Truth (Top Theory Lecture)

1. Truth (Top Theory Lecture) Timothy M.P. Tait Argonne National Laboratory Heavy Flavor Physics 8/13/2005

2. Outline of Lectures • Introduction and Motivation • Top in the Standard Model • Top beyond the Standard Model • Top Decay • Top at e+e- Colliders • Top at Hadron Colliders • QCD Production of Pairs of Tops • Single Top Production • Please feel free to stop me for questions at any time! Tim Tait

3. Lecture I Motivation for Studying Top

4. Outline • Introduction: Why is top interesting? • Top in the Standard Model • Definition • Role • Top Beyond the Standard Model? • MSSM • Topcolor • Composite Top Tim Tait

5. 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 only fermion for which the coupling to the Higgs is important: it is a laboratory in which we can study EWSB. Tim Tait

6. a=1: top a=2: bottom Top in the SM i: color index Top is two separate objects: A left-handed quark doublet. A right-handed quark singlet. H: Higgs (doublet) G: gluons B,Wn: W±, Z, g Tim Tait

7. Feynman Rules • From the Lagrangian we can read off the SM Feynman rules involving top. • Gauge bosons: • Higgs: i t b t t j W+ a t t H Tim Tait

8. 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

9. 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

10. Top’s Role in the SM • Precision EW Physics: • The large top-bottom mass splitting is a strong violation of a custodial SU(2) symmetry (interchanging tR and bR) • This results in large corrections to Dr(DT). • The one loop corrections are so sensitive to the top mass that precision measurements at LEP/SLD could predict mtbefore top was observed at Tevatron. • Once mt was directly measured, could look for subdominant effects like from the Higgs. b Z Z Z Z W W + - b b LEP EWWG Tim Tait

11. Flavor Physics: t b s W W Z Top’s Role in the SM i.e.: Buchalla, Buras, Lautenbacher RMP68,1125 (1996) Precision inputs from the top sector for precision SM predictions. Top’s large mass disrupts the GIM mechanism! Tim Tait

12. Higgs Physics t The large top mass means a strong coupling to the Higgs. Thus, several mechanisms of Higgs production rely on Top. One in particular takes advantage of the fact that top is colored. Loops of top quarks mediate an interaction between Higgs and gluons. Despite being loop suppressed, this process dominates Higgs productionat the LHC! Top also contributes to the Higgs coupling to two photons. Tim Tait

13. Top Beyond the SM

14. Hierarchy Problem • The Standard Model is only an effective theory. We know it should break down and we expect this will happen at energies of order the TeV scale. • Let’s remind ourselves how this works. • The Higgs potential has a dimensionful (“mass”) term and dimensionless (“quartic”) term: • The Higgs VEV, and thus the W/Z masses are linearly related to v. • So lv2can’t be much bigger than M2W and M2Z. • Now imagine that there is some heavy physics that couples to the Higgs. • Heavy gauge bosons left-over from a GUT theory. • Right-handed neutrino needed in the seesaw theory of neutrino masses. • These examples couple to the Higgs directly. • All particles couple to it through gravity. Tim Tait

15. Naturalness • So what does this hypothetical heavy particle do to v2? • It corrects it through loops. At one loop, in the specific case of a GUT gauge boson, the correction looks like: • The GUT scale has appeared as the mass of the vector boson. • In perturbation theory, the v2 measured in experiments (for example, when we measure MW at LEP or CDF) is the sum of the tree level piece plus all of the higher order corrections: • Here we see the issue: the loops should be small, but if the masses that go into the loops are large, then they are huge. • But we don’t know what the tree-level piece (v02) was… • Unless it is of the same order as v2 itself, this will be a fine-tuned cancellation, asking for something to explain it. Tim Tait

16. Supersymmetry • Supersymmetry is the best-motivated and best-studied solution to the hierarchy problem. • The super-partners cancel exactly the big contributions to v2. • As an added bonus, most SUSY theories contain a lightest super-partner which is neutral and stable – a dark matter candidate! • New sources of CP violation and extra DOF can lead to EW baryogenesis! • SUSY has a lot of model parameters (all related to how we break it). • We have some theoretical guidance as to the rough features, but even those arguments aren’t infallible. • Many ideas for SUSY-breaking are on the market: • SUGRA: Gravity mediates SUSY breaking to the MSSM super-partners. • GMSB: Gauge interactions mediate SUSY breaking – a nice solution to the flavor problem. • AMSB: SUSY breaking is transmitted via the super-Weyl anomaly. • gMSB: Extra dimensional gauge interactions transmit SUSY breaking. • “Orbifold SUSY breaking”: SUSY breaking by boundary conditions in an extra dimension. • ???? : Theorists are constantly looking for new ways to mediate SUSY breaking! ~ Tim Tait

