Shape variables at hadron colliders Andrea Banfi ETH Zürich Work done in collaboration with Gavin Salam (LPTHE Jussieu), Giulia Zanderighi (Oxford) and Mrinal Dasgupta, Kamel Khelifa-Kerfa, Simone Marzani (Manchester) HP2.3 – Firenze – 16 September 2010 Andrea Banfi Shapes at hadron colliders
Hadronic final states at the LHC Final states at the LHC are characterised by large hadron multiplicities Shape variables are IR and collinear (IRC) safe observables obtained from suitable combinations of hadron momenta (e.g. event shapes) IRC safety ⇒ Hadronic final states can be described with PT QCD! Andrea Banfi Shapes at hadron colliders
Outline Event shapes at hadron colliders 1 Jet shapes and non-global logarithms 2 Shape variables for New Physics 3 Andrea Banfi Shapes at hadron colliders
Outline Event shapes at hadron colliders 1 Jet shapes and non-global logarithms 2 Shape variables for New Physics 3 Andrea Banfi Shapes at hadron colliders
Event shapes in hadron-hadron collisions Event shapes explore the geometry of hadronic energy-momentum flow (i.e. if hadronic events are planar, spherical, etc.) Two examples: transverse thrust and thrust minor Transverse thrust � i | � q ti · � n t | Thrust minor T t ≡ max � i q ti n t � jet 1 event plane beam � i | � q ti × � n t | T m ≡ transverse � i q ti plane jet 2 Event shapes can involve also longitudinal momenta, e.g. total and heavy-jet mass ρ T , ρ H , total and wide-jet broadening B T , B W , three-jet resolution parameter y 23 All event shapes we consider vanish in the two-jet limit Andrea Banfi Shapes at hadron colliders
Resummation vs fixed order: the example of T m Fixed order predictions (3 jets at NLO) diverge at small T m [Nagy PRD 68 (2003) 094002] s ln n +1 T m + α n s ln n T m } Resummation of large logarithms exp { α n (NLL) restores correct physical behaviour for T m → 0 [AB Salam Zanderighi JHEP 1006 (2010) 038] 12 LO NLO 10 NLL+NLO 8 1/ σ d σ /dT m,g Tevatron, p t1 > 200 GeV 6 4 2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 T m,g Peak of T m distribution where d/dT m ( dσ/dT m ) = 0 ⇒ α s ln T m ∼ 1 Peak position and height stabilised by NLL resummation Andrea Banfi Shapes at hadron colliders
Computer automated resummation: CAESAR General NLL resummation for any suitable event shape is possible with the Computer Automated Expert Semi-Analytical Resummer [AB Salam Zanderighi JHEP 0503 (2005) 073, qcd-caesar.org] Given a computer subroutine that computes V ( k 1 , . . . , k n ) , CAESAR checks whether V is resummable within NLL accuracy 1 performs the NLL resummation using a general master formula 2 The core of the automation lies in high-precision arithmetic to take soft and collinear limits methods of Experimental Mathematics to verify of falsify hypotheses ! CAESAR is not one more parton shower the produced results have the quality of analytical predictions an answer is provided only if NLL accuracy is guaranteed Andrea Banfi Shapes at hadron colliders
Conditions for NLL resummation An event shape V ( k 1 , . . . , k n ) is resummable at NLL accuracy if V ( k ) has a specific functional dependence on a single soft and 1 emission k collinear to a leg ℓ φ k k t � a ℓ � k t θ e − b ℓ η g ℓ ( φ ) V ( k ) = Q l it is (continuously) global, i.e. it is sensitive to soft/collinear 2 emissions in the whole of the phase space it is recursively IRC safe, i.e. it has good scaling properties with 3 respect to multiple emissions X X X X X X X X = Globalness + rIRC safety + QCD coherence ⇒ angular ordered parton branching accounts for all LL and NLL contributions Andrea Banfi Shapes at hadron colliders
Classes of global event shapes In spite of limited detector acceptance | η | < η 0 ( ∼ 5 at the LHC), it is possible to devise global event shapes even in hadron collisions [AB Salam Zanderighi JHEP 0408 (2004) 062] Directly global: measure all hadrons up to η 0 NLL valid up to v ∼ e − c V η 0 , e.g. T m ∼ e − η 0 Exponentially suppressed: event shape in central region C + exponentially suppressed forward term E ¯ C [Similar to recent proposal by Stewart Tackmann Waalewijn PRD 81 (2010) 094035] potentially affected by coherence violating logarithms? [Forshaw Kyrieleis Seymour JHEP 0608 (2006) 059] Recoil: event shape in central region C + recoil term R t, C NLL predictions diverge at small v � q ti e −| η i − η C | E ¯ C ∼ η 0 jet i/ ∈C � � � � � � � � p p � � � � � � R t, C ∼ q ti � � q ti � � = � � � � � � i ∈C i/ ∈C � � � � jet Andrea Banfi Shapes at hadron colliders
