Hidden Valley Processes
- Particle content and properties
- Production processes
- Timelike showers
- Hadronization
- Event information
This Hidden Valley (HV) scenarios have been developed specifically
to allow the study of visible consequences of radiation and
hadronization in a hidden sector, by recoil effect and by decays
back into the visible sector. A key aspect therefore is that
the normal timelike showering machinery has been expanded with a
third kind of radiation, in addition to the QCD and QED ones.
These three kinds of radiation are fully interleaved, i.e.
evolution occurs in a common pT-ordered sequence.
The scenario is described in [Car10]. Furthermore
hadronization in the hidden sector has been implemented.
Three main scenarios for production into and decay out of the
hidden sector can be compared, in each case either for an
Abelian or a non-Abelian gauge group in the HV. Further details
are found in [Car11]. It is strongly recommended that you
read this article, at least sections 2 and 3, and the appendix A,
before you begin any Hidden Valley simulation. The brief physics
paragraphs below are intended as a refresher for people with such
prior knowledge, not as a complete description. In addition, some
recent extensions are described, not (yet) documented elsewhere.
Warning: several alternative hadronization scenarios
will not work in conjunction with Hidden Valley processes, which has
been developed exclusively on top of the default scenario. Known
examples of such incompatible alternatives include
StringPT:thermalModel = on
,
StringPT:mT2suppression = on
and
Ropewalk:RopeHadronization = on
, but there may be more.
Particle content and properties
For simplicity we assume that the HV contains a broken U(1)
or an unbroken SU(N) gauge symmetry. This is used in the
calculation of production cross sections. These could be rescaled
by hand for other gauge groups.
mode
HiddenValley:Ngauge
(default = 3
; minimum = 1
)
is U(1) for Ngauge = 1
, is SU(N) if
Ngauge > 1
. Note that pair production cross sections
contains a factor of Ngauge
for new particles
in the fundamental representation of this group.
A minimal HV particle content has been introduced. Firstly, there is
a set of 12 particles that mirrors the Standard Model flavour
structure, and is charged under both the SM and the HV symmetry groups.
Each new particle couples flavour-diagonally to a corresponding SM
state, and has the same SM charge and colour, but in addition is in
the fundamental representation of the HV colour, as follows:
Dv
, identity 4900001, partner to the normal
d
quark;
Uv
, identity 4900002, partner to the normal
u
quark;
Sv
, identity 4900003, partner to the normal
s
quark;
Cv
, identity 4900004, partner to the normal
c
quark;
Bv
, identity 4900005, partner to the normal
b
quark;
Tv
, identity 4900006, partner to the normal
t
quark;
Ev
, identity 4900011, partner to the normal
e
lepton;
nuEv
, identity 4900012, partner to the normal
nue
neutrino;
MUv
, identity 4900013, partner to the normal
mu
lepton;
nuMUv
, identity 4900014, partner to the normal
numu
neutrino;
TAUv
, identity 4900015, partner to the normal
tau
lepton;
nuTAUv
, identity 4900016, partner to the normal
nutau
neutrino.
Collectively we will refer to these states as Fv
;
note, however, that they need not be fermions themselves.
In addition the model contains the HV gauge particle, either
a HV-gluon or a HV-photon, but not both; see Ngauge
above:
gv
, identity 4900021, is the massless
gauge boson of the HV SU(N) group;
gammav
, identity 4900022, is the massless
gauge boson of the HV U(1) group.
Finally, for the basic HV scenario, there is a new massive particle
with only HV charge sitting in the fundamental representation of the
HV gauge group:
qv
, identity 4900101.
Optionally up to eight different such flavours can be allowed in
the hidden sector, identities 4900101 - 4900108. The actual number
used is set by HiddenValley:nFlav
, see further below.
Currently there are two main production scenarios implemented.
The first is for pair production of one of the
states presented first above, e.g. g g → Dv Dvbar.
Such a Dv can radiate gluons and photons like an SM quark,
but in addition HV-gluons or HV-photons in a similar fashion.
Eventually the Dv will decay like Dv → d + qv.
