1. Truth (Theory Overview) Tim M.P. Tait Fermi National Accelerator Laboratory Hadron Collider Physics Michigan State University 6/15/2004

2. Hadron Collider Physics, 6/15/04 Tim Tait 2 Outline Introduction: Why is top important? Top Decay Production in Pairs Single Top Production Polarization Beyond the Standard Model Outlook

3. Hadron Collider Physics, 6/15/04 Tim Tait 3 The King of Fermions! In the SM, top is superficially much like other fermions. What really distinguishes it is the huge mass, roughly 40x larger than the next lighter quark, bottom. This may be a strong clue that top is special in some way. It also implies a special role for top within the Standard model itself. Top is only fermion for which the coupling to the Higgs is important: it is a laboratory in which we can study EWSB. SM Fermions

4. Hadron Collider Physics, 6/15/04 Tim Tait 4 Top in the Standard Model In the SM, top is the marriage between a left-handed quark doublet and a right-handed quark singlet. This marriage is consummated by EWSB, with the mass (m t ) determined by the coupling to the Higgs (y t ). This structure fixes all of the renormalizable interactions of top, and determines what is needed for a complete description of top in the SM. Mass: linked to the Yukawa coupling (at tree level) through: m t = y t v. Couplings: g S and e are fixed by gauge invariance. The weak interaction has NC couplings, fixed in addition by s 2 W. CC couplings are described by V tb, V ts, and V td.

5. Hadron Collider Physics, 6/15/04 Tim Tait 5 Measurements How well are these quantities known? g S, e, and s 2 W are well known (g S at per cent level, EW couplings at per mil level) from other sectors. m t is reconstructed kinematically at the Tevatron: –Run I: m t = 178 ± 4.3 GeV –Run IIb: prospects to a precision of ± 2 GeV (systematic). V td, V ts, and V tb are (currently) determined indirectly: –V td : 0.004 – 0.014 (< 0.09) –V ts : 0.037 – 0.044 (< 0.12) –V tb : 0.9990 – 0.9993 (0.08 – 0.9993) –These limits assume the 3 (4 + ?) generation SM, reconstructing the values using the unitarity of the CKM matrix. V tb can be measured directly from single top production. PDG: http://pdg.lbl.gov/pdg.html

6. Well, how well do we want to know them? need

7. Hadron Collider Physics, 6/15/04 Tim Tait 7 Flavor Physics: – LEP EWWG Top’s Role in the SM EW Fit: Both require precision inputs from the top sector for precision SM predictions. Buchalla, Buras, Lautenbacher RMP68,1125 (1996) b t s W Z W i.e.:

8. Hadron Collider Physics, 6/15/04 Tim Tait 8 Heinemeyer et al, JHEP 0309,075 (2003) Most importantly, the MSSM only survives the LEP-II bound on m h because of the large y t : (m t < 160 GeV rules out MSSM!) Top Sector and SUSY The large top Yukawa leads to the attractive scenario of radiative electroweak symmetry-breaking: This mechanism is also essential in many little Higgs theories. Top plays an important role in the minimal supersymmetric standard model. SUGRA report, hep-ph/0003154 Radiative EWSB

9. Hadron Collider Physics, 6/15/04 Tim Tait 9 Top Decay SM: BR into W + b ~ 100%. Top decay represents our first glimpse into top’s weak interactions. In the SM, W-t-b is a left- handed interaction:   (1 -  5 ). However, the decay does not offer a chance to measure the magnitude of the W-t-b coupling, but only its structure. This is because the top width is well below the experimental resolutions. Top is the only quark for which  t >>  QCD. This makes top the only quark which we see “bare” (in some sense).  Top spin “survives” non- perturbative QCD (soft gluons). CDF: CDF PRL86, 3233 (2001) V tb >> V ts, V td

10. Hadron Collider Physics, 6/15/04 Tim Tait 10 Rare Decays Many rare decays of top are possible. These can be searched for in large t t samples, using one standard decay to ‘tag’ and verifying the second decay as a rare one. One example is a FCNC: Z-t-c At LEP II, the same physics that results in t Zq would lead to e + e - Z * tq. More possibilities, such as t c , t cg, etc… Solid lines: assume  tc  = 0.78 Dashed lines: assume no t-c- 

11. Hadron Collider Physics, 6/15/04 Tim Tait 11 t t Production At a hadron collider, the largest production mechanism is pairs of top quarks through the strong interaction. (Production through a virtual Z boson is much smaller). At leading order, there are gluon-gluon and quark-anti-quark initial states. At Tevatron, qq dominates (~85%). At LHC, gg is much more important.

