Nucl ear Physi cs B349 ( 1991) 635- 654 Nort h-Hol l and C C NGAND SEMI - I NCLUSI VE CESSES AT L® . RGEx S . CATANI ** and B .R. WEBBER Car endi sh Labor at or y, Uni r er si t y of Cambri dge, Madi ngl ey Road, Cambr i dge CB3 OH3, UK G . MARC' HESI NI Di part i ment o di Fi si ca, Uni r er si t à di Par ma, I NFN, Gi zi ppo Col l egat o di Par ma, I t al y Recei ved 22 June 1990 Usi ng t he QCD coher ent br anchi ng al gori t hm, we comput e t he Deep I nel ast i c Scat t er i ng and Drel l -Yan har d cr oss sect i ons in t he sem i - i ncl usi ve r egi on of l ar ge x . The cal cul at i on is done to next - t o- l eadi ng l ogar i t hm ic accur acy in t he resummat i on of per t ur bat i ve QCD . We compar e t he r esul t s with t he known anal yt i cal expr essi ans to t he s ame accur acy in t he MS subt r act i on s c heme . They coi nci de if one def i nes an i mpr ove- J br anchi ng al gor i t hm sui t abl e f or Mont e Carl o si mul at i on, in whi ch t he t wo-l oop r unni ng coupl i ng const ant and Al t ar el l i - Par i si spl i t t i ng f unct i on ar e used. Ther ef or e such a si mul at i on can be used to measur e . 1j w s f r om t hese sem i - i ncl usi ve cr oss sect i ons . Mor eover we show t hat t he s ame r esul t s can al so be obt ai ned usi ng t he usual one- l oop spl i t t i ng f unct i on, pr ovi ded t he scal e paramet er .1 Mc used in t he Mont e Carl o si mul at i on is r el at ed to ;1 Ms by a comput ed f act or : :1 mc = 1 . 569 .1 Ms ( f or five f l avour s) . 1 . I nt r oduct i on The per t ur bat i ve eval uat i on of physi cal quant i t i es in har d hadr oni c pr ocesses is char act er i zed by t he pr esence of l ar ge doubl e l ogar i t hm i c cor r ect i ons [I], whi ch ar e due t o t he em i ssi on of bot h sof t and col l i near gl uons . In or der to comput e physi cal pr ocesses cor r ect l y it is necessar y to r esum t hese l ar ge cor r ect i ons t o al l or der s in t he QCD coupl i ng const ant « s . Col l i near l ogar i t hm ic cont r i but i ons af f ect any har d pr ocess wi t h det ect ed hadr ons in t he i ni t i al or f i nal st at e . They can be r es ummed by usi ng r enor mal i zât i on gr oup t echni ques [ 2] and by def i ni ng hadr oni c st r uct ur e and f ragment at i on f unct i ons . Sof t l ogari t hms ar e r el evant in t he comput at i on of i nf r ar ed (I R) sensi t i ve qu2^t i - t i es . These can be cl assi f i ed i nt o t wo subcl asses accor di ng to whet her f i nal - st at e Resear ch suppor t ed in par t by t he UK Sci ence and Engi neer i ng Resear ch Counci l and in par t ber t he I t al i an M i ni st er o del l a Pubbl i ca I st r uzi one . On l eave of absence f r om I s t i t ut o Nazi onal e di Fi si ca Nucl ear e, Sezi one di Fi r enze, I t al v. 0550- 3213/ 91/ $03 . 50 ©1991 - El sevi er Sci ence Publ i sher s B.V. ( Nor t h- Hol l and)