Baryon Number, Lepton Number, and Operator Dimension in the Standard Model

We prove that for a given operator in the Standard Model (SM) with baryon number B and lepton number L, that the operator's dimension is even (odd) if (B-L)/2 is even (odd). Consequently, this establishes the veracity of statements that were long observed or expected to be true, but not proven, e.g., operators with B-L=0 are of even dimension, B-L must be an even number, etc. These results remain true even if the SM is augmented by any number of right-handed neutrinos with L=1.Comment: 5 page

Gravitational Effects on Measurements of the Muon Dipole Moments

If the technology for muon storage rings one day permits sensitivity to precession at the order of $10^{-8}$ Hz, the local gravitational field of Earth can be a dominant contribution to the precession of the muon, which, if ignored, can fake the signal for a nonzero muon electric dipole moment (EDM). Specifically, the effects of Earth's gravity on the motion of a muon's spin is indistinguishable from it having a nonzero EDM of magnitude $d_\mu \sim 10^{-29}$ e cm in a storage ring with vertical magnetic field of $\sim$ 1 T, which is significantly larger than the expected upper limit in the Standard Model, $d_\mu \lesssim 10^{-36}$ e cm. As a corollary, measurements of Earth's local gravitational field using stored muons would be a unique test to distinguish classical gravity from general relativity with a bonafide quantum mechanical entity, i.e., an elementary particle's spin.Comment: 5 pages; corrected calculation, qualitative results unchange

Model-Independent Extraction of ∣Vcb∣|V_{cb}| from Bˉ→D∗ℓν‾\bar{B}\rightarrow D^* \ell \overline{\nu}

We fit the unfolded data of $\bar{B}^0\rightarrow D^{*+} \ell \overline{\nu}$ from the Belle experiment, where $\ell \equiv e, \mu$, using a method independent of heavy quark symmetry to extrapolate to zero-recoil and extract the value of $|V_{cb}|$. This results in $|V_{cb}| = (41.9^{~+2.0}_{~-1.9})\times 10^{-3}$, which is robust to changes in the theoretical inputs and very consistent with the value extracted from inclusive semileptonic $B$ decays.Comment: 8 pages, 3 figures; corrected minor typographical error

Hilbert Series and Operator Basis for NRQED and NRQCD/HQET

We use a Hilbert series to construct an operator basis in the $1/m$ expansion of a theory with a nonrelativistic heavy fermion in an electromagnetic (NRQED) or color gauge field (NRQCD/HQET). We present a list of effective operators with mass dimension $d\leq 8$. Comparing to the current literature, our results for NRQED agree for $d\leq 8$, but there are some discrepancies in NRQCD/HQET at $d=7$ and 8.Comment: 13 pages, 1 figure, 3 tables. Minor typographical errors correcte

Lepton-Flavored Dark Matter

In this work, we address two paradoxes. The first is that the measured dark-matter relic density can be satisfied with new physics at O(100 GeV - 1 TeV), while the null results from direct-detection experiments place lower bounds of O(10 TeV) on a new-physics scale. The second puzzle is that the severe suppression of lepton-flavor-violating processes involving electrons, e.g. mu->3e, tau->e mu mu, etc., implies that generic new-physics contributions to lepton interactions cannot exist below O(10 - 100 TeV), whereas the 3.6sigma deviation of the muon g-2 from the standard model can be explained by a new-physics scale < O(1 TeV). Here, we suggest that it may not be a coincidence that both the muon g-2 and the relic density can be satisfied by a new-physics scale < 1 TeV. We consider the possibility of a gauged lepton-flavor interaction that couples at tree level only to mu- and tau-flavored leptons and the dark sector. Dark matter thus interacts appreciably only with particles of mu and tau flavor at tree level and has loop-suppressed couplings to quarks and electrons. Remarkably, if such a gauged flavor interaction exists at a scale O(100 GeV - 1 TeV), it allows for a consistent phenomenological framework, compatible with the muon g-2, the relic density, direct detection, indirect detection, charged-lepton decays, neutrino trident production, and results from hadron and e+e- colliders. We suggest experimental tests for these ideas at colliders and for low-energy observables.Comment: includes additional discussions, results unchange