Spectral Analysis of Jet Substructure with Neural Network: Boosted Higgs Case

Transcription

1 Spectral Analysis of Jet Sustructure with Neural Network: Boosted iggs Case Sung ak Lim Supplementary materials for BOOST 28, Paris, France Jul. 28 ased on S.. Lim, M. M. Nojiri, arxiv: / 26

2 parton parton shower hadronized particles We have to differentiate these non-qcd jets from QCD jets to maximize sensitivity of channels involving oosted particles. We use sustructure oservales on this purpose. 2 / 26 Jets and Boosted Particles A jet is a collimated cluster of particles. It is often produced from a colored parton. q parton parton shower hadronized particles As LC stacking up multi TeV center-of-mass energy events, oosted heavy particles can e produced and form a single collimated cluster of particles similar to the QCD jet. (m EW / ŝ = O(.)) jet h jet

3 Conventional oservales of jet sustructures There are lots of oservales of jet sustructures, which are focussing on a particular sustructure. A few examples are: mass of the mother particle: m jet, trimmed m jet, h vs Z/W n-prong jet: n-sujettiness ratio, D 2, j vs h/z/w vs t sujet p T asymmetry: mass drop tagger, h vs j color charge: jet girth (a kind of width), q vs g color sustructures: jet pull etween sujets, vs h g Q: is there any generic framework that unifies these variales? I want to introduce an analogy from Organic Chemistry. 3 / 26

4 4 / 26 Organic Molecules Organic molecules are complex molecules contains caron, hydrogen, and other atoms. C C C C C O C C C C C O Ethanol Benzene Acetic Acid O ow chemists identified these complex sustructures? Proton Nuclear Magnetic Resonance ( -NMR) Spectroscopy

5 Analogy of Jet Sustructures and Organic Molecules -NMR is a successful example of spectral analysis of molecular sustructures. C 2 C O 3 C C O chemical shift The perturative description of jets is analogous to organic molecules. Spectral analysis -NMR spectroscopy?? Primary geometry Caron skeleton partons from the decay Oservales ydrogen hadronized particles Can we uild a similar analysis framework of jet sustructures? sujet p T asymmetry self corr. R empty region eyond R h: color singlet h R jet large R FSR 2R jet We will introduce a spectral analysis of jet sustructure. 5 / 26

6 A spectral function of jet sustructure We define a inned spectral function of transverse momenta of all particle pairs i and j, p T,i and p T,j, and their angular distance R ij = ηij 2 + φ2 ij, S 2(R; R) = R i,j jet R ij [R,R+ R) This spectral function oserves two-point correlations in a jet. p T,i p T,j, () S 2(R) sujet autocorrelation h R sujet cross-correlation R ( ) S 2(R) = pt 2, + p 2 T, δ(r) + 2p T, p T, δ(r R ). ence, this spectral function contains non-local correlation in jets. The correlations can e used for detailed jet sustructure studies. 6 / 26

7 7 / 26 Physical Interpretation of S 2 (R) dr S 2(R) = ( ) 2 p T,i pt 2,jet, (2) i jet dr R 2 S 2(R) = i,j jet p T,i p T,j R 2 ij 2m 2 jet. (3)

8 8 / 26 IRC safety of S 2 (R) The S 2(R) spectrum is etter to e infrared and collinear (IRC) safe, namely invariant under soft and collinear radiations. Soft radiation: the parton radiates a p T = parton. p p T T p T = Collinear radiation: the parton splits in same direction R. zp p T T ( z)p T Otherwise, the virtual and real corrections in higher order perturation theory do not sum up, and such a IRC unsafe oservales are hard to e estimated from perturative QCD calculations. (KNL theorem) + + = finite (4) S 2(R) is IRC safe ecause soft or collinear radiation does not introduce any new angular scale R.

9 IRC safety of S 2 (R) The S 2(R) spectrum is IRC safe. S 2(R; R) = R i,j jet R ij [R,R+ R) p T,i p T,j, (5) Soft radiation is ignored safely ecause p T,i p T,j = if i or j is a soft radiation. S 2 (R) h R R Collinear radation is okay ecause R does not change and the radiation products always sum up. S 2 (R) h R R Now, let s check how S 2(R) ehaves with more realistic events at the detector level. 9 / 26

10 / 26 A typical iggs jet h sujet p T : symmetric R R jet empty region eyond R h: color singlet 2R jet - φ jet φ p T,jet m jet m jet,tr = 35 GeV = 2 GeV = 7 GeV g S 2(R) = η - η jet ( pt 2, + p 2 T, [ar. unit] Σ i pixel p T,i normalized S 2 (R;.) D 2 D 2,tr =.24 =.7 p h (Y D 2 ) = 99.2% p h (Y D 2 +tr) = 99.6% p h (Y S2 ) = 99.9% p h (Y S2 +tr) = 99.8% R ) δ(r) + 2p T, p T, δ(r R ).

