equation_database.isbn_9780511628788
Functions
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DOI, QCD and collider physics |
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\(gg \to gg\) |
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\(gg \to q\bar{q}\) |
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\(gq \to gq\) |
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\(qq \to qq\) |
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\(q\bar{q} \to gg\) |
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\(q\bar{q} \to q'\bar{q}'\) |
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\(q\bar{q} \to q\bar{q}\) |
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\(qq' \to qq'\) |
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\(q\bar{q}' \to q\bar{q}'\) |
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\(gq \to \gamma^* q\) |
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\(q\bar q \to \gamma^* g\) |
- equation_database.isbn_9780511628788.table_7_1_qqp_qqp(s=s, t=t, u=u)[source]
\(qq' \to qq'\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{\frac{4 s^{2}}{9} + \frac{4 u^{2}}{9}}{t^{2}}\),
\frac{\frac{4 s^{2}}{9} + \frac{4 u^{2}}{9}}{t^{2}}
<apply><divide/><apply><plus/><apply><divide/><apply><times/><cn>4</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply><cn>9</cn></apply><apply><divide/><apply><times/><cn>4</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply><cn>9</cn></apply></apply><apply><power/><ci>t</ci><cn>2</cn></apply></apply>
(4*s**2/9 + 4*u**2/9)/t**2
(4*s.^2/9 + 4*u.^2/9)./t.^2
((4/9)*s^2 + (4/9)*u^2)/t^2
((4/9)*s**2 + (4/9)*u**2)/t**2
((4.0/9.0)*pow(s, 2) + (4.0/9.0)*pow(u, 2))/pow(t, 2)
((4.0/9.0)*std::pow(s, 2) + (4.0/9.0)*std::pow(u, 2))/std::pow(t, 2)
((4.0d0/9.0d0)*s**2 + (4.0d0/9.0d0)*u**2)/t**2
((4_f64/9.0)*s.powi(2) + (4_f64/9.0)*u.powi(2))/t.powi(2)
2 2 4*s 4*u ---- + ---- 9 9 ----------- 2 t
2 2 4⋅s 4⋅u ──── + ──── 9 9 ─────────── 2 t
- equation_database.isbn_9780511628788.table_7_1_qqpb_qqpb(s=s, t=t, u=u)[source]
\(q\bar{q}' \to q\bar{q}'\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{\frac{4 s^{2}}{9} + \frac{4 u^{2}}{9}}{t^{2}}\),
\frac{\frac{4 s^{2}}{9} + \frac{4 u^{2}}{9}}{t^{2}}
<apply><divide/><apply><plus/><apply><divide/><apply><times/><cn>4</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply><cn>9</cn></apply><apply><divide/><apply><times/><cn>4</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply><cn>9</cn></apply></apply><apply><power/><ci>t</ci><cn>2</cn></apply></apply>
(4*s**2/9 + 4*u**2/9)/t**2
(4*s.^2/9 + 4*u.^2/9)./t.^2
((4/9)*s^2 + (4/9)*u^2)/t^2
((4/9)*s**2 + (4/9)*u**2)/t**2
((4.0/9.0)*pow(s, 2) + (4.0/9.0)*pow(u, 2))/pow(t, 2)
