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JHEP04(2015)153 ¯ n − , and n ψ Springer = 1. Such April 8, 2015 -decays into B April 27, 2015 : φ March 30, 2015 : : February 17, 2015 : Accepted Revised Published 10.1007/JHEP04(2015)153 Received doi: can be a good candidate for ψ oscillations, without needing of ¯ n − ψ Published for SISSA by , ψ − n -decays into three (antiquarks). This model ψ . The vector-like pair is defined ‘exotic’ because of a ψ . 3 1501.04660 The Authors. , giving mass to 100 GeV. In this case, the sterile could be (meta)-stable and φ c Phenomenology, Strings and branes phenomenology

− We propose a minimal extension of , generating a Majorana , [email protected] 67010 Assergi AQ, E-mail: Dipartimento di Fisica, Universit`adi L’Aquila, 67010 Coppito AQ, Italy LNGS, Laboratori Nazionali del Gran Sasso, Open Access Article funded by SCOAP ArXiv ePrint: oscillation can be indirectly generatedan by effective two Majorana mass forWIMP-like . dark . Majorana fermion Keywords: and Euclidean D-branes. Asix Post-Sphaleron Baryogenesis quarks is (antiquarks), realized or through suggests through some intriguing B-violatingAntineutron signatures, physics and testable LHC. in Webe also the discuss light next limits as from future, 1 FCNC. in Sterile fermion Neutron- can also sider an ‘exotic vector-like pair’a of scalar color-triplet scalars, field anpeculiar extra mass Majorana term fermion of thea color-triplet mass scalars, term violating could Baryontions be number of generated as the by ∆ Standard exotic Model: instantons open in (un-)oriented a strings class attached of between string-inspired D-brane comple- stacks Abstract: mass for neutron, connected with a mechanism of Post-Sphaleron Baryogenesis. We con- Andrea Addazi ‘Exotic vector-like pair’ of color-triplet scalars JHEP04(2015)153 ]. is 1 10 [ ¯ n − h.c n yr for the + 35 ]. This cor- . This limit ÷ 5 5 34 M δm nn 10 / eV [ 2 ) ∼ 24 ]. For these reasons, − 6 udd 10 decay × − p 9 7 τ . 7 4 ]. The current limit on 4 δm < – 2 7 ]). 2 43 = 2 [ ]). In this paper, we would like to suggest a ]. (For a recent review about phenomenology B 27 7 – 1 – 6 300 TeV on the effective operator ( > yr for neutrinoless double beta decays [ s with 90% C.L., implying 25 M 8 10 10 > × 6 1 νββ 86 12 . 0 s, testing 1000 TeV scale [ for neutron- can be compared with τ 0 10 ] for a short discussion about Neutron-Antineutron physics as a test of a new fifth force yr also considering possibility in the next future to enhance best limit of a factor 3 10 42 1 ], > > /δm > ¯ 26 n ¯ n n – n τ τ 20 = 1 See also [ 4.2 Majorana fermion decays in three quarks (antiquarks) tons 2.1 FCNC bounds and the space of the parameters 4.1 Scalar-decays into six quarks (antiquarks) 1 ¯ n n nesis. Depending on theantineutron particular physics region with LHC, of predicting the a parameters, newThis peculiar this model phenomenology model in does connects collider not physics. neutron- produce decay, and FCNCinteraction can (a be more sufficiently complete suppressed. version is in preparation [ neutron-antineutron is becoming more anding [ more an interesting challenge100: for model build- of and Leptonsimple violations, minimal see model also connecting the [ “Majorana’s question” with a mechanism of Baryoge- transition, violating baryonτ number by ∆ responds to a constraint is particularly loose with respectbers: to other rare processesProton violating decays, Baryon or num- Has the neutron a Majoranahimself mass or proposed not? in This ‘37’, isWe that not do just neutron an not could academic know have question.day a if Majorana we Majorana Majorana get mass understood that term immediatelybers’ existence violations. the of depth In a particular, of “Majorana’s a his fermion” Majorana