

 20 Sep 1996

CP VIOLATION IN TOP PHYSICS AT THE NLC

D. ATWOOD Theory Group, National Jefferson Lab,

A. SONI a Theory Group, Brookhaven National Laboratory, Upton, NY 11973

Top quark is extremely sensitive to non-standard CP violating phases. General strategies for exposing different types of phases at the NLC are outlined. SUSY phase(s) cause PRA in t ! W b. The transverse polarization of the o/ in the reaction t ! bo/* is extremely sensitive to a phase from the charged Higgs sector. Phase(s) from the neutral Higgs sector cause appreciable dipole moment effects and lead to sizable asymmetries in e+e

\Gamma ! t_tH0

and e+e

\Gamma ! t_t*

e_*e.

1 Introduction The standard model (SM) with three families and the CKM phase gives a natural explanation for the size of the observed CP asymmetry in the neutral kaon complex. It also strongly suggests the presence of large CP asymmetries in B-decays making B-physics very suitable for precision extraction of the CKM phase and a quantitative check of the unitarity triangle. Furthermore, the minimum SM with mt , 175 GeV ?? mb; md; ms also leads to the conclusion that CP violation effects in top production and decays have to be extremely small. However, extensions of the SM, invariably lead to new CP violating phase(s). Indeed in most extensions new CP violating phases appear rather naturally. In fact getting rid of non-standard phases in extensions of the SM may be as unnatural as it is to get rid of the CKM phase from the three generation SM. Since it is widely believed that the SM cannot account for baryogenesis CP violation from new physics is very likely a necessity. Therefore, it is important for us to seek optimal strategies to expose different types of non-standard CP violating phases. Based on studies that are so far available the prominent effects of different types of phases appears to be the following:

1. Dipole moment of the top quark could

be large enough, most effectively due to phase(s) from the neutral Higgs sector, to be experimentally accessible.1-4

aPresenter

2. SUSY phase(s) cause interesting partial rate

asymmetry (PRA) effects in decays of the type t ! W b.5-6

3. The transverse polarization of the o/ in the

decay t ! bo/ * is very sensitive to phase(s) originating from the charged Higgs sector. 7

4. CP violating phase(s) due to H0 exchanges

cause large asymmetries8;9 in e+e

\Gamma ! t_tH0

and in e+e

\Gamma ! t_t*e_*e.10;11

2 Top Polarimetry The fact that the top is so heavy has the important consequence that the top quark does not bind into hadrons. All CP violation in the top quark is therefore direct CP. Spin of the top quark becomes a very important observable and its decays become very effective analyzers of its spin.12 The polarization of the top-quark is strongly correlated to the directions of the momentum of the charged lepton in t ! b`*`, or to the W -momentum in t ! bW , or to the direction of the most energetic jet in t ! b + 2jets.13;14 The ability to track the top spin thus plays a crucial role in CP violation tests involving the top quark.

3 Dipole Moment of the Top-Quark In many extensions of the SM the top quark can acquire dipole moment at one loop order.1;2 For example, CP violation phase from a neutral Higgs sector can cause top dipole moment of order 10

\Gamma 20e\Gamma cm i.e. about ten orders of magnitude

1

more than in the SM wherein one needs to go to at least two loop order and it is expected to be

,! 10

\Gamma 30e\Gamma cm. Much attention has recently been

given to detection of the dipole moment form factor. 1;3-4 It should be clear that the form factor has not only a real part but there is also an imaginary part arising at q2 * 4m2t . Since the life-time of the top quark is so short form factor extraction requires simultaneous studies of production and subsequent decay. A multitude of (CP Violating) observables that are TN -odd or TN -even can be constructed using beam polarization, beam momenta, t, _t momenta and/or momenta of various decay products.1;3-4 Under these circumstances it is natural to search for an optimal observable,3 namely, one that is the most efficient for the determination of (e.g.) the real or the imaginary part of the dipole moment form factor for a fixed value of q2. Separating the differential cross-section into a CP conserving (\Sigma 0) and a CP violating (\Sigma 1) piece4

oe(OE) = \Sigma 0(OE) + *\Sigma 1(OE) (1) then the optimal observable, for determination of the dipole moment * is given by4

0opt = \Sigma 1(OE)=\Sigma 0(OE) (2) Studies have shown that the anticipated luminosity at the NLC15-17 of 5 \Theta 1033 cm

\Gamma 2s\Gamma 1 14

should be able to give limits on * to the level of,

10

\Gamma 19e-cm at one sigma.4 Thus observation of

the top dipole moments that are expected in theoretical extensions would present somewhat of a challenge but their feasibility cannot be excluded.

4 PRA and the Supersymmetric Phase5;6 Two studies indicate that, in decays of the type t ! W b, SUSY phase(s) can lead to PRA up to a few %. Experimentally there are two ways to look for these effects. Firstly PRA can be searched for by comparing Vtb with V_t_b. The expectations are that at the NLC, Vtb can be measured to a precision of a few %.15-17 So a difference between Vtb and V_t_b less than about 10% would be rather difficult to detect.

Incidentally, a second way to search for a PRA would be to determine the BR for decays that are not accompanied by a beauty quark i.e. BR into "ugly decays" of the top quark. This would yield the effective CKM angle Vtx into non-beauty

decays. Separation into decays that contain a prompt d-quark versus a prompt s-quark is probably quite unrealistic. However for the purpose of PRA this separation is not necessary. Since PRA in t ! W b can only arise if there are (nonstandard) decays of the top, which provide the needed absorptive parts, it means that CKM unitarity must be violated by Vtx i.e.

jVtxj2 6= [1 \Gamma jVtbj2] (3) For this type of precision studies at the NLC experiments must be able to search for such "ugly decays" (i.e. top decays not accompanied by prompt beauty) with high efficiency. Of course efficiency in b-tagging is also extremely important.

