Shapes at hadron colliders

Transcription

1 Shape variables at hadron colliders ETH Zürich Work done in collaboration with Gavin Salam (LPTHE Jussieu), Giulia Zanderighi (Oxford) and Mrinal Dasgupta, Kamel Khelifa-Kerfa, Simone Marzani (Manchester) HP.3 Firenze 6 September

2 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!

3 Outline Event shapes at hadron colliders Jet shapes and non-global logarithms 3 Shape variables for New Physics

4 Outline Event shapes at hadron colliders Jet shapes and non-global logarithms 3 Shape variables for New Physics

5 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 jet Transverse thrust Thrust minor event plane jet beam transverse plane T t max n t T m i q ti n t i q ti i q ti n t i q ti 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 3 All event shapes we consider vanish in the two-jet limit

6 Resummation vs fixed order: the example of T m Fixed order predictions (3 jets at NLO) diverge at small T m [Nagy PRD 68 (3) 94] Resummation of large logarithms exp{α n s lnn+ T m +α n s lnn T m } (NLL) restores correct physical behaviour for T m [AB Salam Zanderighi JHEP 6 () 38] /σ dσ/dt m,g LO NLO NLL+NLO Tevatron, p t > GeV T m,g Peak of T m distribution where d/dt m (dσ/dt m ) = α s lnt m Peak position and height stabilised by NLL resummation

7 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 53 (5) 73, qcd-caesar.org] Given a computer subroutine that computes V(k,...,k n ), CAESAR checks whether V is resummable within NLL accuracy performs the NLL resummation using a general master formula 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

8 Conditions for NLL resummation An event shape V(k,...,k n ) is resummable at NLL accuracy if V(k) has a specific functional dependence on a single soft and emission k collinear to a leg l k φ ( ) al kt V(k) = e blη k θ t g l (φ) Q l it is (continuously) global, i.e. it is sensitive to soft/collinear emissions in the whole of the phase space 3 it is recursively IRC safe, i.e. it has good scaling properties with 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

9 Classes of global event shapes In spite of limited detector acceptance η < η ( 5 at the LHC), it is possible to devise global event shapes even in hadron collisions [AB Salam Zanderighi JHEP 48 (4) 6] Directly global: measure all hadrons up to η NLL valid up to v e cv η, e.g. T m e η Exponentially suppressed: event shape in central region C + exponentially suppressed forward term E C [Similar to recent proposal by Stewart Tackmann Waalewijn PRD 8 () 9435] potentially affected by coherence violating logarithms? [Forshaw Kyrieleis Seymour JHEP 68 (6) 59] Recoil: event shape in central region C + recoil term R t,c NLL predictions diverge at small v p jet p η E C q ti e η i η C i/ C R t,c q ti i C = q ti i/ C jet

10 Estimate of theoretical uncertainties Theoretical uncertainties are under control and within ±% /σ dσ/dt m,g. a) Tevatron, p t > GeV Asymmetric variation of µ R and µ F around p t = (p t +p t )/ p t / µ R p t matching X scales renorm. + fact. scale b). µ R = µ F.8 µ R µ F c) X =.5... X = d) mod-r. log-r µ R / µ F µ R Rescaling of the argument of the logs to be resummed lnt m ln(xt m ) / X Change the procedure to match NLL with NLO T m,g

11 Sensitivity to hadronisation and underlying event Three-jet fractions are hardly affected by hadronisation and UE Event-shape distributions get large corrections from UE.4.3 partons hadrons hadrons + UE PYTHIA 6.4 DW 6 PYTHIA 6.4 DW partons hadrons hadrons + UE LHC p t > GeV 4 LHC p t > GeV.. σ dσ dln y 3,g σ dσ dρ T,E PT predictions directly compared to data PT consistency checks Suitable for tunings of parton shower parameters Comparison to parton level MC for tests of parton shower Suitable for tests and tunings of UE models

12 NLL vs parton showers: Tevatron high-p t (quark dominated) 5 6 σ dσ dτ,g σ dσ dt m,g σ dσ dρ T,E. σ dσ 5 dln y 3,g Tevatron,.96 TeV p t > GeV, y jets <.7, η C = PARTON LEVEL NO UE NLO+NLL (all uncert.) NLO+NLL (sym. scale uncert.) Alpgen + Herwig (partons) Herwig 6.5 Pythia 6.4 virtuality ordered shower (DW tune) Pythia 6.4 p t ordered shower (SA tune) Agreement between NLL and parton level MC is good for quarkdominated samples

13 NLL vs parton showers: LHC low-p t (gluon dominated) 5 4 σ dσ dτ,g σ dσ dt m,g σ dσ dρ T,E σ dσ dln y 3,g LHC, 4 TeV p t > GeV, y jets <, η C =.5 PARTON LEVEL NO UE NLO+NLL (all uncert.) NLO+NLL (sym. scale uncert.) Alpgen + Herwig (partons) Herwig 6.5 Pythia 6.4 virtuality ordered shower (DW tune) Pythia 6.4 p t ordered shower (SA tune) Sizable differences in gluon dominated samples new tests of initial state gluon branching?

