Search

The strong CP problem can be solved in Parity symmetric theories with electroweak gauge group containing $SU(2)_L \times SU(2)_R$ broken by the minimal Higgs content. Neutrino masses may be explained by adding the same number of gauge singlet fermions as the number of generations. The neutrino masses vanish at tree-level and are only radiatively generated, leading to larger couplings of right-handed neutrinos to Standard Model particles than with the tree-level seesaw mechanism. We compute these radiative corrections and the mixing angles between left- and right-handed neutrinos. We discuss sensitivities to these right-handed neutrinos from a variety of future experiments that search for heavy neutral leptons with masses from tens of MeV to the multi-TeV scale., Comment: 18 pages, 6 figures

We study the simplest theories with exact spacetime parity that solve the strong CP problem and successfully generate the cosmological baryon asymmetry via decays of right-handed neutrinos. Lower bounds are derived for the masses of the right-handed neutrinos and for the scale of spontaneous parity breaking, $v_R$. For generic thermal leptogenesis, $v_R \gtrsim 10^{12}$ GeV, unless the small observed neutrino masses arise from fine-tuning. We compute $v_R$ in terms of the top quark mass, the QCD coupling, and the Higgs boson mass and find this bound is consistent with current data at $1 \sigma$. Future precision measurements of these parameters may provide support for the theory or, if $v_R$ is determined to be below $10^{12}$ GeV, force modifications. However, modified cosmologies do not easily allow reductions in $v_R$ -- no reduction is possible if leptogenesis occurs in the collisions of domain walls formed at parity breaking, and at most a factor 10 reduction is possible with non-thermal leptogenesis. Standard Model parameters that yield low values for $v_R$ can only be accommodated by having a high degree of degeneracy among the right-handed neutrinos involved in leptogenesis. If future precision measurements determine $v_R$ to be above $10^{12}$ GeV, it is likely that higher-dimensional operators of the theory will yield a neutron electric dipole moment accessible to ongoing experiments. This is especially true in a simple UV completion of the neutrino sector, involving gauge singlet fermions, where the bound from successful leptogenesis is strengthened to $v_R \gtrsim 10^{13}$ GeV., Comment: 41 pages, 12 figures

We study the mirror world with dark matter arising from the thermal freeze-out of the lightest, stable mirror particle -- the mirror electron. The dark matter abundance is achieved for mirror electrons of mass 225 GeV, fixing the mirror electroweak scale near $10^8$ GeV. This highly predictive scenario is realized by an axion that acts as a portal between the two sectors through its coupling to the QCD and mirror QCD sectors. The axion is more massive than the standard QCD axion due to additional contributions from mirror strong dynamics. Still, the strong CP problem is solved by this "heavy" axion due to the alignment of the QCD and mirror QCD potentials. Mirror entropy is transferred into the Standard Model sector via the axion portal, which alleviates overproduction of dark radiation from mirror glueball decays. This mirror scenario has a variety of signals: (1) primordial gravitational waves from the first-order mirror QCD phase transition occurring at a temperature near 35 GeV, (2) effects on large-scale structure from dark matter self-interactions from mirror QED, (3) dark radiation affecting the cosmic microwave background, and (4) the rare kaon decay, $K^+ \rightarrow (\pi^+ + \rm{axion})$. The first two signals do not depend on any fundamental free parameters of the theory while the latter two depend on a single free parameter, the axion decay constant., Comment: 35 pages, 9 figures

The naturalness problem of PQ symmetry motivates study of the heavy QCD axion, with masses $m_a >$ 1 MeV generated at scales above the QCD scale, and low values of the PQ symmetry breaking scale, $f_a$. We compute the abundance of such axions in a model-independent way, assuming only that they freeze-out after reheating from inflation, and are not subsequently diluted by new physics. If these axions decay between neutrino decoupling and the last scatter era of the Cosmic Microwave Background (CMB), they dilute the neutrinos and their abundance is constrained by CMB measurements of the energy density in dark radiation, $N_{\rm eff}$. We accurately compute this bound using a numerical code to evolve the axion momentum distribution, including many key processes and effects previously ignored. We assume that the only relevant axion decays are to final states involving Standard Model particles. We determine regions of $(m_a, f_a)$ that will give a signal in $N_{\rm eff}$ at CMB Stage 4 experiments. We similarly compute the $N_{\rm eff}$ bound and CMB Stage 4 signal for heavy axions that can decay to light mirror photons. Finally, we compute the bounds on heavy axions with mass below 1 MeV that decay after the era of CMB last scatter, from their contribution to cold or hot dark matter or $N_{\rm eff}$ at this era., Comment: 40 pages, 17 figures

