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Two Higgs doublet models and CP violating Higgs exchange in e+e−→tt̄Z
12 February 1998
Physics Letters B 419 Ž1998. 340–347
Two Higgs doublet models and CP violating Higgs exchange in eqey™ ttZ S. Bar-Shalom a , D. Atwood b, A. Soni
c
a
b
Physics Dept., UniÕersity of California, RiÕerside, CA 92521, USA Theory Group, Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA c Physics Dept., BrookhaÕen Nat. Lab., Upton, NY 11973, USA Received 9 July 1997 Editor: M. Dine
Abstract Appreciable CP asymmetries Ž; 10%. can arise in the reaction eqey™ ttZ already at tree-leÕel in models with two Higgs doublets. For a neutral Higgs particle, h, with a mass in the range 50 GeV Q m h Q 400 GeV, it may be possible to detect a 2–3 sigma CP-odd effect in eqey™ ttZ in ; 1–2 years of running of a future high energy eqey collider with c.m. energies of ; 1–2 TeV and an integrated luminosity of 200–500 inverse fb. q 1998 Published by Elsevier Science B.V.
A future high energy eqey collider running at c.m. energies of 0.5–2 TeV, often referred to as the Next Linear Collider ŽNLC., will no doubt serve as a very useful laboratory for a detailed study of the properties of the Higgs particleŽs. and that of the top quark w1x. In particular, it may unveil new phenomena, beyond the Standard Model ŽSM. associated with the top Yukawa couplings to scalar particleŽs.. Evidence of such new ttH couplings, if detected at the NLC, can give us important clues about the nature of the scalar potential and of the properties of the scalar particleŽs.. In the SM, the scalar potential is economically composed of only one scalar doublet. Even a mild extension of the SM with an additional scalar doublet w2x, can give rise to rich new phenomena beyond the SM associated with top-Higgs systems, e.g., tree-level CP-violation w3,5x and tree-level flavor-
changing-scalar ŽFCS. transitions w6x, in interaction of neutral scalars with the top quark. Indeed, the top quark, being so heavy, m t ; 175 GeV, is the most sensitive to these new interactions. In this Letter we explore the possibility of detecting tree-leÕel CP-violation in the reaction eqey™ ttZ. We find that in the best cases one needs about one thousand ttZ events to observe a 3-sigma CPnonconserving signal, which, as we will show here, may well be within the experimental reach of the NLC. To some extent, our findings for eq ey™ ttZ are somewhat similar to our previous study of eqey ™ tth where large tree-level CP violation was reported w3x. The process eq ey™ ttZ provides another independent, but analogously, promising venue to search for the signatures of the same CP-odd phase, residing in the top-neutral Higgs coupling, in future experiments.
0370-2693r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 3 7 0 - 2 6 9 3 Ž 9 7 . 0 1 0 3 9 - 3
S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
In the presence of two Higgs doublets the most general Yukawa lagrangian can be written as: L Y s Ui1j qi , L f˜ 1 u j, R q Di1j qi , L f 1 d j, R q Ui 2j qi , L f˜ 2 u j, R q Di2j qi , L f 2 d j, R q h.c. , Ž 1 . where f i for i s 1,2 are the two scalar doublets and Ui kj , Dikj , for k s 1,2, are the Yukawa couplings matrices which are in general non-diagonal. Depending on the assumptions made, one can then obtain different versions of a Two Higgs Doublet Model Ž2HDM.. In particular, if one imposes the discrete symmetries f 1; f 2 ™ yf 1; f 2 and d i, R ;u i, R ™ yd i, R ;y u i, R or y d i, R ;u i, R one arrives at the so called Model I or Model II, respectively, depending on whether the y1r3 and 2r3 charged quarks are coupled to the same or to different scalar doublets. If, in addition, these discrete symmetries are softly violated by a mass-dimension-two term in the Higgs potential, then the real and imaginary parts of the Higgs doublets mix, giving rise to CP-violating scalar-pseudoscalar mixed couplings of a neutral Higgs to fermions already at the tree-level w7x. On the other hand, if one does not impose the above discrete symmetries, one arrives at a most general version of the 2HDM, often called Model III, in which both FCS transitions and CP-nonconserving interactions between the neutral Higgs particles and fermions are present at tree-level Žsee e.g., Luke and Savage in w6x and w8x.. The scalar spectrum of any of the above 2HDM’s consists of three neutral Higgs and two charged Higgs particles. The H k qq and H k ZZ Ž k s 1,2,3 corresponding to the three neutral Higgs particles H k and q stands for quark. interaction lagrangian parts of a general 2HDM can be written as: gW mq k k k LH k q q s y '2 mW H q Ž a q q ibqg 5 . q , gW LH k ZZ s m c kH k gmn Z m Z n . Ž 2. cW Z Note that in the SM the couplings in Eq. Ž2., of the only neutral Higgs present, are a q s 1r '2 ,bq s 0 and c s 1 and there is no phase in the H k qq coupling. In Model II, for up quarks for example w7x: a uk s R 1 krsin b ,
341
where tan b ' ÕurÕd and ÕuŽ Õd . is the vacuum-expectation-value responsible for giving mass to the upŽdown. quark. R is the neutral Higgs mixing matrix which can be parameterized by three Euler angles a 1,2,3 w7x. A general feature of the above 2HDM’s is that only two out of the three neutral Higgs can simultaneously have a coupling to vector bosons and a pseudoscalar coupling to fermions. We will denote these two neutral Higgs by h and H with couplings a hq ,bqh ,c h and a qH ,bqH ,c H , corresponding to the light and heavy neutral Higgs, respectively. 1 Then, an important aspect of these 2HDM’s, which has crucial phenomenological implications for CP-violation, is that these couplings are subject to the constraint bqh c h q bqH c H s 0 w5x. This implies the existence of a ‘‘GIM’’-like cancellation, namely; all CP-violating effects due to the Higgs sector, being proportional to b h c h q b H c H , must vanish when the two Higgs states h and H are degenerate. We now discuss the possibility of having CP-violation, already at the tree-leÕel, driven by 2HDM’s, in our reaction: eq Ž pq . q ey Ž py . ™ q Ž pq . q q Ž pq . q Z Ž pZ . .
Ž 4. In the unitary gauge the reaction in Eq. Ž4. can proceed via the Feynman diagrams depicted in Fig. H is produced Ž H 1. Diagram b, where a pair of ZH is produced either as real or virtual, i.e. m H ) 2 m t or m H - 2 m t respectively. followed by H ™ tt, is the only one where new CP-nonconserving dynamics from the Higgs sector can arise being proportional to the CP-odd phase in the H qq vertex. In particular, all CP-violating effects arise from the interference of diagram b with the diagrams of class a in Fig. 1 and are proportional to the quantity bqH = c H . A detailed cross-section analysis of the reaction eq ey™ ttZ was performed in the SM by Hagiwara et al. in w9x. There, it was found that the Higgs exchange contribution of diagram b in Fig. 1 will be
buk s R 3 krtan b , 1
c k s R 1 k sin b q R 2 k cos b ,
Ž 3.
In some instances we will denote these two neutral Higgs by H . Then H s h or H is to be understood.
