Search

Theoretical physicists describe nature by i) building a theory model and ii) determining the model parameters. The latter step involves the dual aspect of both fitting to the existing experimental data and satisfying abstract criteria like beauty, naturalness, etc. We use the Yukawa quark sector as a toy example to demonstrate how both of those tasks can be accomplished with machine learning techniques. We propose loss functions whose minimization results in true models that are also beautiful as measured by three different criteria - uniformity, sparsity, or symmetry., Comment: 13 pages, 9 figures. arXiv admin note: text overlap with arXiv:2311.00087

The discovery process of building new theoretical physics models involves the dual aspect of both fitting to the existing experimental data and satisfying abstract theorists' criteria like beauty, naturalness, etc. We design loss functions for performing both of those tasks with machine learning techniques. We use the Yukawa quark sector as a toy example to demonstrate that the optimization of these loss functions results in true and beautiful models., Comment: 10 pages, 6 figures; Accepted by "AI for Science" NeurIPS 2023 Workshop

In 2021, to mark the occasion of 2021 was Y\^oichir\^o Nambu's birth centenary, we engaged in writing a historical/scientific description of his most incisive papers. Nambu was the humblest genius we have known, and we expected to find some of his great but forgotten insights. We found one, written in 1947: ``A Note on the Eigenvalue Problem in Crystal Statistics", where he formulates and solves the $(N\times N)$ Ising model in a $2N$-dimensional Hilbert space

At the occasion of his eighty fifth birthday, I wish to to recognize the crucial role that my advisor, Professor Ayalam Balachandran, played in enabling me to evolve from engineering to physics. So many years later, this student presents his latest efforts: the importance of asymmetry in the Yukawa matrices. We start with a purely phenomenological approach with Tri-Bi-Maximal mixing as input: it predicts the value of the CP-violating angle with the three mixing angles within one sigma of their pdf values. To ensure as much naturalness as possible, a model which starts from $SU_5$ and extends to $E_6$ is discussed, in the context of finite family groups which are subgroups $G_2$.

Contribution to the Peter Freund Memorial volume: a glossary of group-theoretic facts that may relate the seven-dimensional Freund-Rubin coset to Yukawa textures., Comment: 10 pages

We extend the recently proposed $SU(5) \times \mathcal{T}_{13}$ model for the asymmetric texture to the up-type quark and seesaw sectors. The hierarchical up-type quark masses are generated from higher-dimensional operators involving family-singlet Higgses, gauge-singlet familons, and vectorlike messengers. The complex-tribimaximal (TBM) seesaw mixing arises from the vacuum structure of a minimal number of familons, resulting in an alignment between the Yukawa and Majorana matrices of the seesaw formula. Introducing four right-handed neutrinos, normal ordering of the light neutrino masses is obtained, with $m_{\nu_1} = 27.6\ \mathrm{meV}$, $m_{\nu_2} = 28.9\ \mathrm{meV}$ and $m_{\nu_3} = 57.8\ \mathrm{meV}$. Their sum almost saturates Planck's cosmological upper bound ($120$ $\text{meV}$). The right-handed neutrino masses are expressed in terms of two parameters for a particular choice of familon vacuum alignment. We predict the $\require{cancel}\cancel{CP}$ Jarlskog-Greenberg invariant to be $|\mathcal{J}| = 0.028$, consistent with the current PDG estimate, and Majorana invariants $|\mathcal{I}_1| = 0.106$ and $|\mathcal{I}_2| = 0.011$. A sign ambiguity in the model parameters leads to two possibilities for the invariant mass parameter $|m_{\beta \beta}|$: $13.02$ or $25.21$ $\text{meV}$, both within an order of magnitude of the most rigorous experimental upper limit ($61$--$165$ $\text{meV}$)., Comment: 36 pages, 2 figures, minor changes to match with the published version

