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 gg -> (LED G*) -> gamma gamma.
Code 5027.
Large Extra Dimensions, parameters
flag
ExtraDimensionsLED:Trunc
(default = off
)
Option to truncate the graviton mass spectrum. Only
concerns the graviton emission processes.
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.
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], the underlying
Breit-Wigner mass distribution has to be matched to the graviton mass
spectrum in order to achieve a high MC efficiency.
The following unparticle emission processes are available.
flag
ExtraDimensionsUnpart:ffbar2UZ
(default = off
)
Scatterings f fbar -> U Z.
Code 5041.
flag
ExtraDimensionsUnpart:ffbar2Ugamma
(default = off
)
Scatterings f fbar -> U gamma.
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
.
This is also the case if the model parameter settings are not applicable.
Code 5043.
flag
ExtraDimensionsUnpart:gg2gammagamma
(default = off
)
Scatterings gg -> (U*) -> gamma gamma.
Code 5044.
Unparticles, parameters
flag
ExtraDimensionsUnpart:Trunc
(default = off
)
Option to truncate the unparticle mass spectrum.
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.
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/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). MEs were taken from the following papers:
(monojets) [Giu99], (mono-Z or -photon) [Che07]
(gammagamma) [Kum08].
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 in [Giu99] and [Giu04].