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S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
Fig. 1. Tree-level Feynman diagrams contributing to eq ey™ ttZ in a two Higgs doublet model. Diagram a represents 8 diagrams in which either Z or g are exchanged in the s-channel and the outgoing Z is emitted from eq,ey,t or t.
almost invisible in a TeV eqey collider for neutral Higgs masses in the range m h - 2 m t . On the contrary, we will show here that if the scalar sector is doubled, then the lightest neutral Higgs may reveal itself through CP-violating interactions with the top quark even if m h - 2 m t . We will sketch below the main characteristics of the total differential crosssection ŽDCS. and focus primarily on its CP-violating part. The tree-level polarized DCS, SŽ0j. , j s y1Ž1. for leftŽright. handed electrons, is in general a 0 sum of two terms: the CP-even and odd terms SqŽ j. 0 0 0 0 and SyŽ j. , respectively, i.e. SŽ j. ' SqŽ j. q SyŽ j. . 0 However, we can furthermore divide S " Ž j. into: 0 0Ž SM . 0Ž H . 0Ž H . SqŽ j. ' SqqŽ j. q SqqŽ j. q SqyŽ j. ,
Ž 5.
0 0Ž H . 0Ž H . SyŽ j. ' SyqŽ j. q SyyŽ j. ,
Ž 6.
terms of the Higgs coupling constants a qH ,bqH and c H defined in Eq. Ž2.. In particular we find: 0Ž H . h h 1 SqqŽ j. s a q c Re Ž P h . fqqŽ j. 2
2 3 q Ž a qh c h . Ž Re Ž P h . fqqŽ j. q Im Ž P h . fqqŽ j. . 2
4 5 q Ž bqh c h . Ž Re Ž P h . fqqŽ j. q Im Ž P h . fqqŽ j. .
q Ž h™H . ,
Ž 7.
0Ž H . h h 1 SqyŽ j. s a q c Im Ž P h . fqyŽ j. q Ž h ™ H . ,
Ž 8.
0Ž H . h h 1 SyqŽ j. s bq c Im Ž P h . fyqŽ j. q Ž h ™ H . ,
Ž 9.
0Ž H . h h 1 SyyŽ j. s bq c Re Ž P h . fyyŽ j. q Ž h ™ H . ,
Ž 10 .
where:
where the first and second subscripts denote the CP property and the TN property ŽTN is the naive time reversal operator defined by replacing time with its negative without switching initial and final states. of the DCS’s in Eqs. Ž5. and Ž6., respectively. The superscript indicates if it is a pure SM contribution, coming from diagrams a and denoted by ŽSM., or interference terms associated with diagram b and 0Ž H . denoted by Ž H .. Thus, for example, SyyŽ j. is the CP-odd, TN -odd polarized DCS, upon which we will concentrate, that emanates from the interference of diagram b with the SM diagrams a in Fig. 1. It is then very simple to identify each of the DCS’s in Eqs. Ž5. and Ž6. associated with the 2HDM-SM and the 2HDM-2HDM interferences in
PH ' Ž s q m2Z y m2H y 2 p P pZ q im H GH .
y1
.
Ž 11 . p ' pyq pq and GH is the width of H . f ml nŽ j. , m,n s qor y , are kinematical functions of phase space which transform like m under CP and like n under TN . A few important remarks are in order at this stage: 1 1 1. The functions fyyŽ j. and fqyŽ j. , being TN -odd, are proportional to the Levi-Civita tensor e Ž py, pq, pq , pq .. 2. There is no term proportional to a qH bqH in the DCS’s at tree-level. 3. The diagrams where the Z is emitted from the incoming electron and positron lines, do not con0Ž H . tribute to SyyŽ j. .
S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347 0Ž H . 0Ž H . 4. SqyŽ j. and SyqŽ j. are proportional to the absorptive part coming from the Higgs propagator, ImŽ P h ., and are therefore not pure tree-level quantities being proportional to the Higgs width. Thus, a consistent calculation of the qy and yq parts of the DCS has to include the full next order Ži.e., 1-loop order. contribution in perturba0Ž H . tion theory. In contrast, SyyŽ j. , being an odd function of TN , is proportional to ReŽ P h . and is therefore a pure tree-level quantity. We will concentrate here on the CP-odd TN -odd 0Ž H . effects emanating from SyyŽ j. which, as mentioned above, is proportional at the tree-level to the interference of the SM-like diagrams where the Z is radiated off the t or t with the Higgs exchange diagram w10x. By measuring a CP-odd TN -odd observable one can extract information on the magnitude of bqH c H . However, note that the full DCS contains more information about the other scalar coupling combinations. Thus with the appropriate optimal observables w11x, it is possible to isolate each coupling combination in Eqs. Ž7. – Ž10., and therefore, in principle, to identify the exact quantum numbers of the neutral Higgs particle, say the lightest one, which is exchanged in diagram b. This technique was applied to the reaction ey eq™ tth by Gunion et al. in w4x. However, we expect that the reaction ey eq™ ttZ will be less sensitive to the CP-even top-Higgs couplings due to the dominating presence of the SM diagrams a depicted in Fig. 1. The CP-odd TN -odd kinematic function of phase 1 0Ž H . space, fyyŽ j. , corresponding to SyyŽ j. , and of relevance to the present analysis is: 1 fyyŽ j.
s y'2
2 g W3
ž / cW3
2
m 2q m2Z
P Z Tq3 c jZe Ž py , pq , pq , pq .
q = j Ž P q q P q . m2Z wy j q Ž s t y s . wj
½
qTq3 c jZP Z Ž P q y P q . f 4 ,
Ž 12 .
where: wj"' Ž sW2 Q q y 12 Tq3 . c jZP Z " Q q sW2 cW2 Pg .
Ž 13 .
Z Here cy1 s 1r2 y sW2 ,c1Z s ysW2 Žrecall that j s Ž . y1 1 for a leftŽright. handed electron.. sW Ž cW . is the sinŽcos. of the weak mixing angle u W and Q q
343
and Tq3 are the charge and z-component of the weak isospin of the quark, respectively. Furthermore:
P Z ' Ž s y m2Z .
y1
,
Pg ' sy1 ,
P qŽ q . ' m2Z q 2 pqŽ q . P pZ
ž
y1
/
,
Ž 14 .
where s s Ž pyq pq . 2 is the c.m. energy squared of the colliding electrons, st ' Ž pq q pq . 2 and we have also defined the CP-odd quantity f ' Ž pyy pq . P Ž pq q pq .. As mentioned earlier, being an odd function of 1 the TN symmetry operation, fyyŽ j. can only probe CP-asymmetries of the TN -odd type in ey eq™ ttZ. This leads us to consider the following dimensionless CP-odd, TN -odd observables: Os
pyP Ž pq = pq . s 3r2
,
Oopt s
0Ž H . Syy
Sq0
.
Ž 15 .
Oopt is an optimal observable in the sense that the statistical error, in the measured asymmetry, is minimized w11x. Also, note that both observables are proportional to e Ž py, pq, pq , pq . since there is only one possible independent triple correlation product Žor equivalently a Levi-Civita tensor. when the final state consists of three particles only and the spins are disregarded. In particular, Oopt is related to O by a multiplication by a CP-even function. The theoretical statistical significance, NSD , in which an asymmetry can be measured in an ideal experiment is given by NSD s A'L st tZ where for the observables O and Oopt the asymmetry A, defined above, is:
(
(
A O f ² O :r ² O 2 : ,
(
A opt f ² Oopt : .
