ork ber C03- vide LBL-36598 h this um e theory y pro on n harge gauge tract DE-A ts from precision yp erc y ts and ma ama w that the generation y 2. In our previous w : atron. 0 w-energy e ectiv ev ber b er and h e sho B , Sendai, 980 Japan. um ade constrain y
atory oup coupling only to bary h, Oce of High Energy and Nuclear or B on n ersit and t of Energy under Con
t U(1) Gauge Boson eak measuremen ab Z w on Num eak scale. W e prop ose a class of mo dels in whic w HEP-PH-9501220e of absence from Departmen ork w v uary 6, 1995 Jan On lea This w y ysics, Division of High Energy Ph 76SF00098. Ph provided byCERNDocumentServer brought toyouby CORE Disclaimer This do cumentwas prepared as an accountofwork sp onsored by the United States Government. While this do cument is b elieved to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or resp onsibility for the accuracy, completeness, or usefulness of any information, apparatus, pro duct, or pro cess disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any sp eci c commercial pro ducts pro cess, or service by its trade name, trademark, manufacturer, or otherwise, do es not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Governmentorany agency thereof, or The Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or re ect those of the United States Governmentorany agency thereof or The Regents of the University of California and shall not b e used for advertising or pro duct endorsement purp oses. Lawrence Berkeley Laboratory is an equal opportunity employer. ii 1 Intro duction In a recent pap er, we considered the phenomenology of a light U(1) gauge b oson that B couples only to baryon numb er [1]. We assumed that the new U(1) gauge symmetry is sp ontaneously broken, and that the mass m is smaller than m . Nevertheless, we B B Z showed that this new gauge b oson could remain undetected, even if the coupling were B comparable to [1, 2]. Since the b oson couples only to quarks, any pro cess that str ong B is relevantto detection also has a signi cant contribution from QCD. Thus, a typical B b oson with m = 50 GeV and =0:1, can remain undetected by `hiding' in the large B B B QCD background. Since the b oson couples only to quarks, it is dicult to detect, just B like the more familiar example of a light gluino in sup ersymmetric mo dels [3]. One of the assumptions in our original analysis [1] was that mixing b etween the and B electroweak gauge b osons was negligible. Mass mixing is not present b ecause we assume that there are no Higgs b osons that carry b oth baryon numb er and electroweak quantum numb ers. However, there is a p ossible o -diagonal kinetic term that mixes the U(1) and B U(1) gauge elds: Y 1 Y Y B L = F F +2cF F + F F : (1.1) kin Y B B 4 Here the F are gauge eld strength tensors, and c is an undetermined coupling constant. Clearly, c must b e quite small so that the kinetic mixing do es not con ict with precision electroweak measurements. Although the phenomenology of the is sp eci ed within the B three dimensional parameter space m - -c,any realistic mo del must reside within the B B narrow region jcj 0 0 constraints. Thus, in our previous work [1], we describ ed the phenomenology in terms B of an e ectively two-dimensional parameter space, the m - plane at c 0. B B The natural question that remains to b e answered is whether there are any mo dels in which c is naturally small enough to satisfy the exp erimental constraints. Our previous results would b e greatly undermined if they were relevant only to mo dels in which the coupling c required ne-tuning at the electroweak scale. In this pap er, we will describ e a class of mo dels in which this kinetic mixing term is absentabove some scale that we assume is not much greater than the top quark mass. Below , a kinetic mixing term is generated only through radiative corrections, so that c() = 0 but c() 6= 0 for <. < < We will show that if 200 GeV 1:3TeV, c() never b ecomes large enough in the low-energy theory to con ict with precision electroweak measurements, even when is as B large as 0:1. We then present a mo del that satis es this b oundary condition. In addition, 1 we show that a mixing term small enough to satisfy the current exp erimental constraints can nonetheless provide us with a p ossible signal for the in the Drell-Yan dilepton B di erential cross sections at hadron colliders. This signal could b e within the reach of the Fermilab Tevatron with the main injector and a luminosity upgrade. The pap er is organized as follows. In the next section we discuss the phenomenological constraints on the kinetic mixing term from precision electroweak measurements. We show that these constraints can b e satis ed if the scale at which the mixing vanishes is just ab ove the electroweak scale. In section 3, we present a mo del with gauged baryon number in which the kinetic mixing term is naturally absentabove . In section 4 we discuss a leptonic signature of the in Drell-Yan dilepton pro duction at hadron colliders. In the B nal section we summarize our conclusions. 