Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results First al ulation of Mueller Navelet jets at LHC at a omplete NLL BFKL o rder Samuel W allon Universit� Pierre et Ma rie Curie and Lab o ratoire de Physique Th�o rique CNRS / Universit� P a ris Sud Orsa y Semina r �High Energy Physi s�, Depa rtment of Physi s & Astronomy , Universit y College London London, Ap ril 15th 2011 in ollab o ration with D. Colferai (Firenze), F. S hw ennsen (DESY), L. Szymano wski (SINS, V a rsa w) JHEP 1012:026 (2010) 1-72 [a rXiv:1002.1365 [hep-ph℄℄ 1 / 36
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Motivations One of the imp o rtant longstanding theo reti al questions raised b y QCD is its b ehaviour in the p erturbative Regge limit s ≫ − t PSfrag repla ements Based on theo reti al grounds, one should identify and test suitable observables in o rder to test this p e ulia r dynami s va uum quantum numb er ha rd s ales: M 2 o r M ′ 2 o r t ≫ Λ 2 where the t − hannel ex hanged state is the so- alled ha rd P omeron t ↓ 1 ( M ′ 2 h 1 ( M 2 h ′ 1 ) 1 ) 2 / 36 ← s → h 2 ( M 2 h ′ 2 ( M ′ 2 2 ) 2 ) 1 , M 2 2 ≫ Λ 2 1 , M ′ 2 2 ≫ Λ 2 QCD QCD QCD
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Ho w to test QCD in the p erturbative Regge limit? What kind of observable? p erturbation theo ry should b e appli able: sele ting external o r internal p rob es with transverse sizes ≪ 1 / Λ QCD ( ha rd γ ∗ , heavy meson ( J/ Ψ , Υ ), energeti fo rw a rd jets) o r b y ho osing la rge t in o rder to p rovide the ha rd s ale. PSfrag repla ements PSfrag repla ements governed b y the "soft" p erturbative dynami s of QCD and not b y its ollinea r dynami s sele t semi-ha rd p ro esses with s ≫ p 2 where p 2 a re t ypi al transverse s ale, all of the same o rder. p → 0 3 / 36 m = 0 θ → 0 m = 0 T i ≫ Λ 2 = ⇒ QCD T i
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Ho w to test QCD in the p erturbative Regge limit? Some examples of p ro esses in lusive: DIS (HERA), di�ra tive DIS, total γ ∗ γ ∗ ross-se tion (LEP , ILC) semi-in lusive: fo rw a rd jet and π 0 p ro du tion in DIS, Mueller-Navelet double jets, di�ra tive double jets, high p T entral jet, in hadron-hadron olliders (T evatron, LHC) ex lusive: ex lusive meson p ro du tion in DIS, double di�ra tive meson p ro du tion at e + e − olliders (ILC), ultrap eripheral events at LHC ( P omeron, O dderon) 4 / 36
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results The sp e i� ase of QCD at la rge s QCD in the p erturbative Regge limit Small values of α S (p erturbation theo ry applies due to ha rd s ales) an b e omp ensated b y la rge ln s enhan ements. ⇒ resummation of series (Balitski, F adin, Kuraev, Lipatov) this results in the e�e tive BFKL ladder P n ( α S ln s ) n 0 1 0 1 B C B C A = + + + · · · + + · · · A + · · · @ A @ reggeon = "dressed gluon" gluon with α P (0) − 1 = C α s Leading Log P omeron ∼ s ( α s ln s ) 2 ∼ s ∼ s ( α s ln s ) e�e tive vertex Balitsky , F adin, Kuraev, Lipatov PSfrag repla ements 5 / 36 = 1 ⇒ σ h 1 h 2 → anything s Im A ∼ s α P (0) − 1 = tot ( C > 0)
PSfrag repla ements Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Op ening the b o xes: Impa t rep resentation γ ∗ γ ∗ → γ ∗ γ ∗ as an example Sudak ov de omp osition: k i = α i p 1 + β i p 2 + k ⊥ i ( p 2 2 = 0 , 2 p 1 · p 2 = s ) write ( k = Eu l. ↔ k ⊥ = Mink.) t − hannel gluons have non-sense p ola rizations at la rge s : ǫ up/down set α 1 = 0 and impa t fa to r 1 = p 2 d 4 k i = s 2 dα i dβ i d 2 k ⊥ i = 2 s p 2 / 1 NS R dβ 1 ⇒ Φ γ ∗ → γ ∗ ( k 1 , r − k 1 ) ⇒ multi-Regge kinemati s α q, ¯ q γ ∗ k 1 r − k 1 α 1 β ր Z d 2 k Z d 2 k ′ is k 2 Φ up ( k, r − k ) k ′ 2 Φ down ( − k ′ , − r + k ′ ) set β n = 0 and M = β 2 (2 π ) 2 k 2 α 2 6 / 36 δ + i ∞ „ s Z « ω dω G ω ( k, k ′ , r ) × 2 πi s 0 δ − i ∞ ← − α n − 1 α ց k n β n γ ∗ R dα n ⇒ Φ γ ∗ → γ ∗ ( − k n , − r + k n ) β q, ¯ ⇒ q
