-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathCheatSheet.tex
273 lines (248 loc) · 9.7 KB
/
CheatSheet.tex
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
%#!lualatex
% Time-stamp: <2024-08-02 20:36:25>
\documentclass[10pt]{CheatSheet}
\usepackage{subfiles,tensor}
\usepackage[inline,shortlabels]{enumitem}
\bibliographystyle{utphys28mod}
\author{Sho Iwamoto / Misho}
\title{HEP-PH Cheat Sheet}
\hypersetup{
pdflang={en-US},
pdfauthortitle={Assistant Professor, National Sun Yat-sen University},
pdfsubject={Sho Iwamoto's cheat sheet for high-energy physics calculation},
pdfcontactemail={[email protected]},
pdfcontacturl={https://www2.nsysu.edu.tw/iwamoto/},
pdfcaptionwriter={Sho Iwamoto},
pdfcopyright={2009–2024 Sho Iwamoto\textLF This document is licensed under the Creative Commons CC BY–NC 4.0 International Public License.},
pdflicenseurl={https://creativecommons.org/licenses/by-nc/4.0/},
}
\setotherlanguages{russian}
\newcommand*\RUSSIAN[1]{\russian#1\endrussian}
\setmathfont{FiraMath-Regular.otf}[range={\dot,\ddot,\dddot}]
\makeatletter
% automatic bibliography
\AtEndDocument{\clearpage\begingroup\hbadness=8000\orig@bibliography{CheatSheet}\endgroup}%
\let\orig@bibliography\bibliography
\let\bibliography\@gobble
% fine tuning of slashed
\def\sla@@#1#2#3#4#5#6{{%
\setbox\z@\hbox{$\m@th#5#6$}%
\setbox\tw@\hbox{$\m@th#5#1$}%
\dimen4\wd\ifdim\wd\z@<\wd\tw@\tw@\else\z@\fi
\dimen@\ht\tw@
\advance\dimen@-\dp\tw@
\advance\dimen@-\ht\z@
\advance\dimen@\dp\z@
\divide\dimen@\tw@
\advance\dimen@-#3\ht\tw@
\advance\dimen@-#3\dp\tw@
\dimen@ii#2\wd\z@
\rlap{\raise-\dimen@\hbox to\dimen4{\hss\kern\dimen@ii\box\tw@\kern-\dimen@ii\hss}}%
\hbox{$\m@th#5#6#4$}}}
\def\slashedW{\@ifnextchar[\slashedW@{\mathpalette{\sla@{/}{0}{0}}W}}
\def\slashedW@[#1]{\mathpalette{\sla@@{/}{0}{0}{#1}}W}
% BIBTeX hack for PDG
\let\bibitemGeneral\@bibitem
\let\bibitemPDG\@lbibitem
\begin{luacode*}
function bibitem(t)
tex.sprint(t:sub(1, 5) == "PDG20" and "\\bibitemPDG[" .. t .. "]" or "\\bibitemGeneral", "{", t, "}")
end
\end{luacode*}
\def\@bibitem#1{\directlua{bibitem(\luastring{#1})}}
% tex.print(string.sub(\luastring{#1}, 1, 5) == "PDG20" and "\\bibitemPDG[#1]" or "\\bibitemGeneral")}{#1}}
\makeatother
\DeclareMathOperator{\gSU}{\mathrm SU}
\DeclareMathOperator{\gSO}{\mathrm SO}
\DeclareMathOperator{\gSL}{\mathrm SL}
\DeclareMathOperator{\gSp}{\mathrm Sp}
\DeclareMathOperator{\gU}{\mathrm U}
\DeclareMathOperator{\gO}{\mathrm O}