The strength of this decay is not set as such, but is implicit in
your choice of width for the Dv state. Thereafter the
d and qv can radiate further within their
respective sectors. The qv, gv and gammav
are invisible.
The second is a variant of a Z' resonance:
Zv
, identity 4900023, a boson that can couple
both to pairs of Standard Model fermions and to qv qvbar
pairs. Mass, total width and branching ratios can be set as convenient.
This opens up for other processes, notably
l^+l^-, q qbar → Zv → qv qvbar.
Some further scenarios can easily be implemented by a brute-force
addition of a new decay channel to an existing particle. An example
would be a Higgs portal, where the Higgs can decay into a
qv qvbar or gv gv pair.
The possibility of a leakage back from the hidden sector will be
considered in the Hadronization section below. For the U(1)
case the gammav normally acquires a mass and can decay back to
a Standard-Model fermion pair, while the qv remains invisible.
The SU(N) alternative remains unbroken, so confinement holds
and the gv is massless. A string like
qv - gv - ... - gv - qvbar can break by the production of
new qv - qvbar pairs, which will produce qv-qvbar
mesons. For this kind of scenarios it makes sense to assume that
qv has spin 1/2, so that QCD provides some guidance.
It is possible to build a rather sophisticated hidden sector
by trivial extensions of the HV flavour content. In most contexts
this would be overkill, since much of the finer details would not
be observable in our sector. The default therefore is a simplified
treatment.
Hidden Valley hadrons in a simple setup
In the default HV-hadron option,
HiddenValley:separateFlav = off
,
the qv can be duplicated in up to
eight copies, with identical properties except for the flavour charge.
Specifically, you can set the mass of the first qv, but
then that value is propagated to the other masses at initialization.
These are assigned codes 4900101 - 4900108. This gives a total of 64
possible lowest-lying mesons. We also include a duplication of that,
into two multiplets, corresponding to the pseudoscalar and vector
mesons of QCD. These are assumed to have the same mass and other
properties. Only the flavour-diagonal ones can decay back into the
Standard-Model sector, however, while the rest remain in the hidden
sector. It is therefore only necessary to distinguish a few states:
pivDiag
, identity 4900111, a flavour-diagonal
HV-meson with spin 0 that can decay back into the Standard-Model sector;
rhovDiag
, identity 4900113, a flavour-diagonal
HV-meson with spin 1 that can decay back into the Standard-Model sector;
pivUp
, identity 4900211, an off-diagonal
HV-meson with spin 0 that is stable and invisible, with an antiparticle
pivDn
with identity -4900211; the particle is
the one where the code of the flavour is larger than that of the
antiflavour;
rhovUp
, identity 4900213, an off-diagonal
HV-meson with spin 1 that is stable and invisible, with an antiparticle
rhovDn
with identity -4900213; again the particle is
the one where the code of the flavour is larger than that of the
antiflavour;
ggv
, identity 4900991, is only rarely used,
to handle cases where it is kinematically impossible to produce an
HV-meson on shell, and it therefore is assumed to de-excite by the
emission of invisible gv-gv v-glueball bound states.
By changing ParticleData
, it is possible to allow decays
also for the off-diagonal Up/Dn mesons, or make either diagonal state
stable. Like for Standard Model particles, it is only necessary to
set the properties of the particle (pivUp, rhovUp
), and
then the ones of the antiparticle (pivDn, rhovDn
) are
mirrored as appropriate. That is, masses and most other properties are
set the same, while decay channels are inverted.
Baryon production is more tricky than meson production, since it depends
strongly on the choice of the SU(N) gauge group, and since it is
not so well understood even in our sector. For SU(2),
where the baryon would consist of two quarks, baryons could be as
common as mesons. No realistic detailed scenario exists for such a
setup. In SU(3) we could guess that baryons give of the order
a 10% correction to the particle production rates, like in our sector,
and that could be relevant for some phenomenology. For SU(4)
and higher, where more quarks are needed to form a baryon, one would
expect a production rate too small to be of any relevance. The current
handling therefore aims at SU(3) applications. (But if you
imagine a low production rate of triquarks, with net anticolour,
then the program will run also for SU(4).) Again, in the
spirit of simplicity, one baryon is introduced in the default scenario:
Deltav
, identity 4901114, an HV-baryon, assumed to be
stable. Normally one would expect a spin 1/2 baryon to be the lightest,
but spin 3/2 here goes together with bookkeeping as if there is only
one flavour. Mass and decay properties can anyway be selected independent
of the spin displayed.
