Single Top (And the Search for New Physics)

1. Single Top (And the Search for New Physics) Tim M.P. Tait Fermi National Accelerator Laboratory CTEQ Summer School Madison, Wisconsin 6/30/2004

2. Outline • Introduction: Why is single top important? • Production modes in the SM • Tools • Beyond the SM • Polarization • Summary Tim Tait

3. The King of Fermions! SM 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 the only fermion for which the coupling to the Higgs is important: it is a laboratory in which we can study EWSB. 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 (mt) determined by the coupling to the Higgs (yt). • 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: mt = ytv. • Couplings: gS and e are fixed by gauge invariance. The weak interaction has NC couplings, fixed in addition by s2W. CC couplings are described by Vtb, Vts, and Vtd. Tim Tait

5. Wm-t-bvertex: Left-handed! Why measure single top? • Single top is our primary means to measure top’s CC interactions. • If top indeed plays a special role in EWSB, we would expect its weak interactions would be the place in which we could realize that it is special. Thus, there is interest beyond t t production. • We know that top has a weak interaction, but not much beyond that. • This information comes from the decay, t W b. • However, because Gt is much smaller than experimental resolutions, it is very difficult to use the decay to measure the magnitude of the weak interaction. • Single top will be visible sometime in the next year(s) at run II! Tim Tait

6. CDF: CDF PRL86, 3233 (2001) Vtb >> Vts, Vtd SM: Vtb, Vts, Vtd • In the SM, the CC interactions are described by Vtb, Vts, and Vtd. • Vts and Vtd are measured indirectly from b physics. • Vtb can be constrained using unitarity. • This assumes the SM, with 3 generations. • Physics beyond the SM can easily modify these results (in a big way). • I.e. a Fourth generation PDG: http://pdg.lbl.gov/pdg.html Tim Tait

7. Overview: Single Top in the SM • Single top quarks are (dominantly) produced at hadron colliders through interactions involving a W boson and b quark. • Thus, rates are directly proportional to • At tree level there are three modes: • S-channel W exchange • Large rates at Tevatron run II, small at LHC. • T-channel W exchange • Dominant mode at Tevatron run II and LHC. • T W associated production • Very tiny at Tevatron run II, large rate at LHC. • At higher orders, these processes mix with each other and with QCD (t t) production combined with top decay. “time” Tim Tait

8. S-channel Mode: Basics • The s-channel mode proceeds through a virtual W boson, which “decays” into t b. The W-boson has time-like momentum. • Thus, it looks quite a bit like high mass e+n production. • The initial state is dominantly u d. This is why it is reasonably large at the Tevatron, but small at LHC. • Experimental Signature: W b b • Top decay: • W boson: Leptonic decay is very helpful with QCD backgrounds. • b jet: together with W, “reconstructs” mt. • b: Quite high pt. Very useful to tag it and thus remove backgrounds, mostly from t-channel mode. Stelzer, Willenbrock PLB357, 125 (1995) Tim Tait

9. S-channel Mode: Beyond LO • At NLO in aS, corrections look a lot like W production. (+ final state corrections). • The inclusive s has been known at NLO for some time. • Differential cross sections are also known at NLO. • Dominant (theoretical) uncertainties: • Top mass: dmt ~ ±5 GeV leads to: ds ~ ±6% • Scale variation: mtb/2 < m < 2 mtb leads to: ds ~ ±5% • PDFs are predominantly valence quarks; reasonably well known, ds ~ ±5% Smith, Willenbrock PRD54,6696 (1996) Mrenna, Yuan PLB416,200 (1998) Harris, Laenen, Phaf, Sullivan, Weinzierl, PRD 66 (02) 054024 Tim Tait

10. S-channel Mode: Polarization • Strong polarization between top spin and “d” quark direction: • This is a consequence of the vector particle exchange • At Tevatron, most d’s come from the anti-proton, implying the top spin correlates at almost 100% with the beam axis. • The helicity basis (or polarization along the direction of motion) is something like 80% in the SM. • This result doesn’t depend on the vector exchange, making the helicity basis an interesting means to study physics beyond the SM. • At the LHC, with no initial anti-proton, the helicity basis is thus still interesting. Mahlon, Parke PLB476 323 (2000); PRD55 7249 (1997) Tim Tait

