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File indexing completed on 2026-06-02 08:17:15
0001 // 0002 // APFEL++ 2017 0003 // 0004 // Author: Valerio Bertone: valerio.bertone@cern.ch 0005 // 0006 0007 #pragma once 0008 0009 #include "apfel/grid.h" 0010 #include "apfel/operator.h" 0011 #include "apfel/set.h" 0012 #include "apfel/dglapbuilder.h" 0013 #include "apfel/tabulateobject.h" 0014 #include "apfel/constants.h" 0015 0016 namespace apfel 0017 { 0018 /** 0019 * @brief Structure that contains all precomputed quantities needed 0020 * to perform the TMD evolution, matching to the collinear PDFs, and 0021 * computation of cross sections, i.e. the perturbative coefficients 0022 * of matching functions, all anomalous dimensions, and hard 0023 * functions. 0024 */ 0025 struct TmdObjects 0026 { 0027 double Threshold; 0028 std::map<int, double> Beta; 0029 std::map<int, double> GammaFq; 0030 std::map<int, double> GammaFg; 0031 std::map<int, double> GammaK; 0032 std::map<int, std::vector<double>> KCS; 0033 std::map<int, std::vector<Set<Operator>>> MatchingFunctionsPDFs; 0034 std::map<int, std::vector<Set<Operator>>> MatchingFunctionsFFs; 0035 std::map<std::string, std::map<int, double>> HardFactors; 0036 }; 0037 0038 /** 0039 * @name TMD object initializers 0040 * Collection of functions that initialise a TmdObjects structure 0041 * for the perturbartive evolution and the matching. 0042 */ 0043 ///@{ 0044 /** 0045 * @brief The InitializeTmdObjects function precomputes the 0046 * perturbative coefficients required for the evolution and matching 0047 * of TMD PDFs and FFs and store them into a 'TmdObjects' structure. 0048 * @param g: the x-space grid 0049 * @param Thresholds: the heavy quark thresholds 0050 * @param IntEps: the integration accuracy (default: 10<SUP>-5</SUP>) 0051 * @return A map of TmdObject objects, one for each possible nf 0052 */ 0053 std::map<int, TmdObjects> InitializeTmdObjects(Grid const& g, 0054 std::vector<double> const& Thresholds, 0055 double const& IntEps = 1e-5); 0056 0057 /** 0058 * @brief The InitializeTmdObjectsDYResScheme function precomputes 0059 * the perturbative coefficients required for the evolution and 0060 * matching of TMD PDFs and FFs and store them into a 'TmdObjects' 0061 * structure. This function applies a resummation-scheme 0062 * transformation to produce the scheme often used in qT resummation 0063 * that has H = 1. 0064 * @param g: the x-space grid 0065 * @param Thresholds: the heavy quark thresholds 0066 * @param IntEps: the integration accuracy (default: 10<SUP>-5</SUP>) 0067 * @return A map of TmdObject objects, one for each possible nf 0068 */ 0069 std::map<int, TmdObjects> InitializeTmdObjectsDYResScheme(Grid const& g, 0070 std::vector<double> const& Thresholds, 0071 double const& IntEps = 1e-5); 0072 0073 /** 0074 * @brief The InitializeTmdObjectsBM function precomputes the 0075 * perturbative coefficients required for the evolution and matching 0076 * of the (gluon) Boer-Mulders TMD PDF and store them into a 0077 * 'TmdObjects' structure. For now, quark and FF TMDs are not filled 0078 * in. 0079 * @param g: the x-space grid 0080 * @param Thresholds: the heavy quark thresholds 0081 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0082 * @return A map of TmdObject objects, one for each possible nf 0083 */ 0084 std::map<int, TmdObjects> InitializeTmdObjectsBM(Grid const& g, 0085 std::vector<double> const& Thresholds, 0086 double const& IntEps = 1e-5); 0087 0088 /** 0089 * @brief The InitializeTmdObjectsSivers function precomputes the 0090 * perturbative coefficients required for the evolution and matching 0091 * of the quark Sivers TMD PDF and store them into a 'TmdObjects' 0092 * structure. For now, gluon