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0001 /****************************************************************************** 0002 * This file is part of libome * 0003 * Copyright (C) 2025 Arnd Behring, Kay Schoenwald * 0004 * SPDX-License-Identifier: GPL-3.0-or-later * 0005 ******************************************************************************/ 0006 0007 /** 0008 * \file 0009 * \brief Type aliases to model the nesting structure of OMEs 0010 */ 0011 0012 #ifndef LIBOME_OME_TYPE_ALIASES_H 0013 #define LIBOME_OME_TYPE_ALIASES_H 0014 0015 #include <apfel/ome/functions.h> 0016 #include <apfel/ome/laurent_polynomial.h> 0017 #include <apfel/ome/piecewise.h> 0018 0019 namespace apfel 0020 { 0021 namespace ome 0022 { 0023 /** 0024 * \defgroup ome-data-types Public data types 0025 * \brief Specialised data types for the objects provided 0026 * @{ 0027 */ 0028 0029 /** 0030 * \name Standard OMEs 0031 * \brief Type aliases for standard x-dependent OMEs, given by a piecewise 0032 * definition based on generalised power series 0033 * @{ 0034 */ 0035 0036 /** 0037 * \brief Truncated power series in \f$x-x_0\f$ 0038 * 0039 * \details 0040 * Truncated power series that takes the value of \f$x-x_0\f$ and returns the 0041 * evaluation of the power series. 0042 */ 0043 template<typename Tnum> using ome_x = laurent_polynomial<Tnum, Tnum>; 0044 0045 /** 0046 * \brief Truncated power series in \f$\log(x-x_0)\f$ and \f$x-x_0\f$ 0047 * 0048 * \details 0049 * Truncated power seires that takes the values of \f$x-x_0\f$ and 0050 * \f$\log(x-x_0)\f$ and returns the evaluation of the power series. 0051 */ 0052 template<typename Tnum> using ome_logx 0053 = laurent_polynomial<Tnum, ome_x<Tnum>, Tnum>; 0054 0055 /** 0056 * \brief Truncated generalised power series in x 0057 * 0058 * \details 0059 * Univariate wrapper for \ref ome_logx, that takes the value of \f$x\f$, 0060 * shifts it using the appropriate function, calculates \f$\log(x-x_0)\f$ 0061 * and evaluates the underlying \ref ome_logx. 0062 */ 0063 template<typename Tnum> using ome_genps 0064 = func_apply<Tnum, func_copy_and_log<Tnum, ome_logx<Tnum>>>; 0065 0066 /** 0067 * \brief Construct an \ref ome_genps object 0068 * 0069 * \details 0070 * Since the template parameter deduction for \ref ome_genps using plain 0071 * constructors is tricky and require manual composition of \ref func_apply 0072 * and \ref func_copy_and_log classes, this helper allows to construct 0073 * \ref ome_genps objects with automatic template parameter deduction. 0074 * 0075 * \tparam Tnum Numerical type 0076 * 0077 * \param apply_function Univariate function that is applied to \f$x\f$ before 0078 * it is passed to the wrapped \ref ome_logx target 0079 * \param target Underlying truncated power series in \f$\log(x-x_0)\f$ and 0080 * \f$x-x_0\f$ 0081 */ 0082 template<typename Tnum> 0083 ome_genps<Tnum> make_ome_genps(std::function<Tnum(Tnum)> apply_function, 0084 ome_logx<Tnum> target) 0085 { 0086 return( 0087 func_apply<Tnum, func_copy_and_log<Tnum, ome_logx<Tnum>>>( 0088 apply_function, 0089 func_copy_and_log<Tnum, ome_logx<Tnum>>(target) 0090 ) 0091 ); 0092 }; 0093 0094 /** 0095 * \brief Piecewise defined OME coefficient in \f$x\f$ 0096 * 0097 * \details 0098 * A collection of generalised power series representations along with the 0099 * intervals on which they are defined. 