Astroparticle Physics

10.7 Constraints on the Number of Neutrino Families 227Fig. 10.7The predicted 4 He mass fraction asa function of η for different valuesof N νe −(m n−m p )/T f . If this occurs at a higher temperature, then theratio is higher, i.e., there are more neutrons available to makehelium, and the helium abundance will come out higher.This can be seen in Fig. 10.7, which shows the predictedhelium abundance as a function of the baryon density. Thethree diagonal bands show the predicted Y P for different valuesof an equivalent number of neutrino families N ν = 3.0,3.2, and 3.4. Of course, this no longer represents the (integer)number of neutrino flavours but rather an effective parameterthat simply gives g ∗ . The data are consistent withN ν = 3 and are clearly incompatible with values muchhigher than this [19].The equivalent number of light (i.e., with masses ≤m Z /2) neutrino families has also been determined at theLarge Electron–Positron (LEP) collider from the total widthof the Z resonance, as was shown in Fig. 2.1 (see also Problem3 in this chapter). From a combination of data from theLEP experiments one finds [20]N ν and helium abundanceaccelerator data on N νN ν = 2.9835 ± 0.0083 . (10.34)Although this is 1.7 times the quoted error bar below 3, itis clear that N ν = 3 fits reasonably well and that any otherinteger value is excluded.Before around 1990, when N ν was determined to highprecision in accelerator experiments, BBN measurements