2 Mixing Constraints To study the e ects of the kinetic mixing term, we could rede ne the gauge elds so that the kinetic terms in the new basis are diagonal and conventionally normalized [4]. However, since we know a priori that the coupling c is much less than 1, it is more convenientto treat the mixing term in Eq. (1.1) as a new p erturbativeinteraction. The Feynman rule corresp onding to the -photon vertex is B 2 ic cos (p g p p ) (2.1) w 0 and for the -Z vertex is B 2 ic sin (p g p p ): (2.2) Z w Note that c = c = c ab ove the electroweak scale, but c and c run di erently in the Z Z low-energy e ective theory b elow m . This can b e seen in Fig. 1. If we assume that b oth top c and c vanish at the scale m ,we can run the couplings down to lower energies Z top to determine the magnitude of mixing that is characteristic of purely radiative e ects. This will give us a useful p oint of reference when we consider the relevant exp erimental constraints. Ifwere less than m , the new physics that is asso ciated with this scale top would have already b een seen in accelerator exp eriments. The extent to which can b e signi cantly larger than m will b e considered later in this section. top The couplings c and c are renormalized by the one quark-lo op diagrams that connect Z the to either the photon or Z .From these diagrams, we obtain the following one-lo op B 2 renormalization group equations p @ 2 B [2N N ] ; (2.3) c ()= u d @ 9 c w and p h i @ 1 B 2 3(N N ) + 4(2N N )s ; (2.4) c ()= d u u d Z w 2 @ 18 s c w w where s (c ) = sin (cos ), and is the ne structure constant. N and N are the w w w w u d numb er of light quark avors with charge 2=3 and 1=3, resp ectively.For = m , and top =0:1, we nd B 3 3 c (m ) 1:5 10 , c (m ) 6:2 10 , Z Z Z 3 2 c (m ) 8:4 10 , c (m ) 3:5 10 , b Z b where m is the b ottom quark mass. As we cross the various quark mass thresholds b elow b m , the rate at which c and c run b ecomes progressively smaller, until the running b Z e ectively stops b elow the hadronic scale 1 GeV. It is our rst job to determine whether the estimates ab ove are consistent with exp erimental limits on c and c . Afterwards, we Z will return to the issue of the running and determine an upp er b ound on the scale . 2.1 -Z Mixing B The most signi cant constraints on c (m ) are shown in Fig. 2. Wehave considered Z Z the e ects of the -Z mixing on the following exp erimental observables: the Z mass, B hadronic width, and forward-backward asymmetries, and the neutral current N and eN deep inelastic scattering cross sections. Wenow consider each of these in turn. Z mass. We determine the shift in the Z mass by computing the shift in the real part of the p ole in neutral gauge b oson propagator. Thus, we set (2) 2 det (p )=0; (2.5) where 0 1 2 2 2 p m +im c s p Z Z Z w Z (2) 2 @ A : (2.6) (p )= 2 2 2 c s p p m + im Z w B B B We nd 2 m m Z Z 2 0:116 c : (2.7) Z 2 2 m m m Z Z B 2 2 Note that the e ect of - mixing app ears at O (c c ), and is negligible. This expression B Z is valid provided that m is not to o close to m .Wehavechecked that this approximation B Z 3 > is accurate if jm m j 10 GeV, which holds over range of m of interest to us in this B Z B pap er. Since m is taken as an input to determine other electroweak parameters, we require Z 2 ^ that the shift in m do es not sp oil the consistency b etween the value of sin determined Z w 2 from the Z decay asymmetries (whichwe call s b elow), and the value extracted from deep 2 inelastic scattering data. The shift in m corresp onding to the uncertaintys is given by Z 2 m 1 2s Z 2 = s ; (2.8) 2 2 m 2s c Z 2 3 where s =0:2317 0:0008 [5]. Thus, we nd m =m < 2:4 10 , requiring that the Z Z 2 ^ shift in sin is no more than a two standard deviation e ect. The contour corresp onding to this b ound is plotted in Fig. 2. Z hadronic width. In Ref. [1] we computed the contribution to the Z hadronic width from (i) direct pro duction Z ! q q , and (ii) the Zqq vertex correction. There is an B B additional contribution to the hadronic width from the Z - mixing that is given by B 2 m p had Z ; (2.9) 1:194 c B Z 2 2 m m had Z B Given that the uncertainty in the Z hadronic width is 0.6% at two standard deviations [5], we obtain the contour shown in Fig. 2. Notice that the constraint that we obtain is weaker for p ositive c due to cancelation b etween the contributions discussed in Ref. [1], and the Z new contribution given in Eq. (2.9). In either case, the hadronic width places the tightest < constrainton c (m ), roughly jc (m )j 0:02. Z Z Z Z Forward-Backward Asymmetries. The -Z mixing term has