Rotations of an axion field in field space provide a natural origin for an era of kination domination, where the energy density is dominated by the kinetic term of the axion field, preceded by an early era of matter domination. Remarkably, no entropy is produced at the end of matter domination and hence these eras of matter and kination domination may occur even after Big Bang Nucleosynthesis. We derive constraints on these eras from both the cosmic microwave background and Big Bang Nucleosynthesis. We investigate how this cosmological scenario affects the spectrum of possible primordial gravitational waves and find that the spectrum features a triangular peak. We discuss how future observations of gravitational waves can probe the viable parameter space, including regions that produce axion dark matter by the kinetic misalignment mechanism or the baryon asymmetry by axiogenesis. For QCD axion dark matter produced by the kinetic misalignment mechanism, a modification to the inflationary gravitational wave spectrum occurs above 0.01 Hz and, for high values of the energy scale of inflation, the prospects for discovery are good. We briefly comment on implications for structure formation of the universe., Comment: 63 pages, 17 figures; v2: references and discussions added; v3: matches journal version; v4: journal references updated

Left-Right symmetric theories solve the strong CP problem and explain the small Higgs quartic coupling at high energy scales via the Higgs Parity mechanism, which forces the Higgs quartic coupling to vanish at the Left-Right symmetry breaking scale. They also predict three right-handed neutrinos; one may be stable and provide dark matter, and another may decay and explain the baryon asymmetry of the universe through leptogenesis. For the dark matter abundance to arise from freeze-out, the required range of the Left-Right symmetry breaking scale is $10^{10}$-$10^{13}$ GeV, in remarkable agreement with the energy scale at which the Higgs quartic coupling vanishes. The allowed parameter space can be probed by the warmness of dark matter, precise measurements of the top quark mass and QCD coupling constant by future colliders and lattice computations, and measurement of the neutrino mass hierarchy., Comment: 6 pages, 2 figures, contribution to the 2021 EW session of the 55th Rencontres de Moriond

The vanishing of the Higgs quartic coupling at a high energy scale may be explained by Intermediate Scale Supersymmetry, where supersymmetry breaks at $(10^9$-$10^{12})$ GeV. The possible range of supersymmetry breaking scales can be narrowed down by precise measurements of the top quark mass and the strong coupling constant. On the other hand, nuclear recoil experiments can probe Higgsino or sneutrino dark matter up to a mass of $10^{12}$ GeV. We derive the correlation between the dark matter mass and precision measurements of standard model parameters, including supersymmetric threshold corrections. The dark matter mass is bounded from above as a function of the top quark mass and the strong coupling constant. The top quark mass and the strong coupling constant are bounded from above and below respectively for a given dark matter mass. We also discuss how the observed dark matter abundance can be explained by freeze-out or freeze-in during a matter-dominated era after inflation, with the inflaton condensate being dissipated by thermal effects., Comment: 22 pages, 9 figures

The standard model Higgs quartic coupling vanishes at $(10^{9}-10^{13})$ GeV. We study $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ theories that incorporate the Higgs Parity mechanism, where this becomes the scale of Left-Right symmetry breaking, $v_R$. Furthermore, these theories solve the strong CP problem and predict three right-handed neutrinos. We introduce cosmologies where $SU(2)_R \times U(1)_{B-L}$ gauge interactions produce right-handed neutrinos via the freeze-out or freeze-in mechanisms. In both cases, we find the parameter space where the lightest right-handed neutrino is dark matter and the decay of a heavier one creates the baryon asymmetry of the universe via leptogenesis. A theory of flavor is constructed that naturally accounts for the lightness and stability of the right-handed neutrino dark matter, while maintaining sufficient baryon asymmetry. The dark matter abundance and successful natural leptogenesis require $v_R$ to be in the range $(10^{10}-10^{13})$ GeV for freeze-out, in remarkable agreement with the scale where the Higgs quartic coupling vanishes, whereas freeze-in requires $v_R \gtrsim 10^9$ GeV. The allowed parameter space can be probed by the warmness of dark matter, precise determinations of the top quark mass and QCD coupling by future colliders and lattice computations, and measurement of the neutrino mass hierarchy., Comment: 46 pages, 16 figures

We propose a baryogenenesis mechanism that uses a rotating condensate of a Peccei-Quinn (PQ) symmetry breaking field and the dimension-five operator that gives Majorana neutrino masses. The rotation induces charge asymmetries for the Higgs boson and for lepton chirality through sphaleron processes and Yukawa interactions. The dimension-five interaction transfers these asymmetries to the lepton asymmetry, which in turn is transferred into the baryon asymmetry through the electroweak sphaleron process. QCD axion dark matter can be simultaneously produced by dynamics of the same PQ field via kinetic misalignment or parametric resonance, favoring an axion decay constant $f_a \lesssim 10^{10}$ GeV, or by conventional misalignment and contributions from strings and domain walls with $f_a \sim 10^{11}$ GeV. The size of the baryon asymmetry is tied to the mass of the PQ field. In simple supersymmetric theories, it is independent of UV parameters and predicts the supersymmtry breaking mass scale to be $\mathcal{O}(10-10^4)$ TeV, depending on the masses of the neutrinos and whether the condensate is thermalized during a radiation or matter dominated era. We also construct a theory where TeV scale supersymmetry is possible. Parametric resonance may give warm axions, and the radial component of the PQ field may give signals in rare kaon decays from mixing with the Higgs and in dark radiation., Comment: 71 pages, 6 Figures

