1. The Number of Light Neutrino Families ● Physics motivation for measurement ● Direct / indirect searches for ● Analysis methodology for ● Single photon trigger and event selection ● Systematic errors and results ● Information from other experiments UCL Lunchtime Seminar Thursday 1 st February '07 Mark Dorman UCL / RAL

2. Physics Motivation for Measurement ● The number of light neutrino families,, is a fundamental parameter of the Standard Model and has been derived by the LEP experiments from measurements of Z decays into light neutrinos which form the invisible Z width. ● The invisible width is of further interest as it is also sensitive to the existence of any other pair of stable and non-detectable weakly interacting particles with mass less than. ● Furthermore the invisible width is sensitive to possible processes outside the Standard Model such as the existence of right-handed neutrinos mixing with the left-handed ones to give a non-integer value for.

3. Indirect Measurement of ● This method involves the analysis of the Z lineshape and the subtraction of the visible partial widths from the total width: ● ● A fit to the cross section for hadronic decays of the Z gives the lineshape parameters and where: and

4. Indirect Measurement of ● Then assuming is made up of light neutrino species each contributing to the invisible width: ● The combined result for the 4 LEP experiments using this method is: (hadrons)

5. Direct Measurement of ● This method involves measuring the cross section for the radiative process. The signature for such events is a single photon from initial state radiation. ● In the SM (and since LEP ran around the Z-pole) this cross section is dominated by the decay of the Z to light neutrino pairs with a small (~3%) contribution from t-channel W exchange: ● The cross section for this process is proportional to.

6. Complementarity of the Methods ● In the absence of new physics the direct and indirect approaches measure the same quantity with different systematic errors although the direct method is statistically limited due to the need for a radiative photon. ● In general the sensitivity of the methods to new physics will vary... ● Example: a fourth unstable neutrino decaying in the detector will not change the answer from the direct method as this would be rejected in an analysis looking for single photon events. However, in the indirect method, unless this decay is accounted in the hadronic or leptonic decays of the Z, the apparent will increase.

7. Analysis Methodology for ● In the direct method the measured quantities correspond to the photon and come into the cross section for via a radiator function: ● And then the effective cross section can be written (to lowest order): where and have the measured values. This equation can then be used by keeping the total width fixed and varying the invisible width to minimize some test statistic. where

8. Analysis Methodology for ● This measurement is optimally carried out at energies a few GeV above the Z mass where the initial state photon radiation brings the electron/positron centre of mass energy down to the Z peak. ● The LEP centre of mass energy was mostly less than this optimal energy but the cross section is still high enough at the Z peak for a meaningful measurement. ● In the above case the initial state photons have low energies and the following experimental conditions must be realised: ● the capacity to trigger on low energy single photons ● a good hermiticity at very low angles to reject the backgrounds that are rapidly increasing in this region

9. Single Photon Trigger ● There are large backgrounds to at low angles and so the single photon trigger required an isolated energy deposit of more than 1 GeV in the barrel ECAL (polar acceptance of ~42-138 o ). ● The trigger efficiency was determined in two ways; from data using radiative Bhabha scattering events and from a detailed simulation. ● Cartoon of single photon trigger: ECAL Tracking Beamline Luminosity Monitor ALR (scintillator counters)

10. Single Photon Trigger ● There are large backgrounds to at low angles and so the single photon trigger required an isolated energy deposit of more than 1 GeV in the barrel ECAL (polar acceptance of ~42-138 o ). ● The trigger efficiency was determined in two ways; from data using radiative Bhabha scattering events and from a detailed simulation. ● Cartoon of single electron trigger (radiative Bhabha): ECAL Tracking Beamline electron positron ALR (scintillator counters) Luminosity Monitor

11. Single Photon Trigger ● The single electron trigger just uses the luminosity monitor and the tracker to select events and then the trigger efficiency can be calculated by seeing if the corresponding ECAL deposit passed the single photon trigger. ● The agreement of the MC with the single electron data (once folded with the single photon energy spectrum) justifies the use of the MC curve.

12. Backgrounds to ● The experimental signature for this process is an electromagnetic shower and an otherwise empty detector and the main sources of background are radiative processes where all final state particles but a photon escape detection. ● The dominant backgrounds are: ● Another potential source of background comes from out of time cosmic rays that emit photon bremsstrahlung when only the barrel ECAL is active. ● radiative Bhabha events ● the process ● 2 photon processes where X is a...

13. Event Selection ● The ECAL cluster energy deposit must be between 1 and 10 GeV and at polar angles between 45 o and 135 o. ● There are a number of cuts to define an 'empty' detector such as no tracks and only a small amount of energy deposited in the luminosity monitors. ● The main contaminations in this sample are radiative Bhabha events where either both the electon and positron escape through the beam pipe ( ) or when one of them escaped between the luminosity monitors and the ALR ( GeV). L3 total data sample from '91-'94 contains 2090.0 events.

14. Systematic Errors ● Many sources of systematic errors where considered, I will mention a couple of them. They are evaluated by performing the cross section fit with these parameters changed according to their maximum variation. ● Trigger Efficiency – this systematic was investigating by altering parameters in the trigger simulation such as calibration constants. ● Radiative Bhabha background subtraction – this systematic can be studied by considering that the MC generator for the process can generate either background events where both the electron and positron are at small angles and the radiative photon is in the barrel or events like the example earlier from the single electron trigger. Comparing the data and MC for the single electron sample can justify the use of the generator in modeling the background contribution.

15. Results ● A maximum likelihood fit to the number of single photon candidates from the cross section measurements at the different centre of mass energies gave: ● And then assuming the standard model coupling of the neutrino pairs to the Z: ● The combined results from the 4 LEP experiments using this method give:

16. Information from Other Experiments ● All experimental results so far can be explained with 3 light neutrino families except for the LSND experiment. LSND requires at least one sterile neutrino (no couplings to the standard model Z). Such a neutrino cannot be seen with collider measurements such as those at LEP and we are eagerly awaiting the results of the MiniBooNE experiment. ● Cosmology can provide answers (or at least limits) as well... ● Solid lines indicate 68% and 95% c.l. contours for D+ 4 He likelihood function; colour shows 95% c.l. contour for WMAP + D likelihood.

17. Backup Slides

18. Z Parameters, Measured v.s. Theory Comparison of experiment and standard model (from PDG): quantity experiment standard model  (hadrons) 1744.4  2.0 1742.2  1.5 MeV  (neutrinos) 499.0  1.5 501.65  0.15 MeV  (l + l - ) 83.984  0.086 84.00  0.03 MeV

19. Relativistic Breit-Wigner Distribution ● A continuous probability distribution with the density function: ● E CM is the centre of mass energy that produces the resonance, M is the mass of the resonance and is it's width. ● The form of this distributions arises from the propagator of the unstable particle which has a denominator of the form: ● Presumably this propagator form can be derived from some plane wave particle wave-function but i'm not sure...