Ž 16 .
Also, st tZ ' s Ž ey eq™ ttZ . is the cross-section and L is the effective luminosity for fully reconstructed ttZ events. In particular, we will take L s e L , where L is the total yearly integrated luminosity 2 and e is the overall efficiency for reconstruction of the ttZ final state. Note that detection of the asymmetries in Eq. Ž16. requires the identification of the t and t as well as the reconstruction of their momenta. Thus, the most suitable scenario is when either the t or the t decays semi-leptonically and the other decays
2
For illustrative purposes, we will choose: L s 200 wfbxy1 for L s 500 wfbxy1 for 's s1.5 TeV w1x.
's s1 TeV and
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S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
order, for certain values of tan b , a 1 , a 2 , a 3 4 and the neutral Higgs mass, there can be a significant difference between the cross-sections predicted by the two-models. For example, with unpolarized incoming electrons and for 's s 1 TeV, m h s 360 GeV and tan b , a 1 , a 2 , a 3 4 s 0.3,pr2,pr4,0 4 , st IItZ , 6 fb, while the SM cross-section is st SM tZ , 3.5 fb. The combined information from a study of the cross-section itself along with CP-violation may be extremely useful in understanding the dynamics of the reaction eq ey™ ttZ although we choose not to pursue in that direction in this paper. Let us first consider an unpolarized incoming electron beam and concentrate on the CP-odd effect associated with Oopt . The effect of the simple triple product O is slightly smaller. In Fig. 3 we present our main results for the expected asymmetry and statistical significance corresponding to Oopt in Model II, as a function of the mass Ž m h . of the light Higgs where, again, m H s 750 GeV. We plot Fig. 2. The cross section Žin wfbx. for the reaction eq ey ™ ttZ, assuming unpolarized electron and positron beams, for Model II with set II and as a function of m h Žsolid and dashed lines. and 's Ždotted and dotted-dashed lines.. Set II means tan b , a 1 , a 2 , a 3 4 ' 0.3,p r2,p r4,0 4 .
hadronically. Distinguishing between t and t in the double hadronic decay case will require more effort and still remains an experimental challenge. In Fig. 2 we plot the cross-section, st IItZ as a function of m h and 's , for Model II with tan b , a 1 , a 2 , a 3 4 s 0.3,pr2,pr4,0 4 which we denote as set II. We will adopt set II later also when discussing the CP-violating effect. Here we have set the mass of the heavier Higgs to be m H s 750 GeV. We see that st IItZ is typically ; few fb for c.m. energies of ; 1–2 TeV; it peaks for m h f 2 m t and 's ; 800 GeV at around 7 fb. 3 Therefore, with L R 10 2 wfbxy1 it may be possible to produce 10 2 – 10 3 ttZ’s at the NLC running with c.m. energies R 1 TeV scale. We also remark that, although the crosssections in the SM and Model II are of the same
3
w x Plots of the SM cross-section, st SM tZ , can be found in 9 , where it was also found that st SM tZ ; few fb.
Fig. 3. The asymmetry, A opt , and scaled statistical significance, NSD r'L , for the optimal observable Oopt as a function of the light Higgs mass m h , for 's s1 TeV and 1.5 TeV. See also caption to Fig. 2.
S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
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Table 1 The statistical significance, NSD , in which the CP-nonconserving effects in eq ey™ ttZ can be detected in one year of running of a future high energy collider with either unpolarized or polarized incoming electron beam. We have used a yearly integrated luminosity of L s 200 and 500 wfbxy1 for 's s 1 and 1.5 TeV, respectively, and an efficiency reconstruction factor of e s 0.5 for both energies. NSD is given for both m H s 750 GeV Žin parentheses. and m H s 1 TeV. Recall that j s 1Žy1. stands for rightŽleft. polarized electrons. Set II means tan b , a 1 , a 2 , a 3 4 ' 0.3,pr2,pr4,0 4
's
ŽTeV.
NSD , for Oopt w eq ey™ ttZ ŽModel II with Set II.x
j m h s 100 GeV
m h s 160 GeV
m h s 360 GeV
1
y1 unpol 1
Ž1.8. 1.7 Ž1.6. 1.6 Ž1.5. 1.5
Ž1.8. 1.8 Ž1.7. 1.6 Ž1.5. 1.5
Ž2.2. 2.2 Ž2.0. 2.0 Ž1.8. 1.8
1.5
y1 unpol 1
Ž2.3. 2.9 Ž2.1. 2.6 Ž1.8. 2.3
Ž2.4. 3.0 Ž2.1. 2.7 Ž1.8. 2.3
Ž2.8. 3.3 Ž2.5. 3.0 Ž2.1. 2.6
NSD r 'L , thus scaling out the luminosity factor from the theoretical prediction and as an illustration, for the free parameters of Model II, we adopt set II defined above, i.e. tan b , a 1 , a 2 , a 3 4 s 0.3,pr2,pr4,0 4 . We remark that the effect is practically insensitive to a 3 , and a 1 s pr2, a 2 s pr4 correspond to the best effect, though not unique. Also, the CP-violating effect is roughly proportional to 1rtan b , it therefore drops as tan b is increased. However, we find that we can still have NSD r 'L ) 0.1 even in the unpolarized case for tan b Q 0.6, a 1 s pr2, a 2 s pr4, a 3 s 0. Evidently the asymmetry is almost insensitive to m h in the range 50 GeV Q m h Q 2 m t where it stays roughly at the 7–8% level for 's ; 1–2 TeV Žsee Fig. 3.. In that range 0.1 Q NSD r 'L Q 0.2; it slightly grows as m h is increased and reaches its peak around m h f 2 m t . For m h ) 2 m t , for which an on-shell h is produced and then decays to a pair of tt, as m h grows the asymmetry drops till it essentially vanishes when m h ™ m H in which case the ‘‘GIM’’ like cancellation, discussed above, applies. Also, with respect to the c.m. energy, both A opt and NSD r 'L reach their peak values at around 's ; 1 TeV for both m h s 100 and 360 GeV and weakly fall as the c.m. energy is increased. For example, we find that with m h s 100Ž360. GeV and e s 0.5, it may be possible to observe a CP-nonconserving effect in the reaction ey eq™ ttZ with a statistical significance of NSD f 1.6Ž2.0. for 's s 1 TeV and L s 200 wfbxy1 , and NSD f 2.1Ž2.5. for 's s 1.5 TeV and L s 500 wfbxy1 if the incoming electrons are unpolarized.
In Table 1 we present NSD for Oopt , in Model II with set II, for polarized and unpolarized electrons. For illustrative purposes, we choose m h s 100,160 and 360 GeV and, as before, we present the numbers for 's s 1 TeV with L s 200 wfbxy1 and for 's s 1.5 TeV with L s 500 wfbxy1 . In both cases we take e s 0.5 assuming that there is no loss of luminosity when the electrons are polarized. 4 Also, to demonstrate the sensitivity of the CP-effect to the mass Ž m H . of the heavy Higgs, we present numbers for both m H s 750 GeV Žshown in the parentheses. and m H s 1 TeV. We see from Table 1 that left polarized incoming electrons can probe CP-violation slightly better than unpolarized ones. In particular, for m H s 1 TeV we find that with left polarized electrons and for 's s 1Ž1.5. TeV, the CP-effect is above the 2Ž3.-sigma level for m h R 2 m t . At c.m. energy 's s 1 TeV the CP-effect is practically insensitive to the choice m H s 750 GeV or m H s 1 TeV. However, we see from the Table that as one goes to 's s 1.5 TeV, m H s 1 TeV can give rise to a 3-sigma signal in the range, 100 GeV Q m h Q 400 GeV, if the electrons are negatively polarized, while with m H s 750 GeV the CP-signal is smaller by about half a sigma. We remark again that the results for the simple observable O exhibit the same behavior though slightly smaller then those for Oopt .