Hidden Valley hadrons in an extended setup
The non-default and more detailed handling of HV-hadrons is switched on
with HiddenValley:separateFlav = on
. In it, each
of the quark and meson flavours are shown explicitly. The quark names
are qvi
, with i
an integer in
the range between 1 and the number of flavours. Similarly, meson names
are pivij
and rhovij
, where i = j
are the flavour-diagonal mesons, else i > j
, with
j
representing the antiquark. The identity codes then are
4900ij
1 for pseudoscalars and 4900ij
3 for
vectors. An antimeson comes with an overall negative sign, and here
i
gives the antiquark.
You are now free to set masses separately for each quark and meson.
So as not have to code up the hadronization for alternative
mass orderings, it is assumed that the quarks are ordered in terms of
an increasing mass, and specifically that the first quark, 4900101,
is the lightest one. You are allowed to have some mass-degenerate states,
of course, and then the ordering between them is irrelevant. As a
consequence of the quark mass ordering, it is also assumed that the
lightest hadron is the one with lowest code, 4900111.
The data tables by default contain identical properties for all diagonal
mesons in a multiplet. Currently there is no explicit implementation of
mixing between them, but the last pseudoscalar meson can be made to
represent a flavour singlet state eta_1, optionally with a
reduced production rate. The name remains of the pivii
type, whatever implicit association you make for this state. More generally,
it is possible to have both mass-degenerate and non-degenerate scenarios,
where in either it is useful to be able to set properties of some mesons
separately. All nondiagonal mesons of a multiplet are also assumed to be
identical and stable by default, although this can be modified as desired.
While the separateFlav = on
option gives more freedom, it also
comes with the need for a more detailed setup, with up to 72 different
meson states that can be given individual properties. (With 8 flavours
each multiplet has 8 diagonal mesons and 28 off-diagonal mesons.
The 28 off-diagonal antimesons have properties that follow from the
respective meson ones.)
A corresponding HV-baryon setup for SU(3) would require
up to 168 spin 1/2 and 120 spin 3/2 states to be specified. As of now,
this appears to be vast overkill, in particular since these states
likely are stable. Therefore the separateFlav = on
option only extends the default model from one to at most eight
different HV-states, with names Deltavi
, and identities
490i
114. That is, we assume there is only one kind of
diquark being produced, 4901103, at a rate that is the sum of all
actual diquarks, but represented by the lightest of all these diquarks,
since this is the one most frequently produced. The use of code 11 should
not be taken literally; the 4901114 state is not assumed to be produced
with any different properties than the other seven states just because
of a seeming identity of all three HV-quarks (as would have been the
case in a picture with complete baryon multiplets).
Some final notes on the separateFlav = on
option.
Firstly, the code is not adapted to allow widely different mass scales
in the hadronization stage proper, but assume not much worse than the
Standard Model u/d/s sector. Further states like c/b
could be produced in the hard process but not during hadronization,
making use of the probFlav
numbers described later.
Secondly, the Zv
by default is set up to couple equally
to all existing HV-quark states, and also couples to all Standard Model
particles, while the Fv
states are set up to couple only
to the first HV-quark flavour. You should remember to adjust decay modes
and branching ratios also for these particles in scenarios where the
HV-quarks are different.
Further particle properties
Only the spin of the HV-gluon or HV-photon is determined unambiguously
to be unity, for the others you can make your choice. The emphasis on
the choice of spinFv
, with spinqv
as derived
from that, comes from the originally studied scenarios in [Car10].
