Mryntu

It sounds like very poor typography, but I am simply looking to shift a wrapfig picture up, but in particular so it would ever so slightly go above the start of the paragraph and into the subsection line. See the attached picture below.

I provide an MWE for the picture and surrounding text (I have simply copied a load of bits from my preamble of my larger document! Apologies for the useless parts in there!).
I expect nothing in my preamble will interrupt this. I have tried putting vspace in both the wrap figure, the tikzpicture and before the entire figure in braces. Even with the abnormal vspace-25cm, it seems to only take the picture up to the very start of the paragraph and section - I want to slightly break this bounding box. Any suggestions would be welcomed.

documentclass[12pt,a4paper,twoside]report
usepackagegraphicx
usepackagefloat
usepackagecaption
usepackagesubcaption
usepackagewrapfig
usepackageamsmath
usepackageamssymb
usepackagephysics
usepackagecaption

usepackagetikz
usetikzlibrarydecorations.markings
usetikzlibraryshapes,arrows
usetikzlibrarycalc
usetikzlibraryarrows.meta
usetikzlibraryintersections,through,backgrounds
usepackagelipsum 


usepackage[a4paper, left=2.5cm, right=2.5cm,
top=2.5cm, bottom=2.5cm]geometry 


begindocument

sectionMotivation and Notation

beginwrapfigurer0textwidth
 vspace-25cm
 begintikzpicture[rotate=90,scale=1.5]
 vspace-5cm
 hspace0.3cm
 foreach a/l in 0/$x_1$,60/$x_0$,120/$x_5$,180/$x_4$,240/$x_3$,300/$x_2$ %a is the angle variable
 draw[line width=.7pt,black,fill=black] (a:1.5cm) coordinate (aa) circle (2pt); 
 node[anchor=202.5+a] at ($(aa)+(a+22.5:3pt)$) l;
 
 draw [line width=.4pt,black] (a0) -- (a60) -- (a120) -- (a180) -- (a240) -- (a300) -- cycle;


 node [label=[red,xshift=0.1cm, yshift=0.0cm]$p_2$] (m1) at ($(a0)!0.65!(a300)$);
 draw[->] (a0) -- (m1);

 node [label=[red,xshift=0.35cm, yshift=-0.2cm]$p_3$] (m2) at ($(a300)!0.65!(a240)$);
 draw[->] (a300) -- (m2);

 node [label=[red,xshift=0.5cm, yshift=-0.5cm]$p_4$] (m3) at ($(a240)!0.65!(a180)$);
 draw[->] (a240) -- (m3);

 node [label=[red,xshift=0.15cm, yshift=-0.8cm]$p_5$] (m4) at ($(a180)!0.65!(a120)$);
 draw[->] (a180) -- (m4);

 node [label=[red,xshift=-0.35cm, yshift=-0.6cm]$p_6$] (m5) at ($(a120)!0.65!(a60)$);
 draw[->] (a120) -- (m5);

 node [label=[red,xshift=-0.3cm, yshift=-0.3cm]$p_1$] (m6) at ($(a60)!0.65!(a0)$);
 draw[->] (a60) -- (m6);
 endtikzpicture
 setlengthbelowcaptionskip-5pt
 captionsetupjustification=centering,margin=5cm
 vspace*-5cm
 hspace0.5cm
 captionA $n$ = 6 representation of $p$-conservation, where the momenta $p^mu$ form a closed contour in dual space.
 labelfig:Diagram_Mom_Con
endwrapfigure

lipsum[1-4] 





enddocument

The easiest to move a wrapfig up is to change intextsep, as it is used also at the bottom, you must insert a rule there to compensate. The drawback is that it moves the text at the side down. One can use vspace-2cm there to compensate.

documentclassarticle
usepackagewrapfig,graphicx,tikz,caption
usetikzlibrarycalc
begindocument
sectionMotivation and Notation

setlengthintextsep-3cm
beginwrapfigurer0textwidth
 begintikzpicture[rotate=90,scale=1.5]
 foreach a/l in 0/$x_1$,60/$x_0$,120/$x_5$,180/$x_4$,240/$x_3$,300/$x_2$ %a is the angle variable
 draw[line width=.7pt,black,fill=black] (a:1.5cm) coordinate (aa) circle (2pt);
 node[anchor=202.5+a] at ($(aa)+(a+22.5:3pt)$) l;
 
 draw [line width=.4pt,black] (a0) -- (a60) -- (a120) -- (a180) -- (a240) -- (a300) -- cycle;


 node [label=[red,xshift=0.1cm, yshift=0.0cm]$p_2$] (m1) at ($(a0)!0.65!(a300)$);
 draw[->] (a0) -- (m1);

 node [label=[red,xshift=0.35cm, yshift=-0.2cm]$p_3$] (m2) at ($(a300)!0.65!(a240)$);
 draw[->] (a300) -- (m2);

