.. _Matrix Elements:
***************
Matrix elements
***************
The following parameters are used to steer the matrix element calculation setup. To learn how to specify the hard scattering process and further process-specific options in its calculation, please also refer to :ref:`Processes`.
.. contents::
:local:
.. _ME_GENERATORS:
ME_GENERATORS
=============
.. index:: ME_GENERATORS
The list of matrix element generators to be employed during the run.
When setting up hard processes, Sherpa calls these generators in order
to check whether either one is capable of generating the corresponding
matrix element. This parameter can also be set on the command line
using option :option:`-m`, see :ref:`Command line`.
The built-in generators are
:option:`Internal`
Simple matrix element library, implementing a variety of 2->2 processes.
:option:`Amegic`
The AMEGIC++ generator published under :cite:`Krauss2001iv`
:option:`Comix`
The `Comix `_ generator published under
:cite:`Gleisberg2008fv`
It is possible to employ an external matrix element generator within
Sherpa. For advice on this topic please contact the authors,
:ref:`Authors`.
.. _RESULT_DIRECTORY:
RESULT_DIRECTORY
================
.. index:: RESULT_DIRECTORY
This parameter specifies the name of the directory which is used by
Sherpa to store integration results and phasespace mappings. The
default is ``Results/``. It can also be set using the command line
parameter :option:`-r`, see :ref:`Command line`. The directory will be
created automatically, unless the option
:option:`GENERATE_RESULT_DIRECTORY: false` is specified. Its location
is relative to a potentially specified input path, see :ref:`Command
line`.
.. _EVENT_GENERATION_MODE:
EVENT_GENERATION_MODE
=====================
.. index:: EVENT_GENERATION_MODE
.. index:: OVERWEIGHT_THRESHOLD
This parameter specifies the event generation mode. It can also be
set on the command line using option :option:`-w`, see :ref:`Command
line`. The three possible options are:
:option:`Weighted`
(alias :option:`W`) Weighted events.
:option:`Unweighted`
(alias :option:`U`)
Events with constant weight, which have been unweighted against the
maximum determined during phase space integration. In case of rare
events with ``w > max`` the parton level event is repeated
``floor(w/max)`` times and the remainder is unweighted. While this
leads to unity weights for all events it can be misleading since the
statistical impact of a high-weight event is not accounted for. In
the extreme case this can lead to a high-weight event looking like a
significant bump in distributions (in particular after the effects
of the parton shower).
:option:`PartiallyUnweighted`
(alias :option:`P`)
Identical to :option:`Unweighted` events, but if the weight exceeds
the maximum determined during the phase space integration, the event
will carry a weight of ``w/max`` to correct for that. This is the
recommended option to generate unweighted events and the default
setting in Sherpa.
For :option:`Unweighted` and :option:`PartiallyUnweighted` events the user may
set :option:`OVERWEIGHT_THRESHOLD: ` to cap the maximal over-weight
``w/max`` taken into account.
.. _SCALES:
SCALES
======
.. index:: SCALES
This parameter specifies how to compute the renormalization and
factorization scale and potential additional scales.
.. contents::
:local:
Sherpa provides several built-in scale setting schemes. For each
scheme the scales are then set using expressions understood by the
:ref:`Interpreter`. Each scale setter's syntax is
.. code-block:: yaml
SCALES: {}
to define a single scale for both the factorisation and renormalisation scale.
They can be set to different values using
.. code-block:: yaml
SCALES: {}{}
In parton shower matched/merged calculations a third perturbative
scale is present, the resummation or parton shower starting scale. It
can be set by the user in the third argument like
.. code-block:: yaml
SCALES: {}{}{}
If the final state of your hard scattering process contains QCD
partons, their kinematics fix the resummation scale for subsequent
emissions (cf. the description of the :option:`METS` scale setter
below). With the CS Shower, you can instead specify your own
resummation scale also in such a case: Set ``CSS_RESPECT_Q2: true``
and use the third argument to specify your resummation scale as above.
.. note::
For all scales their squares have to be given.See
:ref:`Predefined scale tags` for some predefined scale tags.
More than three scales can be set as well to be subsequently used,
e.g. by different couplings, see :ref:`COUPLINGS`.
