(-0sJI'- q5-D 3 5 - - 3 BROOKHAVEN NATIONAL LABORATORY

* CP violat ion and flavor-changing-currents at p+p- colliders

Amarjit Soni Department of Physics, Brookhaven National Laboratory

Upton, NY 11973, USA

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recam- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

* Invited talk at the Symposium on Physics Potential and Development of p+p- Collid- ers, San Francisco, CA, Dec. 1995.

This manuscript has been authored under contract number DEAC02-76CH00016 with the U.S. Depart- ment of Energy. Accordingly, the US. Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.

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CP violation and flavor-changing-currents at p+p- colliders Amarjit Soni a

aBrookhaven National Laboratory Physics Department, Upton, NY 11973

Production and decay (CP) asymmetries at p+p- collider, in extensions of the Standard Model (SM) are reported. Production asymmetries appear to be very promising for a large range of parameters, decays are less effective. Importance of flavor-changing scalar currents involving the top are emphasized. At lepton colliders, the t E final state is uniquely suited for such searches. At a muon collider there is the novel possibility of tree level p+p- + t E . This talk is based on works done in collaboration with David Atwood and Laura Reina [l-41.

1. INTRODUCTION

At this point there are two main en- ergy regimes in which a muon collider ap- pears very attractive [5]. First of all, in the Multi TeV regime, a lepton collider could be very useful as due to its cleanli- ness it could provide important checks to LHC physics. Also it could complement the LHC effort in focusing in on physics issues that emerge to the necessary detail. The common folklore is that multi TeV electron positron colliders may not be fea- sible. If so then muon colliders in that energy regime could be an extremely in- teresting option, if they can be feasible.

Muon-collider in the relatively low en- ergy regime can also be very interesting. At center of mass energy of a few hun- dred GeV it could provide the fascinat- ing and unique possibility of an in depth study of Higgs through the s-channel res- onance [1,6]. Details of the Higgs sector holds answers to many puzzles in Parti-

cle Physics: the origin of mass, its rela- tion to symmetry breaking, the underly- ing nature of fermion families, CP viola- tion etc. The Higgs sector is like a rug under which much of the details of gauge models are swept and a muon collider with its s-channel Higgs capability can act as a microscope for looking under that rug.

In the rest of the talk I will focus on is- sues pertaining to CP violation and flavor- changing neutral currents (FCNC). Here is the outline:

1. Production Asymmetry [l] in p+p- +n.

‘FI+tt;r+r-. 2. Decay Asymmetries [l] in p+p- +

3. e+.!- + t E : A uniquely clean signal for FCNC[3].

4. p+p- + Fl + tE: Tree level flavor- changing-scalar-currents( FCSC) [Z].

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FIGURE 1 . . . .

GeV

Figure 1. The value for Rx as a function of mx for the following three cases: (1) 'FI = H , Q = 7r/4 and xf = 1 (solid) (2) 'FI = A and xf = 1 (dashes) (3) 'FI = A and xl = x d = 5 and xu = 1/5 (dots). In each case the upper branch represents the result for J;; = mx while the lower branch is the result with an energy spread given by S = 10-3

2. 3-CHANNEL HIGGS IN MOD- ELS WITH EXTENDED HIGGS SECTOR [1,6]

Although the X,,,, coupling is very weak its effects get enhanced if the p+p- en- ergy is tuned to be at mx. Defining B,, = B('FI + p+p-) and ax = a(pfp- + 7-t) then the resonance cross section for Higgs boson production is:

For purposes of orientation this may be compared with the point cross section,

Figure 2. The value of for case 1 (see caption to Figure 1) assuming Q = ~ / 4 = A,. y r ) is shown with the solid line, y$$ with the dot-dashed line, yg i ' with the dotted line, and y!?' with the dashed line. (Note y3" is the number of years needed to accumulate a 3a production asymmetry. Note also that the horizontal line, y3" = 1, is drawn to serve as a point of reference.)

where ae is the electromagnetic coupling. So it helps if the Higgs has a narrow width.