((4.0/9.0)*std::pow(s, 2) + (4.0/9.0)*std::pow(u, 2))/std::pow(t, 2)
((4.0d0/9.0d0)*s**2 + (4.0d0/9.0d0)*u**2)/t**2
((4_f64/9.0)*s.powi(2) + (4_f64/9.0)*u.powi(2))/t.powi(2)
2 2 4*s 4*u ---- + ---- 9 9 ----------- 2 t
2 2 4⋅s 4⋅u ──── + ──── 9 9 ─────────── 2 t
- equation_database.isbn_9780511628788.table_7_1_qq_qq(s=s, t=t, u=u)[source]
\(qq \to qq\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(- \frac{8 s^{2}}{27 t u} + \frac{4 \left(s^{2} + t^{2}\right)}{9 u^{2}} + \frac{4 \left(s^{2} + u^{2}\right)}{9 t^{2}}\),
- \frac{8 s^{2}}{27 t u} + \frac{4 \left(s^{2} + t^{2}\right)}{9 u^{2}} + \frac{4 \left(s^{2} + u^{2}\right)}{9 t^{2}}
<apply><plus/><apply><minus/><apply><divide/><apply><times/><cn>8</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply><apply><times/><cn>27</cn><ci>t</ci><ci>u</ci></apply></apply></apply><apply><divide/><apply><plus/><apply><times/><cn>4</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply><apply><times/><cn>4</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply></apply><apply><times/><cn>9</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply><apply><divide/><apply><plus/><apply><times/><cn>4</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply><apply><times/><cn>4</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply><apply><times/><cn>9</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply></apply></apply>
-8*s**2/(27*t*u) + 4*(s**2 + t**2)/(9*u**2) + 4*(s**2 + u**2)/(9*t**2)
-8*s.^2./(27*t.*u) + 4*(s.^2 + t.^2)./(9*u.^2) + 4*(s.^2 + u.^2)./(9*t.^2)
-8/27*s^2/(t*u) + (4/9)*(s^2 + t^2)/u^2 + (4/9)*(s^2 + u^2)/t^2
-8/27*s**2/(t*u) + (4/9)*(s**2 + t**2)/u**2 + (4/9)*(s**2 + u**2)/t**2
-8.0/27.0*pow(s, 2)/(t*u) + (4.0/9.0)*(pow(s, 2) + pow(t, 2))/pow(u, 2) + (4.0/9.0)*(pow(s, 2) + pow(u, 2))/pow(t, 2)
-8.0/27.0*std::pow(s, 2)/(t*u) + (4.0/9.0)*(std::pow(s, 2) + std::pow(t, 2))/std::pow(u, 2) + (4.0/9.0)*(std::pow(s, 2) + std::pow(u, 2))/std::pow(t, 2)
-8.0d0/27.0d0*s**2/(t*u) + (4.0d0/9.0d0)*(s**2 + t**2)/u**2 + ( @ 4.0d0/9.0d0)*(s**2 + u**2)/t**2
-8_f64/27.0*s.powi(2)*t.recip()*u.recip() + (4_f64/9.0)*s.powi(2) + t.powi(2)*u.powi(-2) + (4_f64/9.0)*s.powi(2) + u.powi(2)*t.powi(-2)
2 / 2 2\ / 2 2\ 8*s 4*\s + t / 4*\s + u / - ------ + ----------- + ----------- 27*t*u 2 2 9*u 9*t
2 ⎛ 2 2⎞ ⎛ 2 2⎞ 8⋅s 4⋅⎝s + t ⎠ 4⋅⎝s + u ⎠ - ────── + ─────────── + ─────────── 27⋅t⋅u 2 2 9⋅u 9⋅t
- equation_database.isbn_9780511628788.table_7_1_qqb_qpqpb(s=s, t=t, u=u)[source]
\(q\bar{q} \to q'\bar{q}'\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{4 \left(t^{2} + u^{2}\right)}{9 s^{2}}\),
\frac{4 \left(t^{2} + u^{2}\right)}{9 s^{2}}
