

 1 Dec 95

PHYSICS AT AN e\Gamma e\Gamma FACILITY

FRANK CUYPERS cuypers@pss058.psi.ch Max-Planck-Institut f"ur Physik, F"ohringer Ring 6, D-80805 M"unchen, Germany

We review some of the reactions which can be studied in the e\Gamma e\Gamma mode of a linear collider and may reveal aspects of physics beyond the realm of the standard model. The complementarity to e+e\Gamma scattering is stressed.

1 Introduction There are several important characteristics which differentiate e\Gamma e\Gamma from e+e\Gamma collisions, and justify considering both options on the same footing when it comes to designing the linear colliders of the next generation:

ffl The e\Gamma e\Gamma environment is much cleaner because there is much less standard model activity. In particular, since QCD enters the game only at much higher orders and is always associated with large missing energy, there are no systematic errors due to the possible misidentification of electrons and pions.

ffl Current electron guns can already produce beams with polarizations exceeding 70%. There is no doubt that even further improvements are due. It not clear, however, whether polarized positron beams may ever be obtained at all. The e\Gamma e\Gamma collisions therefore offer the possibility of polarizing both initial states and to perform three independent experiments.

ffl The e\Gamma e\Gamma initial state is not only doubly charged, but also carries a

finite lepton number. This allows to explore fermion number or flavour violating interactions, which are difficult to access in conventional e+e\Gamma annihilations.

These features make the e\Gamma e\Gamma linear collider mode a powerful tool for probing phenomena outside the scope of the standard model 1. We review here several areas where e\Gamma e\Gamma scattering can provide informations which are at least complementary to those that can be gathered in the e+e\Gamma or other operating modes.

2 Z0 Bosons 2 There are many extensions of the standard model which predict the existence of extra neutral vector bosons 3. Most assume lepton universality, so that the generic lagrangian describing the interaction of a heavy neutral vector boson Z0 with the charged leptons can be written

L = e _`fl_ (vZ0 + aZ0 fl5) ` Z0_ ; (1) where vZ0 and aZ0 are the vector and axial couplings. This interaction mediates both e+e\Gamma annihilation and e\Gamma e\Gamma scattering, as depicted in Fig 1.

e\Gamma e\Gamma

e\Gamma e\Gamma fl; Z0;Z0

e\Gamma

e+

_\Gamma _+ fl; Z0;Z0

Figure 1: Lowest order Feynman graphs with a Z0 exchange in e\Gamma e\Gamma and e+e\Gamma collisions.

Of course, if the collider energy is sufficient to sit on the Z0 resonance, the e+e\Gamma option cannot be beaten. However, if the Z0 mass exceeds the collider energy by as little as about 25% the study of angular correlations in Mo/ller scattering turns starts providing stronger evidence for the existence of a Z0 than the e+e\Gamma ! _+_\Gamma reaction. If a Z0 is discovered, both experiments provide complementary bounds on the values of the two couplings vZ0 and aZ0 , as can be observed in Fig. 2.

8????! ????:

ps = 500 GeV Le\Gamma e\Gamma = 10 fb\Gamma 1 Le+e\Gamma = 20 fb\Gamma 1

-1 -0.8 -0.6 -0.4 -0.2

0 0.2 0.4 0.6 0.8

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 aZ0

vZ0

+ + + + +

+ + +

+

+

+ +

e

\Gamma e\Gamma

e+e

\Gamma

Figure 2: Contours of resolvability at 95% confidence of the Z0 couplings around several

possible true values marked with a `+'.

3 Dileptons 4 An important class of grand unified schemes predicts the existence of doubly charged vector gauge fields, which couple universally to leptons. These dileptons would show up as striking resonances in e\Gamma e\Gamma scattering, as depicted in Fig. 3.

e\Gamma e\Gamma

_\Gamma _\Gamma X\Gamma \Gamma

e\Gamma

e+

e+ e\Gamma X\Gamma \Gamma

Figure 3: Lowest order Feynman diagram describing a dilepton exchange in e\Gamma e\Gamma and e+e\Gamma

collisions.