and FF TMDs (i.e. the Collins TMDs) are 0093 * not filled in. In addition, the matching is only present up to 0094 * one loop. 0095 * @param g: the x-space grid 0096 * @param Thresholds: the heavy quark thresholds 0097 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0098 * @return A map of TmdObject objects, one for each possible nf 0099 */ 0100 std::map<int, TmdObjects> InitializeTmdObjectsSivers(Grid const& g, 0101 std::vector<double> const& Thresholds, 0102 double const& IntEps = 1e-5); 0103 0104 /** 0105 * @brief The InitializeTmdObjects function precomputes the 0106 * perturbative coefficients required for the evolution and matching 0107 * of TMD g1 PDFs and FFs and store them into a 'TmdObjects' 0108 * structure. Matching functions are implemented only to one-loop 0109 * order. 0110 * @param g: the x-space grid 0111 * @param Thresholds: the heavy quark thresholds 0112 * @param IntEps: the integration accuracy (default: 10<SUP>-5</SUP>) 0113 * @return A map of TmdObject objects, one for each possible nf 0114 */ 0115 std::map<int, TmdObjects> InitializeTmdObjectsg1(Grid const& g, 0116 std::vector<double> const& Thresholds, 0117 double const& IntEps = 1e-5); 0118 ///@} 0119 0120 /** 0121 * @name TMD builders 0122 * Collection of functions that build a TMD distributions (both PDFs 0123 * and FFs) as Set<Distribution>-valued functions. These functions 0124 * perform evolution and matching either separately or alltogether. 0125 * Also a function for the computation of the hard factors is 0126 * provided. 0127 */ 0128 ///@{ 0129 /** 0130 * @brief Function that returns the matched and evolved TMD PDFs in 0131 * b-space as functions of the final scale and rapidity. 0132 * @param TmdObj: the TMD objects 0133 * @param CollPDFs: the set of collinear PDFs to be matched 0134 * @param Alphas: the strong coupling function 0135 * @param PerturbativeOrder: the logarithmic perturbative order 0136 * @param Ci: the initial-scale variation factor (default: 1) 0137 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0138 * @return Set<Distribution>-valued function of the impact parameter 0139 * b<SUB>T</SUB>, the final renormalisation scale μ, and the 0140 * final rapidity scale ζ representing the evolved TMD PDFs 0141 */ 0142 std::function<Set<Distribution>(double const&, double const&, double const&)> BuildTmdPDFs(std::map<int, TmdObjects> const& TmdObj, 0143 std::function<Set<Distribution>(double const&)> const& CollPDFs, 0144 std::function<double(double const&)> const& Alphas, 0145 int const& PerturbativeOrder, 0146 double const& Ci = 1, 0147 double const& IntEps = 1e-7); 0148 0149 /** 0150 * @brief Function that returns the matched and evolved TMD FFs in 0151 * b-space as functions of the final scale and rapidity. 0152 * @param TmdObj: the TMD objects 0153 * @param CollFFs: the set of collinear PDFs to be matched 0154 * @param Alphas: the strong coupling function 0155 * @param PerturbativeOrder: the logarithmic perturbative order 0156 * @param Ci: the initial-scale variation factor (default: 1) 0157 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0158 * @return Set<Distribution>-valued function of the impact parameter 0159 * b<SUB>T</SUB>, the final renormalisation scale μ, and the 0160 * final rapidity scale ζ representing the evolved TMD FFs 0161 */ 0162 std::function<Set<Distribution>(double const&, double const&, double const&)> BuildTmdFFs(std::map<int, TmdObjects> const& TmdObj, 0163 std::function<Set<Distribution>(double const&)> const& CollFFs, 0164 std::function<double(double const&)> const& Alphas, 0165 int const& PerturbativeOrder, 0166 double const& Ci = 1, 0167 double const& IntEps = 1e-7); 0168 0169 /** 0170 * @brief Function that returns the matched TMD PDFs in b-space. 