.. _Scale setters:
Scale setters
-------------
The scale setter options which are currently available are
:option:`VAR`
The variable scale setter is the simplest scale setter available. Scales
are simply specified by additional parameters in a form which is understood
by the internal interpreter, see :ref:`Interpreter`. If, for example the invariant
mass of the lepton pair in Drell-Yan production is the desired scale,
the corresponding setup reads
.. code-block:: yaml
SCALES: VAR{Abs2(p[2]+p[3])}
Renormalization and factorization scales can be chosen differently.
For example in Drell-Yan + jet production one could set
.. code-block:: yaml
SCALES: VAR{Abs2(p[2]+p[3])}{MPerp2(p[2]+p[3])}
:option:`FASTJET`
If `FastJet `_ is enabled by including
``--enable-fastjet=/path/to/fastjet`` in the ``configure`` options,
this scale setter can be used to set a scale based on jet-, rather
than parton-momenta.
The final state parton configuration is first clustered using
FastJet and resulting jet momenta are then added back to the list of
non strongly interacting particles. The numbering of momenta
therefore stays effectively the same as in standard Sherpa, except
that final state partons are replaced with jets, if applicable (a
parton might not pass the jet criteria and get "lost"). In
particular, the indices of the initial state partons and all EW
particles are uneffected. Jet momenta can then be accessed as
described in :ref:`Predefined scale tags` through the identifiers
``p[i]``, and the nodal values of the clustering sequence can be
used through ``MU_n2``. The syntax is
.. code-block:: yaml
SCALES: FASTJET[]{}
Therein the parameters of the jet algorithm to be used to define the
jets are given as a comma separated list of
* the jet algorithm ``A:kt,antikt,cambridge,siscone`` (default
``antikt``)
* phase space restrictions, i.e. ``PT:``, ``ET:``,
``Eta:``, ``Y:`` (otherwise unrestricted)
* radial parameter ``R:`` (default ``0.4``)
* f-parameter for Siscone ``f:`` (default ``0.75``)
* recombination scheme ``C:E,pt,pt2,Et,Et2,BIpt,BIpt2``
(default ``E``)
* b-tagging mode ``B:0,1,2`` (default ``0``)
This parameter, if specified different from its default 0, allows
to use b-tagged jets only, based on the parton-level constituents of the jets.
There are two options: With ``B:1`` both b and anti-b quarks are
counted equally towards b-jets, while for ``B:2`` they are added with a
relative sign as constituents, i.e. a jet containing b and anti-b is not tagged.
* scale setting mode ``M:0,1`` (default ``1``) It is possible to
specify multiple scale definition blocks, each enclosed in curly
brackets. The scale setting mode parameter then determines, how
those are interpreted: In the ``M:0`` case, they specify
factorisation, renormalisation and resummation scale separately in
that order. In the ``M:1`` case, the ``n`` given scales are used
to calculate a mean scale such that
:math:`\alpha_s^n(\mu_\text{mean})=\alpha_s(\mu_1)\dots\alpha_s(\mu_n)`
This scale is then used for factorisation, renormalisation and
resummation scale.
Consider the example of lepton pair production in association with jets. The
following scale setter
.. code-block:: yaml
SCALES: FASTJET[A:kt,PT:10,R:0.4,M:0]{sqrt(PPerp2(p[4])*PPerp2(p[5]))}
reconstructs jets using the kt-algorithm with R=0.4 and a minimum
transverse momentum of 10 GeV. The scale of all strong couplings is
then set to the geometric mean of the hardest and second hardest
jet. Note ``M:0``.
Similarly, in processes with multiple strong couplings, their
renormalisation scales can be set to different values, e.g.
.. code-block:: yaml
SCALES: FASTJET[A:kt,PT:10,R:0.4,M:1]{PPerp2(p[4])}{PPerp2(p[5])}
sets the scale of one strong coupling to the transverse momentum of
the hardest jet, and the scale of the second strong coupling to the
transverse momentum of second hardest jet. Note ``M:1`` in this
case.
The additional tags :samp:`{MU_22}` .. :samp:`{MU_n2}`
(n=2..njet+1), hold the nodal values of the jet clustering in
descending order.
Please note that currently this type of scale setting can only be done within
the process block (:ref:`Processes`) and not within the (me) section.
..
.. :option:`QCD`
The matrix element is clustered onto a core 2->2 configuration using a
k_T-type algorithm with recombination into on-shell partons.
Scales are defined as the minimum of the largest transverse momentum
during clustering and the lowest invariant mass in the core process.