In scenarios where a Zv
is the main production mechanism
for qv
you must still remember to set spinFv
even if no Fv are to be produced. Notably, HV-hadron multiplets
have been defined assuming that qv is spin 1/2, which is also
the default setup.
mode
HiddenValley:spinFv
(default = 0
; minimum = 0
; maximum = 2
)
The spin of the HV partners of the SM fermions, e.g.
Dv, Uv, Ev and nuEv.
option
0 : spin 0.
option
1 : spin 1/2.
option
2 : spin 1.
mode
HiddenValley:spinqv
(default = 0
; minimum = 0
; maximum = 1
)
The spin of qv when the Fv (the HV partners of
the SM fermions) have spin 1/2. (While, if they have spin 0 or 1,
the qv spin is fixed at 1/2.)
option
0 : spin 0.
option
1 : spin 1.
parm
HiddenValley:kappa
(default = 1.
)
If the Fv have spin 1 then their production
cross section depends on the presence of anomalous magnetic dipole
moment, i.e. of a kappa different from unity. For other spins
this parameter is not used.
flag
HiddenValley:doKinMix
(default = off
)
allow kinematic mixing or not.
parm
HiddenValley:kinMix
(default = 1.
)
strength of kinetic mixing.
You should set the Fv/Zv and qv masses appropriately,
with the latter smaller than the former two (where relevant) to allow
decays. When U(1) hadronization is switched on, you need to set
the gammav mass and decay modes. In this case the qv
mass is a physical one, since there is no confinement.
For SU(N) hadronization instead we need to operate with qv
constituent masses, and relate these to the HV-meson masses. The simplest
relation is that
m_ij = m_i + m_j + K * <sigma_i * sigma_j> / (m_i * m_j)
where m_i, m_j are the constituent quark masses and
m_ij the meson one. The <sigma_i * sigma_j>
factor is the spin-spin expectation value, 1 for a vector and -3 for
a pseudoscalar. Even without knowing the constant K one thus
can conclude that
m_i + m_j = (3 * m_ij,vector + m_ij, pseudoscalar) / 4
which helps define the HV-quark masses. Note that some parameters,
in particular HiddenValley:bmqv2
, have been given
default values based on a scaling related to the lightest HV-quark
mass defined by the equations above. It therefore is relevant to
work with consistently defined HV-quark masses. This still is based
on the lightest HV-quark having a constituent mass of the order of
Lambda_HV
. If this is not the case then further thought
will be required. The HV-baryon masses should suitably be defined
as the sum of the the three constituent masses for SU(3).
Furthermore decay modes also need to be set, and lifetimes if you want
to have displaced vertices.
In the separateFlav = on
option the number of properties
to be set can be very large. Insofar as these still have a somewhat
regular structure, it may be better to write suitable code to set up
all the properties rather than typing in a long command file by hand.
Production processes
There are two main HV production modes implemented, either via particles
charged both under SM and HV groups, or via Z boson coupling to both
sectors.
flag
HiddenValley:all
(default = off
)
Common switch for the group of hard Hidden Valley processes,
as listed separately in the following. The last process is part
of another scenario and is not affected by this switch.
flag
HiddenValley:gg2DvDvbar
(default = off
)
Pair production g g → Dv Dvbar.
Code 4901.
flag
HiddenValley:gg2UvUvbar
(default = off
)
Pair production g g → Uv Uvbar.
Code 4902.
flag
HiddenValley:gg2SvSvbar
(default = off
)
Pair production g g → Sv Svbar.
Code 4903.
flag
HiddenValley:gg2CvCvbar
(default = off
)
Pair production g g → Cv Cvbar.
Code 4904.
flag
HiddenValley:gg2BvBvbar
(default = off
)
Pair production g g → Bv Bvbar.
Code 4905.
flag
HiddenValley:gg2TvTvbar
(default = off
)
Pair production g g → Tv Tvbar.
Code 4906.
flag
HiddenValley:qqbar2DvDvbar
(default = off
)
Pair production q qbar → Dv Dvbar
via intermediate gluon.
Code 4911.
flag
HiddenValley:qqbar2UvUvbar
(default = off
)
Pair production q qbar → Uv Uvbar
via intermediate gluon.
