126 research outputs found
Loop integration results using numerical extrapolation for a non-scalar integral
Loop integration results have been obtained using numerical integration and
extrapolation. An extrapolation to the limit is performed with respect to a
parameter in the integrand which tends to zero. Results are given for a
non-scalar four-point diagram. Extensions to accommodate loop integration by
existing integration packages are also discussed. These include: using
previously generated partitions of the domain and roundoff error guards.Comment: 4 pages, 3 figures, revised, contribution to ACAT03 (Dec. 2003
ΠΠ°ΠΊΠΎΠ½ΠΎΠΌΠ΅ΡΠ½ΠΎΡΡΠΈ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΏΠ΅ΠΊΡΡΠΎΠ² ΠΈ ΡΡΡΡΠΊΡΡΡ ΡΠΎΠ±ΡΡΠ²Π΅Π½Π½ΡΡ ΡΠ»Π΅ΠΊΡΡΠΎΠΌΠ΅Ρ Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ
ΠΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΡΠΈΡΡΠ΅ΠΌΡ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΠΉ Π² Π²ΠΈΠ΄Π΅ Π³Π°ΡΠΌΠΎΠ½ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΠ½ΠΊΡΠΈΠΈ. Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ Π²ΠΎΠΏΡΠΎΡΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ Π·Π°ΠΊΠΎΠ½ΠΎΠΌΠ΅ΡΠ½ΠΎΡΡΠ΅ΠΉ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΏΠ΅ΠΊΡΡΠΎΠ² ΠΈ ΡΡΡΡΠΊΡΡΡ ΡΠΎΠ±ΡΡΠ²Π΅Π½Π½ΡΡ
ΡΠ»Π΅ΠΊΡΡΠΎΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ. ΠΡΡΠ»Π΅Π΄ΡΡΡΡΡ ΠΎΡΠ΅Π½ΠΊΠΈ Π³Π°ΡΠΌΠΎΠ½ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΎΡΡΠ°Π²Π° ΡΠ»Π΅ΠΊΡΡΠΎΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ. ΠΠ±ΠΎΡΠ½ΠΎΠ²ΡΠ²Π°Π΅ΡΡΡ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΡΠ°ΡΡΠΎΡ ΡΠΎΠ±ΡΡΠ²Π΅Π½Π½ΡΡ
ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ Π΄Π»Ρ ΠΎΡΠ΅Π½ΠΊΠΈ ΡΠ΄Π°Π»Π΅Π½Π½ΠΎΡΡΠΈ ΡΠ΅ΠΆΠΈΠΌΠ° ΠΎΡ ΠΏΡΠ΅Π΄Π΅Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ
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