the e ect of slightly shift- B ing the vector coupling of the Z to quarks. Thus, there is a new contribution to the (0;q ) forward-backward asymmetry A in Z decayto q q. Since the exp erimental uncertainty FB (0;b) is smallest for q = b,we use the two standard deviation uncertaintyin A to constrain FB our mo del. We nd that the new contribution is given by 2 p m (0;b) Z ; (2.10) A 0:159 c B Z FB 2 2 m m Z B while the measured value is 0.1070.013 [5]. The resulting b ound is shown in Fig. 2. Notice that this provides a weaker constraint than those we obtained from consideration of the Z mass and width. Deep Inelastic Scattering. The constraints on c from deep inelastic N scattering, and Z from parity-violating eN scattering are muchweaker than the other constraints that we 4 have discussed, and are not shown in Fig. 2. Deep inelastic N scattering can b e describ ed in terms of the parameters , de ned by the e ective four-fermion interaction [5] L(R) i h X G F N 5 5 5 p L = ; (2.11) (1 ) (i)q (1 )q + (i)q (1 + )q L i i R i i 2 i where the sum is over quark avors. We nd that the contribution to the parameters from the -Z mixing is given by B 2 p q 0:766 c ; (2.12) L(R) Z B 2 2 q m B 2 2 where q 20 GeV isatypical squared momentum transfer. The most accurately measured parameter is (d)= 0:438 0:012 [5]. To demonstrate that the uncertainty L in (d) provides only a weak constraint, weevaluate Eq. (2.12) for m 50 GeV and L B 2 0:1. We obtain the b ound jc (q )j < 12:5, at two standard deviations, which gives B Z us jc (m )j < 12:5, b ecause the contribution from the running is small. This is a much Z Z weaker constraint than the others that wehave considered. Parity-violating eN scattering can b e describ ed in terms of two other parameters, C 1 and C , de ned by the e ective four-fermion interaction [5] 2 h i X G F eN 5 5 p L = C e eq q + C e eq q : (2.13) 1i i i 2i i i 2 i The -Z mixing contributes only to the parameter C : B 1i 2 p q C = 1:533 c : (2.14) 1i Z B 2 2 q m B The parameter measured with the least exp erimental uncertaintyis C =0:359 0:041 1d [5]. If we again assume that m = 50 GeV and =0:1, then the b ound on c (m ) B B Z Z following from the two standard deviation uncertaintyin C is jc (m )j < 21:2. This is 1d Z Z even weaker than the constraintwe obtained from N scattering. Note that there are no further constraints on C from the measurements of atomic parity violation b ecause this 1i pro cess involves zero momentum transfer, where the kinetic mixing vanishes. What wehave seen is that the Z -p ole observables place the tightest constraints on the mixing parameter c , while deep inelastic scattering measurements do not provide any Z further constraints. Thus, if jc (M )j < 0:02, we are not likely to encounter any problems Z Z with the precision electroweak measurements that wehave considered in this section. 5 2.2 - Mixing B The coupling c has its most signi cant e ect on a di erent set of observables. Belowwe + consider the e ect of the - mixing on the cross section for e e ! hadr ons, and on the B anomalous magnetic moments of the electron and muon. + e e ! hadr ons. The most imp ortant constrainton c comes from the additional + + + contribution to R, the ratio (e e ! hadrons )= (e e ! ). We nd 2 2 R p s(s m ) s B 2 = 1:803 c +8:938 c ; (2.15) B 2 2 2 2 2 2 2 2 R (s m ) + m (s m ) + m B B B B B B p 1 s is the center of mass energy, and = N m is the width, with N =5 where B F B B B F 9 for the range of m of interest. Notice that the nonstandard contribution to R is maximized B 2 only in the vicinityof s m .For any m of interest, we can constrain c by considering B B p the two standard deviation uncertainty in the value of R measured at s m . The B results are shown in Fig. 3, based on the cumulative data on R taken at various values of p p s and compiled by the Particle Data Group [5]. Since there are values of s that have not b een studied, the constraints on c are strongest when m happ ens to coincide with B p avalue of s at which there is an exp erimental data p ointavailable. Roughly sp eaking, the allowed region of Fig. 3 corresp onds to jc (m )j < 0:01. However, it is clear that the B constraint can b e signi cantly weaker if m happ ens to lie at p oint where less data are B available. Anomalous magnetic moments. At the very lowest energies, we can constrain c by the e ect of the mixing on the anomalous magnetic moments of the electron and muon. Since this provides a muchweaker constraint than the one we obtained from R,we do not show the result in Fig. 3. We nd that the nonstandard contribution to the anomalous magnetic moment a =(g 2)=2 is given by 2 2 a = c c I (r ); (2.16) w where p 2 2 1 r + r 4r r r (r 4r +2) p p I (r )= ln ; (2.17) r+ (r 2) ln(r ) 2 2 2 2 2 r 4r r r 4r 2 2 and r = m =m . Since r is large, we use the asymptotic