Top Quark Physics at the LHC (Theory) Werner Bernreuther RWTH Aachen

Top Quark Physics at the LHC (Theory) Werner Bernreuther RWTH Aachen

Physics Issues: Unique opportunity to investigate interactions of a bare quark at energies a few 100 GeV Dynamics of top production and decay is not explored very precisely so far Profile: mass, charge, spin, decay modes & width Excellent probe of mechanism of electroweak gauge-symmetry breaking New decay modes? t t..., FCNC decays t c? or sizeable FCNC in top production: pp t c X? Good probe also for non-sm parity and/or non-sm CP violation (induced, e.g., by non-standard Higgs bosons)... Strong and electroweak interaction effects of top quarks can be reliably predicted asset!

Role of Top in the SM and beyond Top mass: important parameter for precision electroweak constraints Recent CDF and D0 average: m t = 170.9 ± 1.8 GeV EW fit in SM (LEP EWWG): m H < 182 GeV @ 95 % C.L. 80.5 LEP1 and SLD LEP2 and Tevatron (prel.) 68% CL m W [GeV] 80.4 80.3 α m H [GeV] 114 300 1000 150 175 200 m t [GeV] Flavour physics: top mass and its couplings determine, e.g., rare B decay modes: B X s γ, B s µ + µ, Higgs physics at LHC: Top quark probes (SM) Higgs sector through its Yukawa coupling(s): gg H, associated production t th

Top plays an important role also in many SM extensions: e.g. in MSSM: large top Yukawa coupling rescues MSSM from LEP2 lower bound on m h allows for radiative electroweak symmetry breaking viable scenario in the MSSM This mechanism is also essential for Little Higgs models Top dynamical breaking of electroweak symmetry? i.e., condensation of t L t R or of t L χ R?

OUTLINE Top decay t t production Single top production

Top decay In the SM: t quark decays almost 100 % into t b + W + Top decay width: Γ t = 1.4 GeV lifetime τ t 4 10 25 sec t and t decay before they can form hadronic bound states (t q), (tqq ) top quark quasi-free, instable particle top-quark spin effects are measurable and calculable!

Decay vertex t b + W + tbw vertex bγ µ (f L P L + f R P R )tw µ In the SM: + biσ µν q ν m W (g L P L + g R P R )tw µ + h.c. m b 0 + QCD & EW corrections P rob(h W = +1) 0.1%. Do et al. Exp. determination by helicity analysis; not yet measured precisely at Tevatron. LHC perspectives: f R < 0.06, g L g R < 0.02 Hubaut et al. ; Aguilar-Saavreda et al.

Decays of (polarized) top quarks: semileptonic decays: t b l + ν l, b l + ν l + gluons non-leptonic decays: t b q 1 q 2, b q 1 q 2 + gluons respectively t j b j 1 j 2, j b j 1 j 2 j 3 Differential distributions known at NLO in the SM couplings Czarnecki, Jezabek, Kühn; Fischer et al.; Brandenburg, Si, Uwer;... In particular: Ensemble of top quarks self-analyses its spin polarization 1 dγ Decay distribution of (100 %) polarized t f +... Γ d cos θ = 1 f 2 (1 + c f cos θ f ) Best t-spin analyzers: SL decays: charged lepton, c l = 0.999 NL decays: least energetic non-b jet, c j < = 0.47

Other top decay modes? In SM: Br(t W + s) < 10 3, Br(t W + d) < 10 4 FCNC decays t c g, t c Z, t c γ: Br < 10 11 FCNC modes can be somewhat larger in SM extensions e.g., Br(t cg) < 10 5, Br(t cz) < 10 6 in MSSM (Li et al.; Guasch et al.,...) Decay modes t H + or t t? Tevatron constraints still leave some windows open

Production of top quarks at (future) accelerators tt pairs dominant reaction N t t/year Tevatron: p p 1.96 TeV q q t t 10 4 LHC: pp 14 TeV gg t t 10 7-10 8 ILC: e + e (500 GeV) e + e t t 10 5 single top dominant reaction (N t + N t)/year Tevatron: LHC: u + b W d + t a few 10 3 u + b W d + t 10 6-10 7

t t production at Tevatron and LHC: main reactions within SM: 8 < p p, pp t tx : 2l + n 2 jets + P miss T l + n 4 jets + P miss T n 6 jets t t production dominated by strong interactions: q q t t, gg t t, weak decays of t and t: t blν l (semileptonic), t bq q (non-leptonic) BR(2l) : BR(l + jets) : BR(jets) 0.05 : 0.30 : 0.46 for l = e, µ Tevatron: σ(t t) exp = 7.3 ± 1.2 pb (from l + jets channels) LHC: σ(t t) 830 pb, goal: δσ(t t) exp < 10%