17. SUSY Light Higgs Mass • The MSSM has two Higgs doublets. • In the SM, the Higgs quartic l is a free parameter. The physical Higgs mass is mh2 = lv2. • Remarkably, in the MSSM l is not a free parameter: • This results in a tree-level prediction for mh: • This is corrected at one-loop by top/stop: Tim Tait

18. LEP II • LEP II rules out • The boundary on the right is the MSSM upper limit, assuming M~1 TeV and maximal stop mixing. • The dashed curves are hypothetical exclusions assuming only SM backgrounds. • The MSSM lives in the white sliver. Tim Tait

19. 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

20. SU(2)2: Topflavor A way to escape the bound on mh in the MSSM is to add new gauge interactions – but new interactions for the Higgs usually means new Interactions for top too! 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 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. 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

21. Top-color: Composite Higgs W Bardeen, C Hill, M Lindner PRD41,1647 (1990); C Hill PLB345,483 (1995) • Why is the top so heavy? Top-color tries to answer this by proposing that the Higgs is actually a bound state of top quarks. • It solves the hierarchy problem because there are no fundamental scalar particles. • A new strong force (top-color) forms the Higgs (F) as a bound state of top. • Top is heavy because the Higgs “remembers” that it is made out of top quarks – and couples strongly to them through the top-gluons (g’). • If gTC is large enough, one loop corrections drive the Higgs mass2 negative, triggering EWSB. • However, gTC is also the top Yukawa coupling; to get the right Z mass, yt ~ 1.4 and mt~250 GeV. That is why TC needs to be supplemented with technicolor or a top seesaw to be viable. Tim Tait

22. B Dobrescu, C Hill PRL81, 2634 (1998) Top Seesaw • Top condensation models attempt to explain EWSB and the heavy top by having a Higgs which is a bound-state of top quarks. Top is heavy because the Higgs has a residual strong interaction with its fermion components. • The hierarchy problem is solved because above the condensation scale, there are no fundamental scalar degrees of freedom. • However, the minimal model predicts a top mass which is larger than 250 GeV, in contrast the measured mt from the Tevatron of ~ 175 GeV. • This is because one single interaction must drive EWSB (and thus fit the Z mass) and also produce the top Yukawa coupling. • A very interesting idea to relieve this tension is to have the Higgs be a bound state of tL and a vector-like right-handed top (hR). • Now the large “mass” is just an off-diagonal entry in the mass matrix: • By tuning the new parameters Mhh and Mht, one fits the correct top mass, despite the much larger entry demanded by the Z mass. Tim Tait

23. Composite Top? • A final exciting possibility is that the top as well as the Higgs may be composites of some confined group. • A (supersymmetric) example is the “Fat Higgs with Fat Top” model. • A strongly coupled SU(3) group (not color!) confines at a few TeV, and both the Higgs and the top are bound states of the underlying preons. • There is a residual of the strong coupling between the preons which results in strong coupling between the Higgs and the top quark. • At energies close to the confinement scale, top will stop looking like a point-like particle, and will instead be described by form factors and eventually break into preons. A Delgado, T Tait hep-ph/0504224 Tim Tait

24. Lecture II Top Decays

25. Top Decay: Basics • Top decays through the electroweak interaction into a W boson and (usually) a bottom quark. Decays into strange or down quarks are suppressed by the small CKM elements Vts and Vtd. It is extremely short-lived. • Top is the only quark heavy enough to decay into a real (on-shell) W boson. • The experimental signature is a jet containing a bottom quark and the W decay products. The W boson decays into all of its possible final states (en, mn, tn, or jets). • So we classify top decays by how the W boson decays. • The relative branching ratios are easy to predict just by knowing that the W couplings are universal, and that the light fermion masses are all so small compared to MW that we can ignore them. Further, the CKM elements are nearly diagonal, so counting three colors each of ud and cs, we have: Tim Tait

26. 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). CDF: CDF PRL86, 3233 (2001) Vtb >> Vts, Vtd I Bigi Tim Tait

27. 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 top polarization. Thus, it is a good test of the W-t-b vertex structureand 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

28. 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

29. Decay into H+b Tevatron Run II Higgs Report, hep-ph/0010338 Run II (2 fb-1) • In a theory with extra Higgs doublets, there will be more physical Higgs scalars. • For example, in a model with two Higgs doublets (as minimal SUSY models), 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: Run I At high tan b, H+ decays to tn. At low tan b, H+ decays to cs. Tim Tait

30. Rare Decays t • 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 Current Bounds: Tim Tait

31. Lecture III Top at e+e- Colliders

32. e+ e- Colliders • e+e- colliders are limited in energy compared to hadron colliders. To overcome losses from synchrotron radiation, future high energy lepton colliders will almost certainly be linear colliders. • However, e+e- machines present a very clean environment, and thus can be much more suited for precision physics. • LEP II reached energies slightly above 200 GeV. This was enough to produce a single top quark, though rates are too small in the SM to do so (and none were observed). • A future linear collider with energy ~ 1 TeV and ~ 100 fb-1 will study many aspects of top to an amazing precision. TESLA Coordinates: Scattering angle q azimuth f Beam z-axis transverse direction Tim Tait