<apply><divide/><apply><plus/><apply><times/><cn>4</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply><apply><times/><cn>4</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply><apply><times/><cn>9</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply></apply>
4*(t**2 + u**2)/(9*s**2)
4*(t.^2 + u.^2)./(9*s.^2)
(4/9)*(t^2 + u^2)/s^2
(4/9)*(t**2 + u**2)/s**2
(4.0/9.0)*(pow(t, 2) + pow(u, 2))/pow(s, 2)
(4.0/9.0)*(std::pow(t, 2) + std::pow(u, 2))/std::pow(s, 2)
(4.0d0/9.0d0)*(t**2 + u**2)/s**2
(4_f64/9.0)*t.powi(2) + u.powi(2)*s.powi(-2)
/ 2 2\ 4*\t + u / ----------- 2 9*s
⎛ 2 2⎞ 4⋅⎝t + u ⎠ ─────────── 2 9⋅s
- equation_database.isbn_9780511628788.table_7_1_qqb_qqb(s=s, t=t, u=u)[source]
\(q\bar{q} \to q\bar{q}\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{4 \left(s^{2} + u^{2}\right)}{9 t^{2}} - \frac{8 u^{2}}{27 s t} + \frac{4 \left(t^{2} + u^{2}\right)}{9 s^{2}}\),
\frac{4 \left(s^{2} + u^{2}\right)}{9 t^{2}} - \frac{8 u^{2}}{27 s t} + \frac{4 \left(t^{2} + u^{2}\right)}{9 s^{2}}
<apply><plus/><apply><minus/><apply><divide/><apply><plus/><apply><times/><cn>4</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply><apply><times/><cn>4</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply><apply><times/><cn>9</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply></apply><apply><divide/><apply><times/><cn>8</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply><apply><times/><cn>27</cn><ci>s</ci><ci>t</ci></apply></apply></apply><apply><divide/><apply><plus/><apply><times/><cn>4</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply><apply><times/><cn>4</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply><apply><times/><cn>9</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply></apply></apply>
4*(s**2 + u**2)/(9*t**2) - 8*u**2/(27*s*t) + 4*(t**2 + u**2)/(9*s**2)
4*(s.^2 + u.^2)./(9*t.^2) - 8*u.^2./(27*s.*t) + 4*(t.^2 + u.^2)./(9*s.^2)
(4/9)*(s^2 + u^2)/t^2 - 8/27*u^2/(s*t) + (4/9)*(t^2 + u^2)/s^2
(4/9)*(s**2 + u**2)/t**2 - 8/27*u**2/(s*t) + (4/9)*(t**2 + u**2)/s**2
(4.0/9.0)*(pow(s, 2) + pow(u, 2))/pow(t, 2) - 8.0/27.0*pow(u, 2)/(s*t) + (4.0/9.0)*(pow(t, 2) + pow(u, 2))/pow(s, 2)
(4.0/9.0)*(std::pow(s, 2) + std::pow(u, 2))/std::pow(t, 2) - 8.0/27.0*std::pow(u, 2)/(s*t) + (4.0/9.0)*(std::pow(t, 2) + std::pow(u, 2))/std::pow(s, 2)
(4.0d0/9.0d0)*(s**2 + u**2)/t**2 - 8.0d0/27.0d0*u**2/(s*t) + ( @ 4.0d0/9.0d0)*(t**2 + u**2)/s**2
(4_f64/9.0)*s.powi(2) + u.powi(2)*t.powi(-2) - 8_f64/27.0*s.recip()*t.recip()*u.powi(2) + (4_f64/9.0)*t.powi(2) + u.powi(2)*s.powi(-2)
/ 2 2\ 2 / 2 2\ 4*\s + u / 8*u 4*\t + u / ----------- - ------ + ----------- 2 27*s*t 2 9*t 9*s
⎛ 2 2⎞ 2 ⎛ 2 2⎞ 4⋅⎝s + u ⎠ 8⋅u 4⋅⎝t + u ⎠ ─────────── - ────── + ─────────── 2 27⋅s⋅t 2 9⋅t 9⋅s
- equation_database.isbn_9780511628788.table_7_1_qqb_gg(s=s, t=t, u=u)[source]