0171 * @param TmdObj: the TMD objects 0172 * @param CollPDFs: the set of collinear PDFs to be matched 0173 * @param Alphas: the strong coupling function 0174 * @param PerturbativeOrder: the logarithmic perturbative order 0175 * @param Ci: the initial-scale variation factor 0176 * @return Set<Distribution>-valued function of the impact parameter 0177 * b<SUB>T</SUB> representing the matched TMD PDFs 0178 */ 0179 std::function<Set<Distribution>(double const&)> MatchTmdPDFs(std::map<int, TmdObjects> const& TmdObj, 0180 std::function<Set<Distribution>(double const&)> const& CollPDFs, 0181 std::function<double(double const&)> const& Alphas, 0182 int const& PerturbativeOrder, 0183 double const& Ci = 1); 0184 0185 /** 0186 * @brief Function that returns the matched TMD FFs in b-space. 0187 * @param TmdObj: the TMD objects 0188 * @param CollFFs: the set of collinear FFs to be matched 0189 * @param Alphas: the strong coupling function 0190 * @param PerturbativeOrder: the logarithmic perturbative order 0191 * @param Ci: the initial-scale variation factor 0192 * @return Set<Distribution>-valued function of the impact parameter 0193 * b<SUB>T</SUB> representing the matched TMD FFs 0194 */ 0195 std::function<Set<Distribution>(double const&)> MatchTmdFFs(std::map<int, TmdObjects> const& TmdObj, 0196 std::function<Set<Distribution>(double const&)> const& CollFFs, 0197 std::function<double(double const&)> const& Alphas, 0198 int const& PerturbativeOrder, 0199 double const& Ci = 1); 0200 0201 /** 0202 * @brief Function that returns the mathing functions for the TMD PDFs. 0203 * @param TmdObj: the TMD objects 0204 * @param Alphas: the strong coupling function 0205 * @param PerturbativeOrder: the logarithmic perturbative order 0206 * @param Ci: the initial-scale variation factor 0207 * @return Set<Operator>-valued function of the scale mu 0208 * corresponding to the set of matching functions for PDFs in the 0209 * evolution basis. 0210 */ 0211 std::function<Set<Operator>(double const&)> MatchingFunctionsPDFs(std::map<int, TmdObjects> const& TmdObj, 0212 std::function<double(double const&)> const& Alphas, 0213 int const& PerturbativeOrder, 0214 double const& Ci = 1); 0215 0216 /** 0217 * @brief Function that returns the mathing functions for the TMD FFs. 0218 * @param TmdObj: the TMD objects 0219 * @param Alphas: the strong coupling function 0220 * @param PerturbativeOrder: the logarithmic perturbative order 0221 * @param Ci: the initial-scale variation factor 0222 * @return Set<Operator>-valued function of the scale mu 0223 * corresponding to the set of matching functions for FFs in the 0224 * evolution basis. 0225 */ 0226 std::function<Set<Operator>(double const&)> MatchingFunctionsFFs(std::map<int, TmdObjects> const& TmdObj, 0227 std::function<double(double const&)> const& Alphas, 0228 int const& PerturbativeOrder, 0229 double const& Ci = 1); 0230 0231 /** 0232 * @brief Function that returns the evolution factors for gluon and quarks. 0233 * @param TmdObj: the TMD objects 0234 * @param Alphas: the strong coupling function 0235 * @param PerturbativeOrder: the logarithmic perturbative order 0236 * @param Ci: the initial scale-variation factor (default: 1) 0237 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0238 * @return std::vector<double>-valued function of the impact parameter 0239 * b<SUB>T</SUB>, the final renormalisation scale μ, and the 0240 * final rapidity scale ζ. The 0-th component contains the 0241 * gluon evolution factor, the remaining 12, from 1 to 12, are all 0242 * equal and represent the quark evolution factors. 