Estimate of theoretical uncertainties Theoretical uncertainties are under control and within ± 20% 10 a) Tevatron, p t1 > 200 GeV Asymmetric variation of µ R and µ F around p t = ( p t 1 + p t 2 ) / 2 1/ σ d σ /dT m,g 1 p t / 2 ≤ µ R ≤ 2 p t 0.1 µ R / 2 ≤ µ F ≤ 2 µ R 0.01 0 0.1 0.2 0.3 0.4 0.5 0.6 renorm. + fact. scale 1.4 b) 1.2 µ R = µ F 1 Rescaling of the argument of the 0.8 µ R ≠ µ F logs to be resummed 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 1.4 c) X = 0.5 . . . X = 2.0 ln T m → ln( XT m ) 1 / 2 ≤ X ≤ 2 1.2 X scales 1 0.8 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 Change the procedure to match NLL 1.4 d) mod-R 1.2 matching with NLO log-R 1 0.8 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 T m,g Andrea Banfi Shapes at hadron colliders
Sensitivity to hadronisation and underlying event Three-jet fractions are hardly affected Event-shape distributions get large by hadronisation and UE corrections from UE 0.4 partons partons � PYTHIA 6.4 DW � PYTHIA 6.4 DW hadrons 6 hadrons hadrons + UE hadrons + UE 0.3 LHC p t1 > 200 GeV LHC p t1 > 200 GeV 4 0.2 2 σ d σ 0.1 1 − −− σ d σ − 1 −− dln y 3,g d ρ T,E 0 0 0 0.1 0.2 0.3 -8 -6 -4 -2 Comparison to parton level MC PT predictions directly compared for tests of parton shower to data ⇒ PT consistency checks Suitable for tests and tunings of Suitable for tunings of parton UE models shower parameters Andrea Banfi Shapes at hadron colliders
NLL vs parton showers: Tevatron high- p t (quark dominated) 25 6 σ d σ σ d σ 1 − −− − 1 −− 20 d τ ⊥ ,g dT m,g 4 15 10 2 5 0 0 0 0.05 0.1 0.15 0 0.2 0.4 0.6 15 σ d σ − 1 −− 0.2 d ρ T,E 10 0.1 5 σ d σ − −− 1 dln y 3,g 0 0 -8 -4 0 0.1 0.2 Tevatron, 1.96 TeV NLO+NLL (all uncert.) p t1 > 200 GeV, |y jets | < 0.7, η C = 1 NLO+NLL (sym. scale uncert.) Alpgen + Herwig (partons) PARTON LEVEL NO UE Herwig 6.5 Pythia 6.4 virtuality ordered shower (DW tune) Pythia 6.4 p t ordered shower (S0A tune) Agreement between NLL and parton level MC is good for quark- dominated samples Andrea Banfi Shapes at hadron colliders
NLL vs parton showers: LHC low- p t (gluon dominated) 15 4 σ d σ σ d σ 1 − −− − 1 −− d τ ⊥ ,g dT m,g 10 2 5 0 0 0 0.1 0.2 0 0.2 0.4 0.6 σ d σ 8 0.3 − 1 −− d ρ T,E 6 0.2 4 0.1 σ d σ 1 − −− 2 dln y 3,g 0 0 -8 -4 0 0.1 0.2 0.3 LHC, 14 TeV NLO+NLL (all uncert.) p t1 > 200 GeV, |y jets | < 1, η C = 1.5 NLO+NLL (sym. scale uncert.) Alpgen + Herwig (partons) PARTON LEVEL NO UE Herwig 6.5 Pythia 6.4 virtuality ordered shower (DW tune) Pythia 6.4 p t ordered shower (S0A tune) Sizable differences in gluon dominated samples ⇒ new tests of initial state gluon branching? Andrea Banfi Shapes at hadron colliders
Future developments for global observables Straightforward extension to event shapes in processes with 1 massive particles (Drell-Yan, Higgs, top, SUSY,etc.) Characterisation of boson+jets with hadronic final states (out-of-plane radiation, jet mass, etc.) Suitable event-shape distributions as central-jet vetoes [Stewart Tackmann Waalewijn PRL 105 (2010) 092002] Resummation of transverse momentum distributions 2 Globalness and rIRC safety ⇒ angular ordered branching at NLL LL do not exponentiate in variable space ⇒ CAESAR’s automated predictions diverge for small transverse momentum Check resummability conditions and perform analytic resummation in impact parameter space (see e.g. Z -boson a T distribution) [AB Dasgupta Duran-Delgado JHEP 0912 (2009) 022] Automated NNLL resummation ⇒ new physical picture needed 3 s L m and constants α m due to interplay between logarithms α n s [Becher Schwartz JHEP 0807 (2008) 034] Precision determination of α s ( M Z ) using e + e − event shapes [Abbate Fickinger, Hoang, Mateu Stewart, arXiv:1006.3080 [hep-ph]] Andrea Banfi Shapes at hadron colliders
Outline Event shapes at hadron colliders 1 Jet shapes and non-global logarithms 2 Shape variables for New Physics 3 Andrea Banfi Shapes at hadron colliders
Event shapes inside a jet Jet shapes are defined using hadrons in a single jet Less sensitive to initial-state radiation and underlying event Their distributions depend strongly (at the LL level) on the underlying jet flavour (quark or gluon jet) j 2 Example: angularities of the observed jet, with jet minimum transverse energy E 0 [Ellis Hornig Lee Vermilion Walsh PLB 689 (2010) 82] j 3 Example of angularity: distribution in jet j 1 invariant mass M 2 j 1 M 2 j 4 j 1 � Σ( ρ, E 0 ) = Prob Q 2 < ρ, k ti < E 0 i/ ∈ jets j 5 Andrea Banfi Shapes at hadron colliders
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