Two-loop anomalous dimensions and one-loop renormalization scheme matching factors are calculated for six-quark operators responsible for neutron-antineutron transitions. When combined with lattice QCD determinations of the matrix elements of these o
perators, our results can be used to reliably predict the neutron-antineutron vacuum transition time, $tau_{nbar{n}}$, in terms of basic parameters of baryon-number violating beyond-the-Standard-Model theories. The operators are classified by their chiral transformation properties, and a basis in which there is no operator mixing due to strong interactions is identified. Operator projectors that are required for non-perturbative renormalization of the corresponding lattice QCD six-quark operator matrix elements are constructed. A complete calculation of $delta m = 1/tau_{nbar{n}}$ in a particular beyond-the-Standard-Model theory is presented as an example to demonstrate how operator renormalization and results from lattice QCD are combined with experimental bounds on $delta m$ to constrain the scale of new baryon-number violating physics. At the present computationally accessible lattice QCD matching scale of $sim$ 2 GeV, the next-to-next-to-leading-order effects calculated in this work correct the leading-order plus next-to-leading-order $delta m$ predictions of beyond-the-Standard-Model theories by $< 26%$. Next-to-next-to-next-to-leading-order effects provide additional unknown corrections to predictions of $delta m$ that are estimated to be $< 7%$.
We present a new model of Stealth Dark Matter: a composite baryonic scalar of an $SU(N_D)$ strongly-coupled theory with even $N_D geq 4$. All mass scales are technically natural, and dark matter stability is automatic without imposing an additional d
iscrete or global symmetry. Constituent fermions transform in vector-like representations of the electroweak group that permit both electroweak-breaking and electroweak-preserving mass terms. This gives a tunable coupling of stealth dark matter to the Higgs boson independent of the dark matter mass itself. We specialize to $SU(4)$, and investigate the constraints on the model from dark meson decay, electroweak precision measurements, basic collider limits, and spin-independent direct detection scattering through Higgs exchange. We exploit our earlier lattice simulations that determined the composite spectrum as well as the effective Higgs coupling of stealth dark matter in order to place bounds from direct detection, excluding constituent fermions with dominantly electroweak-breaking masses. A lower bound on the dark baryon mass $m_B gtrsim 300$ GeV is obtained from the indirect requirement that the lightest dark meson not be observable at LEP II. We briefly survey some intriguing properties of stealth dark matter that are worthy of future study, including: collider studies of dark meson production and decay; indirect detection signals from annihilation; relic abundance estimates for both symmetric and asymmetric mechanisms; and direct detection through electromagnetic polarizability, a detailed study of which will appear in a companion paper.
We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm$)^3$ and (11 fm$)^3$ and temperatures between
139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of $N_t=8$. The disconnected chiral susceptibility, $chi_{rm disc}$ shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD ``phase transition is not first order but a continuous cross-over for $m_pi=135$ MeV. The peak location determines a pseudo-critical temperature $T_c = 155(1)(8)$ MeV. Chiral $SU(2)_Ltimes SU(2)_R$ symmetry is fully restored above 164 MeV, but anomalous $U(1)_A$ symmetry breaking is non-zero above $T_c$ and vanishes as $T$ is increased to 196 MeV.
We report on a study of the finite-temperature QCD transition region for temperatures between 139 and 196 MeV, with a pion mass of 200 MeV and two space-time volumes: $24^3times8$ and $32^3times8$, where the larger volume varies in linear size betwee
n 5.6 fm (at T=139 MeV) and 4.0 fm (at T=195 MeV). These results are compared with the results of an earlier calculation using the same action and quark masses but a smaller, $16^3times8$ volume. The chiral domain wall fermion formulation with a combined Iwasaki and dislocation suppressing determinant ratio gauge action are used. This lattice action accurately reproduces the $sua$ and $ua$ symmetries of the continuum. Results are reported for the chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum. We find a pseudo-critical temperature, $T_c$, of approximately 165 MeV consistent with previous results and strong finite volume dependence below $T_c$. Clear evidence is seen for $ua$ symmetry breaking above $T_c$ which is quantitatively explained by the measured density of near-zero modes in accordance with the dilute instanton gas approximation.