\DeclareMathOperator{\aSU}{\mathfrak{su}}
\DeclareMathOperator{\aSO}{\mathfrak{so}}
\DeclareMathOperator{\aSL}{\mathfrak{sl}}
\DeclareMathOperator{\aSp}{\mathfrak{sp}}
\newcommand{\LorTr}[2]{\Lambda^{#1}{}_{#2}}
\def\RANK#1{\langle#1\rangle}
\DeclareMathOperator{\Cl} {\mathrm{Cl}}
\DeclareMathOperator{\GeoA} {\mathcal{G}}
\DeclareMathOperator{\Pin}{\mathrm{Pin}}
\DeclareMathOperator{\Spin}{\mathrm{Spin}}
\DeclareMathOperator{\tAd}{\widetilde{\mathrm{Ad}}}
\newcommand*\req{\circeq}
%\DeclareMathSymbol{\setdiff}{\mathbin}{AMSb}{"025B5}
\newcommand{\setdiff}{\mathbin{\vartriangle}}
\AtBeginDocument{
%\UnicodeMathSymbol{"025B5}{\setdiff}{\mathbin}{diff}
}
\newcommand{\relmiddle}[1]{\mathrel{}\middle#1\mathrel{}}
\newcommand*{\ddP}[2][3]{\frac{\dd^{#1}\ifx3#1\relax\vc{#2}\else#2\fi}{(2\pi)^{#1}}}
\newcommand*\tqL[1][]{\tilde q_{\mathrm{L}#1}}
\newcommand*\tuL[1][]{\tilde u_{\mathrm{L}#1}}
\newcommand*\tdL[1][]{\tilde d_{\mathrm{L}#1}}
\newcommand*\tuR[1][]{\tilde u_{\mathrm{R}#1}}
\newcommand*\tdR[1][]{\tilde d_{\mathrm{R}#1}}
\newcommand*\tlL[1][]{\tilde l_{\mathrm{L}#1}}
\newcommand*\tnuL[1][]{\tilde \nu_{\mathrm{L}#1}}
\newcommand*\teL[1][]{\tilde e_{\mathrm{L}#1}}
\newcommand*\teR[1][]{\tilde e_{\mathrm{R}#1}}
\newcommand*\qL[1][]{q_{\mathrm{L}#1}}
\newcommand*\uL[1][]{u_{\mathrm{L}#1}}
\newcommand*\dL[1][]{d_{\mathrm{L}#1}}
\newcommand*\uR[1][]{u_{\mathrm{R}#1}}
\newcommand*\dR[1][]{d_{\mathrm{R}#1}}
\newcommand*\lL[1][]{l_{\mathrm{L}#1}}
\newcommand*\nuL[1][]{\nu_{\mathrm{L}#1}}
\newcommand*\eL[1][]{e_{\mathrm{L}#1}}
\newcommand*\eR[1][]{e_{\mathrm{R}#1}}
\newcommand*\nR[1][]{n_{\mathrm{R}#1}}
\newcommand*\bqL[1][]{\bar q_{\mathrm{L}#1}}
\newcommand*\buL[1][]{\bar u_{\mathrm{L}#1}}
\newcommand*\bdL[1][]{\bar d_{\mathrm{L}#1}}
\newcommand*\buR[1][]{\bar u_{\mathrm{R}#1}}
\newcommand*\bdR[1][]{\bar d_{\mathrm{R}#1}}
\newcommand*\blL[1][]{\bar l_{\mathrm{L}#1}}
\newcommand*\bnuL[1][]{\bar \nu_{\mathrm{L}#1}}
\newcommand*\beL[1][]{\bar e_{\mathrm{L}#1}}
\newcommand*\beR[1][]{\bar e_{\mathrm{R}#1}}
\newcommand*\bnR[1][]{\bar n_{\mathrm{R}#1}}
\newcommand*\Hu{H\w u}
\newcommand*\Hd{H\w d}
\newcommand*\hu{h\w u}
\newcommand*\huz{h\w u^0}
\newcommand*\hup{h\w u^+}
\newcommand*\hd{h\w d}
\newcommand*\hdz{h\w d^0}
\newcommand*\hdm{h\w d^-}
\newcommand*\thu{\tilde h\w u}
\newcommand*\thuz{\tilde h\w u^0}
\newcommand*\thup{\tilde h\w u^+}
\newcommand*\thd{\tilde h\w d}
\newcommand*\thdz{\tilde h\w d^0}
\newcommand*\thdm{\tilde h\w d^-}
\newcommand*\bthu{\bar{\tilde h}\w u}
