While leptogenesis is a very solid but hard to check contender for the
generation of the observed excess of baryons over anti-baryons in the Universe,
we show that the observation of gauge bosons associated with right-handed
currents at present or future colliders would suffice to disprove its most
canonical mechanism.Comment: Rencontres de la vall\'ee d'Aost

Frère, J-M.

English

arXiv

While leptogenesis is a very solid but hard to check contender for the generation of the observed excess of baryons over anti-baryons in the Universe, we show that the observation of gauge bosons associated with right-handed currents at present or future colliders would suffice to disprove its most canonical mechanism. © Società Italiana di Fisica.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Frère, Jean-Marie

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Can colliders disprove leptogenesis?

While leptogenesis is a very solid but hard to check contender for the generation of the observed excess of baryons over anti-baryons in the Universe, we show that the observation of gauge bosons associated with right-handed currents at present or future colliders would suffice to disprove its most canonical mechanism. © Società Italiana di Fisica / INFN - Laboratori Nazionali di Frascati.SCOPUS: cp.pinfo:eu-repo/semantics/published23rd Rencontres de Physique de la Vallee d'Aoste: Results and Perspectives in Particle Physics - 23rd Physics Conferences in the Aosta Valley 2009. (December 01, 2010). Les Rencontres de Physique de la Vallee d'Aoste: Results and Perspectives in Particle Physics. Frascati Physics Series, 50

While leptogenesis is a very solid but hard to check contender for the generation of the observed excess of baryons over anti-baryons in the Universe, we show that the observation of gauge bosons associated with right-handed currents at present or future colliders would suffice to disprove its most canonical mechanism

