arXiv:1311.6472v2 [hep-ph] 21 Feb 2014 dao smercdr atr(D) e e.[ Ref. See (ADM). matter dark asymmetric of idea eaetebro smer n akmte density, matter dark Ω and asymmetry i.e. that baryon mechanisms the possible of relate has investigations there on Recently, focus physics. been particle stud- and many cosmology motivated in has ies Universe the in density matter † ∗ [ Ref. See scale. breaking low spontaneous the the at number of baryon consequence of stabil- natural which a for is candidate pro- matter ity theory dark simple fermionic This a vides bounds. mechanism Higgs collider the with through with gener- consistent fields new can fields all one for fermionic masses Furthermore, by ate vector-like cancelled numbers. of baryon are set different model simple standard a bary- the adding the in context, anomalies this In onic should number. sphalerons baryon the Therefore, total conserve scale. low spontaneously is the which at symmetry broken gauge local a is number e.g. see context, this [ in Refs. baryogenesis [ see of Ref. symmetry, studies local where for a theories and is realistic number simple baryon For asymme- mecha- baryon the matter. a the dark have of and relation could try the one theories explains spon- scale which In and low nism symmetry at local broken a universe. is taneously observed early number baryon the the the generate where in to asymmetry processes baryon violating baryon of [ scale. Ref. low the and at mechanisms Baryogenesis ADM on of review review recent a ere hog h lcrwa paeos h basic Fig. in The asym- illustrated matter sphalerons. is electroweak dark paradigm the and through baryon metries the generate taneously lcrncaddress: Electronic lcrncaddress: Electronic eproma qiiru hroyai analysis thermodynamic equilibrium an perform We h xsec ftebro smer n oddark cold and asymmetry baryon the of existence The rca obroeei nayter steexistence the is theory any in baryogenesis to Crucial nti ril,w rps e ehns osimul- to mechanism new a propose we article, this In 6 DM ]. aynAymty akMte n oa aynNumber Baryon Local and Matter Dark Asymmetry, Baryon ∼ h ig ehns.W lodsustecs hr n sst uses one where case nature. in the is number discuss number baryon of baryon also conservation We the the if understand betwee mechanism. even relation universe Higgs consistent the a the have in to asymmetry possible baryon w is processes it sphalerons that through show sectors baryonic and matter ere nteuies ntere hr h aynnme i number baryon the where theories in the universe the in metries 5Ω epooeanwmcaimt nesadterlto betwee relation the understand to mechanism new a propose We B B .INTRODUCTION I. hs ehnssaebsdo the on based are mechanisms These . [email protected] fi[email protected] − L smer eeae hog ehns uha leptogenes as such mechanism a through generated asymmetry 1 nti oe baryon model this In . a-lnkIsiuefrNcerPhysics Nuclear for Institute Max-Planck apeceke ,617Hiebr,Germany Heidelberg, 69117 1, Saupfercheckweg ae ieizP´erez Fileviez Pavel atceadAtoPril hsc Division Physics Astro-Particle and Particle 5 o details. for ] 2 o a for ] 1 3 for ] – 5 ], ∗ n ie .Patel H. Hiren and n akmte est.Fnly nscinI ediscuss we results. IV section main asymmetry in the Finally, baryon density. the matter between dark analysis and connection thermodynamic the equilibrium find the and section In perform for we mass. boson mechanisms III gauge gauge different leptophobic local the the a generating discuss is we number and baryon symmetry, where theory the define Higgs a ob- have recent experiments. can the collider with one at consistent servations case properties the third with the boson mechanism. in Higgs the only cases, through However, third broken the and is second number through baryon the mass In its mechanism. the acquires and Stueckelberg boson nature, the in gauge In conserved leptophobic is cases. number possible baryon three In case, in first study complete- the For perform density. candidate. we relic ness, matter matter baryon dark between dark connection and consistent standard asymmetry the a the find of we way, of this and potentials quarks chemical model the connects that the through asymmetry matter dark gener and sphalerons. simultaneous baryon the the of of representation ation Schematic 1: FIG. hsatcei raie sflos nscinI we II section In follows: as organized is article This h akmte ei est n the and density relic matter dark We the number. n baryon total conserve hich oa ymty nteescenarios these In symmetry. local a s Asymmetry Baryon rkna h o cl through scale low the at broken aynaddr atrasym- matter dark and baryon n (MPIK) eSucebr ehns to mechanism Stueckelberg he si rnfre otedark the to transferred is is † Initial Asymmetry ( QQQL Sphalerons ) 3 ψ ¯ R Dark Matter ψ Asymmetric Asymmetric L - 2