11 / 26 A typical QCD jet and jet trimming q hard: m jet hard soft q g soft R jet 2R jet - φ jet φ p T,jet m jet m jet,tr q = 348 GeV = GeV = 53 GeV g η - η jet [ar. unit] Σ i pixel p T,i normalized S 2 (R;.) D 2 = 3.2 D 2,tr = 2.45 p h (Y D 2 ) =.6% p h (Y D 2 +tr) =.4% p h (Y S2 ) =.4% p h (Y S2 +tr) =.2% R normalized S 2,tr(R;.) R Jet trimming removes soft sujets in the jet. Jet trimming helps differentiating hard and soft jet sustructures.

12 2 / 26 Differntiating iggs jets and QCD jets h q sujet p T : symmetric R R jet hard: m jet hard soft empty region eyond R h: color singlet 2R jet q g soft R jet 2R jet S 2(R) contains various information on jet sustructures. But how can we quantify it for classification? Deep Learning

13 Artificial Neural Network p T,jet Input idden idden 2 idden n Output m jet S 2(R) ias nodes Activation: ReLU ReLU ReLU softmax The artificial neural network is a mathematical model of functions motivated from a iological neural network. To make a long story short, the neural network is a function maps inputs to outputs having lots of internal parameters needed to e optimized. ANN({x i }) = f (n) (W (n) f (2) (W (2) jk f () (W () ij x i + () j ) + (2) k ) + (n) ) The network setup for jet sustructure analysis depends on how you interpret jets. 3 / 26

14 Jet as an Image We may interpret the calorimeter energy deposit as an image, and apply image recongition techniques. - φ jet φ p T,jet m jet m jet,tr = 35 GeV = 2 GeV = 7 GeV [ar. unit] p T,i Convolutional neural network g η - η jet Σ i pixel This ANN mimicks human eye and can e used for image recongnition. It focuses on local spatial correlations References: , / 26

15 Jet as a sequential data The parton shower description of jets can e nterpreted as a sequential data. q parton parton shower We may recluster the jet to get a parton shower history and feed this to ANN. Recurrent Nerual Network jet The ANN understand data in sequence and find out correlations y reading data sequentially. Focussing on local temporal correlations References: , / 26

16 6 / 26 Our ANN setup p T,jet Input idden idden 2 idden n Output m jet S 2(R) ias nodes Activation: ReLU ReLU ReLU softmax We used a simple shallow fully-connected neural network. Inputs for S 2(R) analysis N S2 : {x i } S2 = {p T,jet, m jet, S 2 (;.),, S 2 (.9;.)} N S2 +tr : {x i } S2 +tr = {x i } S2 {p T,jet,tr, m jet,tr, S 2,tr (;.),, S 2,tr (.9;.)}

17 Comparison to another variale For comparison, we prepare an ANN anlysis with D 2 variale ( ) e β 2 = e β 3 = D β 2 = p 2 T,jet p 3 T,jet i,j jet i<j i,j,k jet i<j<k p T,i p T,j R β ij, (6) p T,i p T,j p T,k R β ij Rβ jk Rβ ki, (7) e β 3 (e β 2 )3 ( ) 3, (8) For iggs jets, D 2 is small ecause three-point energy correlation have to count soft or collinear radiation. h D β 2 ( ) 3 Inputs for ANN with D 2 N D2 : {x i } D2 = {p T,jet, m jet, D β=2 2 } N D2 +tr : {x i } D2 +tr = {x i } D2 {p T,jet,tr, m jet,tr, D β=2 2,tr } 7 / 26

18 Performance check of ANN with D 2 We first check that the performance of N D2 +tr with The distriutions of iggs jets and QCD jets in the iggs-like proaility p h (Y D2 +tr ) and inputs in {x i } D2 +tr. D 2 5 iggs jets QCD jets fraction of events [%] trimmed D 2 5 iggs jets QCD jets fraction of events [%] m jet p h (Y D 2,tr ) p h (Y D 2,tr ) iggs jets QCD jets p h (Y D 2,tr ) p h (Y D 2,tr ) fraction of events [%] trimmed m jet p h (Y D 2,tr ) p h (Y D 2,tr ) iggs jets QCD jets p h (Y D 2,tr ) p h (Y D 2,tr ) fraction of events [%] N D2 +tr has a tendency to classify jets with small D 2 and m jet 25 GeV as a iggs jet. This ehavior is similar to the conventional cut-ased analysis. Now it looks working well, so let us compare it with N S2 +tr. 8 / 26

19 9 / 26 ROC curve Event preselection: m jet [, 5] GeV. p T,jet [3, 4] GeV. Then R.6 and anti-k T algorithm with R j = finds the collimated cluster well. For iggs jets, at least one parton should e found in the jet. At the iggs tagging efficiency.4 (.2), QCD jet mistag rate of N S2 +tr is reduced y 2.6% (26.7%) compared to that of N D2 +tr. Why S 2(R) is doing etter than D 2?

