Package: coefhl.m Version: v1.0 (Feb. 2011) Description: coefhl is a Mathematica package for the evaluation of the moments of the heavy-light correlators to three loops. Authors: Jens Hoff and Matthias Steinhauser Reference: arXiv:1103.1481v1 (* ---------- *) The Mathematica function Cbar[case, aOrd, zOrd, xd, OPTIONS] provides the moments of the heavy-light correlators where the arguments have the following meaning: case: "v", "a", "s", "p" for vector, axial-vector, scalar, pseudo-scalar correlator aOrd: the correction of O(alpha_s^aOrd) is returned for aOrd = 0, 1 or 2 zOrd: the moment of z^zOrd is returned: zOrd=-1,...,4 z=q^2/m1^2 where q is the external momentum and m1 is the heavier of the two quark masses. xd: (optional parameter) corresponds to x=m2/m1. In case numerical values are given it is assumed that 0<= xd <= 1. OPTIONS: It is possible to set the following options (default values): nl (-> 3) - the number of light flavours, imu (-> 1) - the ratio of the renormalization scale mu and m1, warn (-> True) - a flag for suppressing warning messages, range (-> {0.1,0.5}) - the interval inbetween which the predefined interpolation is used. Note: For the optional parameters to work properly xd must be set explicitely. At one- and two-loop order the analytic results are used to evaluate Cbar[case, aOrd, zOrd]. At three-loop order Cbar[case, aOrd, zOrd] is a piecewise defined function where for x <= x1 and x >= x2 analytical expansions are used. x1=0.1 and x2=0.5 are the default values which can be modified with the option 'range'. Interpolation results are available in the region x1 < x < x2 for zOrd = 1,...,4. The interpolation results are only available for nl=3. Examples for the usage of Cbar[]: Cbar["p", 1, 4] provides the two-loop corrections of the fourth moment of the pseudo-scalar correlator. One can change the renormalization scale to mu = 2*m_1 by Cbar["p", 1, 4, x, imu -> 2]. The one- and three-loop corrections are obtained by changing the second argument to 0 and 2, respectively. At three loops the result is returned as a piecewise defined function as described above. It is possible to access the expressions valid in each of the three segments by using the command Refine[]. E.g., Refine[Cbar["p", 2, 3], {0 <= x && x <= 0.1}] Refine[Cbar["p", 2, 3], {0.5 <= x && x <= 1}] In case the fourth argument of Cbar[] is a number a numerical evaluation is performed: Cbar["p", 0, 4, 0.05]. The following commands reproduce the plot for the three-loop corrections of the third moment of the pseudo-scalar correlator: fct[x_] = N[Cbar["p", 2, 3, x]]; Plot[fct[x], {x, 0, 1}]. The introduction of the function fct[] guarantees that the complex mathematical expressions originating from the three-loop master integrals have to be evaluated only once.