0100 */ 0101 template<typename Tnum> using ome_piecewisex 0102 = piecewise<Tnum, ome_genps<Tnum>>; 0103 0104 /** 0105 * \brief OME coefficients in \f$N_F\f$ 0106 * 0107 * \details 0108 * Polynomial in the number of massless quarks \f$N_F\f$. Each coefficient is 0109 * a function of \f$x\f$. 0110 */ 0111 template<typename Tnum> using ome_nf 0112 = laurent_polynomial<Tnum, ome_piecewisex<Tnum>, Tnum>; 0113 0114 /** 0115 * \brief View type for OME coefficient in \f$N_F\f$ 0116 */ 0117 template<typename Tnum> using ome_nf_view 0118 = laurent_polynomial_view<Tnum, ome_piecewisex<Tnum>, Tnum>; 0119 0120 /** 0121 * \brief OME coefficients in \f$L_M\f$ 0122 * 0123 * \details 0124 * Polynomial in the mass logarithm 0125 * \f$L_M = \log\left(\frac{m^2}{\mu^2}\right)\f$. 0126 * Each coefficient is a function of \f$N_F\f$ and \f$x\f$. 0127 */ 0128 template<typename Tnum> using ome_logm 0129 = laurent_polynomial<Tnum, ome_nf<Tnum>, Tnum, Tnum>; 0130 0131 /** 0132 * \brief View type for OME coefficient in \f$L_M\f$ 0133 */ 0134 template<typename Tnum> using ome_logm_view 0135 = laurent_polynomial_view<Tnum, ome_nf<Tnum>, Tnum, Tnum>; 0136 0137 /** 0138 * \brief OME coefficients in \f$a_s\f$ 0139 * 0140 * \details 0141 * Polynomial in the strong coupling constant 0142 * \f$a_s(\mu) = \frac{\alpha_s(\mu)}{4 \pi} = \frac{g^2(\mu)}{(4 \pi)^2}\f$. 0143 * Each coefficient is a function of \f$L_M\f$, \f$N_F\f$ and \f$x\f$. 0144 * 0145 */ 0146 template<typename Tnum> using ome_as 0147 = laurent_polynomial<Tnum, ome_logm<Tnum>, Tnum, Tnum, Tnum>; 0148 0149 /** 0150 * \brief View type for OME coefficient in \f$a_s\f$ 0151 */ 0152 template<typename Tnum> using ome_as_view 0153 = laurent_polynomial_view<Tnum, ome_logm<Tnum>, Tnum, Tnum, Tnum>; 0154 0155 /** 0156 * @} 0157 */ 0158 0159 0160 /** 0161 * \name Constant OMEs 0162 * \brief Type aliases for constant (x-independent) OMEs 0163 * @{ 0164 */ 0165 0166 /** 0167 * \brief OME coefficients in \f$N_F\f$ 0168 * 0169 * \details 0170 * Polynomial in the number of massless quarks \f$N_F\f$. The coefficients 0171 * are constant numbers. 0172 */ 0173 template<typename Tnum> using ome_nf_const 0174 = laurent_polynomial<Tnum, Tnum>; 0175 0176 /** 0177 * \brief View type for OME coefficient in \f$N_F\f$ 0178 */ 0179 template<typename Tnum> using ome_nf_const_view 0180 = laurent_polynomial_view<Tnum, Tnum>; 0181 0182 /** 0183 * \brief OME coefficients in \f$L_M\f$ 0184 * 0185 * \details 0186 * Polynomial in the mass logarithm 0187 * \f$L_M = \log\left(\frac{m^2}{\mu^2}\right)\f$. 0188 * Each coefficient is a function of \f$N_F\f$. 0189 */ 0190 template<typename Tnum> using ome_logm_const 0191 = laurent_polynomial<Tnum, ome_nf_const<Tnum>, Tnum>; 0192 0193 /** 0194 * \brief View type for OME coefficient in \f$L_M\f$ 0195 */ 0196 template<typename Tnum> using ome_logm_const_view 0197 = laurent_polynomial_view<Tnum, ome_nf_const<Tnum>, Tnum>; 0198 0199 /** 0200 * \brief OME coefficients in \f$a_s\f$ 0201 * 0202 * \details 0203 * Polynomial in the strong coupling constant 0204 * \f$a_s(\mu) = \frac{\alpha_s(\mu)}{4 \pi} = \frac{g^2(\mu)}{(4 \pi)^2}\f$. 0205 * Each coefficient is a function of \f$L_M\f$ and \f$N_F\f$. 