We propose $\mathcal{T}_{13} = \mathcal{Z}_{13} \rtimes \mathcal{Z}_3$ as the underlying non-Abelian discrete family symmetry of the asymmetric texture presented in arXiv:1805.10684 [hep-ph]. Its mod 13 arithmetic distinguishes each Yukawa matrix element of the texture. We construct a model of effective interactions that singles out the asymmetry and equates, without fine-tuning, the products of down-quark and charged-lepton masses at a GUT-like scale., Comment: Major change from previous version: the symmetry $\mathcal{Z}_4$ has been changed to $\mathcal{Z}_5$ to prohibit a new unwanted vertex, 26 pages, version accepted for publication in Physical Review D

As in Greek mythology, the neutrino was born in the mind of Wolfgang Pauli to salvage a fundamental principle. Its existence met with universal skepticism by a scientific community used to infer particles from experiment. Its detection in 1956 brought particle physics acceptance; its chirality explained maximal parity violation in $\beta$ decay; its (apparent) masslessness led theorists to imagine new symmetries. Neutrinos are pioneers of mutli-messenger astronomy, from the Sun, from SNA1987, and now through IceCube's blazar. The discovery of neutrino masses opened a new era in particle physics aswell as unexplored windows on the universe. -Tiny neutrino masses suggest new physics at very short distances through the Seesaw. - Neutrinos and quarks, unified by gauge structure, display different mass and mixing patterns: small quark mixing angles and two large neutrino mixing angles. This difference in mass and mixings in the midst of gauge unification may be an important clue towards Yukawa unification. - Neutrino mixings provide a new source of CP-violation, and may solve the riddle of matter-antimatter asymmetry. We present a historical journey of these "enfants terribles" of particle physics and their importance in understanding our universe., Comment: Invited Talk at the "History of the Neutrino" Conference, September 2018, Paris

We construct a texture where the Seesaw matrix is diagonalized by the TriBiMaximal (TBM) matrix with a phase. All CKM and PMNS angles are within their pdg values, and the mass relations of quarks and charged leptons extrapolated to GUT scale are satisfied, including the Gatto relation. The novel ingredient is the asymmetry of the down-quark and charged lepton Yukawa matrices. Explaining the reactor angle requires a $\require{cancel} \cancel {CP}$ phase in the TBM matrix, resulting in the Jarlskog-Greenberg invariant at $|J|=0.028$, albeit with an undetermined sign. While $SO(10)$ restrains the right-handed neutrino Majorana matrix, the neutrino masses are left undetermined., Comment: 23 pages

Reminiscences of my intellectual and personal interactions with Professor Nambu, and discussion of his contributions to string theory. Switching to my own research, by expressing the string coordinates as bispinors, I suggest a kinematical framework for the interacting (2,0) theory on the light-cone by using chiral constrained "Viking" superfields., Comment: 17 pages, based on talk at the Nambu Memorial Symposium

Using an $SO(10)$-inspired form for the Dirac neutrino mass, we map the neutrino data to right-handed neutrino Majorana mass-matrix, $\mathcal M$, and investigate a special form with \emph{seesaw} tribimaximal mixing; it predicts a normal hierarchy, and the values of the light neutrino masses. It may be generated by mapping the top quark hierarchy onto the vacuum values of familon fields transforming under the family group $\mathcal{ PSL}_2(7)$. We next investigate the hypothesis that these familons play a dual role, generating a hierarchy in the supersymmetric $\mathbf \mu$-mass matrix of Higgses carrying family quantum numbers. A special $\mathcal{ PSL}_2(7)$ invariant coupling produces a $\mu$-matrix with a hierarchy of thirteen orders of magnitude. Only one Higgs field (per hypercharge sector) is light enough (with a $\mu$-mass $\sim 10-100$ GeV) to be destabilized by SUSY soft breaking at the TeV scale, and upon spontaneous symmetry breaking, gives \emph{tree-level} masses for the heaviest family., Comment: 26 pages, no figures

