1. Triple Gauge Couplings and Polarization at the ILC
Ivan Marchesini, LC Forum Munich,

2. Introduction

3. Electro-Weak Sector Gauge group SU(2)LÄU(1)Y.
Non-Abelian SU(2)L Þ gauge bosons self-couplings.
In particular: Triple Gauge Couplings (TGCs) WWV (V = g or Z).
“Accidental” in the theory. Want:
Get for free:

4. Electro-Weak Sector Gauge group SU(2)LÄU(1)Y.
Non-Abelian SU(2)L Þ gauge bosons self-couplings.
In particular: Triple Gauge Couplings (TGCs) WWV (V = g or Z).
“Accidental” in the theory. Want:
Get for free:
Confirmed at LEP. Great success of the gauge theory.

5. Triple Gauge Couplings
TGCs parametrized by the effective Lagrangian (phenomenological, model independent, most general):
14 complex couplings: 28 free parameters.
SM predicts g1Z, g1g, kg and kz = 1 at tree level, others are 0.
Deviations from SM loop-corrections and beyond-SM physics (need at least 10-3 precision).

6. LEP Combined Results
Assumptions on the TGCs used at LEP and in this study:
Real, C- and P- conserving: g1Z, g1g, kg , kz;, lg and lk.
Electromagnetic gauge invariance g1g = 1.
SU(2)LÄU(1)Y local gauge invariance:
5 couplings, 3 independent.
LEP limits (one-parameter fits):
No significant improvement at Tevatron or LHC: O(10-2). <=10-3 precision only at the ILC.

7. Precision and Polarization
ILC baseline includes e- beam long.-polarized of at least 80%.
Possibility of e+ long.-polarization: here 30% and 60% options considered.
Polarized beams (both) are required to:
improve statistics: enhance signal, suppress backgrounds;
analyze the structure of new physics;
precision measurements of (deviations from) the SM.
But: polarization has to be known with high precision (strong impact on the cross-sections).

8. Polarization Measurement at the ILC
3-fold way: complementarity, cross-checks, redundancy.
Upstream polarimeter: high time-granularity, control over left-right polarization differences, correlations (> 1 km from IP).
Downstream polarimeter + spin tracking simulations: measure depolarization effects.
Measurement from Data:
access to luminosity-weighted polarization (at the IP) to complement the polarimeters (check depolarization);
average polarization (long time scale);
need polarimeters to correct for left-right differences;
need high cross-section, polarization-dependent process;
W+W- production ideal: process used for this study.

9. W+W- Production and Polarizationb) c)
a) t-channel. W can couple only to e-L and e+R: only the combination e-Le+R is allowed.
b) c) s-channel. e+ and e- must have opposite polarizations, to give the SM vector boson. Sensitive to TGCs.
momentum
spin
JZ=1 allows vector mediator

10. TGCs and Polarization
Total cross-section for W+W- semi-leptonic decays to muon or electron, at 500 GeV: strong sensitivity to polarization.
Golden channel to measure TGCs (LEP): angular distributions.
Implement simultaneous measurement of polarization and TGCs.

11. W+W- Event Selection

12. Selection
Only semi-leptonic W+W- decays towards electron or muon, q q m n and q q e n :
cleanest reconstruction and lower background;
precise reconstruction of W decay angles: sensitive to TGCs.
Leptonic decay angles (cosq*l and f*l ) and cosqW are used.
Angles describing the hadronic decay have a two-fold ambiguity: not used. e-
lep qW
f*lep
Wlep
q*lep W- W+ e+ n

13. Total
Selection
Fully simulated Monte Carlo events in ILD. Full SM background.
Pre-selection cuts (nº tracks, Ös, PT, total energy).
Force 3 jets, the jet with lower particle multiplicity is associated to the lepton and has to have only one track with pT > 10 GeV.
“Tau-signal” W+W- → q q l t suppression via discriminating variable.
Further cuts (Y cut, isolation, invariant mass, angular cuts).