In writing equation (2) we assumed that the energy of the collider could be tuned to a precision much finer than the Higgs width. This may be difficult to attain for a relatively light mx. To take the energy spread of the beam into account let us assume that the actual value of s is uni-

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formly distributed in the range FIGURE 3

mB(1- 6) < s < m k ( l + 6) (3) Such a spread will lead to a change in the observed rate to [l]:

In our numerical work we will use the value 6 = iob3.

Note that we are imagining here that although the underlying model may have several Higgs doublets, the couplings of a single Higgs boson, 3-1, parameterized in a general form:

( 5 )

are under experimental study. To serve as an illustration we further consider three separate models:

1. 3-1 = H(O++) with Q! = 2 = A j and Xf = 1 for a fermions.

2. 'FI = A(.-+) with Xj = 2 and Xf = 1 for all fermions.

Fig. 1 shows the Higgs production cross sections relative to p+p- + y* + e'e-. In each of the 3 cases mentioned above Rw and R, with 6 = are shown. Note the pronounced effect of the VEV ratio in case (3) due to the fact that the decay to t t is suppressed and the bb and pji modes are enhanced.

Figure 3. The value of y(3u) for case 2

shown with the solid line, and y j r ' with the dashed line. The results for decay asymmetries are also shown: d:?' with the dot-dashed line and GE) with the dot- ted line. In both of the latter cases the lower curve is for P = .9 and the upper curve is for P = 0. See captions to Fig- ures 1 and 2.

assuming A, = A, = At = a/4. yG (3u) is

3. TRANSVERSE POLARIZA- TION ASYMMETRY

Most likely the muons would be corn- ing from the decays of the pions; so the p- would be strongly left-polarized. If the muon polarization could be manipu- lated and preserved during the accelera- tion process then with transversely polar- ized muons a very interesting possibility of probing the CP violation phase(s) in the muon-Higgs coupling arises.

The experiment is the reverse of the classic reaction KL --+ p+p- wherein the

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FIGURE 4

PP- d

10-5 10'6100 k c l I' .,,- m 200 300 400 500 600 800

GeV

Figure 4. The value of y(*) for case 3

shown with the solid line, and yt:) with the dashed line. The results for decay asymmetries are also shown: $@' with the dot-dashed line and with the dot- ted line. Again in both of the latter cases the lower curve is for P = .9 and the up- per curve is for P = 0. See captions to Figures 1 and 2.

assuming A, = A, = At = 7r/4. ybi; (36) is

transverse polarization of muons can be used to search for CP violation. Consider now p+p- + 3-1 with transversely polar- ized muon beams. In the CM frame of p+p- take 5'- to be along z and spin of p- to be along the x direction. Also the p+ spin is taken to be at an angle dP with p- in zy plane. Then the cross section for p+p- + 'FI is:

a(#,) = (1 - cos 2A, cos +p + sin 24, sin #,)a0

where a0 is the unpolarized cross section.

Then a CP-odd asymmetry in the produc- tion arises, given by

a(9O0) - a(-900) , - a(900) + a(-900) A - = sin2A, (7)

Here A, is the CP violating phase in the Higgs fermion coupling given in eqn. Thus this CP violating phase in the underly- ing Lagrangian becomes cleanly measur- able, provided transverse polarization of the beam is possible. Since such a phase (A,) is unconstrained, in principle, large asymmetries are possible.

4. ASYMMETRY DUE TO DE- CAYS OF T AND t

Consider now the reactions p+p- + 3-1 + T+T-, tq1,7]. For these modes CP violation can be searched in the decays of T ' S or t ' s using triple correlation. This is feasible because T and t decays are very effective analyzers of their spins.

In the Higgs rest frame, let the momen- tum of f(t or 7) in the z' direction. De- note the decay products as f --+ z;y; and f + Z j y j . Let $;j be the azimuthal angle between p,; and psi projected on to the x'-y' plane. Then

We then get the CP violating asymmetry as :

For such an asymmetry beam polariza- tion is not essential. However, longitu- dinal polarization of the beams helps to

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increase the signal over the background. The point is that all SM interactions, giv- ing rise to backgrounds preserve the helic- ity, whereas Higgs flips the muon chirality. So if both beams are left polarized with polarization P then the Higgs production is enhanced by (1 + P 2 ) whereas the back- ground is reduced by (1 - P 2 ) .