\(q\bar{q} \to gg\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{\frac{32 t^{2}}{27} + \frac{32 u^{2}}{27}}{t u} - \frac{\frac{8 t^{2}}{3} + \frac{8 u^{2}}{3}}{s^{2}}\),
\frac{\frac{32 t^{2}}{27} + \frac{32 u^{2}}{27}}{t u} - \frac{\frac{8 t^{2}}{3} + \frac{8 u^{2}}{3}}{s^{2}}
<apply><minus/><apply><divide/><apply><plus/><apply><divide/><apply><times/><cn>32</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply><cn>27</cn></apply><apply><divide/><apply><times/><cn>32</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply><cn>27</cn></apply></apply><apply><times/><ci>t</ci><ci>u</ci></apply></apply><apply><divide/><apply><plus/><apply><divide/><apply><times/><cn>8</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply><cn>3</cn></apply><apply><divide/><apply><times/><cn>8</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply><cn>3</cn></apply></apply><apply><power/><ci>s</ci><cn>2</cn></apply></apply></apply>
(32*t**2/27 + 32*u**2/27)/(t*u) - (8*t**2/3 + 8*u**2/3)/s**2
(32*t.^2/27 + 32*u.^2/27)./(t.*u) - (8*t.^2/3 + 8*u.^2/3)./s.^2
((32/27)*t^2 + (32/27)*u^2)/(t*u) - ((8/3)*t^2 + (8/3)*u^2)/s^2
((32/27)*t**2 + (32/27)*u**2)/(t*u) - ((8/3)*t**2 + (8/3)*u**2)/s**2
((32.0/27.0)*pow(t, 2) + (32.0/27.0)*pow(u, 2))/(t*u) - ((8.0/3.0)*pow(t, 2) + (8.0/3.0)*pow(u, 2))/pow(s, 2)
((32.0/27.0)*std::pow(t, 2) + (32.0/27.0)*std::pow(u, 2))/(t*u) - ((8.0/3.0)*std::pow(t, 2) + (8.0/3.0)*std::pow(u, 2))/std::pow(s, 2)
((32.0d0/27.0d0)*t**2 + (32.0d0/27.0d0)*u**2)/(t*u) - ((8.0d0/ @ 3.0d0)*t**2 + (8.0d0/3.0d0)*u**2)/s**2
((32_f64/27.0)*t.powi(2) + (32_f64/27.0)*u.powi(2))/(t*u) - ((8_f64/3.0)*t.powi(2) + (8_f64/3.0)*u.powi(2))/s.powi(2)
2 2 2 2 32*t 32*u 8*t 8*u ----- + ----- ---- + ---- 27 27 3 3 ------------- - ----------- t*u 2 s
2 2 2 2 32⋅t 32⋅u 8⋅t 8⋅u ───── + ───── ──── + ──── 27 27 3 3 ───────────── - ─────────── t⋅u 2 s
- equation_database.isbn_9780511628788.table_7_1_gg_qqb(s=s, t=t, u=u)[source]
\(gg \to q\bar{q}\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{\frac{t^{2}}{6} + \frac{u^{2}}{6}}{t u} - \frac{\frac{3 t^{2}}{8} + \frac{3 u^{2}}{8}}{s^{2}}\),
\frac{\frac{t^{2}}{6} + \frac{u^{2}}{6}}{t u} - \frac{\frac{3 t^{2}}{8} + \frac{3 u^{2}}{8}}{s^{2}}
<apply><minus/><apply><divide/><apply><plus/><apply><divide/><apply><power/><ci>t</ci><cn>2</cn></apply><cn>6</cn></apply><apply><divide/><apply><power/><ci>u</ci><cn>2</cn></apply><cn>6</cn></apply></apply><apply><times/><ci>t</ci><ci>u</ci></apply></apply><apply><divide/><apply><plus/><apply><divide/><apply><times/><cn>3</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply><cn>8</cn></apply><apply><divide/><apply><times/><cn>3</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply><cn>8</cn></apply></apply><apply><power/><ci>s</ci><cn>2</cn></apply></apply></apply>