form I (r ) 1=(3r ). Then B lepton the limit on c corresp onding to a two standard deviation uncertainty in the anomalous magnetic momentis m B c (m )< 0:050 (2.18) GeV 6 for the muon, and m B c (m ) < 0:360 (2.19) e GeV for the electron. Thus, the constraintonc for m > 20 GeV is roughly two orders of B magnitude weaker than the constraints that we obtained from R. 2.3 The Scale It should now b e clear that our original estimate of the sizes of c () and c () fall within Z the b ounds that wehave obtained from consideration of precision electroweak measure- ments. Recall that the estimate that we presented at the b eginning of this section was for c () = c () = 0 at = m .We will now determine how high we can push up b efore Z top wehave unambiguous con ict with the exp erimental constraints. Using the approximate b ound that we obtained for c , c (m ) < 0:02, and assuming m 175 GeV, we nd Z Z Z top < 1:3TeV (2.20) from Eqs. (2.3) and (2.4) with =0:1. We can place comparable b ounds on from the B constraints on c , but the precise result dep ends crucially on the choice for m , as one can B see from Fig. 3. What is interesting ab out Eq. (2.20) is that it implies that the scale of new physics lies at relatively low energies, just ab ove the electroweak scale. We will now show that there is a class of mo dels that satisfy the desired b oundary condition at =. 3 Mo dels with Naturally Small Kinetic Mixing In this section, we present a simple mo del with gauged baryon numb er that naturally satis es the b oundary condition c () = c () = 0 with < 1:3TeV. There are two Z ingredients that are of central imp ortance in the class of mo dels that have small kinetic mixing b elow the electroweak scale. (1) In the full theory, at high energies, the kinetic mixing term is forbidden by gauge invariance. This is the case, for example, if weembed one of the U(1)s in a larger nonab elian group. The mixing term remains vanishing down to the scale at which the gauge symmetry breaks to GU(1) U(1) , where G contains the B Y remaining gauge structure of the theory. (2) Beneath this symmetry breaking scale, the one-lo op diagram that connects the to the hyp ercharge gauge b oson vanishes identically, B so that c and c do not run. This places a constraint on the particle content b eneath the Z symmetry breaking scale, Tr(BY)=0 (3.1) 7 where B and Y are baryon numb er and hyp ercharge matrices, in the basis spanning the entire particle content of the theory. When wegotolower energies and the heaviest particle that contributes to Eq. (3.1) is integrated out, we will generate mixing through radiative corrections, in the way describ ed quantitatively in section 2. In what follows, we will present one example of a mo del with gauged baryon number that is `realistic' in the following sense: (i) the kinetic mixing is naturally small b elow the electroweak scale, (ii) there is a natural mechanism for generating the cosmic baryon asymmetry, and (iii) proton decay is forbidden (up to the usual non-p erturbative e ects) even though U(1) is sp ontaneously broken. It is not our goal to study every asp ect of B the phenomenology of this particular mo del, but rather to demonstrate by example that it is p ossible to construct mo dels with the features (i), (ii), and (iii). In addition, we show that there are new fermions in the mo dels of interest that app ear in chiral representations > of SU(2) U(1) ; these fermions develop electroweak scale masses m , which ensures L Y top that the scale is not to o far ab ove the electroweak scale. Moreover, this implies that detection of the new fermions in this class of mo dels is likely at an upgraded Tevatron or at the LHC. 3.1 A Mo del The gauge structure of the mo del is SU(3) SU(2) U(1) SU(4) ; C L Y H where SU(4) is a horizontal symmetry. In addition to the ordinary three families of the H i standard mo del, f (i =1;2;3), we assume there is a fourth family F ; the horizontal symmetry acts only on the quarks in the four families, which together transform as a 4 under the SU(4) . The U(1) gauge group is emb edded into SU(4) as H B H 0 1 1=3 B C B C 1=3 B C B C : (3.2) B = B C 1=3 @ A 1 While SU(4) is broken at some high scale M ,aswe discuss b elow, the U(1) subgroup H H B remains unbroken down to the electroweak scale. It is easy to verify that the particle content and quantum numb er assignments render the mo del anomaly-free. We will also assume that there are right-handed neutrinos in each of the families. The right-handed neutrinos in the ordinary families acquire Ma jorana masses at a high scale 8 z M , while the one in the fourth family do es not . The fourth family neutrino develops N an electroweak scale Dirac mass, so that the constraint from the invisible decay width of the Z is evaded. The Ma jorana masses for the right-handed neutrinos