Finding heavy particles in single jets

Transcription

1 Finding heavy particles in single jets Christopher Vermilion with teve Ellis and Jon Walsh University of Washington eptember 16, 009 arxiv: , 0909.OON tinyurl.com/jetpruning 1 / 37

2 Why jet substructure? More energy heavy (but not too heavy) particles will have large boost. Tevatron: W is jets, top is 3 jets LHC: both will often be single jets, especially as decay products of heavy new particles Hadronic decays will be messier than leptonic, but maybe if we re clever enough they can still be useful. Examples: V (H b b) at large boost, X t t for heavy X, etc. / 37

3 ecombinative jet algorithms 0. Form a list L of all protojets to be merged. 1. Calculate the distance between all pairs of protojets in L using the metric ρ ij, and the beam distance for each protojet in L using ρ i.. Find the smallest overall distance in the set {ρ i, ρ ij }. 3. If this smallest distance is a ρ ij, merge protojets i and j. eplace the pair of protojets in L with this new merged protojet. If the smallest distance is a ρ i, promote protojet i to a jet and remove it from L. 4. Iterate this process until L is empty. k T : ρ ij min(p Ti, p Tj ) ij /D, ρ i p Ti ; CA : ρ ij ij /D, ρ i 1. 3 / 37

4 Looking for heavy particles in jets Look under the streetlight: jet masses (and subjet masses!) Two problems: Jets, even containing heavy particles, have broad mass distributions. Multi-step decay is not necessarily obvious in substructure. This can be ameliorated (somewhat)! space a 1 max(m dau1, m dau )/m J 4 / 37

5 Kinematics in QCD parton level Part I: m J Fix jet p T, take splitting to be proportional to just the soft/collinear singularity (leading log): dz d 1 dσ n+1 dσ n z 1 1 dσ LL dσ LL σ d(m J /p ) 1 σ dx T J J Z 0.5 Z D dz d 1 δ(x J z(1 z) z ) 1 ln 1 p 1 4x J /D = Θ hd i /4 x J x J Leading log: arb. units dσll xj dxj NLO (EK): dσnlo 1 dxj 0.3 J PT J 500 GeV c PT J 1500 GeV c z min(p T1, p T )/p TJ NB: We are ignoring subjet masses! J xj Σ 5 / 37

6 Kinematics in QCD parton level Part II: z and 1 Undo integrals to get distribution in z or 1, for fixed m J : 1 dσ LL σ dx J dz 1 1 Θ6 zx 4 z J 1 dσ LL σ dx J d 1 1 h Θ r 1 4x J D q 1 4x J 3» Θ z i 1 4x J Θ[D 1 ] q «1 1 4x J / 1 arb. units arb. units z: xj 0.19 xj 0.15 xj 67 xj 4 1 : xj / 37

7 Kinematics in heavy particle decays parton level tart with decay to two massless partons tarting with an unpolarized, hence isotropic, decay in the rest frame, can find distributions in z, 1 numerically. Can also work out analytically in the limit γ 1: dn0 d z z: Γ Γ 3 Γ 4 Γ : dn 0 dz dn 0 d 1 «1 Θ z Θ(z) 1 γ 1 4 γ 1 Θ q 1 4γ dn0 d Γ.5 Γ 3 Γ 4 Γ / 37

8 Kinematics in heavy particle decays parton level Now require reconstruction in a jet! z, all decays: Γ Γ 3 Γ 4 Γ 5 z, requiring 1 < D = : dn0 d z dn d z 0.5 Γ.5 Γ 3 Γ 4 Γ (imagine cutoff at D = ): 15 Γ.5 Γ 3 Γ 4 Γ 5 dn0 d / 37

9 Algorithm effects z: CA kt z 1, CA: 3 1 CA kt 1 : 0 1 z 1, k T : z and 1 for QCD jets, for jets with p T between 500 and 700 GeV with D =. 9 / 37