11. T-channel Mode: Basics • The t-channel mode also proceeds through a virtual W boson, exchanged between a light quark line and a b. The W has space-like momentum. • Thus, it looks something like (“double”) deeply inelastic scattering. • The initial state is dominantly u b. This is why it is reasonably large at both Tevatron and LHC. • Experimental Signature: W b + forward jet • Top decay: • W boson: Leptonic decay is very helpful with QCD backgrounds. • b jet: together with W, “reconstructs” mt. • jet: Moderately high pt. It can be used as a tag to remove backgrounds. Dawson NPB249, 42 (1985) Dicus, Willenbrock PRD34,155 (1986) Yuan PRD41, 42 (1990) Tim Tait

12. T-channel Mode: Beyond LO • At NLO in aS, corrections look like DIS (times two). • The inclusive s has been known at NLO for some time. • Differential cross sections are also known at NLO. • Inclusive rate has resummed “W-gluon fusion” into “W-b fusion”. • Dominant (theoretical) uncertainties: • Top mass: dmt ~ ±5 GeV leads to: ds ~ ±3% • Scale variation: mt/2 < m < 2 mt leads to: ds ~ ±4% • PDFs include gluon/sea; not so well known, ds ~ ±7% Sullivan, Stelzer, Willenbrock PRD56, 5919 (1997) Harris, Laenen, Phaf, Sullivan, Weinzierl, PRD 66 (02) 054024 Tim Tait

13. T-channel Mode: Polarization • Strong polarization between top spin and “d” quark direction: • This is again a consequence of the vector particle exchange • For this process, the d’s are the forward ‘spectator’ jets, implying the top spin correlates at almost 100% with the jet direction. • The process b d t u pollutes this slightly. • The helicity basis is also very highly polarized in the SM: around 83%. Mahlon, Parke PLB476 323 (2000); PRD55 7249 (1997) Tim Tait

14. T W Mode: Basics • The third mode has an on-shell W boson. • Like the other two modes, it is proportional to |Vtb|2. • The fact that the W is real and observable makes it interesting as a direct probe of the W-t-b vertex, with less worry that new physics may be contributing. • The initial state is dominantly g b. This, and the heavy final state, is why it so tiny at Tevatron, but considerable at LHC. • Experimental Signature: W+ W- b • Top decay: • W+ boson: Leptonic decay is very helpful with QCD backgrounds. • b jet: together with W, “reconstructs” mt. • W-: It can be used to remove some QCD backgrounds, but makes the events overall look a lot more like t t, which is huge at the LHC. Tait PRD61, 034001 (2000) Belyaev, Boos, PRD63, 034012 (2001) Tim Tait

15. T W: Beyond LO • Total rate “known” at NLO. • Missing q q initial states. • At NLO, this process mixes with t t followed by top decay. • Uncertainties: • Scale (mt + mW)/2 < m < 2(mt+mw): ds ~ ±5% • PDFs: ds ~ ±10% • Polarization is very complicated, with no known basis resulting in high top polarization. Zhu, hep-ph/0109269 NLO LO Tim Tait

16. t-channel t-channel s-channel LHC t W s-channel t W Single Top in the SM Any day at Run II! Run II Sum of top and anti-top. CDF PRD65, 091102 (2002) DØ PLB517, 282 (2001) Tim Tait

17. W Polarization This is a direct test of the left-handed nature of the W-t-b vertex. SM: Left-handed interaction implies that W’s are all left-handed or longitudinal. SM: Depends onmt & mW: lW correlated with the direction of pe compared with the direction of pb in the top rest frame. The W polarization is independent of the parent polarization. Thus, it is a good test of W-t-b and can be measured with large statistics from QCD production of top pairs. DØ: CDF: CDF PRL84, 216 (2000) DØ hep-ex/0404040 W Polarization Tim Tait

