Mass bounds on a horizontal gauge boson
ALIA. BAGNEID
Department of Physics, Umm Al-Qura University - Makkah, Saudi Arabia
(ricevuto il 2 Giugno 1997; approvato il 14 Luglio 1997)
Summary. — Constraints are obtained on the mass of an additional neutral gauge
boson, Z8, suggested by the Sp(6)L7 U( 1 )Y model, from high-energy pp collider
data. A lower bound is obtained on Z8 mass, MZ8F 410 GeV . Discovery limits for Z8 in a future hadron collider are also studied.
PACS 13.38 – Decays of intermediate bosons.
The standard model (SM) [1] of electroweak interactions has been remarkably successful in describing low-energy neutral- and charged-current processes and in determining the mass of the W and Z bosons [2]. In addition, the recent precision experiments from the CERN e1e2 LEP collider have spectacularly confirmed the
model [3]. However, it is commonly believed that the SM is just the low-energy limit of a more fundamental theory which might contain additional gauge bosons, extra fermions, etc.
In this work, we consider the Sp( 6 )L7 U( 1 )Y model, proposed some time ago [4].
The model predicts the existence of a set of intergenerational, horizontal gauge bosons, keeping the fermion spectrum intact. In the Sp( 6 )L7 U( 1 )Y model, the standard
SU( 2 )Lis unified with the horizontal gauge group GH
(
4 SU( 3 )H)
into an anomaly free,simple Lie group. The six left-handed quarks (or leptons) belong to a 6 of Sp( 6 )L, while
the right-handed fermions are all singlets. It is thus a straightforward generalization of SU( 2 )L into Sp( 6 )L, with the three doublets of SU( 2 )L coalescing into a sextet of
Sp( 6 )L. Sp( 6 ) can be naturally broken into [SU( 2 ) ]34 SU( 2 )17 SU( 2 )27 SU( 2 )3,
where SU( 2 )ioperates on the i-th generation exclusively. Thus the standard SU( 2 )Lis
to be identified with the diagonal SU( 2 ) subgroup of [SU( 2 ) ]3. In terms of the SU( 2 ) i
gauge boson, Ai, the SU( 2 )L gauge bosons are given by A 4
(
1 Ok3)
(A11 A21 A3). Ofthe other orthogonal combinations of Ai, A84
(
1 Ok6)
(A11 A22 2 A3), which exhibitsuniversality only among the first two generations, can have a mass scale in the TeV range [5]. The additional gauge bosons A8, denoted by Z8 and W86, suggest new
physics [6] beyond the standard model. In this work we would like to obtain bounds on the mass of the neutral member from the fact that its decay into lepton pairs has not yet been seen at the Fermi Lab Tevatron.
With the additional neutral gauge boson, Z8, the neutral-current Lagrangian is generalized to contain an additional term:
2 LNC4 eJemm Am1 g1J m 1Zm1 g2J m 2Z 8m , (1)
where g24
k
( 1 2x)O2g14 gOk2 , x 4sin2uW, and g 4eOsin uW. The neutral currentsJ1and J2are given by
J1m4 1 2
!
f cfgm( g f V1 g f Ag5) cf, (2) J2m4 1 2!
f cfgm( g 8 f V 1 g 8 f Ag5) cf, (3) where gV f 4 (T3L2 2 xQ)f, gA f 4 (T3L)f and g 8V f 4 g 8A f4 (T3L)f for the first two generations
and g 8V f
4 g 8A f
4 2 2(T3L)f for the third. Here (T3L)f and Qf are the third component of
the weak isospin and electric charge of fermion f, respectively. After symmetry breaking the weak eigenstates Z and Z8 are related to the mass eigenstate bosons Z1
and Z2by
Z14 Z cos W 1 Z 8 sin W , Z24 2Z sin W 1 Z 8 cos W ,
(4)
Fig. 1. – Gauge boson production cross-section times branching fraction into e1e2pair for Z8, in pp collisions at ks 41.8 TeV, as a function of the gauge boson mass M. The dashed line is for a gauge boson with the couplings of the standard Z, but with mass being a free parameter.
where W denotes the mixing angle between Z and Z8. The neutral-current Lagrangian now reads 2 LNC4 g1
!
i 41 2k
!
f cfgm(g f Vi1 g f Aig5) cfl
Z m i , (5) where gVf1, A14 1 2k
g f V , Acos W 1 g2 g1 g 8V , Af sin Wl
, (6) gVf2, A24 1 2k
2g f V , Asin W 1 g2 g1 g 8V , Af cos Wl
. (7)Several articles have dealt with phenomenological constraints on theoretically motivated, additional neutral gauge bosons [7]. Here, we are interested in obtaining constraints on the mass of Z2 from observed direct search limits at the Tevatron. The
relevant quantity to consider here is sB : the gauge boson production cross-section times the branching fraction into e1e2pair. We calculated sB in pp collisions at ks 4
1 .8 TeV (Fermilab Tevatron) for Z8 (assuming W40). In fact, severe constraints are obtained [8] on the mixing angle
(
NWN G 0 .01)
from the precision experiments at LEP I. In calculating cross-sections we use Martin-Roberts-Stirling set MRS(R1) parton distribution functions [9]. For comparison, we also consider a gauge boson, Z, withFig. 2. – Production cross-section for Z8 in pp collisions at ks414 TeV, times branching fraction into e1e2pair, and into all known fermions, as a function of the gauge boson mass M.
couplings identical to that of the standard Z but with mass a free parameter. The product sB is presented in fig. 1 as a function of the gauge boson mass, M. The 95% c.l. lower limit obtained on sB at ks 41.8 TeV at CDF is sBE3.531024nb [10]. With
this limit, we obtain a direct-search lower bound on Z8 mass,
MZ8F 410 GeV .