12. Hadron Collider Physics, 6/15/04 Tim Tait 12 P. Azzi, hep-ex/0312052 t t Production Rates NNLO-NNNLL+: NLO + soft gluon corrections, re- expanded to NNNLL & some NNLO pieces. “Pure” NLO curve includes PDF uncertainties. At Tevatron, uncertainties in threshold kinematics dominate. PDF uncertainties are also important. At the LHC, uncertainties are of the order of 10% are from the gluon PDFs and variation with the scale . LHC:  tt ~ 850 ± 100 pb tt is a major background to many new physics searches (i.e. Higgs).

13. Hadron Collider Physics, 6/15/04 Tim Tait 13 tt Resonances A neutral boson can contribute to tt production in the s-channel. Many theories predict such exotic bosons with preferential coupling to top: –TC 2, Top Seesaw: top gluons –TC 2, Topflavor: Z’ Search strategy: resonance in tt. Tevatron: up to ~ 850 GeV. LHC: up to ~ 4.5 TeV. Future EW Physics at the Tevatron, TeV-2000 Study Group Hill PLB345,483 (1995) Dobrescu, Hill PRL81, 2634 (1998) Hill PLB345,483 (1995) Chivukula, Simmons, Terning PRD53, 5258 (1996) Nandi, Muller PLB383, 345 (1996) Malkawi, Tait, Yuan PLB385, 304 (1996)

14. Hadron Collider Physics, 6/15/04 Tim Tait 14 Single Top Production Top’s EW interaction. –Three modes: T-channel: q b q’ t S-channel: q q’ t b Associated: g b t W - Any day at Run II!  Tevatron Run I Tevatron Run II LHC  t (NLO) 1.45±0.08 pb1.98±0.13 pb247±12 pb  s (NLO) 0.75±0.07 pb0.88±0.09 pb10.7±0.9 pb  tW (LL) 0.06±0.01 pb0.09±0.02 pb56±8 pb Total2.26±0.11 pb2.95±0.16 pb314±15 pb Harris, Laenen, Phaf, Sullivan, Weinzierl, PRD 66 (02) 054024 Tait, PRD 61 (00) 034001; Belyaev, Boos, PRD 63 (01) 034012 Run I Limits < 12.9 pb < 13.5 pb CDF PRD65, 091102 (2002) DØ PLB517, 282 (2001)

15. Hadron Collider Physics, 6/15/04 Tim Tait 15 s- Versus t-Channels s-channel Mode –Smaller rate –Extra b quark final state –  s  |V tb | 2 –Polarized along beam axis at Tevatron. Sensitive to resonances –Possibility of on-shell production. –Need final state b tag to discriminate from background. t-channel Mode –Dominant rate –Forward jet in final state –  t  |V tb | 2 –Polarized along spectator jet axis (Tevatron & LHC). Sensitive to FCNCs –New production modes. –t-channel exchange of heavy states always suppressed. Mahlon, Parke PLB476 323 (2000); PRD55 7249 (1997)

16. Hadron Collider Physics, 6/15/04 Tim Tait 16 Charged Higgs H +, Top-pion  + RH coupling! Charged Resonance Topflavor: W’ t b Sullivan hep-ph/0306266 He, Yuan PRL83,28 (1999) Simmons, PRD55, 5494 (1997)

17. Hadron Collider Physics, 6/15/04 Tim Tait 17  s -  t Plane Run II LHC Since they are sensitive to different physics and have different, final states,  s and  t should be measured independently! Tait, Yuan PRD63, 014018 (2001) Theory errors only!