4
If the efficiency for ttZ reconstruction is e s 0.25 then our numbers would correspondingly require 2 years of running.
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S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
Before summarizing we wish to emphasize that the analysis performed here for Model II can be generalized to models I and III as well. Recall that in Model II a mass-dimension-two operator, that softly breaks the discrete symmetry which is responsible for natural-flavor-conservation ŽNFC., is needed in order to have CP-violating Higgs-fermion couplings. On the other hand, in Model III there is no NFC and the CP-odd phase in the H k qq vertex can arise from a phase in the Yukawa couplings Ui 2j and Di2j defined in Eq. Ž1. Žfor more details see w8x.. The pseudoscalar coupling in Eq. Ž2., responsible for CP-violation, can be chosen Žin Model III. as bqk A l q w12x, where l q is a free parameter of the model expected to be of O Ž1. w8x. Then the replacement l t f 1rtan b Žfor a given value of tan b in Model II. can give rise to comparable CP-nonconserving effects in eq ey™ ttZ. Thus, the main difference between Model II and Model III arises from the fact that, while in Model II a small tan b is required in order to enhance the CP-odd effect, in Model III the effect is elevated as l t is correspondingly increased. The same argument holds also for other previously suggested CP studies in top systems where the results obtained for Model II can be generalized to Model III. This seems to indicate that even if such CP-violating effects are found in ey eq™ ttZ or other reactions which involve the top-neutral Higgs CP-phase discussed in this paper, it may not be possible to distinguish Model II from Model III, as both models may have a comparable CP-odd phase in the Higgs sector. In that sense, the best way to proceed for correctly classifying the Higgs sector, is to search for large signatures of FC effects in top quark reactions as well. Model III, with FCS couplings to fermions proportional to the fermion masses involved in the FC vertex w12x, may indeed drive such large FC effects in top systems, some of which are eq ey™ tc; tcne ne ; tceq ey; tcZ; ttcc; tcqq and were investigated in w6x. Detection or no detection of these FC signatures along with evidence for CP-violation in the Higgs sector in high energy eqey colliders, may well be the only way to experimentally distinguish between scalar dynamics of a Model II or a Model III origin. To summarize, CP-violation in ey eq™ ttZ at a future high energy eqey collider was studied in the context of 2HDM’s. An important property of this
reaction is that CP-violation arises already at the tree-level through interference of Z emission from the t or t and its emission off a s-channel Z and therefore allowing for a relatively large CP-violating signal. In particular, we found that within a broad range of the lightest Higgs mass, 100 GeV Q m h Q 400 GeV and with c.m. energies between 1–2 TeV the asymmetry can reach the ; 10% level. The corresponding statistical significance, in which it may be observed, is around 2–3 sigma for unpolarized incoming electrons and, if m h R 2 m t , it can reach above 3-sigma for polarized ones and c.m. energy of 's s 1.5 TeV. Bearing the expected difficulty of observing the Higgs exchange effect in eq ey™ ttZ in the SM and with Higgs masses below 2 m t w9x, it is especially gratifying that the CP-effect is sizable and almost insensitive to m h in the range 50 GeV Q m h Q 2 m t GeV. We therefore encourage a detailed scrutiny of the reaction ey eq™ ttZ in the NLC. Such an investigation, especially due to the promising CP-nonconserving effects reported here, may be helpful in unraveling the CP properties of the Higgs sector. This research was supported in part by the US DOE contract numbers DE-AC02-76CH00016 ŽBNL., DC-AC05-84ER40150ŽJefferson Lab. and DE-FG03-94ER40837ŽUCR.. References w1x Proceedings of the Workshop on Physics and Experiments with Linear eq ey Colliders, Eds. F. Harris S. Olsen, S. Pakvasa, X. Tata ŽWorld Scientific, Singapore, 1993.; A. Miyamoto, Y. Fujii, ibid Ž1996.. w2x For a review, see J. Gunion, H. Haber, G. Kane, S. Dawson, The Higgs Hunter’s Guide ŽAddison-Wesley, New York, 1990.. w3x S. Bar-Shalom, D. Atwood, G. Eilam, R. Mendel, A. Soni, Phys. Rev. D 53 Ž1996. 1162; see also Gunion et al., in Ref. w4x. w4x J.F. Gunion, B. Grzadkowski, X.-G. He, Phys. Rev. Lett. 77 Ž1996. 5172. w5x D. Atwood, A. Soni, hep-phr9607481. w6x M.J. Savage, Phys. Lett. B 266 Ž1991. 135; W.S. Hou, Phys. Lett. B 296 Ž1992. 179; M. Luke, M.J. Savage, Phys. Lett. B 307 Ž1993. 387; L.J. Hall, S. Weinberg, Phys. Rev. D 48 Ž1993. R979; D. Atwood, L. Reina, A. Soni, Phys. Rev. Lett. 75 Ž1995. 3800; Phys. Rev. D 53 Ž1996. 1199; W.-S. Hou, G.-L. Lin, Phys. Lett. B 379 Ž1996. 261; S. Bar-Shalom, G. Eilam, A. Soni, J. Wudka, hep-phr9703221 to appear in Phys. Rev. Lett. ŽJuly 1997..
S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347 w7x C.D. Froggat, R.G. Moorhouse, I.G. Knowles, Nucl. Phys. B 386 Ž1992. 63; W. Bernreuther, T. Schroder, T.N. Pham, ¨ Phys. Lett. B 279 Ž1992. 389. w8x For a recent review of Model III, see D. Atwood, L. Reina, A. Soni, Phys. Rev. D 55 Ž1997. 3156. w9x K. Hagiwara, H. Murayama, I. Watanabe, Nucl. Phys. B 367 Ž1991. 257; see also K. Fujii, in the Proceedings of the 4th KEK Topical Conference on Flavor Physics Ž1996., and references therein. w10x We remark that one-loop, CP-odd TN -even, effects in eq ey H ™ ttZ were investigated by B. Grzadkowski ŽPhys. ™ ZH Lett. B 338 Ž1994. 71.. Although asymmetries at the order of
347
50% were found there, the SM-like diagrams of class a in Fig. 1 were ignored in that analysis. Since those diagrams make significant contributions to the rate, therefore, Žas was also mentioned by the author. such large asymmetries will be difficult to materialize unless one is able to experimentally separate the contribution from the Higgs exchange graphs from the rest of the diagrams which lead to the same final state. w11x D. Atwood, A. Soni, Phys. Rev. D 45 Ž1992. 45. w12x T.P. Cheng, M. Sher, Phys. Rev. D 35 Ž1987. 3484; M. Sher, Y. Yuan, Phys. Rev. D 44 Ž1991. 1461.
