Journal ArticleDOI

# Review of Particle Physics

Keith A. Olive1, Kaustubh Agashe2, Claude Amsler3  +223 moreInstitutions (107)
01 Aug 2014-Chinese Physics C (IOP Publishing Ltd.)-Vol. 38, Iss: 10, pp 100001-100001

TL;DR: The review as discussed by the authors summarizes much of particle physics and cosmology using data from previous editions, plus 3,283 new measurements from 899 Japers, including the recently discovered Higgs boson, leptons, quarks, mesons and baryons.

AbstractThe Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,283 new measurements from 899 Japers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as heavy neutrinos, supersymmetric and technicolor particles, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as Supersymmetry, Extra Dimensions, Particle Detectors, Probability, and Statistics. Among the 112 reviews are many that are new or heavily revised including those on: Dark Energy, Higgs Boson Physics, Electroweak Model, Neutrino Cross Section Measurements, Monte Carlo Neutrino Generators, Top Quark, Dark Matter, Dynamical Electroweak Symmetry Breaking, Accelerator Physics of Colliders, High-Energy Collider Parameters, Big Bang Nucleosynthesis, Astrophysical Constants and Cosmological Parameters.

### Introduction

• The authors list coupling-strength and mass limits for light neutral scalar or pseudoscalar bosons that couple weakly to normal matter and radiation.
• A common characteristic among these light bosons φ is that their coupling to Standard-Model particles is suppressed by the energy scale that characterizes the symmetry breaking, i.e., the decay constant f .
• Moreover, the cold dark matter of the universe may well consist of axions and they are searched for in dedicated experiments with a realistic chance of discovery.
• Here the authors focus on “invisible axions” with fA ≫ vweak as the main possibility.
• A number of experiments explore this more general parameter space.

### I.1 Peccei-Quinn mechanism and axions

• Θ̄ ≤ +π is the effective Θ parameter after diagonalizing quark masses, Gaµν is the color field strength tensor, and G̃a,µν ≡ ǫµνλρGaλρ/2, with ε0123 = 1, its dual.
• This symmetry is broken due to the axion’s anomalous triangle coupling to gluons, L = ( φA fA − Θ̄ ) αs 8π GµνaG̃aµν , (2) where φA is the axion field and fA the axion decay constant.
• Color anomaly factors have been absorbed in the normalization of fA which is defined by this Lagrangian.
• “Variant axion models” were proposed which keep fA ∼ vweak while relaxing the constraint of tree-level flavor conservation [16], but these models are also excluded [17].
• Another generic class re- quires at least two Higgs doublets and ordinary quarks and leptons carry PQ charges, the archetype being the DFSZ model [19].

### I.2 Model-dependent axion couplings

• There are non- negligible model-dependent factors and uncertainties.
• In general, a broad range of E/N values is possible [21], as indicated by the yellow band in Figure 1.
• Axions decay faster than the age of the universe if mA >∼ 20 eV. Helioscopes (CAST) Haloscopes (ADMX) T el es co pe s Horizontal Branch Stars KS VZ DF SZ VMB SN 1987A HESS Figure 1: Exclusion plot for axion-like particles as described in the text.
• Ψf is the fermion field, mf its mass, and Cf a model-dependent coefficient.
• In the DFSZ model [19], the tree-level coupling coefficient to electrons is [23].

### Cn = 0 whereas Cp does not vanish within the plausible z range.

• The axion-pion interaction is given by the Lagrangian [28].
• The chiral symmetry-breaking Lagrangian provides an additional term L′Aπ ∝ (m 2 π/fπfA) (π 0π0 + 2π−π+) π0φA. For hadronic axions it vanishes identically, in contrast to the DFSZ model (.

### II. LABORATORY SEARCHES

• II.1 Light shining through walls Searching for “invisible axions” is extremely challenging due to its extraordinarily feeble coupling to normal matter and ra- diation.
• Currently, the most promising approaches rely on the axion-two-photon vertex, allowing for axion-photon conversion in external electric or magnetic fields [5].
• For the Coulomb field of a charged particle, the conversion is best viewed as a scattering process, γ+Ze ↔ Ze+A, called Primakoff effect [29].

