Next-to-leading order corrections to the valon model

Abstract

A seminumerical solution to the valon model at next-to-leading order (NLO) in the Laguerre polynomials is presented. We used the valon model to generate the structure of proton with respect to the Laguerre polynomials method. The results are compared with H1 data and other parametrizations.

Appendix

The functional form of the free parameters of eqs (38)–(40) are given by the following forms in terms of s at LO and NLO analyses.

Coefficients for u valence in U valon are:

At LO

$$\begin{array}{@{}rcl@{}} a_{\mathrm{u}}&=&0.7278+0.306s-0.166s^{2}, \\ b_{\mathrm{u}}&=&-1.388+4.2863s-1.0622s^{2},\\ N_{\mathrm{u}}&=&0.2918+7.137s-2.755s^{2}. \end{array} $$

(A.1)

At NLO

$$\begin{array}{@{}rcl@{}} a_{\mathrm{u}}&=&1.1221-0.3809s+0.0584s^{2}, \\ b_{\mathrm{u}}&=&2.2947+0.3889s+0.0890s^{2},\\ N_{\mathrm{u}}&=&6.9389-2.9848s+0.5170s^{2}. \end{array} $$

(A.2)

Coefficients for d valence in D valon are:

At LO

$$\begin{array}{@{}rcl@{}} a_{\mathrm{d}}&=&1.1071-0.3321s+0.0418s^{2}, \\ b_{\mathrm{d}}&=&2.0465+0.4996s+0.1124s^{2},\\ N_{\mathrm{d}}&=&3.6678-1.3991s+0.1982s^{2}. \end{array} $$

(A.3)

At NLO

$$\begin{array}{@{}rcl@{}} a_{\mathrm{d}}&=&0.9575-0.296s+0.0432s^{2}, \\ b_{\mathrm{d}}&=&2.0757+0.4545s+0.0949s^{2},\\ N_{\mathrm{d}}&=&2.7993-1.1193s+0.1856s^{2}. \end{array} $$

(A.4)

Coefficients for sea quarks in each valon are:

At LO

$$\begin{array}{@{}rcl@{}} a_{\mathrm{s}}&=&-1.4436+2.8924s-1.8425s^{2}+0.3848s^{3}, \\ b_{\mathrm{s}}&=&-7.7792+15.1601s-9.8912s^{2}+2.0796s^{3}, \\ c_{\mathrm{s}}&=&41.904-45.3909s+12.6658s^{2},\\ d_{\mathrm{s}}&=&1.1+0.4045s-0.0887s^{2}, \\ e_{\mathrm{s}}&=&10.3428-22.0348s+12.6556s^{2}-2.4302s^{3}. \end{array} $$

(A.5)

At NLO

$$\begin{array}{@{}rcl@{}} a_{\mathrm{s}}&=&0.0284-0.0075s+0.0151s^{2}, \\ b_{\mathrm{s}}&=&-0.3223+0.0306s-0.0297s^{2},\\ c_{\mathrm{s}}&=&2.7174-2.1371s+0.7825s^{2},\\ d_{\mathrm{s}}&=&4.7717-5.0353s+1.8486s^{2}, \\ e_{\mathrm{s}}&=&-4.7272+3.5907s-1.3427s^{2}. \end{array} $$

(A.6)

Coefficients for gluons in each valon are:

At LO

$$\begin{array}{@{}rcl@{}} a_{\mathrm{g}}&=&13.8745-22.3304s+12.7885s^{2}-2.4801s^{3}, \\ b_{\mathrm{g}}&=&4.6810-8.4594s+4.7656s^{2} -0.9209s^{3},\\ c_{\mathrm{g}}&=&-24.5652+50.4661s-30.147s^{2} +6.0738s^{3},\\ d_{\mathrm{g}}&=&-0.8839+0.0403s-0.0174s^{2}. \end{array} $$

(A.7)

At NLO

$$\begin{array}{@{}rcl@{}} a_{\mathrm{g}}&=&2.4924-1.3797s+0.2349s^{2}, \\ b_{\mathrm{g}}&=&0.3278-0.6287s+0.1026s^{2}, \\ c_{\mathrm{g}}&=&2.9282+0.4685s+0.1035s^{2},\\ d_{\mathrm{g}}&=&-0.8539+0.0055s-0.0075s^{2}. \end{array} $$

(A.8)