Experimental constraints on fourth generation quark masses

0.16 MB·English

by  P. Q. Hung

Experimental constraints on fourth generation quark masses
P.Q. Hung∗
Dept. of Physics, University of Virginia,
382 McCormick Road, P. O. Box 400714,
Charlottesville, Virginia 22904-4714, USA
Marc Sher†
Dept. of Physics, College of William and Mary,
Williamsburg, Virginia 23187, USA
(Dated: February 2, 2008)
The existing bounds from CDF on the masses of the fourth generation quarks, t′ and b′, are
reexamined. Theboundof256 GeVonthet′ massassumesthattheprimary decayofthet′ isinto
8 q+W, which is not the case for a substantial region of parameter space. The bound of 268 GeV
0 on theb′ mass assumes that the branching ratio for b′ →b+Z is very large, which is not only not
0 truefor muchof parameterspace, butisnever truefor b′ masses above255 GeV.Inaddition, it is
2 assumedthattheheavyquarksdecaywithinthesiliconvertexdetector,andforsmallmixingangles
this will not be the case. The experimental bounds, including all of these effects, are found as a
n
function of theother heavy quarkmass and the mixingangle.
a
J

2
The question of whether or not there exist quarks and b′) are taken to be bounded from below at around

and leptons beyond the known three generations has 258 GeV. This lower bound was taken from CDF, who
]
h generated a number of theoretical and experimental boundedthet′mass[6]andtheb′mass[7]. However,CDF
p
investigations[1, 2]. Although direct experimental con- made a number of assumptions. For instance, it was as-
p- straints did not (and do not) rule out a heavy fourth sumed that B(b′ → b+Z)= 100% which yields a lower
e generation, until recently electroweak precision data ap- bound mb′ > 268 GeV. As we will show below, this as-
h peared to disfavour its existence. In addition, there is sumption is not only unjustified, but is in fact false for
[
a strong prejudice against quarks and leptons beyond mb′ > 255 GeV. As a result, the CDF bound weakens

2 the thirdgenerationwhichisusually paraphrasedby the considerably[8]. Furthermore, we show that there exist
v question: Why is the fourth neutrino so much heavier unexplored regions in the mass- mixing angle parameter
3 (mν4 > MZ/2) than the other three? Of course, one space which could prove very useful to future searches.
5 can verywell imagine severalscenarios in which this can Most of the present mass bounds on the fourth gener-
3
“easily”be accomplishedsince muchis yet to be learned ation quarks involved searches done within about 1 cm
4
. about neutrino masses. In the end, it will be the verdict from the beam pipe, inside the silicon vertex detector of
1 of experiments which will be the determining factor. CDF. The customary focus is on the decay of t′ and b′
1
7 Thereisstillthequestion: Whyshouldonebotherwith into quarks of the first three generations, in particular
0 a fourth generation? There might be several answers to into the b quark. As noted above, for example, the most
: that question. First, it is possible that a heavy fourth recent bound on the b′ mass by CDF was obtained by
iv generationmighthelpinbringingtheSU(3)⊗SU(2)L⊗ searching for the decay mode b′ → b+Z. Similarly, the
X U(1)Y couplings close to a unification point at a scale t′ search focused on the decay mode t′ →q+W.
r ∼1016 inthe simplestnon-supersymmetricGrandUnifi- Let us first look at the t′ decay. One can consider two
a
cationmodelSU(5)[3]. Second,itsexistencemighthave regions: (I) mt′ ≤ mb′, and (II) mt′ > mb′. For (I), it is
some interesting connections with the mass of the SM obvious that the main decay mode will be t′ → q+W.
Higgs boson [4]. Last but not least, there is no theo- For (II), whether or not t′ → q + W dominates over
retical reason that dictates the number of families to be t′ →b′+W dependsontheb′ massandthemixingangle
three. We still have no satisfactory explanation for the θbt′. In this region, we calculate the branching ratio for
mystery of family replication. t′ →q+W asa functionofthe parameters. Ifit is lower
than 60%, the CDF bound will not apply (the choice
Recent reexaminations [4, 5] of electroweak precision
of 60% is based on viewing the graph in Ref.[6], and
data led to the conclusion that the possible existence
is somewhat arbitrarywithout a more detailed analysis–
of a fourth generation is not only allowed but its mass
sincetheregionshownisonalogarithmicscale,changing
range is correlated in an interesting way with that of
that number will not noticeably affect the result). If the
the Higgs boson in the minimal Standard Model (SM).
