JET SUBSTRUCTURES OF BOOSTED TOP QUARKS

Transcription

1 JET SUBSTRUCTURES OF BOOSTED TOP QUARKS 李湘楠 [Hsiang nan Li] 北殿義雄 [Yoshio Kitadono] arxiv: 中央研究院 [Academia Sinica] Talk at XS 2014 May 8, 2014

2 Outlines Introduction Boosted top, jet substructure Factorization top jet function, bottom jet function, hard kernel Results mass distribution, energy profile for R(L) handed top Summary

3 Introduction Top quark properties related to EWSB BSM heavy particles decay into boosted top quarks Chirality of BSM physics revealed by helicity of boosted tops How to determine helicity of boosted tops? Polarization of rest top determined by angular distribution of decay products Propose to measure jet substructures energy profiles depend on helicity Require no b tagging, W reconstruction Review articles: F.-P.Schilling (2012), W.Bernreuther (2008), etc.

4 Boosted tops t At LHC(7 14 TeV), even heavy particles (W,Z,h,top...) can be produced with a large velocity = boosted W,Z,h,top... X Boosted top (directly) Boosted top (indirectly) jet New interaction p p X(New particle) p p M X = O(5)TeV E top = O(1) TeV t E top = O(1) TeV t something (model dep.) Boosted top search is important both for SM and BSM (our results is within SM, but possible to extend it to BSM)

5 Jet substructures Decay particles from boosted top collimated in a cone. Difficult to distinguish them from background QCD jets t W b ν e t W b u d leptonc top (1-jet) We need more information about jets, especially inside of jets. hadronic top (3-jets) collimated into a single jet! Take a look at detail in the jet = Study jet substructure!

6 Substructures of quark & gluon jets Ex1 ) Jet energy profile H.n.Li, Z.Li, C.P.Yuan, PRD87,074025(2013) Ex 2) Girth J.Gallicchio, M.D.Schwartz PRL 107,172001(2011) See TASI Lecture, J. Shelton, arxiv: for more detail

7 Energy fractions in L & R tops pick up harder subjet in smallest dij among three transverse separation mainly b subjet in L top mainly d subjet in R top Krohn, Shelton, Wang 2010

8 Scale hierarchy E>>mt>>mJ The two lower scales mt and mj characterize different dynamics, which can be factorized O(mJ) b O(mt) g l light-quark jet heavy-quark kernel

9 1 st -step factorisation at mt/e Take qq tt as am example for our case: Total Production Part Decay Part of Top (semi lep. decay) (closed line of fermions = Dirac trace)

10 Change of fermion flow with Fierz transformation ξ=wilson line vector Factorisation of top decay top-quark jet function

11 Spin decomposition Unpolarised propagator Spin projector Unpol. Pol.(ex. spin up) Pol.(ex. spin down)

12 2 nd step factorisation at mj/mt Factorisation of b jet as well as t jet b jet Squared amplitude Production Factorisation of b jet and spin decomposition Hard kernel Decay (semi leptonic) Anti top top bottom a part of production a part of decay b jet function(replaced with resummed one) Unpol. top

13 Easier to work in rest frame of top first, and then boost Helicity (+ or R, or L) and Boost from Lorentz transformation J. Shelton, Z axis = top spin direction PRD 79, (2009) Boost frame v t Boost frame v t s t s t s t t s t t t jet axis = t spin = R t jet axis = t spin = L For bottom relation between rest frame and boost frame.