20 2 / 26 S 2 (R) and D 2 S 2(R) includes D 2 partially. Let s consider a three-prong jet. S 2(R) R R 2 R 3 Two-point correlation function. dr R β S 2 (R) = 2pT 2,jet eβ 2 (9) Three-point correlation function. e β 3 p T,jet ( R) 3 S 2 (R ; R)S 2 (R 2 ; R)S 2 (R 3 ; R)R β Rβ 2 Rβ 3 () Therefore, we may uild D 2 from S 2(R) if it is required. ow the classifier N S2 +tr is correlated to N D2 +tr and why N S2 +tr is doing etter jo? R

21 2 / 26 Correlation etween taggers ) p h (Y D2,tr iggs jets 48.7% 5.3% QCD jets 56.9% 43.% fraction of events [%] p h (Y S2,tr) ) p h (Y S2,tr For iggs jets, the lower triangular region contains more events compared with the upper triangular region, 5.3% of the total events. For QCD jets, the lower triangular region contains less events, 43.%. ence, N S2 +tr improves signal and ackground ratio S/B from N D2 +tr. Let s check what kinds of jets are located in the off-diagonal region.

22 22 / 26 A jet tagged in S 2 analysis only sujet p T : symmetric h R R jet mild contaminations 2R jet - φ jet φ p T,jet m jet m jet,tr = 347 GeV = 44 GeV = 5 GeV g η - η jet [ar. unit] Σ i pixel p T,i normalized S 2 (R;.) D 2 =.42 D 2,tr =.25 p h (Y D 2 ) = 8.7% p h (Y D 2 +tr) = 9.6% p h (Y S2 ) = 74.4% p h (Y S2 +tr) = 8.7% R normalized S 2,tr(R;.) R This jet looks like a iggs jet ut why N D2 +tr classify it as a QCD jet?

23 23 / 26 A jet tagged in S 2 analysis only D iggs jets QCD jets fraction of events [%] trimmed D 2 trimmed D 2 Event selection: p h (Y D2,tr ) < 3% and p h (Y S2,tr ) > 7%. ANN tries to utilize every information in the inputs. As a result, large D 2 and small trimmed D 2 are signs of large angle soft activity which is a QCD jet s feature compared to a iggs jet. ence N D2 +tr classifies these jets as a QCD jets.

24 p T asymmetric sujets are often occur in QCD jets. Even though this jet is two-prong, it s etter to avoid this jet to enhance S/B ratio as mass drop tagger does. 24 / 26 A jet tagged in D 2 analysis only q sujet p T : asymmetric q g R jet 2R jet - φ jet φ p T,jet m jet m jet,tr q = 364 GeV = 2 GeV = 6 GeV g S 2(R) = η - η jet [ar. unit] Σ i pixel p T,i normalized S 2 (R;.) ( p 2 T, + p 2 T, D 2 =.69 D 2,tr =.5 p h (Y D 2 ) = 76.7% p h (Y D 2 +tr) = 85.2% p h (Y S2 ) = 24.2% p h (Y S2 +tr) = 33.3% R normalized S 2,tr(R;.) R ) δ(r) + 2p T, p T, δ(r R ).

25 A jet tagged in S 2 analysis with trimming only sujet p T : symmetric R moderate contaminations large R FSR h R jet 2R jet - φ jet φ p T,jet m jet m jet,tr = 329 GeV = 47 GeV = 3 GeV g η - η jet [ar. unit] Σ i pixel p T,i normalized S 2 (R;.) D 2 = 2.28 D 2,tr = 2.38 p h (Y D 2 ) = 7.7% p h (Y D 2 +tr) = 7.% p h (Y S2 ) = 8.6% p h (Y S2 +tr) = 82.2% R normalized S 2,tr(R;.) R This jet has two-prong sustructure, ut the sujets are wide and contaminated y other QCD activities. Jet trimming helps differentiating hard and soft sustructure, and N S2 +tr classify this jet as a iggs jet. 25 / 26

26 26 / 26 Conclusion N S2 and N S2 +tr learned non-local correlations in jets from the spectrum. N S2 discriminates etween oosted iggs jets and QCD jets with etter performance compared to N D2. Introducing trimming to S 2(R) helps separating hard and soft sustructures, and the ANN with trimmed oservale outperforms the ANN without trimming. The S 2(R) has information on multi-point correlations and is easily applicale to other jet sustructures.