in the rst three families are crucial to the baryogenesis scenario that we present in the next subsection. An 10 12 interesting choice for the Ma jorana mass scale is M 10 {10 GeV, which is consistent N with the MSW solution to the solar neutrino problem, and the p ossibility that is a hot dark matter particle [6]. The horizontal symmetry SU(4) is broken at a scale M down to U(1) . One can H H B imagine that the symmetry breaks in one step if a numb er of adjoint Higgs b osons, that we will generically call , develop vacuum exp ectation values (VEVs) at the scale M . H However, it is p ossible to generate a hierarchy of fermion Yukawa couplings if we break the symmetry sequentially, in the presence of additional vector-like fermions [7]. The basic idea is as follows: We rst intro duce vector-like fermions with mass M that transform as 4s under SU(4) , and assume that the electroweak Higgs b oson H is a singlet under H the horizontal symmetry. Supp ose that the haveYukawainteractions like L =q + L Hu + M . Then, when the vector-like fermions are integrated out b elow the scale M , R we obtain dimension 5 op erators of the form 1 q H u : (3.3) R L M Notice when the s develop VEVs, op erators like the one in Eq. (3.3) generate Yukawa couplings in the low-energy theory.Now imagine that the horizontal symmetry is broken rst to SU(3) U(1) at the scale M , and then the SU(3) is broken sequentially at H B H H lower scales down to nothing. Then the dimension 5 op erators that wehave describ ed can give rise to a hierarchical pattern of Yukawa couplings. A detailed analysis of the fermion mass matrix in mo dels with horizontal symmetry breaking is b eyond the scop e of this pap er, and we refer the interested reader to the literature [8]. The low-energy particle content of our mo del b elow b oth M and M is listed in the H N Table 1. Here, B refers to the gauge quantum numb er under U(1) , while L is an e ective B non-anomalous global symmetry b elow M .(B L) is another non-anomalous global N extr a symmetry acting on the particles in the fourth family. It is easy to see that the kinetic mixing remains vanishing down to the weak scale. z This is natural if there is another global or lo cal SU(4) acting on the leptons, and if lepton number H emb edded as L = diag(1; 1; 1; 3) in SU(4) is broken by an order parameter with L = 2 (or 10 under H SU(4) ). However, none of the conclusions in this pap er dep ends on whether there exists a horizontal H symmetry for the leptons or not. 9 Table 1: Particle content b elow the horizontal symmetry breaking scale M and the right- H handed neutrino masses M . N particle SU(3) SU(2) U(1) B L (B L) C L Y extr a i q 3 2 1/6 1/3 0 0 L i ordinary families u 3 1 2/3 1/3 0 0 R i i i f , f d 3 1 1/3 1/3 0 0 L R R i (i =1;2;3) l 1 2 1/2 0 1 0 L i e 1 1 1 0 1 0 R Q 3 2 1/6 1 0 1 L U 3 1 2/3 1 0 1 R extra family D 3 1 1/3 1 0 1 R F , F L 1 2 1/2 0 3 +3 L R L E 1 1 1 0 3 +3 R N 1 1 0 0 3 +3 R Ab ove M , the mixing is not allowed b ecause U(1) is emb edded into the non-ab elian H B group SU(4) . This implies that the orthogonality condition (3.1) is satis ed by the particle H content of the full theory.Aswe cross M , presumably all elds whose mass terms are H allowed by the gauge symmetry decouple, but the particles listed in the table do not b ecause they b elong to chiral representations of the gauge group b elow M . One can easily check H that the orthogonalitybetween Y and B remains true b elow M as well given the particle H contentinTable 1. The mixing term is only generated b elow the masses of the particles in the extra family (whichwe will refer to generically as m ) which originate from electroweak F symmetry breaking. Therefore, the mixing term remains vanishing down to the weak scale, i.e., = m m , and the b oundary condition discussed in the previous section is F top naturally achieved. 3.2 Baryogenesis and Proton Stability It is natural to wonder how a cosmic baryon asymmetry can b e generated in a mo del in which baryon numb er is a gauge symmetry at high energies. On the other hand, it is nat- ural to worry ab out proton decay considering that the baryon numb er gauge symmetry is sp ontaneously broken at low energies. We address these two issues in this subsection. With regard to baryogenesis, we will show that the generation of a lepton numb er asymmetry from the decay of the right-handed Ma jorana neutrinos in our mo del can lead to a nonvan- 10 ishing baryon numb er for particles from the ordinary three families, even though the total baryon numb er of the universe remains zero. We describ e this mechanism in some detail, as well as other relevant cosmological issues. Afterwards, we demonstrate that proton decay is forbidden in the mo del, apart from the electroweak non-p erturbative e ects. The rst step in baryogenesis