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DOI 10.1393/ncc/i2010-10526-0Colloquia: LaThuile09IL NUOVO CIMENTO Vol. 32 C, N. 5-6 Settembre-Dicembre 2009Can colliders disprove leptogenesis?J-M. Fre`rePhysique The´orique, Universite´ Libre de Bruxelles - Bruxelles, Belgium(ricevuto il 10 Novembre 2009; pubblicato online il 15 Gennaio 2010)Summary. — While leptogenesis is a very solid but hard to check contender forthe generation of the observed excess of baryons over anti-baryons in the Universe,we show that the observation of gauge bosons associated with right-handed currentsat present or future colliders would suffice to disprove its most canonical mechanism.PACS 12.60.Cn – Extensions of electroweak gauge sector.PACS 11.30.Fs – Global symmetries (e.g., baryon number, lepton number).PACS 98.80.-k – Cosmology.1. – IntroductionThis short article will outline a suggestion, not really for testing leptogenesis in generalterms, but rather to disprove it, should some gauge bosons coupled to the right-handedfermions (we will call them generically “Right-Handed W’s” or WR) be discovered atcurrent or future colliders.We begin by a quick recapitulation of the leptogenesis scheme, insisting on its attrac-tiveness, its robustness, but also on the difficulty to submit it to experimental verification.We will later insist on the fact that extended gauge symmetries are the natural frame-work for leptogenesis, and show that the discovery of right-handed W’s would invalidatethe “canonical” leptogenesis mechanism.Full details of this latter analysis can be found in our common work with ThomasHambye and Gilles Vertongen [1], where a more complete bibliography is also provided.2. – Why leptogenesis?The current excess of baryons (in fact we do not know about matter in general, sincewe cannot count the cosmic background neutrinos) over anti-baryons is one of the bigobservational evidences calling for explanation. A first suggestion came from Grand-Unified theories, more specifically SU(5), but quickly met with an objection related tothe late evolution of the Universe. Anomalies and the resultant non-conservation of Band L, when operative at the electroweak transition could indeed destroy a previouslyc© Societa` Italiana di Fisica / INFN - Laboratori Nazionali di Frascati 329330 J-M. FRE`REgenerated baryon asymmetry on the simple condition that it be consistent with B−L = 0,which is precisely the case in SU(5).The obvious answers are to use this late occasion either as a new source of B generation(electroweak baryogenesis), or as a way to mutate a previously generated asymmetry intothe observed B number: in this latter case, it is necessary that the previous asymmetrysatisfy B − L = 0.As is now well known, the first possibility, despite its elegance, fails in the StandardModel alone, for lack both of sufficient CP violation, and of the out-of-equilibrium com-ponent which requires a first-order phase transition. This can be fixed in more extendedmodels (additional singlets, supersymmetry), but the scheme keeps requiring new CPviolation, and depends very heavily on the poorly controlled dynamics of the B and Lviolation at the phase transition.The choice solution therefore has become leptogenesis [2]. In its canonical form, it isclosely associated to the see-saw mechanism, where heavy right-handed neutrinos coupledby Yukawas to the left-handed ones, are used to generate the very small observed masses.The large Majorana mass of the neutrinos provides the necessary L violation, the smallYukawa couplings provide the out-of-equilibrium decays, in such a way that a very robustL asymmetry is generated at high temperature. At the electroweak phase transition, afraction of this L is converted into a baryonic asymmetry. One of the big advantagesis that this conversion process operates by reaching some equilibrium between B and Lcomponents, and is fairly independent of the precise dynamics of the B violation at the(slow) electroweak phase transition.The difficulty to prove leptogenesis resides precisely in its sturdiness, and its quitegeneric character. Even if the main elements appearing in the calculation of the leptonic(and later baryonic) asymmetry are the same as those governing the (accessible) lightneutrino masses, they intervene in completely different combinations, so that low-energydata are not constraining for the process.In this paper, we will show that, even if leptogenesis is difficult to establish, andfairly resilient as a mechanism, it could still be excluded if WR particles are observed atcolliders.3. – Orders of magnitudeLet us take as a starting point the mass terms for the heavy right-handed neutrinosN , and their Yukawa couplings to the light ones, namely(1) Lmass = −L H˜ λ†ν N −12N mN Nc + h.c.,where λ is a matrix in generation space, H is the Brout-Englert-Higgs doublet (possiblypart of a larger grand-unified multiplet), L are the light left-handed fermions.Since we are just interested here in orders of magnitude, we will use in this paragraphλ as a single number, assuming (wrongly) that all Yukawa couplings are of similar size.We want now to express the conditions (the values of λ) that provide the correct orderof magnitude for light neutrino masses, for the out-of-equilibrium decay of the heavy N ,and for sufficient CP violation.CP violation is provided by the interference of tree-level and one loop diagrams, allcontrolled by λ. Unless there is a special enhancement, we may thus expect the amountof CP violation to be of order λ4, while the direct decays are of order λ2. The proportionCAN COLLIDERS DISPROVE LEPTOGENESIS? 