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results higher o rder o rre tions Higher o rder o rre tions to BFKL k ernel a re kno wn at NLL o rder (Lipatov F adin; Cami i, Ciafaloni), no w fo r a rbitra ry impa t pa rameter resummation impa t fa to rs a re kno wn in some ases at NLL at t = 0 (Ba rtels, Colferai, Giesek e, Kyrieleis, Qiao) fo rw a rd jet p ro du tion (Ba rtels, Colferai, V a a) in the fo rw a rd limit (Ivanov, K otsky , P apa) note: fo r ex lusive p ro esses, some transitions ma y sta rt at t wist3, fo r whi h almost nothing is kno wn. The �rst omputation of the γ ∗ t wist 3 transition at LL has b een p erfo rmed only re ently I. V. Anikin, D. Y. Ivanov, B. Pire, L. Szymano wski and S. W. P n ( α S ln s ) n α S Phys. Lett. B 688:154-167, 2010; Nu l. Phys. B 828:1-68, 2010. γ ∗ → γ ∗ 7 / 36 γ ∗ L → ρ L T → ρ T
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Mueller-Navelet jets: Basi s Mueller Navelet jets Consider t w o jets (hadron paquet within a na rro w one) sepa rated b y a la rge rapidit y, i.e. ea h of them almost �y in the dire tion of the hadron � lose� to it, and with very simila r transverse momenta in a pure LO ollinea r treatment, these t w o jets should b e emitted ba k to ba k at leading o rder: ∆ φ − π = 0 ( ∆ φ = φ 1 − φ 2 = relative azimutal PSfrag repla ements angle) and k ⊥ 1 = k ⊥ 2 . There is no phase spa e fo r (untagged) emission b et w een them la rge - rapidit y ( k ⊥ 2 , φ 2 ) zero rapidit y plane ( k ⊥ 1 , φ 1 ) la rge + rapidit y p ( p 1 ) 8 / 36 axis jet 2 Beam φ 1 φ 2 − π ⊥ jet 1 p ( p 2 )
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Mueller-Navelet jets at LL fails Mueller Navelet jets at LL BFKL PSfrag repla ements in LL BFKL ( ∼ P ( α s ln s ) n ), emission b et w een these jets jet 1 ollinea r strong de o rrelation pa rton (PDF) b et w een the relative azimutal rapidit y gap angle jets, in ompatible with p ¯ T evatron ollider data LL BFKL a ollinea r treatment rapidit y gap Green fun tion at next-to-leading o rder (NLO) an des rib e the data imp o rtant issue: ollinea r non- onservation pa rton (PDF) of energy-momentum − → jet 2 along the BFKL ladder. } A BFKL-based Multi-Regge kinemati s Monte Ca rlo ombined p (LL BFKL) with e-m onservation {z imp roves dramati ally the situation (Orr and Stirling) 9 / 36 |
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Studies at LHC: Mueller-Navelet jets PSfrag repla ements Mueller Navelet jets at NLL BFKL up to no w, the ollinea r jet 1 NLL jet vertex pa rton subseries α s (PDF) NLL w as in luded rapidit y gap only in the ex hanged P omeron state, and not inside the jet verti es NLL BFKL rapidit y gap Sabio V era, S hw ennsen Green fun tion Ma rquet, Ro y on ollinea r the ommon b elief pa rton (PDF) w as that these o rre tions jet 2 NLL jet vertex P ( α s ln s ) n should not b e imp o rtant } Quasi Multi-Regge kinemati s (here fo r NLL BFKL) {z 10 / 36 |
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Jet vertex: LL versus NLL Eu lidian t w o dimensional ve to rs LL jet vertex: PSfrag repla ements PSfrag repla ements k , k ′ = NLL jet vertex: k 0 k 11 / 36 k k − k ′ k ′ k ′ 0
Intro du tion A full NLLx example: Mueller-Navelet jets Pra ti al implementation of the omputation Results Jet vertex: jet algo rithms Jet algo rithms a jet algo rithm should b e IR safe, b oth fo r soft and ollinea r singula rities the most ommon jet algo rithm a re: algo rithms (IR safe but time onsuming fo r multiple jets on�gurations) one algo rithm (not IR safe in general; an b e made IR safe at NLO: Ellis, Kunszt, Sop er) 12 / 36 k t
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