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ファインマンダイアグラム千本ノック in Tikz-Feynhand

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誤り・質問等はコメントへご遠慮なくお願いします。

時間の向きは左から右、掲載内容はグリフィス 素粒子物理学(丸善出版)2章に従います。ゼミの担当範囲のみ。適宜追加します。

電磁相互作用

η対消滅

\begin{equation*}
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex(upper)at(0,1);
                \vertex(lower)at(0,0);
                \propag[fer]($(upper)+(150:1)$)to[edge label=$u$](upper);
                \propag[anti fermion]($(lower)+(-150:1)$)to[edge label=$u$](lower);
                \propag[fer](upper)to(lower);
                \propag[photon](upper)to++(30:1);
                \propag[photon](lower)to++(-30:1);
            \end{feynhand}
        \end{tikzpicture}
    }}
    +\cdots
\end{equation*}

e^+ e^- -> µ^+ µ^-

\begin{tikzpicture}
        \begin{feynhand}
            \vertex (left) at (0,0);
            \vertex (right) at (1,0);
            \propag [fermion] ($(left)+(120:1)$) to [edge label=$e^-$] (left);
            \propag [anti fermion] (left)++(-120:1) to [edge label=$e^+$] (left);
            \propag [photon] (left) to [edge label=$\gamma$] (right);
            \propag [fer] (right) to [edge label=$\mu^-$] ++(60:1);
            \propag [anti fermion] (right) to [edge label=$\mu^+$] ++(-60:1);
        \end{feynhand}
    \end{tikzpicture}

π^0 -> 2γ

\begin{tikzpicture}
        \begin{feynhand}
            \vertex(upper)at(0,1);
            \vertex(lower)at(0,0);
            \propag[fer]($(upper)+(150:1)$)to[edge label=$u$](upper);
            \propag[anti fermion]($(lower)+(-150:1)$)to[edge label=$u$](lower);
            \propag[fer](upper)to(lower);
            \propag[photon](upper)to++(30:1);
            \propag[photon](lower)to++(-30:1);
        \end{feynhand}
    \end{tikzpicture}

弱い相互作用

ニュートリノ・電子散乱

\begin{tikzpicture}
        \begin{feynhand}
            \vertex (upper) at (0,1);
            \vertex (lower) at (0,0);
            \propag [boson] (upper) to [edge label=$Z$] (lower);
            \propag [fermion] ($(150:1)+(upper)$) to [edge label=$\nu_\mu$] (upper);
            \propag [fermion] (upper) to [edge label=$\nu_\mu$] ++(30:1);
            \propag [fermion] ($(-150:1)+(lower)$) to [edge label=$e$] (lower);
            \propag [fermion] (lower) to [edge label=$e$] ++(-30:1);
        \end{feynhand}
\end{tikzpicture}

ニュートリノ・陽子散乱

\begin{tikzpicture}
            \begin{feynhand}
                \vertex (upper) at (0,1);
                \vertex (lower) at (0,0);
                \vertex [particle] (p1) at ($(lower)+(-150:1)$) {$(p)$};
                \vertex [particle] (p2) at ($(lower)+(-30:1)$) {$(p)$};
                \propag [boson] (upper) to [edge label=$Z$] (lower);
                \propag [fermion] ($(150:1)+(upper)$) to [edge label=$\nu_\mu$] (upper);
                \propag [fermion] (upper) to [edge label=$\nu_\mu$] ++(30:1);
                \propag [fermion] (p1) to [edge label=$d$] (lower);
                \propag [fermion] (lower) to [edge label=$d$] (p2);
                \propag [fermion] (p1) to [edge label=$u$] (p2);
                \propag [fermion] (p1) to [quarter right, looseness=0.5, edge label=$u$] (p2);
            \end{feynhand}
\end{tikzpicture}
クォークの閉じ込めに関わるグルーオン交換は以降省略

Coulombの法則 (最低次)

\begin{equation*}
    \vcenter{\hbox{
        \begin{tikzpicture}\begin{feynhand}
            \vertex (upper) at (0,1);
            \vertex (lower) at (0,0);
            \vertex[particle](nw)at($(upper)+(150:1)$){$e^-$};
            \vertex[particle](ne)at($(upper)+(30:1)$){$e^-$};
            \vertex[particle](sw)at($(lower)+(-150:1)$){$e^-$};
            \vertex[particle](se)at($(lower)+(-30:1)$){$e^-$};
            \propag [photon] (upper) to [edge label=$\gamma$] (lower);
            \propag [fermion] (nw) to [edge label'=$k$] (upper);
            \propag [fermion] (upper) to [edge label=$k'$, near end] (ne);
            \propag [fermion] (sw) to [edge label=$p$] (lower);
            \propag [fermion] (lower) to [edge label=$p'$] (se);
        \end{feynhand}\end{tikzpicture}
    }}
    +
    \vcenter{\hbox{
        \begin{tikzpicture}\begin{feynhand}
            \vertex (upper) at (0,1);
            \vertex (lower) at (0,0);
            \vertex[particle](nw)at($(upper)+(150:1)$){$e^-$};
            \vertex[particle](ne)at($(upper)+(30:1)$){$e^-$};
            \vertex[particle](sw)at($(lower)+(-150:1)$){$e^-$};
            \vertex[particle](se)at($(lower)+(-30:1)$){$e^-$};
            \propag [boson] (upper) to [edge label=$Z$] (lower);
            \propag [fermion] (nw) to [edge label'=$k$] (upper);
            \propag [fermion] (upper) to [edge label=$k'$, near end] (ne);
            \propag [fermion] (sw) to [edge label=$p$] (lower);
            \propag [fermion] (lower) to [edge label=$p'$] (se);
        \end{feynhand}\end{tikzpicture}
    }}
\end{equation*}