For a final state f, let y y ) be the num- ber of years needed to accumulate a 3a signal for the CP asymmetry. Then [l]

where Rj is the standard model contribu- tion to a specific final state j and Lo is the integrated luminosity per year.

Let yi3") be the CP asymmetry in the production obtained by monitoring the decay of the Higgs to a final state i and $I""' the decay azimuthal asymmetries for j = t f o r T+T-. We now turn to numerical results for these.

5. NUMERICAL RESULTS FOR THE ASYMMETRIES

Fig. 2-4 show the numericalresults. For illustration a luminosity of 1034cm-2s-1 is used giving Lo = 1041 cm-2yr-1 (taking 1/3 efficiency). We take Xf = n/4 and show results for the 3 cases of Higgs cou- plings outlined above.

Fig. 2 shows y30 for the production asymmetries for various final states for case 1. For mx < 2mw, y30 increases rapidly and is around 1 for mx - 250 GeV.

Case 2 of the coupling is shown in Fig. 3. Also 6 = is used for all the curves here. Since for this case WW, 22 thresh- olds are absent, a small value of y3" per- sists up to m% - 2mt. For m . ~ > 2mt, y;: grows rapidly and becomes 1 around 400 GeV. Decay asymmetries iz and if: are also shown. 6% is about 10 below the tf threshold. ytr grows rapidly over 1 above the t f threshold. The Fig. also shows the effect of longitudinal beam polarization on these two asymmetries. We see that po- larization can improve the effectiveness of the asymmetries by as much as an order of magnitude.

Case (3) of the Higgs coupling is shown in Fig. 4. In this case the production asymmetry ~ ( ~ 1 becomes extremely sen- sitive: it ranges from to over the entire mass range. For this case then the production asymmetries are excellent probes for Higgs mass up to about 800 GeV. Indeed this production asymmetry should be detectable even with L - lo3' cm-2s-1. Also the decay asymmetries are very effective for rnx < 2mt. i iy) is about 0.01 and around 0.1-1 below the ti? threshold. The decay asymmetry there- fore should work very well for m% ,< 300 GeV. For m% ,> 300 GeV the t f channel seems more promising to the extent the L N

4 3 6 )

cmd2sP1 may well be adequate.

6. FLAVOR CHANGING t c CUR- RENTS[2,3]

The fact that the top quark is so much more massive than the other quarks (and leptons) has prompted many to suggest that the top may possess other unusual

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1 E-03

le-04

1 e 4 9 100 200 300 400 500 600 700 800

M, (GeW

Figure 5. Rtc/X4 vs. the common scalar mass, M, for 4 = 200 (solid), 500 (dashed), and 1000 GeV (dot-dashed).

features. In particular, a fascinating pos- sibility is that of enhanced flavor changing tc (or tu) currents(8,9,2,3].

7. e+.!?- + tc : A Uniquely Clean Sig- nature[2]

The lepton colliders (e+e- or p+p-) present a very clean way to search for the flavor changing reaction:

e+e- + t ~ , Zc (11) Since mt >> m,, the reaction leads to a unique, “kinematic” signature: a top can- didate event with more than 1/2 the beam energy! Of course, the additional check will be that opposing jet will be essen- tially massless. So, e.g., at E = 400 GeV, Et - 240 GeV, E, - 160 GeV.

’*04 r------

Figure 6. Rtc/X4 vs. the light scalar mass, Ml, for f i = 500 GeV. Case 1 (solid) i.e., mh = Ml and mA N m* = 1 TeV; case 2 (dashed) i.e., mA = Ml and mh N m5 = 1 TeV; case 3 (dot-dashed) i.e., m* = Ml and mh N mA = 1 TeV.

This clean signature in e+e- for t c is in sharp contrast to hadron colliders. Here there is a tree-level SM background from ud + t& followed by the decays of the &. It appears extremely difficult to separate “prompt” tc from such backgrounds.

