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C. S. Lam

Publications and source records attributed to C. S. Lam.

At least 37 records · Page 2Linked to original sources
arXiv2010

A Higgs Test of Horizontal Symmetry

Identical interactions found in the three families of quarks and leptons suggest the presence of a horizontal symmetry. We discuss how such a symmetry can be tested by measuring the decay rates of Higgs into fermion pairs, and the Higgs production cross section. Depending on the details, there is a chance that the decay widths to the bottom-pair and the tau-pair may be down by more than a factor of 3 or more compared to the usual values, and the fusion production cross section of the Higgs also altered. Whatever the outcome, such a test also serves to constraint horizontal symmetry models.

hep-ph↗
arXiv2010

Horizontal Symmetry from the Bottom Up

A general method to derive horizontal symmetry from a mixing matrix is reviewed. The technique has been applied to deduce leptonic symmetry from the tri-bimaximal neutrino mixing matrix and three of its variations. The question of how the quark mixing can be accommodated within the leptonic symmetry group is discussed, including in this connection an example based on the group $D_4$.

hep-ph↗
arXiv2009

A bottom-up analysis of horizontal symmetry

The group-theoretical method used to derive horizontal symmetry from neutrino mixing is reviewed and expanded. Some misunderstanding in the literature regarding the result is clarified. The method used previously to find vacuum alignments of $S_4$ is applied to compute those of $A_4$ and $S_3$. A study of effective theories based on these three groups shows that in each case there are just enough free parameters to fit all the masses and the remaining mixing parameters. This places constraint on dynamical models because effective theories are just dynamical models with the right-handed fermions integrated out. How quarks may fit into this scheme is briefly discussed.

hep-ph↗
arXiv2008

The Unique Horizontal Symmetry of Leptons

There is a group-theoretical connection between fermion mixing matrices and minimal horizontal symmetry groups. Applying this connection to the tri-bimaximal neutrino mixing matrix, we show that the minimal horizontal symmetry group for leptons is uniquely $S_4$, the permutation group of four objects.

hep-ph↗
arXiv2008

The Horizontal Symmetry for Neutrino Mixing

We argue that the best way to determine horizontal symmetry is from neutrino mixing, and proceed to show that the only finite group capable of yielding the tri-bimaximal mixing for all Yukawa couplings is $S_4$, or any group containing it. The method used is largely group theoretical, but it can be implemented by dynamical schemes in which the Higgs expectation values introduced to break $S_4$ spontaneously are uniquely determined up to an unknown scale for each.

hep-ph↗
arXiv2007

Horizontal Symmetry

The relation between fermion mixing and horizontal symmetry is discussed.

hep-ph↗
arXiv2007

Symmetry of Lepton Mixing

Neutrino mixing is studied from a symmetry perspective, both bottom-up and top-down. In the bottom-up approach, we start from the tri-bimaximal mixing, or one of its three partial patterns, and construct a list of horizontal symmetry groups capable of reproducing the mixng without adjustment of parameters. This list, labeled by an integer $n\ge 3$, is explicitly calculated for $n=3$. In the top-down approach, we start from any finite group possessing a three-dimensional irreducible representation and an order-2 element, give a recipe to determine what mixing pattern it contains, and how to construct a dynamical model to reveal a particular mixing. Finally, we point out that if quark mixing is controlled by symmetry in this way, then there is an exciting possibility to determine most of the CKM mixing parameters by symmetry alone.

hep-ph↗
arXiv2006

Mass Independent Textures and Symmetry

A mass-independent texture is a set of linear relations of the fermion mass-matrix elements which imposes no constraint on the fermionic masses nor the Majorana phases. Magic and 2-3 symmetries are examples. We discuss the general construction and the properties of these textures, as well as their relation to the quark and neutrino mixing matrices. Such a texture may be regarded as a symmetry, whose unitary generators of the symmetry group can be explicitly constructed. In particular, the symmetries connected with the tri-bimaximal neutrino mixing matrix are discussed, together with the physical consequence of breaking one symmetry but preserving another.

hep-ph↗
arXiv2006

Magic Neutrino Mass Matrix and the Bjorken-Harrison-Scott Parameterization

Observed neutrino mixing can be described by a tribimaximal MNS matrix. The resulting neutrino mass matrix in the basis of a diagonal charged lepton mass matrix is both 2-3 symmetric and magic. By a magic matrix, I mean one whose row sums and column sums are all identical. I study what happens if 2-3 symmetry is broken but the magic symmetry is kept intact. In that case, the mixing matrix is parameterized by a single complex parameter $U_{e3}$, in a form discussed recently by Bjorken, Harrison, and Scott.

hep-ph↗
arXiv2005

What if $θ_{13}$ Is Small?