14. Final Selection Reconstructed W invariant mass: 40 << 120 GeV.
The final results:
Signal efficiency ~ 67%.
non-”tau signal” background contamination ~ 6%.
“tau signal” ~ 10%.

15. Measurement of Polarization and TGCs

16. Angular Fit 3D Monte Carlo template (cosq*l , f*l , cosqW).
4 “data” 3D (cosq*l , f*l , cosqW) distributions for the ++, +-, -+, -- helicity sets.
Initially, assumption: |+Pe-| = |-Pe-| and |+Pe+| = |-Pe+|.
Each data sample fitted to the 3D MC template.
Fit iterated for several independent data samples (poissonian random variation): statistical error is the dispersion of the measured fit parameters.

17. Sensitivity: Polarization
Fit 3 TGCs simultaneously to the polarization.
No loss of sensitivity on the polarization with respect to polarization-only measurement: uncorrelated.
High positron polarization measurement much more convenient.

18. Sensitivity: TGCs 30% e+ 60% e+ Absolute precision on the TGCs.
TGCs measurement not significantly influenced by the positron polarization choice.

19. Systematics

20. Systematics Efficiency:
need to be controlled better than 0.5% for the signal, otherwise TGCs sensitivity systematically limited at the 10-3 level (still competitive);
should be possible: at LEP controlled at the 0.1% level.
Luminosity: fine with 10-3 relative precision on the integrated luminosity.
Major systematic effect from |+Pe-| ≠ |-Pe-| and |+Pe+| ≠ |-Pe+|:
using 4 free parameters give too low statistical precision;
difference given by the polarimeters with 0.25% uncertainty;
addressed for the most sensitive technique implemented: the angular fit.

21. Angular Fit + Polarimeters
Effect not fully-negligible for the polarization, but excellent performance still allowed.
Negligible effect on the TGCs measurement.

22. Conclusions

23. Conclusions
Higher positron polarization strongly relevant from the polarization measurement point of view.
Simultaneous fit of TGCs and polarization possible, without loosing sensitivity on the polarization measurement.
Major systematic effect from |+Pe-| ≠ |-Pe-| and |+Pe+| ≠ |-Pe+|: acceptable.
With 60% positron polarization error »0.2% on both polarizations at »300 fb-1.

24. End

25. Additional Slides

26. Cross Sections
σRR
σLL
σRL
σLR
0.25 (1+Pe-)(1+Pe+) e- e+
JZ=0
0.25 (1-Pe-)(1-Pe+) e- e+
0.25 (1+Pe-)(1-Pe+) e- e+
JZ=1
0.25 (1-Pe-)(1+Pe+) e- e+
With longitudinally polarized beams the total cross section can be subdivided into:
σ(Pe-,Pe+) = 0.25 {(1+Pe-)(1+Pe+)σRR+(1-Pe-)(1-Pe+)σLL
+ (1+Pe-)(1-Pe+)σRL + (1-Pe-)(1+Pe+)σLR}.

27. Statistical Advantages - 1
In case of s-channel processes:
σ(Pe-,Pe+) = 0.5 {(1+Pe-)(1-Pe+)σRL +
(1-Pe-)(1+Pe+)σLR}.
It is possible to express this in terms of effective polarization:
σ(Pe-,Pe+) = (1-Pe-Pe+)σ0 [ 1 – Peff ALR],
where:
𝑠 0 = 𝑠 𝐿𝑅 + 𝑠 𝑅𝐿 4 𝐴 𝐿𝑅 = 𝑠 𝐿𝑅 − 𝑠 𝑅𝐿 𝑠 𝐿𝑅 + 𝑠 𝑅𝐿 𝑃 𝑒𝑓𝑓 = 𝑃 𝑒 − − 𝑃 𝑒 + 1− 𝑃 𝑒 − 𝑃 𝑒 +
Peff is always higher. No benefit in Peff in case of only Pe-.