The situation here is just opposite from Z0 production, in the sense that below threshold it is now Bhabha scattering which provides better discovery limits. Still, as in the Z0 case, one may anticipate that both reactions are complementary when it comes to study the couplings of an off-shell dilepton. Of course, once the collider energy comes close to the dilepton resonance, the e\Gamma e\Gamma option is best.

4 Leptoquarks 5 Leptoquarks are predicted by a large number of extensions of the standard model and can appear in many combinations of several quantum numbers 6. One of these quantum numbers is the fermion number F = 0; 2 carried by the leptoquark. It turns out that other experiments are not directly sensitive to F (except for electron-(anti)proton collisions at LEP-LHC, if this option is ever turned on). Therefore, even if a leptoquark is discovered at an e+e\Gamma or another facility, its true nature may remain hidden.

e\Gamma e\Gamma

L0 L2 q

Figure 4: Typical lowest order Feynman diagram describing the production of two leptoquarks (scalar or vector or both) in e\Gamma e\Gamma collisions.

This is where e\Gamma e\Gamma collisions become interesting, because to lowest order they can only produce a pair of leptoquarks, one with fermion number F = 0

and the other with F = 2, as depicted in Fig. 4. Therefore, the observation of such events would demonstrate the simultaneous existence of these two states. Similarly, the non-observation of this mechanism would impose strong bounds on extensions of the standard model.

To estimate the discovery potential, Fig. 5 shows in the (m; *=e) plane the oe = 1 fb curve for one of the five possible types of reactions. Assuming the produced leptoquarks have the same mass, the following general discovery scaling law applies

*

e = 0:35 pm=TeV `

n A L=fb\Gamma 1 '

1=4

m ^ :43ps ; (2)

where e is the charge of the electron, * is the geometric mean of the two leptoquarks' couplings, m is their common mass, n is the required number of events, L is the available luminosity and A is a number ranging between 1 and 24, according to which types of leptoquarks are produced.

8????? ???!

???????? :

ps = :5 TeV

1 TeV 1:5 TeV

2 TeV

0 0.05

0.1 0.15

0.2 0.25

0.3 0.35

0.4 0.45

0.5

0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5 *

e

0@A L=fb

\Gamma 1

n

1A1=4

m [TeV] Figure 5: The parameter space below the curves cannot be explored in e\Gamma e\Gamma scattering.

The thinner osculating parabola is given by Eq. (2).

5 Majorana Neutrinos 7 In the presence of heavy Majorana neutrinos, W \Gamma pairs can be produced in e\Gamma e\Gamma scattering, as depicted in Fig. 6. Low energy experiments severely constrain the masses and mixings of these states, so that with 500 GeV and 10 fb\Gamma 1 no more than about 100 such events are expected 8. In principle, a single occurrence of this fermion number violating transition would suffice to establish a departure from the standard model.

e\Gamma e\Gamma

W \Gamma W \Gamma *M

Figure 6: Lowest order Feynman diagram describing W \Gamma pair-production via Majorana

neutrino exchange in e\Gamma e\Gamma collisions.

However, the higher order electroweak reactions

e\Gamma e\Gamma ! W \Gamma W \Gamma ** (3)!

W \Gamma Z0*e\Gamma (4)! Z0Z0e\Gamma e\Gamma (5)! W +W \Gamma e\Gamma e\Gamma ; (6)

where the Z0's decay invisibly or hadronically, may very well mimic the exotic reaction. Indeed, most of the primary electrons in reactions (4-6) disappear into the beam-pipe 9. As can be gathered from Fig. 7, the cross sections are substantial, so that the leptonic decays of the pair-produced signal W \Gamma 's are unlikely to emerge from the backgrounds. One therefore has to concentrate on the hadronic decays, but then also the Z0's may be mistaken for W \Gamma 's if the jet invariant mass resolution is insufficient.

1 10 100 1000

200 400 600 800 1000 1200 1400 1600 1800 2000 oe [fb]

ps [GeV]

W Z(LL)

W W (LL)

W Z(LR)

ZZ(LL)

ZZ(LR)

ZZ(RR)

Figure 7: Total cross sections for gauge boson pair-production in polarized e\Gamma e\Gamma scattering.