331Fig. 1. – N decay and CP violation.of CP violating decay for each heavy N is thus expected to be of order λ2 (see fig. 1).Since other effects tend to dilute the baryogenesis effect, this amount of CP asymmetrymust exceed the wanted early universe asymmetry, namely  > 10−8.The out-of-equilibrium condition states that the decay rate must be slower than theUniverse expansion at the time of decoupling (that is, roughly at temperature T ≈ mN ).Here g∗ is the effective number of degrees of freedom at that timeΓ  λ2m,(2)Γ  H,H =√g∗T 2/(1019 GeV).We group in table I the various constraints on λ and mN , adding the request to getreasonable light neutrino masses (say, of order 0.01 eV), through the see-saw formulamν = λ2v2/M , where v ≈ 100GeV is the electroweak symmetry breaking.As seen clearly from this table, the leptogenesis mechanism is fairly resilient over awide range of λ, mN , but tuning becomes needed for low values of these parameters. Suchtuning can take place either through adjusting the individual elements of the Yukawacoupling matrix λ, or a considerable enhancement can be found by making the self-energydiagram nearly resonant. This is obviously another kind of tuning, which requests theheavy neutrinos N1, N2, . . . to be nearly degenerate. If the mass splitting is of orderλ2, the CP violation asymmetry can then be considerable. Arguably, very low-energyleptogenesis could then take place [3].Table I. – Bounds on mN (in GeV) for various λ, assuming a light neutrino mass of order0.01 eV.λ Light neutrino mass Out-of-equilibrium decay Enough CP violationmN ∼ (GeV) mN > (GeV)10−5 107 108 needs tuning10−4 109 1010 bordeline10−3 1011 1012 yes10−2 1013 1014 yes10−1 1015 1016 yes1 1017 1018 yes332 J-M. FRE`RE4. – Improving or falsifying leptogenesisAs announced, the main point of this note is to stress that, even if it is extremelydifficult to establish leptogenesis, it could at least be falsified. In particular, we contendthat the observation at present or future colliders (that is in practice in the TeV range)of WR’s would make the canonical form of leptogenesis (the case outlined above, withthe lepton number carried by neutrinos) untenable.The possible observation of a WR will of course be justification enough for its consid-eration! Still, a few words of motivation for such a particle may be useful, and may helpput back in context the whole leptogenesis approach.In my view indeed, introducing singlet fermions like the N ’s of ad hoc mass (quiteseparate from the electroweak and grand-unification scales) and Yukawa couplings, if doneoutside a broader context, is mainly a reparametrization of an effective Lagrangian, andinvolves no less fine tuning than putting by hand the small parameters this constructionreplaces. The situation is entirely different if such new particles are related to a wider(for instance, gauge) structure, in which case a much more compelling picture emerges.Without being specific about the wider gauge structure (one may think of SO(10),E6, or broader schemes), some generators and their associated gauge bosons will typicallyinvolve lR−νR (or in the present notation lR−N) transitions. They will also presumablycouple to the right-handed quark structure. For this reason, we consider specifically thecase of WR. Other effects may be associated with the other members of the extendedstructure, notably extra Z’s, or scalars, but we expect (at least in the case of canonicalleptogenesis considered here) that they will usually play in the same direction.Including the WR sector was of course already considered, notably in [4] and [5]. Inboth cases, the study was involved with very heavy extra gauge bosons, and the waythey would affect leptogenesis and low-energy implications. The most obvious result, asshown in [4] is that the presence of WR will introduce new, CP -conserving decay channels,potentially large, and lead to an extra dilution of the generated lepton asymmetry, upto the point that the case MWR < mN is virtually excluded. This is however by far notthe only effect. Further reduction of leptogenesis is associated to diffusion processes, butquite interestingly, the opposite effect may also arise.As shown indeed in [5], the