### In the other extreme of a macroscopic field, usually a large-scale

• B-field, the momentum transfer is small, the interaction coher- ent over a large distance, and the conversion is best viewed as an axion-photon oscillation phenomenon in analogy to neutrino flavor oscillations [30].
• Photons propagating through a transverse magnetic field, with incident Eγ and magnet B parallel, may convert into axions.
• A practical realization uses a laser beam propagating down the bore of a superconducting dipole magnet (like the bending magnets in high-energy accelerators).
• More recently, several such experiments were performed (see Listings) [33,34].
• The concept of resonantly enhanced photon regeneration may open unexplored regions of coupling strength [35].

### II.2 Photon polarization

• An alternative to regenerating the lost photons is to use the beam itself to detect conversion: the polarization of light propagating through a transverse B field suffers dichroism and birefringence [40].
• This rotation occurs because there is mixing of virtual axions in the E ‖ state, but not for E⊥. Hence, linearly polarized light will develop elliptical polarization.
• The ellipticity limits are better at higher masses, as they fall off smoothly and do not terminate at mA.
• Since then, these findings are attributed to instrumental artifacts [43].
• Recently, the fourth generation setup of the PVLAS experiment has published new results on searches for VMB (see Figure 1) and dichroism [44].

### II.3 Long-range forces

• New bosons would mediate long-range forces, which are severely constrained by “fifth force” experiments [45].
• Those looking for new mass-spin couplings provide significant con- straints on pseudoscalar bosons [46].
• Presently, the most restrictive limits are obtained from combining long-range force measurements with stellar cooling arguments [47].
• For the moment, any of these limits are far from realistic values ex- pected for axions.
• Recently, a method was proposed that can extend the search for axion-mediated spin-dependent forces by several orders of magnitude [48].

### III. AXIONS FROM ASTROPHYSICAL SOURCES

• Low-mass weakly-interacting particles (neutrinos, gravitons, axions, baryonic or leptonic gauge bosons, etc.) are produced in hot astrophysical plasmas, and can thus transport energy out of stars, also known as III.1 Stellar energy-loss limits.
• The authors begin this discussion with their Sun and concentrate on hadronic axions.
• Recently, the limit was improved to G10 < 4.1 (at 3σ), exploit- ing a new statistical analysis that combined helioseismology (sound speed, surface helium and convective radius) and solar neutrino observations, including theoretical and observational errors, and accounting for tensions between input parameters of solar models, in particular the solar element abundances [55].
• The stars on the horizontal branch (HB) in the color-magnitude diagram have reached helium burning with a core-averaged energy release of about 80 erg g−1 s−1, compared to Primakoff axion losses of G210 30 erg g −1 s−1.
• The excluded mA range thus certainly extends beyond the shown.

### 100 keV.

• If axions couple directly to electrons, the dominant emission processes are atomic axio-recombination and axio-deexcitation, axio-bremsstrahlung in electron-ion or electron-electron colli- sions, and Compton scattering [57].
• In fact, they would lead to an extension of the latter to larger brightness.
• Intriguingly, the agreement would improve with a small amount of extra cooling that slightly postpones helium ignition, prefering an electron coupling around αAee ∼ 2.8×10 −27, corresponding to mA cos 2 β′ ∼ 7 meV.
• Recently, it has been pointed out that the best fit simultaneously explaining the extra energy losses of HB stars reported above and the ones of RGs prefers a photon coupling around GAγγ ∼ few × 10 −12 GeV−1 and an electron coupling of order αAee ∼ 10 −27 [59].
• Bremsstrahlung is also efficient in white dwarfs (WDs), where the Primakoff and Compton processes are suppressed by the large plasma frequency.

### WD cooling treatment and new data on the WD luminosity function (WDLF) of the Galactic Disk, found that electron couplings above αAee >∼ 6 × 10

• Lower couplings can not be discarded from the current knowledge of the WDLF of the Galactic Disk.
• The corresponding observations of the pulsating WDs G117-B15A and R548 imply additional cooling that can be interpreted also in terms of similar axion losses [63].
• For realis- tic conditions, even after considerable effort, one is limited to a heuristic estimate leading to F ≈ 1 [51].
• Only about three orders of magnitude in gANN or mA are excluded, a range shown somewhat schematically in Figure 2.
• A possible gap between these two SN 1987A arguments was discussed as the “hadronic axion window” under the assumption that GAγγ was anomalously small [65].

