equation_database.doi_10_1103_PhysRevD_16_3251
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DOI, Jet Structure in e+ e- Annihilation as a Test of QCD and the Quark-Confining String |
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- equation_database.doi_10_1103_PhysRevD_16_3251.equation_2_8(sigma_pt=sigma_pt, alpha=alpha, Q=Q, sum_e_q_squared=sum_e_q_squared)[source]
- Parameters:
sigma_pt – Parton cross section
alpha – Fine structure constant
Q – Mass of the electron pair (virtual photon)
sum_e_q_squared – Sum of electric charges of quarks squared
- Returns:
\(\sigma_{pt} = \frac{4 \pi \alpha^{2} sum_{e q squared}}{Q^{2}}\),
\sigma_{pt} = \frac{4 \pi \alpha^{2} sum_{e q squared}}{Q^{2}}
<apply><eq/><ci><mml:msub><mml:mi>σ</mml:mi><mml:mi>pt</mml:mi></mml:msub></ci><apply><divide/><apply><times/><cn>4</cn><pi/><apply><power/><ci>α</ci><cn>2</cn></apply><ci><mml:msub><mml:mi>sum</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mo> </mml:mo><mml:mi>q</mml:mi><mml:mo> </mml:mo><mml:mi>squared</mml:mi></mml:mrow></mml:msub></ci></apply><apply><power/><ci>Q</ci><cn>2</cn></apply></apply></apply>
Eq(sigma_pt, 4*pi*alpha**2*sum_e_q_squared/Q**2)
sigma_pt == 4*pi*alpha.^2.*sum_e_q_squared./Q.^2
sigma_pt == 4*Pi*alpha^2*sum_e_q_squared/Q^2
(sigma_pt == 4*math.pi*alpha**2*sum_e_q_squared/Q**2)
sigma_pt == 4*M_PI*pow(alpha, 2)*sum_e_q_squared/pow(Q, 2)
sigma_pt == 4*M_PI*std::pow(alpha, 2)*sum_e_q_squared/std::pow(Q, 2)
parameter (pi = 3.1415926535897932d0) sigma_pt == 4*pi*alpha**2*sum_e_q_squared/Q**2
sigma_pt == 4.0*PI*sum_e_q_squared*Q.powi(-2)*alpha.powi(2)
2 4*pi*alpha *sum_e_q_squared sigma_pt = --------------------------- 2 Q
2 4⋅π⋅α ⋅sum_e_q_squared σₚₜ = ────────────────────── 2 Q
- equation_database.doi_10_1103_PhysRevD_16_3251.equation_2_9(sigma=sigma, sigma_pt=sigma_pt, x_1=x_1, x_2=x_2, alpha_C=alpha_C)[source]
- Parameters:
sigma – Cross section
sigma_pt – Parton cross section
x_1 – Quark momentum fraction
x_2 – Antiquark momentum fraction
alpha_C – Colour charge
- Returns:
\(\frac{\frac{d^{2}}{d x_{2}d x_{1}} \sigma}{\sigma_{pt}} = \frac{2 \alpha_{C} \left(x_{1}^{2} + x_{2}^{2}\right)}{3 \pi \left(1 - x_{1}\right) \left(1 - x_{2}\right)}\),
\frac{\frac{d^{2}}{d x_{2}d x_{1}} \sigma}{\sigma_{pt}} = \frac{2 \alpha_{C} \left(x_{1}^{2} + x_{2}^{2}\right)}{3 \pi \left(1 - x_{1}\right) \left(1 - x_{2}\right)}
<apply><eq/><apply><divide/><apply><diff/><bvar><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>2</mml:mi></mml:msub></ci><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>1</mml:mi></mml:msub></ci></bvar><ci>σ</ci></apply><ci><mml:msub><mml:mi>σ</mml:mi><mml:mi>pt</mml:mi></mml:msub></ci></apply><apply><divide/><apply><times/><cn>2</cn><ci><mml:msub><mml:mi>α</mml:mi><mml:mi>C</mml:mi></mml:msub></ci><apply><plus/><apply><power/><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>1</mml:mi></mml:msub></ci><cn>2</cn></apply><apply><power/><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>2</mml:mi></mml:msub></ci><cn>2</cn></apply></apply></apply><apply><times/><cn>3</cn><pi/><apply><minus/><cn>1</cn><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>1</mml:mi></mml:msub></ci></apply><apply><minus/><cn>1</cn><ci><mml:msub><mml:mi>x</mml:mi><mml:mi>2</mml:mi></mml:msub></ci></apply></apply></apply></apply>
Eq(Derivative(sigma, x_1, x_2)/sigma_pt, 2*alpha_C*(x_1**2 + x_2**2)/(3*pi*(1 - x_1)*(1 - x_2)))
Hold[D[sigma, x_1, x_2]]/sigma_pt == (2/3)*alpha_C*(x_1^2 + x_2^2)/(Pi*(1 - x_1)*(1 - x_2))
2 d ---------(sigma) / 2 2\ dx_2 dx_1 2*alpha_C*\x_1 + x_2 / ---------------- = ------------------------ sigma_pt 3*pi*(1 - x_1)*(1 - x_2)
2 d ───────(σ) ⎛ 2 2⎞ dx₂ dx₁ 2⋅α_C⋅⎝x₁ + x₂ ⎠ ────────── = ───────────────────── σₚₜ 3⋅π⋅(1 - x₁)⋅(1 - x₂)
- equation_database.doi_10_1103_PhysRevD_16_3251.bibtex()[source]
DOI, Jet Structure in e+ e- Annihilation as a Test of QCD and the Quark-Confining String
@article{DeGrand:1977sy, author = "DeGrand, Thomas A. and Ng, Yee Jack and Tye, S. H. H.", title = "{Jet Structure in e+ e- Annihilation as a Test of QCD and the Quark-Confining String}", reportNumber = "SLAC-PUB-1950", doi = "10.1103/PhysRevD.16.3251", journal = "Phys. Rev. D", volume = "16", pages = "3251", year = "1977" }