(8)
Given the Tevatron null results on the discovery of new gauge bosons, it is necessary to consider higher collision energies in order to probe higher gauge boson masses. The proposed Large Hadron Collider (LHC) at CERN is expected to achieve a maximum collision energy of ks 414 TeV, with a designed luminosity of L41034cm22s21[11].
We calculated the production cross-section for Z8 at the LHC. In fig. 2, we present the quantity s( pp KZ8X ) B( Z8Ke1e2) as a function of the gauge boson mass. Also shown
is s( pp KZ8X ) B( Z8KAll ), where all three known generations of fermions are contributing to the Z8 width. With the above given luminosity, LHC is expected to achieve an integrated luminosity of 105pb21 per 107
s year of running. For a typical value of MZ8, MZ84 1( 2 ) TeV , a run with the given integrated luminosity would yield approximately 1 .9 3104( 800 ) Z8’s events a year.
In conclusion, the Sp( 6 )L7 U( 1 )Y extension of the standard model gauge group
suggests an additional neutral gauge boson, Z8. Constraints are obtained on the mass of Z8 from the direct search limits at hadron collider. The direct CDF search limits at the Tevatron give a lower bound on MZ8, MZ8F 410 GeV . For MZ84 1( 2 ) TeV , the proposed CERN LHC collider is expected to be capable of producing 1 .9 3104( 800 ) Z8 events a year.
* * *
The author would like to thank W. J. STIRLING for providing the FORTRAN code for the MRS parton distribution functions and T. K. KUOfor useful discussions.
R E F E R E N C E S
[1] WEINBERG S., Phys. Rev. Lett., 19 (1967) 1264; SALAM A., in Elementary Particle Theory:
Relativistic Groups and Analyticity (Noble Symposium No. 8), edited by N. SVARTHOLM (Almqvist and Wiksell, Stokholm) 1968, p. 367.
[2] See, for example, KIM J. E. et al., Rev. Mod. Phys., 53 (1981) 211; BARBIELLINI G. and SANTONIC., Riv. Nuovo Cimento, 9 (1986) 1; AMALDIU. et al., Phys. Rev. D, 36 (1987) 1385; COSTAG., ELLISJ., FOGLIG. L., NANOPOULOSD. V. and ZWIRNER F., Nucl. Phys. B, 297 (1988) 244; LANGACKERP. and LUOM., Phys. Rev. D, 44 (1991) 817.
[3] THE LEP COLLABORATIONS and THE LEP ELECTROWEAK WORKING GROUP, Report No. CERNOPPEO94-187.
[4] KUOT. K. and NAKAGAWAN., Phys. Rev. D, 30 (1984) 2011; Nucl. Phys. B, 250 (1985) 641; BAGNEIDA. A., KUOT. K. and NAKAGAWAN., Int. J. Mod. Phys. A, 2 (1987) 1351.
[5] BARGERV. et al., Int. J. Mod. Phys. A, 2 (1987) 1327.
[6] See, for example, KUOT. K. and NAKAGAWAN., Phys. Rev. D, 31 (1985) 1161; 32 (1985) 306; BARGERV. et al. [3]; PARKG. T. and KUOT. K., Phys. Rev. D, 42 (1990) 3879; 45 (1992) 1720;
Z. Phys. C., 59 (1993) 445; BAGNEIDA. A., KUOT. K. and PARKG. T., Phys. Rev. D, 44 (1991) 2188; RIZZOT. G., Phys. Rev. D, 42 (1990) 3755; HEWETTJ. L. and RIZZOT. G., Phys. Rev. D,
45 (1992) 161; RIZZOT. G., Phys. Rev. D, 46 (1992) 3751; BAGNEIDA. A., Phys. Rev. D, 49 (1994) 3755; KUOT. K. and PARKG. T., Phys. Rev. D, 50 (1994) 3508; KUOT. K., PARKG. T. and ZARLEKM., Nuovo Cimento A, 107 (1994) 757.
[7] See, for example, LANGACKERP., ROBINETTR. W. and ROSNERJ., Phys. Rev. D, 30 (1984) 1470; DURKINL. S. and LANGACKERP., Phys. Lett. B, 166 (1986) 436; AMALDIU. et al. [2]; COSTAG. et al. [2]; BAGNEIDA. A. and KUOT. K., Phys. Rev. D, 38 (1988) 2153; HEWETTJ. L. and RIZZOT. G., Phys. Rep., 183 (1989) 194;DELAGUILAF. et al., Nucl. Phys. B, 361 (1991) 45;DELAGUILAF. et al., Nucl. Phys. B, 372 (1992) 3; LANGACKERP. and LUOM., Phys. Rev.
D, 45 (1992) 278; Rev. Mod. Phys., 64 (1992) 87; ALTARELLIG. et al., Nucl. Phys. B, 405 (1993) 3; ABEF. et al., Phys. Rev. D, 51 (1995) R949.
[8] KUOT. K. and PARKG. T., Phys. Rev. D, 50 (1994) 3508; PARKG. T. and KUOT. K., Int. J.
Mod. Phys. A, 10 (1995) 4387.
[9] MARTINA. D., ROBERTSR. G. and STIRLINGSW. J., Phys. Lett. B, 387 (1996) 419. [10] ABEF. et al., Phys. Rev. D, 51 (1995) R949.