 node [label=[red,xshift=0.5cm, yshift=-0.5cm]$p_4$] (m3) at ($(a240)!0.65!(a180)$);
 draw[->] (a240) -- (m3);

 node [label=[red,xshift=0.15cm, yshift=-0.8cm]$p_5$] (m4) at ($(a180)!0.65!(a120)$);
 draw[->] (a180) -- (m4);

 node [label=[red,xshift=-0.35cm, yshift=-0.6cm]$p_6$] (m5) at ($(a120)!0.65!(a60)$);
 draw[->] (a120) -- (m5);

 node [label=[red,xshift=-0.3cm, yshift=-0.3cm]$p_1$] (m6) at ($(a60)!0.65!(a0)$);
 draw[->] (a60) -- (m6);
 endtikzpicture
 setlengthbelowcaptionskip-5pt
 captionsetupjustification=centering,margin=5cm
 captionA $n$ = 6 representation of $p$-conservation, where the momenta $p^mu$ form a closed contour in dual space.
 labelfig:Diagram_Mom_Con
 rule0pt3.0cm
endwrapfigure

We have described the spinor-helicity formalism as a natural way to encode massless scattering amplitudes. However, we have to impose momentum conservation by hand, since spinor-helicity is derived from a Lorentz invariant foundation, which can be thought of as a subgroup of Poincar'e invariance. The 10-dimensional Poincar'e group includes translations (3 spatial and 1 time) as well as the 6-dimensional Lorentz group, consisting of 3 boosts and 3 rotations. Hence, spinor variables are not invariant under spatial translations, and momentum is not automatically conserved footnotemark.
Since all scattering processes naturally conserve momentum, we would like to have a formalism where both the on-shell massless condition, $p^2 =0$ and momentum conservation, $sum p^mu = 0$ are manifest. This comes in the form of momentum twistors, developed by Hodges as an extension of Penrose's twistor geometry.

footnotetextThis is a well-known consequence of Noether's Theorem. See REFS REMOVED For more explicit details.

%
par
We take inspiration by considering a different geometrical interpretation of momentum conservation. We start by drawing an $n$-sided polygon in dual space, as shown by Figure reffig:Diagram_Mom_Con.
There are two ways to consider defining the polygon; either through the edges or the vertices. Considering the edges, we obtain the traditional statement of momentum conservation; the $n$ edges form a closed contour, which corresponds to the net sum of momenta equalling zero, and no new intuition has been obtained.
par
Let us now define the polygon through the vertices, using a new set of dual coordinates $x_i$ where $i= 1,dots,n$. To ensure our contour is closed, we demand the periodic boundary $x_0 equiv x_n$. The momenta in dual space may now be defined as the difference of these dual coordinates


enddocument

Another possiblity is to use a raisebox and to hide the height from the wrapfig. You must then also set the baseline of the tikzpicture to the north.

documentclassarticle
usepackagewrapfig,graphicx,tikz,caption,lipsum
usetikzlibrarycalc
begindocument
sectionMotivation and Notation

beginwrapfigurer0textwidth
raisebox1cm[0pt]%
begintikzpicture[rotate=90,scale=1.5,baseline=(current bounding box.north)]
 foreach a/l in 0/$x_1$,60/$x_0$,120/$x_5$,180/$x_4$,240/$x_3$,300/$x_2$ %a is the angle variable
 draw[line width=.7pt,black,fill=black] (a:1.5cm) coordinate (aa) circle (2pt);
 node[anchor=202.5+a] at ($(aa)+(a+22.5:3pt)$) l;
 
 draw [line width=.4pt,black] (a0) -- (a60) -- (a120) -- (a180) -- (a240) -- (a300) -- cycle;


 node [label=[red,xshift=0.1cm, yshift=0.0cm]$p_2$] (m1) at ($(a0)!0.65!(a300)$);
 draw[->] (a0) -- (m1);

 node [label=[red,xshift=0.35cm, yshift=-0.2cm]$p_3$] (m2) at ($(a300)!0.65!(a240)$);
 draw[->] (a300) -- (m2);

 node [label=[red,xshift=0.5cm, yshift=-0.5cm]$p_4$] (m3) at ($(a240)!0.65!(a180)$);
 draw[->] (a240) -- (m3);

 node [label=[red,xshift=0.15cm, yshift=-0.8cm]$p_5$] (m4) at ($(a180)!0.65!(a120)$);
 draw[->] (a180) -- (m4);

 node [label=[red,xshift=-0.35cm, yshift=-0.6cm]$p_6$] (m5) at ($(a120)!0.65!(a60)$);
 draw[->] (a120) -- (m5);