14 Future developments for global observables Straightforward extension to event shapes in processes with 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 5 () 9] Resummation of transverse momentum distributions 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 9 (9) ] 3 Automated NNLL resummation new physical picture needed due to interplay between logarithms α n s Lm and constants α m s [Becher Schwartz JHEP 87 (8) 34] Precision determination of α s(m Z) using e + e event shapes [Abbate Fickinger, Hoang, Mateu Stewart, arxiv:6.38 [hep-ph]]

15 Outline Event shapes at hadron colliders Jet shapes and non-global logarithms 3 Shape variables for New Physics

16 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 3 j Example: angularities of the observed jet, with jet minimum transverse energy E [Ellis Hornig Lee Vermilion Walsh PLB 689 () 8] j 4 j 5 j Example of angularity: distribution in jet invariant mass Mj Σ(ρ,E ) = Prob M j Q < ρ, k ti < E i/ jets

17 New sources of NLL contributions Jet-shape distributions like Σ(ρ,E ) are non-global, because no hadrons are measured inside the unobserved jets j,j 3,...,j N Non-global observables receive extra NLL contributions from soft large-angle gluons Non-global logarithms: gluons inside a jet coherently emitting a softer gluon in the interjet region (or viceversa) j These non-abelian contributions are resummed only in the large-n c limit by solving a non-linear evolution equation [Dasgupta Salam PLB 5 () 33; AB Marchesini Smye JHEP 8 () 6]

18 New sources of NLL contributions Jet-shape distributions like Σ(ρ,E ) are non-global, because no hadrons are measured inside the unobserved jets j,j 3,...,j N Non-global observables receive extra NLL contributions from soft large-angle gluons Jet-clustering logarithms: gluons independently emitted in two different angular regions get recombined in the same jet j j Resummed numerically with a generalisation of CAESAR branching algorithm from soft large-angle gluons [AB Dasgupta PLB 68 (5) 49] In the anti-k t algorithm (i.e. jets = circular cones of radius R), jet-clustering logarithms are absent

19 NLL resummation for jet shapes General NLL resummation of jet shapes for well-separated jets with the scale hierarchy p t,jets Q E ρq/r [AB Dasgupta Khelifa-Kerfa Marzani JHEP 8 () 64] ( R Σ(ρ,E ) = Σ sc ρ, Q ) ( R S ng E ρ, Q ) Σ cluster (ρ) E Σ sc is the jet-shape distribution obtained with only soft and collinear real emissions (the CAESAR s way) S ng is the contribution from non-global logarithms S ng ( R ρ, Q E ) ( ) E N ( ) Q = S j S ρq/r ji E i= S ng is the product of individual contributions of each jet Σ cluster (ρ) is the contribution of jet-clustering logs Both non-global and jet-clustering logarithms are finite for R

20 NLL resummation for jet shapes General NLL resummation of jet shapes for well-separated jets with the scale hierarchy p t,jets Q E ρq/r [AB Dasgupta Khelifa-Kerfa Marzani JHEP 8 () 64] ( R Σ(ρ,E ) = Σ sc ρ, Q ) ( R S ng E ρ, Q ) Σ cluster (ρ) E Σ sc is the jet-shape distribution obtained with only soft and collinear real emissions (the CAESAR s way) S ng is the contribution from non-global logarithms S ng ( R ρ, Q E ) ( ) E N ( ) Q = S j S ρq/r ji E i= S ng is the product of individual contributions of each jet Σ cluster (ρ) is the contribution of jet-clustering logs Both non-global and jet-clustering logarithms are finite for R

21 NLL resummation for jet shapes General NLL resummation of jet shapes for well-separated jets with the scale hierarchy p t,jets Q E ρq/r [AB Dasgupta Khelifa-Kerfa Marzani JHEP 8 () 64] ( R Σ(ρ,E ) = Σ sc ρ, Q ) ( R S ng E ρ, Q ) Σ cluster (ρ) E Σ sc is the jet-shape distribution obtained with only soft and collinear real emissions (the CAESAR s way) S ng is the contribution from non-global logarithms S ng ( R ρ, Q E ) ( ) E N ( ) Q = S j S ρq/r ji E i= S ng is the product of individual contributions of each jet Σ cluster (ρ) is the contribution of jet-clustering logs Both non-global and jet-clustering logarithms are finite for R

22 NLL resummation for jet shapes General NLL resummation of jet shapes for well-separated jets with the scale hierarchy p t,jets Q E ρq/r [AB Dasgupta Khelifa-Kerfa Marzani JHEP 8 () 64] ( R Σ(ρ,E ) = Σ sc ρ, Q ) ( R S ng E ρ, Q ) Σ cluster (ρ) E Σ sc is the jet-shape distribution obtained with only soft and collinear real emissions (the CAESAR s way) S ng is the contribution from non-global logarithms S ng ( R ρ, Q E ) ( ) E N ( ) Q = S j S ρq/r ji E i= S ng is the product of individual contributions of each jet Σ cluster (ρ) is the contribution of jet-clustering logs Both non-global and jet-clustering logarithms are finite for R

