A study of microjets Fr ed eric Dreyer work in progress with - PowerPoint PPT Presentation

A study of microjets Fr´ ed´ eric Dreyer work in progress with Gavin Salam, Matteo Cacciari, Mrinal Dasgupta & Gregory Soyez eorique et Hautes ´ Laboratoire de Physique Th´ Energies LHCPhenoNet Paris, June 2014

Outline Introduction 1 Jet algorithms Perturbative properties of jets Generating functionals 2 Evolution equations Observables 3 Inclusive microjet observables Hardest microjet observables Microjet vetoes Filtering & Trimming Conclusion 4

Overview Introduction 1 Jet algorithms Perturbative properties of jets Generating functionals 2 Evolution equations Observables 3 Inclusive microjet observables Hardest microjet observables Microjet vetoes Filtering & Trimming Conclusion 4

Jets Concept Collimated bunches of particles produced by hadronization of a quark or gluon. Jets can emerge from a variety of processes ◮ scattering of partons inside colliding protons, ◮ hadronic decay of heavy particles, ◮ radiative gluon emission from partons, . . . We use jet algorithms to combine particles in order to retrieve information on what happened in the event. No unique or optimal definition of a jet, but good jet definitions are as close as we can get to observing single partons Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 1 / 23

Generalised k t algorithms with incoming hadrons Definition For any pair of particles i , j find the minimum of 1 ∆ R 2 ij d ij = min { k 2 p ti , k 2 p d iB = k 2 p d jB = k 2 p tj } R 2 , ti , tj where ∆ R ij = ( y i − y j ) 2 + ( φ i − φ j ) 2 . If the minimum distance is d iB or d jB , then the corresponding particle 2 is removed from the list and defined as a jet, otherwise i and j are merged. Repeat until no particles are left. 3 The index p defines the specific algorithm p = 1 for the k t algorithm, p = 0 for the Cambridge/Aachen algorithm, and p = − 1 for the anti- k t algorithm Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 2 / 23

Perturbative properties Jet properties will be affected by gluon radiation and g → q ¯ q splitting. In particular, considering gluon emissions from an initial parton for a jet of radius R , then radiation at angles > R reduces the jet energy, radiation at angles < R generates a mass for the jet. We will try to investigate the effects of perturbative radiation on a jet analytically, particularly in the small- R limit. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 3 / 23

Example: Jet mass with emissions at angle θ < R To evaluate the effect of emissions within the reach of the jet definition, we study the mean squared invariant mass of a jet. In the small- R limit we can write for an initial quark � d θ 2 � α s � M 2 � q = dz p 2 t z (1 − z ) θ 2 2 π p qq ( z ) Θ( R − θ ) θ 2 � �� � jet inv. mass = 3 α s π p 2 t R 2 8 C F Figure: Gluon emission within the reach of the jet. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 4 / 23

Example: Jet p t with emissions at angle θ > R We can calculate the average energy difference between the hardest final state jet and the initial quark, considering emissions beyond the reach of the jet. In the small- R limit, we find � O (1) d θ 2 � dz (max[ z , 1 − z ] − 1) α s � ∆ z � hardest = 2 π p qq ( z )Θ( θ − R ) q θ 2 � � = α s 2 ln 2 − 3 π C F ln R + O ( α s ) 8 Figure: Gluon emission beyond the reach of the jet. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 5 / 23

Example: Jet p t with intial gluon We can perform the same calculation in the case of an initial gluon. � O (1) d θ 2 � dz (max[ z , 1 − z ] − 1) α s � ∆ z � hardest = g θ 2 2 π � 1 � × 2 p gg ( z ) + n f p qg ( z ) Θ( θ − R ) � � � � = α s 2 ln 2 − 43 + 7 C A 48 n f T R ln R + O ( α s ) π 96 Figure: Gluon emission or q ¯ q splitting beyond the reach of the jet. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 6 / 23

Microjets Definition Microjets are jets with small values for the jet radius R ≪ 1 Small- R limit relevant in a number of contexts, e.g. In Higgs physics, where complicated dependence on the jet radius appears due to clustering, in particular in the resummation of jet veto logarithms. Decay of heavy particles to boosted W , Z bosons and top quarks. Heavy-ion physics where small values for R are used due to the large background. In high pileup environments, where use of smaller R might help mitigate adverse effects of pileup. Theoretically interesting because α s ln R ≫ α s , therefore calculations simplify and one can investigate all-order structure. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 7 / 23