:option:`METS`
The matrix element is clustered onto a core 2->2 configuration using
an inversion of current parton shower, cf. :ref:`SHOWER_GENERATOR`,
recombining (n+1) particles into n on-shell particles. Their
corresponding flavours are determined using run-time information
from the matrix element generator. It defines the three tags
``MU_F2``, ``MU_R2`` and ``MU_Q2`` whose values are assigned through
this clustering procedure. While ``MU_F2`` and ``MU_Q2`` are defined
as the lowest invariant mass or negative virtuality in the core
process (for core interactions which are pure QCD processes scales
are set to the maximum transverse mass squared of the outgoing
particles), ``MU_R2`` is determined using this core scale and the
individual clustering scales such that
.. math::
\alpha_s(\mu_{R2})^{n+k} = \alpha_s(\text{core}-\text{scale})^k \alpha_s(kt_1) \dots \alpha_s(kt_n)
where k is the order in strong coupling of the core process and k is
the number of clusterings, kt_i are the relative transverse momenta
at each clustering.
The tags ``MU_F2``, ``MU_R2`` and ``MU_Q2`` can then be used
on equal footing with the tags of :ref:`Predefined scale tags` to define
the final scale.
``METS`` is the default scale scheme in Sherpa, since it is employed
for truncated shower merging, see :ref:`Multijet merged event
generation with Sherpa`, both at leading and next-to-leading
order. Thus, Sherpa's default is
.. code-block:: yaml
SCALES: METS{MU_F2}{MU_R2}{MU_Q2}
As the tags ``MU_F2``, ``MU_R2`` and ``MU_Q2`` are predefined by the
``METS`` scale setter, they may be omitted, i.e.
.. code-block:: yaml
SCALES: METS
leads to an identical scale definition.
The ``METS`` scale setter comes in two variants: ``STRICT_METS`` and
``LOOSE_METS``. While the former employs the exact inverse of the
parton shower for the clustering procedure, and therefore is rather
time consuming for multiparton final state, the latter is a
simplified version and much faster. Giving ``METS`` as the scale
setter results in using ``LOOSE_METS`` for the integration and
``STRICT_METS`` during event generation. Giving either
``STRICT_METS`` or ``LOOSE_METS`` as the scale setter results in
using the respective one during both integration and event
generation.
Clusterings onto 2->n (n>2) configurations is possible, see
:ref:`METS scale setting with multiparton core processes`.
This scheme might be subject to changes to enable further classes of
processes for merging in the future and should therefore be seen
with care. Integration results might change slightly between
different Sherpa versions.
Occasionally, users might encounter the warning message
.. code-block:: console
METS_Scale_Setter::CalculateScale(): No CSS history for '' in % of calls. Set \hat{s}.
As long as the percentage quoted here is not too high, this does not pose
a serious problem. The warning occurs when - based on the current colour
configuration and matrix element information - no suitable clustering is
found by the algorithm. In such cases the scale is set to the invariant mass
of the partonic process.
.. _Custom scale implementation:
Custom scale implementation
---------------------------
When the flexibility of the :option:`VAR` scale setter above is not sufficient,
it is also possible to implement a completely custom scale scheme within Sherpa
as C++ class plugin. For details please refer to the :ref:`Customization`
section.
.. _Predefined scale tags:
Predefined scale tags
---------------------
There exist a few predefined tags to facilitate commonly used scale
choices or easily implement a user defined scale.
:option:`p[n]`
Access to the four momentum of the nth particle. The initial state
particles carry n=0 and n=1, the final state momenta start from
n=2. Their ordering is determined by Sherpa's internal particle
ordering and can be read e.g. from the process names displayed at
run time. Please note, that when building jets out of the final
state partons first, e.g. through the ``FASTJET`` scale setter,
these parton momenta will be replaced by the jet momenta ordered in
transverse momenta. For example the process u ub -> e- e+ G G will
have the electron and the positron at positions ``p[2]`` and
``p[3]`` and the gluons on postions ``p[4]`` and ``p[5]``. However,
when finding jets first, the electrons will still be at ``p[2]`` and
``p[3]`` while the harder jet will be at ``p[4]`` and the softer one
at ``p[5]``.
:option:`H_T2`
Square of the scalar sum of the transverse momenta of
all final state particles.
:option:`H_TM2`
Square of the scalar sum of the transverse energies of
all final state particles, i.e. contrary to ``H_T2`` ``H_TM2`` takes
particle masses into account.