Adding an axion-like particle (ALP) to the Standard Model, with a field velocity in the early universe, simultaneously explains the observed baryon and dark matter densities. This requires one or more couplings between the ALP and photons, nucleons, and/or electrons that are predicted as functions of the ALP mass. These predictions arise because the ratio of dark matter to baryon densities is independent of the ALP field velocity, allowing a correlation between the ALP mass, $m_a$, and decay constant, $f_a$. The predicted couplings are orders of magnitude larger than those for the QCD axion and for dark matter from the conventional ALP misalignment mechanism. As a result, this scheme, ALP cogenesis, is within reach of future experimental ALP searches from the lab and stellar objects, and for dark matter., Comment: 24 pages, 3 figures

$SU(2)_L \times SU(2)_R$ gauge symmetry requires three right-handed neutrinos ($ N _i $), one of which, $N_1$, can be sufficiently stable to be dark matter. In the early universe, $ W _R $ exchange with the Standard Model thermal bath keeps the right-handed neutrinos in thermal equilibrium at high temperatures. $N_1$ can make up all of dark matter if they freeze-out while relativistic and are mildly diluted by subsequent decays of a long-lived and heavier right-handed neutrino, $N_2$. We systematically study this parameter space, constraining the symmetry breaking scale of $SU(2)_R$ and the mass of $N_1$ to a triangle in the $(v_R,M_1)$ plane, with $v_R = (10^6 - 3 \times 10^{12})$ GeV and $M_1 = (2\, {\rm keV} - 1 \, {\rm MeV)}$. Much of this triangle can be probed by signals of warm dark matter, especially if leptogenesis from $N_2$ decay yields the observed baryon asymmetry. The minimal value of $v_R$ is increased to $10^8 \, {\rm GeV}$ for doublet breaking of $SU(2)_R$, and further to $10^9 \, {\rm GeV}$ if leptogenesis occurs via $N_2$ decay, while the upper bound on $M_1$ is reduced to 100 keV. In addition, there is a component of hot $N_1$ dark matter resulting from the late decay of $N_2 \rightarrow N_1 \ell^+ \ell^-$ that can be probed by future cosmic microwave background observations. Interestingly, the range of $v_R$ allows both precision gauge coupling unification and the Higgs Parity understanding of the vanishing of the Standard Model Higgs quartic at scale $v_R$. Finally, we study freeze-in production of $N_1$ dark matter via the $W_R$ interaction, which allows a much wider range of $(v_R,M_1)$., Comment: 31 pages, 5 figures. Matches published version. Added references and clarifications

Axion cold dark matter from standard misalignment typically requires a decay constant $f_a~\gtrsim~10^{11}$ GeV. Kinetic misalignment and parametric resonance easily allow lower values of $f_a$ when the radial Peccei-Quinn (PQ) symmetry breaking field takes large initial values. Here, we consider the effects of inflation on kinetic misalignment and parametric resonance. We assume that the initial PQ field value is determined by quantum fluctuations, and is set by the Hubble parameter during inflation, $H_I$, and the PQ field mass. PQ field oscillations begin before or after the completion of reheating after inflation at a temperature $T_R$. We determine the range of $f_a$ and the inflationary parameters $(H_I, T_R)$ consistent with axion dark matter for a quartic potential for the PQ field. We find that $4\times 10^8$ GeV $< f_a < 10^{11}$ GeV can consistently produce axion dark matter. A significant portion of the allowed parameter space predicts rare kaon decays, $K_L \rightarrow (\pi^0 + \rm{missing \; energy})$, and/or suppression of structure formation on small scales., Comment: 40 pages, 6 figures

In the conventional misalignment mechanism, the axion field has a constant initial field value in the early universe and later begins to oscillate. We present an alternative scenario where the axion field has a nonzero initial velocity, allowing an axion decay constant much below the conventional prediction from axion dark matter. This axion velocity can be generated from explicit breaking of the axion shift symmetry in the early universe, which may occur as this symmetry is approximate., Comment: 7+4 pages, 2+2 figures; v2: Supplemental Material and references added, matches journal version

An exact parity replicates the Standard Model giving a Mirror Standard Model, SM $\leftrightarrow$ SM$'$. This "Higgs Parity" and the mirror electroweak symmetry are spontaneously broken by the mirror Higgs, $\left\langle H'\right\rangle = v' \gg \left\langle H\right\rangle$, yielding the Standard Model Higgs as a Pseudo-Nambu-Goldstone Boson of an approximate $SU(4)$ symmetry, with a quartic coupling $\lambda_{SM}(v') \sim 10^{-3}$. Mirror electromagnetism is unbroken and dark matter is composed of $e'$ and $\bar{e}'$. Direct detection may be possible via the kinetic mixing portal, and in unified theories this rate is correlated with the proton decay rate. With a high reheat temperature after inflation, the $e'$ dark matter abundance is determined by freeze-out followed by dilution from decays of mirror neutrinos, $\nu' \rightarrow \ell H$. Remarkably, this requires $v' \sim (10^8 - 10^{10})$ GeV, consistent with the Higgs mass, and a Standard Model neutrino mass of $(10^{-2} - 10^{-1})$ eV, consistent with observed neutrino masses. The mirror QCD sector exhibits a first order phase transition producing gravitational waves that may be detected by future observations. Mirror glueballs decay to mirror photons giving dark radiation with $\Delta N_{\rm eff} \sim 0.03 - 0.4$. With a low reheat temperature after inflation, the $e'$ dark matter abundance is determined by freeze-in from the SM sector by either the Higgs or kinetic mixing portal., Comment: 40 pages, 15 figures

