Truth (Top Theory Lecture)

Truth Truth (Top Theory Lecture)(Top Theory Lecture)

Timothy M.P. TaitTimothy M.P. Tait

Argonne National LaboratoryArgonne National Laboratory

Heavy Flavor Physics8/13/2005

Heavy Flavor Physics, 8/13/05 Tim Tait 2

Outline of LecturesI. Introduction and Motivation

I. Top in the Standard Model

II. Top beyond the Standard Model

II. Top Decay

III. Top at e+e- Colliders

IV. Top at Hadron CollidersI. QCD Production of Pairs of Tops

II. Single Top Production

Please feel free to stop me for questions at any time!

Lecture I

Motivation for Studying Top


Outline

• Introduction: Why is top interesting?

• Top in the Standard Model– Definition– Role

• Top Beyond the Standard Model?– MSSM– Topcolor– Composite Top


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 FermionsSM Fermions


Top in the SM

. .

1

62

3

i i

i j

t

a nS ij W

aY

aS

i i

i j i

i i

ij Yi

i

n

a

L i i y H c

ig T ig

t D t t

D t t t

Q D H

G W B

G t

Q Q

D Q Q Q Q Qi g

i T i g Bg

In 4 component notation:

iL

i iL

i

iL

iR

i

R

tt

Qb

t

tt

=1: top

=2: bottom

Top is two separate objects:A left-handed quark doublet.A right-handed quark singlet.

i: color index

H: Higgs (doublet)G: gluonsB,Wn: W±, Z,


Feynman Rules• From the Lagrangian we can read off the SM Feynman rules involving top.

– Gauge bosons:

– Higgs:

t b t t

W+

sin LW

ei P

2

3i

e aijSgi T

2 2

sin cos

sin1 2 2

n2 3 3

si

W W

W WL RP

ei

P

t

t

H

i

j

a

vti

m


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 = yt v.

• Couplings: gS and e are fixed by gauge invariance. The weak interaction has NC couplings, fixed in addition by s2

W. CC couplings are described by Vtb, Vts, and Vtd.


Measurements• How well are these quantities known?• gS, e, and s2

W 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


LEP EWWG

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 (T).

– The one loop corrections are so sensitive to the top mass that precision measurements at LEP/SLD could predict mt before top was observed at Tevatron.

– Once mt was directly measured, could look for subdominant effects like from the Higgs.

+

b

bb

-Z Z Z Z W W

2 2

2

216 sin cosc

W W

t

Zm

mN


• Flavor Physics:

–

–

Top’s Role in the SM

sB X

2.302

52BR( ) 4.1 10

170 GeVc

ts t t

b

s

V

V

mB X

m

2 3.12

9BR( ) 4.18 100.04 170 GeV

tss

t tV m mB

sB Buchalla, Buras, Lautenbacher RMP68,1125 (1996)

b

t

s

W

Z

W

i.e.:

Top’s large mass disrupts the GIM mechanism!

Precision inputs from the top sector for precision SM predictions.


Higgs Physicst

The large top mass meansa 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 Higgsand gluons. Despite being loop suppressed, this process dominates Higgs production at the LHC!

Top also contributes to the Higgs coupling to two photons.

Top Beyond the SM


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 v2 can’t be much bigger than M2W and M2

Z.

• 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.

vWM g 22 2vV


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.

2

22

16 GUTMg

20

22

22 ...

16v v GUT

gM


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!

~


SUSY Light Higgs Mass• The MSSM has two Higgs doublets.• In the SM, the Higgs quartic is a free parameter. The

physical Higgs mass is mh2 = v2.

• Remarkably, in the MSSM is not a free parameter:

• This results in a tree-level prediction for mh:

• This is corrected at one-loop by top/stop:

2 2 22cos 2h Zm v M

4

2

22

2 2

3log stop mixing

8t

t

th

m

v mm

m

2 2 2W Yg g


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.