:option:`H_TY2(,)`
Square of the scalar sum of the transverse momenta of all final state particles
weighted by their rapidity distance from the final state boost vector. Thus,
takes the form
.. code-block:: latex
H_T^{(Y)} = sum_i pT_i exp [ fac |y-yboost|^exp ]
Typical values to use would by ``0.3`` and ``1``.
:option:`H_Tp2`
Scale setter for lepton-pair production in association with jets only,
implements
.. code-block:: latex
H_T' = sqrt(m_ll^2 + pT(ll)^2) + sum_i pT_i (i not l)
:option:`DH_Tp2(,)`
Implements a version of ``H_Tp2`` which dresses charged particles first.
The parameter ```` can take the following values:
``Cone``, ``kt``, ``CA`` or ``antikt``, while ```` is
the respecitve algorithm's angular distance parameter.
:option:`TAU_B2`
Square of the beam thrust.
:option:`MU_F2, MU_R2, MU_Q2`
Tags holding the values of the factorisation, renormalisation scale and
resummation scale determined through backwards clustering in the
``METS`` scale setter.
:option:`MU_22, MU_32, ..., MU_n2`
Tags holding the nodal values of the jet clustering in the ``FASTJET``
scale setter, cf. :ref:`Scale setters`.
All of those objects can be operated upon by any operator/function known
to the :ref:`Interpreter`.
.. _Scale schemes for NLO calculations:
Scale schemes for NLO calculations
----------------------------------
For next-to-leading order calculations it must be guaranteed that the scale is
calculated separately for the real correction and the subtraction terms,
such that within the subtraction procedure the same amount is subtracted
and added back. Starting from version 1.2.2 this is the case for all
scale setters in Sherpa. Also, the definition of the scale must be
infrared safe w.r.t. to the radiation of an extra parton. Infrared safe
(for QCD-NLO calculations) are:
* any function of momenta of NOT strongly interacting particles
* sum of transverse quantities of all partons (e.g. ``H_T2``)
* any quantity refering to jets, constructed by an IR safe
jet algorithm, see below.
Not infrared safe are
* any function of momenta of specific partons
* for processes with hadrons in the initial state:
any quantity that depends on parton momenta along the beam axis,
including the initial state partons itself
Since the total number of partons is different for different pieces of
the NLO calculation any explicit reference to a parton momentum will
lead to an inconsistent result.
.. _Explicit scale variations:
Explicit scale variations
-------------------------
The factorisation and renormalisation scales in the fixed-order matrix
elements can be varied separately simply by introducing a prefactor
into the scale definition, e.g.
.. code-block:: yaml
SCALES: VAR{0.25*H_T2}{0.25*H_T2}
for setting both the renormalisation and factorisation scales to
H_T/2.
Similarly, the starting scale of the parton shower resummation in a
ME+PS merged sample can be varied using the METS scale setter's third
argument like:
.. code-block:: yaml
SCALES: METS{MU_F2}{MU_R2}{4.0*MU_Q2}
.. _METS scale setting with multiparton core processes:
METS scale setting with multiparton core processes
--------------------------------------------------
.. index:: CORE_SCALE
The METS scale setter stops clustering when no combination
is found that corresponds to a parton shower branching, or if
two subsequent branchings are unordered in terms of the parton shower
evolution parameter. The core scale of the remaining 2->n process then
needs to be defined. This is done by specifying a core scale through
.. code-block:: yaml
CORE_SCALE: {}{}{}
As always, for scale setters which define ``MU_F2``, ``MU_R2`` and
``MU_Q2`` the scale definition can be dropped. Possible core scale
setters are
:option:`VAR`
Variable core scale setter. Syntax is identical to variable scale setter.
:option:`QCD`
QCD core scale setter. Scales are set to harmonic mean of s, t and u. Only
useful for 2->2 cores as alternatives to the usual core scale of the METS
scale setter.
:option:`TTBar`
Core scale setter for processes involving top quarks. Implementation details
are described in Appendix C of :cite:`Hoeche2013mua`.
:option:`SingleTop`
Core scale setter for single-top production in association with one jet.
If the W is in the t-channel (s-channel), the squared scales are set to the
Mandelstam variables ``t=2*p[0]*p[2]`` (``t=2*p[0]*p[1]``).