\newcommand*\bthuz{\bar{\tilde h}\w u^0}
\newcommand*\bthup{\bar{\tilde h}\w u^+}
\newcommand*\bthd{\bar{\tilde h}\w d}
\newcommand*\bthdz{\bar{\tilde h}\w d^0}
\newcommand*\bthdm{\bar{\tilde h}\w d^-}
\newcommand*\tig{\tilde g}
\newcommand*\tiw{\tilde w}
\newcommand*\tib{\tilde b}
\newcommand*\yu[1][]{y_{u#1}}
\newcommand*\yd[1][]{y_{d#1}}
\newcommand*\ye[1][]{y_{e#1}}
\newcommand*\Yu[1][]{Y_{u#1}}
\newcommand*\Yd[1][]{Y_{d#1}}
\newcommand*\Ye[1][]{Y_{e#1}}
\newcommand*\Yn[1][]{Y_{n#1}}
\newcommand*\PL{P_{\,\mathrm L}}
\newcommand*\PR{P_{\,\mathrm R}}
\newcommand*\sw{\si{\mathrm w}}
\newcommand*\cw{\co{\mathrm w}}
\newcommand*\vu{v\w u}
\newcommand*\vd{v\w d}
\newcommand*\dalpha{{\dot\alpha}}
\newcommand*\dbeta{{\dot\beta}}
\newcommand*\dgamma{{\dot\gamma}}
\newcommand*\ddelta{{\dot\delta}}
\newcommand*\bsigma{\bar\sigma}
\newcommand*\btheta{\bar\theta}
\newcommand*\bchi{\bar\chi}
\newcommand*\bpsi{\bar\psi}
\newcommand*\blambda{\bar\lambda}
\newcommand*\neut[1][\relax]{\tilde\chi^0\ifx#1\relax\relax\else_{#1}\fi}
\newcommand*\charPM[1][\relax]{\tilde\chi^\pm\ifx#1\relax\relax\else_{#1}\fi}
\newcommand*\charP[1][\relax]{\tilde\chi^+\ifx#1\relax\relax\else_{#1}\fi}
\newcommand*\charM[1][\relax]{\tilde\chi^-\ifx#1\relax\relax\else_{#1}\fi}
\newcommand*\bneut[1][\relax]{{\bar{\tilde\chi}}^0\ifx#1\relax\relax\else_{#1}\fi}
\newcommand*\bcharPM[1][\relax]{{\bar{\tilde\chi}}^\pm\ifx#1\relax\relax\else_{#1}\fi}
\newcommand*\bcharP[1][\relax]{{\bar{\tilde\chi}}^+\ifx#1\relax\relax\else_{#1}\fi}
\newcommand*\bcharM[1][\relax]{{\bar{\tilde\chi}}^-\ifx#1\relax\relax\else_{#1}\fi}
% for uncertainties and bound
\makeatletter
\newcommand*\unc[2]{\substack{#1\\#2}}
\newcommand*\bound[2]{%
\ifnum#1=68\@bound{*}{#2\relax}\else
\ifnum#1=90\@bound{\diamond}{#2\relax}\else
\ifnum#1=95\@bound{*\!*}{#2\relax}\else
\ifnum#1=99\@bound{\diamond\diamond}{#2\relax}\else
\ifnum#1=1\@bound{*}{#2\relax}\else
\ifnum#1=2\@bound{*\!*}{#2\relax}\else
\ifnum#1=3\@bound{*\!*\!*}{#2\relax}\else
\ifnum#1<10\@bound{#1\sigma}{#2\relax}\else\@bound{#1\%}{#2\relax}\fi\fi\fi\fi\fi\fi\fi\fi
}
\newcommand*\@bound[2]{\ifx\relax#2\relax{}^{#1}\else\stackrel{#1}{#2}\fi}
\newcommand\bounddescription{Confidence levels are shown by the marks $*$, $*\!*$, \mbox{$*\!\!*\!\!*$} (1--3$\sigma$), $\diamond$ (90\%), and $\diamond\diamond$ (99\%).}
\makeatother
% text-like
\newcommand*\ech{\abs{e}}
\newcommand*\TO{\text{--}}
\newcommand*\TWO{\mathbf{2}}
