We present the results of a calculation of deep inelastic electron-photon scattering at a linear collider for very high virtuality of the intermediate gauge boson up to NLO in perturbative QCD. The real photon is produced unpolarized via the Compton back s

2 tained for photon produced by bremsstrahlung o the lepton which is of O( ). Furthermore, by choosing the helicities of laser and electron beams to be opposite, the photon spectrum is peaked at high energies. In this region, about 80% of the energy of the electron/positron beam can be transferred to the backscattered photon. In the following we shall give our predictions for the most advantageous photon spectrum and will therefore consider the backscattered photon obtained for opposite polarizations of electron and laser photon, with x0= 4:83. Our results will be obtained for the cross section e+ e? ! l+X which is related to the cross section for e? ! l+ X as follows, Z d (2) d e e? !l+X= dy 1 dy c d e !l+X: c++

while in the charged current di erential cross section enter the x and Q2 dependent structure functions F2;CC, FL;CC and F3;CC multiplied by weak propagator and coupling factors as follows? d2 CC (e+ !+X )= dxdQ2 Q4 (1 P ) 1 2 2 4 Q2+ MW]2 sin4 w 4 xQ h (1+ (1? y)2 )F2;CC( )

(1? (1? y)2 )xF3;CC? y2FL;CC: (4)

i

MW and W are the W-mass and the weak Wein-

At momentum transfer squared Q2 close to the Z and W masses squared, the deep inelastic cross section for e+ ! l+ X becomes sensitive to contributions from these exchanges 4]. Neutral current deep inelastic events are characterized by the exchange of a photon or a Z boson, and have an electron and a jet (or jets) in the nal state. Charged current events arise via the exchange of a W-boson and contain an undetected neutrino and a jet (or jets) in the nal state. The presence of an neutrino is as usual detected as missing transverse momentum. Having these signatures, those processes constitute potential background sources for searches for new physics at the future e+ e? linear collider. To give a prediction for the size of these contributions is precisely the aim of this study.

3. Deep-Inelastic Electron-Photon scattering

berg angle. P denotes the degree of left-handed longitudinal polarization (P=?1 for left-handed electrons, P= 1 for right-handed electrons). The kinematics of these neutral and charged current reactions is described by the Bjorken variables x and y. Those can be expressed in terms of the four-momentum transfer, Q2, the hadronic energy W, the lepton energies and scattering angles. Indeed we have,2 Q2 x= 2q:p= Q2 Q W 2+ q:p= 1? E cos2 (=2): y= k:p E0

(5)

3.1. Kinematics

The neutral current di erential cross section is parameterized by the x and Q2 dependent structure functions F2;NC and FL;NC, d2 NC (e+ ! e+ X )= dxdQ2 2 2 h(1+ (1? y)2 )F;NC? y2 F;NC i (3) 2 L xQ4

Th

e initial state photon is real and on-shell and the lepton masses can be set to zero. Experimentally, one needs to constrain the lepton scattering angle e to be larger than some minimum angle min . Equivalently, one can also require, 4 2 (1 o )xse Q2> xs (1E c )? c4E 2 (1? c ) e+ o+ o 2> Q2 (x; se; co ) Q (6) with co= cos min and se the electron-photon center-of-mass energy squared. This constraint on the 4-momentum transfer Q2 is shown as a p function of x in Fig. 1 for se= 500 GeVand for min= 5; 10; 20 degrees. The corresponding allowed kinematical regions are then situated between Q2= Q2 (x; se; co) and Q2= xse (corresponding to y= 1).