µ^- 崩壊

\begin{equation*}
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex (upper) at (0,1);
                \vertex (lower) at (0,0);
                \propag [fermion] (upper)++(150:1) to [edge label=$\nu_e$] (upper);
                \propag [fermion] (upper) to [edge label=$e$] ++(30:1);
                \propag [chabos] (lower) to [edge label'=$W^-$] (upper);
                \propag [fermion] (lower)++(-150:1) to [edge label=$\mu$] (lower);
                \propag [fermion] (lower) to [edge label=$\nu_\mu$] ++(-30:1);
            \end{feynhand}
        \end{tikzpicture}
    }}
    =
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex (upper) at (0,1);
                \vertex (lower) at (0,0);
                \propag [fermion] (upper)++(-30:1) to [edge label'=$\nu_e$, near start] (upper);
                \propag [fermion] (upper) to [edge label=$e$] ++(30:1);
                \propag [chabos] (lower) to [edge label=$W^-$] (upper);
                \propag [fermion] (lower)++(-150:1) to [edge label=$\mu$] (lower);
                \propag [fermion] (lower) to [edge label=$\nu_\mu$] ++(-30:1);
            \end{feynhand}
        \end{tikzpicture}
    }}
    =
    i\mathcal{M}(\mu^-\to e^-+\nu_\mu+\bar{\nu}_e).
\end{equation*}

d + ν_e -> u + e

\begin{tikzpicture}
            \begin{feynhand}
                \vertex (upper) at (0,1);
                \vertex (lower) at (0,0);
                \propag [fermion] (upper)++(150:1) to [edge label=$\nu_e$] (upper);
                \propag [fermion] (upper) to [edge label=$e$] ++(30:1);
                \propag [chabos] (lower) to [edge label'=$W^-$] (upper);
                \propag [fermion] (lower)++(-150:1) to [edge label=$d$] (lower);
                \propag [fermion] (lower) to [edge label=$u$] ++(-30:1);
            \end{feynhand}
        \end{tikzpicture}

π^- -> µ^-

\begin{tikzpicture}
            \begin{feynhand}
                \vertex[particle] (left) at (0,0);
                \node[anchor=east]at(left){$(\pi^-)$};
                \vertex (right) at (1,0);
                \propag [fermion] ($(left)+(-120:1)$) to [edge label'=$d$, near start] (left);
                \propag [fer] (left) to [edge label'=$u$, near end] ($(left)+(120:1)$);
                \propag [chabos] (left) to [edge label=$W^-$] (right);
                \propag [fer] (right) to [edge label=$\mu$] ++(60:1);
                \propag [anti fermion] (right) to [edge label=$\nu_\mu$] ++(-60:1);
            \end{feynhand}
        \end{tikzpicture}

β崩壊

\begin{tikzpicture}
            \begin{feynhand}
                \vertex (upper) at (0,1);
                \vertex (lower) at (0,0);
                \vertex [particle] (p1) at ($(lower)+(-150:1)$) {$(n)$};
                \vertex [particle] (p2) at ($(lower)+(-30:1)$) {$(p)$};
                \propag [chabos] (lower) to [edge label=$W^-$] (upper);
                \propag [fermion] ($(-30:1)+(upper)$) to [edge label'=$\nu_e$] (upper);
                \propag [fermion] (upper) to [edge label=$e$] ++(30:1);
                \propag [fermion] (p1) to [edge label=$d$] (lower);
                \propag [fermion] (lower) to [edge label=$u$] (p2);
                \propag [fermion] (p1) to [edge label=$d$] (p2);
                \propag [fermion] (p1) to [quarter right, looseness=0.5, edge label=$u$] (p2);
            \end{feynhand}
        \end{tikzpicture}

∆^0 -> p (弱い相互作用)

\begin{tikzpicture}
            \begin{feynhand}
                \vertex (upper) at (0,1);
                \vertex (lower) at (0,0);
                \vertex [particle] (p1) at ($(lower)+(-150:1)$) {$(\Delta^0)$};
                \vertex [particle] (p2) at ($(lower)+(-30:1)$) {$(p)$};
                \propag [chabos] (lower) to [edge label=$W^-$] (upper);
                \propag [fermion] ($(-30:1)+(upper)$) to [edge label'=$u$] (upper);
                \propag [fermion] (upper) to [edge label=$d$] ++(30:1);
                \propag [fermion] (p1) to [edge label=$d$] (lower);
                \propag [fermion] (lower) to [edge label=$u$] (p2);
                \propag [fermion] (p1) to [edge label=$d$] (p2);
                \propag [fermion] (p1) to [quarter right, looseness=0.5, edge label=$u$] (p2);
            \end{feynhand}
        \end{tikzpicture}

