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.