In [4], the masses of the fourth generation quarks (t′ b′massisbetweenmt′−MW andmt′,thenthethreebody
decay predominates; whereas if it is lower than mt′ −
MW, the two-body decay will dominate. The decay rate
is given in Refs. [9, 10] and repeated (in this specific
context) in equation [52] of Ref. [1].
∗[e-mail]
†[e-mail] In addition, even if the t′ → q+W decay does domi-
2
300
......................................................................................................................
....................................................................................................................
.....................................................................................................................
.....................................................................................................................
....................................................................................................................
280 ....................................................................................................................
....................................................................................................................
.....................................................................................................................
..................................................................................................................... 1
260 ...................................................................................................................
..............................................................................................................
256 ................................................................
............................................................. 260
240 ........................................................... 0.8
240 .........................................................
230 ..................................................... 240
.................................................
eV) 220 .................................................
M (G b' 220 _____ .............................................................................................................................. b + Z) 0.6
200 200 ..................................................................... b' --> 220
................................. R ( 0.4
.............................. B
.............................
..........................
180 ..........................
....... 0.2 200
......
....
160
....
...
0
200 210 220 230 240 250 260
140 M (GeV)
10-18 10-16 10-14 10-12 10-10 10-8 10-6 0.0001 0.01 b'
sin 2!
bt'
FIG. 1: Bound on the t′ mass in the mb′ −sin2θbt′ plane. FIG. 2: B(b′→b+Z) as a function of Mb′ for various Mt′
The shaded region corresponds to the CDF lower bound of
256 GeV.
from the search[11] for a stable t′ (at distances greater
than approximately 3 m).
nate,CDFassumedthatitdecayedwithinapproximately
1 centimeter from the beam pipe. For very small mixing For the bounds on the b′ mass, CDF assumed that
angles,thiswillnotbethecase. Ofcourse,forextremely the branching ratio B(b′ → b+Z) was 100 percent. In
smallmixingangles,suchthatthedecaylengthisgreater Fig. 2, we plot the branching ratio B(b′ → b+Z) as
thanabout3meters,thet′willappeartobeastablepar- a function of mb′ for different values of mt′. Here we
ticle and can be ruled out (above some mass) by stable use the results of [12] where the assumption sinθbt′ =
quark searches. −sinθtb′ = x was made resulting in a GIM cancellation
All of these results are plotted in Fig. 1, where we when mt′ ∼mt. Furthermore, as in [12], we will assume
plot the bound on the t′ mass in the mb′ − sin2θbt′ that |sinθcb′| < x2 so that the decay of b′ into “lighter”
plane. There are three distinct regions. The shaded re- quarks will be mainly into the t quark. Note that this
gion above and to the right of the curve with mt′ =256 assumption may not be justified, and if it is false the
GeVrepresentsthe CDF lowerbound onmt′. Inthis re- branching ratio will be even lower, weakening the CDF
gion, the CDF bound applies. Below the shaded region, bound even further. The decay into t is three-body for
the curves correspond to the new lower bound on mt′ mb′ < mt + mW and two-body otherwise. This is to
fromCDFbasedontherequirementthatthet′ →q+W be compared with b′ → b+Z. This analysis has been
decay is dominant. These curves all end to the left performed in [12] (Table I) and [1] (Fig. 14).
at sin2θbt′ ∼ 6× 10−15. This corresponds to a decay The results are shown in Fig. 2. It can be seen that
lengthofapproximately1cm. (Letusrecallthatpresent B(b′ →b+Z)<100%for a wide range of b′ mass above
searches are sensitive to decays which occur very close 200 GeV. Note that the bound of 268 GeV on mb′ as-
to the beam pipe to a distance of about 1 cm.) To the suming B(b′ → b+Z) = 100% does not hold. As mb′
left of those curves lies an unexplored window situated getsabove200GeV, the decaymode b′ →t+W∗ begins
between sin2θbt′ ∼ 6×10−15 and sin2θbt′ ∼ 2×10−17, to be comparable with the mode b′ → b+Z and starts
corresponding to a distance of roughly 1 cm out to 3 m. to dominate for mb′ ≥ 250 GeV [12]. In particular, for
The far-left of the plot represents the constraint coming mb′ > 255 GeV, the decay b′ → t+W will be into real
3
ferent values of mb′ for different curves in Fig. 3 reflect
thisacceptanceconstraint. Wealsoshowan“unexplored
region”similar to that shownin Fig. 1 for decays occur-
ing between1 cmand3 m,as wellas the regionwhereb′
300
....................................................................................................................... is “stable”. This unexplored region is not vertical, as in
.......................................................................................................................