W, Z, γどうしの結合

\begin{equation*}
    \begin{tikzpicture}
        \begin{feynhand}
            \vertex (center) at (0,0);
            \vertex [particle] (Z) at (0,1) {$Z$};
            \vertex [particle] (Win) at (-150:1) {$W^\pm$};
            \vertex [particle] (Wout) at (-30:1) {$W^\pm$};
            \propag [boson] (Z) to (center);
            \propag [boson] (center) to (Wout);
            \propag [boson] (Win) to (center);
        \end{feynhand}
    \end{tikzpicture}
    \qquad
    \begin{tikzpicture}
        \begin{feynhand}
            \vertex (center) at (0,0);
            \vertex[particle] (nw) at (135:1) {$W$};
            \vertex[particle] (ne) at (45:1) {$W$};
            \vertex[particle] (sw) at (-135:1) {$W$};
            \vertex[particle] (se) at (-45:1) {$W$};
            \propag [boson] (sw) to (center);
            \propag [boson] (se) to (center);
            \propag [boson] (center) to (nw);
            \propag [boson] (center) to (ne);
        \end{feynhand}
    \end{tikzpicture}
    \qquad
    \begin{tikzpicture}
        \begin{feynhand}
            \vertex (center) at (0,0);
            \vertex[particle] (nw) at (135:1) {$W$};
            \vertex[particle] (ne) at (45:1) {$Z$};
            \vertex[particle] (sw) at (-135:1) {$W$};
            \vertex[particle] (se) at (-45:1) {$Z$};
            \propag [boson] (sw) to (center);
            \propag [boson] (se) to (center);
            \propag [boson] (center) to (nw);
            \propag [boson] (center) to (ne);
        \end{feynhand}
    \end{tikzpicture}
\end{equation*}
\begin{equation*}
    \begin{tikzpicture}
        \begin{feynhand}
            \vertex (center) at (0,0);
            \vertex [particle] (Z) at (0,1) {$\gamma$};
            \vertex [particle] (Win) at (-150:1) {$W^\pm$};
            \vertex [particle] (Wout) at (-30:1) {$W^\pm$};
            \propag [photon] (Z) to (center);
            \propag [boson] (center) to (Wout);
            \propag [boson] (Win) to (center);
        \end{feynhand}
    \end{tikzpicture}
    \qquad
    \begin{tikzpicture}
        \begin{feynhand}
            \vertex (center) at (0,0);
            \vertex[particle] (nw) at (135:1) {$W$};
            \vertex[particle] (ne) at (45:1) {$\gamma$};
            \vertex[particle] (sw) at (-135:1) {$W$};
            \vertex[particle] (se) at (-45:1) {$Z$};
            \propag [boson] (sw) to (center);
            \propag [boson] (se) to (center);
            \propag [boson] (center) to (nw);
            \propag [photon] (center) to (ne);
        \end{feynhand}
    \end{tikzpicture}
    \qquad
    \begin{tikzpicture}
        \begin{feynhand}
            \vertex (center) at (0,0);
            \vertex[particle] (nw) at (135:1) {$W$};
            \vertex[particle] (ne) at (45:1) {$\gamma$};
            \vertex[particle] (sw) at (-135:1) {$W$};
            \vertex[particle] (se) at (-45:1) {$\gamma$};
            \propag [boson] (sw) to (center);
            \propag [photon] (se) to (center);
            \propag [boson] (center) to (nw);
            \propag [photon] (center) to (ne);
        \end{feynhand}
    \end{tikzpicture}
\end{equation*}

e^- e^+ -> W^- W^+

\begin{equation*}
    i\mathcal{M}(e^++e^-\to W^++W^-)
    =
    % photon
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex (left) at (0,0);
                \vertex (right) at (1,0);
                \vertex[particle](ep)at(-120:1){$e^+$};
                \vertex[particle](en)at(120:1){$e^-$};
                \vertex[particle](wp)at($(right)+(-60:1)$){$W^+$};
                \vertex[particle](wn)at($(right)+(60:1)$){$W^-$};
                \propag[fer](left)to(ep);
                \propag[fer](en)to(left);
                \propag[photon](left)to[edge label=$\gamma$](right);
                \propag[boson](right)to(wp);
                \propag[boson](right)to(wn);
            \end{feynhand}
        \end{tikzpicture}
    }}
    +
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex (left) at (0,0);
                \vertex (right) at (1,0);
                \vertex[particle](ep)at(-120:1){$e^+$};
                \vertex[particle](en)at(120:1){$e^-$};
                \vertex[particle](wp)at($(right)+(-60:1)$){$W^+$};
                \vertex[particle](wn)at($(right)+(60:1)$){$W^-$};
                \propag[fer](left)to(ep);
                \propag[fer](en)to(left);
                \propag[boson](left)to[edge label=$Z$](right);
                \propag[boson](right)to(wp);
                \propag[boson](right)to(wn);
            \end{feynhand}
        \end{tikzpicture}
    }}
\end{equation*}

