The Number of Neutrinos and the Z Line Shape

Abstract

The Standard Theory can fit any number of fermion families, as long as the number of leptons and quark families are the same. At the time of the conception of LEP, the number of such families was unknown, and it was feared that the Z resonance would be washed out by decaying into so many families of neutrinos! It took only a few weeks in the fall of 1989 to determine that the number is three. The next six years (from 1990 to 1995) were largely devoted to the accurate determination of the Z line shape, with a precision that outperformed the most optimistic expectations by a factor of 10. The tale of these measurements is a bona fide mystery novel, the precession of electrons being strangely perturbed by natural phenomena, such as tides, rain, hydroelectric power, fast trains, not to mention vertical electrostatic separators. The number hidden in the loops of this treasure hunt was 179, the first estimate of the mass of the top quark; then, once that was found, where predicted, the next number was close to zero: the logarithm of Higgs mass divided by that of the Z. Twenty years later, the quality of these measurements remains, but what they tell us is different: it is no longer about unknown parameters of the Standard Theory, it is about what lies beyond it. This is so acutely relevant, that CERN has launched the design study of a powerful Z, W, H and top factory.

The Accelerator Neutrino-Neutron Interaction Experiment

“…Measurements of the Z-boson decay width via electron-positron collisions has provided the most accurate constraint on the total active neutrino flavor count to-date. The number of active light neutrinos N ν is extracted from a measurement of the cross section σ e − e + →Z→f f (s) ≡ σ f (s), described in the Standard Model by [14]…”

“…The combined fit for the number of active neutrino generations is in considerable agreement with 3. Figure from [14]. .…”

“…14) while the axial component can be written as:p(p p )| u(x)γ ρ γ 5 d(x) |n(p n = u p (p p ) γ ρ γ 5 G A (Q 2 ) + q ρ m N γ 5 G P (Q 2 ) + p ρ p + p rho n m N γ 5 G 3 (Q 2 ) u n (p n ) (B.15)WhereQ 2 = −q 2 = −(p ν l − p l ) 2 , m N ≈ m p ≈ m n ,and F a , G a for a = [1, 2, 3, A, P ] are the weak charged-current form factors. F 1 , F 2 are known as the Dirac and Pauli weak chargedcurrent form factors, while G A , G P are the axial and pseudoscalar weak charged-current form factors.…”

Discovery Goals and Opportunities: A Defense of BSM-Oriented Exploration over Signalism

“…In addition to finding evidence for these elementary particles, a SM confirmation discovery can be said to involve any qualitative property or manifestation of the theory that had not yet been observed. Examples of these include the presence of CP violation in B decays [9,19], discovered in 2001, observation of CP violation in charm decays [5], discovered very recently, and the existence of three active species of light neutrinos [29].…”

“…In the framework of the Standard Model, a fifth light neutrino is, however, unlikely" [54]. Very quickly after the turn-on of LEP and SLC, measurements of invisible final states of the Z width suggested 3.12 ± 0.19 as of October 1989 [29]. By the time a final analyses were being completed on the precision electroweak data at LEP/SLC the precision completely ruled out anything but 3 neutrino species "assuming that only invisible Z decays are to neutrinos coupled according to SM expectations" [98].…”