proposal; is mass for but related neutron to to- implies baryon a or neutron-antineutron lepton num- 1 Introduction 5 Beyond the toy-model: string-inspired standard model and exotic instan- 6 Conclusions 3 LHC physics 4 Post-sphaleron baryogenesis Contents 1 Introduction 2 A model for a neutron Majorana mass JHEP04(2015)153 3 and / ]. Then, ], M.Gell- 8 12 1000 TeV, has hyper- oscillations, physics, but − ) = 2 Y ¯ n ¯ n Y ( 3, − 3. We call this − / B / (an their antipar- ψ 1; 0), with a mass 2 n ]. In this case Baryon i , 3, − Y / = 2 Majorana Mass 43 (1 = 2 , , and i ψ 41 X B ) = = 1, i.e one color-triplet B – ψ ]: (NMS-)SM is obtained X 39 ) = 1 B ( − 56 – X Y n ( 53 B , 29 , ], have been proposed later. 28 , for example, could be a spectacular = 1 oscillations, without needing of a 18 , T ], R.Mohapatra and G.Senjanovic [ | / 15 B 11 , ]. jjE broken by exotic instantons, producing only ∆ 14 | has hypercharge 29 → 3, and the other has , is a metastable fermion of mass 1 – 2 – / X 28 ψ pp . c = 1 s. In this case a Neutron-Antineutron transition can 8 B ], by Yanigida [ dynamically ] and type III [ 10 can be a good candidate of WIMP Dark Matter. 10 17 , = 1 exotic mass term! In a broad sense, we have a see- – 9 ' ψ 13 B 2 / ¯ n − - is n R τ 3. Baryon and Lepton numbers are ], / ' ¯ n 29 , color indices of SU(3) . This is a gauge singlet with zero Baryon number, zero , − ψ 28 τ ) = 0. We also consider a Majorana sterile h.c This model is inspired by proposals in [ i, j ) = +2 Y ' 3 + ( Y , ( 2 L ψ − Y n µψψ τ ) = The paper is organized as follows: in section 2, we describe the model for a Majo- This model can connect Neutron-Antineutron oscillations to Dark Matter problem An exotic vector-like pairs could be not only indirectly searched in The main model’s feature: we introduce an ‘exotic’ mixing mass term for a vector- The see-saw mechanism type I for the wasProbably, originally the most proposed similar by mechanism Minkowski of [ the one proposed here is in [ 2 3 X ( Mann, P.Ramond and R.Slanskyother mechanisms [ called type II [ number is violated by a baryonic ‘RH neutron’, with a B-violating Majorana mass term. We introduce a vector-like pairticles) of with (complex) color-tripletcharge scalars L term zero hypercharge. conclusions. 2 A model for a neutron Majorana mass Majorana mass for Neutron. rana neutron also discussLHC suppression physics; of in FCNCs; section insible 4, section string-inspired connections 3, scenario with we for discuss Baryogenesis; the implications in effective for model section proposed, 5, in we section discuss 6, a we pos- present our rather than to Baryogenesis.an exchange Infact, of if a virtualwith exotic vector-like pair canbe generate generated as a combination of these two particular B-violating operators, such asautomatically a suppressed mass in term this for model a vector-like [ pair Proton decay is also at LHC, withsignature peculiar of exotic processes: vector-like pairs and dark matter. saw mechanism for neutron, involvingfermions. a non-diagonal mass matrixas for a scalars low rather energy than Euclidean limit of D-branes. open (un)-oriented Euclideannew strings, D-branes non-perturbative attached are between mass D-brane exotic terms,particular, stacks stringy violating in and [ vector-like instantons, U(1)s, that rather can than induce axial-ones. In like pair of colorscalar scalar has triplets, a violating different baryon baryonone number number with as unit. respect ∆ to the Onean other scalar ‘exotic triplet antiscalar triplet vector-like by has could exactly pair’. be connected We propose to a that ∆ existence of a ∆ JHEP04(2015)153 (2.3) (2.1) (2.2) and their Baryon and . The central propagator Y h.c Y , 1 + L 0 0 0 0 0 0 X ] − +2 jk [ h.c Y h.c + i + X ijk 3 3 3 3 3  Y / / / / / ijk † 0 0 k R  1 1 2 0 d Y − − 2 Y j R M u m i , their hypercharges 2 1 Y Y + 2 = y X 3 +1 3 +2 3 +1 3 3 – 3 – † U(1) / / / / / + 0 0 h.c 2 4 1 YB X × i R − +2 +1 − +2 − +2 + 2 X i ψd m i Y i X = SU(2) 1 X y 2 0 × 3) 3) 3) = 3) mass M 3) / / / / / 4 L Y 1) 2 = − L − − 1; 1; +2 , 1; 2) . 