FROM HIGGS PRODUCTION IN POSITRON-ELECTRON ANNIHILATION THE NUMBER OF NEUTRINOS CAN BE DETEFMINED
A. Van Proeyen Universiteit Leuven, Instituut voor Theoretische Fysica B- 3030 Leuven, Belgium
ABSTRACT
Neutrino counting can, apart from the process e e -* yw also be done from e e •* H v v at LEP energies. Depending on the mass of the Higgs the cross-section is higher, equal or lower than that of the first process.
* Work «supported by "Na\:iariaal Fonds voor Wetenschappelijk Onderzoek", Belgium. 1.
Recently, Ma and Okada found that the study of the process e e~-*y\>\> 2 can determine the number of neutrino types.Gaemers, Gastmans and Renard redid the calculation and inserted the effects of the Z-particle. We examined the Higgs production in the electron-positron annihilation, and found that also this process (e e -• Hw ) can measure the number- of neutrino types. If the Higgs mass is not too large the cross-section is even higher.
The energy dependence of the cross-section has a characteristic behaviour, dependent on the mass of the Higgs particle. Possible means for detection uf the Higgs particle are discussed in ref.3.
The coupling of the Higgs particle to other particles is proportional to their masses. Therefore the main contribution comes from the graphs where the Higgs couples to the intermediate bosons. This gives us the
Feynman diagrams of fig.l. In the t-channel diagram (b), the W-pole cannot be reached. Tharefore we will suppose the W-mass much larger than the energy term in the denominator of the W-propagator. This can cause not more than a factor of two in graph b. But the calculation showed that for energies of the electron and the positron smaller than 1O0 GeV the contribution of this diagram is much smaller than that of diagram a. This main graph (a) occurs as many times as there are types of neutrinos.
We take the same notations as in refs.l and 2, namely;
E : energy of the electron and the positron
M^: Z-mass Li
rz: Z-width M : total number of neutrino types
m.^: TOSS of the Higgs
e,,: Weinberg angle
xE: energy of the Higgs
y : cosine of thd angle under which the Higgs is emitted relative to
the beam axis. 2.
n If we neglect the electron mass
XE2 2M )T do <4* ,4 vft#- zVgA + j_, 2 2 ^ " 12„ sin 2286W * "«£2
2 [(1-y2) (x2E2 - m2.) + 8E2(1 - x + %? ) ] H 4E2 where T = (ME2 - M2.)*!^ + 4E2(l-x) - M2,) " M^ r2
N : [(4E2-M^)2 + M2. r2][(n^ 4 4E2(l-x) - M2,)2 + M2, r2 ]
- 1/2 sA
2 ^ = - 1/2 • 2 sin ew
If we also suppose that the Z can decay into 3 charged leptons, 3 quarks of charge 2/3, 3 quark- of charge - 1/3, and N neutrinos the Z-width is
3 r z _£—L [21 + N - 48 sin' &, + 64 sin 6,. ] Z 12w/? v W W
The energy of the Higgs is restricted in the domain
V XE « E • iff
We integrate over the total range of x, and over
- 1/2 « y * 1/2 or 60° f 9 <120° such, that only the Higgs particles which are not emitted in the forward or backward region have to be detected. 3.
Figures 2,3 and h give the cross-section in function of the energy for a very small Higgs mass, for m, = 10 GeV and for nv, = 40 GeV. Each time
N is taken to be 3,10,100 and 1000. We taken
sin fly = 0.22 such that
Mj, = 90 GeV, gv = - 0.06 and r„ is
N = 3 IV, = 2.6 GeV v Z N = 10 IV, = 3.7 GeV v L N =100 IV, = 18 GeV v Z N =1000 IV, = 161 GeV v Z
We observe that when the Higgs mass is larger than the width of the
Z-resonance there are 2 peaking regions in the cross-section. The first
starts at E = 45 GeV. At that energy the left Z-particle from diagram (a)
is on its mass-shell. When the energy of each incoming particle is at least -y- higher, the right Z-particle is on its mass-shell, and we
see the second peak in the cross-section.
The value of the cross-section is larger than that for e e •*• -yvv if ro, £ 10 GeV. For larger Higgs masses it becomes smaller. Therefore this
process can be used for the determination of the number of neutrinos when
LEP will be working and when the Higgs will be discovered with a mass which
is not too high.
ACKNOWLEDGMENT
We are grateful to R. Gastmans for suggesting this subject to us. 4.
REFERENCES
1. E. Ma and J. Okada, Htyu.Rcv.Letters 4_1, 287 (1978).
2. K.J.F. Gaemeri;, R. Gastirmis ai«l F.H. Retard, "Neutrino counting in
e e collisions", preprint IXTA/liJ' ^5, Ansterdam 1978.
3. J. Ellis, M.K. Gaillard ai id D.V. Nanopoulos, Niiol.Phys. B10G , 19? (197b).
K.J.F. Ga.3net-o and C.J. Gouikirii;, H.ys. i.et t . 77B, 37') (1978).
4. Use wan matte of fhe alRHauic muii|*ilat ion pro^um RI'.DUOE, A.C. llcani,
REDUCL-? Uswr's Kinual, UUti (197.0.
E>. J. Ellis arid M.K. Gaillard Ln "lliyuii:; with very liij'.li miT^y f o~
colliding boams'V-'ERN 7f»-lK (197f,). FIGURE CAPTIONS
Fig.l. Main contributions to e e~ •* H vv Fig.2. Cross-section in function of beam energy for a very low Higgs mass and different numbers of neutrino-types. Fig.3. Cross-section if the Higgs HBSS is 10 GeV Fig.4. Cross-section if the Higgs nass is *v0 GeV H
(a)
Fig.1 n*ct 1 1 1 1 - rM E mHf«0 I o II 1 | !
> -35 f 10 — IV i y
% O - ƒ 1 1 \\Ny= 100 -
io"36h—1 j
-1 ^^fi^iooo
10-3 7 /""l i i 1*0 50 60 ,n wl' 70 eE (GeV) Fig. 2 AO 50 60 70 e In wl E (GeV) Fig. 3 oteV-^Hvv) (cm2) o eb U) en T T" II II IT] i T" -1—T~T III
II O O (TO
/ i 1 i i 1 1 1 1 i • _..! 1 1 1 1 M