Lepton Number Conservation, Long-lived Quarks and Superweak Bileptonic Decays
aa r X i v : . [ h e p - ph ] A p r April 2015
Lepton Number Conservation, Long-lived Quarks andSuperweak Bileptonic Decays
Paul Howard Frampton ∗ Oxford, UK.
Abstract
In the upcoming LHC Run 2, at √ s ∼
13 TeV, it is suggested to seek unusuallycharged ( Q = − / /
3) quarks with mass M Q ∼ L = +2 and − Y with mass M Y ∼ . pp which contains twoseparated jets together with two pairs of correlated like-sign charged leptons. Such aprocess was inaccessible energetically in LHC Run 1 with √ s ∼ ∗ e-mail address: [email protected] Introduction
In addition to the theoretical predictions for the LHC of supersymmetry and dark matter,the discovery of either of which would be revolutionary, it is worth being more conser-vative and to consider instead the ancient art of model-building in gauge theories whichextend the standard model and are motivated and testable. In particular, we here suggestthat LHC experimentalists seek unusually-charged quarks ( Q = − / , +5 /
3) which areproduced strongly and decay slowly by weaker than weak interactions, are constrained tolie below 4 TeV, and motivated by an explanation of three families.The 331 model [1, 2] has provoked sufficient interest that there exist a number of studiesof its phenomenological ramifications. One aspect which has, however, escaped muchattention is the issue of lepton number ( L ) conservation and the role it plays in suppressingthe decay rate for the heavy quarks. Although there are reviews of 331 bilepton physics[3, 4], the slow decays of the 331 heavy quarks have not been previously emphasized. Theupgraded LHC seems tailor-made for discovery of these heavy quarks and its Run 2 couldexpose them.The familiar quarks ( u, d, c, s, t, b ) have baryon number B = 1 / L = 0. The familiarleptons ( e − , µ − , τ − , ν e , ν µ , ν τ ) have B = 0 and L = 1. The exotically-charged quarks ofthe 331 model carry nonzero L as follows: D and S have B = 1 / L = 2; T has B = 1 / L = − µ − → e − + ¯ ν e + ν µ (1)with a long lifetime τ µ ∼ × − s according [5, 6] to the tree-level formula τ µ = g M µ πM W (2)where g is the electroweak SU (2) gauge coupling with g = 8 M W G F . Other than themuon, the only long-lived charged particles in the standard model are the stable electronand proton. But there may be about to appear an entirely new breed of metastable chargedelementary particles to enter this small group.It is well-known and investigated that if there exists a fourth family of quarks, then theycan mix only very little with the first three families because the 3 × L con-servation. The consequent superweak interaction is mediated by Y bilepton intermediatevector bosons in the 331-model and a possible particle discovery at LHC is of a sibling tothe W ± . For instance Y − mediates the abnormal muon decay µ − → e − + ν e + ¯ ν µ (3)which is suppressed relative to the normal decay, Eqs. (1,2) by a factor f = ( M W /M Y ) . (4)and, given M W ≃
80 GeV, the question is whether the value of M Y can be arbitrarilylarge. In the present context the answer is no.In the 331-model there is an important theoretical upper limit M Y ≤ T eV for the sym-metry breaking to the standard model, arising from the renormalization group behaviorof the electroweak mixing angle and the group embedding. The value sin θ ( M Z ) = 0 . θ ( E ) = 0 . SU (2) L ⊂ SU (3) L , at E = 4 TeV. This was first analysed in [1] and has beenmuch more recently confirmed in [11]. This intrinsic 331 upper limit is what underlies theclaim that the new physics is at a mass scale especially befitting LHC’s Run 2.Theoretically then M Y < ∼ M Y ≥ . M Y = 2 . ≃ √ M W ) as an illustration whereupon the suppression factor f inEq. (4) is f ≃ − . The experimental upper limit for process Eq.(3) is [12] disappointing,the branching ratio being restricted merely to ≤ . ∼ − .By superweak interaction we therefore mean the weak interaction further suppressed forbilepton mediation by the factor f in Eq.(4) relative to the W exchange. Superweaknessimplies that the exotic quarks ( D, S, T ) are long-lived.2
Long-Lived Quarks
In the 331-model which requires exactly three families there are three additional exoticquarks(
