Hadronic decay of top quarks as a new channel to search for the top properties at the SM & physics beyond the SM

Transcription

1 Hadronic decay of top quarks as a new channel to search for the top properties at the SM & physics beyond the SM S. M. Moosavi Nejad Yazd University February 15,

2 Top Quark (History and Motivations) Light quarks (u, d, s) led us to the Parton Model of the SM From the Charm quark, we learned that the SM is a consistent theory. Moreover, its discovery confirmed QCD as the quantum theory of the strong interactions J/ψ( 3 S 1 ), η c ( 1 S 0 ) From the Bottom quark, we learned that a complete third family exists. Also, the weak CP violation is a part of the SM Top quark was discovered by the CDF and D0 experiments at the Tevatron in 1995 Its remarkably large mass, still the largest of any known elementary particle: m t = ± 0.51 ± 0.71 GeV However, top discovered 22 years ago, the top quark has not yet taught us fundamentally new insights The top may well do this in the coming decade after all, a belief that rests on top s attributes LHC is a superlative top factory, producing about 90 million top quark pairs per year of running at design c.m. energy s = 14 TeV and design luminosity cm 2 s 1 in each of the four experiments 2

3 Top couplings in the Standard Model Various elementary interactions of top quark field t(x µ ) in the SM Lagrangian, read: The charged weak interaction of the top quark with other quarks is left-handed and flavor-changing: g w 2 2 V tf t(x)γ µ (1 γ 5 )f (x)w µ (x), f = d, s, b Its neutral weak interaction is flavor-conserving and parity violating g w t(x)γ µ [(1 8 4 cos θ w 3 sin2 θ w ) γ 5 ]t(x)z µ (x) Its interaction with gluons is a vector-like coupling, involving an SU(3) generator (T a ) in the fundamental representation g s t i (x)γ µ Tij a t j (x)gµ(x) a i, j = 1, 2, 3 a = 1, 2, 8 Top interaction with photons is also simply vector-like as 2 3 e[ t(x)γ µ t(x)a µ (x)] Its interaction with the Higgs field h(x) is of the Yukawa type y t h(x) t(x)t(x), y t = 2m t /v, v =< h > 0 Effective interactions such as for flavour-changing neutral currents, occur due to loop corrections which are so small 3

4 Top beyond the Standard Model Driving most motivations for physics beyond the Standard Model is the fact that the Higgs mass seems unnaturally small. Renormalized Higgs mass: mh 2 = m0h 2 + ( 3 8π 2 y t 2 )Λ 2 9 [top] + ( 64π 2 g 2 )Λ 2 [vector bosons] 1 +( 64π 2 λ2 )Λ 2 [Higgs] where Λ is ultraviolet cut-off regulator when Λ is of order, the GUT scale, cancellations to many digits are required among these contributions. Being the main troublemaker, the top may in fact also point to possible new physics in which this problem is avoided A popular model is supersymmetry where stop quark loops naturally provide the cancellations of the that divergence problems 4

5 Top quark features Top width is sufficiently large (Γ t 2GeV) no hadronization Rapid decay of the top quark moreover enables transmission of top quark spin information to final states The width-to-mass ratio Γ t /m t of the top quark is small enough that, the notion of top quark as a stable particle makes sense Top decay characteristics play important roles in its studying at colliders Narrow width approximation (NWA), factorizes the production and decay processes Accurate measurements of CDF Collaboration of ratio R = B(t Wb)/B(t Wq) [q = d, s or b] : V tb 1 B(t b + W ) 1. At the LHC, the following decay mode is a likely one to study: 5

6 B-hadron energy distribution from unpolarized top decay Main process b B meson t W ν e e+ Definition of Top-rest frame and the polar angle θ in the W + rest frame 6

7 Custom approaches in perturbative QCD ZM-VFN scheme or Zero Mass: 1 MS Factorization scheme: dγ MS (t bw + ( e + ν e )) Db,g B (z, µ f ) 2 Partonic decay rate with m b = 0 is free of log(mb 2/m2 t ) 3 Non-perturbative fragmentation functions Db,g B are needed. GM-VFN scheme or General Mass: 1 Factorization scheme: dˆγ Db,g B ( x B z, µ F ) 2 dˆγ = d Γ(m b 0) dγ sub : removing collinear logarithms 3 dγ sub = lim mb 0 d Γ(m b 0) d Γ(m b = 0) Non-perturbative fragmentation function: Simple Power (Standard) model: D(x; µ 0, α, β) = Nx α (1 x) β Peterson model: D(x, µ 0, ɛ) = N x(1 x)2 [(1 x) 2 +ɛx] 2 Note:(N, α, β) and (N, ɛ) determined by fitting energy distribution of B-hadron in e e + annihilation. 7

