Mueller Navelet jets at LHC: An observable to reveal high - PowerPoint PPT Presentation

Mueller Navelet jets at LHC: An observable to reveal high energy resummation e�e ts? Bertrand Du lou� Lab o ratoire de Physique Th�o rique d'Orsa y P a ris, Ma y 20th 2013 in ollab o ration with L. Szymano wski (NCBJ W a rsa w), S. W allon (UPMC & LPT Orsa y) D. Colferai; F. S hw ennsen, L. Szymano wski, S. W allon, JHEP 1012:026 (2010) 1-72 [a rXiv:1002.1365℄ B.D., L. Szymano wski, S. W allon, a rXiv:1208.6111 B.D., L. Szymano wski, S. W allon, a rXiv:1302.7012 (to app ea r in JHEP) 1 / 23

Motivations One of the imp o rtant longstanding theo reti al questions raised b y QCD is limit s ≫ − t its b ehaviour in the p erturbative Regge 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 t ↓ 1 ( M ′ 2 h 1 ( M 2 h ′ 1 ) 1 ) ← s → va uum quantum numb er 2 ( M ′ 2 h 2 ( M 2 h ′ 2 ) 2 ) s ales: M 2 1 , M 2 2 ≫ Λ 2 r M ′ 2 1 , M ′ 2 2 ≫ Λ 2 r t ≫ Λ 2 QCD QCD QCD ha rd o o the t − hannel where ex hanged state is the so- alled ha rd P omeron 2 / 23

The di�erent regimes of QCD Y = ln 1 x Q s Saturation PSfrag repla ements erturbative Non-p BFKL DGLAP ln Q 2 3 / 23

Resummation in QCD: DGLAP vs BFKL of α S Small values (p erturbation theo ry applies due to ha rd s ales) an b e omp ensated b y la rge loga rithmi enhan ements. n ( α S ln A) n of � ⇒ resummation series DGLAP BFKL k T n +1 ≪ k T n x 1 , k T 1 x n +1 ≪ x n x 1 , k T 1 x 2 , k T 2 x 2 , k T 2 PSfrag repla ements PSfrag repla ements in k T in x strong o rdering strong o rdering � ( α S ln Q 2 µ 2 ) n s 0 ) n � ( α S ln s When √ s b e omes very la rge, it is exp e ted that a BFKL des ription is needed to get a urate p redi tions 4 / 23

Ho w to test QCD in the p erturbative Regge limit? What kind of observables? p erturbation theo ry should b e appli able: sizes ≪ 1 / Λ QCD sele ting external o r internal p rob es with transverse o r b y rge t ho osing la in o rder to p rovide the ha rd s ale PSfrag repla ements p → 0 PSfrag repla ements governed b y the soft p erturbative dynami s of QCD m = 0 θ → 0 and not b y its ollinea r dynami s m = 0 with s ≫ p 2 T i ≫ Λ 2 where p 2 ⇒ QCD T i sele t semi-ha rd p ro esses a re t ypi al transverse s ale, all of the same o rder 5 / 23

rge s The sp e i� ase of QCD at la QCD in the p erturbative Regge limit The amplitude an b e written as:     A = + + + · · · + + · · ·  + · · ·        ∼ s ( α s ln s ) 2 ∼ s ∼ s ( α s ln s ) this an b e put in the follo wing fo rm : ← Impa t fa to r ← Green's fun tion ← Impa t fa to r 6 / 23

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 n ( α S ln s ) n α S � resummation impa t fa to rs a re kno wn in some ases at NLL γ ∗ → γ ∗ at t = 0 (Ba rtels, Colferai, Giesek e, Kyrieleis, Qiao; Balitski, Chirilli) fo rw a rd jet p ro du tion (Ba rtels, Colferai, V a a) in lusive p ro du tion of a pair of hadrons sepa rated b y a la rge interval of rapidit y (Ivanov, P apa) γ ∗ L → ρ L in the fo rw a rd limit (Ivanov, K otsky , P apa) 7 / 23

Mueller-Navelet jets: Basi s Mueller-Navelet jets Consider t w o jets (hadrons �ying 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 rder: ∆ φ − π = 0 ( ∆ φ = φ 1 − φ 2 = ba k at leading o relative azimuthal and k ⊥ 1 = k ⊥ 2 PSfrag repla ements angle) . There is no phase spa e fo r (untagged) emission b et w een them p ( p 1 ) la rge - rapidit y axis jet 2 ( k ⊥ 2 , φ 2 ) Beam φ 1 φ 2 − π zero rapidit y ⊥ plane jet 1 ( k ⊥ 1 , φ 1 ) la rge + rapidit y p ( p 2 ) 8 / 23

Master fo rmulas k T -fa to rized di�erential ross-se tion d σ � � d 2 k 1 d 2 k 2 d | k J 1 | d | k J 2 | d y J 1 d y J 2 = d φ J 1 d φ J 2 x 1 × Φ( k J 1 , x J 1 , − k 1 ) k J 1 , φ J 1 , x J 1 k 1 , φ 1 → × G ( k 1 , k 2 , ˆ s ) PSfrag repla ements k 2 , φ 2 → x 2 k J 2 , φ J 2 , x J 2 × Φ( k J 2 , x J 2 , k 2 ) x J = | k J | √ s e y J � with Φ( k J 2 , x J 2 , k 2 ) = d x 2 f ( x 2 ) V ( k 2 , x 2 ) f ≡ PDF 9 / 23