( ) 115 GeVSMhm


• Most importantly, the MSSM only survives the LEP-II bound on mh because of the large yt:

• (mt < 160 GeV rules out MSSM!)

Heinemeyer et al, JHEP 0309,075 (2003)

• 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

Top Sector and SUSY


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 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)

A way to escape the bound on mh

in the MSSM is to add new gaugeinteractions – but new interactionsfor the Higgs usually means newInteractions for top too!


Top-color: Composite Higgs• 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 () 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.

2 2

2 2

22 *

TC TC

TC TC

TC TC TC

t t tQ Q Qg g

M M

M g

Q

QtgtQ

t

22 2 2

2...

8c TC

TC TC

N gm M M

W Bardeen, C Hill, M Lindner PRD41,1647 (1990);

C Hill PLB345,483 (1995)


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 (R).

• Now the large “mass” is just an off-diagonal entry in the mass matrix:

• By tuning the new parameters M and Mt, one fits the correct top mass, despite the much larger entry demanded by the Z mass.

B Dobrescu, C Hill PRL81, 2634 (1998)

t

0 ~ 250GeV

M MR

L LR

tt


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

Lecture II

Top Decays


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 (e, , , 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:

: : : : : :( ) ( ) ( ) 1 1 1( jets) 6BR W e BR W BR W BR W


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).

τ+X21%

μ+jets15%

e+jets15%

e+e1%

e+μ2%

μ+μ1%

jets45%

CDF:

2

0.310.242 2 2

BR( )0.94

BR( )t

td tts

b

b

Vt Wb

t Wq VV V

CDF PRL86, 3233 (2001) Vtb >> Vts, Vtd

I Bigi


W Polarization• 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 on mt & mW:

– W 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 structure and can be measured with large statistics from QCD production of top pairs.

2

0 2 2

# longitudinal W's

Tota70%

l # W's 2t

W t

m

M mf

DØ: 0 0.56 0.31 0.04f

0 0.91 0.37 0.13f CDF:

CDF PRL84, 216 (2000)DØ hep-ex/0404040


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:

top

anti-top

2

2 2

2

2 2

2

L e b L tW W

b R e L tW W

tb

tb

gu P u u P u

p M

gu P u u P u

p M

V

V

M


Decay into H+b• 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:

Tevatron Run II Higgs Report,hep-ph/0010338

+ cot

v- - coupling :

at

tH

v

nb R L

t bPm m

P

Run I

Run II (2 fb-1)

At high tan , H+ decays to .At low tan , H+ decays to cs.1

2

tanH

H


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-

32

2

1( )

2cos

v

RW

t

t

Zc

Ztc

Q tg

W H c Z c

m

Top Physics, hep-ph/0003033

t

Current Bounds:

Lecture III

Top at e+e- Colliders


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.

Coordinates:

azimuth

Beam

Scattering angle

z-axis

transverse direction

TESLA


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 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

t

t


Threshold Scan• 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 S(mt).

• The threshold turn-on is known to NLO in QCD.

• Combined with the top pT distribution, the mass and S can be disentangled.

Curves: mt±100 MeV

Tesla TDR

A Hoang, T Teubner PRD58, 114023 (1998)


Threshold Scan: Fit

mt can be measured to about 100 MeV.

Tesla TDR


ttH

• 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.

Tesla TDR

Mh = 120 GeV

Juste, Merino hep-ph/9910301

√s = 800 GeV

Lecture IV

Top at Hadron Colliders


Hadron Colliders• 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.

Fermilab

z-axis

Coordinates:

azimuth

Beam

rapidity y

log z

z

E py

E p


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 2 / 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.

1 21 2 / /1 2

,1 2 ˆ( ) a H

ab H

b

H H f fX dF x dx Xa Fx x b


PDFs

LHCTevatron


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.


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 pbtt is a major background to many new physics searches (i.e. Higgs).


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.


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 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)

2 * *

2 2 *

sin costan

1 sin


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 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.