0206 */ 0207 template<typename Tnum> using ome_as_const 0208 = laurent_polynomial<Tnum, ome_logm_const<Tnum>, Tnum, Tnum>; 0209 0210 /** 0211 * \brief View type for OME coefficient in \f$a_s\f$ 0212 */ 0213 template<typename Tnum> using ome_as_const_view 0214 = laurent_polynomial_view<Tnum, ome_logm_const<Tnum>, Tnum, Tnum>; 0215 0216 /** 0217 * @} 0218 */ 0219 0220 0221 /** 0222 * \name Plus function part of OMEs 0223 * \brief Type aliases for plus function part of OMEs 0224 * @{ 0225 */ 0226 0227 /** 0228 * \brief Coefficients of the basic plus functions 0229 * 0230 * \details 0231 * This polynomial contains the coefficients of the basic plus functions 0232 * \f[ 0233 * D_k(x) = \left[\frac{\log^k(1-x)}{1-x}\right]_+ 0234 * \f] 0235 * In practice, it takes the numerical value of \f$\log(1-x)\f$ and 0236 * calculates the polynomial 0237 * \f[ 0238 * \sum_k \log^k(1-x) c_k 0239 * \f] 0240 * and the division by \f$(1-x)\f$ is done one level above in the hierarchy 0241 * in \ref ome_plusfunc. The coefficients \f$c_k\f$ are constant numbers. 0242 */ 0243 template<typename Tnum> using ome_plusfunc_coeff 0244 = laurent_polynomial<Tnum, Tnum>; 0245 0246 /** 0247 * \brief Sum of basic plus functions 0248 * 0249 * \details 0250 * This models a sum of basic plus distributions 0251 * \f[ 0252 * f_+(x) = \sum_k c_k \left[\frac{\log^k(1-x)}{1-x}\right]_+ 0253 * \f] 0254 * It takes the argument x, shifts it to \f$(1-x)\f$, takes the logarithm 0255 * and passes it to the underlying \ref ome_plusfunc_coeff. The result is 0256 * then divided by \f$(1-x)\f$ before being returned. 0257 */ 0258 template<typename Tnum> using ome_plusfunc 0259 = func_plusfunc_omx<Tnum, ome_plusfunc_coeff<Tnum>>; 0260 0261 /** 0262 * \brief OME coefficients in \f$N_F\f$ 0263 * 0264 * \details 0265 * Polynomial in the number of massless quarks \f$N_F\f$. The coefficients 0266 * are (plus) functions of \f$x\f$. 0267 */ 0268 template<typename Tnum> using ome_nf_plus 0269 = laurent_polynomial<Tnum, ome_plusfunc<Tnum>, Tnum>; 0270 0271 /** 0272 * \brief View type for OME coefficient in \f$N_F\f$ 0273 */ 0274 template<typename Tnum> using ome_nf_plus_view 0275 = laurent_polynomial_view<Tnum, ome_plusfunc<Tnum>, Tnum>; 0276 0277 /** 0278 * \brief OME coefficients in \f$L_M\f$ 0279 * 0280 * \details 0281 * Polynomial in the mass logarithm 0282 * \f$L_M = \log\left(\frac{m^2}{\mu^2}\right)\f$. 0283 * Each coefficient is a function of \f$N_F\f$ and \f$x\f$. 0284 */ 0285 template<typename Tnum> using ome_logm_plus 0286 = laurent_polynomial<Tnum, ome_nf_plus<Tnum>, Tnum, Tnum>; 0287 0288 /** 0289 * \brief View type for OME coefficient in \f$L_M\f$ 0290 */ 0291 template<typename Tnum> using ome_logm_plus_view 0292 = laurent_polynomial_view<Tnum, ome_nf_plus<Tnum>, Tnum, Tnum>; 0293 0294 /** 0295 * \brief OME coefficients in \f$a_s\f$ 0296 * 0297 * \details 0298 * Polynomial in the strong coupling constant 0299 * \f$a_s(\mu) = \frac{\alpha_s(\mu)}{4 \pi} = \frac{g^2(\mu)}{(4 \pi)^2}\f$. 0300 * Each coefficient is a function of \f$L_M\f$, \f$N_F\f$ and \f$x\f$. 0301 */ 0302 template<typename Tnum> using ome_as_plus 0303 = laurent_polynomial<Tnum, ome_logm_plus<Tnum>, Tnum, Tnum, Tnum>; 0304 0305 /** 0306 * \brief View type for OME coefficient in \f$a_s\f$ 0307 */ 0308 template<typename Tnum> using ome_as_plus_view 0309 = laurent_polynomial_view<Tnum, ome_logm_plus<Tnum>, Tnum, Tnum, Tnum>; 0310 0311 /** 0312 * @} 0313 */ 0314 0315 /** 0316 * @} 0317 */ 0318 } 0319 } 0320 0321 #endif
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