How relevant are small- R effects? We can evaluate numerically how important the effect of perturbative ln R terms is on the microjet p t . Taking R = 0 . 1 we find that quark-induced jets have a hardest microjet p t ∼ 10 − 15% smaller than the original quark, gluon-induced jets have a hardest microjet p t ∼ 20 − 30% smaller than the original gluon. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 8 / 23

How relevant are small- R effects? We can evaluate numerically how important the effect of perturbative ln R terms is on the microjet p t . Taking R = 0 . 1 we find that quark-induced jets have a hardest microjet p t ∼ 10 − 15% smaller than the original quark, gluon-induced jets have a hardest microjet p t ∼ 20 − 30% smaller than the original gluon. How important can contributions from higher orders be, e.g. ( α s ln R ) n , especially at smaller values of R ? We will approach this question using generating functionals. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 8 / 23

Overview Introduction 1 Jet algorithms Perturbative properties of jets Generating functionals 2 Evolution equations Observables 3 Inclusive microjet observables Hardest microjet observables Microjet vetoes Filtering & Trimming Conclusion 4

Evolution variable t Start with a parton and consider emissions at successively smaller angular scales. We introduce an evolution variable t corresponding to the integral over the collinear divergence weighted with α s � 1 ∞ � α s b 0 � n d θ 2 α s ( p t θ ) = 1 1 2 π ln 1 � t = θ 2 R 2 2 π b 0 n R 2 n =1 10 GeV 0.4 20 GeV 50 GeV 0.3 200 GeV 2 T eV t 0.2 20 T eV 0.1 0.0 -4 -3 -2 -1 0 10 10 10 10 10 R Figure: Plot of t as a function of R down to Rp t = 1 GeV for p t = 0 . 01 − 20 TeV . Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 9 / 23

Generating functional Definition Q ( x , t 1 , t 2 ) is the generating functional encoding the parton content one would observe when resolving a quark with momentum xp t at scale t 1 on an angular scale t 2 > t 1 (ie. R 1 ≫ R 2 ). The mean number of quark microjets of momentum zp t produced from a quark of momentum p t are � dn q ( z ) = δ Q (1 , 0 , t 2 ) � � δ q ( z ) dz � ∀ q ( z )=1 , g ( z )=1 We can formulate an evolution equation for the generating functionals � � � Q ( x , 0 , t ) = Q ( x , δ t , t ) 1 − δ t dz p qq ( z ) � � � + δ t dz p qq ( z ) Q ( zx , δ t , t ) G ((1 − z ) x , δ t , t ) . The gluon generating functional G ( x , t 1 , t 2 ) is defined the same way. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 10 / 23

Evolution equations We can then easily rewrite the equation on slide [10] as a differential equation, Quark � dQ ( x , t ) = dz p qq ( z ) [ Q ( zx , t ) G ((1 − z ) x , t ) − Q ( x , t )] . dt The same procedure in the gluon case yields, Gluon � dG ( x , t ) = dz p gg ( z ) [ G ( zx , t ) G ((1 − z ) x , t ) − G ( x , t )] dt � + dz n f p qg ( z ) [ Q ( zx , t ) Q ((1 − z ) x , t ) − G ( x , t )] . Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 11 / 23

Solving the evolution equations We can solve these equations order by order as a power expansion in t , writing t n � Q ( x , t ) = n ! Q n ( x ) , n t n � G ( x , t ) = n ! G n ( x ) . n Furthermore the evolution equations can be used to perform an all-order resummation of ( α s ln R ) n terms. These methods allow us to calculate observables in the small-R limit up to a fixed order in perturbation theory, or to resum them to all orders numerically. Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 12 / 23

Overview Introduction 1 Jet algorithms Perturbative properties of jets Generating functionals 2 Evolution equations Observables 3 Inclusive microjet observables Hardest microjet observables Microjet vetoes Filtering & Trimming Conclusion 4

Inclusive microjet observables Definition Given a parton of flavour i , the inclusive microjet fragmentation function f incl j / i ( z , t ) is the inclusive distribution of microjets of flavour j carrying a momentum fraction z . The inclusive microjet fragmentation function satisfies a DGLAP-like equation. The inclusive microjet spectrum is given by � dp ′ d σ jet d σ i � t f incl jet / i ( p t / p ′ = t , t ) p ′ dp ′ dp t p t t t i Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 13 / 23

Inclusive microjet fragmentation function Peak at 1 is original parton, peak at 0 is soft gluon microjets. t = 0.02 10 4 quark gluon 10 2 1 f 10 − 2 10 − 4 0.0 0.2 0.4 0.6 0.8 1.0 x Preliminary Fr´ ed´ eric Dreyer (LPTHE) Microjets LHCPhenoNet 14 / 23