Jets (and photons) at the LHC. J. Huston LPC March 10, 2010

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1 Jets (and photons) at the LHC J. Huston LPC March 10, 2010

2 More references

3 Understanding cross sections at the LHC we have to understand QCD (at the LHC) PDF s, PDF luminosities and PDF uncertainties LO, NLO and NNLO calculations K-factors benchmark cross sections and pdf correlations underlying event and minimum bias events jet algorithms and jet reconstruction Sudakov form factors

4 The LHC will be a very jetty place You can actually estimate this from Sudakov form factors (see tomorrow)

5 Some definitions TeV4LHC The fundamental challenge to interpret experimentally observed final states is that pqcd is most easily applied to the short-distance degrees of freedom, i.e. to quarks and gluons, while the long-distance degrees of freedom seen in the detectors are color-singlet bound states The overall scattering process evolves from the incoming longdistance hadrons in the beams, to the short-distance scattering process, to the long-distance outgoing final states The separation of these steps is essential both conceptually and calculationally

6 Dynamic range

7 Inclusive jet production at the LHC Over very wide dynamic range; accesses highest p T values at LHC pdf uncertainty is sizeable at the highest transverse momenta, as at Tevatron At low p T, most jets are gluon-induced, as at the Tevatron

8 A word about jets Most of the interesting physics signatures at the Tevatron and LHC involve final states with jets of hadrons A jet is reconstructed from energy depositions in calorimeter cells and/or from charged particle track momenta, and ideally is corrected for detector response and resolution effects so that the resultant 4-vector corresponds to that of the sum of the original hadrons The jets can be further corrected, for hadronization effects, back to the parton(s) from which the jet originated,or the theory can be corrected to the hadron level The resultant measurements can be compared back to parton shower predictions, or to the short-distance partons described by fixed-order pertubative calculations

9 another word about jets We pick out from the incident beam particles, the short-distance partons that participate in the hard collision The partons selected can emit radiation prior to the short distance scattering leading to initial state radiation The remnants of the original hadrons, with one parton removed, will interact with each other, producing an underlying event Next comes the short-distance, large momentum transfer scattering process that may change the character of the scattering partons, and/or produce more partons the cross section for this step is calculated to fixed order in pqcd

10 still another word about jets Then comes another color radiation step, when many new gluons and quark pairs are added to the final state The final step in the evolution to the long distance states involves a nonperturbative hadronization process that organizes the colored degrees of freedom This non-perturbative hadronization step is accomplished in a modeldependent fashion

11 Jet algorithms at LO At (fixed) LO, 1 parton = 1 jet why not more than 1? I have to put a ΔR cut on the separation between two partons; otherwise, there s a collinear divergence. LO parton shower programs effectively put in such a cutoff log 1 ΔR 34 But at NLO, I have to deal with more than 1 parton in a jet, and so now I have to talk about how to cluster those partons i.e. jet algorithms

12 Jet algorithms at NLO At (fixed) LO, 1 parton = 1 jet why not more than 1? I have to put a ΔR cut on the separation between two partons; otherwise, there s a collinear divergence. LO parton shower programs effectively put in such a cutoff At NLO, there can be two partons in a jet, life becomes more interesting and we have to start talking about jet algorithms to define jets the addition of the real and virtual terms at NLO cancels the divergence NB: the difference between jet algorithms at LO and NLO will have important consequences for comparisons of matrix elements: see tomorrow A jet algorithm is based on some measure of localization of the expected collinear spray of particles Start with an inclusive list of particles/partons/calorimeter towers/topoclusters End with lists of same for each jet and a list of particles not in any jet; for example, remnants of the initial hadrons Two broad classes of jet algorithms cluster according to proximity in space: cone algorithms cluster according to proximity in momenta: k T algorithms

13 What do I want out of a jet algorithm? It should be fully specified, including defining in detail any pre-clustering, merging and splitting issues It should be simple to implement in an experimental analysis, and should be independent of the structure of the detector It should be boost-invariant It should be simple to implement in a theoretical calculation it should be defined at any order in perturbation theory it should yield a finite cross section at any order in perturbation theory it should yield a cross section that is relatively insensitive to hadronization effects It should be IR safe, i.e. adding a soft gluon should not change the results of the jet clustering It should be collinear safe, i.e. splitting one parton into two collinear partons should not change the results of the jet clustering