Physics Letters B 419 Ž1998. 340–347
Two Higgs doublet models and CP violating Higgs exchange in eqey™ ttZ S. Bar-Shalom a , D. Atwood b, A. Soni
c
a
b
Physics Dept., UniÕersity of California, RiÕerside, CA 92521, USA Theory Group, Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA c Physics Dept., BrookhaÕen Nat. Lab., Upton, NY 11973, USA Received 9 July 1997 Editor: M. Dine
Abstract Appreciable CP asymmetries Ž; 10%. can arise in the reaction eqey™ ttZ already at tree-leÕel in models with two Higgs doublets. For a neutral Higgs particle, h, with a mass in the range 50 GeV Q m h Q 400 GeV, it may be possible to detect a 2–3 sigma CP-odd effect in eqey™ ttZ in ; 1–2 years of running of a future high energy eqey collider with c.m. energies of ; 1–2 TeV and an integrated luminosity of 200–500 inverse fb. q 1998 Published by Elsevier Science B.V.
A future high energy eqey collider running at c.m. energies of 0.5–2 TeV, often referred to as the Next Linear Collider ŽNLC., will no doubt serve as a very useful laboratory for a detailed study of the properties of the Higgs particleŽs. and that of the top quark w1x. In particular, it may unveil new phenomena, beyond the Standard Model ŽSM. associated with the top Yukawa couplings to scalar particleŽs.. Evidence of such new ttH couplings, if detected at the NLC, can give us important clues about the nature of the scalar potential and of the properties of the scalar particleŽs.. In the SM, the scalar potential is economically composed of only one scalar doublet. Even a mild extension of the SM with an additional scalar doublet w2x, can give rise to rich new phenomena beyond the SM associated with top-Higgs systems, e.g., tree-level CP-violation w3,5x and tree-level flavor-
changing-scalar ŽFCS. transitions w6x, in interaction of neutral scalars with the top quark. Indeed, the top quark, being so heavy, m t ; 175 GeV, is the most sensitive to these new interactions. In this Letter we explore the possibility of detecting tree-leÕel CP-violation in the reaction eqey™ ttZ. We find that in the best cases one needs about one thousand ttZ events to observe a 3-sigma CPnonconserving signal, which, as we will show here, may well be within the experimental reach of the NLC. To some extent, our findings for eq ey™ ttZ are somewhat similar to our previous study of eqey ™ tth where large tree-level CP violation was reported w3x. The process eq ey™ ttZ provides another independent, but analogously, promising venue to search for the signatures of the same CP-odd phase, residing in the top-neutral Higgs coupling, in future experiments.
0370-2693r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 3 7 0 - 2 6 9 3 Ž 9 7 . 0 1 0 3 9 - 3
S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
In the presence of two Higgs doublets the most general Yukawa lagrangian can be written as: L Y s Ui1j qi , L f˜ 1 u j, R q Di1j qi , L f 1 d j, R q Ui 2j qi , L f˜ 2 u j, R q Di2j qi , L f 2 d j, R q h.c. , Ž 1 . where f i for i s 1,2 are the two scalar doublets and Ui kj , Dikj , for k s 1,2, are the Yukawa couplings matrices which are in general non-diagonal. Depending on the assumptions made, one can then obtain different versions of a Two Higgs Doublet Model Ž2HDM.. In particular, if one imposes the discrete symmetries f 1; f 2 ™ yf 1; f 2 and d i, R ;u i, R ™ yd i, R ;y u i, R or y d i, R ;u i, R one arrives at the so called Model I or Model II, respectively, depending on whether the y1r3 and 2r3 charged quarks are coupled to the same or to different scalar doublets. If, in addition, these discrete symmetries are softly violated by a mass-dimension-two term in the Higgs potential, then the real and imaginary parts of the Higgs doublets mix, giving rise to CP-violating scalar-pseudoscalar mixed couplings of a neutral Higgs to fermions already at the tree-level w7x. On the other hand, if one does not impose the above discrete symmetries, one arrives at a most general version of the 2HDM, often called Model III, in which both FCS transitions and CP-nonconserving interactions between the neutral Higgs particles and fermions are present at tree-level Žsee e.g., Luke and Savage in w6x and w8x.. The scalar spectrum of any of the above 2HDM’s consists of three neutral Higgs and two charged Higgs particles. The H k qq and H k ZZ Ž k s 1,2,3 corresponding to the three neutral Higgs particles H k and q stands for quark. interaction lagrangian parts of a general 2HDM can be written as: gW mq k k k LH k q q s y '2 mW H q Ž a q q ibqg 5 . q , gW LH k ZZ s m c kH k gmn Z m Z n . Ž 2. cW Z Note that in the SM the couplings in Eq. Ž2., of the only neutral Higgs present, are a q s 1r '2 ,bq s 0 and c s 1 and there is no phase in the H k qq coupling. In Model II, for up quarks for example w7x: a uk s R 1 krsin b ,
341
where tan b ' ÕurÕd and ÕuŽ Õd . is the vacuum-expectation-value responsible for giving mass to the upŽdown. quark. R is the neutral Higgs mixing matrix which can be parameterized by three Euler angles a 1,2,3 w7x. A general feature of the above 2HDM’s is that only two out of the three neutral Higgs can simultaneously have a coupling to vector bosons and a pseudoscalar coupling to fermions. We will denote these two neutral Higgs by h and H with couplings a hq ,bqh ,c h and a qH ,bqH ,c H , corresponding to the light and heavy neutral Higgs, respectively. 1 Then, an important aspect of these 2HDM’s, which has crucial phenomenological implications for CP-violation, is that these couplings are subject to the constraint bqh c h q bqH c H s 0 w5x. This implies the existence of a ‘‘GIM’’-like cancellation, namely; all CP-violating effects due to the Higgs sector, being proportional to b h c h q b H c H , must vanish when the two Higgs states h and H are degenerate. We now discuss the possibility of having CP-violation, already at the tree-leÕel, driven by 2HDM’s, in our reaction: eq Ž pq . q ey Ž py . ™ q Ž pq . q q Ž pq . q Z Ž pZ . .
Ž 4. In the unitary gauge the reaction in Eq. Ž4. can proceed via the Feynman diagrams depicted in Fig. H is produced Ž H 1. Diagram b, where a pair of ZH is produced either as real or virtual, i.e. m H ) 2 m t or m H - 2 m t respectively. followed by H ™ tt, is the only one where new CP-nonconserving dynamics from the Higgs sector can arise being proportional to the CP-odd phase in the H qq vertex. In particular, all CP-violating effects arise from the interference of diagram b with the diagrams of class a in Fig. 1 and are proportional to the quantity bqH = c H . A detailed cross-section analysis of the reaction eq ey™ ttZ was performed in the SM by Hagiwara et al. in w9x. There, it was found that the Higgs exchange contribution of diagram b in Fig. 1 will be
buk s R 3 krtan b , 1
c k s R 1 k sin b q R 2 k cos b ,
Ž 3.
In some instances we will denote these two neutral Higgs by H . Then H s h or H is to be understood.