Nevertheless, the backgrounds (3-6) can easily be removed by considering their total hadronic energy or transverse momentum distributions. These are

depicted in Fig. 8 for reaction (4) and show basically no overlap with the (smoothed) Dirac distributions centered at ps and 0, which are expected from the 2-body reaction e\Gamma e\Gamma ! W \Gamma W \Gamma . Therefore, a Majorana signal cannot be mistaken for any standard model process.

8! :

ps = 500 GeV

beams left polarized

0 4 8 12

0 0.1 0.2 0.3 0.4 0.5 [TeV\Gamma 1]

[TeV]

1 oe

doe dp?WZ 1

oe

doe dEWZ

Figure 8: Transverse momentum and energy distributions of the W \Gamma Z0-pair in reaction (4). 6 Selectrons 10;11 Selectrons, the supersymmetric scalar partners of the electrons 12, can be pairproduced in e\Gamma e\Gamma scattering via the exchange of four neutralinos, as depicted in Fig. 9.

e\Gamma e\Gamma

~e\Gamma ~e\Gamma ~O/0i (i = 1 : : : 4)

Figure 9: Lowest order Feynman diagram describing selectron production via the exchange

of neutralinos in e\Gamma e\Gamma collisions.

This reaction is described elsewhere in these proceedings 13. Let us just repeat here that it suffers from very little standard model backgrounds and is thus ideally suited for discovering the selectron. Moreover, the background-free environment allows for a very precise kinematical (hence model-independent) measurement of the mass of the lightest neutralino, which in the minimal supersymmetric standard model escapes detection. Similarly, since no hefty energy or transverse momentum cuts are required to separate signal from background, possible cascade decays of the selectron will be clearly observable 11.

7 Higgs Bosons 14;15;16 The hunt for the standard model Higgs boson is certainly one of the most pressing issues in high energy physics today. Also an e\Gamma e\Gamma experiment may provide further information about this mysterious sector via Z0 fusion 14, as depicted in Fig. 10. Here again, the low standard model background is an important asset.

e\Gamma e\Gamma

e\Gamma e\Gamma H Z0

Z0

Figure 10: Lowest order Feynman diagram describing the production of the standard model

Higgs bosons in e\Gamma e\Gamma collisions.

Similarly, the W fusion mechanism depicted in the first diagram of Fig. 11 can produce two charged Higgs', which typically arise in a two doublet Higgs model 15. This reaction, which involves the full spectrum of neutral Higgs', is a particularly sensitive probe of the extended Higgs nature.

e\Gamma e\Gamma

*e *e H\Gamma H\Gamma

W

W h; H; A

e\Gamma

e\Gamma

_\Gamma _\Gamma H\Gamma \Gamma

Figure 11: Lowest order Feynman diagrams describing the production of charged Higgs

bosons in e\Gamma e\Gamma collisions.

The full potential of e\Gamma e\Gamma collisions, though, is realized in the search for a doubly charged Higgs 16, which could be produced in the s-chanel reaction of Fig. 11. The corresponding exotic Higgs representation is not necessarily ruled out by the observation that ae = 1, if its neutral member has no vacuum expectation value. The exploration of this doubly charged resonance by an energy scan would provide most remarkable information about the Higgs sector.

8 Anomalous Gauge Couplings 17;18 Vector boson self-couplings are one of the most eminent consequences of a non-abelian symmetry. Their form is precisely dictated by the gauge principle, so that any deviation may provide crucial information about the new physics lurking at the TeV scale.

To parametrize our ignorance about the latter, it is customary to consider an effective lagrangian of the form 19

LW W Veff = \Gamma igV ^g1V iW yfffiW ff \Gamma W yffWfffij V fi + ^V W yffWfiV fffi (7)

+ *

V

M 2W W

y fffiW

fioeV oeff* (V = fl; Z) ;

where Vfffi = @ffVfi \Gamma @fi Vff and Wfffi = @ffWfi \Gamma @fi Wff. The standard model prediction is recovered by setting ^V = g1V = 1 and *V = 0. Other C and/or P violating anomalous terms can also be added, and there are similar extensions of the quartic part of the lagrangian. These anomalous couplings are determined or constrained within particular models.

e\Gamma e\Gamma

e\Gamma *e W \Gamma fl; Z0 W \Gamma

e\Gamma e\Gamma

e\Gamma *e W \Gamma

fl; Z0

+ \Delta \Delta \Delta

Figure 12: Lowest order Feynman diagram involving a triple gauge vertex and one of its

backgrounds in e\Gamma e\Gamma collisions.

e\Gamma e\Gamma

e\Gamma *e Z0 W \Gamma Z0 W \Gamma

e\Gamma e\Gamma

e\Gamma

*e W \Gamma Z0

fl; Z0

+ \Delta \Delta \Delta

Figure 13: Lowest order Feynman diagram involving a quartic gauge vertex and one of its

many backgrounds in the reaction (4).