Code 4912.
flag
HiddenValley:qqbar2SvSvbar
(default = off
)
Pair production q qbar → Sv Svbar
via intermediate gluon.
Code 4913.
flag
HiddenValley:qqbar2CvCvbar
(default = off
)
Pair production q qbar → Cv Cvbar
via intermediate gluon.
Code 4914.
flag
HiddenValley:qqbar2BvBvbar
(default = off
)
Pair production q qbar → Bv Bvbar
via intermediate gluon.
Code 4915.
flag
HiddenValley:qqbar2TvTvbar
(default = off
)
Pair production q qbar → Tv Tvbar
via intermediate gluon.
Code 4916.
flag
HiddenValley:ffbar2DvDvbar
(default = off
)
Pair production f fbar → Dv Dvbar
via intermediate gamma*/Z^*.
Code 4921.
flag
HiddenValley:ffbar2UvUvbar
(default = off
)
Pair production f fbar → Uv Uvbar
via intermediate gamma*/Z^*.
Code 4922.
flag
HiddenValley:ffbar2SvSvbar
(default = off
)
Pair production f fbar → Sv Svbar
via intermediate gamma*/Z^*.
Code 4923.
flag
HiddenValley:ffbar2CvCvbar
(default = off
)
Pair production f fbar → Cv Cvbar
via intermediate gamma*/Z^*.
Code 4924.
flag
HiddenValley:ffbar2BvBvbar
(default = off
)
Pair production f fbar → Bv Bvbar
via intermediate gamma*/Z^*.
Code 4925.
flag
HiddenValley:ffbar2TvTvbar
(default = off
)
Pair production f fbar → Tv Tvbar
via intermediate gamma*/Z^*.
Code 4926.
flag
HiddenValley:ffbar2EvEvbar
(default = off
)
Pair production f fbar → Ev Evbar
via intermediate gamma*/Z^*.
Code 4931.
flag
HiddenValley:ffbar2nuEvnuEvbar
(default = off
)
Pair production f fbar → nuEv nuEvbar
via intermediate gamma*/Z^*.
Code 4932.
flag
HiddenValley:ffbar2MUvMUvbar
(default = off
)
Pair production f fbar → MUv MUvbar
via intermediate gamma*/Z^*.
Code 4933.
flag
HiddenValley:ffbar2nuMUvnuMUvbar
(default = off
)
Pair production f fbar → nuMUv nuMUvbar
via intermediate gamma*/Z^*.
Code 4934.
flag
HiddenValley:ffbar2TAUvTAUvbar
(default = off
)
Pair production f fbar → TAUv TAUvbar
via intermediate gamma*/Z^*.
Code 4935.
flag
HiddenValley:ffbar2nuTAUvnuTAUvbar
(default = off
)
Pair production f fbar → nuTAUv nuTAUvbar
via intermediate gamma*/Z^*.
Code 4936.
flag
HiddenValley:ffbar2Zv
(default = off
)
Production f fbar → Zv where Zv is a generic
resonance that couples both SM fermion pairs and a qv qvbar
pair. Not part of the framework of the above processes, but as an
alternative, that currently is the more popular one. Code 4941.
Timelike showers
One key point of this HV scenario is that radiation off the
HV-charged particles is allowed. This is done by the standard
final-state showering machinery. (HV particles are not produced
in initial-state radiation.) All the (anti)particles Fv
and qv have one (negative) unit of HV charge. That is,
radiation closely mimics the one in QCD. Both QCD, QED and HV
radiation are interleaved in one common sequence of decreasing
emission pT scales. Each radiation kind defines a set of
dipoles, usually spanned between a radiating parton and its recoil
partner, such that the invariant mass of the pair is not changed
when a radiation occurs. This need not follow from trivial colour
assignments, but is often obvious. For instance, in a decay
Qv → q + qv the QCD dipole is between the q and
the hole after Qv, but qv becomes the recoiler
should a radiation occur, while the role of q and qv
is reversed for HV radiation. The selection of recoilers in subsequent
emissions is regulated by the TimeShower:recoilToColoured
switch within the QCD and HV sectors separately.