2; +1 2; 1; , 1; +2 , 1; 0) , , ψ , , Y , X −Y ¯ 3 , ¯ 3 ( ( ¯ 3 (1 (3 L (1 (3 ( (1 R R R L . We also report Standard quarks and for a comparison. L Fields X Y ψ q u d l e and B,L X has a peculiar mixing mass term . Note that all interactions terms are B-preserving, exception for mixing term . Diagram inducing a Neutron-Antineutron transition. The white blobs indicate the 1 . New matter fields introduced with respect to SM. We report their representation with X − Y These fields, compatible with gauge invariances, can interact with fields as Figure 1 mixing mass term between theis vector-like the pair Majorana of color fermion scalar triplets With these interactions, onein can figure construct a Neutron-Antineutron transitions as shown and mass terms for respect to SM gaugeLepton group numbers SU(3) Table 1 JHEP04(2015)153 ], ψ 2 28 has − GeV (2.4) (2.5) 5 n 3 M 10 is higher / 2 − ψ ) , leading to a 1 α l α ' udd , compatible with q = 6 operators, for N µ Y Z D = 1; this is simple to is mass of fermion ), and we can write 2 L µ is a natural candidate Y ), without other dangerous , but the smallest mass i ψ  2 0 TeV, generating a lot of 2 2.3 + ) is a (meta)stable particle, M 10 2 Y 1 )–( ÷ Y ψ m 6 ( , where 2.2        2 2 can be seen as a combination , s: − 1 10 1 √ 0 2 )–( 8 y 1 2 X 2 Y ' 0 0 = 10 2.1 m m µ −M Y ' ]. + ( 2 0 ¯ 2 Y n as a real parameter. We can decompose 28 4 0 0 0 with leptonic sector are suppressed, in order to 300 TeV. So, one can consider different ψ = 1. Effective operator ( 0 m M τ . In particular diagrams (b) in figure M > , ψ 2 0 B ) and M 4 ' 2 2 ]. Alternatively, in a string-inspired model like [ Y X 2 , 0 0 X q i M m X nψ 52 – 4 – , −M are not , they not have Lepton numbers, in τ )). 10 TeV and ± + 2 0 51 Y 2 X ]. 2 Y 1 − , 0 0 2.4 , we have to consider not X m M m 1 X 38 ( with – ) as 2 M + implies        2 ' 1 ¯ n . This can be also compatible with Majorana masses for neutrini √ 35 in order to satisfy experimental limits. A trivial choice Y 2 0 2 X . We assume ¯ n = , TeV. In this last case, the fermion Z − 1 µ = 2 Y m − M , 2 eff Y ÷ ψ  , times coupling constants 3 , X n 5 X , shown in figure 2 1 2 is automatically avoided! [ M is not a Right-handed neutrino, it has a Lepton number equal to zero. / and 10 1 . Note that Gauss [ Y 2 X ) , can be avoided through opportune discrete symmetry ψ , and = 0 4 Λ × 2 µ 1 7 − Λ 4 0 XY 2 ± ψ X 0 M λ 10 ' qqql/ M − M 0 414 s, from Ultra Cold Neutron experiments, in condition of suppressed qqql/ < n 4 = 300 TeV, automatically saturating the bound. On the other hand, we = ( ≥ M µ |B| τ , violating baryon number as ∆ ] = M jk 0 [ Y M i X ijk In this model, we are not generating a proton decay process, if the mass of More precisely, in estimation of = 1 operators like = 2. We also note that  We assume that other possible interactions of 2 0 4 L B . Experimental bound on our case. Werealize are just assuming with that a∆ our discrete model symmetry is notFor a violating complete lepton classification numberstring of as constraints gauge ∆ on discrete Discrete symmetries,R-parity symmetries, protecting is dynamically see the broken [ proton byoperators. Exotic by Instantons, For generating instance, ( a direct exchange of one avoid other dangerous effectiveproton operators. decay operator For example,∆ possible extra operators like than proton mass. 2.1 FCNC boundsFCNC and in the space physics of are the generated parameters in our model. The strongest effects can come from