+

-

Spin-up and spin-down (top) are inferred using

the direction of the e from the top decay.

is the angle between the e and the t spin-axis.

cos

-1 0 1

Spin-down

Spin-up

tbar spin is mostly:

spin-up spin-down


Top Yukawa Couplingv

1MStMS

t

My

WWH

bbH

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 mt itself: a few %.– Higgs radiated from tt pair is probably the best bet.

• LHC: yt to about 10-15% for mh < 200 GeV.

NLO: Dawson, Jackson, Orr, Reina, Wackeroth, PRD 68, 034022 (2003)


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.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)

Single Top Production


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 t 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!

32

...8 2

ttF t

b

mV

G

W-t-b vertex:

512

tbgV Left-handed!


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

CDF:

2

0.310.242 2 2

BR( )0.94

BR( )t

td tts

b

b

Vt Wb

t Wq VV V

CDF PRL86, 3233 (2001) Vtb >> Vts, Vtd

PDG: http://pdg.lbl.gov/pdg.html

0.9739 0.9751 0.221 0.227 0.0029 0.0045

0.221 0.227 0.9730 0.974

0.0370.0048 0.014 0.9990 0.9

4

0

0.039 0.0

.043

4

9

4

9 2

0.9730 0.9746 0.2174 0.2241 0.003 0.0044

0.213 0.226 0.968 0.975 0.03

0.07 00.0 .8

9 0.

0 9993

044

.11

2† 2 21 1ub cb tbV VV V V


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.

2

tbV“time”


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+ 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.

2 2*

2 2

/ 2W W

W udud d L u t L b t R d u L b

W W

tbtb

g p p M g VgV u P u g u P u u P u u P u

M M

V

s sV

Stelzer, Willenbrock PLB357, 125 (1995)


S-channel Mode: Beyond LO• At NLO in S, corrections look a lot like W production. (+ final state corrections).

• The inclusive has been known at NLO for some time.

• Differential cross sections are also known at NLO.• Dominant (theoretical) uncertainties:

– Top mass: mt ~ ±5 GeV leads to: ~ ±6%

– Scale variation: mtb/2 < < 2 mtb leads to: ~ ±5%

– PDFs are predominantly valence quarks; reasonably well known, ~ ±5%

Harris, Laenen, Phaf, Sullivan, Weinzierl, PRD 66 (02) 054024

Smith, Willenbrock PRD54,6696 (1996)

Mrenna, Yuan PLB416,200 (1998)


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) 2

2

2 udt R d u L

tbb

W

g Vu P

su u P u

M

V


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.


– jet: Moderately high pt. It can be used as a tag to remove backgrounds.

2 2*

2 2

/ 2W W

W udud d L u t L b t R d u L b

W W

tbtb

g p p M g VgV u P u g u P u u P u u P u

M M

V

t tV

Dawson NPB249, 42 (1985)Dicus, Willenbrock PRD34,155 (1986) Yuan PRD41, 42 (1990)


T-channel Mode: Beyond LO• At NLO in S, corrections look like DIS (times two).• The inclusive 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: mt ~ ±5 GeV leads to: ~ ±3%– Scale variation: mt/2 < < 2 mt leads to: ~ ±4%– PDFs include gluon/sea; not so well known, ~ ±7%

Harris, Laenen, Phaf, Sullivan, Weinzierl, PRD 66 (02) 054024

Sullivan, Stelzer, Willenbrock PRD56, 5919 (1997)


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)

2

2

2 udt R d u L

tbb

W

g Vu P

tu u P u

M

V


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.


– 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)


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 < < 2(mt+mw): ~ ±5%

– PDFs: ~ ±10%

• Polarization is very complicated, with no known basis resulting in high top polarization.

LO

NLO

Zhu, hep-ph/0109269


t-channel

t W

s-channel

LHC

t-channel

s-channel

t W

Single Top in the SM

Any day at Run II!

