default = 0.054; minimum = 0.0)
dimensionless coupling, which enters quadratically in all 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.

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 uses the same implementation as the corresponding unparticle processes, see further details below.

The graviton emission processes are implemented using the conventions described in [Ask09]. As also discussed in [Ask09], the underlying Breit-Wigner mass distribution has to be matched to the graviton mass spectrum in order to achieve a high MC efficiency.

The virtual graviton exchange processes uses the parameters defined in [Giu99].

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.

Large Extra Dimensions, parameters

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

parm  ExtraDimensionsLED:MD   (default = 2000.; minimum = 0.0)
Fundamental scale of gravity in D = 4 + n dimensions.

parm  ExtraDimensionsLED:LambdaT   (default = 2000.; minimum = 0.0)
Ultraviolet cutoff parameter for the virtual graviton exchange processes.

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.
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 (further information below).
option 3 : Form factor, using mu = E_jet(further information below).

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

Unparticles, production processes

As mentioned above, the similar unparticle and graviton processes share the same implementations. The unparticle processes, however, only uses the dedicated unparticle parameters below. The unparticle is also assigned the PDG code 5000039 and is therefore called Graviton in the event record. Further details about the common implementations are given below.

All unparticle processes follow the parameter conventions described in [Ask09]. As also discussed in [Ask09], for unparticle emission the underlying Breit-Wigner mass distribution has to be matched to the unparticle mass spectrum in order to achieve a high 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 l , 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 l. 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 = 1.0)
Unparticle renormalization scale.

parm  ExtraDimensionsUnpart:lambda   (default = 1.0)
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

Common LED and unparticle implementation

Since the cross sections of the available LED and corresponding (spin-2) unparticle processes only differ by some constant factors they share the same implementation. The intention is that this should both minimize the amount of code needed as well as emphasize the rather small differences between the models from a phenomenological point of view.

The main documentation for the common LED graviton/unparticle implementation together with the parameter conventions used is presented in [Ask09]. Since this paper is focused on graviton/unparticle emission some complementary information, not covered in [Ask09], is summarized below.

The spin-2 unparticle and graviton processes share the same matrix elements (ME), apart from monojet production where only graviton emission is available in the case of spin-2. MEs were taken from the following papers: (monojets) [Giu99], [Che07], [Riz08], (mono-Z or -photon) [Che07], (gammagamma) [Che07], [Kum08], (llbar) [Che07]. All unparticle processes (spin-0, spin-1 and spin-2) have an universal unparticle - SM coupling, lambda, implemented according to the effective operators in [Che07]. The virtual graviton exchange processes are obtained from the spin-2 unparticle MEs by setting dU = 2 and lambda^2 * Chi = 4 pi, which reproduces the graviton formulas also in [Giu04].

Form factor

For the LED processes a form factor of the coupling to gravity in extra dimensions have been implemented according to [Hew07]. The form factor becomes relevant as the hard scale, mu^2, of the process approaches the D-dimensional Planck scale. It depends on one additional parameter, t, which is related the unknown details of how the gravitational coupling runs. t is of order 1 and [Hew07] argues that it should be less than or about 2.

If the option ExtraDimensionsLED:CutOffMode = 2 is used the hard scale mu^2 is set by using SigmaProcess:renormScale2. In this case the options 1 and 4 corresponds to what was used in [Hew07] for the graviton emission and virtual graviton exchange processes respectively. For the graviton emission processes it is also possible to use mu = E_jet in the center-of-mass system by setting ExtraDimensionsLED:CutOffMode = 3. Option 2 and 3 are equivalent for the virtual graviton exchange.