Physics Letters B 608 (2005) 87–94 www.elsevier.com/locate/physletb Constraints on the parity-violating couplings of a new gauge boson C. Bouchiat, P. Fayet Laboratoire de Physique Théorique de l’ENS (UMR 8549 CNRS), 24 rue Lhomond, 75231 Paris cedex 05, France Received 19 October 2004; accepted 15 December 2004 Available online 7 January 2005 Editor: G.F. Giudice Abstract High-energy particle physics experiments allow for the possible existence of a new light, very weakly coupled, neutral gauge boson (the U boson). This one permits for light (spin- 1 or spin-0) particles to be acceptable Dark Matter candidates, by inducing 2 + − sufficient (stronger than weak) annihilation cross sections into e e . They could be responsible for the bright 511 keV γ ray line observed by INTEGRAL from the galactic bulge. Such a new interaction may have important consequences, especially at lower energies. Parity-violation atomic-physics experiments provide strong constraints on such a U boson, if its couplings to quarks and electrons violate parity. With the constraints coming from an unobserved axionlike behaviour of this particle, they favor a pure vector coupling of the U boson to quarks and leptons, unless the corresponding symmetry is broken sufficiently above the electroweak scale. 2004 Elsevier B.V. All rights reserved. 1. Introduction This only applies directly, in fact, to heavy neutral gauge bosons. For light gauge bosons having small The SU(3) × SU(2) × U(1) standard model gives a couplings to Standard Model particles, the discussion very good description of strong and electroweak phe- is different [1]. When the mass mU of the exchanged nomena, so that the possible existence, next to the boson is small (compared to the momentum transfer gluons, photon, W ± and Z, of an additional neutral |q2| ), propagator effects are important. U-induced gauge boson, called here the U boson, is severely con- cross sections then generally decrease with energy,as strained. The U contributions to neutral-current ampli- for electromagnetic ones, as soon as |q2| gets larger ≈ 2 tudes should be sufficiently small, as well as its mixing than mU (as for Z-exchanges, above the Z mass), with the Z. According to the usual belief, any such and may be sufficiently small, if the U couplings are new interaction must be weaker than ordinary weak small enough. In particular, the existence of a new interactions, or it would have been seen already. light gauge boson U having couplings f to matter par- ticles such that f 2 g2 + g 2 E-mail addresses: [email protected] (C. Bouchiat), ∼ (or ∼ G ), (1) [email protected] (P. Fayet). 2 2 F mU mZ 0370-2693/$ – see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2004.12.065 88 C. Bouchiat, P. Fayet / Physics Letters B 608 (2005) 87–94 for example, is not necessarily excluded by high- U-induced Dark Matter annihilation cross section into + − 2 energy scattering experiments. Experiments performed e e (σannvrel/c) also includes, naturally, a vdm low- at lower energies, such as those measuring parity- energy suppression factor (as desirable to avoid exces- violation effects in atomic physics (as we shall discuss sive γ rays from residual light Dark Matter annihila- here), or neutrino scattering cross sections at lower tions [9]). This requirement is satisfied, in the case of a | 2| 1 q , are particularly relevant to search for such a par- spin- 2 Dark Matter particle axially coupled to the U, ticle, and constrain its properties [1–3]. if this one is vectorially coupled to electrons [8]. Let us recall, however, that even if it is very weakly A new interaction stronger than weak interactions coupled, a light spin-1 U boson could still have de- could seem, naively, to be ruled out experimentally. tectable interactions. And this, even in the limit in In fact, however, the U-mediated Dark-Matter/Matter which its couplings f to quarks and leptons would interactions should be stronger than ordinary weak almost vanish, a very surprizing result indeed (appar- interactions but only at lower energies, when weak in- ently)! teractions are really very weak. But weaker at higher In fact a very light spin-1 U boson behaves in this energies, at which they are damped by U propagator → → | 2| 2 case (f very small, mU very small) very much effects (for s or q >mU ), when weak-interaction as a quasimassless spin-0 axionlike particle, if the cur- cross sections, still growing with energy like s,be- rent to which it is coupled includes a (non-conserved) come important. The smallness of the U couplings to axial part.1 This axionlike behavior then restricts ordinary matter (f ), as compared to e, by several or- rather strongly its