The vanishing of the Higgs quartic coupling of the Standard Model at high energies may be explained by spontaneous breaking of Higgs Parity. Taking Higgs Parity to originate from the Left-Right symmetry of the $SO(10)$ gauge group, leads to a new scheme for precision gauge coupling unification that is consistent with proton decay. We compute the relevant running of couplings and threshold corrections to allow a precise correlation among Standard Model parameters. The scheme has a built-in solution for obtaining a realistic value for $m_b/m_\tau$, which further improves the precision from gauge coupling unification, allowing the QCD coupling constant to be predicted to the level of 1 % or, alternatively, the top quark mass to 0.2 %. Future measurements of these parameters may significantly constrain the detailed structure of the theory. We also study an $SO(10)$ embedding of quark and lepton masses, showing how large neutrino mixing is compatible with small quark mixing, and predict a normal neutrino mass hierarchy. The strong CP problem may be explained by combining Higgs Parity with space-time parity., Comment: 39 pages, 9 figures

An exact spacetime parity replicates the $SU(2) \times U(1)$ electroweak interaction, the Higgs boson $H$, and the matter of the Standard Model. This "Higgs Parity" and the mirror electroweak symmetry are spontaneously broken at scale $v' = \left\langle{H'} \right\rangle \gg \left\langle{H}\right\rangle$, yielding the Standard Model below $v'$ with a quartic coupling that essentially vanishes at $v'$: $\lambda_{SM}(v') \sim 10^{-3}$. The strong CP problem is solved as Higgs parity forces the masses of mirror quarks and ordinary quarks to have opposite phases. Dark matter is composed of mirror electrons, $e'$, stabilized by unbroken mirror electromagnetism. These interact with Standard Model particles via kinetic mixing between the photon and the mirror photon, which arises at four-loop level and is a firm prediction of the theory. Physics below $v'$, including the mass and interaction of $e'$ dark matter, is described by $\textit{one fewer parameter}$ than in the Standard Model. The allowed range of $m_{e'}$ is determined by uncertainties in $(\alpha_s, m_t, m_h)$, so that future precision measurements of these will be correlated with the direct detection rate of $e'$ dark matter, which, together with the neutron electric dipole moment, will probe the entire parameter space., Comment: 29 pages, 5 figures. Matches published version. Added references and clarifications

We study interactions of cosmological relics, $X$, of mass $m$ and electric charge $qe$ in the galaxy, including thermalization with the interstellar medium, diffusion through inhomogeneous magnetic fields and Fermi acceleration by supernova shock waves. We find that for $m \mathop{}_{\textstyle \sim}^{\textstyle <} 10^{10} q \; ~{\rm GeV}$, there is a large flux of accelerated $X$ in the disk today, with a momentum distribution $\propto 1/p^{2.5}$ extending to $(\beta p)_{max} \sim 5 \times10^4 q \; ~{\rm GeV}$. Even though acceleration in supernova shocks is efficient, ejecting $X$ from the galaxy, $X$ are continually replenished by diffusion into the disk from the halo or confinement region. For $m \mathop{}_{\textstyle \sim}^{\textstyle >} 10^{10} q \; ~{\rm GeV}$, $X$ cannot be accelerated above the escape velocity within the lifetime of the shock. The accelerated $X$ form a component of cosmic rays that can easily reach underground detectors, as well as deposit energies above thresholds, enhancing signals in various experiments. We find that nuclear/electron recoil experiments place very stringent bounds on $X$ at low $q$; for example, $X$ as dark matter is excluded for $q$ above $10^{-9}$ for any $m$. For larger $q$, stringent bounds on the fraction of dark matter that can be $X$ are set by Cherenkov and ionization detectors. Nevertheless, very small $q$ is highly motivated by the kinetic mixing portal, and we identify regions of $(m,q)$ that can be probed by future experiments., Comment: 56 pages, 20 figures. Matches published version. Added discussion on EDGES result, clarifications, and references