8 Hadronization Perturbative and non-perturbative sections: Hadron production through electron-positron annihilation: e e + γ/z 0 q q Hadron + Jets 8

9 Extraction the Fragmentation Functions Non-perturbative fragmentation functions: Simple Power (Standard) model: D(x; µ 0, α, β) = Nx α (1 x) β Peterson model: D(x, µ 0, ɛ) = N x(1 x)2 [(1 x) 2 +ɛx] 2 Note: Free parameters are determined by fitting as dσ Exp (e e + q q B + jet) = d ˆσ(e e + q q) D B q DGLAP evolution equation to achieve to non-pff; D B a ( x B z, µ F ): d D d log µ 2 i (x B, µ F, m b ) = j F where: P ij (x B, α s (µ F )) = αs (µ F ) 2π and P (0) 1 x B dz z P ij( xbz, α s (µ F ) ) D j (z, µ F, m b ) P(0) ij (x B ) + ( α s (µ F )) 2P (1) 2π ij (x B ) + O(αs 3 ) ij (x B ) and P (1) ij (x B ) are well-known Altarelli-Parisi splitting functions. 9

10 Bottom and gluon fragmentation into B-hadron g B-Hadron FF b B-Hadron FF 0.6 D B (x B ) x B Comparison of the non-perturbative fragmentation functions of b B and g B at µ = m t = 174 GeV in the Power model fitted to the OPAL, ALEPH and SLD data using µ 0F = m b = 4.5 Gev 10

11 Angular Decay Distribution for : t b + W + ( e + + ν e ) at NLO Feynman diagram and Rest frames Angular Decay Distribution at NLO using fixed x b and fixed x g : 1 Γ 0 1 Γ 0 d 2ˆΓ dx b d cos θ = Ĥ (1 + cos θ)2 + Ĥ 3 8 (1 cos θ)2 + Ĥ sin2 θ d 2ˆΓ dx g d cos θ = Î (1 + cos θ)2 + Î 3 8 (1 cos θ)2 + Î sin2 θ Where: Γ 0 = ΓBorn,Had Γ Born,Lep 11

12 Feynman Diagrams at NLO Virtual Corrections: Real Corrections: 12

13 Technical details We work in ZM-VFN scheme or massless-scheme where m b = 0 To extract the infrared (IR) and ultraviolet (UV) divergences, we use dimensional regularization to regulate all singularities. d 4 p g d D (2π) 4 p g µ4 D (2π) D In this scheme, all divergences regularized in D = 4 2ɛ dimensions the renormalized amplitude of the virtual corrections is e M loop = 2 ɛ µ(p W )ū(p b, s b ){Λ µ + δλ µ }u(p t, s t ) 2 sin θ W For the counter term of the vertex, one has: Λ ct = 1 2 (δz b + δz t )γ µ (1 γ 5 ) The wave function renormalization constant reads δz t = αs(µ R) 4π C F ( γ E + 3 ln 4πµ2 F + 4), ɛ UV ɛ IR mt 2 δz b = αs(µ R) 4π C F ( 1 1 ) ɛ UV ɛ IR 13

14 Covariant approach and Covariant projectors Completeness relation: M 2 λ=0,± ɛµ (λ)ɛ ν (λ), λ=0,± ɛµ (λ)ɛ ν (λ) = g µν + pµ W pν W m 2 W Longitudinal helicity: ( ɛ µ (0)ɛ ν (0) = ω p µ P W 2 t pt.p W p µ mw 2 W )( ) pt ν pt.p W p ν mw 2 W ω = m2 W m 2 t Transverse-plus and transverse-minus helicities: ɛ µ (±)ɛ ν (±) = ( g µν pµ W pν W m 2 W iɛ µναβ m t P W (p t) α (p W ) β ) ( ω p µ P W 2 t )( pt.p W p µ mw 2 W pt ν where: ɛ 0123 = 1 and P W 2 = (m t E b E g ) 2 m 2 W pt.p W p ν mw 2 W ) 14

15 Analytical results at NLO Desired quantity 1 Γ 0 d 2ˆΓ dx b d cos θ = Ĥ (1 + cos θ)2 + Ĥ 3 8 (1 cos θ)2 + Ĥ sin2 θ, Where: x b = E b E max b Ĥ 00 = 1 1+2ω δ(1 x b) + α S 2π(1+2ω) C F 2ω { ( 1 ɛ + γ E log 4π) Ĥ = 1+2ω δ(1 x b) + α S ω π(1+2ω) C F Ĥ ++ = { ( 1 ɛ + γ E log 4π) α S ω 2π(1+2ω) C F D(x b ) ( ( ) 3 2 δ(1 x b) + 1+x 2 b (1 x b ) + + ˆB(x } b ) ) 3 2 δ(1 x b) + 1+x 2 b (1 x b ) + } + Ĉ(x b) 2 15