33. Top Production • At energies greater than 2 mt, the dominant process for producing top is e+e- t tbar through off-shell photon or Z boson. • The cross section near threshold is of order 1 pb, so for 100 fb-1, one expects roughly 100,000 top pairs. • By determining the final spins of the top quarks, and by using polarized beams, the top couplings to the Z and g can be extracted for individual chiral operators. • These couplings can be measured to the level of a few per cent, and are difficult to measure at a hadron collider because of large QCD backgrounds. Tesla TDR Tim Tait

34. Threshold Scan A Hoang, T Teubner PRD58, 114023 (1998) • By scanning in energy close to the production threshold, one can precisely measure the top mass. • Though toponium states don’t really have time to form before top decays, they affect the shape of the turn-on and thus offer an opportunity to measure aS(mt). • The threshold turn-on is known to NLO in QCD. • Combined with the top pTdistribution, the mass and aS can be disentangled. Tesla TDR Curves: mt±100 MeV Tim Tait

35. Threshold Scan: Fit Tesla TDR mt can be measured to about 100 MeV. Tim Tait

36. ttH Tesla TDR • Higgs bosons may be radiated from top quarks. This offers a chance to measure the top Yukawa coupling directly from the rate of the process. • Theoretically, this process is known at NLO in QCD. • Experimentally, the results are known only for a single Higgs mass and decay channel into bb. • With large data samples on the order of 1000 fb-1, the H-t-t coupling can be measured to the level of a few percent. √s = 800 GeV Mh = 120 GeV Juste, Merino hep-ph/9910301 Tim Tait

37. Lecture IV Top at Hadron Colliders

38. Coordinates: rapidity y azimuth f Beam Hadron Colliders Fermilab • Hadron colliders can reach very large energies, and have played an important role in discovering heavy states (including top). • However, the large backgrounds from hadronic processes is a challenge when signals are small. • Further, the fact that we don’t know the partonic center of momentum frame makes it impossible to reconstruct the kinematics of an event exactly. • Currently, there are two machines of interest to top physics. • Tevatron Run II, at 2 TeV, already has collected about 500 pb-1 and expected to collect several fb-1. • LHC, expected to start in 2008 at 14 TeV, and to collect around 100 fb-1. z-axis Tim Tait

39. Hadro-production • At a hadron collider, we must reconcile the fact that what we have control over theoretically are scatterings of quarks and gluons (partons), but what we collide experimentally are hadrons. • The parton distribution functions (PDFs) are the bridge between hadronic initial states and partonic reactions. • Consider production of some final state F from initial hadrons H1 and H2: • The non-perturbative physics is contained in the functions f. These also contain all possible collinear emission of partons, resumming large logs to improve perturbation theory. • The factorization theorem implies that these functions are universal. So once we measure them in some process, we can compute any other process. (Higher order corrections in L2 / Q2 are usually tiny for processes involving top which have Q ~ mt). • Because they have resummed an infinite number of soft or collinear emissions, the cross sections derived from them are necessarily inclusive quantities. Tim Tait

40. PDFs LHC Tevatron Tim Tait

41. 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

42. 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

43. t t Production Rates • An impressive array of cross section measurements are performed across many top decay channels. • Measurements help to test & tune the variety of cutting edge QCD predictions on the market. Tim Tait

44. Top-Anti-top Spin Correlations • In the qq initiated sub-process, the spin of the top and the anti-top are correlated because the intermediate particle is a vector (gluon). • If the top were massless, this would result in perfect anti-alignment of the t and anti-t spins. • However, many tops are produced close to threshold, for which the helicity basis is not optimal. • In that case, the basis along the beam axis is better because it takes advantage of the (massless) q & qbar polarizations. • The correlations are maximized if one chooses to define the spin along the axis y defined by: • This interpolates between the two bases and results in the cleanest separation between spin-up and spin-down tops. G Mahlon S Parke PLB411, 173 (1997) Tim Tait

45. Spin Correlations • At LHC, the effect is completely washed out by the dominance of the gg initial state. • At Tevatron, q qbar dominates and the optimal basis results in a 92% spin correlation. • This result is intimately tied to the SM tt production mechanism. If there is physics beyond the SM in tt production, one could see it as a break-down of the expected distributions. • (However, because the y basis itself makes heavy use of the SM physics, it is difficult to use to identify the new physics). • To make practical use of it, one must further see how it is washed out by actual observables such as the direction of the charged lepton momentum in a top leptonic decay. tbar spin is mostly: spin-up spin-down Spin-down Spin-up -1 0 1 Tim Tait

46. 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

47. 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

48. Single Top Production

49. 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

50. 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