is that a lepton asymmetry is generated from the CP- violating decays of the right-handed Ma jorana neutrinos. If we takeinto account the e ect of the electroweak anomaly at a temp erature at or ab ove the electroweak phase transition [9], chemical equilibrium leads to non-vanishing lepton and baryon numb ers in b oth the ordinary and extra families. Finally, the quarks in the extra family decayinto those of the ordinary families, so that a cosmic over-density of fourth-generation particles is avoided. The rst step is exactly the one prop osed in Ref. [10 ] (see also [11] for the sup ersymmetric case.). The Yukawainteractions coupling the right-handed neutrinos to the lepton doublets violate CP in general; thus, the decay of the right-handed neutrinos can generate a net lepton asymmetry. The analysis of chemical equilibrium including the electroweak anomaly e ect is more complicated than in the Minimal Standard Mo del [12 ]. Note that the total lepton number L =(N +N ) 3(N + N + N ) (3.4) l e L E N is non-anomalous contrary to the minimal case, and is broken only by the small Ma jorana masses of the left-handed neutrinos generated by the seesaw mechanism [13]. In addition, there are the non-anomalous conserved quantum numb ers 1 B = (N + N + N ) (N + N + N ); (3.5) q u d Q U D 3 and (B L) = (N + N + N )+3(N +N +N ); (3.6) extr a Q U D L N E where `extra' refers to fourth generation particles. The decay of the right-handed neutri- nos generates only L, while b oth B and (B L) remain vanishing. Y also remains extr a vanishing by gauge invariance. Since the numb er densities of the various sp ecies are pro- p ortional to their chemical p otentials at the lowest order, we can derive nontrivial relations by considering the constraints imp osed bychemical equilibrium. The chemical equilibrium due to the Yukawainteractions implies = + = ; (3.7) q u H d H = ; (3.8) l e H 11 = + = ; (3.9) Q U H D H = + = ; (3.10) L N H E H while the electroweak anomaly e ect requires 9 +3 +3 + =0: (3.11) q l Q L Here, refers to the chemical p otential of a particle of sp ecies i, and H is the standard i electroweak Higgs b oson. Then we nd 1 B / (18 +9 +9 ) (6 +3 +3 )=0; (3.12) q u d Q U D 3 (B L) / (6 +3 +3 ) + 3(2 + + )=0; (3.13) extr a Q U D L N E 1 2 1 Y / (18 +6 )+ (9 +3 ) (9 +3 ) q Q u U d D 6 3 3 1 (6 +2 ) (3 + ) 2 =0; (3.14) l L e E H 2 L / (6 +3 ) 3(2 + + ) 6=0: (3.15) l e L E N Solving these constraints, we obtain 108 N + N + N = L; (3.16) q u d 137 101 L; (3.17) N + N = l e 137 36 N + N + N = L; (3.18) Q U D 137 12 N + N + N = L: (3.19) L E N 137 Thus, we see explicitly that the non-vanishing lepton numb er generated by the decayof the right-handed neutrinos will b e partially converted to a nonvanishing baryon number for particles from the ordinary families, as well as nonvanishing baryon and lepton numb ers for particles from the extra family. One p otential cosmological problem with this scenario is that the particles from the extra family could overclose the Universe. The constraints from primordial nucleosynthesis imply that baryons in the ordinary families must have a present cosmic density in the range 2 h =0:010{0:15, where h =0:4{1 is the reduced Hubble constant [14]. On the other b 0 0 hand, the quarks and leptons in the extra family have also acquired an asymmetry that will remain until the present. Based on the predicted ratio of these asymmetries, the new 12 contributions to the cosmic density are m F = ; (3.20) Q;U;D b m p 1 m F = ; (3.21) L;E ;N b 3 m p where m is the mass of the proton. Even in the extreme case where =0:01, the fourth p b > generation particles would overclose the Universe when m 100 GeV. One might hop e F that these fourth generation particles could b e candidates for cold dark matter. How- ever, there are very strong observational constraints against dark matter that is strongly interacting [15 ], charged [16] or comp osed of Dirac neutrinos [17]. Fortunately, this problem can b e avoided b ecause baryon number is spontaneously bro- ken, and we can nd a way to make the fourth generation particles decay. Supp ose that U(1) is broken by an electroweak-singlet Higgs eld with the following quantum numb ers B x under SU(3) SU(2) U(1) U(1) : C L Y B (1; 1; 1) : +4=3 Then the following dimension- ve op erators are the only ones for the quarks that are consistent with the gauge symmetry b elow M , H 1 L = (qUH + QuH +qDH + QdH )+h:c: (3.22) 5 M V (Of course, there are similar op erators involving the lepton elds.) One could imagine that these op erators are generated by the exchange of a heavy vector-like quark with mass M . As a consequence of Eq. (3.22), particles in the extra family can decayinto ordinary V particles. The decay rate is given by ! 