Question: In statistics used in particle physics, one often says that whatever is not the parameter of interest, is a nuisance parameter.
For example, wikipedia :
<https://en.wikipedia.org/wiki/Nuisance_parameter>
" a nuisance parameter is any parameter which is not of immediate interest but which must be accounted for in the analysis of those parameters which are of interest."

This note describes the formalism used in particle physics :
<https://arxiv.org/pdf/1007.1727.pdf>

Let's consider the typical likelihood at particle physics experiments
$L=\sigma\times efficiency \times L \times Pdf\_{signal} + n\_b \times Pdf\_{bkg}$

where $\sigma$ (which is a cross-section and has absolutely no relationship with dispersion of a gaussian) is the parameter of interest, $efficiency$ is the efficiency of signal (taken from simulation), $L$ is the luminosity, $n\_b$ is the number of background.

Are signal efficiency of selection and luminosity, nuisance parameters in a particle physics statistics treatment ?
If not, why, since they seem to fullfill the criteria of the sentence "it is not a parameter of interest".

Answer: 
In the first row of your table, you have superscripts $c, c, d, b, b, a$ for compositions $A, B, C, D, E, F,$ respectively.

The superscripts mean that $A$ and $B$ are not
significant from each other in a statistical sense.
Also, that $D$ and $E$ are not significantly different. However, significant differences were
found between $A$ and $C,$ between $B$ and $C,$
between $E$ and $F$ (among other differences).

More generally, it is important to understand that "lack of
significant difference" is not the same thing as "exact equality".

In a similar analysis of this kind with $A$ significantly different from $C,$ you may have $B$ with an intermediate value between $A$ and $C$ and
yet not be able to decide from the data whether
to "group" $B$ with $A,$ $B$ with $C,$ or neither.
That's why some of the rows in your table have
items with double (indecisive) superscripts.
Each subscript letter that is different for each parameter shows a significant difference, for example here: in the first row: there is no significant difference between A and B, nor is there a difference between D and E, but:
A and B are different from other groups, and F is different from all groups, and so on.