possible existence and properties, ders of magnitude, and of the resulting U amplitudes implying that the corresponding gauge symmetry be compared to electromagnetic ones, can then account broken at a scale at least somewhat above the elec- for the fact that these particles have not been observed troweak scale; or even at a very high scale, according yet. The U boson, in addition, may well have dominant to the “invisible U-boson” mechanism [1,5]. invisible decay modes into unobserved Dark Matter It is also possible that the new current to which the particles. U couples is purely vectorial, involving a linear com- We indicated in may 2003 that a gamma ray sig- bination of the conserved B, L and electromagnetic nature from the galactic centre at low energy could currents, as in a class of models discussed in Refs. [5, be due to the existence of a light new gauge boson, 6]. In this case there is no such axionlike behavior inducing annihilations of Light Dark Matter particles of the U boson. No significant extra contribution to into e+e− [7]. The observation, a few months later, by parity-violation effects is then to be expected. the satellite INTEGRAL of a bright 511 keV γ ray We now turn to the recent suggestion of Light Dark line from the galactic bulge [10], requiring a rather Matter particles. Contrasting with the heavy WIMPs, large number of annihilating positrons, may then be such as the neutralinos of supersymmetry, light (an- viewed as originating from Light Dark Matter anni- 1 1 nihilating) spin- 2 or spin-0 particles can also be ac- hilations [11]. Indeed spin-0, or as well spin- 2 parti- ceptable Dark Matter candidates. This requires, how- cles, could be responsible for this bright 511 keV line, ever, that they annihilate very efficiently, necessitating which does not seem to have an easy interpretation in new interactions, as induced by a light U boson [7,8]. terms of known astrophysical processes [8,12].One The required annihilation cross sections (≈ 4–10 pb, should, however, also keep in mind that Light Dark depending on whether Dark Matter particles are self- Matter particles may still exist, even if they are not re- conjugate or not), must be significantly larger than sponsible for this line. (And that a light U boson may weak-interaction cross sections (for this energy), oth- be present, even if Light Dark Matter particles do not erwise the relic abundance would be too large! The exist at all.2) 1 This is very similar to what happens in supersymme- 3 2 try/supergravity theories, in which a very light spin- 2 gravitino does In addition, a U that would be both extremely light and ex- not decouple in the κ → 0 limit, but interacts (proportionately to tremely weakly coupled would lead to a new long-range force, 2 1 κ/m3/2 or 1/Λss) like the massless spin- 2 goldstino of global su- and to the possibility of (apparent) violations of the Equivalence persymmetry (a feature largely used in “GMSB” models) [4]. Principe. C. Bouchiat, P. Fayet / Physics Letters B 608 (2005) 87–94 89 Returning to Standard Model particles, a new inter- We now proceed with the phenomenological analy- action that would be stronger than weak interactions sis, expressing the relevant couplings in the La- at lower energies (at least when dealing with Light grangian density as follows: Dark Matter particle annihilations) could have impor- µ tant implications on ordinary physics, especially at L =−eAµJ em lower energies or momentum transfer,evenifithas − 2 + 2 µ − 2 µ no significant influence on high-energy neutral current Zµ g g J3 sin θJem processes. − U fγ¯ µ(f − γ f )f. (2) As we shall see, parity-violation atomic-physics ex- µ Vf 5 Af f =l,q periments [13] provide new strong constraints on such − a gauge boson – whether light or heavy – if its cou- P = 1 γ5 The left- and right-handed projectors are L 2 , plings to quarks and electrons violate parity, then re- 1+γ5 PR = (so that a left-handed U-current would cor- quiring that the corresponding symmetry be broken 2 = = 0 1 significantly above the electroweak scale. respond to fV fA), with γ5 1 0 ,andthemetric (+−−−). The relevant terms in the Z weak neutral current are given by 2. The effective weak charge of a nucleus µ µ J = J − sin2 θJµ Z 3 em 1 1 Such models, in which the standard gauge group = eγ¯ µγ e + − + s2 eγ¯ µe 4 5 4 is extended to include SU(3) × SU(2) × U(1) × extra-U(1) at least, have been discussed in detail. They 1 µ 1 2 2 µ − uγ¯ γ5u + − s uγ¯ u involve an additional neutral gauge boson U (which 4 4 3 may also be called Z or Z), initially associated, be- 1 ¯ µ 1 1 2 ¯ µ U( ) + dγ γ5d + − + s dγ d, (3) fore gauge symmetry breaking, with the extra- 1 4 4 3 generator.