### 10 years reveals an unusually fast cooling rate. This may be interpreted as a hint for extra cooling by axion neutron bremsstrahlung, requiring a coupling to the neutron of size [66]

• In fact, as recently pointed out, the more rapid cooling of the superfluid core in the neutron star may also arise from a phase transition of the neutron condensate into a multicomponent state [68].
• Finally, let us note that if the interpretation of the various hints for additional cooling of stars reported in this section in terms of emission of axions with mA ∼meV were correct, SNe would lose a large fraction of their energy as axions.
• There is no apparent way of detecting it or the axion burst from the next nearby SN.
• The main focus has been on axion-like particles with a two-photon vertex.
• Later, the Tokyo axion helioscope used a superconducting magnet on a tracking mount, viewing the Sun continuously.

### They reported |GAγγ | < 6×10

• This experiment was recommissioned and a similar limit for masses around 1 eV was reported [73].
• The hardware includes grazing-incidence x- ray optics with solid-state x-ray detectors, as well as a novel x-ray Micromegas position-sensitive gaseous detector.
• To cover larger masses, the magnet bores are filled with a gas at varying pressure.
• Going to yet larger masses in a helioscope search is not well motivated because of the cosmic hot dark matter bound of mA <∼ 1 eV (see below).
• Such a next-generation axion helioscope may also push the sensitivity in the product of couplings to photons and to electrons, GAγγgAee, into a range beyond stellar energy-loss limits and test the hypothesis that.

### WD cooling is dominated by axion emission [78].

• Other Primakoff searches for solar axions and ALPs have been carried out using crystal detectors, exploiting the coherent conversion of axions into photons when the axion angle of incidence satisfies a Bragg condition with a crystal plane [79].
• Solar axions and ALPs would convert in the Earth magnetic field on the far side and could be detected [80].
• Therefore, while the product BL can be large, realistic sensitivities are usually restricted to very low-mass particles, far away from the “axion band” in a plot like Figure 1.
• Searches for linearly polarised emission from magnetised white dwarfs [86] and changes of the linear polarisation from radio galaxies (see, e.g., Ref. [87]) provide limits close to GAγγ ∼ 10 −11 GeV−1, for masses mA <∼ 10 −7 eV and mA <∼ 10 −15 eV, respectively, albeit with uncertainties related to the underlying assumptions.
• The situation is not conclusive at present [90], but the possible role of photon-ALP oscillations in TeV γ-ray astronomy is tantalizing [91].

### 2155 [93], see Figure 1.

• Last but not least, it was found that observed soft X-ray excesses in many galaxy clusters may be explained by the conversion of a hypothetical cosmic ALP background (CAB) radiation, corresponding to an effective number △Neff of extra neutrinos, into photons in the cluster magnetic fields [94].
• When their Compton wavelength is of order of the black hole size, they form bound states around the black hole nucleus.
• For black holes lighter than 107 solar masses, accretion cannot replenish the spin of the black hole.
• The existence of destabilizing ultralight bosonic fields thus leads to gaps in the mass vs. spin plot of rapidly rotating black holes.
• Long lasting, monochromatic gravitational wave signals, which can be distinguished from ordinary astrophysical sources, are expected to be produced by axions transitioning between the levels of the gravitational atom and axions annihilating to gravi- tons.

### IV. COSMIC AXIONS

• In the early universe, axions are produced by processes in- volving quarks and gluons [96].
• Cosmological precision data provide restrictive constraints on a possible hot dark-matter fraction that translate into mA <∼ 1 eV [97], but in detail depend on the used data set and assumed cosmological model.
• This excess radiation provides additional limits up to very large axion masses [99].
• After the breakdown of the PQ symmetry, the axion field relaxes somewhere in the “bottom of the wine bottle” potential.
• Near the QCD epoch, topological fluctua- tions of the gluon fields such as instantons explicitly break the PQ symmetry, the very effect that causes dynamical PQ symmetry restoration.

### CDM density, ΩCDMh

• Much smaller axion masses (much higher PQ scales) would still be possible if the PQ symmetry is broken during inflation and not restored afterwards.
• The initial value Θ̄i may just happen to be small enough in today’s observable universe (“anthropic axion window” [103]) .
• Since the axion field is then present during inflation and thus subject to quantum fluctuations, the non-observation of the associated isocurvature fluctuations in the CMB puts severe constraints in the (fA, r) plane, where r is the ratio of the power in tensor to the one in scalar fluctuations [104].
• (21) However, the additional contribution from the decay of topo- logical defects suffers from significant uncertainties.
• According to Sikivie and collaborators, these populations are comparable to the re-alignment contribution [106].