This also includes matrix-element corrections to the
first/hardest HV emission for a number
of decay processes, with colour, spin and mass effects included
[Nor01]. They were calculated within the context of the
particle content of the MSSM, however, which does not include spin 1
particles with unit colour charge. In such cases spin 0 is assumed
instead. By experience, the main effects come from mass and colour
flow anyway, so this is not a bad approximation. (Furthermore the
MSSM formulae allow for gamma_5 factors from wave
functions or vertices; these are even less important.) There are some
processes where no corrections at all are included currently, notably
for gammav emission in an Qv → q + qv decay.
In such cases hard emissions are likely to be overestimated,
but by experience not by a big amount.
An emitted gv can branch in its turn,
gv → gv + gv. This radiation may affect momenta
in the visible sector by recoil effect, but this is a minor
effect relative to the primary emission of the gv.
While the default model has a fixed Hidden Valley coupling
alpha_HV, some further work [Scw15] has considered
the impact of a running coupling. This is included as options at
the one-, two- and three-loop level. Beta functions up three-loop
and definitions of higher-order Lambda follow [Rit97],
[Yao06] and [Pro07]. The running is handled by the
AlphaSUN
class, for lack of better alternatives put in
the StandardModel.h
and StandardModel.cc
files,
and are documented on the
Standard-Model Parameters
page.
flag
HiddenValley:FSR
(default = off
)
switch on final-state shower of gv or gammav
in a HV production process.
mode
HiddenValley:alphaOrder
(default = 0
; minimum = 0
; maximum = 3
)
Order at which alpha_HV runs. This switch has no function for
the U(1) case, where alpha_HV is always fixed, but only
for the SU(N) ones. For a running alpha_HV it is
possible either to set the alpha_HV value at a reference scale
or to set a Lambda scale, see further the next four entries.
option
0 : zeroth order, i.e. alpha_HV is kept
fixed at the value alphaFSR below.
option
1 : first order, with the beta function based
on Ngauge and Nflav.
option
2 : second order, with the beta function based
on Ngauge and Nflav.
option
3 : third order, with the beta function based
on Ngauge and Nflav.
parm
HiddenValley:alphaFSR
(default = 0.1
; minimum = 0.0
)
The alpha_HV coupling strength of gv/gammav emissions.
When HiddenValley:alphaOrder = 0
, or for a U(1)
scenario, this value is fixed. For an SU(N) model with
alphaOrder
above zero, i.e. when alpha_HV
runs, it is the value at the reference scale below. It corresponds to
alpha_strong of QCD or alpha_em of QED. For shower
branchings such as Dv → Dv + gv the coupling is multiplied
by C_F = (N^2 - 1) / (2 * N) for an SU(N) group and
for gv → gv + gv by N.
parm
HiddenValley:alphaFSRrefScale
(default = 91.188
; minimum = 0.0
)
A reference scale, where the HiddenValley:alphaFSR
value
above is defined, in case of a running coupling. Default value is the
Z^0 mass, by analogy with QCD, but it can be picked to
whatever is convenient.
flag
HiddenValley:setLambda
(default = off
)
By default an HiddenValley:alphaFSR
value is defined
at a reference scale, as outlined above, and then converted to a
Lambda_HV scale for usage in the relevant running-coupling
expressions. If setLambda
is on, instead the
Lambda_HV value can be set directly below.
parm
HiddenValley:Lambda
(default = 0.4
; minimum = 0.01
)
the Lambda_HV parameter used for the case of a running
alpha_HV(Q^2) when HiddenValley:setLambda = on
.
This Lambda_HV is used in the respective one-, two- or
three-loop alpha_HV(Q^2) expression, depending on
HiddenValley:alphaOrder
.
parm
HiddenValley:pTminFSR
(default = 0.44
; minimum = 0.1
)
lowest allowed pT of emission. Should be greater than
or equal to 1.1 times Lambda, or it will be reset
automatically.