\newcommand*\THREE{\mathbf{3}}
\newcommand*\THREEbar{\overline{\mathbf{3}}}
\newcommand*\MSbar{\overline{\mathrm{MS}}\xspace}
\newcommand*\Nambu{\JA{南部}\xspace}
\newcommand*\Lubanski{Luba\'nski\xspace}
\newcommand*\AstroSun{☉}
\newcommand*\AstroEarth{⊕}
\newcommand*\pmmm{\mathord{+}\mathord{-}\mathord{-}\mathord{-}}
\newcommand*\mppp{\mathord{-}\mathord{+}\mathord{+}\mathord{+}}
\begin{document}
\setcounter{page}{0}
\nocite{PDG2018,PDG2020,PDG2024}
\begin{maketitle}
\vspace{20mm}
\subsection*{Important notes}
\begin{itemize}
\item Minkowski metric: $\eta=(+,-,-,-)$ unless otherwise noted.
\item Levi-Civita symbol: $\nep^{12}=\nep_{12}=\nep^{123}=\nep_{123}=\nep^{1234}=\nep_{1234}=\cdots=1$.
\item Levi-Civita Lorentz tensor: $\vep^{0123}=-\vep_{0123}=1$.
\item Pauli matrices: $\sigma^i\coloneq\{\sigma_x, \sigma_y, \sigma_z\}$, hence $\sigma_i = -\sigma^i$ for $i=1,2,3$, unless otherwise noted.
\item Symbols with $\C{\text{this color}}$ are under a locally-defined convention different from this CheatSheet.
\item Elementary charge: $\ech\simeq0.303$, always in absolute-value symbols. Note $\epsilon_0=1/(\mu_0c^2)=1$.
\end{itemize}
\makeatletter
\begin{tikzpicture}[remember picture,overlay]
\node[xshift=\@total@leftsep,yshift=25.5mm,anchor=south west,align=left,text width=\textwidth] at (current page.south west) {%
\href{https://creativecommons.org/licenses/by-nc/4.0/}{\includegraphics[width=2.2cm]{figs/by-nc.pdf}}\\[.4em]
\noindent\textsf{\color{gray}\small%
Visit \url{https://github.com/misho104/hepphCheatSheet} for further information, updates, and to report issues.}
};
\node[xshift=-\@total@leftsep+26mm,yshift=32mm,align=left,text width=\textwidth,anchor=south east] at (current page.south east) {%
\noindent\textsf{\small\color{gray}%
This document is licensed under
\href{https://creativecommons.org/licenses/by-nc/4.0/}{the Creative Commons CC--BY--NC 4.0 International Public License.}\\
You may use this document only if you do in compliance with the license.}
};
\end{tikzpicture}
\makeatother
\end{maketitle}
\subfile{notation}
\clearpage
\subfile{kinematics}
\clearpage
\subfile{spinors}
%\subfile{spinors_more}
\clearpage
\subfile{gaugetheory}
\clearpage
\subfile{Calculation}
\clearpage
\subfile{loop}
\clearpage
\subfile{cosmology}
\clearpage
\subfile{StandardModel}
\clearpage
\subfile{StandardModelValues}
\clearpage
\subfile{Neutrino}
\clearpage
\subfile{SUSY}
\clearpage
\subfile{MSSM}
\clearpage
\appendix
\subfile{mathematics}
\end{document}