### 1) domain walls, such as the KSVZ model, and

• Moreover, the spatial axion density variations are large at the QCD transition and they are not erased by free streaming.
• When matter begins to dominate the universe, grav- itationally bound “axion mini clusters” form promptly [109].

### A significant fraction of CDM axions can reside in these bound objects.

• In the above predictions of the fractional cosmic mass density in axions, the exponent, 1.19, arises from the non- trivial temperature dependence of the axion mass mA(T ) = √ χ(T )/fA, which has been obtained from the dilute instanton gas/liquid approximation (DIGA).
• Lattice QCD provides a first principle technique to determine the topological susceptibil- ity χ(T ) in the relevant temperature range around the QCD phase transition.
• The latter has been done recently in the quenched framework (neglecting the ef- fects of light quarks) and compared with the prediction of the DIGA [110,111].
• In the case of a neutralino LSP, saxion and axino production in the early universe have a strong impact on the neutralino and axion abundance.
• Finally, it is worth mentioning that the non-thermal pro- duction mechanisms attributed to axions are indeed generic to bosonic weakly interacting ultra-light particles such as ALPs: a wide range in GAγγ – mA parameter space outside the ax- ion band can generically contain models with adequate CDM density [114].

### IV.2 Telescope searches

• The two-photon decay is extremely slow for axions with masses in the CDM regime, but could be detectable for eV masses.
• The signature would be a quasi-monochromatic emis- sion line from galaxies and galaxy clusters.
• An early search in three rich Abell clus- ters [115], and a recent search in two rich Abell clusters [116], exclude the “Telescope” range in Figure 1 and Figure 2 unless the axion-photon coupling is strongly suppressed.
• Of course, axions in this mass range would anyway provide an excessive hot DM contribution.
• Very low-mass axions in halos produce a weak quasi- monochromatic radio line.

### 298 < mA < 363 µeV [117]. However, this combination of mA and GAγγ does not exclude plausible axion models.

• The limits of Figure 2 suggest that axions, if they exist, provide a significant fraction or even perhaps all of the cos- mic CDM.
• In a broad range of the plausible mA range for CDM, galactic halo axions may be detected by their resonant conversion into a quasi-monochromatic microwave signal in a high-Q electromagnetic cavity permeated by a strong static B field [5,118].
• Other new concepts for searching for axion dark matter are also being investigated.
• Another alternative to the microwave cavity technique is based on a novel detector architecture consisting of an open, Fabry-Perot resonator and a series of current-carrying wire planes [130].
• The QUAX (QUaerere AXions) experiment aims at exploiting MR inside a magnetized material [135].

### Conclusions

• There is a strengthening physics case for very weakly cou- pled ultralight particles beyond the Standard Model.
• The el- egant solution of the strong CP problem proposed by Peccei and Quinn yields a particularly strong motivation for the axion.
• In many theoretically appealing ultraviolet completions of the Standard Model axions and axion-like particles occur automati- cally.
• Moreover, they are natural cold dark matter candidates.
• Perhaps the first hints of their existence have already been seen in the anomalous excessive cooling of stars and the anomalous transparency of the Universe for VHE gamma rays.

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###### Q1. What are the contributions in this paper?

The Review summarizes much of particle physics and cosmology. All the particle properties and search limits are listed in Summary Tables. The authors also give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. The complete Review is published online in a journal and on the website of the Particle Data Group ( http: //pdg. lbl. gov ). The printed PDG Book contains the Summary Tables and all review articles but no longer includes the detailed tables from the Particle Listings. A Booklet with the Summary Tables and abbreviated versions of some of the review articles is also available. The 2016 edition of Review of Particle Physics should be cited as: C. Patrignani et al. ( Particle Data Group ), Chinese Physics C, 40, 100001 ( 2016 ) c ©2016 Regents of the University of California ∗The publication of the Review of Particle Physics is supported by the Director, Office of Science, Office of High Energy Physics of the U. S. Department of Energy under Contract No. DE–AC02–05CH11231 ; by the European Laboratory for Particle Physics ( CERN ) ; by an implementing arrangement between the governments of Japan ( MEXT: Ministry of Education, Culture, Sports, Science and Technology ) and the United States ( DOE ) on cooperative research and development ; by the Institute of High Energy Physics, Chinese Academy of Sciences ; and by the Italian National Institute of Nuclear Physics ( INFN ).

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