Matrix Element Method and its Application for ILC Physics Analysis - PowerPoint PPT Presentation

Matrix Element Method and its Application for ILC Physics Analysis Junping Tian, Keisuke Fujii (KEK) Dec. 16-18 @ Tokusui Workshop 2014, KEK, Tsukuba

what is Matrix Element Method reconstructing the likelihood of each event is alway one central task in any physics analysis: (i) best classifier to separate signal from background, L S /L B (Neyman-Pearson lemma); (ii) maximize likelihood to exact some parameters such as coupling, mass, etc. usual approach: (i) multivariate method such MLP, BDT — though very robust, due to correlation, non-linearity, hard to approach true likelihood; (ii) projected 1D or 2D likelihood, i.e. recoil mass fitting or template fitting in hadronic BRs — lose other information. in fact, true likelihood of a event from one scattering process is given by its differential cross section —> Matrix Element Method = approach the true likelihood of every event L 2

Application of MEM used in discovery of top quark (precision top mass measurement) at Tevatron (D0, Phys. Rev. D 87,055006) used in discovery of Higgs (H—>ZZ*—>4l) at LHC, as well as in Higgs J CP measurement (CMS, Phys. Rev. D 89, 092007; A. Caudron @ LCWS14) though not a new method, generally not widely used comparing to other multivariate method; at LHC often only Higgs decay part of matrix element is used, due to not precisely known initial state (need integrate pdf for production part) best application would be at lepton collider + imaging detector = well defined initial state + precisely measured final states even though, it’s not that simple: ISR + Beam-strahlung; detector transfer function; missing neutrino and particle spin not directly measured d 3 p j d 3 p k i | a ) = 1 Z Z Y Y L ( p vis W i ( p vis i | p k , a )] | M ( p j , p k ; a ) | 2 [ ][ (2 π ) 3 2 E j (2 π ) 3 2 E k σ a j ∈ inv . k ∈ vis . 3

status of developing MEM for ILC Physics Analysis just started in this year; first goal was to develop the tool to calculate matrix element for various e+e- processes in full simulation analysis a working version has been released and available in latest ilcsoft- v01-17-06: Physsim-v00-01 including HELLib, c++ version of HELAS (KEK-91-11), and LCME, matrix element calculation for specific processes have been implemented: ZH, νν H and eeH (VBF), ZHH, νν HH (VBF); ZZ, WW, eeZ (VBF), ZZZ and ZZH following talk —> basic verification; look into MEM performance in analyses of eeH (via ZZ-fusion), recoil mass and Higgs self-coupling svn co https://svnsrv.desy.de/basic/physsim/Physsim/trunk 4

method to verify calculated matrix element idea: re-weight each event by 1/|ME| 2 , all distribution should become uniform test sample: ZHH @ 500 GeV, generated without ISR and BS 1 original events weighted by | ME | 2 15 10 × 900 22 800 20 18 700 16 600 14 500 12 400 10 8 300 6 200 4 100 2 0 0 3 3 2 2 1 1 0 100 0 100 φ φ (Z) 95 (Z) 95 -1 -1 90 90 f -2 f -2 M(Z) / GeV M(Z) / GeV 85 85 -3 -3 φ F : azimuthal angle defined in Z rest frame of fermion from Z—>ff 5

application (I): e+e- —> e+e-H e + e + simplest application, same final Z states, generator level H Z testing principle: whether MEM can e − e − be better than other MVA or not? H e + carefully tuned MVA (input Z e + variables cover complete information) versus just ratio of ME e − Z e - ratio of ME signal efficiency .vs. background rejection 1 Backgr rejection (1-eff) - + e e H (ZZ-fusion) 0.08 0.98 - + e e H (ZH) Normalized 0.06 MEM 0.96 MLP 0.04 0.94 BDT Likelihood 0.02 0.92 0 0.9 -20 -10 0 10 0.95 0.96 0.97 0.98 0.99 1 ln(L /L ) Signal eff 1 0 6

application (II): recoil mass analysis e + H X Z μ + e − Z X μ − based on fully simulated and reconstructed samples momentum of Higgs are reconstructed by recoil technique don’t look at Higgs decay —> sum of matrix element for all decay modes —> equivalently multiply M( μμ H) with Higgs propagator, similarly for μμΖ for purpose, first tried without ISR and BS 1 M = M( µ + µ − H ) p 2 H − m 2 H + im H Γ H 7

matrix element: reconstructed .vs. truth (w/o ISR and beam strahlung) M = M( µ + µ − H ) Entries 0.06 ME (truth) 500 ME (reconstructed) Normalized 400 0.04 300 200 0.02 100 0 0 -0.4 -0.2 0 0.2 0.4 -18 -16 -14 -12 -10 -8 (ME_rec-ME_truth)/ME_truth ln(L) ME can be reconstructed with a resolution ~5% 8

matrix element: signal .vs. background (ZZ) (normalized to expected number of events w/ 250 fb -1 ) 1 1 M = M( µ + µ − H ) M = M( µ + µ − Z ) p 2 H − m 2 p 2 Z − m 2 H + im H Γ H Z + im Z Γ Z w/o ISR and BS 120 - + H (ZH) µ µ 100 - + Z (ZZ) µ µ 80 Entries 60 40 20 0 -5 0 5 10 ln(L /L ) 1 0 without any other selection except recoil mass > 110 GeV, already very well separated 9