14 Results (top jet function) input light-particle jet function from Li et al 2013 calculate H to LO predict top jet function Helicity minus top (Left) > Helicity plus top(right) due to V Ainteraction in top decay vertex But this is not suitable to distinguish R and L consider jet substructure

15 Jet energy profile Consider a small cone (angle r: 0 < r < R t ) in top jet. Accumulate the sub jet energy in the small cone. b jet t jet t jet axis (Jet energy profile) This ratio describe a spread of energy in the small cone r caused by the sub jet distribution

16 Repeat the same factorization procedure, we can derive Hard part Then energy profile becomes top jet energy function Phase space b jet energy function b jet energy function, LO* Resummation factor H.n.Li, Z.Li, C.P.Yuan, PRD87,074025(2013)

17 Top jet energy profile Top jet energy dependence 2TeV 1TeV Top jet radius dependence R t =0.7 R t =0.4 R t = TeV Left > Right tendency (L is faster than R) again. L R deference decrease as E jt increase. Top jet radius dependence is not so large.

18 L R difference Ratio of (L R)/average, average=(r+l)/2 L R difference is large at small r region (L R)/average is about 30(10)%, at r=0.1 for 1(2)TeV top jet. L R deference decrease as E jt increase again.

19 Discussion Why Left(h= ) is larger than Right(h=+)? Angular distribution obeys V A interaction κ b : b quark s spin analysing power = 0.4 Large probability b Favoured decay s t Low probability b Dominant decay direction of b jet is opposite to top spin s t Integration range t L has a larger chance to go in the jet cone! b s t t t jet axis = t spin = R t jet axis = t spin = L

20 Summary Helicity/Chirality dependence of jet substrucuture for polarized t jets. PQCD factorization and resummation effects. Energy profile of L(helicity ) top jet is larger than R(helicity +) top jet. Jet substructure is useful for studying helicity (chirality) of tops. Need hundreds boosted tops (as integrated L = 10 fb^ 1) Will extend to hadronic tops and all kinds of boosted heavy objects (W, Z, H, charged Higgs, W, )

21 A question Right handed top decays? R top decay is suppressed by 1 vt in hard kernel, vt being top velocity. This factor cancels in ratio. (\slash k_t + m_t)(1 + \gamma^5 \slash s_t) = \slash k_t + \gamma^5 m_t \slash s_t ~ \slash k_t + \gamma^5 \slash k_t (for a right-handed boosted top, s_t is almost collimated with k_t) = (1 + \gamma^5) \slash k_t = (1 + \gamma^5) (\slash k_t + m_t) Then we will have P_L(1+\gamma^5) = 0

22 Extra Slides

23 Chiral structure of top sector FCNC in top decay: arxiv: (atlas),cms PAS TOP No Signal. Constraint on Br(t Zq) < 0.93%(ATLAS), <0.34%(CMS) W boson polarisation in top decay: (ATLAS), sensitive to Wtb vertex structure. F 0 = 0.67±0.07, F L = 0.32±0.04, F R = 0.01±0.05. V L is OK, constraint on BSM. Spin correlation : arxiv: (ATLAS) A helicity = 0.40±0.06(stat.)±0.08(syst.) Consistent with NLO SM. D0 (3.1σ) t spin correlation exists (5.1σ) double spin asymmetry

24 Helicity and Chirality u spinor and v spinor at high energies Peskin-Schroeder, p.144 Helicity plus/minus spin state Helicity plus Helicity minus Chirality(chiral rep.) Helicity coincide with Chirality

25 Boosted top Many BSMs contain heavy particles typically heavier than 1TeV. We call it BSM here and it will produce energetic top quarks. Ex) scalar top [SUSY], KK particle [Extra Dim.] LHC[7TeV] pp BSM+X BSM Top+X Top bw Tevatron [2TeV] Fitzpatrick,Kaplan,Randall,Wang (2007) Agashe,Belyaev,Krupovnickas,Perez, Virzi (2008) pp Top+X Top bw Energetic top = Boosted top Almost Rest top Rest frame analysis doesn t work well at LHC. Study of spin reconstruction for boosted top is necessary.

