By Cafarella, A
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Extra info for QCD at hadron colliders and in Ultra High Energy Cosmic Rays
1 x02 ln x2 − x02 x2 x1 x2 +τ x1 x02 +x2 x01 x01 )(x2 − x02 ) + ´½º × Ö ÒÓÖÑ Ð Þ Ø ÓÒ × Ð µR Þ Ø ÓÒ × Ð µF = M º Ï Ö ÐÐ Ø ÒØ Ý = + Ö ×ÔÓÒ× Ð µ Ø Ö ÒØ Ó Ø ÓÒ Ð ÐÓ × Ö × ØØ Ö Ò ×º Ì × ××Ù Û ÐÐ Ò × Ø ØÓ Ó Ò Ò ÑÓÖ ØÓÖ¹ ÓÖ Ø × ØÛÓ × Ð × ÛÓÙÐ (log(µ2F /µ2R )) ×
Ù×× ÛØ Ø ÓØ ÒØ Ø Ð ÒØ ÚÓÐÙØ ÓÒ Ò ÓÑÔÙØ Ø ÓÒ Ó µ ÔØ Ö ½º Ø Ö Ø ×ÓÐÙØ ÓÒ Ó Ê À × ØÓØ Ð ÖÓ×× × Ø ÓÒ¸ Û Ö Ì ÜÔÖ ×× ÓÒ Ó Ø Ó É Ò x¹×Ô ÆÄÇ ÑÔÐ Ñ ÒØ Ø ÓÒ× Ø × ÑÓÖ Ö Ð Ú Ò º ÄÇ ÖÓ×× × Ø ÓÒ × ÕÙ Ø × ÑÔÐ Ò ØÖ ¿¿ × 2α2 d∆T σ ˆ (0) = cos(2φ)δ(x1 − x01 )δ(x2 − x02 ) .
S Bn (x) n Cn (x) n β(αs ) L + 2αs β(αs ) L . n! n! +αs2 ∞ + n=0 ÆÓØ Ø Ö×Ø ×ÙÑ ×Ø ÖØ× Ø n = 1¸ ØØ Ú Q 2 Ù× Ø Ô Ò Ò º ÌÖ Ò ÓÖÑ Ò n → n − 1 Ò Ø ÜÔ Ò× ÓÒ Ó Ø Ø ÔÖ Ú ÓÙ× ÓÖÑÙÐ ÙÒ
Ø ÓÒ ´¾º µ Ò Ò Ð Ø Ò n = 0 Ø ÖÑ Ò ´¾º½¼µ Ó × ÒÓØ Ö×Ø ×ÙÑ¸ Ù× Ò Ø n=0 + Ø Ö ¹ÐÓÓÔ ÐÐ Ø ÖÑ× Ó ÓÖ Ö αs4 ÓÖ ÑÓÖ ¸ Ø ÓÑ × ∞ ´¾º½ µ β0 β1 2 β2 3 An+1 (x) n L − αs − αs − α 2 n! 4π 16π 64π 3 s Bn+1 (x) n β0 β0 Cn+1 (x) n β1 3 αs + L − αs2 − L − αs3 2 n! 4π 16π n! 4π ÔØ Ö ¾º ÆÆÄÇ ÜØ Ò× ÓÒ Ó Ø + Í× Ò Ø ×ÓÐÙØ ÓÒ Ó Ø Ê β0 Cn (x) n β0 β1 3 Bn (x) n L − αs2 − αs + 2 L − αs3 2 n!
0, ±1, 0, . . , 0, ±1, ... (x) = H±(k+1), ±(l+1), ... (x) .