Studies at LHC: Mueller-Navelet jets ( ∼ � ( α s ln s ) n in LL BFKL ), the emission b et w een these jets leads to a strong de o rrelation b et w een the with p ¯ p jets, in ompatible T evatron ollider data � ( α s ln s ) n subseries α s up to re ently , the NLL w as in luded only in the Green's fun tion, and not inside the jet verti es Sabio V era, S hw ennsen Ma rquet, Ro y on the imp o rtan e of these o rre tions w as not kno wn 10 / 23

( √ s = 7 Results: symmetri on�guration T e V) Results fo r a symmetri on�guration In the follo wing w e sho w results fo r 35 GeV < | k J 1 | , | k J 2 | < 60 GeV 0 < y 1 , y 2 < 4 . 7 These uts allo w us to ompa re our p redi tions with re ent results p resented b y CMS at DIS 2013 (CMS-P AS-FSQ-12-002) on | k J 1 | and | k J 2 | . note: unlik e exp eriments w e have to set an upp er ut W e have he k ed that va rying this ut do esn't mo dify our results signi� antly . 11 / 23

Results Cross-se tion σ [nb] 10000 1000 100 35 GeV < | k J 1 | < 60 GeV 35 GeV < | k J 2 | < 60 GeV 10 0 < y 1 < 4 . 7 1 0 < y 2 < 4 . 7 PSfrag repla ements 0.1 pure LL LL vertex + NLL Green fun. 0.01 NLL vertex + NLL Green fun. 0.001 Y 4 5 6 7 8 9 The e�e t due to NLL o rre tions to the jet vertex is of the same o rder of magnitude as the e�e t due to NLL o rre tions to the Green's fun tion. 12 / 23

Results to s 0 and µ R = µ F Cross-se tion: stabilit y with resp e t hanges ∆ σ σ 2.5 µ F → µ F / 2 µ F → 2 µ F 2 √ s 0 → √ s 0 / 2 √ s 0 → 2 √ s 0 35 GeV < | k J 1 | < 60 GeV 1.5 35 GeV < | k J 2 | < 60 GeV 0 < y 1 < 4 . 7 1 PSfrag repla ements 0 < y 2 < 4 . 7 0.5 0 -0.5 Y 4 5 6 7 8 9 NLL vertex + NLL Green fun. w.r.t s 0 and µ r 5 < Y < 9 Our result is rather stable hoi es fo . 13 / 23

Results Relative va riation of the ross se tion when using other PDF sets than MSTW 2008 ∆ σ σ 0.5 0.4 ABKM09 CT10 HERAPDF 1.5 0.3 NNPDF 2.1 35 GeV < | k J 1 | < 60 GeV 0.2 35 GeV < | k J 2 | < 60 GeV 0.1 0 < y 1 < 4 . 7 0 0 < y 2 < 4 . 7 -0.1 PSfrag repla ements -0.2 -0.3 -0.4 -0.5 Y NLL vertex + NLL Green fun. 4 5 6 7 8 9 NLO DGLAP 14 / 23

Results rrelation � cos ϕ � Azimuthal o � cos ϕ � 1.2 1 35 GeV < | k J 1 | < 60 GeV 0.8 35 GeV < | k J 2 | < 60 GeV 0 < y 1 < 4 . 7 0.6 0 < y 2 < 4 . 7 0.4 PSfrag repla ements 0.2 pure LL LL vertex + NLL Green fun. NLL vertex + NLL Green fun. 0 Y 4 5 6 7 8 9 The e�e t of NLL o rre tions to the jet vertex is very imp o rtant , � cos ϕ � in Y A t full NLL a ura y is very �at and very lose to 1. 15 / 23

Results rrelation � cos ϕ � Azimuthal o � cos ϕ � 1.2 1 35 GeV < | k J 1 | < 60 GeV 0.8 35 GeV < | k J 2 | < 60 GeV 0 < y 1 < 4 . 7 0.6 0 < y 2 < 4 . 7 PSfrag repla ements 0.4 pure LL 0.2 LL vertex + NLL Green fun. NLL vertex + NLL Green fun. CMS data 0 Y 4 5 6 7 8 9 None of the BFKL omputations des rib e the data very w ell 16 / 23

Results rrelation � cos ϕ � Azimuthal o � cos ϕ � 1.2 1 35 GeV < | k J 1 | < 60 GeV 0.8 35 GeV < | k J 2 | < 60 GeV 0 < y 1 < 4 . 7 0.6 0 < y 2 < 4 . 7 PSfrag repla ements 0.4 0.2 pure LL NLL vertex + NLL Green fun. LL vertex + NLL Green fun. CMS data 0 Y 4 5 6 7 8 9 None of the BFKL omputations des rib e the data very w ell of s 0 and µ R = µ F The result at NLL is still rather dep endent on the hoi e 17 / 23

Results of � cos ϕ � Relative va riation when using other PDF sets than MSTW 2008 ∆ � cos ϕ � � cos ϕ � 0.04 ABKM09 CT10 HERAPDF 1.5 NNPDF 2.1 35 GeV < | k J 1 | < 60 GeV 0.02 35 GeV < | k J 2 | < 60 GeV 0 < y 1 < 4 . 7 0 0 < y 2 < 4 . 7 -0.02 PSfrag repla ements -0.04 Y 4 5 6 7 8 9 NLL vertex + NLL Green fun. of s 0 and µ R = µ F The result at NLL is still rather dep endent on the hoi e � cos ϕ � do es not dep end strongly on the PDF set 18 / 23