# Z yields jets+. gamma. as a signal for R-parity violation Page: 4 of 8

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3

as in the Z, —> Ii7 process, the VF-boson loop is numerically much larger than the fermionic

case! The partial width for this new decay mode is directly proportional to the square of the / ju

R-parity violating coupling (generically represented by A below) and is given by

T(Z

. , = ‘WMl (,_ < V(NQ/(4.-2g;^)V

I92n3m2j\ M% J \ c six\0wcos6w J

(5)

x

Ih{x,y) - h(x>y)|2+ \h{x,y)\2

where and T(l are the mass, charge, and third component of weak iso-spin, respectfully,

of the internal fermion, Nc is the number of colors of the fermion, xw = sin2 0W, x = 4m2/m2,

y = Arrij/Mz, and the integrals /1)2 are given in Ref.[8]. This expression includes the contribution

from the decay into one generation of sneutrino and anti-sneutrino. In our numerical results we

use Mz — 91.175 GeV, F(Z —> /.i+/./~) = 0.0838 GeV, and a.-^ = 0.233 as given by LEP[6],

In the case of the LQ D operator the internal fermion is restricted to be a down-type quark (d,s,

or b), The integrals Ili2 are proportional to m2/Af| yielding an overall rate which is proportional

to T ~ Mz(Xl)2v‘j(m2j/Mz), where vj is the vector coupling constant of the internal fermion to

the Z-boson. Clearly, the b-quark gives the dominant contribution in this case. This is fortuitous

since, as discussed above, it is the third generation R-parity violating couplings which are the

least constrained! The width for Zj —-> £7 in this case, relative to that for Z —» fi~, is

presented in Fig. 2 as a function of the sneutrino mass for various values of A' (taking mj = 5

GeV). The corresponding rate for Z —> Ihf with mu = mp is also displayed in the figure for

comparison. Note that the present limit on the sneutrino mass from the invisible width of the Z

gives[9] mp > 41.1 GeV, and that the mass bound from sneutrino pair production with R-parity

violating decays, Z —> vv — > A jets, would lie in the range m; > 40 — 45 GeV. Correspondingly,

LEP results place[6] rnn > 57 GeV. The rate for Z —> £7 falls off faster as the sneutrino mass

increases, than that for Z —> H7. It is clear that the R-parity violating coupling must be quite

large in order for this process to be observable and that the high luminosity LEP option would

be needed.

For the LLE operator, / = e,/r, or r in Fig. 1 so in this case the r lepton gives the largest

contribution, Here, the Z —* i>7 partial width is now proportional to T ~ MzX2v2{m2r!M'z) and

gives a rate which is smaller by 2 orders of magnitude (for A = A') than that shown in figure 2.

Even for A = 1 the rates for Z —> £7 are clearly unobservable in this case.

If the R-parity violating couplings are large enough for this new Z decay to occur at a visible

rate via the LQD operator, then the sneutrino will in turn also decay through these couplings to

v —y 66. The partial width for this subsequent decay is

F(F -> bb)

3

16 7T

(6)

where we have again assumed that the dominant A' is generation conserving. In this case, the

topology for this reaction would be exactly the same as for Z —> H7 with H —*• 66. If these

couplings are not as large, then the sneutrino could also decay via its MSSM mechanism u —► Au,

where A represents the LSP, with an event signature of a photon plus.missing pr-

Supersymmetric models with R-parity violation have a particularly rich phenomenoicgy, which

results in strikingly different signatures than for the MSSM. Here, we have examined one inter-

esting possibility in these models, a new rare decay mode of the Z-boson, Z —> £7. We have

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Hewett, J.L. Z yields jets+. gamma. as a signal for R-parity violation, article, February 1, 1992; United States. (https://digital.library.unt.edu/ark:/67531/metadc1066975/m1/4/: accessed March 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.