The eigenvalues are (two-two degeneracies, as manifest in ( magnetic fields eigenvalue of mass matrix of the color complex scalarsmass as matrix, in basis ( interesting physics for LHC, ascorresponding discussed to later. Another branchfor could WIMP be dark matter,of and two Feynman oscillations diagram inand figure not a virtualoscillations one are in propagator, in this case. Note that actual best limits on a mass scale ψ choices of parameters could be can also consider for example M JHEP04(2015)153 , , 0 0 ¯ D ¯ K Kγ , we . So, − 2 X − 6 → 0 − 0 m B B K 10 ' , 0 2 0 10 TeV, it is ∼ ¯ . has to be D ]. 5 M / − 24 28 − 1 θ ) 0 µ 4 0 = D and = 1 , 0 2 X M 0 13 θ ¯ m K M 6 − . This strongly motivates 10 2 0 scale ( transitions leading to − ' K µ ¯ n 8 sγ 2 Y ]. This is mediated by two sterile − 0 − m → 28 M b n . and it can stay also near TeV scale. − l , are suppressed, practically avoiding 2 + . b) Diagrams of neutral-meson oscillations, . b) X in a B Y , φl m 1000 TeV. However, these FCNC are not . In neutral ’ oscillations 12 − , with mixing angles l ≤ − 3 & 2 Y + µ – 5 – m Y Kl m ' → 2 + B λ and 100 GeV! As a consequence, the lightest eigenstate of mass are possible if 2 2 X are strongly suppressed in this case, but enough for neutron- ÷ m ψψ Y . b) diagram for neutral meson-antimeson oscillation [ ’s mass up to ' ’s mass. In particular, assuming → = 1 Y 0 2 − X s µ and ¯ λ etc. any effects are suppressed as B , X − Y 0 0 of X . ): ¯ ¯ B transitions leading to D , Y ψ 0 s 2.5 − − l B , + 0 0 ) can elude FCNC’s constraints of figure and four sl B B 5 . . a) Diagram for meson decays into two mesons [ , . . a) FCNCs tree-level diagrams mediated by ψ 2 → 0 ¯ b D − . c) 0 matrix ( Other FCNC’s contributions,any directly current involving observations asD shown in figure a direct research of exotic color scalar triplets (the lightest eigenstate) at LHC. In next directly constraining obtain, from ( mixings between antineutron transitions: anconsidered. prefactor This of stronglyenough 10 afflicts a estimations light of parameters: for Figure 4 φγ contribute to neutral meson-antimesonetc. oscillations such These as constrain Figure 3 Figure 2 mediated by two JHEP04(2015)153 T , 5 / > jjE ψψ X m → → . From 0 T ˜ q channels. / q ,B 0 jjE , or colliders’ ¯ tjj t D 4 . We can reach → 2 ± 400 GeV; λ and pp , shown in (b)-(c) -(b), around 1 TeV j : in order to satisfy − ]. 3 l 5 GeV. B . µ > + 2 45 m , sl → ' 44 ≤ 2 → µ / could be a (meta)stable par- b B ψ 7 GeV [ -(a). Compatible with FCNCs dis- and 500 GeV µ > 5 µ > m > sγ -decays into three-quarks (antiquarks). , compatible with FCNCs’ bounds. For . Suppose 2 X 0 0 ψ → , with mass eigenvalues m ,B ± b 0 Z D 'M ); essentially the same of squarks ˜ m ψ − – 6 – λ ≤ at LHC; b) Diagram leading to 4 , m µ 200 GeV; X T / m ], but these are not lower than FCNC ones cited above. 10 TeV. A possible diagram of direct production of the jjE 49 − µ > . An interesting signature for LHC is 1 is represented in figure 1 TeV, strongly suppressing decays in figure → ∼  'X 0 X − 2 TeV) [ X −Y M . Z m ], compatible with limits from the other channels discussed above. , with eigenvalue − 50 Z 200 GeV > , can be generated if 2 X 4 may have is unbounded from below. As a consequence, m µ X → -decays into six-quarks (antiquarks), ii) . a) Missing energy channel φ . Possible deviations in these are predicted in our model, with similar limits of su- compose all Dark Matter, from WIMP relic abundance ]. For limits, 4 ψ We also mention limits from top-jet and di-jets channels, in figure Other effects generated in our model are ¯ n 48 If , 5 − 47 Figure 5 4 Post-sphaleron baryogenesis In the proposed mode, one cannesis: envisage two i) simple mechanisms for post-sphaleron baryoge- ticle visible at LHC as transversescenario, missing Neutron-Antineutron energy physics and is Dark directly Matter connected Direct Detection. to the In Dark this Matter(top-jet question. 