Hadronization
By default the HV particles with no Standard Model couplings
are not visible. Their presence can only be deduced by the
observation of missing (transverse) momentum in the event as a
whole. In the current implementation it is possible to simulate
two different scenarios where activity can leak back from the
hidden sector.
The first possibility is relevant for the U(1) scenario.
The U(1) group may be broken, so that the gammav
acquires a mass. Furthermore, the gammav may have a
small mixing angle with the normal photon, or with some Z'
state or other mediator, and may thus decay back into Standard
Model particles. The qv still escapes undetected;
recall that there is no confinement in the U(1) option.
In order to enable this machinery two commands are necessary,
4900022:m0 = ...
to set the gammav mass
to the desired value, and 4900022:onMode = on
to enable
gammav decays. The default gammav decay
table contains all Standard Model fermion-antifermion pairs,
except top, with branching ratios in proportion to their coupling
to the photon, whenever the production channel is allowed by
kinematics. This table could easily be tailored to more specific
models and needs. For instance, for a mass below 1 - 2 GeV, it
would make sense to construct a table of exclusive hadronic decay
channels rather than go the way via a hadronizing quark pair.
The gammav are expected to decay so rapidly that no
secondary vertex will be detectable. However, it is possible to
set 4900022:tau0
to a finite lifetime (in mm) that
will be used to create separated secondary vertices.
The second, more interesting, possibility is relevant for the
SU(N) scenarios. Here the gauge group remains unbroken, i.e.
gv is massless, and the partons are confined. Like in
QCD, the HV-partons can therefore be arranged in one single
HV colour-ordered chain, with a qv in one end, a
qvbar in the other, and a varying number of
gv in between. Each event will only contain (at most)
one such string, (i) since perturbative branchings
gv → qv qvbar have been neglected, as is a reasonable
approximation for QCD, and (ii) since HV colours are assigned in the
N_C → infinity limit, just like in the handling of
string fragmentation in QCD. The HV-string can then fragment by the
nonperturbative creation of qv qvbar pairs, leading to
the formation of HV-mesons along the string, each with its
qv from one vertex and its qvbar from
the neighbouring one.
Since, so far, we have only assumed there to be one qv
species, all produced qv qvbar HV-mesons are of the
same flavour-diagonal species. Such an HV-meson can decay back to
the normal sector, typically by whatever mediator particle allowed
production in the first place. In this framework the full energy put
into the HV sector will leak back to the normal one. To allow more
flexibility, a possibility of n_Flav different
qv species is introduced. By default they are all assumed
to have the same mass and other properties, but distinguished by
some flavour-like property. Only the flavour-diagonal ones can decay,
meaning that only a fraction (approximately) 1/n_Flav of the
HV-energy leaks back, while the rest remains in the hidden sector.
A more differential description of all the states can be set up
for the HiddenValley:separateFlav = on
option, as
already noted.
This scenario contains more parameters than the first one, for the
U(1) group. They can be subdivided into two sets. One is
related to particle properties, both for qv and for the
two different kinds of HV-mesons, here labeled 4900111 and 4900113
for the diagonal ones, and +-4900211 and +-4900213 for the
off-diagonal ones, plus optionally an 4901114 baryon. Furthermore the
hvMesonDiag decay modes need to be set up. Like with the
gammav in the U(1) option, the default
rhovDiag
decay table is based on the branching ratios
of an off-shell photon, while the ones of the pivDiag
are assumed proportional to the squared mass, times a (HV-)colour
factor of 3 where relevant.
The second set are fragmentation parameters that extend or replace
the ones used in normal string fragmentation. Some of them are not
encoded in the same way as normally, however, but rather scale as
the qv mass is changed, so as to keep a sensible default
behaviour. This does not mean that deviations from this set should
not be explored, or that other scaling rules could be preferred
within alternative scenarios. These parameters are as follows.
flag
HiddenValley:fragment
(default = off
)
switch on string fragmentation of the HV partonic system.