14 Jet algorithms The algorithm should behave in a similar manner (as much as possible) at the parton, particle and detector levels

15 (Legacy) cone algorithms The cone algorithm is most often used in hadron-hadron colliders perhaps most intuitive draw a cone of radius R in η-φ space But where to start the cone? use seeds (towers, particles, partons ) of energy ~1 GeV to save computing time R cone = streetlight approach ( Δη) 2 + Δφ ( ) 2 combine seed towers with other towers within a radius R of the seed tower re-calculate jet centroid using new list of towers inside cone lather, rinse, iterate until a stable solution is found typically use R~0.7 for inclusive measurements; R~0.4 for complex measurements, such as t-tbar But you may end up with overlapping jet cones (starting from different jet seeds) So need to come up with a provision for splitting/merging merge 2 jets if overlap energy is > f*p T (smaller jet) f= Note: partons (at NLO) don t know nothing about splitting/ merging experience says f=0.75 is best

16 Midpoint cone algorithm But this type of cone algorithm is not infra-red safe, since the two partons in the figure on the right will/will not be clustered into a single jet depending on whether or not a soft gluon is present at the midpoint also (in Run 1 at the Tevatron) used E T and η, rather than p T and y Fundamental difference between data and fixed order pert QCD data has seeds everywhere So the Midpoint algorithm was devised seeds were placed at the midpoints between nearby protojets used in Run 2 at the Tevatron this works for 2->3 final states (NLO inclusive), but not for 2->4 (NNLO inclusive) where I may cluster 3 partons in 1 jet

17 Seedless cone algorithm Put seeds everywhere Can be time-consuming Enter the SISCone algorithm Seedless Infrared Safe Cone jet algorithm G. Salam, G. Soyez, arxiv: uses a geometric approach to find all distinct cones with a speed similar to that of the Midpoint algorithm Still have the split/merge issue and the issue of dark towers Differences with the midpoint algorithm typically of the order of 1 percent or so in practice see later discussion, however

18 k T (recombination) algorithms Cluster particles nearby in momentum space first The k T algorithm is IR and collinear safe No overlapping of jets No biases from seed towers But the jets are sensitive to soft particles and the area can depend on pileup bad hair day

19 The k T family of jet algorithms p=1 p=0 p=-1 the regular k T jet algorithm Cambridge-Aachen algorithm anti-k T jet algorithm Cacciari, Salam, Soyez 08 also P-A Delsart 07 soft particles will first cluster with hard particles before clustering among themselves no split/merge leads mostly to constant area hard jets d ij = min p 2p 2p T,i, p T, j 2p d ii = p T,i ( ) ΔR ij #1 algorithm for ATLAS, CMS D 2 2

20 Cone and k T jet algorithms at NLO Let s set the p T of the second parton = z that of the first parton and let them be separated by a distance d (=ΔR) Then in regions I and II (on the left), the two partons will be within R cone of the jet centroid and so will be contained in the same jet ~10% of the jet cross section is in Region II; this will decrease as the jet p T increases (and α s decreases) at NLO the k T algorithm corresponds to Region I (for D=R); thus at parton level, the cone algorithm is always larger than the k T algorithm not necessarily true at the hadron level d z=p T2 /p T1

21 Jets at NLO continued Construct what is called a Snowmass potential The minima of the potential function indicates the positions of the stable cone solutions the derivative of the potential function is the force that shows the direction of flow of the iterated cone The midpoint solution contains both partons

22 Back to jet algorithms For some events, the jet structure is very clear and there s little ambiguity about the assignment of towers to the jet But for other events, there is ambiguity and the jet algorithm must make decisions that impact precision measurements If comparison is to hadronlevel Monte Carlo, then hope is that the Monte Carlo will reproduce all of the physics present in the data and influence of jet algorithms can be understood more difficulty when comparing to parton level calculations CDF Run II events

23 Jets don t consist of 1 fermi partons but have a spatial distribution Can approximate this as a Gaussian smearing of the spatial distribution of the parton energy the effective sigma ranges between around 0.1 and 0.3 depending on the parton type (quark or gluon) and on the parton p T Note that because of the effects of smearing that the midpoint solution is (almost always) lost thus region II is effectively truncated to the area shown on the right the solution corresponding to the lower energy parton can also be lost resulting in dark towers Jets in real life