26 Problem of Boosted top Because of kinematic effect of special relativity, decay products almost collimate each other t less information for angle distributions. We have to use other kinematical variables. There are only energies which are left to us. e narrow angles ν b What kind of observables which contain these energies are sensitive to top spin??? Note: No jets definition here

27 What is jets? Jets = Phenomena that energetic hadrons move along an axis. (typically we don t care the particle content) Theory of jets Sterman (Weinberg) introduced the jets in e + e - hadrons process within QCD. e e + Observation of jets q Jets have radius 3 Jets in ee collisions Experimentally, 2jets at SPEAR(SLAC), 3-jets(qq+g) at PETRA (3-jets contribute to the discovery of gluon) G.Sterman, S.Weinberg, PRL 39,1436(1977). g Jet energy = (Σ energy in cone) Jet mass = (Σ momenta in cone) 2 q G.Hanson et al, PRL 35,1609(1975). TASSO, MARK, PLUTO, JADE ( ).

28 Fierz transformation is key point. (I ij = Unit Dirac Matrix) Re arrange fermion line(trace) Apply for b quark trace in squared amplitude. b quark line is factorised! LO Jet function = δ(m 2 J m 2 b) (b Jet = b quark) How about higher order?? final state cut = Insertion of Dirac Matrices

29 Negative spin analyzing power of b quark Possible helicity configurations (m b =0) 3 rd spin component s z = 1/2 b helicity λ b = 1/2 t W z axis helicity λ w = 1 b λ b = 1/2 s z = 1/2 t W λ w = 0 Decay oppositely to top spin vanishes(m b =0) s z = 1/2 s z = 1/2 b λ b = 1/2 t W λ w = 0 b λ b = 1/2 t W λ w = 0 Decay oppositely to top spin vanishes(m b =0)

30 Resummation of large logs (technical) Step 0: Resummation of large logs Insertion of Wilson line Step 1: Derive an evolution eq. for jet function in terms of Wilson line C can be calculable in pqcd Step 2: Evaluate the kernel C and solve the differential eq. = resummation of large logs. Step 3: Replace LO jet function with the resummed one. J.C.Collins, Perturbative Quantum Chromodynamics (World Scientific)

31 Resummation eikonal factors by Wilson Line Definition of the jet function: J Space-time Eikonal factors Evolution eq. for Jet function in Feynman diagrams Light-Cone vector For b-quark J.C.Collins, Perturbative Quantum Chromodynamics (World Scientific) Scale change Vetex structure change Right handed sided reduces to the following factorised form evolution kernels C can be calculable in pqcd (Resummation of Eikonal factors)

32 Factorisation of RG eq. for jet function at two loops. H n,li, Zhao Li, C.P.Yuan, arxiv: Factorisation of LO virtual soft kernels Factorisation of LO real soft kernels Factorisation of LO hard kernels = A special vertex in Feynman rule of Wilson line

33 Results of Jet function in Mellin space Perturvative part Non Perturvative part Matching part at NLO (long analytical expressions) Inverse Mellin transformation

34 Top production at LHC ttar pair production = 170 pb single top production = O(50) pb Millions of Top quarks are produced for L=10 fb 1 LHC as top quark factory!

35 Nature of Top Spin Top decay (100% t bw) > life time vs. Hadronisation time < Top decays before the hadronisation: u(ν) angles, energy distribution reflects the information of the bare top quark : measurement of bare quark indirectly (different from other quarks!) spin t W b d(e)

36 Motivation of this work Generalised Chiral structure in top sector Weak vertex of the top quark is sensitive to the Chiral structure Highly boosted top: Helicity = Chirality boosted top jets will be useful for study of Chiral structures in a generalised top sector Is there any difference between R and L in the top jet substructure? How is it different? Which is larger R or L? If sensitive to R(L), useful to study Chiral structure with jet substructure

37 Factorised cross section (t-jet mass distribution) Decomposition of two spin states Hard part Normalised mass distribution top jet function Phase space depends on only top jet function top spin Polarised top-jet function (at rest frame of top) J b e t ν