including everything: ISR + beam spectrum normalized to 1 normalized to <E> @ 250 fb-1 120 + - + - H (w/o ISR and BS) H (w/o ISR and BS) µ µ µ µ + - + - H (w/ ISR and BS) H (w/ ISR and BS) µ µ µ µ - 100 - + + Z (w/o ISR and BS) Z (w/o ISR and BS) µ µ µ µ 0.3 ZZ_sl (w/ ISR and BS) ZZ_sl (w/ ISR and BS) Normalized 80 Entries 0.2 60 40 0.1 20 0 0 60 80 100 120 140 160 -5 0 5 10 ln(L /L ) Recoil Mass / GeV 1 0 ISR + BS significantly degraded the separation power against ZZ any chance to recover ISR and BS? 10

proposal to recover ISR ISR enters detector: identification (see T. Tomita’s study, eff ~ 90%) what if ISR goes to beam pipe? (dominant) 4 unknown: 3 P H + 1 P γ 4C —> we can resolve it! | P z ( γ ) | = | P ( γ ) | P x ( H ) = √ s sin θ P y ( H ) = − P y ( Z ); 2 − P x P z ( H ) = − ( P z ( Z ) + P z ( γ ) q P 2 z ( H ) + m 2 ( H ) + | P ( γ ) | = √ s E ( Z ) + t ( H ) + P 2 2 − 2 √ s ( E ( Z ) − P x ( Z ) sin θ P ( γ ) = s cos 2 θ 2 ) + m 2 ( H ) − m 2 ( Z ) 2[ P z ( Z ) ± ( √ s − E ( Z ))] n.b.: there are two possible solutions! and Higgs mass has to be known 11

resolved ISR versus truth (one of the two solutions are selected according to z-momentum of visible part ) (resolved) / GeV 40 20 0 ISR P -20 -40 -20 0 20 40 P (truth) / GeV ISR looks working well 12

matrix element after ISR recovery (signal μμ H) w/ ISR recovery 400 w/o ISR recovery 300 Entries 200 100 0 -0.4 -0.2 0 0.2 0.4 (L - L ) / L truth rec truth matrix element is significantly closer to truth (almost recover to the case with ISR and BS, as shown in previous slides ) 13

role of ISR in case of background ZZ 120 ) / GeV M(recoil) > 110 GeV 100 1 γ 80 E( 60 40 20 0 0 20 40 60 80 100 120 E( ) / GeV γ 2 ISR is the main reason to have recoil mass > 110 GeV analysis including ISR recover for both ZH and ZZ is ongoing 14

application (III): Higgs self-coupling H H H H e + e + e + e + H Z Z Z Z H H H H e − e − e − e − Z Z Z Z use ME to help jet pairing 0.08 ZHH use ME ratio of ZHH and ZZH to ZZH improve background suppression 0.06 Normalized use ME of different ZHH 0.04 diagrams to improve significance of Higgs self-coupling 0.02 in any case, a major challenge is 0 -60 -40 -20 0 20 to handle missing neutrinos in b- ln(L /L ) 1 0 jet (invariant mass of bb-bar is very asymmetric) ongoing… 15

summary and next step MEM = approach true likelihood of every event, maximal use of well defined initial states, precisely measured final states and precise theoretical calculation at ILC; has potential to be applied for all physics analysis ILC; now in its initial stage, tools are being developed and improved; calculated ME are verified by first look; better performance than other MVA are seen in idea case; several applications are looked into, representing various aspects of challenges to use MEM for real analyses. a new idea to resolve ISR is proposed and looks promising a main step next is to include detector transfer function 16

back up 17

what Physsim package provides hellib: C++ version of HELAS (by K. Fujii), subroutines to calculate generic parts of one Feynman diagram, i.e. wave function, vertex, propagator, amplitude, etc.); LCME: implementation of matrix element calculation for specific e+e- processes, i.e. e+e- —> ZH, νν H, ZZ, etc. example processors to calculate ME in marlin framework what Physsim does not provide radiative correction automatically generate all possible Feynman diagrams for given final states integrate ME with detector transfer function or unmeasured kinematics (yet-to-be supported) d 3 p j d 3 p k i | a ) = 1 Z Z Y Y L ( p vis W i ( p vis i | p k , a )] | M ( p j , p k ; a ) | 2 [ ][ (2 π ) 3 2 E j (2 π ) 3 2 E k σ a j ∈ inv . k ∈ vis . 18

update of package more processes implemented previous: ZH, νν H (VBF), eeH (VBF), ZHH, νν HH (VBF) new: ZZ, WW, eeZ, ZZZ, ZZH on the way: νν Z (VBF), ttH, WWH new features switch to allow Z not decay, i.e. for ZZ as background in recoil mass analysis switch to allow Higgs decay, i.e. add Breit-Wigner structure only or full ME be able to select Feynman diagrams, i.e. in ZHH case, four diagrams. switch to return differential cross (default) or amplitude squared only support for anomalous couplings (gHZZ, gHWW) 19