arXiv subjects

Alon E. Faraggi

Publications and source records attributed to Alon E. Faraggi.

At least 55 records · Page 3Linked to original sources

arXiv2016

The 750 GeV diphoton LHC excess and Extra Z's in Heterotic-String Derived Models

The ATLAS and CMS collaborations recently recorded possible di-photon excess at 750 GeV and a less significant di-boson excess around 1.9 TeV. Such excesses may be produced in heterotic-string derived Z' models, where the di-photon excess may be connected with the Standard Model singlet scalar responsible for the Z' symmetry breaking, whereas the di-boson excess arises from production of the extra vector boson. Additional vector-like states in the string Z' model are instrumental to explain the relatively large width of the di-photon events and mandated by anomaly cancellation to be in the vicinity of the Z' breaking scale. Wilson line breaking of the non-Abelian gauge symmetries in the string models naturally gives rise to dark matter candidates. Future collider experiments will discriminate between the high-scale heterotic-string models, which preserve the perturbative unification paradigm indicated by the Standard Model data, versus the low scale string models. We also discuss the possibility for the production of the di-photon events with high scale $U(1)_{Z^\prime}$ breaking.

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arXiv2015

Extra $Z^\prime$s and $W^\prime$s in Heterotic--String Derived Models

The ATLAS collaboration recently recorded possible excess in the di--boson production at the di--boson invariant mass at around 2 TeV. Such an excess may be produced if there exist additional $Z^\prime$ and/or $W^\prime$ at that scale. We survey the extra $Z^\prime$s and $W^\prime$s that may arise from semi--realistic heterotic string vacua in the free fermionic formulation in seven distinct cases including: $U(1)_{Z^\prime}\in SO(10)$; family universal $U(1)_{Z^\prime}$ not in $SO(10)$; non--universal $U(1)_{Z^\prime}$; hidden sector $U(1)$ symmetries and kinetic mixing; left--right symmetric models; Pati--Salam models; leptophobic and custodial symmetries. Each case has a distinct signature associated with the extra symmetry breaking scale. In one of the cases we explore the discovery potential at the LHC using resonant leptoproduction. Existence of extra vector boson with the reported properties will significantly constrain the space of allowed string vacua.

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arXiv2015

Spinor-vector duality and light Z' in heterotic string vacua

We discuss the construction of heterotic--string models that allow for the existence of an extra $Z^\prime$ at low scales. One of the main difficulties encountered is that the desired symmetries tend to be anomalous in the prevailing three generation constructions. The reason is that these models utilise the symmetry breaking pattern $E_6\rightarrow SO(10)\times U(1)_ζ$ by GGSO projections. Consequently, $U(1)_ζ$ becomes anomalous. The spinor--vector duality that was observed in the fermionic $Z_2\times Z_2$ orbifold compactifications is used to construct a phenomenological three generation Pati--Salam heterotic--string model in which $U(1)_ζ$ is anomaly free and therefore can be a component of a low scale $Z^\prime$. The model implies existence of matter states at the $Z^\prime$ breaking scale, which are required for anomaly cancelation. Moreover, the string model gives rise to exotic states, which are $SO(10)$ singlets but carry exotic $U(1)_ζ$ charges. These states arise due to the breaking of $E_6$ by discrete Wilson lines and provide natural dark matter candidates. Initial indications suggest that the existence of additional gauge symmetries at the TeV scale may be confirmed in run II of the LHC experiment.

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arXiv2015

Large volume susy breaking with a solution to the decompactification problem

We study heterotic ground states in which supersymmetry is broken by coupling the momentum and winding charges of two large extra dimensions to the R-charges of the supersymmetry generators. The large dimensions give rise to towers of heavy string thresholds that contribute to the running of the gauge couplings. In the general case, these contributions are proportional to the volume of the two large dimensions and invalidate the perturbative string expansion. The problem is evaded if the susy breaking sectors arise as a spontaneously broken phase of N=4 -> N=2 -> N=0 supersymmetry, provided that N=4 supersymmetry is restored on the boundary of the moduli space. We discuss the mechanism in the case of Z_2 x Z_2 orbifolds, which requires that the twisted sector that contains the large extra dimensions has no fixed points. We analyse the full string partition function and show that the twisted sectors distribute themselves in non-aligned N=2 orbits, hence preserving the solution to the string decompactification problem. Remarkably, we find that the contribution to the vacuum energy from the N=2 -> N=0 sectors is suppressed, and the only substantial contribution arises from the breaking of the N=4 sector to N=0.