presence of WR may play a determinant role when the Npopulation has been destroyed through inflation and needs to be rebuilt. If, as sometimesassumed, the N do not couple directly to the reheating process, small Yukawa couplings(associated to particularly light neutrinos) would in fact preclude the rebuilding of asufficient population. In that case, the presence of right-handed gauge interactions savesthe day, and destroys the possible lower limits on neutrino masses which could be induced.5. – The main effectsWe start thus by including the new interaction term(3) LWR =g√2WμR(u¯RγμdR + N¯γμ lR).The most evident effect is on the decay channels. Since these are CP -conserving, theyintroduce a dilution of the asymmetry (0) generated in the standard case:(4)  =Γ(l)N − Γ(l)NΓ(l)tot + Γ(WR)tot≡ (0) Γ(l)totΓ(l)tot + Γ(WR)tot.CAN COLLIDERS DISPROVE LEPTOGENESIS? 333Fig. 2. – Main results: the panel on the left gives for MWR = 3TeV the efficiencies reachedas a function of mN and m˜1 = v2λ†νλν11/mN (zf refers to the scale at which the decouplingof the sphaleron conversion mechanism is assumed). The panel on the right gives the lowerlimit acceptable for the WR mass (in GeV) assuming a maximal leptonic asymmetry due to CPviolation ( = 1).We denote the abundances Yi ≡ ni/s, YB ≡ YB − YB¯ , YL ≡ YL − YL¯, where ni thecomoving number density of the species “i”, “eq” refering to the equilibrium numberdensity, and s the comoving entropy density. In a now standard notation,(5) YB = YL rL→B = εN η YeqN (T  mN ) rL→B,where rL→B is the conversion rate of lepton to baryon number at the electroweak phasetransition, and η is referred to as the efficiency, and involves all the effects of evolutionof the lepton number under the Boltzmann equations.To facilitate the discussion, we will now slightly depart from the usual conventions,and will include the above-mentioned dilution effect (that is, the factor Γ(l)totΓ(l)tot+Γ(WR)totap-pearting in eq. (4)) in the expression of the efficiency η. Using this convention, → 0.We now set to examine if the dilutions effects due to a light WR are sufficient to makecanonical leptogenesis impossible. For this purpose, we can, in the above convention,replace  by the largest possible value. While both degenerate and non-degenerate casesare considered in [1], we will consider here the least favorable situation (for our purposeof disproving the mechanism), namely  = 1 (thus allowing for resonance enhancement).A very important effect arises from the scatterings. Indeed, the WR have the im-portant property of interacting with gauge strength with the right-handed quarks in thethermal plasma. This keeps them in thermal equilibrium, but also enhances the effect ofthe scatterings, since the “relic” N particles interact through WR with normally abun-dant quarks and light leptons (at the difference of the case where the relic particles mustannihilate mutually).The results are most easily read from fig. 2, where we give (in the rightmost panel),the lower bound on MWR compatible with leptogenesis. The values, given in GeV areclearly out of reach of the currently operating or planned colliders (we find a lower bound334 J-M. FRE`REof 18TeV in the present case). As an example, we also list (in the leftmost panel) theactual efficiencies (which would also be the lepton number generated, in case  = 1) forMWR = 3TeV, a value reachable at the LHC (remember that a leptonic excess of at least10−8 must be generated to accommodate the currently observed matter asymmetry).The above considerations put some new urgency to the quest at colliders for WRbosons, or possibly even light N . In particular, the search [6] should be extended toinclude the situation where the N is heavier than the WR, a case where the exclusion ofleptogenesis is even more severe.∗ ∗ ∗This work was performed in collaboration with Thomas Hambye and Gilles Ver-tongen, with support from IISN and Belgian Science Policy (PAI VI/11)REFERENCES[1] Frere J. M., Hambye T. and Vertongen G., JHEP, 0901 (2009) 051.[2] Fukugita M. and Yanagida T., Phys. Lett. B, 174 (1986) 45; for recent reviews see, e.g.,Strumia A., Davidson S., Nardi E. and Nir Y., arXiv:0802.2962 [hep-ph].[3] Covi L., Roulet E. and Vissani F., Phys. Lett. B, 384 (1996) 169, Pilaftsis A., Phys.Rev. D, 56 (1997) 5431, Flanz M., Paschos E. A. and Sarkar U., Phys. Lett. B, 345(1995) 248; 382 (1996) 447 (Erratum).[4] Carlier S., Frere J. M. and Ling F. S., Phys. Rev. D, 60 (1999) 096003 [arXiv:hep-ph/9903300]; Ma E., Sarkar S. and Sarkar U., Phys. Lett. B, 458 (1999) 73.[5] Cosme N., JHEP, 0408 (2004) 027 [arXiv:hep-ph/0403209].[6] Bayatian G. L. et al. (CMS Collaboration), CMS physics: Technical design report,CERN/LHCC 2006-021; Buescher V., Carena M. S., Dobrescu B. A., Mrenna S.,Rainwater D. and Schmitt M., arXiv:hep-ph/0608322.

Can colliders disprove leptogenesis?

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