scholarly journals Root bundles and towards exact matter spectra of F-theory MSSMs

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Martin Bies ◽  
Mirjam Cvetič ◽  
Ron Donagi ◽  
Muyang Liu ◽  
Marielle Ong
Keyword(s):  
Standard Model ◽  
Deformation Theory ◽  
Gauge Coupling ◽  
Line Bundles ◽  
Fractional Powers ◽  
Physical Demand ◽  
Nodal Curves ◽  
Counting Procedure ◽  
All Solutions ◽  
Matter Curve

Abstract Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also known as root bundles and can be thought of as generalizations of spin bundles. We explain how these root bundles are linked to inequivalent F-theory gauge potentials of a G4-flux.While this observation is interesting in its own right, it is particularly valuable for F-theory Standard Model constructions. In aiming for MSSMs, it is desired to argue for the absence of vector-like exotics. We work out the root bundle constraints on all matter curves in the largest class of currently-known F-theory Standard Model constructions without chiral exotics and gauge coupling unification. On each matter curve, we conduct a systematic “bottom”-analysis of all solutions to the root bundle constraints and all spin bundles. Thereby, we derive a lower bound for the number of combinations of root bundles and spin bundles whose cohomologies satisfy the physical demand of absence of vector-like pairs.On a technical level, this systematic study is achieved by a well-known diagrammatic description of root bundles on nodal curves. We extend this description by a counting procedure, which determines the cohomologies of so-called limit root bundles on full blow-ups of nodal curves. By use of deformation theory, these results constrain the vector-like spectra on the smooth matter curves in the actual F-theory geometry.

scholarly journals Complete leading-order standard model corrections to quantum leptogenesis

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Paul Frederik Depta ◽  
Andreas Halsch ◽  
Janine Hütig ◽  
Sebastian Mendizabal ◽  
Owe Philipsen
Keyword(s):  
Standard Model ◽  
Gauge Coupling ◽  
Thermal Bath ◽  
Leading Order ◽  
Boltzmann Equations ◽  
The Standard Model ◽  
Majorana Neutrinos ◽  
Infinite Loop ◽  
First Time ◽  
The Universe

Abstract Thermal leptogenesis, in the framework of the standard model with three additional heavy Majorana neutrinos, provides an attractive scenario to explain the observed baryon asymmetry in the universe. It is based on the out-of-equilibrium decay of Majorana neutrinos in a thermal bath of standard model particles, which in a fully quantum field theoretical formalism is obtained by solving Kadanoff-Baym equations. So far, the leading two-loop contributions from leptons and Higgs particles are included, but not yet gauge corrections. These enter at three-loop level but, in certain kinematical regimes, require a resummation to infinite loop order for a result to leading order in the gauge coupling. In this work, we apply such a resummation to the calculation of the lepton number density. The full result for the simplest “vanilla leptogenesis” scenario is by $$ \mathcal{O} $$ O (1) increased compared to that of quantum Boltzmann equations, and for the first time permits an estimate of all theoretical uncertainties. This step completes the quantum theory of leptogenesis and forms the basis for quantitative evaluations, as well as extensions to other scenarios.

scholarly journals Dark moments for the Standard Model?

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Thomas G. Rizzo
Keyword(s):  
Standard Model ◽  
Magnetic Dipole ◽  
Parameter Space ◽  
Gauge Coupling ◽  
Large Mass ◽  
Mass Scale ◽  
Complex Scalar ◽  
Quantum Numbers ◽  
The Standard Model ◽  
Model Setup

Abstract If dark matter (DM) interacts with the Standard Model (SM) via the kinetic mixing (KM) portal, it necessitates the existence of portal matter (PM) particles which carry both dark and SM quantum numbers that will appear in vacuum polarization-like loop graphs. In addition to the familiar ∼ eϵQ strength, QED-like interaction for the dark photon (DP), in some setups different loop graphs of these PM states can also induce other coupling structures for the SM fermions that may come to dominate in at least some regions of parameter space regions and which can take the form of ‘dark’ moments, e.g., magnetic dipole-type interactions in the IR, associated with a large mass scale, Λ. In this paper, motivated by a simple toy model, we perform a phenomenological investigation of a possible loop-induced dark magnetic dipole moment for SM fermions, in particular, for the electron. We show that at the phenomenological level such a scenario can not only be made compatible with existing experimental constraints for a significant range of correlated values for Λ and the dark U(1)D gauge coupling, gD, but can also lead to quantitatively different signatures once the DP is discovered. In this setup, assuming complex scalar DM to satisfy CMB constraints, parameter space regions where the DP decays invisibly are found to be somewhat preferred if PM mass limits from direct searches at the LHC and our toy model setup are all taken seriously. High precision searches for, or measurements of, the e+e− → γ + DP process at Belle II are shown to provide some of the strongest future constraints on this scenario.

scholarly journals Gauge coupling unification in the Standard Model

2005 ◽  
Vol 624 (3-4) ◽  
pp. 233-238 ◽  
Author(s):  
V. Barger ◽  
Jing Jiang ◽  
Paul Langacker ◽  
Tianjun Li
Keyword(s):  
Standard Model ◽  
Gauge Coupling ◽  
The Standard Model

scholarly journals IMPLICATIONS OF NONUNIVERSAL SOFT MASSES FOR GAUGE COUPLING UNIFICATION

