• S.Betts, J.Conboy, J.Couchman and P.Dervan were at the OPAL plenary last week.

• News from OPAL week: The parameters for the anomalous coupling are no longer Alpha_WPhi, Alpha_BPhi and Alpha_W. Instead we will use delta g^Z, delta kapa_gamma, lambda_gamma and lambda_Z.

• G.Bella is preparing the 183 GeV paper. All analysis on all topologies will be included, so its going to be a big on.

• J.Thomas is going out to CERN for the month of July.

Jim presented work he had done on an investigation into how the W production and decay angles constrain the anomalous TGV coupling coefficients. This work has already been written up by Jim, so I just stole it from his web page.

CosTh

The W- production angle

CosTh*1

The f1 production angle in the W- rest frame

phi1

Phi of f1 , relative to the W+W- production plane.

Although it is known that CosTh has a strong dependence on AlphaW and AlphaWphi, and thet the decay angles show no strong dependence on the TGV couplings, it is not so obvious how the correlations between the angles vary with the TGV coefficients. [ For example, the correlation <Phi1 - Phi3> could show a strong dependence on the Alphas even though the projections Phi1, Phi3 do not ]

Calculation of all 10 correlation coefficients was briefly considered, but rejected because

• For a symmetric Phi distribution, the mean value is undefined and so it is not obvious how the correlations should be calculated
• The angles CosTh* and Phi can only be determined for leptonic W decays at present.

The variation of the 8 coefficients F2 to F9 with CosTh were determined for the 3 standard TGV models using the following OPAL MonteCarlo runs :-

4933

Standard model

4935

Alpha_wphi = +1

4936

Alpha_wphi = -1

5333

Alpha_bphi = +2

5334

Alpha_bphi = -2

5335

Alpha_w = +2

5336

Alpha_w = -2

The distributions were made using generated track parameters for all hadronic and semi-leptonic events, without any cuts. Page 1 shows the 5 TGV angles, normalised to the generated cross-section (as listed on the www page for each run). The SM value (solid line) is compared with a positive (dashed) or negative (dotted) value of alpha Pages 2 and 3 show the variations of F2-F5, F6-F9. SM value (open circle) is compared with positive (dashed error bar) and negative (dotted error bar) values of alpha. The coefficients F6 to F9 show little CosTh dependence in the standard model, and very small variations with any alpha; I doubt that they are of any use with the statistics anticipated at LEP 2.

Varying Alpha_w_phi between +/- 1 produces large variations in CosTh, and some change in Phi. The CosTh dependence of F2, F3, F4 and F5 also affected.

Varying Alpha_w between +/- 2 produces very similar variations in the CosTh and the Phi distributions. The CosTh dependence of F3 and F4 changes in a similar manner to the Alpha_w_phi case. Only F5 (which does not vary with Alpha_w) and F2 (which has a different CosTh dependence than that produced by Alpha_w_phi) appear to be able to discriminate between the two models. This presumably explains the high degree of correlation observed in the 2D fits to these two models ( Ref. 2).

Varying Alpha_b_phi between +/- 2 produces very little change in the cross section or the projected angles. F2, F4 show a slight variation when Alpha_b_phi = -2, but Alpha_b_phi = +2 is (suspiciously) close to the standard model value in cross-section and all distributions.

Conclusions

The two parameters (F2 and F5) which might discriminate between variations of Alpha_w and Alpha_w_phi are both invariant under interchange of fermions f1 and f2 . Consequently, inclusion of the (folded) W => jj angular distributions in a 2D fit (to Alpha_w and Alpha_w_phi) may well improve the 2D fit significantly, even if the 1D fits are little changed

References