900 GeV, di-jets 1 cussed above, We call two massthe eigenstates lowest as eigenstate LHC physics, practically this channel, we can[ put limit on1000 GeV ( 3 LHC physics As discussed in section 2, aantineutron direct physics production allow of the e.v.l.p islightest possible: mass eigenstate bounds of from neutron- processes. In the following discussion, we will assume figure persymmetric models [ section, we will discuss theseshown in aspects. figure We also noten that possible decays as JHEP04(2015)153 is a V ∼ (4.1) down ∗ φ . In the V − r . r φ φ top M are the mass V ± ∗ as generated by λ V ] ψ 2 y † 2 y µ [ we will mean 4 0 φ , where T r M ] 0 M 1 , converting y † 1 y W [ 'M T r − λ = . For the moment, the mass of v  V ), suppressing the amplitude as ψ ∗ y -decays, and for + V r 2.4 ] φ λ = 2, and the dynamical scalar decaying is 2 , we can revert all arrows in Feynman diagrams, y √ µ † 2 / ψ ) y i [ – 7 – φ T r + ] 2 r , with 1 µ φ v y 4 0 † 1 + y , considering the mass parameter of [ M v 1 we show decay diagrams, at tree level and one-loop. We = ( 6 , at tree level, as φ M < φ > T r ψ : the first is a tree level contribution, but also one loops contributions, as -decays we will always mean In figure q y φ 6 6 . ' → ). φ φ M . tree 2.5 . Because of Majorana particle q , acquiring a vev scale 6¯ φ up M → − φ is the diagonalizing matrix of masses ( . Decay V , as cited above. under the assumption bottom 12 More precisely we can rewrite 6 − where 10 eigenvalues in ( following discussions, for can evaluate the amplitude 4.1 Scalar-decays into six quarksWe can (antiquarks) reverse diagram ina figure scalar field free parameter, and obtaining We discuss these two in the following. Figure 6 the one shown, have toCKM be correction considered. to One-loop contribution decay in amplitude figure through is an an example exchange of of electroweak a JHEP04(2015)153 (4.6) (4.4) (4.5) (4.2) (4.3) ) with ), times 4.1 200 MeV, 200 MeV). 4.1 ÷ ' ! from MIT bag 8 0 6 13 (with dimension GeV φ M QCD 4 ) has to be smaller M µ loop GeV 4.3

− 5 1 2 − ]  2 b y 10 † 2 m 2 W t y × ]). Φ [ m 3 . ) 31 µm T r q 0 2 P l 2 6¯ ¯ ]  T 1 M ¯ n y ]. 2 → 2 n ' − † 1 / 8 0 ¯ y 1 ∗ 32 O φ [ [ g 13 φ . From this we can get M n > 2 Γ( 4 | T r ¯ 66 loop T . φ − M 2 µ V − − 1 Γ 9 ∗ 1 P l ) ) |O q Φ ' π ¯ n M 6 IV ) td (2 – 8 – ¯ V < T → ( ∗ s ≡ ub ) = φ H V is the square modulus of the amplitude ( q ¯ n ' 6¯ 2 V n Γ( φ ' ∗ ¯ ¯ T O ) final state: γ φ ) V → q ¯ n c n T 5 TeV: we can get bounds on the vector-like pair mixing φ . ( 0 ' S ' 1) Γ  , and (or 6¯ ' ÷ 2 q loop 3 π φ ) + Γ( can be found solving the equation − − q 1 M ¯ 6 T 128 10 ) is a function depending on the mass of the quarks closing the / M 4 → 4 ∼ − a numerical factor coming from a numerical integration in the phase φ 2 1) (the the top and bottom masses, in dominant contribution). However, M λ 18 6 ÷ − ∼ 3 = Γ( is depending also on vector-like pair. A precise evaluation of such a formula − 10 1 ] = φ λ ). We consider a decay temperature indicatively between 100 × Γ 200 GeV and (10 loop loop ew 7 ] (confirmed also by recent lattice calculations [ and Majorana fermion mass, well compatible with the ones coming from neutron- is the number of degrees of freedom at − − ÷ T ' 0 1 1 ( ∗ 30 c g M I' 100 Finally, we can evaluate the primordial baryon asymmetry parameter, directly related Considering the case of a Post-sphaleron baryogenesis: the rate ( At three level, the decay rate of One-loop corrections from the electroweak sector can be evaluated as (assuming all the < H ∼ S ¯ antineutron physics. to the observed baryon asymmetry: So, a post sphaleron