We examine the theoretical motivations for long-lived particle (LLP) signals at the LHC in a comprehensive survey of Standard Model (SM) extensions. LLPs are a common prediction of a wide range of theories that address unsolved fundamental mysteries such as naturalness, dark matter, baryogenesis and neutrino masses, and represent a natural and generic possibility for physics beyond the SM (BSM). In most cases the LLP lifetime can be treated as a free parameter from the $\mu$m scale up to the Big Bang Nucleosynthesis limit of $\sim 10^7$m. Neutral LLPs with lifetimes above $\sim$ 100m are particularly difficult to probe, as the sensitivity of the LHC main detectors is limited by challenging backgrounds, triggers, and small acceptances. MATHUSLA is a proposal for a minimally instrumented, large-volume surface detector near ATLAS or CMS. It would search for neutral LLPs produced in HL-LHC collisions by reconstructing displaced vertices (DVs) in a low-background environment, extending the sensitivity of the main detectors by orders of magnitude in the long-lifetime regime. In this white paper we study the LLP physics opportunities afforded by a MATHUSLA-like detector at the HL-LHC. We develop a model-independent approach to describe the sensitivity of MATHUSLA to BSM LLP signals, and compare it to DV and missing energy searches at ATLAS or CMS. We then explore the BSM motivations for LLPs in considerable detail, presenting a large number of new sensitivity studies. While our discussion is especially oriented towards the long-lifetime regime at MATHUSLA, this survey underlines the importance of a varied LLP search program at the LHC in general. By synthesizing these results into a general discussion of the top-down and bottom-up motivations for LLP searches, it is our aim to demonstrate the exceptional strength and breadth of the physics case for the construction of the MATHUSLA detector., Comment: 213 pages, 73 figures. Extended Section 2 to add more detailed discussion of LLP reconstruction and analysis, and background rejection. Updated comparison of MATHUSLA RH neutrino sensitivity to other experiments. Updated analysis of long-lived ALPs produced in weak-scale processes and decaying to jets. Various clarifications, fixed typos, and added references. Results and conclusions unchanged

A $Z_2$ symmetry that extends the weak interaction, $SU(2)_L \rightarrow SU(2)_L \times SU(2)'$, and the Higgs sector, $H(2) \rightarrow H(2,1) + H'(1,2)$, yields a Standard Model quartic coupling that vanishes at scale $v' = ~\gg~$. Near $v'$, theories either have a "prime" sector, or possess "Left-Right" (LR) symmetry with $SU(2)' = SU(2)_R$. If the $Z_2$ symmetry incorporates spacetime parity, these theories can solve the strong CP problem. The LR theories have all quark and lepton masses arising from operators of dimension 5 or more, requiring Froggatt-Nielsen structures. Two-loop contributions to $\bar{\theta}$ are estimated and typically lead to a neutron electric dipole moment of order $10^{-27}$e cm that can be observed in future experiments. Minimal models, with gauge group $SU(3) \times SU(2)_L \times SU(2)_L \times U(1)_{B-L}$, have precise gauge coupling unification for $v' = 10^{10\pm1}$ GeV, successfully correlating gauge unification with the observed Higgs mass of $125$ GeV. With $SU(3) \times U(1)_{B-L}$ embedded in $SU(4)$, the central value of the unification scale is reduced from $10^{16-17}$ GeV to below $10^{16}$ GeV, improving the likelihood of proton decay discovery. Unified theories based on $SO(10) \times CP$ are constructed that have $H+H'$ in a ${\bf 16}$ or ${\bf 144}$ and generate higher-dimensional flavor operators, while maintaining perturbative gauge couplings., Comment: 36 pages, 5 figures

The QCD axion is a good dark matter candidate. The observed dark matter abundance can arise from misalignment or defect mechanisms, which generically require an axion decay constant $f_a \sim \mathcal{O}(10^{11})$ GeV (or higher). We introduce a new cosmological origin for axion dark matter, parametric resonance from oscillations of the Peccei-Quinn symmetry breaking field, that requires $f_a \sim (10^8 -10^{11})$ GeV. The axions may be warm enough to give deviations from cold dark matter in Large Scale Structure., Comment: 6 pages, 2 figures; v2: discussions and references added

We consider two copies of the Standard Model, interchanged by an exact parity symmetry, P. The observed fermion mass hierarchy is described by suppression factors $\epsilon^{n_i}$ for charged fermion $i$, as can arise in Froggatt-Nielsen and extra-dimensional theories of flavor. The corresponding flavor factors in the mirror sector are $\epsilon'^{n_i}$, so that spontaneous breaking of the parity P arises from a single parameter $\epsilon'/\epsilon$, yielding a tightly constrained version of Minimal Mirror Twin Higgs, introduced in our previous paper. Models are studied for simple values of $n_i$, including in particular one with SU(5)-compatibility, that describe the observed fermion mass hierarchy. The entire mirror quark and charged lepton spectrum is broadly predicted in terms of $\epsilon'/\epsilon$, as are the mirror QCD scale and the decoupling temperature between the two sectors. Helium-, hydrogen- and neutron-like mirror dark matter candidates are constrained by self-scattering and relic ionization. In each case, the allowed parameter space can be fully probed by proposed direct detection experiments. Correlated predictions are made as well for the Higgs signal strength and the amount of dark radiation., Comment: 43 pages, 15 figures