2 1 v h i m ; (3.23) F F 8 M m V F where v = 246 GeV is the exp ectation value of the electroweak Higgs H , and h i is the scale of baryon numb er symmetry breaking whichwe assume is around the electroweak scale. It is now clear that the particles in the extra family can decaywell b efore nucleosynthesis 15 < as long as M 10 GeV. Note that the decay of particles in the extra family gives an V x This charge assignment can b e emb edded into SU(4) 15 representation, which allows the op erator in H Eq. (3.22). 13 additional contribution to the cosmic baryon asymmetry of the ordinary particles that do es not cancel out the original asymmetry that we obtained in Eq. (3.16). The particles (esp ecially quarks) in the fourth generation could b e pro duced at the Tevatron or LHC. Their signatures dep end on whether they leave the detector b efore or 11 < after they decay.IfM 10 GeV, they decay inside the detector and leave a signature V similar to that of the top quark. In this case, the fourth generation fermions must have masses larger than 140 GeV [18]. If M is larger, they could b e detected b efore they V decay. A search for stable color-triplet quarks was carried out by CDF [19], but the present constraint is rather weak (50{116 GeV ruled out at 95 % C.L.). An imp ortant p oint in this mo del is that proton decay is forbidden even though baryon number is spontaneously broken. Any baryon-numb er violating e ects can b e describ ed in terms of e ective op erators with p owers of the order parameter h i which breaks U(1) . B k m n The general structure of such an op erator is O = q l , where q is a quark eld, l lepton, and k ; m; n are integers. Since lepton elds carry integer charges and neutral, the p ower k has to b e a multiple of three, k =3l where l is another integer. Then the k factor q carries baryon number l which has to b e comp ensated by the baryon number of , (4=3)n. Therefore n also has to b e a multiple of three, n =3p, and the op erator has the form 12 3 p m O =(q ) l ; (3.24) { which has dimension 21p +(3=2)m. Not only is this op erator extremely suppressed by powers of a high mass scale, it also cannot contribute to proton decay b ecause the quark eld is raised to a p ower that is to o large. Thus, there is no p erturbative contribution to proton decay in this mo del. There could b e a contribution from the electroweak instanton e ect, but the decay rate due to the anomaly is known to b e extremely tiny [20]. Therefore, nucleon decay is e ectively forbidden in this mo del. Finally, one mightworry that exchange may lead to avor-changing neutral current B b ecause it is coupled to a matrix diag(1; 1; 1; 3) in the avor space of the mo del. Mixing between the ordinary and extra families gives rise to o -diagonal coupling for the . B However as seen ab ove, the mixing is suppressed bya power of h i=M , and the o - V diagonal coupling b etween di erent generations by a square of this suppression factor. All > constraints from avor-changing neutral currents are avoided when M 100 TeV. A V similar lower b ound applies to the mass of the horizontal gauge b osons in SU(3) . H { This op erator can b e written in an explicitly SU(2) U(1) symmetric way: e.g. for m =0, p=1, L Y 4 4 3 O=(qq) d . 14 4 Leptonic Signals Wehave shown that there is a class of mo dels with gauged baryon numb er in which the kinetic mixing b etween the hyp ercharge and baryon numb er gauge b osons is naturally small b elow the electroweak scale. Nevertheless, a small amount of mixing is not necessarily a bad thing, b ecause it can provide us with a p ossible leptonic signature for our mo del. In this section we consider the new contribution to the Drell-Yan pro duction of lepton pairs at hadron colliders. In particular, we show that the signal may b e within the reachofan upgraded Tevatron. The quantityofinterest is d =dM , the di erential cross section as a function of the lep- ton pair invariant mass. One can obtain the desired result from the conventional expression for the Drell-Yan di erential cross section by making the substitutions r 2 s^ B i i 2 g ! g + c c s (4.1) Z w V V w 2 3 s^ m + im B B B and r 1 s^ B i i c c Q ! Q ; (4.2) w 2 3 s^ m + im B B B i wheres ^ is the parton center of mass energy squared. Here Q is the the quark charge in i units of e, and eg =(2c s ) is the vector coupling of the Z to a quark of avor i, with w w V i i 2 g = T 2Q s . 