scenarioT impose limits on themass masses’ ratios. For example, supposing The decay temperature where eters, the variations onpurposes). this integration are of thethan order of the 1 Hubble %,Γ not rate important at for abetween our electroweak temperature phase transition near and the the QCD electroweak phase phase transition (Λ transition epoch: with space times combinatoric factors (practically independent from the ratios of mass param- the present bounds on neutron-antineutronrunning prefactors physics. connecting In high energy principle, physicsantineutron we of physics. have baryogenesis also with This low to prefactor energy consider neutron- is around 10 a phase space factor for a 6 mass [Φ one-loop in figure there are also other possible contributions,which closing Φ 1-loops involving the vector-likeis pairs, not in necessary for our purposes. It is a good approximation to compare directly ( couplings in where model [ JHEP04(2015)153 ÷ 5 / (4.7) (4.8) φ (4.10) M ' . As a con- ¯ φ T , as requeired ), we can find s. ]. γ M 10 46 4.7 /n ) 10 !# b ¯ is below electroweak n − 2 W 2 φ 8 µ − M 3m b 10 in the propagators. However, n ' ] , ψ 1 + 2 ¯ n = ( Y y , n

2 † 2 τ B )) X  -decay: η ln , in which φ 2 − k 1 P l 4.2 ¯ 2 φ 2 W φ d Tr[y λ r j 1 M ¯ 20%) (4.9) m φ M d y − φ i 9 † 1 ¯ ÷ Γ M u y 2 + 4 , 1 , where V / λ k p 1 ∗ ∗ 1 + 10 d 6 g ), the region of the parameters discussed in  . j V " ÷ 0 ]). 5 d 9 (10% b i = k − 4.5 u 33 2 W ' m [ t – 9 – ckµ 10 ∼ m → m 10 , k φ = ∼ 2 ¯ 3 − ψ T final ¯ q  ), and y initial M π ¯ are (considering ( s q s ¯ 10 q ] k ub 6 2 2.5 V × y = ∼ D ∗ qqq, † 2 td 4096 y / V D → B [ D ∼ † 2 08) ψ η . y Γ 0 T r = 1 V ∗ 1), c ± V ∼ 04 π 1000 GeV suppresses the contribution from the vertex. Cimparing ). Also Self-energy contributions (or wave-function renormalizations) give not 2 generated entropy into the primordial plasma. The dilution can be . 2 k g 32 ÷ φ 4.6 = (6 ' is at the decays’ epoch. This can be estimated as 500 V  exp B /s  η φ φ n , but this has to be normalized with the dilution factor. We obtain (assuming all are mass eigenvalues in ( M 9 = parametrize also extra suppressions from the couplings). From ( as the one shown in figure one-loop vertex contribution. So the asymmetry is controlled by ÷ ± 8 φ 7 k V λ r −  10, the decay of So, we can conclude that this mechanism can generate baryon asymmetry in our Uni- Finally, we also have to consider the dilution of the baryon asymmetry: 10 One can consider also 1-loop contributions coming involving also / 7 φ ∼ one can numerically evaluatesto these the contributions contributions in andimportant ( discover contributions for that our they estimations. are subdominant with respect scale. In thisevaluated scenario, as color triplets cannot be detected at LHC. The decay ratewhere can be verse, during athermal Post-Sphaleron equilibrium; epoch, ii) CP-violating satisfying processes all iii) B-violating Sakharov’s processes4.2 conditions [ i.e i) Majorana out fermionAlternatively, decays of we can in consider three directly quarks (antiquarks) (where  couplings near one i.e observations ( where M evaluate as the ratio of entropy density before and after With sequence, this bound with the othersection one 2 coming are from well ( compatible.and As naturally a predicts consequence, a a neutron-antineutron Post-sphaleron oscillation baryogenesis of is possible the electroweak sector, i.e CKMvertices CP violating contributions. The contribution from 1-loop It is necessary to evaluate this including 1-loop CP-violating contributions coming from JHEP04(2015)153 . 6 ' ψ D (1),  ]. 