0243 */ 0244 std::function<std::vector<double>(double const&, double const&, double const&)> EvolutionFactors(std::map<int, TmdObjects> const& TmdObj, 0245 std::function<double(double const&)> const& Alphas, 0246 int const& PerturbativeOrder, 0247 double const& Ci = 1, 0248 double const& IntEps = 1e-7); 0249 0250 /** 0251 * @brief Function that returns the evolution factors for gluon and 0252 * quarks. As compared to "EvolutionFactors", this function isolates 0253 * the double logs into gammaK. This is reminiscent of the 0254 * qT-resummation typical way of computing the Sudakov form factor. 0255 * @param TmdObj: the TMD objects 0256 * @param Alphas: the strong coupling function 0257 * @param PerturbativeOrder: the logarithmic perturbative order 0258 * @param Ci: the initial scale-variation factor (default: 1) 0259 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0260 * @return std::vector<double>-valued function of the impact parameter 0261 * b<SUB>T</SUB>, the final renormalisation scale μ, and the 0262 * final rapidity scale ζ. The 0-th component contains the 0263 * gluon evolution factor, the remaining 12, from 1 to 12, are all 0264 * equal and represent the quark evolution factors. 0265 */ 0266 std::function<std::vector<double>(double const&, double const&, double const&)> EvolutionFactorsK(std::map<int, TmdObjects> const& TmdObj, 0267 std::function<double(double const&)> const& Alphas, 0268 int const& PerturbativeOrder, 0269 double const& Ci = 1, 0270 double const& IntEps = 1e-7); 0271 0272 /** 0273 * @brief Function that returns the evolution factor for quarks. 0274 * @param TmdObj: the TMD objects 0275 * @param Alphas: the strong coupling function 0276 * @param PerturbativeOrder: the logarithmic perturbative order 0277 * @param Ci: the initial scale-variation factor (default: 1) 0278 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0279 * @return double-valued function of the impact parameter 0280 * b<SUB>T</SUB>, the final renormalisation scale μ, and the 0281 * final rapidity scale ζ. It returns the quark evolution 0282 * factor. 0283 */ 0284 std::function<double(double const&, double const&, double const&)> QuarkEvolutionFactor(std::map<int, TmdObjects> const& TmdObj, 0285 std::function<double(double const&)> const& Alphas, 0286 int const& PerturbativeOrder, 0287 double const& Ci = 1, 0288 double const& IntEps = 1e-7); 0289 0290 /** 0291 * @brief Function that returns the evolution factor for quarks with 0292 * explicit dependence on the resummation-scale parameter. 0293 * @param TmdObj: the TMD objects 0294 * @param Alphas: the strong coupling function 0295 * @param PerturbativeOrder: the logarithmic perturbative order 0296 * @param xi: the resummation-scale parameter (default: 1) 0297 * @param Ci: the initial scale-variation factor (default: 1) 0298 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0299 * @return double-valued function of the impact parameter 0300 * b<SUB>T</SUB>, the final renormalisation scale μ, and the 0301 * final rapidity scale ζ. It returns the quark evolution 0302 * factor. 0303 */ 0304 std::function<double(double const&, double const&, double const&)> QuarkEvolutionFactorxi(std::map<int, TmdObjects> const& TmdObj, 0305 std::function<double(double const&)> const& Alphas, 0306 int const& PerturbativeOrder, 0307 double const& xi = 1, 0308 double const& Ci = 1, 0309 double const& IntEps = 1e-7); 0310 0311 /** 0312 * @brief Function that returns the evolution factor for the gluon. 0313 * @param TmdObj: the TMD objects 0314 * @param Alphas: the strong coupling function 0315 * @param PerturbativeOrder: the logarithmic perturbative order 0316 * @param Ci: the initial scale-variation factor (default: 1) 0317 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0318 * @return double-valued function of the impact parameter 0319 * b<SUB>T</SUB>, the final renormalisation scale μ, and the 0320 * final rapidity scale ζ. It returns the gluon evolution 0321 * factor. 