10 Algorithm effects, cont m J cut: 5x CA, parton 5x KT, jet 5x KT, parton m J and m ubj cuts: m J cut: 0 1 m J and m ubj cuts: z and 1 for top quark decays at the parton-level and from Monte Carlo events. The parton-level curve is integrated over the observed γ t distribution. D= 10 / 37

11 Event effects : Masses QCD jets, CA top jets, CA QCD jets, k T top jets, k T space m J with and without underlying event, for QCD and top jets, using CA and k T jets. Jets have p T between 500 and 700 GeV, and D =. 11 / 37

12 Event effects : z and z for QCD jets CA, UE CA, no UE 10x KT, UE 10x KT, no UE z for top jets for QCD jets for top jets 0 Θ space z and with and without underlying event, for QCD and top jets. Jets have p T between 500 and 700 GeV, and D =. 1 / 37

13 A way out Problem: We would like to use m J (and possibly m ubj ) and z to distinguish heavy particle jets from QCD background, BUT For CA, metric strongly shapes z distribution for QCD and decays, pushing it toward zero. The present of UE contributions (and pile-up!) tends to add small-z, large particles to the jet, also broadening the mass peak for decays. k T doesn t bias substructure as much, but has poorer mass resolution. olution: ystematically remove soft, large-angle mergings from found jets. We call this pruning. 13 / 37

14 Pruning defined Find jets with your favorite jet algorithm. For each jet, run another jet algorithm on its constituents. This can be the same algorithm, but it doesn t have to be! The second algorithm must be a recombination algorithm with sensible substructure. At each recombination step in the second algorithm, test the condition: min ( ) p Ti, p Tj /pti+j < z cut AND 1 > D cut If this condition is true, discard the lower pt (softer) branch it is not included in the final jet. esulting jet is the pruned jet. Choices to make: Jet finding algorithm (including D/) Jet pruning algorithm Parameters z cut and D cut Punchline: You don t have to think about these very hard! 14 / 37

15 ome effects of pruning: masses (CA) unpruned QCD jets unpruned top jets pruned QCD jets CA, UE CA, no UE pruned top jets space m J with and without underlying event, for QCD and top jets. Jets have p T between 500 and 700 GeV, and D =. 15 / 37

16 ome effects of pruning: masses (k T ) unpruned QCD jets unpruned top jets pruned QCD jets KT, UE KT, no UE pruned top jets space m J with and without underlying event, for QCD and top jets. Jets have p T between 500 and 700 GeV, and D =. 16 / 37

17 ome effects of pruning: z and unpruned QCD jets CA, UE CA, no UE 10x KT, UE 10x KT, no UE pruned QCD jets CA, UE CA, no UE KT, UE KT, no UE unpruned top jets 0 Θ pruned top jets 0 Θ space z and with and without underlying event, for QCD and top jets. Jets have p T between 500 and 700 GeV, and D =. 17 / 37

18 Two related subjet methods Mass-Drop and Filtering (Higgs) (arxiv: ; Butterworth, Davison, ubin, alam) 1. tarting with found jet, traverse merging history along heavier branch, looking for mass drop and a splitting that is not too asymmetric: m daughter /m branch < µ cut (= 7), y min(p T i,p T j) m ij > y cut(= 9). branch This branching must have two b-tags.. Uncluster below this branching down to = cut (= min(0.3, b b/)). 3. Take 3 hardest subjets capturing hardest radiation, but filtering soft UE. 18 / 37

19 Two related subjet methods Top Tagging (arxiv: ; Kaplan, ehermann, chwartz, Tweedie) 1. tarting with found jet, traverse merging history along harder branch, looking for splitting with z i p i T /pjet T > z cut, > cut. This is the top-level splitting. Throw out branches with z i < z cut and continue. If both z i fail, this is an irreducible branching. If < cut, stop. This is an irreducible splitting.. epeat on the two daughters of the found branch. 3. esult is 1-4 subjets. equire 3 or Additional cuts can be made on the subjet kinematics / 37

20 W W, t t studies W W ignal: semileptonic W + W Background: (W lν)+1, partons (g, u, d, s, c) matched t t ignal: full hadronic t t Background:,3,4 parton multijet (g, u, d, s, c) matched Generated with MadGraph interfaced with Pythia. MLM matching DWT tune 0 / 37