We present the results of a numerical search for the Dirac Yukawa matrices of the Standard Model, consistent with the quark and lepton masses and their mixing angles. We assume a diagonal up-quark matrix, natural in $\bs{\m Z_7 \rtimes \m Z_3}$, Bimaximal or Tri-bimaximal seesaw mixing, and $SU(5)$ unification to relate the down-quark and charged lepton Dirac Yukawa matrices using Georgi-Jarlskog mechanisms. The measured value of $\theta_{13}$ requires an asymmetric down-quark Yukawa matrix. Satisfying the measured values of both $\theta_{13}$ and the electron mass restricts the number of solutions, underlying the importance of the recent measurement of the reactor angle., Comment: 59 pages, 10 figures, 18 tables. Mathematica file included as an ancillary file

We describe the early evolution of theories with fermion-boson symmetry, Comment: To appear in the special issue of the EPJ C journal entitled "SUSY after the Higgs discovery"

We present a model in which the Supersymmetric Standard Model is augmented by the family symmetry $\bs{\m Z_7 \rtimes \m Z_3}$. Motivated by $SO(10)$, where the charge two-thirds and neutral Dirac Yukawa matrices are related, we propose, using family symmetry, a special form for the seesaw Majorana matrix; it contains a squared correlated hierarchy, allowing it to mitigate the severe hierarchy of the quark sector. It is reproduced naturally by the invariant operators of $\bs{\m Z_7 \rtimes \m Z_3}$, with the hierarchy carried by familon fields. In addition to relating the hierarchy of the $\Delta I_{\rm w}=1/2$ to the $\Delta I_{\rm w}=0$ sector, it contains a Gatto-Sartori-Tonin like relation, predicts a normal hierarchy for Tri-bimaximal and Golden Ratio mixings, and gives specific values for the light neutrino masses., Comment: 33 pages, 1 figure. This revised version omits a section where a particular linear combination of dimension-five operators was mistakenly claimed to produce the special form of the Majorana matrix. The main changes are to the Introduction, Sec. 5.1 of the previous version, and Summary and Conclusions. In addition to minor changes throughout, we have corrected an erroneous sign in Eq. 19

In this paper delivered by Murray Gell-Mann at the Stony Brook Supergravity Workshop in 1979, several paths to unification are discussed, from N=8 supergravity to $SU_5$, $SO_{10}$, and $E_6$. Generalizations of $SO_{10}$ to spinor representations of larger groups are introduced. A natural mechanism for generating tiny neutrino masses is proposed in the context of $SO_{10}$, and finally, focus on $SU_3$ rather than $SU_2$ or $SO_3$ family symmetries is noted., Comment: Retro-preprint of 1979 paper. Originally published in Supergravity, P. van Nieuwenhuizen and D.Z. Freedman, eds, North Holland Publishing Co, 1979

We present a toy model in which the Higgs sector fields transform as non-Abelian representations of a family symmetry group, and consider the possibility that the extra family partners of the Higgs particles act as messengers for both supersymmetry and family symmetry breakings. Although such mediation schemes generically produce family dependent soft supersymmetry breaking terms at the messenger scale, we demonstrate the existence of a focusing mechanism which may erase such hierarchies through renormalization group running., Comment: 38 Pages, 11 Figures. Updated file to include minor changes, update figures, and to correct errors in Eq. 4.15. An error was found in the first version soft masses (Eq.4.15), however the conclusions of the paper are unaffected. We have included the Journal reference and DOI

The SuperConformal theory in three space-time dimensions with SO(16) $R$-symmetry, 128 bosons, and 128 fermions, cannot sustain interactions. This result is obtained using both light-cone superspace techniques which rely on algebraic consistency, and covariant methods which rely on SO(16) Fierz identities which fail to produce the desired algebra., Comment: 14 pages

Five elementary lectures delivered at TASI 2011 on the Standard Model, its extensions to neutrino masses, flavor symmetries, and Grand-Unification.

