The remaining terms are new.

Numerical Results
-----------------

The asymptotic expression for the photon wave function $\varphi(u)$ is given by $\chi(\mu) 6 u (1-u)$ at a renormalisation scale $\mu^2=1\;\!{\rm{GeV}}^2$, where $\chi(\mu)$ is the so called magnetic susceptibility of the quark condenstate. It has been argued that the full DA does not differ much from the asymptotic expression [@Braun:1988qv] as sum rule calculations showed a small coefficient for the next-to-leading order term. Thus, henceforth, we will use $\varphi(1/2)=3/2 \chi(\mu)$.

The value of $\chi$ is not very well known. The first detailed study using QCD sum rules yielded $\chi(1/2)=4.4 \;\!{\rm{GeV}}^{-2}$ [@Belyaev:1984ic; @Balitsky:1985aq], whereas a local duality approach [@Balitsky:1983xk] found $\chi(1/2) \approx 3.3\;\!{\rm{GeV}}^{-2}$. The latest estimate for $\chi(\mu=1{\rm GeV})$ gives a value of $3.15 \;\!{\rm GeV}^{-2}$ [@Ball:2002ps] and, assuming asymptotic DAs, leads to $\varphi(1/2)\approx 4.73 {\rm GeV}^{-2}$.

The higher-twist photon DAs are known to next-to-leading order in conformal spin. The corresponding expressions are collected in Appendix \[A\].

Furthermore, we need the numerical values for the coupling constant $|\lambda_{P}|^2$, the continuum threshold $s_{P}$ as well as the Borel window for $t$. The continuum threshold can be determined from the most fundamental sum rule for the nucleon, namely those for the coupling constant. We obtain 