(t**2/6 + u**2/6)/(t*u) - (3*t**2/8 + 3*u**2/8)/s**2
(t.^2/6 + u.^2/6)./(t.*u) - (3*t.^2/8 + 3*u.^2/8)./s.^2
((1/6)*t^2 + (1/6)*u^2)/(t*u) - ((3/8)*t^2 + (3/8)*u^2)/s^2
((1/6)*t**2 + (1/6)*u**2)/(t*u) - ((3/8)*t**2 + (3/8)*u**2)/s**2
((1.0/6.0)*pow(t, 2) + (1.0/6.0)*pow(u, 2))/(t*u) - ((3.0/8.0)*pow(t, 2) + (3.0/8.0)*pow(u, 2))/pow(s, 2)
((1.0/6.0)*std::pow(t, 2) + (1.0/6.0)*std::pow(u, 2))/(t*u) - ((3.0/8.0)*std::pow(t, 2) + (3.0/8.0)*std::pow(u, 2))/std::pow(s, 2)
((1.0d0/6.0d0)*t**2 + (1.0d0/6.0d0)*u**2)/(t*u) - ((3.0d0/8.0d0)*t @ **2 + (3.0d0/8.0d0)*u**2)/s**2
((1_f64/6.0)*t.powi(2) + (1_f64/6.0)*u.powi(2))/(t*u) - ((3_f64/8.0)*t.powi(2) + (3_f64/8.0)*u.powi(2))/s.powi(2)
2 2 2 2 t u 3*t 3*u -- + -- ---- + ---- 6 6 8 8 ------- - ----------- t*u 2 s
2 2 2 2 t u 3⋅t 3⋅u ── + ── ──── + ──── 6 6 8 8 ─────── - ─────────── t⋅u 2 s
- equation_database.isbn_9780511628788.table_7_1_gq_gq(s=s, t=t, u=u)[source]
\(gq \to gq\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{s^{2} + u^{2}}{t^{2}} + \frac{- \frac{4 s^{2}}{9} - \frac{4 u^{2}}{9}}{s u}\),
\frac{s^{2} + u^{2}}{t^{2}} + \frac{- \frac{4 s^{2}}{9} - \frac{4 u^{2}}{9}}{s u}
<apply><plus/><apply><divide/><apply><plus/><apply><power/><ci>s</ci><cn>2</cn></apply><apply><power/><ci>u</ci><cn>2</cn></apply></apply><apply><power/><ci>t</ci><cn>2</cn></apply></apply><apply><divide/><apply><minus/><apply><minus/><apply><divide/><apply><times/><cn>4</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply><cn>9</cn></apply></apply><apply><divide/><apply><times/><cn>4</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply><cn>9</cn></apply></apply><apply><times/><ci>s</ci><ci>u</ci></apply></apply></apply>
(s**2 + u**2)/t**2 + (-4*s**2/9 - 4*u**2/9)/(s*u)
(s.^2 + u.^2)./t.^2 + (-4*s.^2/9 - 4*u.^2/9)./(s.*u)
(s^2 + u^2)/t^2 + (-4/9*s^2 - 4/9*u^2)/(s*u)
(s**2 + u**2)/t**2 + (-4/9*s**2 - 4/9*u**2)/(s*u)
(pow(s, 2) + pow(u, 2))/pow(t, 2) + (-4.0/9.0*pow(s, 2) - 4.0/9.0*pow(u, 2))/(s*u)
(std::pow(s, 2) + std::pow(u, 2))/std::pow(t, 2) + (-4.0/9.0*std::pow(s, 2) - 4.0/9.0*std::pow(u, 2))/(s*u)
(s**2 + u**2)/t**2 + (-4.0d0/9.0d0*s**2 - 4.0d0/9.0d0*u**2)/(s*u)
(s.powi(2) + u.powi(2))/t.powi(2) + (-4_f64/9.0*s.powi(2) - 4_f64/9.0*u.powi(2))/(s*u)
2 2 4*s 4*u 2 2 - ---- - ---- s + u 9 9 ------- + ------------- 2 s*u t
2 2 4⋅s 4⋅u 2 2 - ──── - ──── s + u 9 9 ─────── + ───────────── 2 s⋅u t
- equation_database.isbn_9780511628788.table_7_1_gg_gg(s=s, t=t, u=u)[source]
\(gg \to gg\)
The invariant matrix elements squared for two-to-two parton subprocesses with massless partons. The colour and spin indices are averaged (summed) over initial (final) states.