.. _COUPLINGS:
COUPLINGS
=========
.. index:: COUPLINGS
Within Sherpa, strong and electroweak couplings can be computed at any scale
specified by a scale setter (cf. :ref:`SCALES`). The :option:`COUPLINGS` tag
links the argument of a running coupling to one of the respective scales.
This is better seen in an example. Assuming the following input
.. code-block:: yaml
SCALES: VAR{...}{PPerp2(p[2])}{Abs2(p[2]+p[3])}
COUPLINGS:
- "Alpha_QCD 1"
- "Alpha_QED 2"
Sherpa will compute any strong couplings at scale one,
i.e. ``PPerp2(p[2])`` and electroweak couplings at scale two,
i.e. ``Abs2(p[2]+p[3])``. Note that counting starts at zero.
.. _KFACTOR:
KFACTOR
=======
.. index:: KFACTOR
This parameter specifies how to evaluate potential K-factors in the hard
process. This is equivalent to the :option:`COUPLINGS` specification of Sherpa
versions prior to 1.2.2. Currently available options are
:option:`None`
No reweighting
:option:`VAR`
Couplings specified by an additional parameter in a form which is understood
by the internal interpreter, see :ref:`Interpreter`. The tags :kbd:`Alpha_QCD`
and :kbd:`Alpha_QED` serve as links to the built-in running coupling implementation.
If for example the process ``g g -> h g`` in effective theory is computed,
one could think of evaluating two powers of the strong coupling at the Higgs mass scale
and one power at the transverse momentum squared of the gluon.
Assuming the Higgs mass to be 120 GeV, the corresponding reweighting would read
.. code-block:: yaml
SCALES: VAR{...}{PPerp2(p[3])}
COUPLINGS: "Alpha_QCD 1"
KFACTOR: VAR{sqr(Alpha_QCD(sqr(120))/Alpha_QCD(MU_12))}
As can be seen from this example, scales are referred to as :kbd:`MU_*2`,
where :kbd:`**` is replaced with the appropriate number.
Note that counting starts at zero.
It is possible to implement a dedicated K-factor scheme within Sherpa.
For advice on this topic please contact the authors, :ref:`Authors`.
.. _YUKAWA_MASSES:
YUKAWA_MASSES
=============
.. index:: YUKAWA_MASSES
This parameter specifies whether the Yukawa couplings are evaluated
using running or fixed quark masses: ``YUKAWA_MASSES: Running`` is the
default since version 1.2.2 while ``YUKAWA_MASSES: Fixed`` was the
default until 1.2.1.
.. _Dipole subtraction:
Dipole subtraction
==================
.. index:: DIPOLES_ALPHA
.. index:: DIPOLES_KAPPA
.. index:: DIPOLES_NF_GSPLIT
.. index:: DIPOLES_AMIN
This list of parameters can be used to optimize the performance when
employing the Catani-Seymour dipole subtraction :cite:`Catani1996vz`
as implemented in Amegic :cite:`Gleisberg2007md`. The dipole
parameters are specified as subsettings to the ``DIPOLES`` setting,
like this:
.. code-block:: yaml
DIPOLES:
ALPHA:
NF_GSPLIT:
# other dipole settings ...
The following parameters can be customised:
:option:`LPHA`
Specifies a dipole cutoff in the nonsingular region :cite:`Nagy2003tz`.
Changing this parameter shifts contributions from the subtracted real
correction piece (RS) to the piece including integrated dipole terms (I),
while their sum remains constant. This parameter can be used to optimize
the integration performance of the individual pieces.
Also the average calculation time for the subtracted real correction
is reduced with smaller choices of "ALPHA" due to the (on average)
reduced number of contributing dipole terms. For most processes
a reasonable choice is between 0.01 and 1 (default). See also
:ref:`Choosing DIPOLES ALPHA`
:option:`AMIN`
Specifies the cutoff of real correction terms in the infrared reagion
to avoid numerical problems with the subtraction. The default is 1.e-8.
:option:`NF_GSPLIT`
Specifies the number of quark flavours that are produced from
gluon splittings. This number must be at least the number of massless
flavours (default). If this number is larger than the number of massless
quarks the massive dipole subtraction :cite:`Catani2002hc` is employed.
:option:`KAPPA`
Specifies the kappa-parameter in the massive dipole subtraction formalism
:cite:`Catani2002hc`. The default is 2.0/3.0.
*