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arXiv2015

A Light Z' Heterotic-String Derived Model

The existence of an extra Z' inspired from heterotic-string theory at accessible energy scales attracted considerable interest in the particle physics literature. Surprisingly, however, the construction of heterotic--string derived models that allow for an extra Z' to remain unbroken down to low scales has proven to be very difficult. The main reason being that the U(1) symmetries that are typically discussed in the literature are either anomalous or have to be broken at a high scale to generate light neutrino masses. In this paper we use for that purpose the self duality property under the spinor vector duality, which was discovered in free fermionic heterotic-string models. The chiral massless states in the self--dual models fill complete 27 representations of E6. The anomaly free gauge symmetry in the effective low energy field theory of our string model is $SU(4)_C\times SU(2)_L\times SU(2)_R\times U(1)_ζ$, where $U(1)_ζ$ is the family universal $U(1)$ symmetry that descends from E6, and is typically anomalous in other free fermionic heterotic-string models. Our model therefore allows for the existence of a low scale Z', which is a combination of $B-L$, $T_{3_L}$ and $T_{3_R}$. The string model is free of exotic fractionally charged states in the massless spectrum. It contains exotic SO(10) singlet states that carry fractional, non--E6 charge, with respect to $U(1)_ζ$. These non-E6 states arise in the string model due to the breaking of the E6 symmetry by discrete Wilson lines. They represent a distinct signature of the string vacua and cannot arise in E6 Grand Unified Theories. They may provide viable dark matter candidates.

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arXiv2015

Classification of SU(4) X SU(2) X U(1) Heterotic-String Models

The free fermionic construction of the heterotic string in four dimensions produced a large space of three generation models with the underlying $SO(10)$ embedding of the Standard Model states. The $SO(10)$ symmetry is broken to a subgroup directly at the string scale. Over the past few years free fermionic models with the Pati-Salam and flipped $SU(5)$ subgroups have been classified. In this paper we extend this classification program to models in which the $SO(10)$ symmetry is broken at the string level to the $SU(4)\times SU(2)_L\times U(1)_R$ (SU421) subgroup. The subspace of free fermionic models that we consider corresponds to symmetric ${\mathbb{Z}}_2 \times {\mathbb{Z}}_2$ orbifolds. We provide a general argument that shows that this class of SU421 free fermionic models cannot produce viable three generation models.

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arXiv2015

Hamilton--Jacobi meet Möbius

Adaptation of the Hamilton--Jacobi formalism to quantum mechanics leads to a cocycle condition, which is invariant under $D$--dimensional Möbius transformations with Euclidean or Minkowski metrics. In this paper we aim to provide a pedagogical presentation of the proof of the Möbius symmetry underlying the cocycle condition. The Möbius symmetry implies energy quantization and undefinability of quantum trajectories, without assigning any prior interpretation to the wave function. As such, the Hamilton--Jacobi formalism, augmented with the global Möbius symmetry, provides an alternative starting point, to the axiomatic probability interpretation of the wave function, for the formulation of quantum mechanics and the quantum spacetime. The Möbius symmetry can only be implemented consistently if spatial space is compact, and correspondingly if there exist a finite ultraviolet length scale. Evidence for non--trivial space topology may exist in the cosmic microwave background radiation.

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arXiv2015

The Möbius Symmetry of Quantum Mechanics

The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under $D$--dimensional Möbius transformations with respect to the Euclidean or Minkowski metrics. The invariance under global Möbius transformations implies that spatial space is compact. Furthermore, it implies energy quantisation and undefinability of quantum trajectories without assuming any prior interpretation of the wave function. The approach may be viewed as conventional quantum mechanics with the caveat that spatial space is compact, as dictated by the Möbius symmetry, with the classical limit corresponding to the decompactification limit. Correspondingly, there exists a finite length scale in the formalism and consequently an intrinsic regularisation scheme. Evidence for the compactness of space may exist in the cosmic microwave background radiation.