24 Jets in real life In NLO theory, can mimic the impact of the truncation of Region II by including a parameter called R sep only merge two partons if they are within R sep *R cone of each other R sep ~1.3 ~4-5% effect on the theory cross section; effect is smaller with the use of p T rather than E T (see extra slides) really upsets the theorists (but there are also disadvantages) Dark tower effect is also on order of few (<5)% effect on the (experimental) cross section

25 Try this out in Monte Carlo Take W + 2 parton events, run SISCone 0.7 algorithm on parton level, hadron level (not shown) and topocluster level Plot the probability for the two sub-jets to merge as a function of the separation of the original two partons in ΔR Color code: red: high probability for merging blue: low probability for merging Parton level reconstruction agrees with naïve expectation Topocluster level reconstruction agrees with need for R sep

26 Comparison of k T and cone results Remember at NLO the k T algorithm corresponds to Region I (for D=R); thus at parton level, the cone algorithm is always larger than the k T algorithm Let s check this out with CDF results after applying hadronization corrections Nice confirmation of the perturbative picture

27 k T /midpoint ratios for all rapidities

28 SISCone vs Midpoint The SISCone jet algorithm developed by Salam et al is preferred from a theoretical basis, as there is less IR sensitivity from not requiring any seeds as the starting point of a jet less contribution from UE for SISCone algorithm SISCone corrections are smaller So far, at the Tevatron, we have not explicitly measured a jet cross section using the SISCone algorithm, although studies are underway, but we have done some Monte Carlo comparisons for the inclusive cros sections Differences of the order of a few percent at the hadron level reduce to <1% at the parton level

29 New k T algorithm k T algorithms are typically slow because speed goes as O(N 3 ), where N is the number of inputs (towers, particles, ) Cacciari and Salam (hep-ph/ ) have shown that complexity can be reduced and speed increased to O(N) by using information relating to geometric nearest neighbors should be useful for LHC already implemented in ATLAS and CMS Optimum is if analyses at LHC use both cone and k T algorithms for jet-finding universal benchmark need experience now from the Tevatron

30 Balancing act for jet precision There are fluctuations in radiation, hadronization and in UE subtraction Perturbative radiation quark Δp T α C s A p π T lnr gluon Δp T α C s F p π T lnr Hadronization quark gluon Δp T C F R Underlying event 0.4 GeV Δp T C A 0.4 GeV R Δp T R GeV re-evaluate in the presence of pileup

31 ATLAS jet reconstruction Using calibrated topoclusters, ATLAS has a chance to use jets in a dynamic manner not possible in any previous hadron-hadron calorimeter, i.e. to examine the impact of multiple jet algorithms/ parameters/jet substructure on every data set blobs of energy in the calorimeter correspond to 1/few particles (photons, electrons, hadrons); can be corrected back to hadron level rather than jet itself being corrected similar to running at hadron level in Monte Carlos

32 Jet areas determined by clustering ghost particles of vanishing energy; see jet references note that the k T algorithm has the largest jet areas, SISCone the smallest and anti-k T the most regular

33 Jet areas in presence of pileup pileup nibbles away at perimeter of jet

34 Area-based correction See presentations of Brian Martin in ATLAS jet meetings.

35 Photons at the LHC: isolation From a theoretical perspective, it s best to apply a Frixione-style isolation criterion, in which the amount of energy allowed depends on the distance from the photon; this has the advantage of removing the fragmentation contribution for photon production, as well as discriminating against backgrounds from jet fragmentation But most of the energy in an isolation cone is from underlying event/pileup At Les Houches, we developed: (1) an implementation of the Frixione isolation appropriate for segmented calorimeters (2) a hybrid technique that separates the UE/pileup energy from fragmentation contributions using the jet density approach

36 Jet masses Very useful if looking for resonance in boosted jet (top jet) Naturally produced by QCD radiation In NLO pert theory phase space from pdf s p J,µ p µ J = M 2 = f p J NLO s α s ( p J ) ( p J R) Rule-of-thumb M 2 NLO ~ 0.2p JR dimension jet size

37 Jet masses Sudakov suppression for low jet masses fall-off as 1/m 2 due to hard gluon emission algorithm suppression at high masses jet algorithms tend to split high mass jets in two

38 SpartyJet J. Huston, K. Geerlings, Brian Martin Michigan State University P-A. Delsart, Grenoble Sparty SpartyJet.html/ If interested for ATLAS, please contact

39 and now to Brian

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