0322 */ 0323 std::function<double(double const&, double const&, double const&)> GluonEvolutionFactor(std::map<int, TmdObjects> const& TmdObj, 0324 std::function<double(double const&)> const& Alphas, 0325 int const& PerturbativeOrder, 0326 double const& Ci = 1, 0327 double const& IntEps = 1e-7); 0328 0329 /** 0330 * @brief Analytic evolution factor for the quark TMD 0331 * @param TmdObj: container of the anomalous dimensions with a fixed number of active flavours 0332 * @param mu0: the strong coupling reference scale 0333 * @param Alphas0: the value of the strong coupling and mu0 0334 * @param kappa: the resummation-scale parameter 0335 * @param kappa0: the ratio mu0 / M (i.e. the alphas reference scale over the hard scale) 0336 * @param PerturbativeOrder: the logarithmic perturbative accuracy 0337 * @return the quark Sudakov form factor as function of the impact parameter b 0338 */ 0339 std::function<double(double const&)> QuarkAnalyticEvolutionFactor(TmdObjects const& TmdObj, 0340 double const& mu0, 0341 double const& Alphas0, 0342 double const& kappa, 0343 double const& kappa0, 0344 int const& PerturbativeOrder); 0345 0346 /** 0347 * @brief Analytic evolution factor for the gluon TMD 0348 * @param TmdObj: container of the anomalous dimensions with a fixed number of active flavours 0349 * @param mu0: the strong coupling reference scale 0350 * @param Alphas0: the value of the strong coupling and mu0 0351 * @param kappa: the resummation-scale parameter 0352 * @param kappa0: the ratio mu0 / M (i.e. the alphas reference scale over the hard scale) 0353 * @param PerturbativeOrder: the logarithmic perturbative accuracy 0354 * @return the gluon Sudakov form factor as function of the impact parameter b 0355 */ 0356 std::function<double(double const&)> GluonAnalyticEvolutionFactor(TmdObjects const& TmdObj, 0357 double const& mu0, 0358 double const& Alphas0, 0359 double const& kappa, 0360 double const& kappa0, 0361 int const& PerturbativeOrder); 0362 0363 /** 0364 * @brief Function that returns the perturbative part of the 0365 * Collins-Soper kernel for quarks. 0366 * @param TmdObj: the TMD objects 0367 * @param Alphas: the strong coupling function 0368 * @param PerturbativeOrder: the logarithmic perturbative order 0369 * @param Ci: the initial scale-variation factor (default: 1) 0370 * @param IntEps: the integration accuracy (default: 10<SUP>-7</SUP>) 0371 * @return double-valued function of the impact parameter 0372 * b<SUB>T</SUB> and of the the final renormalisation scale μ. It 0373 * returns perturbative part of the Collis-Soper kernel for quarks. 0374 */ 0375 std::function<double(double const&, double const&)> CollinsSoperKernel(std::map<int, TmdObjects> const& TmdObj, 0376 std::function<double(double const&)> const& Alphas, 0377 int const& PerturbativeOrder, 0378 double const& Ci = 1, 0379 double const& IntEps = 1e-7); 0380 0381 /** 0382 * @brief Function that returns the hard factor. 0383 * @param Process: the string corresponding to the process requested 0384 * @param TmdObj: the TMD objects 0385 * @param Alphas: the strong coupling function 0386 * @param PerturbativeOrder: the logarithmic perturbative order 0387 * @param Cf: the final scale-variation factor (default: 1) 0388 * @return double-valued function of the final renormalisation scale μ 0389 */ 0390 std::function<double(double const&)> HardFactor(std::string const& Process, 0391 std::map<int, TmdObjects> const& TmdObj, 0392 std::function<double(double const&)> const& Alphas, 0393 int const& PerturbativeOrder, 0394 double const& Cf = 1); 0395 ///@} 0396 }
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