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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]. ∗[email protected] †[email protected] 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. 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