equation_database.isbn_9780471887416
Functions
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QUARKS AND LEPTONS: AN INTRODUCTORY COURSE IN MODERN PARTICLE PHYSICS |
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spin and color averaged matrix element for electron-positron annihilation into quark-antiquark-gluon final state |
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spin averaged Compton amplitude |
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unpolarized \(e^-\mu^- \to e^-\mu^-\) scattering amplitude |
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unpolarized \(e^-e^+ \to \mu^-\mu^+\) scattering amplitude |
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Differential cross section for \(e^+e^- \to \mu^+\mu^-\) in the center of mass frame |
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Cross section for \(e^+e^- \to \mu^+\mu^-\) |
- equation_database.isbn_9780471887416.equation_6_30(e=e, s=s, t=t, u=u)[source]
unpolarized \(e^-\mu^- \to e^-\mu^-\) scattering amplitude
- Parameters:
e – Elementary charge
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{2 e^{4} \left(s^{2} + u^{2}\right)}{t^{2}}\),
\frac{2 e^{4} \left(s^{2} + u^{2}\right)}{t^{2}}
<apply><divide/><apply><times/><cn>2</cn><apply><power/><ci>e</ci><cn>4</cn></apply><apply><plus/><apply><power/><ci>s</ci><cn>2</cn></apply><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply><apply><power/><ci>t</ci><cn>2</cn></apply></apply>
2*e**4*(s**2 + u**2)/t**2
2*e.^4.*(s.^2 + u.^2)./t.^2
2*e^4*(s^2 + u^2)/t^2
2*e**4*(s**2 + u**2)/t**2
2*pow(e, 4)*(pow(s, 2) + pow(u, 2))/pow(t, 2)
2*std::pow(e, 4)*(std::pow(s, 2) + std::pow(u, 2))/std::pow(t, 2)
2*e**4*(s**2 + u**2)/t**2
2*e.powi(4)*(s.powi(2) + u.powi(2))/t.powi(2)
4 / 2 2\ 2*e *\s + u / -------------- 2 t
4 ⎛ 2 2⎞ 2⋅e ⋅⎝s + u ⎠ ────────────── 2 t
- equation_database.isbn_9780471887416.equation_6_31(e=e, s=s, t=t, u=u)[source]
unpolarized \(e^-e^+ \to \mu^-\mu^+\) scattering amplitude
- Parameters:
e – Elementary charge
s – Mandelstam variable s
t – Mandelstam variable t
u – Mandelstam variable u
- Returns:
\(\frac{2 e^{4} \left(t^{2} + u^{2}\right)}{s^{2}}\),
\frac{2 e^{4} \left(t^{2} + u^{2}\right)}{s^{2}}
<apply><divide/><apply><times/><cn>2</cn><apply><power/><ci>e</ci><cn>4</cn></apply><apply><plus/><apply><power/><ci>t</ci><cn>2</cn></apply><apply><power/><ci>u</ci><cn>2</cn></apply></apply></apply><apply><power/><ci>s</ci><cn>2</cn></apply></apply>
2*e**4*(t**2 + u**2)/s**2
2*e.^4.*(t.^2 + u.^2)./s.^2
2*e^4*(t^2 + u^2)/s^2
2*e**4*(t**2 + u**2)/s**2
2*pow(e, 4)*(pow(t, 2) + pow(u, 2))/pow(s, 2)
2*std::pow(e, 4)*(std::pow(t, 2) + std::pow(u, 2))/std::pow(s, 2)
2*e**4*(t**2 + u**2)/s**2
2*e.powi(4)*(t.powi(2) + u.powi(2))/s.powi(2)
4 / 2 2\ 2*e *\t + u / -------------- 2 s
4 ⎛ 2 2⎞ 2⋅e ⋅⎝t + u ⎠ ────────────── 2 s
- equation_database.isbn_9780471887416.equation_6_32(sigma=sigma, Omega=Omega, alpha=alpha, s=s, theta=theta)[source]
Differential cross section for \(e^+e^- \to \mu^+\mu^-\) in the center of mass frame
- Parameters:
sigma – cross section
Omega – solid angle
alpha – fine structure constant
s – Mandelstam variable s
theta – scattering angle of the muons
- Returns:
\(\frac{d}{d \Omega} \sigma = \frac{\alpha^{2} \left(\cos^{2}{\left(\theta \right)} + 1\right)}{4 s}\),
\frac{d}{d \Omega} \sigma = \frac{\alpha^{2} \left(\cos^{2}{\left(\theta \right)} + 1\right)}{4 s}
<apply><eq/><apply><diff/><bvar><ci>Ω</ci></bvar><ci>σ</ci></apply><apply><divide/><apply><times/><apply><power/><ci>α</ci><cn>2</cn></apply><apply><plus/><apply><power/><apply><cos/><ci>θ</ci></apply><cn>2</cn></apply><cn>1</cn></apply></apply><apply><times/><cn>4</cn><ci>s</ci></apply></apply></apply>
Eq(Derivative(sigma, Omega), alpha**2*(cos(theta)**2 + 1)/(4*s))
Hold[D[sigma, Omega]] == (1/4)*alpha^2*(Cos[theta]^2 + 1)/s
