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Equal-mass vacuum and Euclidean continuation#
A separate Taylor method fills the equal-mass gap in the RMT charts.
0 2.343907238689458890601562 equal-mass sunset / transformed Taylor series
1 2.236792700212646510529264 equal-mass sunset / transformed Taylor series
3 1.697946461195426121941926 equal-mass sunset / transformed Taylor series
6 1.052354070777636885702782 equal-mass sunset / transformed Taylor series
import mpmath as mp
from ramanujan_qft import ScalarEdge, ScalarGraph, integrate_sunset_taylor, integrate_graph_rmt
for momentum in (0, 1, 3, 6):
graph = ScalarGraph([ScalarEdge(0, 1, 1)]*3,
{0: [momentum], 1: [-momentum]})
result = integrate_sunset_taylor(graph, dps=25)
print(momentum, mp.nstr(result.value, 25), result.method)
if momentum == 6:
rmt = integrate_graph_rmt(graph, dps=25)
with mp.workdps(40):
assert abs(result.value-rmt.value) <= result.error_estimate+rmt.error_estimate
Total running time of the script: (0 minutes 1.822 seconds)