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arXiv2014

String Phenomenology: Past, Present and Future Perspectives

The observation of a scalar resonance at the LHC, compatible with perturbative electroweak symmetry breaking, reinforces the Standard Model parameterisation of all subatomic data. The logarithmic evolution of the SM gauge and matter parameters suggests that this parameterisation remains viable up to the Planck scale, where gravitational effects are of comparable strength. String theory provides a perturbatively consistent scheme to explore how the parameters of the Standard Model may be determined from a theory of quantum gravity. The free fermionic heterotic string models provide concrete examples of exact string solutions that reproduce the spectrum of the Minimal Supersymmetric Standard Model. Contemporary studies entail the development of methods to classify large classes of models. This led to the discovery of exophobic heterotic-string vacua and the observation of spinor-vector duality, which provides an insight to the global structure of the space of (2,0) heterotic-string vacua. Future directions entail the study of the role of the massive string states in these models and their incorporation in cosmological scenarios. A complementary direction is the formulation of quantum gravity from the principle of manifest phase space duality and the equivalence postulate of quantum mechanics, which suggest that space is compact. The compactness of space, which implies intrinsic regularisation, may be tightly related to the intrinsic finite length scale, implied by string phenomenology.

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arXiv2014

Classification of Flipped SU(5) Heterotic-String Vacua

We extend the classification of the free fermionic heterotic-string vacua to models in which the SO(10) GUT symmetry at the string scale is broken to the flipped SU(5) subgroup. In our classification method, the set of basis vectors defined by the boundary conditions which are assigned to the free fermions is fixed and the enumeration of the string vacua is obtained in terms of the Generalised GSO (GGSO) projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the analysis of the entire string spectrum to be programmed in to a computer code therefore, we performed a statistical sampling in the space of 2^{44} (approximately 10^{13}) flipped $SU(5)$ vacua and scanned up to 10^{12} GGSO configurations. For that purpose, two independent codes were developed based on JAVA and FORTRAN95. All the results presented here are confirmed by the two independent routines. Contrary to the corresponding Pati-Salam classification, we do not find exophobic flipped SU(5) vacua with an odd number of generations. We study the structure of exotic states appearing in the three generation models that additionally contain a viable Higgs spectrum. Moreover, we demonstrate the existence of models in which all the exotic states are confined by a hidden sector non-Abelian gauge symmetry as well as models that may admit the racetrack mechanism.

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arXiv2013

Energy Quantisation and Time Parameterisation

We show that if space is compact, then trajectories cannot be defined in the framework of quantum Hamilton--Jacobi equation. The starting point is the simple observation that when the energy is quantized it is not possible to make variations with respect to the energy, and the time parameterisation t-t_0=\partial_E S_0, implied by Jacobi's theorem and that leads to group velocity, is ill defined. It should be stressed that this follows directly form the quantum HJ equation without any axiomatic assumption concerning the standard formulation of quantum mechanics. This provides a stringent connection between the quantum HJ equation and the Copenhagen interpretation. Together with tunneling and the energy quantization theorem for confining potentials, formulated in the framework of quantum HJ equation, it leads to the main features of the axioms of quantum mechanics from a unique geometrical principle. Similarly to the case of the classical HJ equation, this fixes its quantum analog by requiring that there exist point transformations, rather than canonical ones, leading to the trivial hamiltonian. This is equivalent to a basic cocycle condition on the states. Such a cocycle condition can be implemented on compact spaces, so that continuous energy spectra are allowed only as a limiting case. Remarkably, a compact space would also imply that the Dirac and von Neumann formulations of quantum mechanics essentially coincide. We suggest that there is a definition of time parameterisation leading to trajectories in the context of the quantum HJ equation having the probabilistic interpretation of the Copenhagen School.

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arXiv2013

Proton Stability, Gauge Coupling Unification and a Light $Z^\prime$ in Heterotic-string Models

We explore the phenomenological viability of a light Z' in heterotic-string models, whose existence has been motivated by proton stability arguments. A class of quasi-realistic string models that produce such a viable Z' are the Left-Right Symmetric (LRS) heterotic-string models in the free fermionic formulation. A key feature of these models is that the matter charges under U(1)_Z' do not admit an E6 embedding. The light Z' in the LRS heterotic-string models forbids baryon number violating operators, while allowing lepton number violating operators, hence suppressing proton decay yet allowing for sufficiently small neutrino masses via a seesaw mechanism. We show that the constraints imposed by the gauge coupling data and heterotic-string coupling unification nullify the viability of a light Z' in these models. We further argue that agreement with the gauge coupling data necessitates that the U(1)_Z' charges admit an E6 embedding. We discuss how viable string models with this property may be constructed.