23 NLL resummation for jet shapes General NLL resummation of jet shapes for well-separated jets with the scale hierarchy p t,jets Q E ρq/r [AB Dasgupta Khelifa-Kerfa Marzani JHEP 8 () 64] ( R Σ(ρ,E ) = Σ sc ρ, Q ) ( R S ng E ρ, Q ) Σ cluster (ρ) E Σ sc is the jet-shape distribution obtained with only soft and collinear real emissions (the CAESAR s way) S ng is the contribution from non-global logarithms S ng ( R ρ, Q E ) ( ) E N ( ) Q = S j S ρq/r ji E i= S ng is the product of individual contributions of each jet Σ cluster (ρ) is the contribution of jet-clustering logs Both non-global and jet-clustering logarithms are finite for R

24 Impact of non-global logarithms Toy example: two jets in e + e annihilation with the anti-k t algorithm ( R Σ ng ρ, Q ) ( ) ( ) E Q = S meas E ρq/r S unmeas E Non-global logarithms arise when emissions in two different angular regions have widely separated characteristic scales Non-global logs modify the the peak height in distributions It is not possible to play with scales so as to get rid simultaneously of all non-global logarithms dσ Σ dρ.5 S Ρ E GeV

25 Outline Event shapes at hadron colliders Jet shapes and non-global logarithms 3 Shape variables for New Physics

26 Which shapes for new physics? New Physics events are generally broader than dijet events SUSY multi-jet event Black hole production Use event shapes to discriminate among different topologies?

27 Discrimination between two- and multi-jet events Consider a maximally symmetric event in the transverse plane N = N = 3 N = 4... N = 8 Event shapes can discriminate between two- and multi-jet events Current event shapes are not monotonic with number of jets no distinction among different multi-jet samples.. V(N) / V circ ρ T,C pheri S,g phero S,g F g T m,g V(N) / V circ τ,g 5 N B T,C 5 N

28 Sensitivity to spherical topologies Consider two selected 3-jet events atη = with Herwig parton shower Event (generic) Event (Mercedes) p t = 88 GeV, φ = p t = 666 GeV, φ = p t = 588 GeV, φ = 3π/4 p t = 666 GeV, φ = π/3 p t3 = 588 GeV, φ 3 = 3π/4 p t3 = 666 GeV, φ 3 = π/3 IRC safe shape variables give better resolution in discriminating among different topologies in a given n-jet sample Variables like B T,C or ρ T,C, equally sensitive to transverse and longitudinal degrees of freedom, better suited for identification of massive particle decays pheri S,g generic 3-jet Mercedes F g generic 3-jet Mercedes B T,C generic 3-jet Mercedes V circ /N dn/dv V circ /N dn/dv V circ /N dn/dv V / V circ V / V circ V / V circ

29 Sensitivity to spherical topologies Consider two selected 3-jet events atη = with Herwig parton shower Event (generic) Event (Mercedes) p t = 88 GeV, φ = p t = 666 GeV, φ = p t = 588 GeV, φ = 3π/4 p t = 666 GeV, φ = π/3 p t3 = 588 GeV, φ 3 = 3π/4 p t3 = 666 GeV, φ 3 = π/3 IRC safe shape variables give better resolution in discriminating among different topologies in a given n-jet sample Variables like B T,C or ρ T,C, equally sensitive to transverse and longitudinal degrees of freedom, better suited for identification of massive particle decays

30 Sensitivity to spherical topologies Consider two selected 3-jet events atη = with Herwig parton shower Event (generic) Event (Mercedes) p t = 88 GeV, φ = p t = 666 GeV, φ = p t = 588 GeV, φ = 3π/4 p t = 666 GeV, φ = π/3 p t3 = 588 GeV, φ 3 = 3π/4 p t3 = 666 GeV, φ 3 = π/3 IRC safe shape variables give better resolution in discriminating among different topologies in a given n-jet sample Variables like B T,C or ρ T,C, equally sensitive to transverse and longitudinal degrees of freedom, better suited for identification of massive particle decays pheri S,g generic 3-jet rotated F g generic 3-jet rotated B T,C generic 3-jet rotated V circ /N dn/dv 6 4 V circ /N dn/dv 6 4 V circ /N dn/dv V / V circ V / V circ V / V circ

31 Summary Phenomenology of global event shapes at hadron colliders is very rich and challenging First ever NLL+NLO predictions with full theoretical uncertainties Event shapes extremely useful for tuning of MC shower and UE Event-shape measurements have been performed at the Tevatron and are being performed at the LHC Resummation of non-global observables remains extremely tricky Non-global logarithms are well understood in the large-n c limit Jet-clustering logarithms can be computed at all orders but very little general features are known (e.g. behaviour with jet radius) Coherence violating logarithms might have large impact Important research directions Better event shapes for New Physics searches Transverse momentum resummations (e.g. t t, dijets) Automated NNLL for global observables