It is very important to search for flavor- changing tc currents. Indeed just as im- portant as, say, p + ey. So the existence of specific models that predict such reac- tions quantitatively should not be neces- sary. Just as continuous experimental ef- forts are directed towards improving our knowledge of p -+ ey, KL + pe etc. we need to continually improve the bounds on

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t c ; e+,- -+ tc is just about the best way. 10'

l e - 0 4 . - I . . . ~ I I ....... ... . . . . . . . . . . _._ ..... .. . . . . . . . .. . . .. 18-05 -

le-06 - ,;,/ . . :

18-08 :

4 8 - 0 9 , ' ' ' ' ' ' ' ' 200 300 403 500 600 7W 800 900 1oM)

sqrt(s) (GeV)

Figure 7. RtC/X4 vs. f i with it& = 200 GeV for case 1 (solid), case 2 (dashed) and case 3 (dot-dashed).

8. 2HDM with FCSC (MODEL 111) [2,3,81

Figure 8. The value of A ( H ) is shown as a function of mx for scenario 1 (dash-dot) and for scenario 2 (dots). The value of At, is shown in case 1 for 6 = 0 (upper solid curve); S = lop3 (middle solid curve) and S = (lower solid curve). The value of Rtc is shownin case 2 for 6 = 0 (upper dashed curve) and S = (lower dashed curve).

etc. that flavor-changing transitions in- volving the 1st family of quarks, must be severely suppressed[lO]. This can be ac- commodated, in a natural fashion by pa- rameterizing the Higgs-fermion coupling strength as:

A mild extension of the SM with an ex- tra Higgs doublet leads naturally to flavor- changing-scalar-currents (FCSC). Such a version of 2HDM is called Model 3. The Then FCSC with light quarks are sup- model is particularly useful for cataloging pressed and those involving the top quark the strength of the flavor-changing cou- enhanced. plings, which must be extracted from ex- In such a model, efe- 4 tc arised at periments. It is clear, though, from the one loop order. The coupling relation phenomenology of K-R, B d - & oscillation (eqn.12) is used and the cross section for

t c is normalized as [ 31 : a(e+e- + t~ + fc)

a(e+e- + y -+ p+p-) RtC f

Figs. 4-7 show the numerical results for various scenarios of assumed neutral and charged scalar masses; Dependence on the beam energy is shown in Fig. 7 . Thus RtC - 0(10-5) is possible for a range of parameters for fi 2 400 GeV. Note that Rtc is very sensitive to X and scales as X4.

9. p+p- + tc AT A TREE-LEVEL! E21

A muon collider offers the novel pos- sibility of flavor changing tc currents at tree-level, in Model 111. Parameterizing the %*tc vertex as

(14)

where PL,R = coefficients, in general. Then

and XL,R are complex

Once again we normalize the rate p+p- + 3.1 + tc to ptfp- + y* + e+e-. Fig.8 shows the normalized ratio Rtc including the effect of beam spread. We see that with a cm-2s-1 luminosity several hundred t Z are possible.

Since the decays of the top quark can be used to analyze its spin study of the top decays can be used to solve for XL, XR. Only a few hundred events are needed for this purpose[2].

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2. D. Atwood, L. Reina and A. Soni, Phys. Rev. Lett. 75 (1995) 3800.

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5. See also the talks by V. Barger, J. Gu- nion and by T. Han in these proceed- ings. V. Barger, M.S. Berger, J.F. Gunion, and T. Han, Phys. Rev. Lett. 75 (1995) 1462.

7. See also, B. Grzqdkowski and J. F. Gunion, Phys. Lett. B350, 218 (1995).

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9. M.J. Savage, Phys. Lett. B266, 135 (1991); W.S. Hou, Phys. Lett. B296, 179 (1992); L.J. Hall and %Weinberg, Phys. Rev. D48, R979 (1993); G.C. Branco, P.A. Parada, M.N. Rebelo, UWTHPH-1994-51, (1995); T. Han, R.D. Peccei, and X. Zhang, preprint

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