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Introduc#On to QCD and Jet Physics

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Introduc#On to QCD and Jet Physics HASCO 2017 Introduc)on to QCD and Jet Physics Vincenzo Cavasinni Universita’ di Pisa and INFN Summary Introduc)on to the QCD -The color interacBon -AsymptoBc Freedom -The QCD elementary cross secBons Jets -Jet Formaon and reconstrucBon -jet reconstrucBon algorithms -jet energy calibraon Rc -jet cross secBons measurement p p -jets For searching new physics R c Evidence for a new quark interaction and a new quantum number: the color e+e− → q( jet)q( jet) Ratio : e+e− → µ+µ− Several other evidences for color eg : Γ(π 0 →γγ) BR(τ → qq 'ν) V. Cavasinni University oF Pisa and INFN Interaction between colored quarks: the Quantum Chromo Dynamics, QCD is mediated by a massless vector particle: the gluon « ex of exchange of colored gluon. q q q qb r qb r qb r rb br qr qb qr qb qr qb q q b r qr qr br rb rr « We would expect 9 gluons: SU(3) algebra: 3 * 3= 8 + 1 octet: singlet: « But color is confined: and a singlet gluon would be not confined: « -> long range force…. V. Cavasinni University oF Pisa and INFN Implicaons of colored gluons • Gluon can interact with itselF αs→ 2 (not the case For photons) αs → • AsymptoBc Freedom q q a) As in QED there are effect from vacuum polarization: αS the result into a shielding of the carge 2 the αS decreases as Q →0 (screening) In QCD there are additional gluon loops: q q Their effecs are ooposite to the vacuum polarization: b) q q The color charge is propagated (tube of charge). As a result : αS 2 αS increases as Q →0 (antiscreening) q q The antiscreening effects dominate V. Cavasinni University oF Pisa and INFN " 2 2 % 2 2 αS (µ ) Q David Gross, αS (Q ) = αS (µ )$1− ( 33− 2 f )ln +...' # 12π µ 2 & Frank Wilczek and David Politzer, 1973 The vacuum polarization depends on the number of 2 2 gluon-loop effect Active quarks f (Q >4mq ) By summing up the leading log terms (geometric series: Σlnn ~ 1/(1-ln)): α (µ 2 ) 2 S QCD “running coupling constant” α S (Q ) = ⇒ α (µ 2 ) Q2 1+ S (33− 2 f )ln 12π µ 2 2 Q2→∞ αS (Q ) ###→0 (if 33 > 2 f) :The asymptotic freedom Perturbation theory can be applied. But αS=0.1-1 and, differently than α, 2 2 2 2 It varies appreciably with Q . Defining ln Λ = lnµ −12π /[(33− 2 f )αS (µ )] We have only 1 parameter : Λ∼100-200 ΜeV ~ 1 fm-1 12π to be extracted experimentally (QCD has not α (Q 2 ) = S 2 2 a natural scale as in QED (me)). (33− 2 f )ln Q / Λ 2 2 Conversely if Q ~ Λ , αS is large,>1: interaction becomes strong,confinement?? V. Cavasinni University oF Pisa and INFN From αS we can extract Λ, but with poor sensivity 100<Λ<400 MeV In the same Q interval α varies αS ~ 0.32 (Q=2 GeV)From 1/137 to 1/128 ~0.12 (Q=100 GeV) + − e e ( pp) → 3 jets q ex. + + − ∝αS e αS e e ( pp) → 2 jets e- q N.B. Λ depends on the active quark number q e+ - e q Other processes to extract αS V. Cavasinni University oF Pisa and INFN The Standard Model Lagrangian Gauge boson (gluon) selF interacBons Gauge boson (gluon)-quark interacBons V. Cavasinni University oF Pisa and INFN 8 processes QCD tree level cross sections Combridge, Kripfganz Ranft (1977) t,s,u of the incoming partons (quarks or gluons) t = −s(1− cosθ * ) / 2, u = −s(1+ cosθ * ) / 2 There is also the triple gluon vertex : ggg They are in the ratio 64/9 (color) Absent in QED Values at θ*=90o 2 d 2 σ παS |M|2 , averaged on initial color and spin * = M d cosθ 2s and summed up on the final ones V. Cavasinni University oF Pisa and INFN The elementary cross sections have to be weighted by the initial parton pdf’s 5 10 30 years of “jet physics” 103 101 10-1 LHC 13 Partons, after the scattering, evolve towards the 10-3 “parton showering” and hadronisation (jets) ≈10 7 10-5 LHC 13/Tevatron Tevatron 10-7 SppC 1 2 3 4 pT,jet(TeV) V. Cavasinni University oF Pisa and INFN Jet physics What jets are? QCD InteracBons between quarks and gluons (proton consBtuents) yield quarks and gluons that, however, are not directly accessible (color confinement): in Fact their Fragment into a bunch oF collimated hadrons (pion, kaons, neutros, protons,..): a “jet” oF parBcles. So idenBFying and measuring jets, allows the reconstrucBon oF the kinemacs oF the elementary QCD interacBons. Credits to: C.Roda – Lectures on “Jet Physics”, Pisa University, 2017. A dijet event A dijet event at the p-pbar collider at LHC NoBce that the two jets have to be balanced in Pt also in the lab, but not necessarily in longitudinal momentum (opposite rapidity) because the two primary interacBng proton partons can have