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S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
Fig. 1. Tree-level Feynman diagrams contributing to eq ey™ ttZ in a two Higgs doublet model. Diagram a represents 8 diagrams in which either Z or g are exchanged in the s-channel and the outgoing Z is emitted from eq,ey,t or t.
almost invisible in a TeV eqey collider for neutral Higgs masses in the range m h - 2 m t . On the contrary, we will show here that if the scalar sector is doubled, then the lightest neutral Higgs may reveal itself through CP-violating interactions with the top quark even if m h - 2 m t . We will sketch below the main characteristics of the total differential crosssection ŽDCS. and focus primarily on its CP-violating part. The tree-level polarized DCS, SŽ0j. , j s y1Ž1. for leftŽright. handed electrons, is in general a 0 sum of two terms: the CP-even and odd terms SqŽ j. 0 0 0 0 and SyŽ j. , respectively, i.e. SŽ j. ' SqŽ j. q SyŽ j. . 0 However, we can furthermore divide S " Ž j. into: 0 0Ž SM . 0Ž H . 0Ž H . SqŽ j. ' SqqŽ j. q SqqŽ j. q SqyŽ j. ,
Ž 5.
0 0Ž H . 0Ž H . SyŽ j. ' SyqŽ j. q SyyŽ j. ,
Ž 6.
terms of the Higgs coupling constants a qH ,bqH and c H defined in Eq. Ž2.. In particular we find: 0Ž H . h h 1 SqqŽ j. s a q c Re Ž P h . fqqŽ j. 2
2 3 q Ž a qh c h . Ž Re Ž P h . fqqŽ j. q Im Ž P h . fqqŽ j. . 2
4 5 q Ž bqh c h . Ž Re Ž P h . fqqŽ j. q Im Ž P h . fqqŽ j. .
q Ž h™H . ,
Ž 7.
0Ž H . h h 1 SqyŽ j. s a q c Im Ž P h . fqyŽ j. q Ž h ™ H . ,
Ž 8.
0Ž H . h h 1 SyqŽ j. s bq c Im Ž P h . fyqŽ j. q Ž h ™ H . ,
Ž 9.
0Ž H . h h 1 SyyŽ j. s bq c Re Ž P h . fyyŽ j. q Ž h ™ H . ,
Ž 10 .
where:
where the first and second subscripts denote the CP property and the TN property ŽTN is the naive time reversal operator defined by replacing time with its negative without switching initial and final states. of the DCS’s in Eqs. Ž5. and Ž6., respectively. The superscript indicates if it is a pure SM contribution, coming from diagrams a and denoted by ŽSM., or interference terms associated with diagram b and 0Ž H . denoted by Ž H .. Thus, for example, SyyŽ j. is the CP-odd, TN -odd polarized DCS, upon which we will concentrate, that emanates from the interference of diagram b with the SM diagrams a in Fig. 1. It is then very simple to identify each of the DCS’s in Eqs. Ž5. and Ž6. associated with the 2HDM-SM and the 2HDM-2HDM interferences in
PH ' Ž s q m2Z y m2H y 2 p P pZ q im H GH .
y1
.
Ž 11 . p ' pyq pq and GH is the width of H . f ml nŽ j. , m,n s qor y , are kinematical functions of phase space which transform like m under CP and like n under TN . A few important remarks are in order at this stage: 1 1 1. The functions fyyŽ j. and fqyŽ j. , being TN -odd, are proportional to the Levi-Civita tensor e Ž py, pq, pq , pq .. 2. There is no term proportional to a qH bqH in the DCS’s at tree-level. 3. The diagrams where the Z is emitted from the incoming electron and positron lines, do not con0Ž H . tribute to SyyŽ j. .
S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347 0Ž H . 0Ž H . 4. SqyŽ j. and SyqŽ j. are proportional to the absorptive part coming from the Higgs propagator, ImŽ P h ., and are therefore not pure tree-level quantities being proportional to the Higgs width. Thus, a consistent calculation of the qy and yq parts of the DCS has to include the full next order Ži.e., 1-loop order. contribution in perturba0Ž H . tion theory. In contrast, SyyŽ j. , being an odd function of TN , is proportional to ReŽ P h . and is therefore a pure tree-level quantity. We will concentrate here on the CP-odd TN -odd 0Ž H . effects emanating from SyyŽ j. which, as mentioned above, is proportional at the tree-level to the interference of the SM-like diagrams where the Z is radiated off the t or t with the Higgs exchange diagram w10x. By measuring a CP-odd TN -odd observable one can extract information on the magnitude of bqH c H . However, note that the full DCS contains more information about the other scalar coupling combinations. Thus with the appropriate optimal observables w11x, it is possible to isolate each coupling combination in Eqs. Ž7. – Ž10., and therefore, in principle, to identify the exact quantum numbers of the neutral Higgs particle, say the lightest one, which is exchanged in diagram b. This technique was applied to the reaction ey eq™ tth by Gunion et al. in w4x. However, we expect that the reaction ey eq™ ttZ will be less sensitive to the CP-even top-Higgs couplings due to the dominating presence of the SM diagrams a depicted in Fig. 1. The CP-odd TN -odd kinematic function of phase 1 0Ž H . space, fyyŽ j. , corresponding to SyyŽ j. , and of relevance to the present analysis is: 1 fyyŽ j.
s y'2
2 g W3
ž / cW3
2
m 2q m2Z
P Z Tq3 c jZe Ž py , pq , pq , pq .
q = j Ž P q q P q . m2Z wy j q Ž s t y s . wj
½
qTq3 c jZP Z Ž P q y P q . f 4 ,
Ž 12 .
where: wj"' Ž sW2 Q q y 12 Tq3 . c jZP Z " Q q sW2 cW2 Pg .
Ž 13 .
Z Here cy1 s 1r2 y sW2 ,c1Z s ysW2 Žrecall that j s Ž . y1 1 for a leftŽright. handed electron.. sW Ž cW . is the sinŽcos. of the weak mixing angle u W and Q q
343
and Tq3 are the charge and z-component of the weak isospin of the quark, respectively. Furthermore:
P Z ' Ž s y m2Z .
y1
,
Pg ' sy1 ,
P qŽ q . ' m2Z q 2 pqŽ q . P pZ
ž
y1
/
,
Ž 14 .
where s s Ž pyq pq . 2 is the c.m. energy squared of the colliding electrons, st ' Ž pq q pq . 2 and we have also defined the CP-odd quantity f ' Ž pyy pq . P Ž pq q pq .. As mentioned earlier, being an odd function of 1 the TN symmetry operation, fyyŽ j. can only probe CP-asymmetries of the TN -odd type in ey eq™ ttZ. This leads us to consider the following dimensionless CP-odd, TN -odd observables: Os
pyP Ž pq = pq . s 3r2
,
Oopt s
0Ž H . Syy
Sq0
.
Ž 15 .
Oopt is an optimal observable in the sense that the statistical error, in the measured asymmetry, is minimized w11x. Also, note that both observables are proportional to e Ž py, pq, pq , pq . since there is only one possible independent triple correlation product Žor equivalently a Levi-Civita tensor. when the final state consists of three particles only and the spins are disregarded. In particular, Oopt is related to O by a multiplication by a CP-even function. The theoretical statistical significance, NSD , in which an asymmetry can be measured in an ideal experiment is given by NSD s A'L st tZ where for the observables O and Oopt the asymmetry A, defined above, is:
(
(
A O f ² O :r ² O 2 : ,
(
A opt f ² Oopt : .
