Neutrino Physics at a Muon Collider Page: 4 of 18
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p~ -+ vj + ve + e-,
p+ -+ -, + v, + e+. (1)
The thin pencil beams of neutrinos for experiments will be produced from
long straight sections in either the collider ring or a ring dedicated to neutrino
physics. From relativistic kinematics, the forward hemisphere in the muon rest
frame will be boosted, in the lab frame, into a narrow cone with a characteristic
opening half-angle, 8,,, given in obvious notation by
B~ sin96, = 1/1y = 10 . (2)
For the example of 250 GeV muons, the neutrino beam will have an opening
half-angle of approximately 0.4 mrad. The final focus regions around collider
experiments are important exceptions to equation 2 since the muon beam
itself will have an angular divergence in these regions that is large enough to
significantly spread out the neutrino beam.
For TeV-scale neutrinos, the neutrino cross-section is approximately pro-
portional to the neutrino energy, E,,. The charged current (CC) and neutral
current (NC) interaction cross sections for neutrinos and antineutrinos have
numerical values of :
UuNNC0.23 En x0 2 m
v _C C( 0.3N for X 1 TeV x 10- cm 2. (3)
k - NC 0.13
These cross sections are easily converted into approximate experimental
event rates for the example of a 250+250 GeV collider with a 200 meter
straight section and the example design parameters used for this workshop.
For a general purpose detector subtending the boosted forward hemisphere of
the neutrino beam:
V1 - CC 2.6
Nubr f v~, - NC J0.8
Number of e - CC events/yr ~ 1.4 x 107 x l[g.cm-2], (4)
ie - NC 0.5
where l is the detector length. For a long baseline detector in the center of
the neutrino beam:
v" - CC 1.4
Number of ve - NC events/yr ~ 0.7 x 107 X (L[km])2 (5)
e - NC 0.2
where M is the detector mass and L the distance from the neutrino source.
These event rates are several orders of magnitude higher than in today's
neutrino beams from accelerators.
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King, B. J. Neutrino Physics at a Muon Collider, article, February 1998; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc708723/m1/4/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.