We give a relatively simple explanation of the light-cone supergraph prediction for the UV properties of the maximally supersymmetric theories. It is based on the existence of a dynamical supersymmetry which is not manifest in the light-cone supergraphs. It suggests that N=4 supersymmetric Yang-Mills theory is UV finite and N=8 supergravity is UV finite at least until 7 loops whereas the $n$-point amplitudes have no UV divergences at least until $L=n+3$. Here we show that this prediction can be deduced from the properties of light-cone supergraphs analogous to the light-by-light scattering effect in QED. A technical aspect of the argument relies on the observation that the dynamical supersymmetry action is, in fact, a compensating field-dependent gauge transformation required for the retaining the light-cone gauge condition $A_+=0$., Comment: 9 pages

The light-cone superspace version of the d=3, N=8 superconformal theory of Bagger, Lambert and Gustavsson (BLG) is obtained as a solution to constraints imposed by OSp(2,2|8) superalgebra. The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformation., Comment: 45 pages, v2: reference added, minor typos corrected, published version

The recently formulated Bagger-Lambert-Gustavsson (BLG) theory in three dimensions is described in terms of a constrained chiral superfield in light-cone superspace. We discuss the use of Superconformal symmetry to determine the form of its interactions, in complete analogy with N=4 SuperYang-Mills in four dimensions., Comment: Invited Talk at Shifmania, St PAul-Minneapolis, May 2009

Assuming that finite family symmetries are gauged, we derive discrete anomaly conditions for various non-Abelian groups. We thus provide new constraints for flavor model building, in which discrete non-Abelian symmetries are employed to explain the tri-bimaximal mixing pattern in the lepton sector., Comment: 28 pages, Section 6 slightly extended, matches published version

We derive the non-linear action of E8(8) on the constrained chiral superfield in the light-cone superspace with eight complex Grassmann variables. We construct (to lowest order in the coupling) the sixteen dynamical supersymmetries which generate a Hamiltonian with E8(8) invariance in three space-time dimensions, and show that it has only interactions with even powers of the coupling constant., Comment: 17 pages, v2: A few sentences added, few typos corrected, JHEP version

We construct all quintic invariants in five variables with simple Non-Abelian finite symmetry groups. These define Calabi-Yau three-folds which are left invariant by the action of A_5, A_6 or PSL_2(11)., Comment: 18 pages, typos corrected, matches published version

We use the Cremmer-Julia E_7(7) non-linear symmetry of N=8 Supergravity to derive its order $\kappa^2$ on-shell Hamiltonian in terms of one chiral light-cone superfield. By requiring that E_7(7) commute with the super-Poincare group, we deduce to lowest non-trivial order in $\kappa$, the light cone E_7(7) transformations of all fields of the theory, including the graviton. We then derive the dynamical supersymmetry transformation to order $\kappa^2$, and express the Hamiltonian as a quadratic form in the chiral superfield., Comment: 21 pages, v2. the order-\kappa^2 form of the dynamical supersymmetry transformation corrected. v3. references and a few comments added, version to appear in JHEP

The recently measured unexpected neutrino mixing patterns have caused a resurgence of interest in the study of finite flavor groups with two- and three-dimensional irreducible representations. This paper details the mathematics of the two finite simple groups with such representations, the Icosahedral group A_5, a subgroup of SO(3), and PSL_2(7), a subgroup of SU(3)., Comment: 42 pages, matches published version, references added

I worked on String Theory over a period of five years during the First String Era, the most intellectually satisfying years of my scientific life. One of the early prospectors in the String Theory Mine, I was fortunate enough to contribute to the birth of this subject, which retains after these many years, its magical hold on our imaginations and expectations., Comment: Contribution to the "Birth of String Theory" Commemorative Volume

The Non-Abelian finite group PSL_2(7) is the only simple subgroup of SU(3) with a complex three-dimensional irreducible representation. It has two maximal subgroups, S_4 which, along with its own A_4 subgroup, has been successfully applied in numerous models of flavor, as well as the 21 element Frobenius group Z_7 x Z_3, which has gained much less attention. We show that it can also be used to generate tri-bimaximal mixing in the neutrino sector, while allowing for quark and charged lepton hierarchies., Comment: 15 pages, matches published version, updated references

