Azimuthal decorrelations between jets in QCD

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1 Azimuthal decorrelations between jets in QCD Andrea Banfi ETH Zurich q q p 1 p 1

2 Outline Azimuthal decorrelations in QCD hard processes Dijets in the back-to-back region Phenomenology of azimuthal decorrelations in DIS Joining soft-collinear and BFKL resummation?

3 Azimuthal decorrelations Azimuthal decorrelations between jets are directly sensitive to QCD radiation Tuning of MC event generators (PYTHIA DW) 1/ dijet d dijet / d dijet DØ p T > 180 GeV ( 8000) 130 < p T < 180 GeV ( 400) 100 < p T < 130 GeV ( 20) 75 < p T < 100 GeV HERWIG PYTHIA PYTHIA increased ISR (CTEQ6L) /2 3 /4 dijet (rad)

4 Azimuthal decorrelations Azimuthal decorrelations between jets are directly sensitive to QCD radiation Tuning of MC event generators (PYTHIA DW) Test of fixed order QCD predictions [Nagy 01] Data / NLO Theory p T > 180 GeV 130 < p T < 180 GeV DØ µ r, µ f dependence PDF uncertainty < p T < 130 GeV 2 NLOJET++ (CTEQ6.1M) 1 75 < p T < 100 GeV /2 3 /4 dijet (rad)

5 Azimuthal decorrelations Azimuthal decorrelations between jets are directly sensitive to QCD radiation Tuning of MC event generators (PYTHIA DW) Test of fixed order QCD predictions [Nagy 01] Access to unexplored regimes of QCD (BFKL, unintegrated parton densities) [Hautmann Jung 08] d 2 #/dxd (pb) (theo-dat)/dat < x < < x < < x < Andrea Banfi D

6 Azimuthal decorrelations Azimuthal decorrelations between jets are directly sensitive to QCD radiation Tuning of MC event generators (PYTHIA DW) Test of fixed order QCD predictions Access to unexplored regimes of QCD (BFKL, unintegrated parton densities) [Hautmann Jung 08] d 2 #/dxd (pb) (theo-dat)/dat < x < < x < < x < Andrea Banfi D The distribution in φ information on QCD dynamics can gives an incredible amount of

7 Dijets beyond LO Dijet azimuthal correlations: beyond fixed order Back-to-back region: multiple soft-collinear emissions Back-to-back region: sensitivity to multiple soft-collinear emissions q P k p 1 1 p 2 2 } X p 2 2 k Small-x regime: large phase space for multiple hard gluons p 1 1 φ π k t p t,1 p 2 t1 Small-x regime: large phase space for multiple initial-state hard gluons q p 2 φ π k t p t1 p 2 t,1 p 1 k 1 p 2 k 1 k 2 p 1 φ = 2 5 π 1 φ 2 5 π 1 k 3 k 2 P } X k 3 Andrea Banfi Dijets

8 Comparison theory vs data Fixed order QCD predictions fail both for small and large Problems at large also for BFKL inspired approaches d 2 #/dxd (pb) (theo-dat)/dat Dijet azimuthal decorrelations are directly sensitive to QCD radiation Test fixed order QCD predictions and tune Monte Carlo event generators Explore new features of QCD dynamics φ (BFKL effects, unintegrated pdfs) < x < < x < < x < φ ] -1 [ rad dσ dijet d ϕ dijet σ 1 dijet 10 [Hautmann Jung 08] 3 10 d 2 #/dxd (pb) p > 300 GeV p ( 10 ) T 200 < p 140 < p 110 < p 80 < p T T T T -1 L = 2.9 pb s = 7 TeV y < 1.1 < 300 GeV ( 10 < 200 GeV ( 10 k < 140 GeV ( 10) < 110 GeV π /2 2 π/3 5π/6 π [ rad ] 3 ) 2 ) CMS < x < < x < < x < Neither NLO nor BFKL account for large Andrea Banfi Dijets which dominate the distribution at (theo-dat)/dat φ π ln(π φ) QCD Predictions LO ϕ p 1 NLO µ = µ = p r f T CTEQ dijet terms

9 IR sensitive jet observables The physics underlying azimuthal decorrelations at is present in many jet cross sections dijet rates with symmetric cuts jet transverse energy imbalance event shape distributions with jets as inputs jet cross sections developing an infrared sensitivity ZEUS φ π E t [AB Dasgupta 03] E t = E t1 E t2! DIJET (pb) Common Jet Cuts E LAB T > 5 GeV E BRE T > 5 GeV ZEUS DISENT µ 2 R=Q 2 DISENT µ 2 R=E 2 T/4 MEPJET µ 2 R=E 2 T/ BRE, cut Pythia6E T,1 (GeV) 1 N dn/dln T m,c Data/MC Pythia6 Pythia8 Herwig++ MadGraph+Pythia6 Alpgen+Pythia6 Data CMS -1 s = 7 TeV, L = 3.2 pb ln T m,c Pythia6

10 Soft-collinear effects (I) Radiation outside the jets p jet,1 = p 1 and p jet,2 = p 2 q k p 1 p 2 p 2 k p 1 φ π k t p t1 sin φ P } X Multiple gluon emissions collinear to the beam give φ π φ in 1 p t,jet i/ jets k ti sin φ i Same as in Drell-Yan first transverse momentum resummations involving coloured particles in final state

11 Soft-collinear effects (II) Radiation inside one jet q p jet,1 = p 1 but p jet,2 = p 2 p 1 k p 2 p jet,2 p 2 k p 1 P } X If one uses a vectorial recombination scheme the two jets remain back-to-back, i.e. φ = π p t,jet = p t2 + k t Azimuthal decorrelation is insensitive to radiation inside the jets, i.e. it is a non-global observable What is so special about non-global observables?