3L V w p Our results for d =dM in a pp collision at s =1:8TeV are shown in Fig. 4 for one lepton sp ecies, integrated over the rapidityinterval 1 Set I I structure functions [21 ]. This range in rapiditywas chosen to b e consistent with the CDF detector coverage [22]. The solid line shows the conventional di erential cross section, (with c = c = 0), while the dotted lines give our results for c = c =0:01. For Z Z the values of m shown, the results do not dep end strongly on the precise choice for c . B Z Around the mass there is a noticeable excess of events b eyond the exp ected background. B Because this excess is an interference e ect, it dep ends linearly on c .We show the excess in the total dielectron plus dimoun signal in a bin of size dM surrounding the mass in B Table 2, for m = 30, 40, and 50 GeV. The statistical signi cance of the signal assuming B 1 1 1 integrated luminosities of 1 fb and 10 fb is also shown. The largest excess at 1 fb , 1 is a 5.4 standard deviation e ect for m = 30 GeV. However, with 10 fb of integrated B luminosity,even the excess at 50 GeV would b e detectable at the 9.4 sigma level. This simple analysis is sucient for a qualitative understanding of the signal we might exp ect to nd at the Tevatron, with b oth the main injector, and a luminosity upgrade. Wehave not 15 Table 2: Excess Dielectron plus Dimuon Pro duction at the Tevatron. m dM Background Excess statistical signi cance B 1 1 (GeV) (GeV) (fb) (fb) 1fb 10 fb 30 2 3468 320 5.4 17.2 40 4 2798 208 3.9 12.4 50 4 1422 112 3.0 9.4 included the eciency of the cuts and acceptance, but it is rather high even in a realistic + + analysis (93 % for e e and 82 % for in CDF analysis [22]). A more exhaustive study, including the eciency of the cuts and detector acceptance, as well as a comparison of the shap e of the di erential cross section to that exp ected in our mo del is required for a more accurate assessment of the discovery p otential for this mo del at the Tevatron. It is interesting to note that even if the coupling is smaller than 0.1, and the jet physics B discussed in Ref. [1] is no longer of relevance, the mixing e ect that we discuss here could still b e signi cant enough to provide a clear signal for the mo del. 5 Conclusions Wehave shown that there are mo dels with gauged baryon numb er in which kinetic mix- ing b etween the baryon numb er and hyp ercharge gauge b osons is naturally absentabove the electroweak scale. Since the mixing is generated only through radiative corrections at lower energies, the resulting e ective theory is consistent with precision electroweak mea- surements even when is as large as 0:1, as we showed quantitatively in section 2. The B exciting feature of the typ e of mo dels that we prop osed is that the baryon numb er gauge b oson can b e lighter than m with a large gauge coupling, and yet b e hidden in existing B Z LEP and Tevatron data. This is the p oint that we emphasized in Ref. [1]. However, even if the the coupling is not large enough to pro duce an unambiguous hadronic signal, we B have shown that the kinetic mixing term may give us another means for detecting the B via its contribution to Drell-Yan dilepton pro duction at hadron colliders. With b oth the main injector and a luminosity upgrade, this signal mayeventually b e within the reachof the Fermilab Tevatron. Acknowledgments 16 We are grateful to Lawrence Hall for useful comments. We thank Don Gro om from the Particle Data Group for providing us with compiled data on R. This work was supported by the Director, Oce of Energy Research, Oce of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE- AC03-76SF00098. 17 References [1] C.D. Carone and H. Murayama, LBL-36338, Nov. 1994. [2] Shortly after Ref. [1], qualitatively similar conclusions were presented in S. Davidson and D. Bailey, UTPT-94-33. [3] For a comprehensive review, see H.E. Hab er, SCIPP-93-21, hep-ph/930823 5, and ref- erences therein. For constraints from LEP, see G.R. Farrar, Phys. Lett. B265, 395 (1991); R. Munoz-T ~ apia and W.J. Stirling, Phys. Rev. D49, 3763 (1994). [4] For very small m (in the MeV range), this approach can b e found in A.E. Nelson B and N. Tetradis, Phys. Lett. B221, 80 (1989). [5] Review of Particle Prop erties, Phys. Rev. D50, 1173 (1994). [6] See for a review on neutrino physics, M. Fukugita and T. 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Eichten, I. Hinchli e, K. Lane, C. Quigg, Rev. Mo d. Phys. 56, 579 (1984). [22] CDF Collab oration, F. Ab e et al., Phys. Rev. D49 R1 (1994). 19 Figure Captions Fig. 1. Running of c and c , assuming c () = c () = 0 at = 250 GeV. Z Z Fig. 2. Constraints on c (m ) from the two standard deviations of the exp erimental Z Z uncertainties in the Z mass, hadronic width, and Z ! b b forward-backward asymmetry. Fig. 3. Constraints on c (m ) from the two standard deviations of the exp erimental B p uncertaintyin R measured at various s as compiled by the Particle Data Group. The running of c corresp onding to = 200 GeV is shown for comparison. Fig. 4. Drell-Yan dilepton di erential cross section as a function of the lepton pair invariant mass, integrated over the rapidityinterval jy j < 1, for one lepton sp ecies. The dashed curves include the e ect of exchange, assuming c (m )=c (m )=0:01, for B B Z B m = 30, 40, and 50 GeV, resp ectively. B 20