....................................................................................................................... Fig. 1, since the rate for b′ → b+Z is very sensitive to
....................................................................................................................... the t′ mass.
.......................................................................................................................
280 ....................................................................................................................... In summary, we reexamined the experimental bounds
.......................................................................................................................
....................................................................................................................... on the masses of the fourth generation quarks: the t′
...................................................................................................................... and b′ quarks. We divide the search into three distance
......................................................................................................................
260 ..................................................................................................................... regions as measured from the center of the beam pipe:
.....................................................................................................................
255 ............................................................................. 1) d = 0 cm to ∼ 1 cm, 2) d ∼ 1 cm to 3 m and 3)
.................................................................... d > 3 m. The first region is one where most searches at
V) 240 ........................................................
e240 the Tevatron have been performed. We have computed
G ................................................
M (t' 230 .......................................... the lower bounds on the t′ and b′ masses under the re-
................................... quirement that t′ and b′ decay primarily into quarks of
............................
the first three generations as shown in Fig. 1 and Fig.
220 ..........................
...................... 3. For b′, we found that the CDF lower bound on its
..................
mass can never exceed 255 GeV, contrary to an earlier
................
200 ............. claimof268GeVwhichhadmadeuseofthe assumption
200
.......... B(b′ →b+Z)=100%andwhichisnotcorrectwhenthe
190
...... b′massexceeds200GeV. Fort′,boundsareshown,start-
ing with the CDF bound 256 GeV. Region (3) (greater
180
than 3 m) is bounded by searches for stable quarks. Re-
10-15 10-13 10-11 10-9 10-7 10-5 0.001 0.1 gion (2) (between 1 cm and 3 m) is unexplored and cor-
sin2! responds to a rangeof mixing angle sin2θbt′ ∼6×10−15
tb' and sin2θbt′ ∼ 2 × 10−17. Such a small mixing angle
might seem unlikely, but it could arise very naturally
in a 3 + 1 scenario. For example, if one simply had a
Z2 symmetry in which the fourth generation fields were
FIG. 3: Bound on theb′ mass in themt′−sin2θtb′ plane. oddandallotherfields wereeven,thenthe mixing angle
would vanish. However, discrete symmetries will gener-
ally be broken by Planck mass effects, which can lead to
particles, and thus this decay will always dominate. The sin2θbt′ of MW/MPl ∼ 10−17. Thus, such a small mix-
CDF bound can thus never exceed 255 GeV. Using Fig.
inganglecouldbenatural,andweurgeourexperimental
2,weestimatethe acceptanceforb′ →b+Z ashadbeen
colleaguestoexplorethisregion. Ifthefourthgeneration
done by CDF [7]. The results are then used as inputs
quarksareindeedfoundinthisregion,itwouldshedlight
into our analysis of the bounds on the b′ mass.
on the question of family replication.
The b′ decay is treatedin a similar fashion. Again, we
subdivide the decayinto tworegions: (I) mb′ ≤mt′, and
2
(II) mb′ > mt′. Different curves in the mt′ −sin θtb′
plane correspond to different values of mb′ for which b′ Acknowledgments
does not decay into t′. This is shown in Fig. 3. Here, we
take into account the value of B(b′ → b+Z) (denoted PQH is supported by the US Department of Energy
by β in [7]) as obtained from Fig. 2 for a given mt′ and under grantNo. DE-A505-89ER40518. MS is supported
mb′. We then use this number to obtain the acceptance by the NSF under grant No. PHY-0554854. We thank
asgivenby[7]whichisscaledbyafactor1−(1−β)2. Dif- David Stuart for useful communications.