In the basis where the charged lepton mass matrix is diagonal, the left-handed neutrino mass matrix is invariant under the permutation of the second and third generations if, and only if, the reactor angle $θ_{13}$ is zero and the atmospheric mixing angle $θ_{23}$ is maximal. In the presence of the seesaw mechanism, this symmetry leads to an inverted hierarchy, with $m_3=0$. This inverted mass spectrum is doubly protected if the right-handed neutrinos also have a 2-3 symmetry.

hep-ph↗
arXiv2005

Neutrino 2-3 Symmetry and Inverted Hierarchy

Neutrino oscillation data indicate the presence of a 2-3 symmetry for the left-handed neutrinos. We show that this symmetry between the second and third generations cannot be extended to include the charged leptons, no matter what basis we use. We point out that if this symmetry is also independently valid for the right-handed neutrinos, then the active neutrino spectrum is inverted, with $m_3=0$. This conclusion remains valid even when the left-handed 2-3 symmetry is broken by a non-maximal atmospheric mixing angle $θ_{23}$, or a non-zero reactor angle $θ_{13}$. As previously shown by Mohapatra, Nasri, and Yu, such a symmetry also gives rise to interesting consequences on the leptogenesis asymmetry parameter $ε_1$.

hep-ph↗
arXiv2004

Back-Reaction of Cosmological Perturbations in the Infinite Wavelength Approximation

Cosmological perturbations in an expanding universe back-react on the space-time in which they propagate. Calculations to lowest non-vanishing order in perturbation theory indicate that super-Hubble-scale fluctuations act as a negative and time-dependent cosmological constant and may thus lead to a dynamical relaxation mechanism for the cosmological constant. Here we present a simple model of how to understand this effect from the perspective of homogeneous and isotropic cosmology. Our analysis, however, also shows that an effective spatial curvature is induced, indicating potential problems in realizing the dynamical relaxation of the cosmological constant by means of back-reaction.

hep-th↗
arXiv2004

Invariant and Group Theoretical Integrations over the U(n) Group

In a previous article, an `invariant method' to calculate monomial integrals over the U(n) group was introduced. In this paper, we study the more traditional group-theoretical method, and compare its strengths and weaknesses with those of the invariant method. As a result, we are able to introduce a `hybrid method' which combines the respective strengths of the other two methods. There are many examples in the paper illustrating how each of these methods works.

math-ph↗
arXiv2003

Invariant Integration over the Unitary Group

Integrals for the product of unitary-matrix elements over the U(n) group will be discussed. A group-theoretical formula is available to convert them into a multiple sum, but unfortunately the sums are often tedious to compute. In this paper, we develop an alternative method in which these sums are avoided, and group theory is rendered unnecessary. Only unitarity and the invariance of the Haar measure are required for the computation. The method can also be used to get a closed expression for the simpler integral of monomials over a hypersphere.

math-ph↗
arXiv2003

The Absorptive Extra Dimensions

It is well known that gravity and neutrino oscillation can be used to probe large extra dimensions in a braneworld scenario. We argue that neutrino oscillation remains a useful probe even when the extra dimensions are small, because the brane-bulk coupling is likely to be large. Neutrino oscillation in the presence of a strong brane-bulk coupling is vastly different from the usual case of a weak coupling. In particular, some active neutrinos could be absorbed by the bulk when they oscillate from one kind to another, a signature which can be taken as the presence of an extra dimension. In a very large class of models which we shall discuss, the amount of absorption for all neutrino oscillations is controlled by a single parameter, a property which distinguishes extra dimensions from other mechanisms for losing neutrino fluxes.

hep-ph↗
arXiv2003

Probing Extra Dimensions with Neutrino Oscillations

In the braneworld scenario, gravity and neutrino oscillation can both be used to detect the presence of an extra dimension. We argue that neutrino oscillation is particularly suitable if the size of the extra dimension is small, in which case the signature for the extra dimension is the disappearance of active neutrino fluxes into the bulk, caused by the destructive interference from the Kaluza-Klein states. We discuss a class of models to illustrate this general feature.

hep-ph↗
arXiv2002

Perturbative Computation of Glueball Superpotentials

Using N=1 superspace techniques in four dimensions we show how to perturbatively compute the superpotential generated for the glueball superfield upon integrating out massive charged fields. The technique applies to arbitrary gauge groups and representations. Moreover we show that for U(N) gauge theories admitting a large N expansion the computation dramatically simplifies and we prove the validity of the recently proposed recipe for computation of this quantity in terms of planar diagrams of matrix integrals.

hep-th↗