16 Our prediction: Energy distribution of B-meson considering helicity contributions of W-boson 1/Γ 0 d 2 Γ NLO /(dx B dcosθ) (t B+X) Total(NLO) H 0 0 H - - H + + Peterson model /Γ 0 d 2 Γ ++ /(dx B dcosθ) (t B+X) x B x B Comparison of the NLO contributions of the longitudinal and the transverse-minus and the transverse-plus helicity of the W + -boson in the B-hadron energy distribution. Initial factorization scale is µ 0 = 10.0 GeV. 16

17 Numerical results Angular distribution of differential decay rate 1 Γ 0 d 2ˆΓ dx b d cos θ = Ĥ (1 + cos θ)2 + Ĥ 3 8 (1 cos θ)2 + Ĥ sin2 θ O(α s ) radiative corrections to three helicity rates m t = 174GeV, m W = 80GeV, α s (m t ) = ˆΓ LO 00 = 1 0 dx b ˆΓ LO = 1 0 dx b ˆΓ LO ++ = 1 0 dx b Hˆ 00 LO NLO = = ˆΓ 00 = ˆ H LO 00 = = ˆΓ NLO = Hˆ 00 LO NLO = 0.0 = ˆΓ ++ = Theoretical and Experimental results from CDF Collaboration ˆΓ 00 ˆΓ = , ˆΓ = , Γ EXP 00 Γ = 0.91 ± 0.37(stat) ± 0.13(syst) ˆΓ ˆΓ ++ ˆΓ = Γ EXP ++ Γ = 0.11 ±

18 B-hadrons from polarized top decays: t( ) W + + B + X Due to the top short lifetime ( s) it retains its full polarization content when it decays. This allows one to study the top spin state using the angular distributions of its decay products. θ φ θ θ φ θ 18

19 Angular decay distribution Angular distribution of differential decay rate dγ dx B d cos θ P dφ P = 1 4π ( dγ A dx B + P dγ B dx B cos θ P + P dγ C dx B sin θ P cos φ P ) where x B = E B /E max b and 0 P 1 Definition of the polar angle θ P and the azimuthal angle φ P in the top quark rest frame. P is the polarization vector of the top quark θ φ θ 19

20 Technical details To evaluate the doubly differential decay rate, the angular integral has to be written as d D 1 p H = p D 2 dp H H dω H in which dω = π dφ P d cos φ P D 3 2 Γ( D 3 2 )(sin θ P) D 4 (sin φ P ) D 4 When integrating over the phase space for the real gluon radiation, terms of the form (1 x b ) 1 2ɛ arise which are due to the radiation of a soft gluon in top decay. We use the following expression (1 x b ) 1 2ɛ = 1 ( ) 1 2ɛ δ(1 x b) + 1 x b ( ) ln(1 xb ) 2ɛ 1 x b + The unpolarized Dirac string is replaced by u(p t, s t )ū(p t, s t ) = ( p t + m t ) s t u(p t, s t )ū(p t, s t ) = 1/2(1 γ 5 s t )( p t + m t ) + 20

21 Numerical analysis dγ NLO dφ 1P d cos θ 1P dγ NLO 2 dφ 2P d cos θ 2P } = ΓNLO A 4π { P cos θ 1P P sin θ 1P cos φ 1P } { P cos θ 2P P sin θ 2P cos φ 2P = ΓNLO A 4π x B -spectrum in the ZM-VFN scheme considering the unpolarized (dashed line) and polarized (solid line) partial decay rates at NLO dγ/dx B [GeV] t B+X (First frame) dγ A /dx dγ B /dx dγ C /dx dγ/dx B [GeV] t B+X (Second frame) dγ A /dx dγ B /dx dγ C /dx x B x B 21

22 Top in beyond Standard Model In particle physics, a two-higgs-doublet model (2HDM) is an extension of the Standard Model in which a second Higgs doublet is added to the Higgs sector of the SM The addition of the second Higgs doublet, after spontaneous symmetry breaking, leads to five physical states: 1 The light and heavy CP-even neutral Higgs bosons h and H (m H > m h ) 2 The CP-odd pseudoscalar Higgs A 3 Two charged Higgs bosons H ± Such a model has six free parameters: 1 Four Higgs masses (m h, m H, m A, m H ±) 2 Ratio of the vacuum expectation values of the two electrically neutral components of the two Higgs doublets (tan β =< H 2 > / < H 1 >) 3 A mixing angle (α) Note: The experimental observation of charged Higgs bosons would indicate physics beyond the SM 22

