1. Trilinear Gauge Couplings at TESLA Photon Collider Ivanka Božović - Jelisavčić & Klaus Mönig DESY/Zeuthen

2. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop TGCs in W-pair production - sensitive observables Measurement of anomalous   and  at a photon collider at TESLA Summary

3. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop TGCs in W-pair production - sensitive observables In order to understand the mechanism EW symmetry is broken, self interaction of the gauge bosons can be used to reveal a structure of the underlying gauge group. In particular, W-pair production at high energies is a sensitive process to the possible scenarios of EWSB. W-pair production in  collisions is dominated by single diagram. Due to spin-1 t-channel exchange, the cross-section for W-pair production becomes flat in the ‘picobarn region’, above threshold up to 1 TeV center-of-mass energy.   WW WW WW

4. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop High production cross section of W pairs in  collisions allows cuts to be successively applied, so the signal can be extracted with a ratio to background of 27:1

5. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop A potential of different observables for analysis of the anomalous TGCs has been discussed. We study the effect of anomalous dipole coupling parameter   on differential cross-section for W-pair production in  collisions and on W polarization fractions reconstructed from W production and decay angle distributions.

6. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop ‘W production angle’ - the polar angle of the outgoing W with respect to the e - beam direction ‘W decay angle’ - the angle of fermion with respect to the W flight direction, reconstructed in the W rest frame Azimuthal angle of the fermion in the plane orthogonal to W direction, where the axes are defined in such a way that the electron beam is contained in X-W plane. Measurement of triple gauge couplings in W-pair production is in principle based on several sensitive angular observables: These information can be combined (i.e. by using the optimal observables method) in order to determine anomalous coupling parameters.

7. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop Tools: –SIMDET V3 - A Parametric Monte Carlo for a TESLA Detector –Analytic formula for total (differential) cross-section (E.Yehudai, Phys. Rev. D11(44)1991) based on helicity amplitudes for different initial and final states (G. Belanger et al., ENSLAPP-A- 473/94, hep-ph/9405359) –WHIZARD Monte Carlo generator based on tree-level matrix elements for multi particle processes. Sample of 10 5 mixed W decays is generated at = 500 GeV

8. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop The shape and the size of the total cross-section for W-pair production is dominated by transverse W mode

9. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop The cross-section to produce one L and one T W from a Jz=0 initial two- photon state is 0 in the Standard Model. Production of two longitudinal Ws (LL) for both initial two- photon states is suppressed in the Standard Model. TT/LL/LT: 99.9/0.1/0.0,   =0 TT/LL/LT: 96.3/1.4/2.3,   =0 TT LL LT TT LT LL

10. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop TT/LL/LT: 99.9/0.1/0,   =0 TT LL LT  /  SM   =1.01   =0.99 Although Ws from initial two-photon state Jz=0 do not exhibit a polarization structure, differential cross-section is sensitive up to 2% to 10 -2 variation of parameter  . This effect is more pronounced in the forward region.

11. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop However, Jz=2 state exhibits a structure over the W polar angle range. This implies that longitudinal Ws could be partially recovered in the central region. Fraction

12. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop TT LL LT TT/LL/LT: 70/16/14,   =0 Differential cross-section as a function of W production and decay angle, can be used to extract the polarization fractions from simulated (experimental) data, even without identification of charges of the decay products. (M. Bilenky et al., Nuc. Phys. B409(1993)22)

13. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop Jz=2

14. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop Similarly, one-dimensional decay angle distribution can be fitted in order to determine fraction of polarization states T=TT+TL and L=LL+LT

15. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop WHIZARD results follow the trend predicted using numerical function, however they deviated for several sigmas. Possible explanation for it might be due to the fact that function, differently from WHIZARD, generates cross-sections for on-shell Ws. If we generated on-shell W pairs with WHIZARD as well, the numerical prediction of the function will be confirmed: TT/LL/LT, 70±3/16±1/15±1. As well, by restricting W mass narrower around it’s nominal value (i.e. |  M W |<2 (1) GeV), the WHIZARD prediction for W mixed decays converges towards on-shell approximation. This implies that contribution from tree-level non-resonant processes to production of off-shell W pairs could possibly explain the effect.

16. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop Recovering longitudinally polarized Ws (LL, LT) from initial two- photon state Jz=2, their fraction can be determined with a statistical error of order ~10 -3 for an integrated luminosity of ~ 120 fb -1. This would make accessible the ~2% effect of deviation of W’s longitudinal fractions from their SM values, for anomalous   =0.01 coupling.   =1.01   =0.99 F ac /F SM

17. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop   = 0.90   = 1.10   = 0.99   = 1.01 Dominance of the transverse W modes even when angular cuts are imposed, makes Jz=0 channel not promising to exploit the sensitivity of W polarization fractions to anomalous dipole coupling parameter  .

18. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop Measurement of   and  From the 2D decay angle distributions of the accepted data the dipole and quadrupole coupling parameters can be fitted. The statistical error and systematic effect of the error of luminosity have been estimated. Acceptance Decay angle W1 Decay angle W2 3D-Acc.

19. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop With an integrated luminosity of 110 fb -1, that would correspond to one year of running TESLA photon collider at center-of-mass energy of 400 GeV, C and P conserving couplings (  ,  ) could be measured with a statistical error of order of 10 -4.

20. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop Systematic error on dipole coupling parameter introduced by the error of luminosity of ~1% is of the same order as the statistical error. Measurement of  can not be significantly improved by more precise luminosity measurement. By increasing a center-of-mass energy of photon collisions from 400 GeV to 800GeV, total error of these parameters can be reduced for approximately 20% (less then in e + e - case).

21. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop Summary In  collisions, both differential cross-section for W- pair production (Jz=0 state) and W polarization fractions (Jz=2) are sensitive observables to anomalous dipole coupling. With an integrated luminosity of order of 100 (120) fb -1, these observables can be measured with a statistical error of 10 -3. This would make accessible the ~2% effect of their deviation from the Standard Model values for anomalous   =0.01 coupling.

22. 12 -15 April, St. Malo, FranceECFA/DESY Linear Collider Workshop With an integrated luminosity of 110 fb -1, that would correspond to one year of running TESLA photon collider at center-of-mass energy of 400 GeV, C and P conserving couplings (  ,  ) could be measured with a statistical error of order of 10 -4. By increasing a center-of-mass energy of photon collisions from 400 GeV to 800GeV, total error of these parameters can be reduced for approximately 20%. Taking into account the fact that the full information on W polarization structure (i.e.azimuthal angle ‘  ’) in not included yet into analysis, as well as more realistic simulation of data (variable photon energy spectrum), there is no yet definite answer on photon collider potential to study anomalous TGCs.