Λ崩壊

\begin{equation*}
    64\%
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex(lower)at(0,0);
                \vertex(upper)at(0,1);
                \vertex[particle](lambda)at(-150:1){$\Lambda$};
                \vertex[particle](p)at(-30:1){$p^+$};
                \vertex[particle](pi)at($(upper)+(30:1)$){$\pi^-$};
                \propag[fer](lambda)to[edge label'=$u$](p);
                \propag[fer](lambda)to[quarter right, looseness=0.5, edge label'=$d$](p);
                \propag[fer](lambda)to[edge label=$s$](lower);
                \propag[fer](lower)to[edge label=$u$](p);
                \propag[chabos](lower)to[edge label=$W^-$](upper);
                \propag[fer](pi)to[quarter right, looseness=0.5, edge label'=$u$](upper);
                \propag[fer](upper)to[quarter right, looseness=0.5, edge label'=$d$](pi);
            \end{feynhand}
        \end{tikzpicture}
    }}
    +
    36\%
    \vcenter{\hbox{
        \begin{tikzpicture}\begin{feynhand}
            \vertex(left)at(-.5,0);
            \vertex(right)at(.5,0);
            \vertex(top)at(0,2);
            \vertex(center)at(0,1);
            \vertex[particle](lambda)at(-150:1.5){$\Lambda$};
            \vertex[particle](n)at(-30:1.5){$n$};
            \vertex[particle](uu)at(1,2){$u\bar{u}$};
            \vertex[particle](dd)at($(center)+(1,.5)$){$d\bar{d}$};
            \propag[fer](lambda)to[edge label'=$u$](n);
            \propag[fer](lambda)to[quarter right, looseness=0.5, edge label'=$d$](n);
            \propag[fer](lambda)to[edge label=$s$](left);
            \propag[fer](left)to[edge label'=$u$](right);
            \propag[fer](right)to[edge label=$d$](n);
            \propag[chabos](left)to[edge label=$W^-$](top);
            \propag[chabos](right)to[edge label'=$W^+$, near start](center);
            \propag[fer](top)to[quarter left](uu);
            \propag[fer](uu)to(top);
            \propag[fer](center)to(dd);
            \propag[fer](dd)to[quarter left](center);
        \end{feynhand}\end{tikzpicture}
    }}
\end{equation*}

Ξ^- -> Λ

\begin{tikzpicture}\begin{feynhand}
            \vertex(upper)at(0,1);
            \vertex(lower)at(0,0);
            \vertex[particle](s)at($(lower)+(-150:1)$){$\Xi^-$};
            \vertex[particle](pi)at($(upper)+(30:1)$){$\pi^-$};
            \vertex[particle](lambda)at($(lower)+(-30:1)$){$\Lambda$};
            \propag[fer](s)to[edge label=$s$](lower);
            \propag[chabos](lower)to[edge label=$W^-$](upper);
            \propag[fer](lower)to[edge label'=$u$](lambda);
            \propag[anti fermion](upper)to[quarter right, edge label'=$\bar{u}$](pi);
            \propag[fermion](upper)to[quarter left, edge label=$d$](pi);
        \end{feynhand}\end{tikzpicture}

∑^- -> n

\begin{tikzpicture}\begin{feynhand}
        \vertex(upper)at(0,1);
        \vertex(lower)at(0,0);
        \vertex[particle](sigma)at($(lower)+(-150:1)$){$\Sigma^-$};
        \vertex[particle](n)at($(lower)+(-30:1)$){$n$};
        \vertex[particle](pi)at($(upper)+(30:1)$){$\pi^-$};
        \propag[fer](sigma)to[edge label=$s$](lower);
        \propag[fer](lower)to[edge label'=$u$, near end](n);
        \propag[chabos](lower)to(upper);
        \propag[fermion](upper)to[quarter left, edge label=$d$](pi);
        \propag[anti fermion](upper)to[quarter right, edge label'=$\bar{u}$](pi);
    \end{feynhand}\end{tikzpicture}

u + anti ν_e -> d + e^+

\begin{tikzpicture}
        \begin{feynhand}
            \vertex(upper)at(0,1);
            \vertex(lower)at(0,0);
            \propag[fer]($(lower)+(-150:1)$)to[edge label=$u$](lower);
            \propag[anti fermion]($(upper)+(150:1)$) to[edge label=$\bar{\nu}_e$, near start](upper);
            \propag[chabos](upper)to(lower);
            \propag[fer](lower)to[edge label=$d$]++(-30:1);
            \propag[anti fermion](upper)to[edge label=$e^+$, near end]++(30:1);
        \end{feynhand}
    \end{tikzpicture}

Ξ^- -> Λ + π^-

\begin{tikzpicture}
        \begin{feynhand}
            \vertex(lower)at(0,0);
            \vertex(upper)at(0,1);
            \propag[fer]($(lower)+(-150:1)$)to[edge label=$s$](lower);
            \propag[chabos](lower)to(upper);
            \propag[fer](lower)to[edge label=$u$]++(-30:1);
            \propag[fer](upper)to[edge label=$d$]++(30:1);
            \propag[antfer](upper)to[edge label=$\bar{u}$]++(-30:1);
        \end{feynhand}
    \end{tikzpicture}

Ξ^0 -> p + π^-

\begin{tikzpicture}
        \begin{feynhand}
            \vertex(left)at(0,0);
            \vertex(lower)at(1,-1);
            \vertex(right)at(1,0);
            \vertex(upper)at(1,1);
            \vertex(xi)at($(left)+(-150:1)$){$\Xi^0$};
            \vertex(p)at($(right)+(-30:1)$){$p$};
            \vertex(pi)at($(upper)+(1,0)$){$\pi^-$};
            \propag[fer](xi)to[edge label=$s$](left);
            \propag[fer](left)to(right);
            \propag[fer](right)to[edge label=$d$](p);
            \propag[fer](xi)to[edge label'=$s$](lower);
            \propag[fer](lower)to[edge label'=$u$](p);
            \propag[chabos](right)to(lower);
            \propag[chabos](left)to(upper);
            \propag[fer](upper)to[half left, edge label=$d$](pi);
            \propag[antfer](upper)to[half right, edge label'=$\bar{u}$, near start](pi);
        \end{feynhand}
    \end{tikzpicture}