23 Charged Higgs (H ± ) production The production mechanisms and decay modes of charged Higgs bosons depend on their masses m H ± At hadron colliders, for light charged Higgs bosons (m H < m t m b ) the primary production mechanism is: t t H ± W b b, while for heavy charged Higgs, associated production of th + is dominant Figure: Example of lowest-order Feynman diagrams for the production of light (left) and heavy (center and right) charged Higgs bosons 23

24 Search for light charged Higgs: t bh + BH + + X Our proposal to search for H ± at LHC is to evaluate dγ/dx B of the process t bh + BH + + X, where x B = E B /Eb max = 2m t E B /(mt 2 mh 2 ) which is the normalized energy fraction of B-meson Factorization theorem: dγ = x max i dx i dγ (µ R, µ F )Di B ( x B, µ F ) dx B x i dx i x i i=b,g x min i dγ/dx i (i = b, g) is the Wilson coefficients at each level, where x i = E i /Eb max Di B (z, µ F ) refers to the nonperturbative fragmentation function 24

25 Wilson coefficients for t bh + L I H ± [V ij m ui A u ū i (1 γ 5 )d j + V ij m dj A d ū i (1 + γ 5 )d j ] +H.c. The Born term amplitude for t bh + can be expressed as a superposition of scalar and pseudoscalar coupling factors or as a superposition of right- and left-chiral coupling factors: M 0 = ū b (a1 + bγ 5 )u t = ū b {g t 1 + γ γ 5 + g b }u t 2 Higgs coupling factors in model 1 (type-i 2HDM): g W a = 2 V tb (m t m b ) cot β 2m W b = g W 2 V tb (m t + m b ) cot β 2m W Higgs coupling factors in model 2 (type-ii 2HDM): a = b = g W 2 V tb (m t cot β + m b tan β) 2m W g W 2 V tb (m t cot β m b tan β) 2m W 25

26 Results from ATLAS tan β Median expected exclusion Observed exclusion 95% CL Observed +1σ theory Observed 1σ theory Expected exclusion 2011 Observed exclusion 2011 ATLAS Preliminary max s=8 TeV m h Ldt = 19.5 fb 1 Data 2012 τ+jets m H + [GeV] Figure: Exclusion region in the MSSM tan β m H + parameter space for m H + = GeV. The blue region is excluded 26

27 Numerical analysis For numerical analysis: m t = GeV, m W = GeV and V tb = The total quark decay width: Γ tot t = Γ SM t bw + ΓMSSM t bh where Γ SM t bw = GeV Energy distribution of B-hadron from top decay in the SM and 2HDM Figure: Our predictions for x B -spectrum taking m H = 100 GeV and tan β = 10 27

28 Analysis of Higgs production through polarized top decay The angular distribution of the differential decay width dγ/dx B of a polarized top quark (t( ) bh + (+g) BH + + X ) is given by d 2 Γ = 1 (dγunpol dx B d cos θ P 2 dx B ± P dγpol dx B cos θ P ) P : the degree of the top quark polarization [0 P 1] P t 2 1 P 3 P 28

29 Numerical results for dγ(t( ) BH + + X )/dx B Our predictions for the energy spectrum of B-mesons produced through polarized top quark decay in the 2HDM (t( ) BH + + Jet) taking different values of tan β and m H 29

30 dγ(t( ) BH + + X )/dxb in two different Helicity frames The NLO energy spectrum of B-mesons from polarized top decays, in the first and second helicity coordinate systems. The energy distributions obtained in two various systems are different and the size of NLO correction is larger in the system 2. For more comparison, we also plotted the energy distribution of B-mesons through unpolarized top quark decays xb -spectrum in the type-i 2HDM for the polarized and unpolarized top decays in two different helicity coordinate systems. 30 S. M. Moosavi Nejad Yazd University Hadronic decay of top quarks as a new channel to search for the top proper

31 Summary and Conclusion Top is an object of interest and its attractiveness is due to: Its interaction with the Higgs boson A tool to search for new physics beyond the SM To investigate the mechanism of electroweak symmetry breaking Of particular interest are the distribution in the B-hadron energy in the top quark rest frame, t b( B + X ) + W + ( e + + ν e ) LHC will allow for the study of this dominant decay mode The present work introduces a new channel to indirect search for the charged Higgs boson through the top decay. Any deviation of the total spectrum of bottom-flavored meson from the SM predictions is a reason for the existence of charged Higgs Last word: Top will remain in the focus of attention for a good many more years. 31