Pictures Paths Particles Processes

16 November 7, 2013
scenario of a single neutral Higgs boson, we can then also infer the Higgs selfinteraction
vertices. At the end of the day we have then the complete content
of the (minimal) electroweak Standard Model.
Finally, several Appendices deal with issues that are by themselves interesting
enough but the inclusion of which inside the main text would hold up the
course of the argument too long to my taste.
0.3 Basic tools
0.3.1 Units
The fundamental constants 10 of relativistic quantum field theory are the speed
of light in vacuo :
c = 299792458 m
sec ,
and Planck’s (or rather Dirac’s) constant
¯h = 1.054571628(53) × 10 −34 Joule sec .
Compared to the scales of our everyday experiences, ¯h is miniscule and c is
huge : in the world of elementary particles, they are just about right. We can
see this as follows. It is customary to replace our human-scale meters, kilograms
and seconds by what may be called fundamental units of mass, length and time :
M f = 1.7826618 10 −27 kg ,
L f = 1.9732696 10 −16 m ,
T f = 6.5821190 10 −25 sec .
In terms of these units, we have precisely
¯h = M f L f
2
T f
, c = L f
T f
,
so that both ¯h and c have the numerical value one ; and the unit of energy turns
out to be
M f L f
2
T f
2
= 1.6021765 10 −10 Joule = 1 GeV .
The mass and size of the proton are of the same order as M f and L f , respectively,
and T f is roughly the time scale of strong interactions. The use of
fundamental units is attractive since you won’t have to write factors of c and ¯h,
and one then expresses both length and time in inverse GeV, and mass in GeV.
10 The values quoted here are taken from the 2008 Review of Particle Physics, C. Amsler
et al. (Particle Data Group), Physics Letters B667(2008)1. The numbers in brackets denote
the experimental error in the last digits. The speed of light is known exactly since it is, in
fact, simply our definition of the meter.