28. Statistical Advantages - 2
The asymmetry ALR, sin2qeff and the precision on its measurement can be expressed as:
where:
AobsLR is the measured asymmetry.
Equal precision on the two beams polarizations:
x = DPe-/Pe- = DPe+/Pe+ is assumed.
𝐴 𝐿𝑅 = 1 𝑃 𝑒𝑓𝑓 𝐴 𝐿𝑅 𝑜𝑏𝑠 ∣ 𝐷 𝐴 𝐿𝑅 𝐴 𝐿𝑅 ∣ = ∣ 𝐷 𝑃 𝑒𝑓𝑓 𝑃 𝑒𝑓𝑓 ∣
𝐴 𝐿𝑅 = 2 1−4 sin 2 θ 𝑒𝑓𝑓 −4 sin 2 θ 𝑒𝑓𝑓 2

29. Chiral Quantum Numbers

30. Reducing ++ -- Combinations

31. Finer Binning

32. Preselection Cuts
Selection studied using fully simulated events in ILD.
Full SM background included.
Here e.g. 20 fb-1, +30% e+, -80% e- polarization.
√s>100 GeV
tracks>10
PT>5GeV
SumE<500 GeV

33. Jets Requirements
Force 3 jets (Durham). Two jets are for the hadronic decay. One jet associated to the lepton (jet with lower number of particles).
Cut on the y variable of the jet finder (goodness of clustering).

34. Further Cuts Requirements on the jet associated to the lepton:
isolated (theta-phi isolation > 0.5);
one track with pT > 10 GeV.
cosqW >
cosqW > -0.95
Isolation cut

35. “Tau-signal” Suppression
Reconstruction semi-leptonic decays q q t n less clean:
further neutrino in the final state from tau decay;
worse charge reconstruction of the lepton.
Suppression by means of a discriminating variable:
 2 E lep s   m W lep m W true  2 >1

36. Decay Angles
Example of the impact of anomalous TGCs on the angular distributions.

37. Simulation of the TGCs “Recalculate” feature in Whizard:
change a parameter (TGC value);
rescan the sample;
weight given by the ratios of the new matrix element values to the old ones.
Dependence of the differential cross-sections from the TGCs is quadratic. 3 independent TGCs → 9 parameters for each event:

38. Simulation of the TGCs
Scan each event 9 times, for 9 different TGCs sets, getting the 9 weights R.
Solve the system in order to get the A,...,I coefficients:

39. Technique 1: Blondel Scheme
Needs data to be collected for all the four sign combinations of polarization: ++, --, +- and -+.
Assumption: |+Pe-| = |-Pe-| and |+Pe+| = |-Pe+| (polarimeters necessary to get deviations).
From the cross sections for the different polarization signs, it is possible to get the polarization:
∣ 𝑃 𝑒 ± ∣ = 𝑠 −+ + 𝑠 +− − 𝑠 −− − 𝑠 ++ ± 𝑠 −+ ∓ 𝑠 +− + 𝑠 −− − 𝑠 𝑠 −+ + 𝑠 +− + 𝑠 −− + 𝑠 ++ ± 𝑠 −+ ∓ 𝑠 +− − 𝑠 −− + 𝑠 ++

40. Technique 2: Angular Fit
3D Monte Carlo template (cosq*l , f*l , cosqW).
4 “data” 3D (cosq*l , f*l , cosqW) distributions for the ++, +-, -+, -- helicity sets.
Initially, assumption: |+Pe-| = |-Pe-| and |+Pe+| = |-Pe+|.
Each data sample fitted to the 3D MC template.
Fit iterated for several independent data samples (poissonian random variation): statistical error is the dispersion of the measured fit parameters.

41. Results
60% e+
30% e+
Luminosity equally shared between the four sign combinations of the polarization.
Angular fit technique more sensitive.
High positron polarization extremely more convenient.