Anomalous triple 17 or quartic 18 vertices can be probe through W \Gamma production in e\Gamma e\Gamma scattering, as depicted in Figs 12 and 13. In the case of a strongly interacting Higgs sector, for instance, for which the anomalies are severely constrained, these reactions are described with more details elsewhere in these proceedings 20. Let us only mention here, that in general the use of polarized beams significantly enhances the resolving power, as is clearly demonstrated in Fig. 14. This resolving power is comparable to what can be achieved with a similar analysis and assumptions in other linear collider modes, such as e+e\Gamma , e\Gamma fl or flfl scattering.

8????! ????:

ps = 500 GeV Le\Gamma e\Gamma = 10 fb\Gamma 1 hadronic W \Gamma decays only

-0.2 -0.15

-0.1 -0.05

0 0.05

0.1 0.15

0.2

-0.1 -0.05 0 0.05 0.1 kZ-1

kg-1

LR LL Figure 14: Contours of detectability at different confidence levels (O/2 = 2; 4; 6) of ^fl and ^Z for LL and LR polarizations. The remaining couplings assume their standard model values.

9 Conclusion To summarize, we have described a few processes predicted by extensions of the standard model, which may be observed at an e\Gamma e\Gamma facility. Some of these reactions are outstanding, in the sense that no other experiment can perform as well (e.g., the search for Majorana neutrinos or the identification of F = 0 and F = 2 leptoquarks). Other reactions deliver informations which are comparable and complementary to those obtainable in other collider modes (e.g., Z0 searches or anomalous gauge couplings).

Considering the potential benefits and the relative ease with which a positron beam can be replaced by an electron beam at a linear collider, e\Gamma e\Gamma collisions emerge as a worthy endeavour for the high energy physics community.

References This list of references is by no means exhaustive. However, most of the cited papers have been published recently and contain the references to the relevant earlier publications. A more and nearly complete e\Gamma e\Gamma bibliography can be accessed on the WWW at http://pss058.psi.ch/cuypers/e-e-.html.

1. C.A. Heusch, Proc. of the 1st Arctic Workshop on Future Physics and

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T.G. Rizzo, Phys. Rev. D46 (1992) 910. 5. F. Cuypers, MPI-PHT-95-107, Santa Cruz e\Gamma e\Gamma Workshop, Santa Cruz,

CA, 4-5 Sep 1995 . 6. W. Buchm"uller, R. R"uckl, D. Wyler Phys. Lett. B191 (1987) 442. 7. cf., e.g., C.A. Heusch, P. Minkowski, Nucl. Phys. B416 (1994) 3;

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Nucl. Phys. B430 (1994) 231 . 10. F. Cuypers, G.J. van Oldenborgh, R. R"uckl, Nucl. Phys. B409 (1993)

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H.E. Haber, G.L. Kane, Phys. Rep. 117 (1985) 75. 13. Selectron Searches in e\Gamma e\Gamma , flfl and flfl Scattering, these proceedings. 14. K.I. Hikasa, Phys. Lett. B164 (1985) 385; erratum, ibid. B195 (1987)

623. 15. T.G. Rizzo, SLAC-PUB-95-7031, Santa Cruz e\Gamma e\Gamma Workshop, Santa

Cruz, CA, 4-5 Sep 1995 . 16. J.F. Gunion, UCD-95-36, Santa Cruz e\Gamma e\Gamma Workshop, Santa Cruz, CA,

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Physics Potential, Munich/Annecy/Hamburg, 1992-93, DESY 93-123C, p. 177, Ed. P. Zerwas, and references therein. 20. Manifestations of Strong Electroweak Symmetry Breaking in e\Gamma e\Gamma Scattering, these proceedings.