[1] For an extensive discussion and a comprehensive list and M. Sher, Phys. Rev. D 63, 053001 (2001)
of references prior to 2000, see P. H. Frampton, [arXiv:hep-ph/0011077]; A. Arhrib and W. S. Hou,
P. Q. Hung and M. Sher, Phys. Rept. 330, 263 (2000) Phys.Rev.D64,073016(2001)[arXiv:hep-ph/0012027];
[arXiv:hep-ph/9903387]. H. Ciftci and S. Sultansoy, Mod. Phys. Lett. A
[2] F. del Aguila, M. Perez-Victoria and J. Santi- 18, 859 (2003) [arXiv:hep-ph/0107321]; D. Choudhury,
ago, JHEP 0009, 011 (2000) [arXiv:hep-ph/0007316]; T. M. P. Tait and C. E. M. Wagner, Phys. Rev. D 65,
J. E. Cieza Montalvo and M. D. Tonasse, Nucl. Phys. 053002 (2002) [arXiv:hep-ph/0109097]; J. A. Aguilar-
B 623, 325 (2002) [arXiv:hep-ph/0008196]; S. Nie Saavedra, Phys. Rev. D 67, 035003 (2003) [Erratum-
4
ibid. D 69, 099901 (2004)] [arXiv:hep-ph/0210112]; A. N. Rozanov and M. I. Vysotsky, Phys. Lett. B
A. Arhrib and W. S. Hou, Eur. Phys. J. C 27, 529, 111(2002) [arXiv:hep-ph/0111028]; V.A.Novikov,
555 (2003) [arXiv:hep-ph/0211267]; J. E. Cieza Mon- L. B. Okun, A. N. Rozanov and M. I. Vysotsky, JETP
talvo and M. D. Tonasse, Phys. Rev. D 67, 075022 Lett.76,127(2002) [PismaZh.Eksp.Teor.Fiz. 76,158
(2003) [arXiv:hep-ph/0302235]; D. E. Morrissey and (2002)] [arXiv:hep-ph/0203132].
C. E. M. Wagner, Phys. Rev. D 69, 053001 (2004) [6] J. Conway et al. [CDF Collaboration],
[arXiv:hep-ph/0308001]; P. Q. Hung, Int. J. Mod. Phys. http://www-cdf.fnal.gov/physics/new/top/2005/ljets/tprime/gen6
A20,1276(2005)[arXiv:hep-ph/0406257];G.A.Kozlov, /public.html
A.N.Sisakian, Z.I. Khubua,G. Arabidze, G.Khoriauli [7] T. Aaltonen et al. [CDF Collaboration], Phys. Rev. D
andT.Morii, J.Phys.G 30,1201 (2004); J.A.Aguilar- 76, 072006 (2007) [arXiv:0706.3264 [hep-ex]].
Saavedra, Phys. Lett. B 625, 234 (2005) [Erratum-ibid. [8] In their paper, CDF actually referred to any particle
B 633, 792 (2006)] [arXiv:hep-ph/0506187]; A. T. Alan, whichdecaysintob+Z,notjustasequentialfourthgen-
A. Senol and N. Karagoz, Phys. Lett. B 639, 266 erationquark.Thus,insomemodelstheiranalysiswould
(2006) [arXiv:hep-ph/0511199]; M. Y. Khlopov, Pisma be relevant (for example, in some models with isosinglet
Zh. Eksp. Teor. Fiz. 83, 3 (2006) [JETP Lett. 83, 1 quarks). However, we are pointing out that the bounds
(2006)] [arXiv:astro-ph/0511796]; R. Mehdiyev, S. Sul- are substantially weakened if one assumes that the new
tansoy,G.UnelandM. Yilmaz, Eur.Phys.J.C 49, 613 particle is a sequential fourth generation quark. The ex-
(2007) [arXiv:hep-ex/0603005]; J. A. Aguilar-Saavedra, ample in their paper of a sequential fourth generation
PoS TOP2006, 003 (2006) [arXiv:hep-ph/0603199]; quarkwasusedsincetheproductioncross sectioniswell
A. Arhrib and W. S. Hou, JHEP 0607, 009 (2006) understood, unlike that of other models
[arXiv:hep-ph/0602035]. [9] W.S.HouandG.G.Wong,Phys.Rev.D49,3643(1994)
[3] P. Q. Hung, Phys. Rev. Lett. 80, 3000 (1998) [arXiv:hep-ph/9308312].
[arXiv:hep-ph/9712338]. [10] I. I. Y. Bigi, Y. L. Dokshitzer, V. A. Khoze, J. H.Kuhn
[4] G.D.Kribs,T.Plehn,M.SpannowskyandT.M.P.Tait, and P. M. Zerwas, Phys.Lett. B 181, 157 (1986).
arXiv:0706.3718 [hep-ph]. [11] D.E.Acostaetal.[CDFCollaboration],Phys.Rev.Lett.
[5] H. J. He, N. Polonsky and S. f. Su, Phys. Rev. D 90, 131801 (2003) [arXiv:hep-ex/0211064].
64, 053004 (2001) [arXiv:hep-ph/0102144]; M. Mal- [12] P.H.FramptonandP.Q.Hung,Phys.Rev.D58,057704
toni, V. A. Novikov, L. B. Okun, A. N. Rozanov (1998) [arXiv:hep-ph/9711218].
and M. I. Vysotsky, Phys. Lett. B 476, 107 (2000)
[arXiv:hep-ph/9911535]; V. A. Novikov, L. B. Okun,