∑^- -> n

\begin{tikzpicture}
        \begin{feynhand}
            \vertex(lower)at(0,0);
            \vertex(upper)at(0,1);
            \propag[fer]($(lower)+(-150:1)$)to[edge label=$s$](lower);
            \propag[chabos](lower)to(upper);
            \propag[fer](lower)to[edge label=$u$]++(-30:1);
            \propag[fer](upper)to[edge label=$e$]++(30:1);
            \propag[antfer](upper)to[edge label=$\bar{\nu}_e$]++(-30:1);
        \end{feynhand}
    \end{tikzpicture}

強い相互作用

∆^0 -> p (強い相互作用)

\begin{tikzpicture}
            \begin{feynhand}
                % \vertex (top) at (0,1.5);
                \vertex (upper) at (0,1);
                \vertex (lower) at (0,0);
                \vertex [particle] (p1) at ($(lower)+(-150:1)$) {$(\Delta^0)$};
                \vertex [particle] (p2) at ($(lower)+(-30:1)$) {$(p)$};
                \vertex [particle] (pi) at ($(30:1)+(lower)$) {$(\pi^-)$};
                \propag [gluon] (lower) to (upper);
                \propag [fermion] (pi) to [edge label'=$u$, near start] (lower);
                \propag [fermion] (upper) to [edge label=$d$] (pi);
                \propag [fermion] (p1) to [edge label=$d$] (upper);
                \propag [fermion] (lower) to [edge label=$u$] (p2);
                \propag [fermion] (p1) to [edge label=$d$] (p2);
                \propag [fermion] (p1) to [quarter right, looseness=0.5, edge label=$u$] (p2);
            \end{feynhand}
        \end{tikzpicture}

∆^0 -> n

\begin{tikzpicture}
        \begin{feynhand}
            \vertex (upper) at (0,1);
            \vertex (lower) at (0,0);
            \vertex [particle] (p1) at ($(lower)+(-150:1)$) {$(\Delta^0)$};
            \vertex [particle] (p2) at ($(lower)+(-30:1)$) {$(n)$};
            \vertex [particle] (pi) at ($(30:1)+(lower)$) {$(\pi^0)$};
            \propag [gluon] (lower) to (upper);
            \propag [fermion] (pi) to [edge label'=$d$, near start] (lower);
            \propag [fermion] (upper) to [edge label=$d$] (pi);
            \propag [fermion] (p1) to [edge label=$d$] (upper);
            \propag [fermion] (lower) to [edge label=$d$] (p2);
            \propag [fermion] (p1) to [edge label=$d$] (p2);
            \propag [fermion] (p1) to [quarter right, looseness=0.5, edge label=$u$] (p2);
        \end{feynhand}
    \end{tikzpicture}

φ -> 2K

\begin{tikzpicture}\begin{feynhand}
            \vertex[particle](phi)at(-1.5,0){$\phi$};
            \vertex(nw)at(-.5,.5);
            \vertex(ne)at(.5,.5);
            \vertex(sw)at(-.5,-.5);
            \vertex(se)at(.5,-.5);
            \vertex[particle](kn)at(1.5,1){$K^-$};
            \vertex[particle](kp)at(1.5,-1){$K^+$};
            \propag[fer](phi)to[edge label=$s$](nw);
            \propag[anti fermion](phi)to[edge label'=$s$](sw);
            \propag[gluon](nw)to(ne);
            \propag[gluon](sw)to(se);
            \propag[fer](ne)to[edge label=$u$](se);
            \propag[fer](nw)to[quarter left](kn);
            \propag[anti fermion](ne)to(kn);
            \propag[anti fermion](sw)to[quarter right](kp);
            \propag[fermion](se)to(kp);
        \end{feynhand}\end{tikzpicture}

φ -> 3π (OZI則切断)

ハサミの絵文字を出すにはbbdingパッケージが必要。

\begin{tikzpicture}\begin{feynhand}
            \vertex[particle](phi)at(-1.5,0){$\phi$};
            \vertex(nw)at(-.5,1);
            \vertex(ne)at(.5,1);
            \vertex(w)at(-.5,0);
            \vertex(e)at(.5,0);
            \vertex(sw)at(-.5,-1);
            \vertex(se)at(.5,-1);
            \vertex[particle](pp)at(2,1.5){$\pi^+$};
            \vertex[particle](p0)at(2,0){$\pi^0$};
            \vertex[particle](pn)at(2,-1.5){$\pi^-$};
            \propag[fer](phi)to[edge label=$s$](nw);
            \propag[anti fermion](phi)to[edge label'=$s$](sw);
            \draw[dash dot](0,1.5)--(0,-1.5);
            \node (scissors) at(0,1.5) {\ScissorRight};
            \propag[fer](nw)to(w);
            \propag[fer](w)to(sw);
            \propag[gluon](nw)to(ne);
            \propag[gluon](w)to(e);
            \propag[gluon](sw)to(se);
            \propag[anti fermion](ne)to[edge label=$d$](pp);
            \propag[fer](e)to[edge label'=$u$, near start](pp);
            \propag[fer](ne)to[quarter left](p0);
            \propag[anti fermion](se)to[quarter right](p0);
            \propag[anti fermion](e)to(pn);
            \propag[fer](se)to[edge label'=$d$](pn);
        \end{feynhand}\end{tikzpicture}