II. LOCAL BARYON NUMBER It is important to mention that the idea of using the Higgs mechanism to understand the breaking of local In order to understand the conservation or violation of baryon number was proposed by A. Pais in Ref. [9]. See Baryon number in nature we can study a simple model also Refs. [10, 11] for other theories defined at the high where baryon number is a local symmetry. The theory is scale where baryon number is conserved. For previous based on the gauge group studies where the dark matter candidate has baryon num- ber see Refs. [12–14]. SU(3)C ⊗ SU(2)L ⊗ U(1)Y ⊗ U(1)B. In this article we will investigate scenario 3 in detail An anomaly-free theory is defined by including additional since we can have a consistent model with cosmology and fermions that account for anomaly cancellation. A simple particle physics. We will also present the final result for set of fields is given by the first two scenarios. Symmetry Breaking and Mass Generation: In order 1 1 to generate masses in a consistent way we extend the ΨL ∼ (1, 2, − ,B1), ΨR ∼ (1, 2, − ,B2), 2 2 scalar sector with a new Higgs boson S to allow for (1) B ηR ∼ (1, 1, −1,B1), ηL ∼ (1, 1, −1,B2), spontaneous breaking of baryon number,

χR ∼ (1, 1, 0,B1), and χL ∼ (1, 1, 0,B2) , SB ∼ (1, 1, 0, −3). (3) where we use the convention that Q = T3+Y to define the normalization of hypercharge. Requirement of anomaly Notice that the baryon number of the new scalar field is cancellation implies the relation determined once we impose the condition that we need to generate vector-like masses for the new fermions. The B1 − B2 = −3, (2) relevant interactions of the new fields are on the assignment of baryon number to the new fermions. −L ⊃ Y1Ψ¯ LHηR + Y2Ψ¯ RHηL + Y3Ψ¯ LHχ˜ R Notice that the baryon numbers of the vector-like fields ¯ ˜ ¯ must be different. Since the local baryon number is + Y4ΨRHχL + λ1ΨLΨRSB + λ2η¯RηLSB an abelian symmetry we can generate mass for the new + λ3χ¯RχLSB + h.c. (4) gauge boson ZB associated with U(1)B with or without For the special case B1 = −B2, terms such as a1χLχLSB the Higgs mechanism. Therefore, we consider here three † different cases: and a2χRχRSB are allowed. However, we will focus on the more generic case where B1 6= −B2 and where the • Scenario 1: The Stueckelberg mechanism generates dark matter annihilation through ZB is not velocity sup- mass for the leptophobic gauge boson ZB, and the pressed [14]. new fermions acquire mass only from the standard Once the new Higgs SB acquires a vacuum expectation model (SM) Higgs boson. See for example Ref. [7] value spontaneously breaking local U(1)B, no operator for the application of the Stueckelberg mechanism mediating proton decay is generated, and the scale for in this context. Unfortunately, because of its siz- baryon number violation can be very low. For the bounds able couplings to the new fermions, this scenario on the mass of a leptophobic neutral gauge boson see predicts a reduced branching fraction of the Higgs Refs. [15, 16]. decay to two photons that is at variance with col- The model enjoys three anomaly-free symmetries: lider experiments. Of course, one can add a set of scalar fields with negative couplings to offset the • B − L in the Standard Model sector is conserved in diphoton branching fraction. But we do not see the usual way. We will refer to this symmetry as this possibility as very appealing. See Ref. [8] for (B − L)SM . the study of the Higgs decays in theories with extra chiral fermions. • The accidental η global symmetry in the new sec- tor. Under this symmetry the new fields transform • Scenario 2: Using the Higgs mechanism with a new in the following way: scalar field SB with baryon number assignment dif- iη ferent from ±3 we can generate mass only for the ΨL,R → e ΨL,R, gauge boson ZB. As in the first scenario one will iη ηL,R → e ηL,R, run into problems with the predictions of the SM iη Higgs decays. It is important to mention that these χL,R → e χL,R. two scenarios are equivalent in the case when the new Higgs is heavy. This conserved charge will determine the dark matter asymmetry as pointed out in models with • Scenario 3: The third scenario corresponds to the vector-like fermions in Ref. [17]. Notice that this case when a new scalar field SB has baryon num- symmetry guarantees the stability of the lightest ber ±3. This allows for vector-like masses for all field in the new sector. Therefore, when this new new fermionic fields in the theory. This scenario is field is electrically neutral, one can have a candi- consistent with bounds from colliders. date for cold dark matter in the Universe. 3