Status of Theory (SM results): Spin-averaged cross sections σ(pp, p p t tx), dσ/dp T,... known to orderi α 3 s + resummed threshold logarithms α 3 s, z = Q 2 /ŝ h ln(1 z) 1 z (Nason et al.; Beenakker et al.; Bonciani et al.; Kidonakis et al.; Cacciari et al.;...) recent progress towards NNLO (O(α 4 s )) computations of σ t t (Mitov, Moch, Czakon) cross section for t t+ jet at NLO QCD (Dittmaier, Uwer, Weinzierl); important background to Higgs searches: weak boson fusion W + W H, and t th. Differential cross sections pp, p p t tx final states, including the t and t spin d.o.f. known to NLO QCD + O(α 2 s α W ) corrections (W.B., Brandenburg, Si,Uwer) allows prediction of t t spin correlations; large QCD-dominated effect. Mixed QCD-weak interaction corrections (O(α 2 s α W )): (Beenakker et al.; W.B.,Fücker, Si; Kühn, Scharf, Uwer) irrelevant for σ t t, but important for p T and M t t distributions for large p T, M t t TeV (weak Sudakov logs) + Precision goals, e.g., for t t cross section: Tevatron: δσ(t t) th 10% goal for LHC: δσ(t t) th 5% (scale and PDF uncertainties)

Determination of the top quark mass Fitting methods at Tevatron: template method, matrix element method, ideogram method,... Recent CDF & D0 average: m exp t = 170.9 ± 1.8 GeV Expts. use Born matrix elements in their fitting procedures Experimental issues: (b) jet energy scale, b tagging, underlying events,... m exp t has an error of 1 % but which mass is measured? relation to mass parameter in Lagrangian? top mass used in Monte Carlos? Problem hard to address - but becomes relevant now Goals: δm exp t 1.3 GeV (Tevatron), 1 GeV (LHC) NLO QCD predictions for hadronic t t production typically use on-shell mass m pole which seems natural choice. m pole t has ambiguity of O(Λ QCD ), but may eventually be replaced by some short-distance mass parameter; i.e., this is not the problem. t,

m top from peak of invariant mass distribution Consider, e.g., reactions pp, p p ttx l ν l j b + j b j 1 j 2 + soft hadrons Top mass may be determined from position of the peak of invariant mass distribution dσ/dm t, M t = q (p jb + p j1 + p j2 ) 2. Obviously, peak position differs from m pole t because of soft QCD effects (i.p. color recombination): in perturbation theory: non-factorizable QCD corr. to hard scattering 2 6 matrix elements. computed to O(α 3 s ) (Beenakker et al.; W.B., Fücker, Meyer, Si) small effect: shift of peak maximum with respect to m pole t non-perturbative soft QCD effects; esp. color exchange between t, t decay products and beam remnants. Recent analysis by Skands, Wicke using a Monte Carlo model: δm t 0.5 GeV (color recombination) Errors already partially included in present data analyses? only by < 100 MeV. and δm t 1 GeV (parton shower)

Recent interesting analysis by Fleming et al., but applicable only to e + e production far above threshold: e + e t tx Define short distance jet mass m J as maximum of a perturbatively calculable jet function ( distorted Breit-Wigner) m J m pole t in perturbation theory parameterize soft QCD effects (cross-talk between the 2 hemisphere jets in the above simple kinematic situation); requires input from exp. jet analyses

t, t polarization and t t spin correlations polarization of t, t in hadronic t t production (very) small, 1%: t polarization in production plane (parity-violating) due to weak interactions, e.g., < s t ˆk t > normal polarization (P-even, T-odd) due to QCD absorptive parts t t spin correlations: large effect in the SM, dominated by QCD. < (â s t )(ˆb s t) > = A/4 Strength depends on the choice of reference axes â, ˆb. Choices: â = ˆk t, ˆb = ˆk t (helicity basis; good for LHC) â = ˆb = ˆp (beam basis; good for Tevatron) Top polarization, t t spin correlations at level of final states: non-isotropic angular distributions and non-zero angular correlations with resp. to chosen reference axes: Suitable analysis channels: t t l + l + (l = e, µ) and lepton + jets channels: t t l + j + where j = j b or j <.

Predictions at level of t, t decay products Consider, e.g., dilepton channels pp, p p t t + X l + l + X. double distribution: 1 σ d 2 σ d cos θ + d cos θ = 1 4 {1 + B 1 cos θ + + B 2 cos θ C cos θ + cos θ } θ + = (l +, â), θ = (l, ˆb) in resp. t, t rest frames. B 1,2 polarization of t, t. In SM: B 1, B 2 < 1% (W.B.,Fücker, Si) dσ/d cos θ ± sensitive to non-sm P-violating interactions C t t spin correlations. All-order formula (factorizable corrections): C = A c + c opening angle distribution also sensitive to t t spin correlations: 1 dσ σ d cos φ = 1 2 φ = (l +, l ) in resp. t, t rest frames. (1 D cos φ)

