A J. dσ /d p t. p T. assume 6. dσ / dp T 1/ p T
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1 Kinemtics rpiity. ) Prouction of, W, Z. ) Direct Photon Prouction. C) Jet prouction. D) rpiity Kinemtics y (or ) is useful for hron-hron Rpiity collisions. pply the PCD formlism, nee lrge To in the process invrint mss of lepton, scle W; Z; trnsverse momentum p T of jet. pir; c.m. frme with z-xis in the bem. Choose ny prticle with mss m n momentum For Pseuorpiity =, log (tn(=2)) y if m. CD in hron-hron collisions Fctoriztion, Initil stte, hr scttering, nl stte γ, W, Z, J = ( + ;, ; ). ene rpiity y = 1 2! +, log = (e y (2 + m 2 )=2; e,y (2 + m 2 )=2; ) Trnsformtion uner boost long z-xis +! e! + ;,! e,!, ;! y! y +! becuse Goo, the c.m. frme isn't so specil E) Hevy urk prouction.
2 oson prouction in Vector collisions hron-hron the \Drell-Yn" process Consier +! ( =W=Z) + X = X y = e y M 2 =s; x = e,y M 2 =s x 1 Z Z 1 f ( ;) f b ( ;) ^ b() ^ b =y is clculte to orer N s When re corrections of orer N+1 there proof of fctoriztion is not obvious ue initil-stte strong to not interctions oes is sve by the interply between grphs, ue It unitrity, cuslity, n guge invrince. to \clinche" the csefor urk-prton moel This successful ccount of +! + X! with reltively lrge \kfctor" NLO bout the vliity of the perturbtive concern but the origin for this ws unerstoo. series; With the NLO result, fctor of 1 3 multiplying nive formulws neee to get greement the normliztion. This corroborte the nee in the color egree of freeom for urks. for Comments on vector boson prouction Historiclly importnt on mny ccounts Dominnt prouction mechnism Let cross-section t high energies Fctorize γ, W, Z process LO! =W=Z (originl Drell-Yn) - + X (for pion n proton bems on nucleon `+`, trgets), using f (x; ) erive from DIS. x x +O(( m M )p ) ;b y then NLO subprocesses s. We integrte over ; ;W;Z's re mostly t M. 2 cuse LO hol grph by grph
3 continue... Comments clcultion les to non-trivil p T istri- NLO { vector boson cn recoil ginst the bution stte prton-jet. ut NLO result iverges nl p T! 0, even if the integrte cross-section t nite. This is the rst exmple of \two- is problem" which nees generliztion of scle PCD formlism { resummtion. the Z prouction t hron colliers is importnt W; both for untittive unerstning of the Moel (precision mesurement of EW Stnr n stringent tests of CD), n prmeters the stuy of signls n bckgrouns for for Physics serches. New Direct photon prouction +! + X the nl stte hs zero mss, the lrge Since scle which mkes the PCD for- momentum pplicble is provie by observing the mlism t some lrge p T. subprocesses Leing s the \NLO" grphs for DY. sme this hs been regre s primry Historiclly, to probe the gluon prton istribution process the nucluon. of #1 rel photons consist of ) Compliction \point-like" component; n \hron-like" the ltter in terms of photon frgmenttion component, functions of urks n gluons. contributions to Hronic photon prouction irect + b! c +! + X ; b; c; urks & gluon
4 photon prouction continue... Direct #2 oth the k-fctor n the Compliction (up to fctor of 2). mesurements #3 steeply flling p T spec- Compliction of is extremely sensitive to smll bronenintrum of initil-stte prton \k T ". of such broening multi-soft-gluon Sources t high energies; non-perturbtive ef- rition t low energies. fects these mke irect photon prouction very ll cross section is ssume to hve (\jets"). stnr fctore form the T E wht o we men by jet? ut enition (\jet lgorithm") must be \infr- sfe", so tht the corresponing PCD re will be well-ene. clcultion Inclusive Jet prouction of the NLO clcultion re scle-epenence over the rnge of current experimentl lrge cn mesure One sections to cross J mke jets, +! jet + X 10-4 ssume 6 σ / p T 1/ p T ie is tht the prtons in the nl stte into collimte sprys of physicl prticles turn σ / p t 10-5 P R R 1x 1x f ( ;) f b ( ;) ^b () E ;b T p T Cone lgorithms most often use in hron colliers. Clustering lgorithms mostly use in e + e, colliers. Recent progrms to clcultejet cross-sections for \rbitrry jet lgorithms". llow lively subject of current stuy.
5 urk prouction Hevy constitutes \hevy urk"? Wht shouln't we lso inclue contributions igrms, ue to chrm prtons insie the nucleon? fctoriztion formuls for hevy urk Three prouction m= 0 Prtonic Formlism of Hevy urks c, b, (t) How { Simple pproch Zero-mss pproximtion Shoul the chrm urk hevy is \hevy"? t Tevtron energies be consiere observe \hevy"? enition fc; b; tg urks rehevy, Conventionl fu; ; sg re light. (criterion M ) while ll hevy urk problems re eul! Not Simple cse top prouction t the Tevtron ue to igrms initite by light prtons re hevy-urk pir-cretion process - Not so cler wht bout chrm prouction the Tevtron? In ition to the pir-cretion t - Zero-mss Fctoriztion orem Σ = g, u,, s, c, b, (t) (ll ctive flvors) f ctive flvor ll urks with m H < n fl () Usul prton istributions re generte in this scheme EHL,..., MRS, CTE i.e. F 2 (x,) = u + + s + c + b NLO σ^ ll prton msses m = 0 MSbr Subtr. hevy-vor excittion process ll populr pplictions re bse on this scheme Pythi, Herwig, Isjet ; EKS, JetR, vntge Simple n intuitive Limittions mss effects neglecte (except for threshols) Not pproprite for ~ m H is relly multi-lrge-scle problem M ; p T ; p s. This pproprite tretment of the problem e- pens on the reltive sizes of these scles.
6 Hevy urk Formlism of c, b, (t) Fixe-flvor-number (FFN) Scheme Generl Formlism of Hevy urk Prtons c, b, (t) Mss-inepenent pproch (Witten, Collins-Wilczek-Zee, COT,...Collins) Pir-cretion only { Hevy-mss pproch Σ = g, u,, s (light fl. only) f σ hevy urk m H "lrge" No col. Subtr. number of urk flvor n fl =3 (for c) fixe, inep. of Generlize (m = / 0) Fctoriztion orem Σ = g, u,, s, c, b, (t) (ll ctive flvors) f σ^ urk mss m H = / 0 Mss Subtr. Lepto-prouction hro-prouction ctive flvor ll urks with m H < n fl () Lenen, Smith, vn Neerven...et.l "Hevy flvor cretion" (HC) "Gluon-fusion process" NLO clcultion Nson, Dwson, Ellis Mngno, Riolfi, Fixione. vntge "Simple" one-scle clcultion Limittions no ctive H prton t ny energy; contins powers of log(/m H ) ; Lrge theoreticl uncertinty Not pproprite for >> m H Key fetures f (x,) obey the usul (MSbr) evolution es. σ(,m H ) is free from lrge log(/m H ) fter mss subtr. Proper limits for ~ m H reuces to the FFN hevy urk scheme; for >> m H reuces to the zero-mss prton moel vntge intuitively "obvious"; theoreticlly more complete price to py more complicte to implement; mss subtr. nees to be clculte.
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