arXiv subjects
Publications and source records attributed to Lawrence Hall.
What is the form of the neutrino mass matrix which governs the oscillations of the atmospheric and solar neutrinos? Features of the data have led to a dominant viewpoint where the mass matrix has an ordered, regulated pattern, perhaps dictated by a flavor symmetry. We challenge this viewpoint, and demonstrate that the data are well accounted for by a neutrino mass matrix which appears to have random entries.
Theories where the Standard Model fields reside on a 3-brane, with a low fundamental cut-off and extra dimensions, provide alternative solutions to the gauge hierarchy problem. However, generating flavor at the TeV scale while avoiding flavor-changing difficulties appears prohibitively difficult at first sight. We argue to the contrary that this picture allows us to lower flavor physics close to the TeV scale. Small Yukawa couplings are generated by ``shining'' badly broken flavor symmetries from distant branes, and flavor and CP-violating processes are adequately suppressed by these symmetries. We further show how the extra dimensions avoid four dimensional disasters associated with light fields charged under flavor. We construct elegant and realistic theories of flavor based on the maximal U(3)^5 flavor symmetry which naturally generate the simultaneous hierarchy of masses and mixing angles. Finally, we introduce a new framework for predictive theories of flavor, where our 3-brane is embedded within highly symmetrical configurations of higher-dimensional branes.
If spacetime contains large compact extra dimensions, the fundamental mass scale of nature, $Lambda$, may be close to the weak scale, allowing gravitational physics to significantly modify electroweak symmetry breaking. Operators of the form $(1/Lambda^2) |phi^* D phi|^2$ and $(1/Lambda^2) phi^* W B phi$, where $W$ and $B$ are the SU(2) and U(1) field strengths and $phi$ is the Higgs field, remove the precision electroweak bound on the Higgs boson mass for values of $Lambda$ in a wide range: $4 TeV < Lambda < 11 TeV$. Within this framework, there is no preference between a light Higgs boson, a heavy Higgs boson, or a non-linearly realized SU(2)xU(1) symmetry beneath $Lambda$. If there is a Higgs doublet, then operators of the form $(1/Lambda^2) phi^* phi (G^2, F^2)$, where $G$ and $F$ are the QCD and electromagnetic field strengths, modify the production of the Higgs boson by gluon-gluon fusion, and the decay of the Higgs boson to 2 photons, respectively. At Run II of the Tevatron collider, a 2-photon signal for extra dimensions will be discovered if $Lambda$ is below 2.5 (1) TeV for a Higgs boson of mass 100 (300) GeV. Furthermore, such a signal would point to gravitational physics, rather than to new conventional gauge theories at $Lambda$. The discovery potential of the LHC depends sensitively on whether the gravitational amplitudes interfere constructively or destructively with the standard model amplitudes, and ranges from $Lambda$ = 3 - 10 (2 - 4) TeV for a light (heavy) Higgs boson.
Recent improvements to the limit of Delta M_{B_s} imply that pure superweak theories, while not excluded, no longer provide a good fit to the data. A class of general superweak theories is introduced in which all flavor changing interactions are governed by an approximate flavor symmetry which gives a ``3 mechanism''. These theories are in good agreement with data, and predict low values for |V_{td}|, |V_{ub}/V_{cb}|, B(K^+ to pi^+ nu nubar), epsilon'/epsilon and CP asymmetries in B decays, and high values for Delta M_{B_s} and f_B sqrt{B_B}. An important example of such a theory is provided by weak scale supersymmetric theories with soft CP violation. The CP violation originates in the squark mass matrix, and, with phases of order unity, flavor symmetries can yield a correct prediction for the order of magnitude of epsilon_K.
A grand unified $SU(5)$ theory is constructed with a hierarchical breaking of a $U(2)$ flavor symmetry. The small parameters of the squark and slepton mass matrices, necessary to solve the supersymmetric flavor-changing problem, and the inter-generational quark and lepton mass hierarchies are both generated from the $U(2)$ symmetry breaking parameters. The flavor interactions of the theory are tightly constrained, with just 10 free real parameters for both the fermion and scalar sectors. All but one of the 8 small fermion mass ratios, and all of the 3 small Cabibbo-Kobayashi-Maskawa mixing angles, can be understood without introducing small dimensionless Yukawa parameters. Predictions are made for 2 of the Cabibbo-Kobayashi-Maskawa mixing angles and for 2 of the fermion masses. The six flavor mixing matrices which appear at the neutralino vertices, and which in general are arbitrary unitary matrices, are determined in terms of just a single free parameter.
In a generic supersymmetric extension of the Standard Model, whether unified or not, a simple and well motivated U(2) symmetry, acting on the lightest two generations, completely solves the flavour changing problem and necessarily leads to a predictive texture for the Yukawa couplings.
The flavor changing and CP violating phenomena predicted in supersymmetric unified theories as a consequence of the large top quark Yukawa coupling, are investigated in the quark sector and compared with related phenomena in the lepton sector, considered previously. In particular we study $\varepsilon_K$, $\varepsilon_K'/\varepsilon_K$, $Δm_B$, $b\to sγ$, the neutron electric dipole moment, $d_n$, and CP violation in neutral $B$ meson decays, both in minimal~SU(5) and~SO(10) theories. The leptonic signals are generically shown to provide more significant tests of quark-lepton unification. Nevertheless, mostly in the~SO(10) case, a variety of hadronic signals is also possible, with interesting correlations among them.
The smallness of fermion masses and mixing angles has recently been been attributed to approximate global $U(1)$ symmetries, one for each fermion type. The parameters associated with these symmetry breakings are estimated here directly from observed masses and mixing angles. It turns out that although flavor changing reaction rates may be acceptably small in electroweak theories with several scalar doublets without imposing any special symmetries on the scalars themselves, such theories generically yield too much CP violation in the neutral kaon mass matrix. Hence in these theories CP must also be a good approximate symmetry. Such models provide an alternative mechanism for CP violation and have various interesting phenomenological features.
The fermion mass and mixing angle predictions of a recently proposed framework are investigated for large b and $τ$ Yukawa couplings. A new allowed region of parameters is found for this large $\tan β$ case. The two predictions which are substantially altered, $m_t$ and $\tan β$, are displayed, including the dependence on the inputs $|V_{cb}|$, $m_c$, $m_b$ and $α_s$. A simple restriction on this framework yields an additional prediction, for $|V_{cb}|$. If the b,t, and $τ$ Yukawas are equal at the GUT scale then $|\Vcb|$ is predicted and the top quark mass is constrained to lie in the range $\mt = 179. \pm 4.$ GeV.
Using supersymmetric grand unified theories, we have recently invented a framework which allows the prediction of three quark masses, two of the parameters of the Kobayashi-Maskawa matrix and tan $β$, the ratio of the two vevs. These predictions are used to calculate $ε$ and $ε'$ in the kaon system, B meson mass mixing and the size of CP asymmetries in the decays of neutral B mesons to explicit final states of given CP.