In all supersymmetric theories, gravitinos, with mass suppressed by the Planck scale, are an obvious candidate for dark matter; but if gravitinos ever reached thermal equilibrium, such dark matter is apparently either too abundant or too hot, and is excluded. However, in theories with an axion, a saxion condensate is generated during an early era of cosmological history and its late decay dilutes dark matter. We show that such dilution allows previously thermalized gravitinos to account for the observed dark matter over very wide ranges of gravitino mass, keV < $m_{3/2}$ < TeV, axion decay constant, $10^9$ GeV < $f_a$ < $10^{16}$ GeV, and saxion mass, 10 MeV < $m_s$ < 100 TeV. Constraints on this parameter space are studied from BBN, supersymmetry breaking, gravitino and axino production from freeze-in and saxion decay, and from axion production from both misalignment and parametric resonance mechanisms. Large allowed regions of $(m_{3/2}, f_a, m_s)$ remain, but differ for DFSZ and KSVZ theories. Superpartner production at colliders may lead to events with displaced vertices and kinks, and may contain saxions decaying to $(WW,ZZ,hh), gg, \gamma \gamma$ or a pair of Standard Model fermions. Freeze-in may lead to a sub-dominant warm component of gravitino dark matter, and saxion decay to axions may lead to dark radiation., Comment: 30 pages, 4 figures

A new scheme for lightest supersymmetric particle (LSP) dark matter is introduced and studied in theories of TeV supersymmetry with a QCD axion, $a$, and a high reheat temperature after inflation, $T_R$. A large overproduction of axinos ($\tilde{a}$) and gravitinos ($\tilde{G}$) from scattering at $T_R$, and from freeze-in at the TeV scale, is diluted by the late decay of a saxion condensate that arises from inflation. The two lightest superpartners are $\tilde{a}$, with mass of order the TeV scale, and $\tilde{G}$ with mass $m_{3/2}$ anywhere between the keV and TeV scales, depending on the mediation scale of supersymmetry breaking. Dark matter contains both warm and cold components: for $\tilde{G}$ LSP the warm component arises from $\tilde{a} \rightarrow \tilde{G}a$, while for $\tilde{a}$ LSP the warm component arises from $\tilde{G} \rightarrow \tilde{a}a$. The free-streaming scale for the warm component is predicted to be of order 1 Mpc (and independent of $m_{3/2}$ in the case of $\tilde{G}$ LSP). $T_R$ can be as high as $10^{16}$ GeV, for any value of $m_{3/2}$, solving the gravitino problem. The PQ symmetry breaking scale $V_{PQ}$ depends on $T_R$ and $m_{3/2}$ and can be anywhere in the range $(10^{10} - 10^{16})$ GeV. Detailed predictions are made for the lifetime of the neutralino LOSP decaying to $\tilde{a}+ h/Z$ and $\tilde{G}+h/Z/\gamma$, which is in the range of $(10^{-1}-10^6)$m over much of parameter space. For an axion misalignment angle of order unity, the axion contribution to dark matter is sub-dominant, except when $V_{PQ}$ approaches $10^{16}$ GeV., Comment: 43 pages, 16 figures

In a Mirror Twin World with a maximally symmetric Higgs sector the little hierarchy of the Standard Model can be significantly mitigated, perhaps displacing the cutoff scale above the LHC reach. We show that consistency with observations requires that the Z2 parity exchanging the Standard Model with its mirror be broken in the Yukawa couplings. A minimal such effective field theory, with this sole Z2 breaking, can generate the Z2 breaking in the Higgs sector necessary for the Twin Higgs mechanism. The theory has constrained and correlated signals in Higgs decays, direct Dark Matter Detection and Dark Radiation, all within reach of foreseen experiments, over a region of parameter space where the fine-tuning for the electroweak scale is 10-50%. For dark matter, both mirror neutrons and a variety of self-interacting mirror atoms are considered. Neutrino mass signals and the effects of a possible additional Z2 breaking from the vacuum expectation values of B-L breaking fields are also discussed., Comment: 42 pages, 8 figures; additional references and discussion on higgs physics and dark matter

Perturbative supersymmetric gauge coupling unification is possible in six theories where complete SU(5) TeV-scale multiplets of vector matter account for the size of the reported $750~{\rm GeV}$ diphoton resonance, interpreted as a singlet multiplet $S = (s+ia)/\sqrt{2}$. One of these has a full generation of vector matter and a unified gauge coupling $\alpha_G \sim 1$. The diphoton signal rate is enhanced by loops of vector squarks and sleptons, especially when the trilinear $A$ couplings are large. If the $SH_u H_d$ coupling is absent, both $s$ and $a$ can contribute to the resonance, which may then have a large apparent width if the mass splitting from $s$ and $a$ arises from loops of vector matter. The width depends sensitively on $A$ parameters and phases of the vector squark and slepton masses. Vector quarks and/or squarks are expected to be in reach of the LHC. If the $SH_uH_d$ coupling is present, $a$ leads to a narrow diphoton resonance, while a second resonance with decays $s \rightarrow hh, W^+ W^-,ZZ$ is likely to be discovered at future LHC runs. In some of the theories a non-standard origin or running of the soft parameters is required, for example involving conformal hidden sector interactions., Comment: 26 pages, 11 figures