2 / 2 \ d alpha *\cos (theta) + 1/ ------(sigma) = ------------------------ dOmega 4*s
2 ⎛ 2 ⎞ d α ⋅⎝cos (θ) + 1⎠ ──(σ) = ──────────────── dΩ 4⋅s
- equation_database.isbn_9780471887416.equation_6_33(sigma=sigma, alpha=alpha, s=s)[source]
Cross section for \(e^+e^- \to \mu^+\mu^-\)
- Parameters:
sigma – cross section
alpha – fine structure constant
s – Mandelstam variable s
- Returns:
\(\sigma = \frac{4 \pi \alpha^{2}}{3 s}\),
\sigma = \frac{4 \pi \alpha^{2}}{3 s}
<apply><eq/><ci>σ</ci><apply><divide/><apply><times/><cn>4</cn><pi/><apply><power/><ci>α</ci><cn>2</cn></apply></apply><apply><times/><cn>3</cn><ci>s</ci></apply></apply></apply>
Eq(sigma, 4*pi*alpha**2/(3*s))
sigma == 4*pi*alpha.^2./(3*s)
sigma == (4/3)*Pi*alpha^2/s
(sigma == (4/3)*math.pi*alpha**2/s)
sigma == (4.0/3.0)*M_PI*pow(alpha, 2)/s
sigma == (4.0/3.0)*M_PI*std::pow(alpha, 2)/s
parameter (pi = 3.1415926535897932d0) sigma == (4.0d0/3.0d0)*pi*alpha**2/s
sigma == (4_f64/3.0)*PI*alpha.powi(2)*s.recip()
2 4*pi*alpha sigma = ----------- 3*s
2 4⋅π⋅α σ = ────── 3⋅s
- equation_database.isbn_9780471887416.equation_6_113(e=e, s=s, u=u)[source]
spin averaged Compton amplitude
- Parameters:
e – Elementary charge
s – Mandelstam variable s
u – Mandelstam variable u
- Returns:
\(2 e^{4} \left(- \frac{s}{u} - \frac{u}{s}\right)\),
2 e^{4} \left(- \frac{s}{u} - \frac{u}{s}\right)
<apply><times/><cn>2</cn><apply><power/><ci>e</ci><cn>4</cn></apply><apply><minus/><apply><minus/><apply><divide/><ci>s</ci><ci>u</ci></apply></apply><apply><divide/><ci>u</ci><ci>s</ci></apply></apply></apply>
2*e**4*(-s/u - u/s)
2*e.^4.*(-s./u - u./s)
2*e^4*(-s/u - u/s)
2*e**4*(-s/u - u/s)
2*pow(e, 4)*(-s/u - u/s)
2*std::pow(e, 4)*(-s/u - u/s)
2*e**4*(-s/u - u/s)
2*e.powi(4)*(-s/u - u/s)
4 / s u\ 2*e *|- - - -| \ u s/
4 ⎛ s u⎞ 2⋅e ⋅⎜- ─ - ─⎟ ⎝ u s⎠
- equation_database.isbn_9780471887416.equation_11_35(N=N, x_q=x_q, x_qbar=x_qbar)[source]
spin and color averaged matrix element for electron-positron annihilation into quark-antiquark-gluon final state
- Parameters:
N – Normalization factor
x_q – Quark momentum fraction
x_qbar – Antiquark momentum fraction
- Returns:
\(\frac{N \left(x_{q}^{2} + x_{\bar{q}}^{2}\right)}{\left(1 - x_{q}\right) \left(1 - x_{\bar{q}}\right)}\),
\frac{N \left(x_{q}^{2} + x_{\bar{q}}^{2}\right)}{\left(1 - x_{q}\right) \left(1 - x_{\bar{q}}\right)}
<apply><divide/><apply><times/><ci>N</ci><apply><plus/><apply><power/><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>q</mml:mi></mml:msub></ci><cn>2</cn></apply><apply><power/><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>qbar</mml:mi></mml:msub></ci><cn>2</cn></apply></apply></apply><apply><times/><apply><minus/><cn>1</cn><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>q</mml:mi></mml:msub></ci></apply><apply><minus/><cn>1</cn><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>qbar</mml:mi></mml:msub></ci></apply></apply></apply>
N*(x_q**2 + x_qbar**2)/((1 - x_q)*(1 - x_qbar))
N.*(x_q.^2 + x_qbar.^2)./((1 - x_q).*(1 - x_qbar))
N*(x_q^2 + x_qbar^2)/((1 - x_q)*(1 - x_qbar))
N*(x_q**2 + x_qbar**2)/((1 - x_q)*(1 - x_qbar))
N*(pow(x_q, 2) + pow(x_qbar, 2))/((1 - x_q)*(1 - x_qbar))
N*(std::pow(x_q, 2) + std::pow(x_qbar, 2))/((1 - x_q)*(1 - x_qbar))
N*(x_q**2 + x_qbar**2)/((1 - x_q)*(1 - x_qbar))
N*(x_q.powi(2) + x_qbar.powi(2))/((1 - x_q)*(1 - x_qbar))
/ 2 2\ N*\x_q + x_qbar / ---------------------- (1 - x_q)*(1 - x_qbar)
⎛ 2 2⎞ N⋅⎝x_q + x_q̅ ⎠ ─────────────────── (1 - x_q)⋅(1 - x_q̅)
- equation_database.isbn_9780471887416.bibtex()[source]
QUARKS AND LEPTONS: AN INTRODUCTORY COURSE IN MODERN PARTICLE PHYSICS
@book{Halzen:1984mc, author = "Halzen, F. and Martin, Alan D.", title = "{QUARKS AND LEPTONS: AN INTRODUCTORY COURSE IN MODERN PARTICLE PHYSICS}", isbn = "978-0-471-88741-6", year = "1984" }