Predictions to NLO QCD (PDF input: CTEQ6L and CTEQ6.1M) W.B., A. Brandenburg, Z.G. Si, P.Uwer Tevatron, s = 1.96 TeV LHC, s = 14 TeV ll LO NLO LO NLO C hel 0.471 0.352 0.319 0.326 C beam 0.928 0.777 0.005 0.072 D 0.297 0.213 0.217 0.237 l + j C hel 0.240 0.168 0.163 0.158 C beam 0.474 0.370 D 0.151 0.101 0.111 0.115 good choices: beam basis for Tevatron, helicity basis and opening angle distribution (D) for LHC order α W α 2 s weak interaction corrections only a few percent (W.B., M. Fücker, Z.G. Si ) effects enhanced by suitable cuts on M t t LHC study of dilepton and lepton + jets events at the detector level: F. Hubaut et al.: δd 4%, δc hel 6% spin observables useful for probing the dynamics of t t production & decay sensitive to anomalous gt t couplings (P. Haberl, O. Nachtmann, A. Wilch), to residual effects of heavy resonances,...

Other observables sensitive to BSM physics: p T distribution of top, and t t invariant mass distribution M t t = p (p t + p t) 2. Precise SM predictions required, mixed weak-qcd corrections of O(α W α 2 s ) become relevant (weak Sudakov logs) esp. for large p T, M t t 1 TeV. Size of mixed contributions at LHC: pp t t + X W.B., M. Fücker, Z.G. Si; J. Kühn, A. Scharf, P. Uwer ratio (dσ weak /dp T ) / (dσ LO /dp T ) ratio (dσ weak /dm t t) / (dσ LO /dm t t) -0 0-0.05-0.05-0.1-0.15-0.1-0.2 500 1000 1500 2000 p [GeV] T 1000 2000 3000 4000 M tt [GeV] solid: m H = 120 GeV, dashed: m H = 200 GeV

Main interest: Search for heavy resonances that strongly couple to t t Extensions of SM, e.g. supersymmetric extensions, top-condensation, extra dim. models... heavy resonances ϕ J that strongly couple to top quarks ϕ J : could be a Higgs boson, a bound state, a KK excitation... many investigations (more recent ones: Lillie et al., Djouadi et al.,...) Example: 2HDMs or MSSM Higgs boson A with J P C = 0 + A may be heavy, m A > 300 GeV A / W + W, ZZ in lowest order, but A can strongly couple to top quarks at LHC gg A t t final state gg t t final state interference of amplitudes leads to typical peak-dip resonance structure

LHC: pp A + X t t + X l+ Jets Example: m A = 400 GeV, Γ A = 12 GeV, tan β = 4 t t invariant mass distribution 1 σ (W.B., Flesch, Haberl) dσ dm t t 0.04 0.02 0 400 500 600 700 exp. resolution and understanding of non-resonant background crucial

Single top production: weak PSfraginteractions replacements involved PSfrag inreplacements production; in SM: PSfrag σ t replacements V tb 2 source of polarized g tops g in SM: t channel s channel tw mode W + W + u W d W u d b W + t u d b b t d b b t d b d b g W Predictions: Harris et al., Campbell et al.,...(nlo QCD) Kidonakis (NLO QCD + resummed threshold logs) σ T ev [pb] 1.0 0.44 <0.1 (NLO QCD) 1.15(7) 0.54(4) 0.14(3) (resummed) σ LHC t [pb] 154 6.2 30 (NLO QCD) 150(6) 7.8(7) 44(5) (resummed) σ t LHC [pb] 89 3.8 30 (NLO QCD) Recent evidence for single top production at Tevatron: D0 collab. (Dec. 2006) σ t channel + σ s channel + c.c. modes = 4.9 ± 1.4 pb V A coupling V tb f L = 1.3 ± 0.2

Different final states for t-, s-channel and associated tw production Large backgrounds from W b b, W + jets, t t,... At LHC: S/B increases as compared to Tevatron t-channel: u + b d W + t: largest rate, in final state: forward (d) jet, t polarization largest along axis spectator jet (Mahlon, Parke). s-channel: u + d W t + b: smallest rate, extra b jet in final state, PDF uncertainites are smallest V tb from σ s channel. Goal: δv tb 5% Production channels sensitive to different signals of new physics: t-channel flavor-changing neutral currents t c, tū production a few pb in unconstrained MSSM (Liu et al.) larger t c cross section in top-color type models (Cao et al.) tw mode charged Higgs bosons g + b t + H + c.c. mode s-channel new charged boson resonances u + d t W + b X+ or c + b t + b where, e.g., X + = H + (charged Higgs), or Π + (top-pion)

Conclusions Physics of top quarks remains to be fully explored, both in t t and in single top production & decay Unique opportunity to investigate the interactions of a bare quark below attometer scale Excellent probe of mechanism of EWSB, of possible heavy resonances, of possible FCNC interactions in the I W = +1/2 quark sector,... SM predictions for top as a signal at LHC in reasonably good shape. Spin effects useful tools in exploring the dynamics of top quarks unique feature (as compared to b, c,..), Some challenges for theory: Interpretation of m exp t (at < 1% level) in terms of Lagrangian mass Precise predictions of distributions σ t t to NNLO QCD