18. top anti-top Top Polarization • Top Polarization • Single tops have close to 100% polarization for the correct choice of basis. Even the helicity basis makes an interesting prediction. • t polarization correlates with pe: Tim Tait

19. Tools • Pythia (Herwig) • Leading order, no polarization. • S-channel in Pythia: kludged together • Probably best used in tandem with MADevent or COMPhep • ONETOP • Leading Order; interfaced with Pythia • All processes, including polarization • ZTOP • Next to leading order (differential) s- and t-channels, no polarization coded. • Publicly available soon. • MCFM • Next to leading order (s- and t-), leading order tW. • Version coming soon including single top processes. • Will include final state radiation off of top. Tim Tait

20. How to Make Single Tops BEYONDthe Standard Model Tim Tait

21. Counting Dimension  H, Vm m : 3/2 : 1 : 1 New Interactions • A model independent way to study new physics is provided by effective Lagrangians, adding interactions beyond those in the SM. • The SM already contains all renormalizable interactions (with couplings of mass dimension 4 or less); we must include non-renormalizable terms. • Couplings for ‘higher dimensional’ operators have negative dimension so that the Lagrangian stays at dimension 4: • This theory makes sense as an expansion in energy. Observables depend on En / Ln, so provided E << L, the expansion makes sense. • Gauge symmetries of the Standard Model such as SU(3) invariance, etc. are still respected by the new interactions. • They can be understood as residual effects from very heavy particles. Tim Tait

22. Nonstandard Top Interactions • Top may couple in a funny way to strange, down, or bottom: • All of these modify all three single top rates. • But aren’t these operators dimension 4? • Yes, but their SU(2)xU(1) description was dimension 6! • Top may have FCNC’s with up or charm and Z/g/g: These new interactions can arise in many models. They lead to new single top modes, top decays, and more exotic processes … Tim Tait

23. s s s s s-channel: over-all rate unchanged, but now we produce ts 1/3 of the time. t-channel and tW: The rates themselves change, because now there is significant production from an initial state strange quark, with a larger probability than bottom to be found at high x in the proton. But we needed to tag the b quark to see the s-channel at all! New Charged Interactions • As my first case, I turn on the W-t-s coupling: • To be perverse, at the same time I turn on a negative W-t-b: • I chose this because it looks like the SM with a funny CKM matrix: • Clearly, all three single top cross sections change: Tim Tait

24. FCNC Interactions • As a second example, consider a FCNC interaction of Z-t-c: • We could have chosen Z-t-u, instead (or as well). Note left- and right-handed versions – influence polarization! • New s-channel and tZ modes: • …which won’t be counted by the usual single top analyses, because there is no extra b or W. • T-channel mode: • Like the W-t-s story, takes advantage of larger c content of proton compared to b. t Z s-channel t-channel Tim Tait

25. Charged Resonances • A charged resonance (which couples to t and b) can mediate single top production in the same way the W boson does in the SM. • In many theories (I’ll show a couple in a moment), such objects prefer to couple to the third generation, which makes top a particularly good place to look for them. • Generically, I will refer to a scalar of this type as a “charged Higgs” and a vector of this type as a W’. • These clearly affect the s- and t-channel rates, and turns on new processes (tW’ and tH-) analogous to tW. • First let’s run through some models which contain these objects, then see what they do to single top. Tim Tait

26. W’ : “ Topflavor ” SU(2)1 x SU(2)2 x U(1)Y • Generically, W’ bosons come from extending the EW gauge sector to include new forces. • The usual SU(2)L is the diagonal combination. • The SU(2) x SU(2) breaking occurs through a Higgs S, which is a bi-doublet under both SU(2)’s. • This model has been called “Topflavor”: a separate weak interaction for the 3rd family. Extra SU(2) group contains additional W and Z bosons! Recently proposed to increase mh in the MSSM! Chivukula, Simmons, Terning PRD53, 5258 (1996) Muller, Nandi PLB383, 345 (1996) Malkawi, Tait, Yuan PLB385, 304 (1996) Batra, Delgado, Kaplan, Tait, JHEP 0402,043 (2004) Tim Tait