0 as a − (4.11) 57 U 8 2 × E cannot be exchanges) ψ U(1) ± . Under the contributions , µ × ¯ q W . q Y : they go-out of  , ¯ q , attached between ¯ q → X Sp(2) ¯ Y ± T < µ , λ × → X ψψ ψ + q (1) or U(3) 0 4 0 U ) decays. For is the fermionic part of a superfield can be constructed, similarly to 1 q , and an antisymmetric Mirror Plane × (¯ M 3 φ ψ q 5 3 CY U(1) ckµ → × = ψ ¯ q ¯ q – 10 – ¯ q of U(2) ) cited above. From this, we can estimate ¯ 7 × T qqq, . 4 are scalar parts of superfields → ψ Y ) is simplified as Γ , 2-brane intersecting with ordinary ones. In this way, we X 4.10 E ,( 0 -(a): 7 'M 1 (natural couplings), ulteriorly suppressed by by dilution factor for − ∼ λ k ]: a IIA (un)-oriented string theory, with stacks of D6 ordinary branes, and  + 28 , for λ 9 − . a) (Sub)-system of D-branes stacks generating our toy-model content of fields at low 10 ÷ , as discussed in the previous subsection. We conclude that also mechanism seems a stantons 1 8 We mention that, recently, a toy model for a supersymmetric non-local QFT was discussed in [ , recovering at low energy limit U(3) = 1 susy, R-parity preserving. A possible simplified scheme of D-brane stacks (sub)- living between two U(1) stacks. Finally, also contains also color factor 6 in numerator). We are assuming 8 − − − c mirror plane Ω, respectively.Ψ On the otherWe hand, can introduce angenerate Exotic interactions between Grassmann moduli (or modulini), living between Euclidean and D2-branes, wrappingΩ 3-cycles on N system is shown in figure a U(3) stack and a U(1) stack, and a U(3) stack and its mirror twin, with respect the In this section, weString-Inspired class would of like model, to embeddingterm the discuss for Standard the a Model, vector-like possible generating pairssuggested an in explanation [ exotic We of suggest mass the a little toy-model, different variant with respect to the one 10 viable way to generate the observed Baryon asymmetry. 5 Beyond the toy-model: string-inspired standard model and exotic in- However, we have alsoequilibrium at to the consider sameproduced, scattering temperature for processes. lack ofto baryon phase asymmetry space. generation. Extralead So, one-loop to one electroweak corrections dominant has ( 10 also contributions to as consider ( ( assumption Figure 7 energy limit. b) Mixed-Disk amplitudes generating an Exotic mass term for JHEP04(2015)153 3, 3, / / , an 2 (5.2) (5.3) (5.1) 8 − = 1 ckelberg 3 u c ) = 1. On the Y − ( mass. Y ˜ g jk − m 4 = Y i , 2 − anomalies give equal X E ) = c S 3 . As shown figure X ijk − N 3 (  e 2 S Y can be generated by two E CY S 3 M ] = − ˜ g Y e Y j , [ m S τ i U(1) X 3 τ M T r ∼ c do not introduce extra anomalous ij 2 0 = Y Y j , M τ i + X (1) + τ i 0 ij U X Y i 0 1 . For intersecting D-brane model considered c + ] = 1 and i 7 ντ X + X i [ ∼ 1 – 11 – is the parameterize by geometric moduli of the -(b). In fact, from these, ντ 00 T r 2 6 7 E D S U(1) − 1 − τdωe 6 c e 3 D d = − 2 Z Y U(2). So the hypercharge is a combination of four abelian E 2 , generated by one-loop corrections, containing one gaugino, and a L E ⊂ Y S , 2 U(1) − X e S M ), a consistent assignation of hypercharges, = ]. Anomalies that could appear as a serious problem in gauge models, is defined as a linear of U(1) stacks: 2 5.1 Y E U(2), U(1) 59 , ], a non-perturbative mass term between W ⊂ 58 1. 28 2 is the String scale and are the color indices of the U(3)-stack. A new superpotential term, not allowed , U(1) − S . Exotic mass for 7 = and a gaugino (, zino or ), with M i, j 0 1 Y mixing induced by Exotic Instantons (white blob with dashed lines). c We would like to note that all contributions on irreducible gauge anomalies, cancel As in [ Y , ψ are introduced as in any string-inspired model, with masses generated by a St¨ , = (Ψ) = 0, and the ones of SM , can be found. In particular, we find 0 X X 1 contributions with respect to SMand fields opposite content. For contributions instance, because