The large neutrino mixing angles have generated interest in finite subgroups of SU(3), as clues towards understanding the flavor structure of the Standard Model. In this work, we study the mathematical structure of the simplest non-Abelian subgroup, Delta(3n^2). Using simple mathematical techniques, we derive its conjugacy classes, character table, build its irreducible representations, their Kronecker products, and its invariants., Comment: 29 pages, one table, typos corrected, matches published version

Within the broad context of quark-lepton unification, we investigate the implications of broken continuous family symmetries which result from requiring that in the limit of exact symmetry, the Dirac mass matrices yield hierarchical masses for the quarks and charged leptons, but lead to degenerate light neutrino masses as a consequence of the seesaw mechanism, without requiring hierarchical right-handed neutrino mass terms. Quark mixing is then naturally small and proportional to the size of the perturbation, but lepton mixing is large as a result of degenerate perturbation theory, shifted from maximal mixing by the size of the perturbation. Within this approach, we study an illustrative two-family prototype model with an SO(2) family symmetry, and discuss extensions to three-family models., Comment: 23 pages

The symmetries of the N=4 SuperYang-Mills theory on the light-cone are discussed, solely in terms of its physical degrees of freedom. We derive explicit expressions for the generators of the PSU(2,2|4) superalgebra, both in the free theory, and to all orders in the gauge coupling of the classical theory. We use these symmetries to construct its Hamiltonian, and show that it can be written as a quadratic form of a fermionic superfield., Comment: 29 pages, published version, references added, typos correcte

Quark-lepton unification suggests Cabibbo-sized effects in lepton mixings, which we call Cabibbo haze. We give simple examples and explore possible Wolfenstein-like parametrizations of the MNSP matrix which incorporate leptonic Cabibbo shifts. We find that the size of the CHOOZ angle is not always correlated with the observability of CP violation., Comment: 10 pages

We show that Supergravity in eleven dimensions can be described in terms of a constrained superfield on the light-cone, without the use of auxiliary fields. We build its action to first order in the gravitational coupling constant \kappa, by "oxidizing" (N=8,d=4) Supergravity. This is simply achieved, as for N=4 Yang-Mills, by extending the transverse derivatives into superspace. The eleven-dimensional SuperPoincare algebra is constructed and a fourth order interaction is conjectured., Comment: 18 pages

We consider how the continuous spin representation (CSR) of the Poincare group in four dimensions can be generated by dimensional reduction. The analysis uses the front-form little group in five dimensions, which must yield the Euclidean group E(2), the little group of the CSR. We consider two cases, one is the single spin massless representation of the Poincare group in five dimensions, the other is the infinite component Majorana equation, which describes an infinite tower of massive states in five dimensions. In the first case, the double singular limit j,R go to infinity, with j/R fixed, where R is the Kaluza-Klein radius of the fifth dimension, and j is the spin of the particle in five dimensions, yields the CSR in four dimensions. It amounts to the Inonu-Wigner contraction, with the inverse K-K radius as contraction parameter. In the second case, the CSR appears only by taking a triple singular limit, where an internal coordinate of the Majorana theory goes to infinity, while leaving its ratio to the KK radius fixed., Comment: 22 pages; some typos corrected

We introduce superspace generalizations of the transverse derivatives to rewrite the four-dimensional N=4 Yang-Mills theory into the fully ten-dimensional N=1 Yang-Mills in light-cone form. The explicit SuperPoincare algebra is constructed and invariance of the ten-dimensional action is proved., Comment: 15 pages

We introduce a new parametrization of the MNS lepton mixing matrix which separates the hierarchical Grand Unified relations among quarks and leptons. We argue that one large angle stems from the charged leptons, the other from the seesaw structure of the neutral lepton mass matrix. We show how two large mixing angles can arise naturally provided there are special requirements on the Dirac ($\Delta I_{\rm w}=1/2$) and Majorana ($\Delta I_{\rm w}=0$) masses. One possibility is a correlated hierarchy between them, the other is that the $\Delta I_{\rm w}=0$ Majorana mass has a specific texture; it is Dirac-like for two of the three families., Comment: 15 pages, no fig, some refs. added