27. Charged Higgs: H+ • In the SM, the Higgs doublet contains a pair of charged scalars, and two (real) neutral scalars. • However, after EWSB, the charged and one of the neutral scalars are “eaten”: they come become the longitudinal W and Z bosons. • The one remaining boson is the Higgs particle. • In a theory with extra Higgs doublets, there will be more “left-overs” which become physical Higgses. • For example, in a model with two Higgs doublets (as minimal SUSY models for example), there will be a pair of charged Higgses, and three neutral Higgs after EWSB. • Because the fermion masses come from interactions with the Higgs, the 3rd generation (and top particularly) generically couples much more strongly. For example in SUSY: Tim Tait Right-handed coupling!

28. Top Pion: p+ • Charged Higgs-like objects also occur in theories with dynamical electroweak symmetry-breaking. • As an example, let’s consider Topcolor-assisted-Technicolor (TC2). • Technicolor works pretty well to generate W/Z masses, but has problems with the large top mass. Generic solutions aren’t consistent with precision EW data. • To help technicolor out with the top mass, Chris Hill introduced a new force which was an SU(3) ‘color’ interaction which only top feels. • This force adds some extra EWSB by forming a Higgs doublet as a bound state of top quarks. This extra EWSB couples strongly to top, and provides a large mass. • This again looks something like a two Higgs doublet model. The extra scalars are expected to be among the lightest of the new states. • They couple strongly to top by construction, and very weakly to other fermions. • Their phenomenology is very similar to the charged Higgs of SUSY. Tim Tait

29. How does H± affect single top? S-channel mode: the intermediate particle is time-like, and can go on-shell. Large enhancements are possible, provided there is enough energy. T-channel mode: the particle is space-like and never goes on-shell. The extra contribution to the cross section is always very tiny. He, Yuan PRL83,28 (1999) p± /H± s > 0! t < 0! Tim Tait

30. W’ • We can repeat a similar analysis for the W’. • The s-channel process can show a large enhancement if there is enough energy for the W’ to be produced on-shell. • The t-channel mode shows no large enhancement, because the additional cross section is suppressed by the heavy mass. • The topflavor W’ has left-handed couplings, and thus does not alter the expectations for top polarization compared to the SM. Sullivan hep-ph/0306266 Simmons, PRD55, 5494 (1997) Tim Tait

31. s-channel Mode Smaller rate Extra b quark final state ssa |Vtb|2 in SM Sensitive to resonances Possibility of on-shell production. Need final state b tag to discriminate from background: no FCNCs. t-channel Mode Dominant rate Forward jet in final state sta |Vtb|2 in SM Sensitive to FCNCs New production modes. t-channel exchange of heavy states always suppressed. s- Versus t-Channels Tim Tait

32. All Together • We have seen how the s-channel mode is sensitive to charged resonances. • The t-channel mode is more sensitive to FCNCs and new interactions. • The tW mode is a more direct measure of top’s coupling to W and a down-type quark (down, strange, bottom). • From a theoretical point of view, they teach us different things. • From an experimental point of view, they have different signatures and different systematics. • Even in the SM, they can be used together in a helpful way: Vtb • Each rate is a different quantity proportional to |Vtb|2 • They provide an important cross-check on Vtb even in the SM. • Of course, if there is new physics in single top production, the fact that each mode responds differently can already give us a hint as to what form the new physics takes, even before we see it manifest clearly. Tim Tait

33. Tait, Yuan PRD63, 014018 (2001) ss-st Plane Theory + statistical (2 fb-1) 3s deviation curves Run II LHC Tim Tait

34. More Exotic Stuff Tim Tait

35. SM like No W coupling No t coupling yt = -1 x ytSM Tait, Yuan PRD63, 014018 (2001) 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? Tim Tait