Ž 16 .
Also, st tZ ' s Ž ey eq™ ttZ . is the cross-section and L is the effective luminosity for fully reconstructed ttZ events. In particular, we will take L s e L , where L is the total yearly integrated luminosity 2 and e is the overall efficiency for reconstruction of the ttZ final state. Note that detection of the asymmetries in Eq. Ž16. requires the identification of the t and t as well as the reconstruction of their momenta. Thus, the most suitable scenario is when either the t or the t decays semi-leptonically and the other decays
2
For illustrative purposes, we will choose: L s 200 wfbxy1 for L s 500 wfbxy1 for 's s1.5 TeV w1x.
's s1 TeV and
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S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
order, for certain values of tan b , a 1 , a 2 , a 3 4 and the neutral Higgs mass, there can be a significant difference between the cross-sections predicted by the two-models. For example, with unpolarized incoming electrons and for 's s 1 TeV, m h s 360 GeV and tan b , a 1 , a 2 , a 3 4 s 0.3,pr2,pr4,0 4 , st IItZ , 6 fb, while the SM cross-section is st SM tZ , 3.5 fb. The combined information from a study of the cross-section itself along with CP-violation may be extremely useful in understanding the dynamics of the reaction eq ey™ ttZ although we choose not to pursue in that direction in this paper. Let us first consider an unpolarized incoming electron beam and concentrate on the CP-odd effect associated with Oopt . The effect of the simple triple product O is slightly smaller. In Fig. 3 we present our main results for the expected asymmetry and statistical significance corresponding to Oopt in Model II, as a function of the mass Ž m h . of the light Higgs where, again, m H s 750 GeV. We plot Fig. 2. The cross section Žin wfbx. for the reaction eq ey ™ ttZ, assuming unpolarized electron and positron beams, for Model II with set II and as a function of m h Žsolid and dashed lines. and 's Ždotted and dotted-dashed lines.. Set II means tan b , a 1 , a 2 , a 3 4 ' 0.3,p r2,p r4,0 4 .
hadronically. Distinguishing between t and t in the double hadronic decay case will require more effort and still remains an experimental challenge. In Fig. 2 we plot the cross-section, st IItZ as a function of m h and 's , for Model II with tan b , a 1 , a 2 , a 3 4 s 0.3,pr2,pr4,0 4 which we denote as set II. We will adopt set II later also when discussing the CP-violating effect. Here we have set the mass of the heavier Higgs to be m H s 750 GeV. We see that st IItZ is typically ; few fb for c.m. energies of ; 1–2 TeV; it peaks for m h f 2 m t and 's ; 800 GeV at around 7 fb. 3 Therefore, with L R 10 2 wfbxy1 it may be possible to produce 10 2 – 10 3 ttZ’s at the NLC running with c.m. energies R 1 TeV scale. We also remark that, although the crosssections in the SM and Model II are of the same
3
w x Plots of the SM cross-section, st SM tZ , can be found in 9 , where it was also found that st SM tZ ; few fb.
Fig. 3. The asymmetry, A opt , and scaled statistical significance, NSD r'L , for the optimal observable Oopt as a function of the light Higgs mass m h , for 's s1 TeV and 1.5 TeV. See also caption to Fig. 2.
S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
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Table 1 The statistical significance, NSD , in which the CP-nonconserving effects in eq ey™ ttZ can be detected in one year of running of a future high energy collider with either unpolarized or polarized incoming electron beam. We have used a yearly integrated luminosity of L s 200 and 500 wfbxy1 for 's s 1 and 1.5 TeV, respectively, and an efficiency reconstruction factor of e s 0.5 for both energies. NSD is given for both m H s 750 GeV Žin parentheses. and m H s 1 TeV. Recall that j s 1Žy1. stands for rightŽleft. polarized electrons. Set II means tan b , a 1 , a 2 , a 3 4 ' 0.3,pr2,pr4,0 4
's
ŽTeV.
NSD , for Oopt w eq ey™ ttZ ŽModel II with Set II.x
j m h s 100 GeV
m h s 160 GeV
m h s 360 GeV
1
y1 unpol 1
Ž1.8. 1.7 Ž1.6. 1.6 Ž1.5. 1.5
Ž1.8. 1.8 Ž1.7. 1.6 Ž1.5. 1.5
Ž2.2. 2.2 Ž2.0. 2.0 Ž1.8. 1.8
1.5
y1 unpol 1
Ž2.3. 2.9 Ž2.1. 2.6 Ž1.8. 2.3
Ž2.4. 3.0 Ž2.1. 2.7 Ž1.8. 2.3
Ž2.8. 3.3 Ž2.5. 3.0 Ž2.1. 2.6
NSD r 'L , thus scaling out the luminosity factor from the theoretical prediction and as an illustration, for the free parameters of Model II, we adopt set II defined above, i.e. tan b , a 1 , a 2 , a 3 4 s 0.3,pr2,pr4,0 4 . We remark that the effect is practically insensitive to a 3 , and a 1 s pr2, a 2 s pr4 correspond to the best effect, though not unique. Also, the CP-violating effect is roughly proportional to 1rtan b , it therefore drops as tan b is increased. However, we find that we can still have NSD r 'L ) 0.1 even in the unpolarized case for tan b Q 0.6, a 1 s pr2, a 2 s pr4, a 3 s 0. Evidently the asymmetry is almost insensitive to m h in the range 50 GeV Q m h Q 2 m t where it stays roughly at the 7–8% level for 's ; 1–2 TeV Žsee Fig. 3.. In that range 0.1 Q NSD r 'L Q 0.2; it slightly grows as m h is increased and reaches its peak around m h f 2 m t . For m h ) 2 m t , for which an on-shell h is produced and then decays to a pair of tt, as m h grows the asymmetry drops till it essentially vanishes when m h ™ m H in which case the ‘‘GIM’’ like cancellation, discussed above, applies. Also, with respect to the c.m. energy, both A opt and NSD r 'L reach their peak values at around 's ; 1 TeV for both m h s 100 and 360 GeV and weakly fall as the c.m. energy is increased. For example, we find that with m h s 100Ž360. GeV and e s 0.5, it may be possible to observe a CP-nonconserving effect in the reaction ey eq™ ttZ with a statistical significance of NSD f 1.6Ž2.0. for 's s 1 TeV and L s 200 wfbxy1 , and NSD f 2.1Ž2.5. for 's s 1.5 TeV and L s 500 wfbxy1 if the incoming electrons are unpolarized.
In Table 1 we present NSD for Oopt , in Model II with set II, for polarized and unpolarized electrons. For illustrative purposes, we choose m h s 100,160 and 360 GeV and, as before, we present the numbers for 's s 1 TeV with L s 200 wfbxy1 and for 's s 1.5 TeV with L s 500 wfbxy1 . In both cases we take e s 0.5 assuming that there is no loss of luminosity when the electrons are polarized. 4 Also, to demonstrate the sensitivity of the CP-effect to the mass Ž m H . of the heavy Higgs, we present numbers for both m H s 750 GeV Žshown in the parentheses. and m H s 1 TeV. We see from Table 1 that left polarized incoming electrons can probe CP-violation slightly better than unpolarized ones. In particular, for m H s 1 TeV we find that with left polarized electrons and for 's s 1Ž1.5. TeV, the CP-effect is above the 2Ž3.-sigma level for m h R 2 m t . At c.m. energy 's s 1 TeV the CP-effect is practically insensitive to the choice m H s 750 GeV or m H s 1 TeV. However, we see from the Table that as one goes to 's s 1.5 TeV, m H s 1 TeV can give rise to a 3-sigma signal in the range, 100 GeV Q m h Q 400 GeV, if the electrons are negatively polarized, while with m H s 750 GeV the CP-signal is smaller by about half a sigma. We remark again that the results for the simple observable O exhibit the same behavior though slightly smaller then those for Oopt .