18. Hadron Collider Physics, 6/15/04 Tim Tait 18 Polarization W Polarization –SM: Depends on m t & m W : –This is a direct test of the left- handed nature of the W-t-b vertex. – W correlated with the direction of p e compared with the direction of p W in the top rest frame. Top Polarization –t t production: no net t. –  t and t are correlated by s- channel gluon (vector). –Single t: ~100% polarization. –t polarization correlates with p e Mahlon, Parke PLB411, 173 (1997) DØ:DØ: CDF: CDF PRL84, 216 (2000) DØ hep-ex/0404040

19. Hadron Collider Physics, 6/15/04 Tim Tait 19 Top Yukawa Coupling Maltoni, Rainwater, Willenbrock, PRD66, 034022 (2002) SM prediction for the t coupling to the Higgs: We’d like to directly verify the relation to roughly the same precision as m t itself: a few %. –Higgs radiated from tt pair is probably the best bet. LHC: y t to about 10-15% for m h < 200 GeV. NLO: Dawson, Jackson, Orr, Reina, Wackeroth, PRD 68, 034022 (2003)

20. Hadron Collider Physics, 6/15/04 Tim Tait 20 Outlook Top is unique as a laboratory for EWSB and fermion masses. Its huge mass may be a clue that it is special, and it plays an important role in the SM and beyond. Theory is in good shape for current experiments. t t at the LHC will challenge us to go to another order of pQCD. Single top production will most likely be observed within a year. This will be the first direct measurement of top’s weak interactions. Direct measurements of m t at Tevatron are essential for the EW fit. Direct measurements of V tb will come from single top. A direct measurement of y t from tth at LHC provided: m H < 200 GeV. V td ? V ts ? Still only indirectly. Z-t-t? Seems difficult at a hadron machine… (ttZ?) A TeV linear collider can tackle this at the < % level, and can improve on others such as mt (~100-200 MeV).

21. Supplementary Slides

22. Hadron Collider Physics, 6/15/04 Tim Tait 22 SU(2) 2 : Topflavor SU(2) 1 x SU(2) 2 x U(1) Y The usual SU(2) L is the diagonal combination. The SU(2) x SU(2) breaking occurs through a Higgs  which is a bi-doublet under both SU(2)’s. This model has been called “Topflavor”: a separate weak interaction for the 3 rd family. Chivukula, Simmons, Terning PRD53, 5258 (1996) Muller, Nandi PLB383, 345 (1996) Malkawi, Tait, Yuan PLB385, 304 (1996) Recently proposed to increase m h in the MSSM! Batra, Delgado, Kaplan, Tait, JHEP 0402,043 (2004)

23. Hadron Collider Physics, 6/15/04 Tim Tait 23 Hints from b Couplings? Choudhury, TT, Wagner, PRD65, 053002 (2002) 2.5  deviation If top is special, b, its EW partner, must be as well. Right-handed b couplings measured at LEP deviate from the SM at the ~ 3  level. Left-handed at ~ 2 . It has been argued that this goes beyond the statistical significance, because of the role of A b FB in m H fit. The “beautiful mirror” solution requires an extra top-like quark with mass < 300 GeV. Chanowitz PRL87, 231802 (2001)

24. Hadron Collider Physics, 6/15/04 Tim Tait 24 Phenomenology: H + Rare Top Decay: t H + b –Tevatron Run II (2 fb -1 ) : –LHC (100 fb -1 ): g b t H - at LHC! (100 fb -1 ): Breakdown of MSSM Higgs mass relation: Testable through pp A 0 H + at LHC (100 fb -1 ): Cao, Kanemura, Yuan hep-ph/0311083 Marcela + ~ 1 billion friends, hep-ph/0010338 CERN top Yellow Book, hep-ph/0003033 NLO: Berger, Han, Jiang, Plehn hep-ph/0312286Les Houches Higgs Report, hep-ph/0203056

25. Hadron Collider Physics, 6/15/04 Tim Tait 25 Tait, Yuan PRD63, 014018 (2001) SM like No W coupling No t coupling y t = -1 x y t SM Single Top + Higgs Very small in the SM because of an efficient cancellation between two Feynman graphs. Thus, a sensitive probe of new physics. Observable at LHC?