Only relevant for SU(N) scenarios.
mode
HiddenValley:nFlav
(default = 1
; minimum = 1
; maximum = 8
)
number of different flavours assumed to exist in the hadronization
description, leading to approximately 1/n_Flav of the
produced HV-mesons being flavour-diagonal and capable to decay back
to Standard Model particles.
flag
HiddenValley:separateFlav
(default = off
)
By the choice of nFlav
above, a wide set of HV-mesons
are implied, and in principle all of their properties have to be
set separately. For the default off
option it is assumed
that the dividing line goes between mesons with on- or off-diagonal
flavour content. Thus only four separate mesons need be defined
pivDiag, rhovDiag, pivUp/pivDn, rhovUp/rhovDn
,
plus optionally a Deltav
baryon, which greatly simplifies
the task of defining masses, decay modes, and branching ratios.
parm
HiddenValley:probDiquark
(default = 0.
; minimum = 0.
; maximum = 1.
)
probability that the string breaks by "diquark-antidiquark" production
rather than quark-antiquark one. This then leads to an adjacent
baryon-antibaryon pair in the flavour chain. Currently only one kind
of diquark is implemented, implying at most eight different baryons
if separateFlav = on
, else only one. The value should be
in the ballpark of 0.1 for SU(3), but should be kept at zero
for bigger gauge groups. It cannot be trusted for SU(2),
so it may be better to keep it zero there as well.
pvec
HiddenValley:probFlav
(default = {1.,1.,1.,1.,1.,1.,1.,1.}
; minimum = 0.
; maximum = 1.
)
production suppression at a string break for either of the
nFlav
different flavour-antiflavour possibilities that
are allowed. Corresponds to the exp(-pi * m_q^2 / kappa)
tunneling suppression factor used in normal string fragmentation
to explain why s quarks are less frequently produced than
u,d ones. When nFlav
is less than 8 the trailing
positions are not used, but they should still be set to ensure
consistent handling.
parm
HiddenValley:probVector
(default = 0.75
; minimum = 0.
; maximum = 1.
)
fraction of HV-mesons that are assigned spin 1 (vector), with the
remainder spin 0 (pseudoscalar). Assuming the qv have
spin 1/2 and the mass splitting is small, spin counting
predicts that 3/4 of the mesons should have spin 1.
parm
HiddenValley:probKeepEta1
(default = 1.0
; minimum = 0.
; maximum = 1.
)
multiplicative factor suppressing the production rate of the diagonal
pseudoscalar meson with the largest code, for now assumed to be the
eta_1 flavour-singlet state of the multiplet.
parm
HiddenValley:aLund
(default = 0.3
; minimum = 0.0
; maximum = 2.0
)
The a parameter of the Lund symmetric fragmentation function.
See the normal fragmentation
function description for the shape of this function.
parm
HiddenValley:bmqv2
(default = 0.8
; minimum = 0.2
; maximum = 2.0
)
The b parameter of the Lund symmetric fragmentation function,
multiplied by the square of the qv mass. This scaling ensures
that the fragmentation function keeps the same shape when the
qv mass is changed (neglecting transverse momenta).
parm
HiddenValley:rFactqv
(default = 1.0
; minimum = 0.0
; maximum = 2.0
)
r_qv, i.e. the Bowler correction factor to the Lund symmetric
fragmentation function, which could be made weaker or stronger than
its natural value.
parm
HiddenValley:sigmamqv
(default = 0.5
; minimum = 0.0
)
the width sigma of transverse momenta in the HV fragmentation
process, normalized to the qv mass. This ensures that
sigma scales proportionately to m_qv.
See the normal fragmentation
pT description for conventions for factors of 2.
Event information
For the SU(N) QCD-like scenarios, also the related HV colours
are bookkept. The normal colour tag locations cannot be reused,
since some particles carry both normal and HV colours.
Instead a small vector is located in the Event
class,
where the HV colour tags can be stored for HV-coloured particles only.
This information can be accessed for each particle, see the
Particle Properties page,
the Particle::colHV/acolHV/colsHV
methods.
As a complement to the normal event record, the
Event::listHVcols()
method lists the particles
that have HV colours and which colour tags those carry; see
the Event Record page.
Also some other methods are found there.