We introduce a class of unified supersymmetric axion theories with unified and PQ symmetries broken by the same set of fields at a scale $\sim 2\times 10^{16}$ GeV. A typical domain wall number of order 30 leads to an axion decay constant $f_a$ of order $10^{15}$ GeV. Inflation generates a large saxion condensate giving a reheat temperature $T_R$ below the QCD scale for supersymmetry breaking of order $1-10$ TeV. Axion field oscillations commence in the saxion matter-dominated era near the QCD scale, and recent lattice computations of the temperature dependence of the axion mass in this era allow a controlled calculation of the axion dark matter abundance. A successful prediction of this abundance results for an initial axion misalignment angle of order unity, $\theta_i \sim 1$. A highly correlated set of predictions is discussed for $f_a$, $T_R$, the supersymmetric Higgs mass parameter $\mu$, the amount of dark radiation $\Delta N_{eff}$, the proton decay rate $\Gamma(p \rightarrow e^+ \pi^0)$, isocurvature density perturbations and the $B$-mode of the cosmic microwave background. The last two are particularly interesting when the energy scale of inflation is also of order $10^{16}$ GeV., Comment: 29 pages, 7 figures; v2, version published in Physical Review D

We consider the NMSSM extended to include one vector-like family of quarks and leptons. If (some of) these vector-like matter particles, as the Higgs doublets, have Yukawa couplings to the singlet S that exceed unity at about the same scale $\Lambda \lesssim 10^3$ TeV, this gives the order 40 % enhancement of the tree level Higgs boson mass required in the MSSM to reach 125 GeV. It is conceivable that the Yukawa couplings to the singlet S, although naively blowing up close to $\Lambda$, will not spoil gauge coupling unification. In such a case the unified coupling $\alpha_X$ could be interestingly led to a value not far from unity, thus providing a possible explanation for the number of generations. The characteristic signal is an enhanced resonant production of neutral spin zero particles at LHC, that could even explain the putative diphoton resonance hinted by the recent LHC data at 750 GeV., Comment: 15 pages, 8 figures, 1 table. v2: clarifications added in sections 2 and 3, figures updated, matches published version

A recent signal of 750 GeV diphotons at the LHC can be explained within the framework of supersymmetric unification by the introduction of vector quarks and leptons with Yukawa couplings to a singlet S that describes the 750 GeV resonance. We study the most general set of theories that allow successful gauge coupling unification, and find that these Yukawa couplings are severely constrained by renormalization group behavior: they are independent of ultraviolet physics and flow to values at the TeV scale that we calculate precisely. As a consequence the vector quarks and leptons must be light; typically in the region of 375 GeV to 700 GeV, and in certain cases up to 1 TeV. The 750 GeV resonance may have a width less than the experimental resolution; alternatively, with the mass splitting between scalar and pseudoscalar components of S arising from one-loop diagrams involving vector fermions, we compute an apparent width of 10s of GeV., Comment: 10 pages, 6 figures; to appear in JHEP

Dark matter, $X$, may be generated by new physics at the TeV scale during an early matter-dominated (MD) era that ends at temperature $T_R \ll {\rm TeV}$. Compared to the conventional radiation-dominated (RD) results, yields from both Freeze-Out and Freeze-In processes are greatly suppressed by dilution from entropy production, making Freeze-Out less plausible while allowing successful Freeze-In with a much larger coupling strength. Freeze-In is typically dominated by the decay of a particle $B$ of the thermal bath, $B \rightarrow X$. For a large fraction of the relevant cosmological parameter space, the decay rate required to produce the observed dark matter abundance leads to displaced signals at LHC and future colliders, for any $m_X$ in the range ${\rm keV} < m_X < m_B$ and for values of $m_B$ accessible to these colliders. This result applies whether the early MD era arises after conventional inflation, when $T_R$ is the usual reheat temperature, or is a generic MD era with an alternative origin. In the former case, if $m_X$ is sufficiently large to be measured from kinematics, the reheat temperature $T_R$ can be extracted. Our result is independent of the particular particle physics implementation of $B \rightarrow X$, and can occur via any operator of dimension less than 8 (4) for a post-inflation (general MD) cosmology. An interesting example is provided by DFS axion theories with TeV-scale supersymmetry and axino dark matter of mass GeV to TeV, which is typically overproduced in a conventional RD cosmology. If $B$ is the higgsino, $\tilde h$, Higgs, W and Z particles appear at the displaced decays, $\tilde h \rightarrow h \tilde a, Z \tilde a$ and $\tilde h^\pm \rightarrow W^\pm \tilde a$. The scale of axion physics, $f$, is predicted to be in the range $(3\times10^8 - 10^{12})$ GeV and, over much of this range, can be extracted from the decay length., Comment: 26 pages + appendices, 13 figures; v2, JCAP version