切断後

\begin{tikzpicture}\begin{feynhand}
            \vertex[particle](phi)at(-1.5,0){$\phi$};
            \vertex(nww)at(-.75,1);
            \vertex(nw0)at(-.25,1);
            \vertex(nw)at(0,1);
            \vertex(ne)at(.5,1);
            \vertex(ww)at(-.75,0);
            \vertex(w0)at(-.25,0);
            \vertex(w)at(0,0);
            \vertex(e)at(.5,0);
            \vertex(sww)at(-.75,-1);
            \vertex(sw0)at(-.25,-1);
            \vertex(sw)at(0,-1);
            \vertex(se)at(.5,-1);
            \vertex[particle](pp)at(2,1.5){$\pi^+$};
            \vertex[particle](p0)at(2,0){$\pi^0$};
            \vertex[particle](pn)at(2,-1.5){$\pi^-$};
            \propag[fer](phi)to[edge label=$s$](nww);
            \propag[anti fermion](phi)to[edge label'=$s$](sww);
            \propag[fer](nww)to(ww);
            \propag[fer](ww)to(sww);
            \propag[gluon](nww)to(nw0);
            \propag[gluon](nw)to(ne);
            \propag[gluon](ww)to(w0);
            \propag[gluon](w)to(e);
            \propag[gluon](sww)to(sw0);
            \propag[gluon](sw)to(se);
            \propag[anti fermion](ne)to[edge label=$d$](pp);
            \propag[fer](e)to[edge label'=$u$, near start](pp);
            \propag[fer](ne)to[quarter left](p0);
            \propag[anti fermion](se)to[quarter right](p0);
            \propag[anti fermion](e)to(pn);
            \propag[fer](se)to[edge label'=$d$](pn);
        \end{feynhand}\end{tikzpicture}

Δ^+ -> p + π^0

\begin{tikzpicture}
        \begin{feynhand}
            \vertex[particle](u00)at(0,-.5){$u$};
            \vertex[particle](u01)at(1,-.5){$u$};
            \vertex[particle](u0)at(0,0){$u$};
            \vertex[particle](u1)at(0,2){$u$};
            \vertex[particle](u2)at(1,0){$u$};
            \vertex[particle](u3)at(1,.5){$u$};
            \vertex[particle](u4)at(1,1.5){$\bar{u}$};
            \vertex[particle](u5)at(1,2){$u$};
            \vertex(v0)at(.3,2);
            \vertex(v1)at(.6,1);
            \propag[fer](u00)to(u01);
            \propag[fer](u0)to(u2);
            \propag[fer](u1)to(v0);
            \propag[fer](v0)to(u5);
            \propag[gluon](v0)to(v1);
            \propag[antfer](v1)to(u4);
            \propag[fer](v1)to(u3);
        \end{feynhand}
    \end{tikzpicture}

2p -> ∑^+ K^0 n π^0 π^+

\begin{tikzpicture}
        \begin{feynhand}
            % LHS
            \vertex[particle](u0)at(0,0){$u$};
            \vertex[particle](u1)at(0,.5){$u$};
            \vertex[particle](d0)at(0,1){$d$};
            \vertex[particle](u2)at(0,7.5){$u$};
            \vertex[particle](u3)at(0,8){$u$};
            \vertex[particle](d1)at(0,8.5){$d$};
            % RHS sigma+
            \vertex[particle](u4)at(3,0){$u$};
            \vertex[particle](u5)at(3,.5){$u$};
            \vertex[particle](s0)at(3,1){$s$};
            % RHS K0
            \vertex[particle](s1)at(3,2){$\bar{s}$};
            \vertex[particle](d2)at(3,2.5){$d$};
            % RHS pi+
            \vertex[particle](u6)at(3,3.5){$u$};
            \vertex[particle](d3)at(3,4){$\bar{d}$};
            % RHS pi0
            \vertex[particle](d4)at(3,5){$\bar{d}$};
            \vertex[particle](d5)at(3,5.5){$d$};
            \vertex[particle](u7)at(3,6){$\bar{u}$};
            \vertex[particle](u8)at(3,6.5){$u$};
            % RHS n
            \vertex[particle](u9)at(3,7.5){$u$};
            \vertex[particle](d6)at(3,8){$d$};
            \vertex[particle](d7)at(3,8.5){$d$};
            % int vertex
            \vertex(v0)at(1,1.5);
            \vertex(v1)at(1,3);
            \vertex(v2)at(1,5.25);
            \vertex(v3)at(1,6.25);
            \vertex(v4)at(2,1.5);
            \vertex(v5)at(2,3);
            \vertex(v6)at(2,5.25);
            \vertex(v7)at(2,6.25);
            % propag
            \propag[fer](u0)to(u4);
            \propag[fer](u1)to(v1);
            \propag[fer](v1)to(v0);
            \propag[fer](v0)to(u5);
            \propag[fer](v2)to(u6);
            \propag[fer](d0)to(v3);
            \propag[fer](v3)to(d6);
            \propag[fer](d1)to(d7);
            \propag[gluon](v0)to(v4);
            \propag[gluon](v1)to(v5);
            \propag[gluon](v2)to(v6);
            \propag[gluon](v3)to(v7);
            % quark anti quark
            \propag[fer](v4)to(s0);
            \propag[anti fermion](v4)to(s1);
            \propag[fer](v5)to(d2);
            \propag[anti fermion](v7)to(u7);
            \propag[anti fermion](v6)to(d3);
            \propag[fer](v6)to(d5);
            \propag[fer](v7)to(u9);
            % top lines
            \propag[anti fermion, top](v5)to(d4);
            \propag[fer, top](u2)to(v2);
            \propag[fer, top](u3)to(u8);
        \end{feynhand}
    \end{tikzpicture}