12 Non-global logarithms Soft-collinear resummations heavily rely on independent emission approximation for QCD radiation X X X X X X X X = This picture breaks down for non-global observables [Dasgupta Salam 01] q(x, Q 2 ) (H R ) (H C) New soft large-angle contributions arise when harder gluons emit a softer gluon in the observed region

13 Non-global logs in jets All observables involving jets are in principle affected by non-global logarithms [AB Dasgupta 03] Non-global logarithms depend on the jet algorithm and on the recombination scheme (imal for anti-kt and reduced for clustering algorithms) [Appleby Seymour 02] j 1 j 1 For clustering algorithms there are further clustering logarithms that spoil independent emission as well! [AB Dasgupta 05]

14 Who s afraid of NG logs?

15 Who s afraid of NG logs? Non-global logs are soft large-angle non-abelian contributions resummed by solving a non-linear equation Dynamics of NG logs is understood both in the context of interjet energy flow and of jet cross sections (e.g. dependence on jet algorithm and jet radius) Clustering logarithms can be computed numerically and analytically estimated as a power series in the jet radius NG and clustering logs have a small impact on transverse momentum resummations [Dasgupta Salam 01] [AB Marchesini Smye 02] [Dasgupta Salam 02] [AB Dasgupta Khelifa-Kerfa Marzani 10] [AB Dasgupta 05] [Delenda Appleby AB Dasgupta 06] [AB Dasgupta 03]

16 Global is better Non-global jet cross sections have various drawbacks Resummation of NG logs can only be performed in the large limit N c Predictions for non-global observables depend heavily on the details of the observation region (jet algorithm, recombination scheme, jet radius, etc.) Global observables are not sensitive to the details of the interjet region, except from universal soft anomalous dimensions, a.k.a. the fifth form factor Is it possible to devise global dijet cross sections? [Dasgupta Salam 01] [AB Marchesini Smye 02] [Dasgupta Salam 02] [AB Dasgupta Khelifa-Kerfa Marzani 10] [Kidonakis Oderda Sterman 98] [AB Salam Zanderighi 05] [Dokshitzer Marchesini 06]

17 Pt recombination scheme Sensitivity to radiation inside the jets with the recombination scheme q global observable! p t weighted [AB Dasgupta 08] p 1 k p 2 p jet,2 p 2 k p 1 P } X φ jet,2 = p t2 φ 2 + k t φ p t2 + k t φ = π k t p t1 sin φ (π φ) Novel kind of one-dimensional momentum cancellation π φ out 1 p t,jet i jets k ti sin 3 φ i

18 Soft gluon resummation Resummation of soft-collinear gluons is performed in space with the same phylosophy as for φ in DY b 1 σ dσ d = 2 π 0 Novel Sudakov exponent db cos(b ) f 1(µ F / b) f 2 (µ F / b) f 1 (µ F ) f 2 (µ F ) e R in( b) initial state (DY type) e R out( b) final state R out ( b) accounting for softcollinear radiation inside the outgoing jets Tr[He Γ t( b) Me Γt( b) ] Tr[HM] soft large angle R out ( b) = i 2 Θ 3 C i Q 0 Ei p t dk t 2α s (k t ) k t π ln E i k t 0 dη 2 k t p t e 2η sin φ 3 1 b C out 3 α s π ln2 b

19 Dijet phenomenology in DIS Dijet events with p HCM and t,jet > 5GeV 1 <η lab jet < 2.5 d!/(dx dq 2 d" #) [pb/(gev 2 deg)] NLL LO NLO Q 2 = 67 GeV 2 x B = 2.86 $ " # [deg] Both LO and NLO predictions diverge at φ π Resummation approaches a plateau for expected for one-dimensional cancellations φ π, as

20 Non-perturbative effects Size of non-perturbative effects to perform the integration b change in prescriptions d!/(dx dq 2 d" #) [pb/(gev 2 deg)] b < b b < b /2 b < µ F R p b -> (1+b 2 ) 1/2 Q 2 = 67 GeV 2 x B = 2.86 $ " # [deg] b Cutting off the integral at a scale corresponding to the size of the proton gives a huge difference high sensitivity to intrinsic transverse momentum of the proton

21 Problems at small x The height of the plateau at φ π resummation coefficient constant is determined also by Σ(L) (1 + C 1 (L)) Σ res (L) C 1 (L) =Σ 1 (L) H 12 L 2 H 11 L 2 x g C 1 (g) +xq C 1 (q) 1.5 C 1 (L) Q 2 = 67 GeV 2 x B = 2.86 % At the largest value of L = ln(! " # $) x B the coefficient constant becomes C 1 larger than one resummation of small-x effects in?

22 Complementary approaches Summary of all-order resummation of azimuthal decorrelations at small and large φ Soft-collinear resummation Plateau (random walk) around φ = π Hard emissions only at fixed order Described by shower MC at Tevatron (large x), not at HERA (small x) Analytical calculations at NLL+NLO Small-x resummation Unintegrated parton distributions at φ = π Multiple hard emissions via BFKL or CCFM Described at HERA by CASCADE, no results for hadron colliders yet No analytical control over MC accuracy

23 Conclusions Azimuthal dijet decorrelations are rich in information on QCD dynamics at soft and hard scales In the quasi back-to-back region it is possible to resum multiple soft-collinear enhancements first transverse momentum resummation with final-state coloured particles Sensitivity to intrinsic transverse momentum of the proton and to multiple hard gluon emissions (BFKL) Description of LHC data requires a joint effort from different QCD communities