We investigate symmetry breaking patterns from replicated gauge groups which generate anomaly-free and family-dependent U(1) symmetries. We discuss the extent to which these symmetries can explain the observed hierarchies of fermion masses and mixings., Comment: 25 pages

Quarks and leptons charges and interactions are derived from gauge theories associated with symmetries. Their space-time labels come from representations of the non-compact algebra of Special Relativity. Common to these descriptions are the Lie groups stemming from their invariances. Does Nature use Exceptional Groups, the most distinctive among them? We examine the case for and against their use. They do indeed appear in charge space, as the Standard Model fits naturally inside the exceptional group $E_6$. Further, the advent of the $E_8\times E_8$ Heterotic Superstring theory adds credibility to this venue. On the other hand, their use as space-time labels has not been as evident as they link spinors and tensors under space rotations, which flies in the face of the spin-statistics connection. We discuss a way to circumvent this difficulty in trying to generalize eleven-dimensional supergravity., Comment: Plenary Talk delivered at Groupe 24 Conference, Paris, July 2002

The recent neutrino data seem to favor two large and one small mixing angles and a hierarchy of their squared mass differences. We discuss these within the context of hierarchical neutrino masses. We show that this scheme suggests a specific neutrino mass matrix with mild fine-tuning. We then present a Froggatt-Nielsen model that reproduces this matrix.

We construct Wigner's continuous spin representations of the Poincar\'e algebra for massless particles in higher dimensions. The states are labeled both by the length of a space-like translation vector and the Dynkin indices of the {\it short little group} $SO(d-3)$, where $d$ is the space-time dimension. Continuous spin representations are in one-to-one correspondence with representations of the short little group. We also demonstrate how combinations of the bosonic and fermionic representations form supermultiplets of the super-Poincar\'e algebra. If the light-cone translations are nilpotent, these representations become finite dimensional, but contain zero or negative norm states, and their supersymmetry algebra contains a central charge in four dimensions., Comment: 19 pages

Nature's attraction to unique mathematical structures provides powerful hints for unraveling her mysteries. None is at present as intriguing as eleven-dimensional M-theory. The search for exceptional structures specific to eleven dimensions leads us to exceptional groups in the description of space-time. One specific connection, through the coset $F_4/SO(9)$, may provide a generalization of eleven-dimensional supergravity. Since this coset happens to be the projective space of the Exceptional Jordan Algebra, its charge space may be linked to the fundamental degrees of freedom underlying M-theory., Comment: 29 pages, Latex. Contribution to Francqui Foundation Meeting in the honor of Marc Henneaux, October 2001, Brussels

Reminiscences on the String origins of Supersymmetry are followed by a discussion of the importance of confusing bosons with fermions in building superstring theories in 9+1 dimensions. In eleven dimensions, the kinship between bosons and fermions is more subtle, and may involve the exceptional group $F_4$., Comment: 9 pages, Macros included. Contribution to ``30 Years of Supersymmetry", University of Minnesota

We present a comprehensive study of five-dimensional brane-world models for neutrino physics based on flat compactifications. Particular emphasis is put on the inclusion of bulk mass terms. We derive a number of general results for such brane-world models with bulk mass terms. In particular, in the limit of small brane-bulk couplings, the electroweak eigenstates are predominantly given as a superposition of three light states with non-trivial small admixtures of bulk states. As a consequence, neutrinos can undergo standard oscillations as well as oscillation into bulk Kaluza-Klein states. We use this structure to construct a specific model based on Z_2 orbifolding and bulk Majorana masses which is compatible with all observed oscillation phenomena. The solar neutrino deficit is explained by oscillations into sterile bulk states while the atmospheric neutrino deficit is due to mu - tau oscillations with naturally maximal mixing. In addition, the model can accommodate the LSND result and a significant neutrino dark matter component. We also analyze the constraints from supernova energy loss on neutrino brane-world theories and show that our specific model is consistent with these constraints., Comment: 45 pages, Latex, 1 eps-figure