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(- \frac{9 s t}{2 u^{2}} - \frac{9 s u}{2 t^{2}} + \frac{27}{2} - \frac{9 t u}{2 s^{2}}\),
- \frac{9 s t}{2 u^{2}} - \frac{9 s u}{2 t^{2}} + \frac{27}{2} - \frac{9 t u}{2 s^{2}}
<apply><plus/><apply><minus/><apply><minus/><apply><divide/><apply><times/><cn>9</cn><ci>s</ci><ci>t</ci></apply><apply><times/><cn>2</cn><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply></apply><apply><divide/><apply><times/><cn>9</cn><ci>s</ci><ci>u</ci></apply><apply><times/><cn>2</cn><apply><power/><ci>t</ci><cn>2</cn></apply></apply></apply></apply><apply><minus/><apply><divide/><cn>27</cn><cn>2</cn></apply><apply><divide/><apply><times/><cn>9</cn><ci>t</ci><ci>u</ci></apply><apply><times/><cn>2</cn><apply><power/><ci>s</ci><cn>2</cn></apply></apply></apply></apply></apply>
-9*s*t/(2*u**2) - 9*s*u/(2*t**2) + 27/2 - 9*t*u/(2*s**2)
-9*s.*t./(2*u.^2) - 9*s.*u./(2*t.^2) + 27/2 - 9*t.*u./(2*s.^2)
-9/2*s*t/u^2 - 9/2*s*u/t^2 + 27/2 - 9/2*t*u/s^2
-9/2*s*t/u**2 - 9/2*s*u/t**2 + 27/2 - 9/2*t*u/s**2
-9.0/2.0*s*t/pow(u, 2) - 9.0/2.0*s*u/pow(t, 2) + 27.0/2.0 - 9.0/2.0*t*u/pow(s, 2)
-9.0/2.0*s*t/std::pow(u, 2) - 9.0/2.0*s*u/std::pow(t, 2) + 27.0/2.0 - 9.0/2.0*t*u/std::pow(s, 2)
-9.0d0/2.0d0*s*t/u**2 - 9.0d0/2.0d0*s*u/t**2 + 27.0d0/2.0d0 - @ 9.0d0/2.0d0*t*u/s**2
-9_f64/2.0*t*u*s.powi(-2) - 9_f64/2.0*s*u*t.powi(-2) - 9_f64/2.0*s*t*u.powi(-2) + 27_f64/2.0
9*s*t 9*s*u 27 9*t*u - ----- - ----- + -- - ----- 2 2 2 2 2*u 2*t 2*s
9⋅s⋅t 9⋅s⋅u 27 9⋅t⋅u - ───── - ───── + ── - ───── 2 2 2 2 2⋅u 2⋅t 2⋅s
- equation_database.isbn_9780511628788.table_7_2_qq_ag(s=s, t=t, u=u, N=N)[source]
\(q\bar q \to \gamma^* g\)
Lowest order processes for virtual photon production. The colour and spin indices are averaged (summed) over initial (final) states. For a real photon (s + t + u) = 0 and for SU(3) we have N = 3
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
N – Number of colors
- Returns:
\(\frac{\left(N^{2} - 1\right) \left(2 s \left(s + t + u\right) + t^{2} + u^{2}\right)}{N^{2} t u}\),
\frac{\left(N^{2} - 1\right) \left(2 s \left(s + t + u\right) + t^{2} + u^{2}\right)}{N^{2} t u}
<apply><divide/><apply><times/><apply><minus/><apply><power/><ci>N</ci><cn>2</cn></apply><cn>1</cn></apply><apply><plus/><apply><times/><cn>2</cn><ci>s</ci><apply><plus/><ci>s</ci><ci>t</ci><ci>u</ci></apply></apply><apply><power/><ci>t</ci><cn>2</cn></apply><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply><apply><times/><apply><power/><ci>N</ci><cn>2</cn></apply><ci>t</ci><ci>u</ci></apply></apply>