SU(3) other hand, of anomalous extraZ U(1) are introducedmechanism with [ respect to SM gauge group: new 3-cycles wrapped by the Euclideanexotic D2-brane in mass the term Calabi-Yau can beψ generated, in a supersymmetric model, as a loopeach of other, susy partners in this D-brane construction. In fact, at perturbative level, is obtained, integrating out modulini: where mixed-disk amplitudes, shown in figure where where U(1) charges. From ( Y c a construction like the one suggestedin in figure figure Figure 8 ψ intersections, and ordinary superfields. Let us discuss the consistency of the hypercharges in JHEP04(2015)153 . ¯ n − ψ and . An exotic ψ ψ − ]. Recently, geodetic n ) cannot be intro- 64 ]. – 5.3 65 62 = 1 oscillations, B , and a scalar giving mass to ψ – 12 – 300 yr. We have also considered, an alternative scenario, ), which permits any use, distribution and reproduction in ∼ ¯ n n τ CC-BY 4.0 9 ]. This article is distributed under the terms of the Creative Commons 61 , ]. 60 66 , = 1. In particular, we got limits on exotic mixing mass parameter from LHC 29 , B We conclude that this model, postulating an exotic vector-like pair of color-triplet Finally, we would like to remark that, an exotic mass term ( The mechanism has St¨uckelberg a lot of different intriguing applications. Let us mention that a Lorentz 28 9 Attribution License ( any medium, provided the original author(s) and source are credited. Violating Massive gravity caninstabilities be of Lorentz St¨uckelberg realized Violating Massive through gravity a were mechanism discussed St¨uckelberg [ in [ and Luca Di Luzio forreferee interesting for conversations. his I important alsopart would comments by like and the to MIUR suggestions. thank research the grant The “Theoretical anonymous work Astroparticle Physics” of PRIN A.A. 2012CPPYP7. Open was supported Access. in Acknowledgments A.A would like to thanks Galileowhere Galilei Institute this for paper Theoretical Physics was for prepared. the hospitality, I would like to thank Massimo Bianchi, Zurab Berezhiani which the exotic mass term is generated by non-perturbativescalars, exotic deserves stringy attention istantons. for itssible peculiarity connections with and fundamental simplicity, issues especiallyogy and considering its such its implications as pos- in neutron-antineutron B-violations physics phenomenol- and LHC. epoch, and we predict ageneration neutron-antineutron transition of with experiments: a timein interesting for which the the next sterileantineutron fermion transition is can a be metastableFinally, we WIMP-like generated have particle. by also shown two In a ∆ this possible case, completion a and explanation neutron- of such a toy-model, in Dark Matter. Intriplet particular, scalars, we have a introduced sterilevector-like just pair Majorana one is fermion exotic characterized by vector-likeby an pair ∆ extra of peculiar color- massphysics. term, We violating have baryon seen number how Baryogenesis can be realized, also during the post-sphaleron 6 Conclusions In this paper, wefor have the discussed neutron, a connecting Majorana’s simple proposal alternative to model deep issues generating regarding a Baryogenesis Majorana and mass mechanism [ duced by-hand, at perturbative level,ken, because without of the R-parity, generation i.e ofin R-parity other [ is dangerous dynamically bro- R-parity violating operators, as explained are cancelled by Generalized Chern-Simons (GCS) terms as a generalized Green-Schwarz JHEP04(2015)153 , D ]. Z. 12 Phys. , B 94 , SO(10) (1980) 1534 (1977) 421 ]. Phys. Rev. (1937) 171 Conf. Proc. SPIRE , 64 , (2004) IN 14 Phys. Rev. [ 92 , B 67 SPIRE , World Scientific, IN JETP Lett. [ Phys. Lett. , , ]. ]. 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