5 Transverse Polarization of the o/ due to

a Charged Higgs Phase.7

The transverse polarization of the o/ in the decay t ! bo/ * is extremely sensitive to the presence of a CP violating phase from the charged Higgs sector. The effects are large as they originate from tree level interferences and also the W propagator is on-shell and causes a "resonance" enhancement. There is a CP-odd, TN -odd transverse polarization asymmetry sensitive to the real part of the W -propogator and a CP-odd, TN even transverse polarization asymmetry that is driven by the imaginary part of the resonant W propogator. The second type of asymmetry does not occur in K ! ss_* or B ! D(D

\Lambda )o/ *. . . . In

top decays both types of asymmetries are quite large. For mH , 200 GeV they can be as big as 50% and for mH , 400 GeV they can be in the range 5-20%. At the NLC, at ps = 500 GeV, with a luminosity of 5 \Theta 1033 cm

\Gamma 2s\Gamma 1 we may be

able to probe asymmetries larger than about 6% with three sigma sensitivity. Clearly, the ability to measure the polarization of the o/ would be a very important feature in experiments at the NLC.

6 Neutral Higgs CP in e+e

\Gamma ! t_tH0.

CP violation phase due to a neutral Higgs sector leads to very interesting effects that occur through the interference of two tree graphs (see Fig.1).8 Without using beam polarization and/or t, _t spin, there is only one triple correlation that is possible, i.e. (~pe+ \Gamma ~pe\Gamma ) \Delta (~pt \Theta ~p_t). The resulting, TN -odd,

2

e+ eiii

q qZ,g

e+ e- q

q Z Z,c

H

e+ e- q

q Z,g

H

H 0

0

0 0 i ii

Figure 1: Tree-level Feynman diagrams contributing to CP

violation in e+e

\Gamma ! t_tH0 in the two Higgs doublet model

asymmetries are in the 10-25% range. The cross section is about a few fb. Thus these asymmetries should be observable if the projected luminosity of 2 \Theta 1034 cm

\Gamma 2s\Gamma 1 could be reached for a

1 TeV machine. The method is most suitable for a relatively light Higgs, mH0 ,! 2mW , as then the BR(H0 ! b_b) is substantial. Gunion et al.9 have extended the study of this reaction. With the use of generalized optimal observables they claim that at E = 1:5 TeV the NLC would enable determination of the basic couplings for H_tt, H_tfl5t and HZZ vertices and thereby clarify the nature of the Higgs boson.9

7 Neutral Higgs Phase in e+e

\Gamma !

* _*W +W

\Gamma .

This reaction is extremely interesting as it also leads to a TN -odd polarization asymmetry that arises at tree-level.10 Furthermore, the resonant Higgs propagator leads to enhanced effects resulting in the possibility of substantial asymmetries

, 10-50%. The relevant Feynman graphs are shown in Fig. 2.

Actually there are three types of polarization asymmetries that are of interest. To define these let us introduce, in the rest frame of the t, the basis vectors: \Gamma ^ezff(~pW+ + ~pW\Gamma ); ^eyff(~pW+ \Theta ~pW\Gamma ) and ^ex = ^ey \Theta ^ez. Let Pj (for j = x; y; z) be the polarization of the t along ^ex, ^ey or ^ez. Similarly for_ t. Combining the information from t; _t we define the CP violating asymmetries:

Ax = 12 (px + _px); Ay = 12(py \Gamma _py)

Az = 12 (pz + _pz) (4) So Ax and Az are TN -even requiring absorptive parts whereas Ay is TN -odd requiring real Feynman amplitude. Therefore Ay arises from interference among the tree level graphs in Fig. 2. Near resonance Ax also arises primarily from these tree graphs; the Higgs width provides the necessary absorptive parts. Az, though, receives additional contributions from loop graphs.

In addition to CP violating polarization asymmetries there is also an interesting CP-even, TN odd asymmetry that is quite sizable. We should be able to use it to determine the Higgs width in SM as well as in its extensions.

The works of Ref. 10,11, on the reaction e+e

\Gamma ! t_t*e_*e, are complementary. Ref. 10 deals

with interference of a neutral Higgs exchange with the other SM graphs of Fig. 2. Ref. 11 ignores that contribution to CP violation and focuses primarily on interference between two neutral Higgs occurring in a 2HDM.

8 Summary SM causes negligible CP violating effects in top physics whereas many types of extensions lead to large effects therein. The top can receive a large dipole moment from neutral Higgs CP. The latter can also cause significant asymmetries in e+e

\Gamma ! t_tH0 and e+e\Gamma ! t_t*e_*e arising at tree

level. SUSY phase(s) can cause PRA in t ! W b. Phase(s) from the charged Higgs sector result in large transverse polarization of o/ in t ! bo/ *.

There is thus the exciting possibility that the parameters needed for understanding of baryogenesis could be extracted or verified through CP

3

t t Z,

W

W

t t W W H H

t t b

W

W

(c)

(b) (a)

Figure 2: The Feynman diagrams that participate in the sub-process W +W

\Gamma ! t_t. The blob in Fig.2a represents

the width of the Higgs resonance and the cut across the

blob is to indicate the imaginary part.

violation studies of the top quark in accelerator experiments.

Acknowledgments This research was supported in part by the USDOE contracts DC-AC05-84ER40150 (CEBAF) and DE-AC-76CH00016 (BNL).

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