• Above the symmetry breaking scale, total baryon The new λi interactions implies number BT carried by particles in both, the stan- −µΨ + µΨ + µ =0, dard model and the new sector is also conserved. L R SB Here we will assume that the symmetry breaking −µχR + µχL + µSB =0, (11)

scale for baryon number is low, close to the elec- −µηR + µηL + µSB =0, troweak scale. while the Yi couplings give us We shall specialize to the case when the dark matter is −µΨL − µ0 + µχR =0, SM singlet-like and is a Dirac fermion χ = χL + χR. The −µΨL + µ0 + µηR =0, interaction relevant for dark matter annihilation into SM (12) quarks via ZB is given by −µΨR − µ0 + µχL =0,

µ −µΨR + µ0 + µηL =0. L⊃ gBχγ¯ µZB (B2PL + B1PR) χ, (5) Conservation of electric charge Qem = 0 implies where PL and PR are the left- and right-handed pro- jectors, and gB is the U(1)B gauge coupling constant. 6(µuL + µuR ) − 3(µdL + µdR ) − 3(µeL + µeR )+

We now proceed to derive the relationship between the 2µ0 − µΨL − µΨR − µηL − µηR =0. (13) baryon asymmetry and dark matter density. Electroweak sphalerons satisfies the conservation of total baryon number, and the associated ‘t Hooft operator is III. BARYON AND DARK MATTER 3 ¯ ASYMMETRIES (QQQL) ψRψL . (14) Therefore, the sphalerons give us an additional equilib- We recall the thermodynamic relationship between the rium condition between the standard model particles and number density asymmetry n+ − n− and the chemical new degrees of freedom potential in the limit µ ≪ T : 3(3µuL + µeL )+ µΨL − µΨR =0. (15) ∆n n+ − n− 15g µ Notice that the sphalerons play the crucial role of trans- = = 2 , (6) s s 2π g∗ξ T ferring the asymmetry from the standard model sector to the dark matter sector. where g counts the internal degrees of freedom, s is the The total baryon number is conserved above the sym- entropy density, and g is the total number of relativistic ∗ metry breaking scale. Therefore the requirement of degrees of freedom. Here ξ = 2 for fermions and ξ = 1 B = 0 gives for bosons. T In order to derive the relationship between the baryon 15 BT = 2 3(µuL + µuR + µdL + µdR ) asymmetry and the dark matter relic density, we define 4π g∗T h the densities associated with the conserved charges in this + B1(2µΨL + µηR + µχR )+ B2(2µΨR + µηL + µχL ) theory. Following the notation of Ref. [18], the B − L asymmetry in the SM sector is defined in the usual way − 6µSB )i =0, (16) 15 Putting together the above relations, we find the follow- ∆(B − L)SM = 2 3(µuL + µuR + µdL + µdR 4π g∗T ing system of equations satisfied by the chemical poten- tials: −µνL − µeL − µeR ), (7) 15 and the η charge density is given by ∆(B−L)SM = 2 (12µuL − 9µeL +3µ0), 4π g∗T 15 15 η µ µ ∆η = (4µΨL +4µΨR ), ∆ = 2 2 ΨL +2 ΨR π2g T 4π g∗T (8) 4 ∗ + µ + µ + µ + µ . 0=6µuL + (2B1 − 3)µΨL + (2B2 + 3)µΨR , χL χR ηL ηR
0=3µuL +8µ0 − 3µeL − µΨL − µΨR , Isospin conservation T3 = 0 implies 0=9µuL +3µeL + µΨL − µΨR . (17) µuL = µdL , µeL = µνL , µ+ = µ0 . (9) Now, the system of equations above can be solved to yield Standard Model interactions give us the following equi- the final baryon asymmetry in the SM sector in terms of librium conditions for the chemical potentials [18]: ∆(B − L)SM and ∆η to yield

µuR = µ0 + µuL , SM 15 Bf ≡ 2 (12µuL ) µdR = −µ0 + µuL , (10) 4π g∗T

µeR = −µ0 + µeL . = C1 ∆(B − L)SM + C2 ∆η, (18) 4 where we find the values model quarks through the interaction with the leptopho- bic gauge boson ZB. As investigated in Ref. [14], one 32 (15 − 14B2) C1 = and C2 = . (19) can have a large cross section in agreement with the con- 99 198 straints from direct detection.