Run I LimitsTevatron

Run IILHC

t (NLO) < 13.5 pb 1.98±0.13 pb 247±12 pb

s (NLO) < 12.9 pb 0.88±0.09 pb 10.7±0.9 pb

tW (LL) 0.09±0.02 pb 56±8 pb

Total 2.95±0.16 pb 314±15 pbCDF PRD65, 091102 (2002)DØ PLB517, 282 (2001)

Run II

Sum of top and anti-top.


Tools• Pythia (Herwig)– Leading order, no polarization.– S-channel in Pythia: kludged together– T-channel kinematics not very well represented– 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.


How to Make Single Tops

BEYOND

the Standard Model


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 / n, so provided E << , 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.

Counting Dimension

H, V

: 3/2: 1: 1

3/ 2 3/

dimensiondimension

2 1

0 4

Vg

3/ 2 3/ 2 3

dimension -2

2

dimension 6

/ 2 3/ 2

1


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/:

. .2

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dL

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S R Li

R L

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†

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Wts

WtsL

DH H Q Q

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These new interactionscan arise in many models.They lead to new single top modes, top decays,and more exotic processes …


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:

0.9745 0.224 0.0037 0.9745 0.224 0.0037

0.224 0.9737 0.042 0.224 0.9737 0.042

0.008 0.00.040 0.0.9991 0.83508 55SM Effective

0.41WtsL

0.164WtbL

s-channel: over-all rate unchanged, but now we produce t s 1/3 of the time.

s

t-channel and tW: The rates themselves change, because now thereis significant production from an initial state strange quark, with alarger probability than bottom to be found at high x in the proton.

s

s

s

But we needed to tag the b quark to see the s-channel at all!


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).

. .cos R L

W

Ztc ZtcR L

gt c t cP cZP h

• 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.

Note left- and right-handedversions – influence polarization!

s-channel

t-channel

t Z


New Particles• 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 (t W’ and t H-) analogous to t W.

• First let’s run through some models which contain these objects, then see what they do to single top.


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:

+ cot

v- - coupling :

at

tH

v

nb R L

t bPm m

P

Right-handed coupling!


Top Pion: +

• 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.


• 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.

± / H±

He, Yuan PRL83,28 (1999)

2

2

H H

H

Hs M M

g

i

M

2

2

H

H

t M

g

M

s > 0!

t < 0!


W’

Sullivan hep-ph/0306266

Simmons, PRD55, 5494 (1997)

• 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.


s- Versus t-Channels• s-channel Mode

– Smaller rate– Extra b quark final state

– s |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

– t |Vtb|2 in SM

• Sensitive to FCNCs– New production modes.– t-channel exchange of

heavy states always suppressed.


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.


Tait, Yuan PRD63, 014018 (2001)

s-t Plane

Run II

LHC

Theory + statistical (2/100 fb-1) 3 deviation curves


More Exotic Stuff


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)


R-parity II: Slepton ExchangeR-parity violating interactions whichViolate lepton number can produceSingle tops through exchange of theSuper-partners of leptons (sleptons)In either the s- or t- channels.

Oakes, Whisnant, Yang, Young, Zhang PRD57, 534 (1998)


Tait, Yuan PRD63, 014018 (2001)

SM likeNo W couplingNo t couplingyt = -1 x yt

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?


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.– Many models predict special properties for top.

• Top decays into Wb in the SM. Rare decays would be a clear sign of physics beyond the SM.

• e+e- Colliders can measure properties of top precisely.• Hadron colliders

– Single top production will most likely be observed within a year. This will be the first direct measurement of top’s weak interactions.

– QCD Production of t tbar pairs is a good place to look for new resonances, and a test of the strong interactions of top.

– SM makes definite predictions for spin, and they can be tested.• It will be exciting to learn the TRUTH about top!

Truth (Top Theory Lecture)

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Transcript of Truth (Top Theory Lecture)