unbalanced momentum (pdf’s) V. Cavasinni University of Pisa and INFN Why do we care about jets: QCD studies Background of many other physics processes Jets will be the background for nearly all searches: σ(ET>100 GeV) ~ µb Signal processes: • SUSY involving heavy particles: σ(squark-squark @ M~ 1 TeV)~ pb • SM Higgs: σ(Higgs @ M=125 GeV)~ 20 pb QCD background is 5-6 order of magnitude higher than signals. Control of details of jet reconstruction √s (TeV) and calibration is essential. V. Cavasinni University of Pisa and INFN Part 1 – jet formation and reconstruction V. Cavasinni University of Pisa and INFN How a jet is generated V. Cavasinni University of Pisa and INFN How a jet is generated Probability to emit gluon Integral is over energy of Gluon and angle of gluon Integral diverges if E or theta are small… QCD has to be renormalised. V. Cavasinni University of Pisa and INFN In QCD quarks and gluons can radiate (αS) Probability to αS emit a gluon gluon αS Integral is over energy of Gluon and angle of gluon Integral diverges if E or theta are small… QCD has to be renormalised. V. Cavasinni University of Pisa and INFN Jet generaon Probability to emit a gluon V. Cavasinni University of Pisa and INFN Jet generaon Gluon can turn into a quark-antiquark pair V. Cavasinni University of Pisa and INFN Jet generaon V. Cavasinni University of Pisa and INFN Jet generaon and reconstrucBon Detector V. Cavasinni University of Pisa and INFN Jet generaon and recontsrucBon Detector Parton jets Truth jets Reconstructed jets V. Cavasinni University of Pisa and INFN Jet idenBficaon Transverse view oF a collision e+e- ->hadrons (jets) the cleanest situaon How many jets in this event: It is clear they are 2! V. Cavasinni University of Pisa and INFN Jet idenBficaon Vista Transverse view oF a collision trasversale di una collisionee+e- -> hadrons (jets) the e+ e- cleanest situaon: only jets in final state How many jets in this event: It is clear they are 2! V. Cavasinni University of Pisa and INFN Jet idenBficaon How many jets in this event: And in this one? It is clear they are 2! V. Cavasinni University of Pisa and INFN Jet idenBficaon How many jets in this event: And in this one? It is clear they are 2! V. Cavasinni University of Pisa and INFN Jet idenBficaon How many jets in this event: And in this one? It is clear they are 2! V. Cavasinni University of Pisa and INFN It is necessay to implement a “jet algorithm” to identify jets in the event and consequently to measure their 4-momenta V. Cavasinni University of Pisa and INFN Jet Algorithms Jet algorithm: a set of rules that define how to ”cluster” jets from a collection of input signals from calorimeters and tracking O(1k) calorimetric signals (clusters, cells) à reconstructed jets O(100) hadrons produced from fragmentation à truth jets O(10) à parton jets The different jet types give different views oF the same event and allow to compare measurements (reconstructed jets) to predicBons (truth jets, parton jets) à comparison between predicBons and measurements. V. Cavasinni University of Pisa and INFN Jet algorithm • The physics results (new particle discoveries, coupling measurements, PDFs…)should not depend on the particular jet algorithm used • Testing a measurement with different jet algorithms, or with different values of parameter for a jet algorithms is a very important test that allows to verify that the measurement is robust with respect to QCD radiations, hadronizations … • Exception: the sensitivity of a measurement may depend on the “resolution” with which the event is investigated … A dependence that we should avoid …. à V. Cavasinni University of Pisa and INFN Jet algorithms • Two cathegories: • Cone: a cone is build with Lorentz invariant quantities: RC and particles are collected within this cone: Rc 2 2 p p RC ≈ Δφ + Δη Rc • Sequential: start from single elements: track or, calorimetric cluster and try to recontruct back the branching effects due to the QCD showering and recombining the various elements with a “distance” algorithm between them. V. Cavasinni University oF Pisa and INFN The kt algorithm family • A family of sequential algorithms characterized by a specific “distance” definition used to join two tracks or calorimeter cluster The general definition is`: ΔR2 d = min(k 2α ,k 2α )⋅ ij ti tij R2 2α kti = tranverse momentum of the element i diB = kti ktij = relative transverse momentum between elements i,j α = 1 à Inclusive kt algorithm α = 0 à only angular distances – Cambridge-Achen algorithm € α = -1 à Antikt algorithm V.
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