pp -> pppp^-

\begin{equation*}
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex(upper)at(0,1);
                \vertex(lower)at(0,0);
                \propag[fer]($(lower)+(-150:1)$)to(upper);
                \propag[fer](lower)to++(-30:1);
                \propag[gluon](lower)to(upper);
                \propag[fer](upper)to++(30:1);
                \propag[anti fermion](upper)to++($(-30:1)+(0,-.5)$);
            \end{feynhand}
        \end{tikzpicture}
    }}
    \times\cdots
\end{equation*}
フェルミオン線は適宜u, dなどを取る

n + anti n -> 3π

\begin{tikzpicture}[xscale=2]
        \begin{feynhand}
            % LHS
            \vertex[particle](u0)at(0,0){$\bar{u}$};
            \vertex[particle](d0)at(0,.5){$\bar{d}$};
            \vertex[particle](d1)at(0,1){$\bar{d}$};
            \vertex[particle](d2)at(0,2.5){$d$};
            \vertex[particle](d3)at(0,3){$d$};
            \vertex[particle](u1)at(0,3.5){$u$};
            % RHS
            \vertex[particle](u2)at(1,0){$\bar{u}$};
            \vertex[particle](d4)at(1,.5){$d$};
            \vertex[particle](d5)at(1,1.5){$\bar{d}$};
            \vertex[particle](d6)at(1,2){$d$};
            \vertex[particle](d7)at(1,3){$\bar{d}$};
            \vertex[particle](u3)at(1,3.5){$u$};
            % vertex
            \vertex(left)at(.3,1.75);
            \vertex(right)at(.6,2.5);
            % propag from left
            \propag[antfer](u0)to(u2);
            \propag[antfer](d0)to(d5);
            \propag[antfer](d1)to(left);
            \propag[fer](d2)to(left);
            \propag[fer](u1)to(u3);
            % propag between v
            \propag[gluon](left)to(right);
            % propag to right
            \propag[fer](right)to(d6);
            \propag[antfer](right)to(d7);
            % propag top
            \propag[fer, top](d3)to(d4);
        \end{feynhand}
    \end{tikzpicture}

π^- p -> Λ K

\begin{tikzpicture}
        \begin{feynhand}
            \vertex(left)at(0,0);
            \vertex(right)at(1,0);
            \vertex[particle](u0)at($(left)+(-150:1)$){$u$};
            \vertex[particle](u1)at($(left)+(150:1)$){$\bar{u}$};
            \vertex[particle](s0)at($(right)+(-30:1)$){$s$};
            \vertex[particle](s1)at($(right)+(30:1)$){$\bar{s}$};
            \vertex[particle](d0)at($(u1)+(0,.5)$){$d$};
            \vertex[particle](d1)at($(s1)+(0,.5)$){$d$};
            \propag[fer](u0)to(left);
            \propag[antfer](u1)to(left);
            \propag[gluon](left)to(right);
            \propag[fer](right)to(s0);
            \propag[antfer](right)to(s1);
            \propag[fer](d0)to(d1);
        \end{feynhand}
    \end{tikzpicture}

複合ダイアグラム

e^- e^+ -> µ^- µ+ (最低次)

\begin{equation*}
    i\mathcal{M}(e^-+e^+\to\mu^-+\mu^+)
    =
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex (left) at (0,0);
                \vertex (right) at (1,0);
                \propag [fermion] ($(left)+(120:1)$) to [edge label=$e^-$] (left);
                \propag [anti fermion] (left)++(-120:1) to [edge label=$e^+$] (left);
                \propag [photon] (left) to [edge label=$\gamma$] (right);
                \propag [fer] (right) to [edge label=$\mu^-$] ++(60:1);
                \propag [fer] (right) to [edge label=$\mu^+$] ++(-60:1);
            \end{feynhand}
        \end{tikzpicture}
    }}
    +
    \vcenter{\hbox{
        \begin{tikzpicture}
            \begin{feynhand}
                \vertex (left) (0,0);
                \vertex (right) (1,0);
                \propag [fer] (left)++(120:1) to [edge label=$e^-$] (left);
                \propag [anti fermion] (left)++(-120:1) to [edge label=$e^+$] (left);
                \propag [photon] (left) to [edge label=$Z$] (right);
                \propag [fer] (right) to [edge label=$\mu^-$] ++(60:1);
                \propag [anti fermion] (right) to [edge label=$\mu^+$] ++(-60:1);
            \end{feynhand}
        \end{tikzpicture}
    }}
    +\cdots
    .
\end{equation*}