36. R-parity Violating SUSY • In SUSY theories, if R-parity is violated, super-partners can contribute at tree level to SM processes such as single top. • Such interactions generally lead to p decay, constraining their size. • However, for the 3rd family such bounds are much weaker. • In this example, there is s-channel stop ‘production’ followed by decay into top through R-conserving interactions into neutralino and top. Berger, Harris, Sullivan PRD63,115001 (2001) Tim Tait

37. R-parity II: Slepton Exchange R-parity violating interactions which Violate lepton number can produce Single tops through exchange of the Super-partners of leptons (sleptons) In either the s- or t- channels. Oakes, Whisnant, Yang, Young, Zhang PRD57, 534 (1998) Tim Tait

38. Summary • 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. • Single top production will most likely be observed within a year. This will be the first direct measurement of top’s weak interactions. • There are three modes: s-channel, t-channel, and associated production with a W. All three are a measure of top’s CC weak interactions. • S-channel mode: appreciable at run II, sensitive to new charged resonances. • T-channel mode: dominant at run II and LHC, sensitive to non-standard couplings of top. • tW mode: only visible at LHC, largely sensitive only to top’s CC weak interactions. • SM makes definite predictions for spin, and they can be tested. • It will be exciting to learn the TRUTH about top! Tim Tait

39. Supplementary Slides

40. Measurements • How well are these quantities known? • gS, e, and s2W are well known (gS at per cent level, EW couplings at per mil level) from other sectors. • mt is reconstructed kinematically at the Tevatron: • Run I: mt = 178 ± 4.3 GeV • Run IIb: prospects to a precision of ± 2 GeV (systematic). • Vtd, Vts, and Vtb are (currently) determined indirectly: • Vtd: 0.004 – 0.014(< 0.09) • Vts: 0.037 – 0.044(< 0.12) • Vtb: 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. • Vtb can be measured directly from single top production. PDG: http://pdg.lbl.gov/pdg.html Tim Tait

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

42. 2.5 s deviation Hints from b Couplings? • 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 s level. • Left-handed at ~ 2 s. • It has been argued that this goes beyond the statistical significance, because of the role of AbFB in mH fit. • The “beautiful mirror” solution requires an extra top-like quark with mass < 300 GeV. Chanowitz PRL87, 231802 (2001) Choudhury, TT, Wagner,PRD65, 053002 (2002) Tim Tait

43. More Phenomenology of H+ Marcela Carena + ~ 1 billion friends, hep-ph/0010338 • 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 A0H+ at LHC (100 fb-1): CERN top Yellow Book, hep-ph/0003033 NLO: Berger, Han, Jiang, Plehn hep-ph/0312286 Les Houches Higgs Report, hep-ph/0203056 Cao, Kanemura, Yuan hep-ph/0311083 Tim Tait

44. 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. Tim Tait

45. P. Azzi, hep-ex/0312052 LHC: stt~850 ± 100 pb tt is a major background to many new physics searches (i.e. Higgs). 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 m. Tim Tait

46. 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: • TC2, Top Seesaw: top gluons • TC2, Topflavor: Z’ • Search strategy: resonance in tt. • Tevatron: up to ~ 850 GeV. • LHC: up to ~ 4.5 TeV. 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) Future EW Physics at the Tevatron, TeV-2000 Study Group Tim Tait

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

48. CDF: CDF PRL86, 3233 (2001) Vtb >> Vts, Vtd 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: gm (1 - g5). • 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 Gt >> LQCD. This makes top the only quark which we see “bare” (in some sense). • Top spin “survives” non-perturbative QCD (soft gluons). Tim Tait

49. 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 cg, t cg, etc… Solid lines: assume ktcg = 0.78 Dashed lines: assume no t-c-g Top Physics, hep-ph/0003033 Tim Tait

50. 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! Harris, Laenen, Phaf, Sullivan, Weinzierl, PRD 66 (02) 054024 Tait, PRD 61 (00) 034001; Belyaev, Boos, PRD 63 (01) 034012 Run I Limits < 13.5 pb < 12.9 pb CDF PRD65, 091102 (2002) DØ PLB517, 282 (2001) Tim Tait Now in MCFM!