4
If the efficiency for ttZ reconstruction is e s 0.25 then our numbers would correspondingly require 2 years of running.
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S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347
Before summarizing we wish to emphasize that the analysis performed here for Model II can be generalized to models I and III as well. Recall that in Model II a mass-dimension-two operator, that softly breaks the discrete symmetry which is responsible for natural-flavor-conservation ŽNFC., is needed in order to have CP-violating Higgs-fermion couplings. On the other hand, in Model III there is no NFC and the CP-odd phase in the H k qq vertex can arise from a phase in the Yukawa couplings Ui 2j and Di2j defined in Eq. Ž1. Žfor more details see w8x.. The pseudoscalar coupling in Eq. Ž2., responsible for CP-violation, can be chosen Žin Model III. as bqk A l q w12x, where l q is a free parameter of the model expected to be of O Ž1. w8x. Then the replacement l t f 1rtan b Žfor a given value of tan b in Model II. can give rise to comparable CP-nonconserving effects in eq ey™ ttZ. Thus, the main difference between Model II and Model III arises from the fact that, while in Model II a small tan b is required in order to enhance the CP-odd effect, in Model III the effect is elevated as l t is correspondingly increased. The same argument holds also for other previously suggested CP studies in top systems where the results obtained for Model II can be generalized to Model III. This seems to indicate that even if such CP-violating effects are found in ey eq™ ttZ or other reactions which involve the top-neutral Higgs CP-phase discussed in this paper, it may not be possible to distinguish Model II from Model III, as both models may have a comparable CP-odd phase in the Higgs sector. In that sense, the best way to proceed for correctly classifying the Higgs sector, is to search for large signatures of FC effects in top quark reactions as well. Model III, with FCS couplings to fermions proportional to the fermion masses involved in the FC vertex w12x, may indeed drive such large FC effects in top systems, some of which are eq ey™ tc; tcne ne ; tceq ey; tcZ; ttcc; tcqq and were investigated in w6x. Detection or no detection of these FC signatures along with evidence for CP-violation in the Higgs sector in high energy eqey colliders, may well be the only way to experimentally distinguish between scalar dynamics of a Model II or a Model III origin. To summarize, CP-violation in ey eq™ ttZ at a future high energy eqey collider was studied in the context of 2HDM’s. An important property of this
reaction is that CP-violation arises already at the tree-level through interference of Z emission from the t or t and its emission off a s-channel Z and therefore allowing for a relatively large CP-violating signal. In particular, we found that within a broad range of the lightest Higgs mass, 100 GeV Q m h Q 400 GeV and with c.m. energies between 1–2 TeV the asymmetry can reach the ; 10% level. The corresponding statistical significance, in which it may be observed, is around 2–3 sigma for unpolarized incoming electrons and, if m h R 2 m t , it can reach above 3-sigma for polarized ones and c.m. energy of 's s 1.5 TeV. Bearing the expected difficulty of observing the Higgs exchange effect in eq ey™ ttZ in the SM and with Higgs masses below 2 m t w9x, it is especially gratifying that the CP-effect is sizable and almost insensitive to m h in the range 50 GeV Q m h Q 2 m t GeV. We therefore encourage a detailed scrutiny of the reaction ey eq™ ttZ in the NLC. Such an investigation, especially due to the promising CP-nonconserving effects reported here, may be helpful in unraveling the CP properties of the Higgs sector. This research was supported in part by the US DOE contract numbers DE-AC02-76CH00016 ŽBNL., DC-AC05-84ER40150ŽJefferson Lab. and DE-FG03-94ER40837ŽUCR.. References w1x Proceedings of the Workshop on Physics and Experiments with Linear eq ey Colliders, Eds. F. Harris S. Olsen, S. Pakvasa, X. Tata ŽWorld Scientific, Singapore, 1993.; A. Miyamoto, Y. Fujii, ibid Ž1996.. w2x For a review, see J. Gunion, H. Haber, G. Kane, S. Dawson, The Higgs Hunter’s Guide ŽAddison-Wesley, New York, 1990.. w3x S. Bar-Shalom, D. Atwood, G. Eilam, R. Mendel, A. Soni, Phys. Rev. D 53 Ž1996. 1162; see also Gunion et al., in Ref. w4x. w4x J.F. Gunion, B. Grzadkowski, X.-G. He, Phys. Rev. Lett. 77 Ž1996. 5172. w5x D. Atwood, A. Soni, hep-phr9607481. w6x M.J. Savage, Phys. Lett. B 266 Ž1991. 135; W.S. Hou, Phys. Lett. B 296 Ž1992. 179; M. Luke, M.J. Savage, Phys. Lett. B 307 Ž1993. 387; L.J. Hall, S. Weinberg, Phys. Rev. D 48 Ž1993. R979; D. Atwood, L. Reina, A. Soni, Phys. Rev. Lett. 75 Ž1995. 3800; Phys. Rev. D 53 Ž1996. 1199; W.-S. Hou, G.-L. Lin, Phys. Lett. B 379 Ž1996. 261; S. Bar-Shalom, G. Eilam, A. Soni, J. Wudka, hep-phr9703221 to appear in Phys. Rev. Lett. ŽJuly 1997..
S. Bar-Shalom et al.r Physics Letters B 419 (1998) 340–347 w7x C.D. Froggat, R.G. Moorhouse, I.G. Knowles, Nucl. Phys. B 386 Ž1992. 63; W. Bernreuther, T. Schroder, T.N. Pham, ¨ Phys. Lett. B 279 Ž1992. 389. w8x For a recent review of Model III, see D. Atwood, L. Reina, A. Soni, Phys. Rev. D 55 Ž1997. 3156. w9x K. Hagiwara, H. Murayama, I. Watanabe, Nucl. Phys. B 367 Ž1991. 257; see also K. Fujii, in the Proceedings of the 4th KEK Topical Conference on Flavor Physics Ž1996., and references therein. w10x We remark that one-loop, CP-odd TN -even, effects in eq ey H ™ ttZ were investigated by B. Grzadkowski ŽPhys. ™ ZH Lett. B 338 Ž1994. 71.. Although asymmetries at the order of
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50% were found there, the SM-like diagrams of class a in Fig. 1 were ignored in that analysis. Since those diagrams make significant contributions to the rate, therefore, Žas was also mentioned by the author. such large asymmetries will be difficult to materialize unless one is able to experimentally separate the contribution from the Higgs exchange graphs from the rest of the diagrams which lead to the same final state. w11x D. Atwood, A. Soni, Phys. Rev. D 45 Ž1992. 45. w12x T.P. Cheng, M. Sher, Phys. Rev. D 35 Ž1987. 3484; M. Sher, Y. Yuan, Phys. Rev. D 44 Ž1991. 1461.