The small and negative value of the Standard Model Higgs quartic coupling at high scales can be understood in terms of anthropic selection on a landscape where large and negative values are favored: most universes have a very short-lived electroweak vacuum and typical observers are in universes close to the corresponding metastability boundary. We provide a simple example of such a landscape with a Peccei-Quinn symmetry breaking scale generated through dimensional transmutation and supersymmetry softly broken at an intermediate scale. Large and negative contributions to the Higgs quartic are typically generated on integrating out the saxion field. Cancellations among these contributions are forced by the anthropic requirement of a sufficiently long-lived electroweak vacuum, determining the multiverse distribution for the Higgs quartic in a similar way to that of the cosmological constant. This leads to a statistical prediction of the Higgs boson mass that, for a wide range of parameters, yields the observed value within the 1$\sigma$ statistical uncertainty of $\sim$ 5 GeV originating from the multiverse distribution. The strong CP problem is solved and single-component axion dark matter is predicted, with an abundance that can be understood from environmental selection. A more general setting for the Higgs mass prediction is discussed., Comment: 30 pages, 10 figures; v2, JHEP version

The observed values of the cosmological constant {\it and} the abundance of Dark Matter (DM) can be successfully understood, using certain measures, by imposing the anthropic requirement that density perturbations go non-linear and virialize to form halos. This requires a probability distribution favoring low amounts of DM, i.e. low values of the PQ scale $f$ for the QCD axion and low values of the superpartner mass scale $\tilde{m}$ for LSP thermal relics. In theories with independent scanning of multiple DM components, there is a high probability for DM to be dominated by a single component. For example, with independent scanning of $f$ and $\tilde{m}$, TeV-scale LSP DM and an axion solution to the strong CP problem are unlikely to coexist. With thermal LSP DM, the scheme allows an understanding of a Little SUSY Hierarchy with multi-TeV superpartners. Alternatively, with axion DM, PQ breaking before (after) inflation leads to $f$ typically below (below) the projected range of the current ADMX experiment of $f = (3 - 30) \times 10^{11}$ GeV, providing strong motivation to develop experimental techniques for probing lower $f$., Comment: 32 pages, 14 figures, version published on JHEP

The measured values of the weak scale, $v$, and the first generation masses, $m_{u,d,e}$, are simultaneously explained in the multiverse, with all these parameters scanning independently. At the same time, several remarkable coincidences are understood. Small variations in these parameters away from their measured values lead to the instability of hydrogen, the instability of heavy nuclei, and either a hydrogen or a helium dominated universe from Big Bang Nucleosynthesis. In the 4d parameter space of $(m_u,m_d,m_e,v)$, catastrophic boundaries are reached by separately increasing each parameter above its measured value by a factor of $(1.4,1.3,2.5,\sim5)$, respectively. The fine-tuning problem of the weak scale in the Standard Model is solved: as $v$ is increased beyond the observed value, it is impossible to maintain a significant cosmological hydrogen abundance for any values of $m_{u,d,e}$ that yield both hydrogen and heavy nuclei stability. For very large values of $v$ a new regime is entered where weak interactions freeze out before the QCD phase transition. The helium abundance becomes independent of $v$ and is determined by the cosmic baryon and lepton asymmetries. To maintain our explanation of $v$ from the anthropic cost of helium dominance then requires universes with such large $v$ to be rare in the multiverse. Implications of this are explored, including the possibility that new physics below 10 TeV cuts off the fine-tuning in $v$., Comment: 26 pages plus appendix, 13 figures

A class of supersymmetric grand unified theories is introduced that has a single scale below the cutoff, that of the supersymmetry breaking masses $\tilde{m}$. For a wide range of the dimensionless parameters, agreement with the observed mass of the Higgs boson determines $\tilde{m} \sim 10^9-10^{13} {\rm GeV}$, yielding Intermediate Scale Supersymmetry. We show that within this framework it is possible for seesaw neutrino masses, axions, and inflation to be described by the scale $\tilde{m}$, offering the possibility of a unified origin of disparate phenomena. Neutrino masses allowing for thermal leptogenesis can be obtained, and the axion decay constant lies naturally in the range $f_a \sim 10^9-10^{11} {\rm GeV}$, consistent with a recent observational suggestion of high scale inflation. A minimal $SU(5)$ model is presented that illustrates these features. In this model, the only states at the grand unified scale are those of the heavy gauge supermultiplet. The grand unified partners of the Higgs doublets have a mass of order $\tilde{m}$, leading to the dominant proton decay mode $p \rightarrow \bar{\nu} K^+$, which may be probed in upcoming experiments. Dark matter may be winos, with mass environmentally selected to the TeV scale, and/or axions. Gauge coupling unification is found to be successful, especially if the wino is at the TeV scale., Comment: 27 pages, 7 figures; minor corrections, references and discussion added