 node [label=[red,xshift=-0.3cm, yshift=-0.3cm]$p_1$] (m6) at ($(a60)!0.65!(a0)$);
 draw[->] (a60) -- (m6);
 endtikzpicture
captionbbb
endwrapfigure
We have described the spinor-helicity formalism as a natural way to encode massless scattering amplitudes. However, we have to impose momentum conservation by hand, since spinor-helicity is derived from a Lorentz invariant foundation, which can be thought of as a subgroup of Poincar'e invariance. The 10-dimensional Poincar'e group includes translations (3 spatial and 1 time) as well as the 6-dimensional Lorentz group, consisting of 3 boosts and 3 rotations. Hence, spinor variables are not invariant under spatial translations, and momentum is not automatically conserved footnotemark.
Since all scattering processes naturally conserve momentum, we would like to have a formalism where both the on-shell massless condition, $p^2 =0$ and momentum conservation, $sum p^mu = 0$ are manifest. This comes in the form of momentum twistors, developed by Hodges as an extension of Penrose's twistor geometry.

footnotetextThis is a well-known consequence of Noether's Theorem. See REFS REMOVED For more explicit details.

%
par
We take inspiration by considering a different geometrical interpretation of momentum conservation. We start by drawing an $n$-sided polygon in dual space, as shown by Figure reffig:Diagram_Mom_Con.
There are two ways to consider defining the polygon; either through the edges or the vertices. Considering the edges, we obtain the traditional statement of momentum conservation; the $n$ edges form a closed contour, which corresponds to the net sum of momenta equalling zero, and no new intuition has been obtained.
par
Let us now define the polygon through the vertices, using a new set of dual coordinates $x_i$ where $i= 1,dots,n$. To ensure our contour is closed, we demand the periodic boundary $x_0 equiv x_n$. The momenta in dual space may now be defined as the difference of these dual coordinates


enddocument

The conceivably easiest way to move the tikzpicture up is to adjust its bounding box. All I did was to add

path[use as bounding box] (-3,-3) rectangle (3,2);

(and to do the rotate in a scope because otherwise it is confusing) to get

documentclass[12pt,a4paper,twoside]report
usepackagefloat
usepackagecaption
usepackagesubcaption
usepackagewrapfig
usepackageamsmath
usepackageamssymb
usepackagecaption

usepackagetikz
usetikzlibrarydecorations.markings
usetikzlibraryshapes,arrows
usetikzlibrarycalc
usetikzlibraryarrows.meta
usetikzlibraryintersections,through,backgrounds
usepackagelipsum 


usepackage[a4paper, left=2.5cm, right=2.5cm,
top=2.5cm, bottom=2.5cm]geometry 


begindocument

sectionMotivation and Notation

beginwrapfigurer0textwidth
 begintikzpicture
 path[use as bounding box] (-3,-3) rectangle (3,2);
 beginscope[rotate=90,scale=1.5]
 foreach a/l in 0/$x_1$,60/$x_0$,120/$x_5$,180/$x_4$,240/$x_3$,300/$x_2$ %a is the angle variable
 draw[line width=.7pt,black,fill=black] (a:1.5cm) coordinate (aa) circle (2pt); 
 node[anchor=202.5+a] at ($(aa)+(a+22.5:3pt)$) l;
 
 draw [line width=.4pt,black] (a0) -- (a60) -- (a120) -- (a180) -- (a240) -- (a300) -- cycle;


 node [label=[red,xshift=0.1cm, yshift=0.0cm]$p_2$] (m1) at ($(a0)!0.65!(a300)$);
 draw[->] (a0) -- (m1);

 node [label=[red,xshift=0.35cm, yshift=-0.2cm]$p_3$] (m2) at ($(a300)!0.65!(a240)$);
 draw[->] (a300) -- (m2);

 node [label=[red,xshift=0.5cm, yshift=-0.5cm]$p_4$] (m3) at ($(a240)!0.65!(a180)$);
 draw[->] (a240) -- (m3);

 node [label=[red,xshift=0.15cm, yshift=-0.8cm]$p_5$] (m4) at ($(a180)!0.65!(a120)$);
 draw[->] (a180) -- (m4);

 node [label=[red,xshift=-0.35cm, yshift=-0.6cm]$p_6$] (m5) at ($(a120)!0.65!(a60)$);
 draw[->] (a120) -- (m5);

 node [label=[red,xshift=-0.3cm, yshift=-0.3cm]$p_1$] (m6) at ($(a60)!0.65!(a0)$);
 draw[->] (a60) -- (m6);
 endscope
 endtikzpicture
 setlengthbelowcaptionskip-5pt
 captionsetupjustification=centering,margin=5cm
 vspace*-5cm
 hspace0.5cm
 captionA $n$ = 6 representation of $p$-conservation, where the momenta $p^mu$ form a closed contour in dual space.
 labelfig:Diagram_Mom_Con
endwrapfigure

lipsum[1-4] 

enddocument

Or with

 path[use as bounding box] (-3,-3) rectangle (3,1);