D, S, T ), one in each family. The gauge group is SU (3) C × SU (3) L × U (1) and forthe first family the quarks are in the triplet and three singlets of SU (3) L u α d α D α L ¯ D L.α , ¯ d L.α , ¯ u L,α , (5)and similarly for the second family c α s α S α L ¯ S L.α , ¯ s L.α , ¯ c L,α . (6)The quarks of the third family are assigned differently, in one antitriplet and three singlets T α t α b α L ¯ b L.α , ¯ t L.α , ¯ T L,α . (7)The established weak gauge bosons ( W − , W , W − ) with W ≡ Zcosθ + γ sin θ are aug-mented by five more, a Z ′ and four bileptons ( Y + , Y ++ ) ( L = −
2) and ( Y − , Y −− )( L = +2).The superweak decays of D are (we exhibit only the muonic decays, the most readilydetected) D → u + Y −− → u + µ − + µ − (8)has a displaced vertex in the silicon detector. There is the alternative equally long-liveddecay D → d + Y − → d + µ − + ν µ , (9)but the neutrino ν µ makes process Eq. (9) far more challenging to detect than Eq.(8).The sequential second family exotic quark S has similar long-lived decays S → c + Y −− → c + µ − + µ − S → s + Y − → s + µ − + ν µ (10)In the 331 model the third family, on the other hand, the T has Q = +4 / L = − T → b + Y ++ → b + µ + + µ + T → t + Y + → t + µ + + ¯ ν µ (11)3he antiquarks ( ¯ D, ¯ S, ¯ T ) have superweak decays into the corresponding charge conjugatefinal states ¯ D → ¯ u + Y ++ → ¯ u + µ + + µ + ¯ D → ¯ d + Y + → ¯ d + µ + + ν µ ¯ S → ¯ c + Y ++ → ¯ c + µ + + µ + ¯ S → ¯ s + Y + → ¯ s + µ + + ν µ ¯ T → ¯ b + Y −− → ¯ b + µ − + µ − ¯ T → ¯ t + Y − → ¯ t + µ − + ¯ ν µ (12)We take M Y = 2 . M T > M S > M D with M D ∼ DD pair production by stronginteractions so the most interesting event would be pp → ¯ DD + any.By strong interactions, two gluons can produce the ¯ DD pair, practicable only at Run 2 ofthe LHC with 13 TeV. The ¯ D, D quarks being long-lived will travel a macroscopic distancefrom the production vertex.The ¯
D, D quarks decay to bileptons and the most striking signature would surely be anevent with ¯ D → ¯ u + Y ++ → ¯ u + µ + + µ + (13)and the counterpart D → u + Y −− → u + µ − + µ − (14)In Eqs.(13,14), the light quarks ¯ u, u will hadronize to high-energy jets which the LHCphysicists are well equipped to reconstruct. The two jets will originate from the separatedisplaced decay vertices for ¯ D and D . The like-sign pairs of muons will centre around aninvariant bilepton mass M Y ∼ . µ − ν µ , e − e − , e − ν e , τ − τ − , etc. 4 Discussion
The two most heralded targets for the LHC, beyond the Higgs boson, were to confirmweak-scale supersymmetry and to produce dark matter. If weak-scale supersymmetryexisted, it was expected to appear in the 2009-2013 Run 1 at ∼ ∼ − GeVto black holes with mass ∼ GeV so it would now require remarkably good fortune forit to show up at the LHC. The possibility of extra spatial dimensions large enough to bedetected at the LHC is not strongly motivated.There are not many theoretical models with a strong reason to expect the relevant newphysics scale to be specifically in the LHC Run 2 (13 TeV) regime, as opposed to theRun 1 (8 TeV) one. Among these, the 331 model does naturally contain an multi-TeVscale [1, 11] in its analysis. Its long-lived charged quarks are predicted in the appropriatemass range hence more likely to be produced in Run 2 than Run 1. The signature of suchan event is striking and although this would not immediately explain all the parametersof the standard model it will give a second stronger explanation of why there exist threefamilies beyond the ingenious observation in [8] that it accommodates the observed CPviolation in flavor-changing weak interactions.If such a discovery is made, what is the next step in the theory? It would suggest evenfurther cousins of the W and Y gauge bosons which could appear in additional SU (3)factors. Nonabelian subsumption of the U (1) Y gauge group factor is hinted at by avoidanceof the Landau pole. At present this remains idle speculation until an electroweak SU (3)has empirical evidence which would, nevertheless, firmly justify the construction of higherenergy apparatus to answer further questions.5 eferences [1] P.H. Frampton, Phys. Rev. Lett. D46,
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