(N**2 - 1)*(2*s*(s + t + u) + t**2 + u**2)/(N**2*t*u)
(N.^2 - 1).*(2*s.*(s + t + u) + t.^2 + u.^2)./(N.^2.*t.*u)
(N^2 - 1)*(2*s*(s + t + u) + t^2 + u^2)/(N^2*t*u)
(N**2 - 1)*(2*s*(s + t + u) + t**2 + u**2)/(N**2*t*u)
(pow(N, 2) - 1)*(2*s*(s + t + u) + pow(t, 2) + pow(u, 2))/(pow(N, 2)*t*u)
(std::pow(N, 2) - 1)*(2*s*(s + t + u) + std::pow(t, 2) + std::pow(u, 2))/(std::pow(N, 2)*t*u)
(N**2 - 1)*(2*s*(s + t + u) + t**2 + u**2)/(N**2*t*u)
(N.powi(2) - 1)*(2*s*(s + t + u) + t.powi(2) + u.powi(2))/(N.powi(2)*t*u)
/ 2 \ / 2 2\ \N - 1/*\2*s*(s + t + u) + t + u / ------------------------------------ 2 N *t*u
⎛ 2 ⎞ ⎛ 2 2⎞ ⎝N - 1⎠⋅⎝2⋅s⋅(s + t + u) + t + u ⎠ ──────────────────────────────────── 2 N ⋅t⋅u
- equation_database.isbn_9780511628788.table_7_2_gq_aq(s=s, t=t, u=u, N=N)[source]
\(gq \to \gamma^* q\)
Lowest order processes for virtual photon production. The colour and spin indices are averaged (summed) over initial (final) states. For a real photon (s + t + u) = 0 and for SU(3) we have N = 3
- Parameters:
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
N – Number of colors
- Returns:
\(- \frac{s^{2} + \frac{t \left(s + t + u\right)}{u} + u^{2}}{N}\),
- \frac{s^{2} + \frac{t \left(s + t + u\right)}{u} + u^{2}}{N}
<apply><minus/><apply><divide/><apply><plus/><apply><power/><ci>s</ci><cn>2</cn></apply><apply><divide/><apply><times/><ci>t</ci><apply><plus/><ci>s</ci><ci>t</ci><ci>u</ci></apply></apply><ci>u</ci></apply><apply><power/><ci>u</ci><cn>2</cn></apply></apply><ci>N</ci></apply></apply>
-(s**2 + t*(s + t + u)/u + u**2)/N
-(s.^2 + t.*(s + t + u)./u + u.^2)./N
-(s^2 + t*(s + t + u)/u + u^2)/N
-(s**2 + t*(s + t + u)/u + u**2)/N
-(pow(s, 2) + t*(s + t + u)/u + pow(u, 2))/N
-(std::pow(s, 2) + t*(s + t + u)/u + std::pow(u, 2))/N
-(s**2 + t*(s + t + u)/u + u**2)/N
-(s.powi(2) + t*(s + t + u)/u + u.powi(2))/N
/ 2 t*(s + t + u) 2\ -|s + ------------- + u | \ u / --------------------------- N
⎛ 2 t⋅(s + t + u) 2⎞ -⎜s + ───────────── + u ⎟ ⎝ u ⎠ ─────────────────────────── N
- equation_database.isbn_9780511628788.bibtex()[source]
DOI, QCD and collider physics
@book{Ellis:1996mzs, author = "Ellis, R. Keith and Stirling, W. James and Webber, B. R.", title = "{QCD and collider physics}", doi = "10.1017/CBO9780511628788", isbn = "978-0-511-82328-2, 978-0-521-54589-1", publisher = "Cambridge University Press", volume = "8", month = "2", year = "2011" }