DOC: manual formulation of helicity amplitudes for pgamma->LambdaKPi #104
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shenvitor
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Sep 2, 2024
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shenvitor
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- Closes Manually formulate symbolic helicity amplitude for pγ → ΛKπ #103
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| "three_half = sp.Rational(3, 2)\n", | ||
| "five_half = sp.Rational(5, 2)\n", | ||
| "seven_half = sp.Rational(7, 2)" |
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I would only define half and then write e.g. 3 * half
| "wigner_d_11_R1 = Wigner.d(half, λ1prime, λ1, zeta_1_1)\n", | ||
| "wigner_d_00_R1 = Wigner.d(half, λ0prime, λ0, zeta_1_0)\n", | ||
| "wigner_d_11_R2 = Wigner.d(half, λ1prime, λ1, zeta_2_1)\n", | ||
| "wigner_d_00_R2 = Wigner.d(half, λ0prime, λ0, zeta_2_0)\n", | ||
| "wigner_d_11_R3 = Wigner.d(half, λ1prime, λ1, zeta_3_1)\n", | ||
| "wigner_d_00_R3 = Wigner.d(half, λ0prime, λ0, zeta_3_0)\n", |
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I would not define these intermediate variables. It's easier to read (and debug) if the Wigner.d functions are called inline, especially because the A1_aligned definition fits on one line (you may need to write λ1p). The problem is that it is easy to make typos in these kind of repetitive variable name definitions.
| "zeta_1_0, zeta_1_1, zeta_2_0, zeta_2_1, zeta_3_0, zeta_3_1 = sp.symbols(\n", | ||
| " r\"\\zeta_{1(1)}^0 \\zeta_{1(1)}^1 \\zeta_{2(1)}^0 \\zeta_{2(1)}^1 \\zeta_{3(1)}^0 \\zeta_{3(1)}^1\"\n", | ||
| ")\n", |
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In this case I would use sp.Symbol and define each zeta separately. It's more scalable and helps finding bugs if each symbol definition is below the other.
| "A1 = (\n", | ||
| " formualte_A1(\"K^{*}(1410)^+\", 1)\n", | ||
| " + formualte_A1(\"K^{*}(1680)^+\", 1)\n", | ||
| " + formualte_A1(\"K^{*}(892)^+\", 1)\n", | ||
| " + formualte_A1(\"K^{*}_0(1430)^+\", 0)\n", | ||
| " + formualte_A1(\"K^{*}_0(700)\", 0)\n", | ||
| " + formualte_A1(\"K^{*}_2(1430)\", 2)\n", | ||
| " + formualte_A1(\"K^{*}_3(1780)\", 3)\n", | ||
| " + formualte_A1(\"K^{*}_4(2045)\", 4)\n", | ||
| ")\n", | ||
| "A1" |
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This will need to be automated, i.e., some loop over the formulate_A1() is more something like formulate_chain_amplitude_a1() and formulate_a1() creates the coherent sum of those chain amplitudes.
| " r\"s_{31} m_{\\Sigma^*} \\Gamma_{\\Sigma^*} C_{\\Sigma^*}\"\n", | ||
| ")\n", | ||
| "theta31, phi31, delta = sp.symbols(r\"theta_31 phi_31 \\delta_{\\lambda_\\Sigma^*1/2}\")\n", | ||
| "d_s = sp.Function(r\"d_{\\lambda_\\Sigma^*1/2}^{1/2}\")\n", |
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Replace with Wigner.d and use directly inline in the expression definition
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "A1 = (\n", |
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Be careful not to overwrite the previous A1 definition. This should be the A1_expr, or even something like a mapping of sp.Symbol to sp.Expr as dictionary. Something like:
amplitudes = {}
amplitudes[A1[-half, +half]] = formulate_A1(...) + ...
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