21 W, top finding jets per bin histogram fit W width GeV pca CA pkt kt A sample mass fit for CA jets from t t events p T bin GeV W window widths vs. p T bin in the W W sample, using D =. 1 / 37

22 tatistical measures w rel : relative jet mass window ɛ = N (pa) N (A) = N (pa)/n B (pa) N (A)/N B (A) = N (pa)/ N B (pa) N (A)/ N B (A) A is the plain algorithm, pa is the pruned version / 37

23 esults, fixed D W s, CA jets tops, CA jets W s, k T jets tops, k T jets T space T T pt GeV elative statistical measures w rel, ɛ,, and vs. p T for W s and tops, using CA and k T jets with D =. 3 / 37

24 esults, fitted D W s, CA jets T space tops, CA jets T W s, k T jets T tops, k T jets pt GeV elative statistical measures w rel, ɛ,, and vs. p T for W s and tops, using CA and k T jets with D chosen for each bin. 4 / 37

25 Further questions How to apply pruning to theory predictions? Algorithm choices? Where can pruning be useful? Expand on this understanding of jet substructure can we be smarter than just looking for mass bumps? Good, easy software to explore this with? 5 / 37

26 Conclusions Pruning jets can improved the effectiveness of heavy particle searches. The optimal input parameters do not depend strongly on the sample. Pruning makes large D jets more robust to contributions from UE, PU, etc. 6 / 37

27 Bonus slides 7 / 37

28 W (H b b) ignal: (W lν)(h b b) BG: (W lν)b b(j) matched Look for single jets, D =, 300 GeV < p T < 400 GeV (no cuts on lepton side) tatistics: CA: w rel = 0.57 w rel = 9 k T ɛ = 0.76 ɛ = 0.77 = 1.75 =.35 = 1.16 = / 37

29 W (H b b), masses jet mass mjet Entries Mean M jet mass, pruned 1400 PUNEDmjet EGmjet Entries Mean Overflow / 37

30 Absolute metrics abs pca CA pkt kt ɛ abs, W s abs pca CA pkt kt ɛ abs, tops pt bin GeV T fake pca CA pkt kt ɛ fake, W s fake pca CA pkt kt 5 ɛ fake, tops T pt bin GeV ɛ abs ɛ fake # of top jets in the signal sample # of parton-level tops in the p T range # of top jets in the background sample # of unpruned jets in the p T range 30 / 37

31 Varying D cut W s, CA jets tops, CA jets W s, k T jets tops, k T jets wrel top sample W sample cut T cut T Dcut m pt Dcut m pt pt ranges in GeV 31 / 37

32 Varying z cut W s, CA jets tops, CA jets W s, k T jets tops, k T jets wrel top sample W sample pt ranges in GeV cut cut zcut zcut 3 / 37

33 Pruning vs. other methods 500 jet mass Top-tagging Pruned Higgs Normal CA Note: Only subjet methods are included (no b-tags, no kinematic cuts) 33 / 37

34 Pruning vs. other methods 34 / 37

35 Comparing CA and k T W s, CA vs. k T tops, CA vs. k T W s, pca vs. pk T tops, pca vs. pk T wpa A A pa pa A A pa pa A T space A T pa T pa pt GeV elative statistical measures comparing CA to k T jets and pruned CA to pruned k T jets vs. p T for W s and tops, using D =. 35 / 37

36 mearing 1500 CA unsmeared smeared CA unpruned pruned jets per bin jets per bin k T unsmeared smeared 1000 k T unpruned pruned jets per bin jets per bin space t t events with Gaussian energy smearing. The jets have p T of GeV and D =. σ(e) = p a E + b + c E a = 5, b = 0.5, c = 3, (from ATLA detector paper) 36 / 37

37 mearing W s, CA jets tops, CA jets W s, k T jets tops, k T jets T space T elative statistical measures w rel, ɛ,, and vs. p T T pt GeV 37 / 37