Here we have used the anomaly-free condition B1 = We now briefly discuss scenarios 1 and 2 mentioned −3+ B2. Requiring that the dark matter asymmetry in the previous section. In the case of scenario 1, where is bounded from above by the observed dark matter den- the leptophobic gauge boson mass is generated through sity, the Stueckelberg mechanism, the extra fermions get mass only from the SM Higgs. We repeat the same analysis |nχ − nχ¯|≤ nDM , (20) and find the connection between the baryon asymmetry and the dark matter density where the values of C1 and we find the following upper bound on the dark matter C2 are mass: St 16 St (9 − 7B2) ΩDM C2Mp C1 = and C2 = . (22) Mχ ≤ . (21) 53 53 |ΩB − C1Mp∆nB−L| The bound in Eq. (21) is relaxed due to the larger C2 Here Mp is the proton mass and ∆nB−L = s∆(B−L)SM . for a given value of B2, allowing for heavier dark matter. As one can appreciate, this bound is a function of the If we study the case in scenario 2, where S carries B B L B baryon number 2, and the − asymmetry generated charge B 6= ±3, we find the same relationship between through a mechanism such as leptogenesis. Therefore, in baryon asymmetry and dark matter density as in the general one could say that we can have a consistent rela- Stueckelberg case. Unfortunately, in these two cases tion between the baryon and dark matter asymmetries. the dark matter cannot be SM singlet-like because one Because the denominator can be small, the RHS could be does not have vector-like mass terms and it is difficult large allowing for a large dark matter mass. In Fig. (2), to satisfy bounds from dark matter direct detection n we display the allowed values for ∆ B−L for the choice experiments. B2 = −1. In order that the thermal component of dark matter does not oversaturate the observed density, one must un- derstand how it can be minimized by considering anni- hilation mechanisms. This issue has been studied in de- IV. CONCLUDING REMARKS tail in Ref. [14]. In the case when the dark matter is light (Mχ < 500 GeV), one needs to postulate a new an- We have proposed a new mechanism to simultane- nihilation channel assuming, for example, a light extra ously generate the baryon and dark matter asymme- gauge boson which mixes with the U(1)Y gauge boson tries through the electroweak sphalerons. This is realized [1]. When the dark matter is heavy (Mχ > 500 GeV), in theories with low scale spontaneously broken gauged the thermal component of the dark matter relic density baryon symmetry. This mechanism provides an interest- can be small due to the annihilation into two standard ing theoretical framework to relate the baryon asymme- try and the dark matter asymmetric density in the uni-

WΧ £ 5 WB verse. We have investigated this issue in different scenar- ios corresponding to different schemes for the generation 5.0 of mass for the leptophobic gauge boson. In these scenarios the B − L asymmetry generated Allowed through a mechanism such as leptogenesis is transferred L

p 3.0 Region to the dark matter sector through sphaleron processes M 

B which conserve total baryon number. We have shown W H 2.0

L that it is possible to have a consistent relation between - B

n dark matter relic density and baryon asymmetry in the D 1.5 universe even if the baryon number is broken at the low scale. We refer to this class of models as “Asymmetric 1.0 Baryonic Dark Matter”. These results can be applied to more general theo- 1 10 100 1000 5 50 500 ries where lepton number is also gauged, as proposed in MΧHGeVL Refs. [3–5]. In this case one can assume that the lepton number is broken at the high scale and a B − L asymme- FIG. 2: Bounds on the initial asymmetry ∆nB−L in units of try is generated through leptogenesis. ΩB per proton mass, which satisfies the upper bound on the Acknowledgments: P.F.P. thanks M.B. Wise for discus- B − dark matter relic density Eq. (21), for the choice 2 = 1. sions. 5

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