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arXiv2013

The Quantum Closet

The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under D-dimensional finite Mobius transformations. The invariance of the cocycle condition under finite Mobius transformations implies that space is compact. Additionally, it implies energy quantisation and the undefinability of quantum trajectories. I argue that the decompactification limit coincides with the classical limit. Evidence for the compactness of the universe may exist in the Cosmic Microwave Background Radiation.

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arXiv2012

The Equivalence Postulate of Quantum Mechanics, Dark Energy and The Intrinsic Curvature of Elementary Particles

The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underly the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant under $D$--dimensional Mobius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of the D-dimensional quantum Hamilton--Jacobi equation. In this approach, the solutions of the associated Schrodinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrodinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. I propose that the quantum potential, which is always non-trivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multi--particle case the quantum potential, as well as the mass, are cumulative.

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arXiv2011

OPERA data and The Equivalence Postulate of Quantum Mechanics

An interpretation of the recent results reported by the OPERA collaboration is that neutrinos propagation in vacuum exceeds the speed of light. It has been further been suggested that this interpretation can be attributed to the variation of the particle speed arising from the Relativistic Quantum Hamilton Jacobi Equation. I show that this is in general not the case. I derive an expression for the quantum correction to the instantaneous relativistic velocity in the framework of the relativistic quantum Hamilton-Jacobi equation, which is derived from the equivalence postulate of quantum mechanics. While the quantum correction does indicate deviations from the classical energy--momentum relation, it does not necessarily lead to superluminal speeds. The quantum correction found herein has a non-trivial dependence on the energy and mass of the particle, as well as on distance travelled. I speculate on other possible observational consequences of the equivalence postulate approach.

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arXiv2011

Leptophobic Z' in Heterotic-String Derived Models

The CDF collaboration's recent observation of an excess of events in the Wjj channel may be attributed to a new Abelian vector boson with suppressed couplings to leptons. While D0 finds no evidence of an excess, the CDF data provide an opportunity to revisit an old result on leptophobic Z' in heterotic-string derived models. We re-examine the conditions for the existence of a leptophobic U(1) symmetry, which arises from a combination of the U(1)_{B-L} symmetry and the horizontal flavour symmetries, to form a universal U(1) symmetry. While the conditions for the existence of a leptophobic combination are not generic, we show that the left-right symmetric free fermionic heterotic-string models also admit a leptophobic combination. In some cases the leptophobic U(1) is augmented by the enhancement of the colour group, along the lines of models proposed by Foot and Hernandez.

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arXiv2011

Proton Stability and Light $Z^\prime$ Inspired by String Derived Models

Proton stability is one of the most perplexing puzzles in particle physics. While the renormalizable Standard Model forbids proton decay mediating operators due to accidental global symmetries, many of its extensions introduce such dimension four, five and six operators. Furthermore, it is, in general, expected that quantum gravity only respects local gauge, or discreet, symmetries. String theory provides the arena to study particle physics in a consistent framework of perturbative quantum gravity. An appealing proposition, in this context, is that the dangerous operators are suppressed by an Abelian gauge symmetry, which is broken near the TeV scale. A viable U(1) symmetry should also be anomaly free, be family universal, and allow the generation of fermion masses via the Higgs mechanism. We discuss such U(1) symmetries that arise in quasi--realistic free fermionic heterotic--string derived models. Ensuring that the U(1) symmetry is anomaly free at the low scale requires that the Standard Model spectrum is augmented by additional states that are compatible with the charge assignments in the string models. We construct such string--inspired models and discuss some of their phenomenological implications.

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arXiv2011

T-branes and Yukawa Couplings

We consider various configurations of T-branes which are non-abelian bound states of branes and were recently introduced by Cecotti, Cordova, Heckman and Vafa. They are a refinement of the concept of monodromic branes featured in phenomenological F-theory models. We are particularly interested in the T-branes corresponding to Z3 and Z4 monodromies, which are used to break E7 or E8 gauge groups to SU(5) GUT. Our results imply that the up-type and down-type Yukawa couplings for the breaking of E7 are zero, whereas up-type and down-type Yukawa couplings, together with right handed neutrino Yukawas are non-zero for the case of the breaking of E8. The dimension four proton decay mediating term is avoided in models with either E7 or E8 breaking.

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