TSIL_COMPLEX TSIL_Bp (TSIL_REAL X, TSIL_REAL Y, TSIL_COMPLEX S, TSIL_REAL QQ)
{
if (X < TSIL_TOL) {
TSIL_Warn("Bp", "B(x',y) is undefined for x=0.");
return TSIL_Infinity;
}
if (TSIL_CABS(1.0L - S/(X+Y+2.0L*TSIL_SQRT(X*Y))) < TSIL_TOL) {
TSIL_Warn("Bp", "B(x',y) is undefined at s = (sqrt(x) + sqrt(y))^2.");
return TSIL_Infinity;
}
if (TSIL_CABS(S) < TSIL_TOL) {
if (TSIL_FABS(1.0L - X/Y) < TSIL_TOL)
return (-0.5L/X);
else
return 1.0L/(Y-X) + Y*TSIL_LOG(X/Y)/((Y-X)*(Y-X));
}
if (TSIL_CABS(1.0L - (X + Y - 2.0L*TSIL_SQRT(X*Y))/S) < TSIL_TOL)
return (1.0L - TSIL_SQRT(Y/X) +0.5L*TSIL_LOG(Y/X))/(X + Y - 2.0L*TSIL_SQRT(X*Y));
else
return ((X-Y-S)*TSIL_B(X,Y,S,QQ) + (X+Y-S)*TSIL_LOG(X/QQ)
-2.0L*TSIL_A(Y,QQ) + 2.0L*(S-X))/TSIL_Delta(S,X,Y);
}
int main (int argc, char *argv[])
{
TSIL_DATA result; /* Top-level TSIL data object */
TSIL_REAL qq; /* Ensures correct basic type; see also TSIL_COMPLEX */
TSIL_REAL x, g, lambda;
TSIL_COMPLEX pi1, pi1prime, pi2, s1, s2;
TSIL_REAL factor = 1.0L/(16.0L*PI*PI);
/* If incorrect number of args, print message on stderr and exit: */
if (argc != 5)
TSIL_Error("main", "Expected 4 arguments: m^2, g, lambda, and Q^2", 1);
/* Note cast to appropriate floating-point type for safety */
x = (TSIL_REAL) strtold(argv[1], (char **) NULL);
g = (TSIL_REAL) strtold(argv[2], (char **) NULL);
lambda = (TSIL_REAL) strtold(argv[3], (char **) NULL);
qq = (TSIL_REAL) strtold(argv[4], (char **) NULL);
/* All loop integrals have a common squared-mass argument x: */
TSIL_SetParameters (&result, x, x, x, x, x, qq);
/* For the pole mass calculation, evaluate two-loop integrals at s = x: */
TSIL_Evaluate (&result, x);
/* Assemble one- and two-loop mass squared results: */
pi1 = 0.5L*lambda*TSIL_A(x,qq) - 0.5L*g*g*TSIL_B(x,x,x,qq);
pi1prime = -0.5L*g*g*TSIL_dBds(x, x, x, qq);
pi2 = - 0.5L*g*g*g*g*TSIL_GetFunction(&result, "M")
- 0.5L*g*g*g*g*TSIL_GetFunction(&result, "Vzxyv")
+ g*g*g*TSIL_GetFunction(&result, "Uzxyv")
- (1.0L/6.0L)*lambda*lambda*TSIL_GetFunction(&result, "Svyz")
+ 0.25L*lambda*g*g*TSIL_POW(TSIL_GetFunction(&result, "Bxz"), 2)
+ 0.25L*lambda*lambda*TSIL_A(x,qq)*(TSIL_A(x,qq)/x + 1.0L)
- 0.5L*lambda*g*g*TSIL_A(x,qq)*TSIL_Bp(x, x, x, qq)
- 0.25L*lambda*g*g*TSIL_I2p(x,x,x,qq);
s1 = x + factor*pi1;
s2 = x + factor*pi1 + factor*factor*(pi2 + pi1*pi1prime);
printf("Tree-level squared mass: %lf\n", (double) x);
printf("One-loop pole squared mass: %lf\n", (double) s1);
printf("Two-loop pole squared mass: %lf\n", (double) s2);
return 0;
}
TSIL_COMPLEX TSIL_dBds (TSIL_REAL x,
TSIL_REAL y,
TSIL_COMPLEX s,
TSIL_REAL qq)
{
TSIL_REAL thxy, psxy, sqrtx, sqrty, alphax, alphay, temp;
TSIL_COMPLEX Btemp, result;
if (x < y) {temp = y; y = x; x = temp;}
if (x + TSIL_CABS(s) < TSIL_TOL) {
TSIL_Warn("TSIL_dBds", "dBds(0,0) is undefined when s=0.");
return TSIL_Infinity;
}
if (TSIL_CABS(s/x) < TSIL_TOL) return TSIL_BprimeAtZero (x, y, qq);
thxy = TSIL_Th2 (x, y);
psxy = TSIL_Ps2 (x, y);
sqrtx = TSIL_SQRT(x);
sqrty = TSIL_SQRT(y);
alphax = TSIL_Alpha(x,qq);
alphay = TSIL_Alpha(y,qq);
if (TSIL_CABS(1.0L - s/thxy) < TSIL_TOL) {
TSIL_Warn("TSIL_dBds", "dBds(x,y) is undefined at threshold.");
return TSIL_Infinity;
}
if (TSIL_CABS(1.0L - s/psxy) < TSIL_TOL) {
return (0.5L * alphax * (1.0L + sqrty/sqrtx)
- 0.5L * alphay * (1.0L + sqrtx/sqrty)
+ 2.0L * (sqrty - sqrtx) )/TSIL_POW(sqrtx - sqrty,3);
}
Btemp = TSIL_B (x, y, s, qq);
result = (0.5L/s) * (
(thxy * Btemp - s + (sqrtx + sqrty)*(alphax + alphay))/(s - thxy)
+ (psxy * Btemp - s + (sqrtx - sqrty)*(alphax - alphay))/(s - psxy));
return result;
}
