Tags and keywords
Sometimes Wikipedia uses the spelling 'flavor' and sometimes 'flavour'; in this trail 'flavour' is used throughout.
Before addressing the concrete quark types, the following snippet provides some more specific information about what was until now the lepton-specific ValueType
It seems that this concept of 'generation' in fact applies equally to quarks and leptons, both of which are elementary particles, spin-1/2 particles, and fermions. A new intermediate abstraction
ElementaryFermion has been introduced that extends
SpinHalfParticle (which is always a
ElementaryParticle. We'll see later how this has now also been added to the relevant lepton and fermion diagrams.
Rather than using a verbose name like 'ElementaryFermionGeneration' there is now just ValueType
Generation, but it is now owned by the block
ElementaryFermion as indicated by the containment operator.
Concerning including data on each
elementaryCharge (which is ultimately a SysML Real) a tool issue has to be addressed. For quarks these are always fractions, but (unlike with symbolic alegbra) one can't enter fractions like 2/3 into a Real in the MagicDraw SysML Plugin or Cameo Systems Modeler® tools. Rather than repeating numbers like '0.66666666 ... ' everywhere, it is calculated using SysML Parametrics.
chargeFraction:Fraction is used, where
Fraction is a structured ValueType with Integer attributes 'num' (for numerator) and 'den' (for denominator). The
/elementaryCharge is redefined as derived, and bound via a usage of the ConstraintBlock
QuarkElementaryCharge to the fractional parts, with the constraint equation
out = num/den.
The charge fractions are specified using InstanceSpecifications with the slightly HACKED yet effective names '+2/3', '-1/3', '-2/3', '+1/3' (the names play no roles in the actual calculations).
For example, when the calculation is run in Cameo Systems Modeler® or Cameo Simulation Toolkit® for charge fraction +2/3 and with the built-in maths engine (which handles the conversion from Integer to a floating point type automatically), the result is 0.6666666666666666. That might not be quite accurate enough for professional particle physics calculations (we don't want protons with charge 0.9999999...), but note one can delegate to many external maths engines such as Mathematica.
The next "matter" (oops, that pun again) is how to handle the antiparticles. The language used throughout the Wikipedia articles on particles is a bit inconsistent concerning this. This snippet is clear:
In this SysML model this is handled consistently (as done before before for leptons) by using intermediate abstractions that encapsulate aspects common to both the «matter» and «antimatter» variants within each flavour. For example, the block
AbstractUp has redefined value properties
flavour = up,
generation = 1st, and
isStable = true. The specific «matter» «particle»
isAntiMatter = false and
chargeFraction = +2/3, whereas the counterpart «antimatter» «particle»
isAntiMatter = true and
chargeFraction = -2/3.
As earlier in the trail, the symmetric anti-particle relationship is handled in two separate ways. There is an «antiparticle» Dependency from each «matter» particle block to its corresponding «antimatter» block, and vice-versa; and there is an Association
Anti with symmetrically redefined property ends
antiParticle. One need not, of course, show all of this verbose information on every final presentation diagram.
This minor tool limitation means the symbols could not be entered for most of the «antimatter» variants:
This slide diagram also illustrates a nice short-cut version of Parsing Analysis you can use when a document has lots of data in tables. There is a «document» Wikipedia:Quark:Table of properties, which refers to a link within the page. A SysML Trace has been drawn (shown in very faint purple) from each of the redefined
chargeFraction value properties to indicate that the value has not just been plucked out of the air, and is traceable to a domain source document. You can then list the computed 'tracedFrom' elements on the source «document» symbol.
Finally, remember that:
So these snippets have not yet been treated in detail:
Interpreting 'up and down quarks are generally stable' by redefining
isStable = true in
AbstractDown may be a bit dangerous, but will have to do for now until further sourced information comes along.
If you are a physicist following this, you may have noticed that there are many other quantum numbers and properties of quarks that don't appear here yet. There is no obligation to do everything at once. When using the Webel Parsing Analysis recipe for SysML® we proceed step-by-step collecting information, subsets of which can then be exposed in dedicated presentation diagrams according to the intended audience.