Ξ^- -> n

\begin{tikzpicture}\begin{feynhand}
            \vertex(nw)at(-1,1);
            \vertex(ne)at(1,1);
            \vertex(w)at(-1,0);
            \vertex(e)at(1,0);
            \vertex(sw)at(-1,-1);
            \vertex(se)at(1,-1);
            \vertex(xi)at($(sw)+(-135:1)$){$\Xi^-$};
            \vertex(pi)at($(ne)+(45:1)$){$\pi^-$};
            \vertex(n)at($(se)+(-45:1)$){$n$};
            \propag[fer](xi)to[edge label=$s$](nw);
            \propag[fer](xi)to[edge label=$s$](sw);
            \propag[chabos](nw)to[edge label=$W^-$](ne);
            \propag[fer](nw)to[edge label=$u$](w);
            \propag[anti fermion](ne)to(w);
            \propag[chabos](sw)to(se);
            \propag[gluon](w)to(e);
            \propag[fer](ne)to[edge label=$d$](pi);
            \propag[anti fermion](e)to[edge label'=$\bar{u}$](pi);
            \propag[fer](e)to(se);
            \propag[fer](se)to[edge label=$d$](n);
            \propag[fer](sw)to[edge label'=$u$](n);
        \end{feynhand}\end{tikzpicture}

D^0 -> K^- π^+

\begin{tikzpicture}\begin{feynhand}
            \vertex(upper)at(0,1);
            \vertex(lower)at(0,0);
            \vertex(ne)at(1,1);
            \vertex(e)at(1,0);
            \vertex[particle](d)at($(lower)+(-150:1)$){$D^0$};
            \vertex[particle](pi)at($(e)+(-60:1)$){$\pi^+$};
            \vertex[particle](k)at($(ne)+(60:1)$){$K^-$};
            \propag[fer](d)to[edge label=$c$](upper);
            \propag[anti fermion](d)to[edge label'=$\bar{u}$, near start](lower);
            \propag[chabos](lower)to(upper);
            \propag[fermion](upper)to(ne);
            \propag[gluon](ne)to(e);
            \propag[anti fermion](e)to(k);
            \propag[fer](e)to[edge label=$u$](pi);
            \propag[anti fermion](lower)to[edge label'=$\bar{d}$](pi);
            \propag[fer](ne)to[edge label=$s$](k);
        \end{feynhand}\end{tikzpicture}

D^0 -> 2π

\begin{tikzpicture}\begin{feynhand}
            \vertex(upper)at(0,1);
            \vertex(lower)at(0,0);
            \vertex(ne)at(1,1);
            \vertex(e)at(1,0);
            \vertex[particle](d)at($(lower)+(-150:1)$){$D^0$};
            \vertex[particle](pi)at($(e)+(-60:1)$){$\pi^+$};
            \vertex[particle](k)at($(ne)+(60:1)$){$\pi^-$};
            \propag[fer](d)to[edge label=$c$](upper);
            \propag[anti fermion](d)to[edge label'=$\bar{u}$, near start](lower);
            \propag[chabos](lower)to(upper);
            \propag[fermion](upper)to(ne);
            \propag[gluon](ne)to(e);
            \propag[anti fermion](e)to(k);
            \propag[fer](e)to[edge label=$u$](pi);
            \propag[anti fermion](lower)to[edge label'=$\bar{d}$](pi);
            \propag[fer](ne)to[edge label=$d$](k);
        \end{feynhand}\end{tikzpicture}

D^0 -> K^+ π^-

\begin{tikzpicture}\begin{feynhand}
            \vertex(upper)at(0,1);
            \vertex(lower)at(0,0);
            \vertex(ne)at(1,1);
            \vertex(e)at(1,0);
            \vertex[particle](d)at($(lower)+(-150:1)$){$D^0$};
            \vertex[particle](pi)at($(e)+(-60:1)$){$K^+$};
            \vertex[particle](k)at($(ne)+(60:1)$){$\pi^-$};
            \propag[fer](d)to[edge label=$c$](upper);
            \propag[anti fermion](d)to[edge label'=$\bar{u}$, near start](lower);
            \propag[chabos](lower)to(upper);
            \propag[fermion](upper)to(ne);
            \propag[gluon](ne)to(e);
            \propag[anti fermion](e)to(k);
            \propag[fer](e)to[edge label=$u$](pi);
            \propag[anti fermion](lower)to[edge label'=$\bar{s}$](pi);
            \propag[fer](ne)to[edge label=$d$](k);
        \end{feynhand}\end{tikzpicture}

µ^- -> 3e

\begin{tikzpicture}
        \begin{feynhand}
            \vertex(left)at(0,0);
            \vertex(center)at(1,0);
            \vertex(upper)at(1,1);
            \vertex(right)at(2,0);
            \propag[fer]($(left)+(-150:1)$)to[edge label=$\mu$](left);
            \propag[antfer](left)to[edge label'=$\nu_\mu$]($(left)+(-30:1)$);
            \propag[chabos](left)to(center);
            \propag[chabos](center)to(right);
            \propag[photon](center)to(upper);
            \propag[fer](upper)to[edge label=$e^-$]++(-30:1);
            \propag[antfer](upper)to[edge label=$e^+$]++(30:1);
            \propag[fer](right)to[edge label=$e^-$]++(-30:1);
            \propag[antfer](right)to[edge label=$\bar{\nu}_e$, near end]++(30:1);
        \end{feynhand}
    \end{tikzpicture}

∑^+ -> p

\begin{tikzpicture}
        \begin{feynhand}
            \vertex(left)at(0,0);
            \vertex(right)at(1,0);
            \vertex(upper)at(0.5,1);
            \propag[fer]($(left)+(-150:1)$)to[edge label=$s$](left);
            \propag[fer](left)to(right);
            \propag[fer](right)to[edge label=$d$]++(-30:1);
            \propag[chabos](left)to(upper);
            \propag[chabos](upper)to(right);
            \propag[photon](upper)to++(30:1);
        \end{feynhand}
    \end{tikzpicture}

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