1996 ◽  
Vol 11 (05) ◽  
pp. 903-920 ◽  
Author(s):  
RICHARD ALTENDORFER ◽  
TATSUO KOBAYASHI
Keyword(s):  
Standard Model ◽  
Supersymmetric Standard Model ◽  
Minimal Supersymmetric Standard Model ◽  
Model Building ◽  
Gauge Coupling ◽  
String Model ◽  
Gauge Couplings ◽  
Gaugino Masses

We study the gauge coupling unification of the minimal supersymmetric standard model with nonuniversal soft scalar and gaugino masses. The unification scale of the gauge couplings is estimated for nonuniversal cases. It is sensitive to the nonuniversality. It turns out that these cases can be combined with the assumption of string unification, which leads to a prediction of sin 2 θW(MZ) and k1, the normalization of the U (1)Y generator. String unification predicts that k1=1.3–1.4. These values have nontrivial implications for string model building. Two-loop corrections are also calculated. Some of these cases exhibit a large discrepancy between experiment and string unification. We calculate string threshold corrections to explain the discrepancy.

scholarly journals A road towards a beyond the Standard Model model

2022 ◽  
Vol 258 ◽  
pp. 06003
Author(s):  
Giancarlo Rossi
Keyword(s):  
Standard Model ◽  
Chiral Symmetry ◽  
Top Quark ◽  
Gauge Coupling ◽  
Spontaneous Breaking ◽  
Strong Interactions ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Strongly Interacting ◽  
Fermion Masses

In this talk we describe examples of renormalizable strongly interacting field theories where chiral symmetry, broken at the UV cutoff by the presence of some irrelevant d > 4 operators in the fundamental Lagrangian, is recovered at low energy owing to the tuning of certain Lagrangian parameters. The interference of UV effects with IR features coming from the spontaneous breaking of the recovered chiral symmetry yields non perturbatively generated elementary fermion masses parametrically expressed by formulae of the kind mq ~ Cq(α)ΛRGI with α the gauge coupling constant and ΛRGI the RGI scale of the theory. Upon introducing EW interactions, this mechanism can be extended to give mass to EW bosons and leptons and can thus be used as an alternative to the Higgs scenario. In order to give the top quark and the weak gauge bosons a mass of the phenomenologically correct order of magnitude, the model must necessarily include (yet unobserved) super-strongly interacting massive fermions endowed, besides ordinary Standard Model interactions, with super-strong interactions with a RGI scale, ΛT ΛQCD in the few TeV range. Though limited in its scope (here we ignore hypercharge and leptons and discuss only the case of one family neglecting weak isospin splitting), the model opens the way to a solution of the naturalness problem and an understanding of the fermion mass hierarchy.

scholarly journals Investigating BSM Models with Large Scale Separation

2018 ◽  
Vol 175 ◽  
pp. 08007 ◽  
Author(s):  
Anna Hasenfratz ◽  
Claudio Rebbi ◽  
Oliver Witzel
Keyword(s):  
Fixed Point ◽  
Standard Model ◽  
Large Scale ◽  
Gauge Coupling ◽  
Model Systems ◽  
Beyond The Standard Model ◽  
Heavy Flavor ◽  
Scale Separation ◽  
The Standard Model ◽  
Effective Description

Mass-split systems based on a conformal infrared fixed point provide a lowenergy effective description of beyond the standard model systems with large scale separation. We report results of exploratory investigations with four light and eight heavy flavors using staggered fermions, and up to five different values for the light flavor mass, five different heavy flavor masses, and two values of the bare gauge coupling.

scholarly journals Gauge coupling unification in the exceptional supersymmetric Standard Model

2007 ◽  
Vol 650 (1) ◽  
pp. 57-64 ◽  
Author(s):  
S.F. King ◽  
S. Moretti ◽  
R. Nevzorov
Keyword(s):  
Standard Model ◽  
Supersymmetric Standard Model ◽  
Gauge Coupling

scholarly journals Classifying affine line bundles on a compact complex space

2019 ◽  
Vol 6 (1) ◽  
pp. 103-117
Author(s):  
Valentin Plechinger
Keyword(s):  
Line Bundle ◽  
Deformation Theory ◽  
Complex Space ◽  
Main Idea ◽  
Difficult Problem ◽  
Line Bundles ◽  
Compact Complex Space ◽  
Affine Line ◽  
Picard Functor

AbstractThe classification of affine line bundles on a compact complex space is a difficult problem. We study the affine analogue of the Picard functor and the representability problem for this functor. Let be a compact complex space with . We introduce the affine Picard functor which assigns to a complex space the set of families of linearly -framed affine line bundles on parameterized by . Our main result states that the functor is representable if and only if the map is constant. If this is the case, the space which represents this functor is a linear space over whose underlying set is , where is a Poincaré line bundle normalized at . The main idea idea of the proof is to compare the representability of to the representability of a functor considered by Bingener related to the deformation theory of -cohomology classes. Our arguments show in particular that, for = 1, the converse of Bingener’s representability criterion holds

scholarly journals STRING SCALE GAUGE COUPLING UNIFICATION WITH VECTOR-LIKE EXOTICS AND NONCANONICAL U(1)Y NORMALIZATION

2007 ◽  
Vol 22 (32) ◽  
pp. 6203-6218 ◽  
Author(s):  
V. BARGER ◽  
JING JIANG ◽  
PAUL LANGACKER ◽  
TIANJUN LI
Keyword(s):  
Standard Model ◽  
Gauge Coupling ◽  
Independent Sets ◽  
Tree Level ◽  
New Approach ◽  
Quantum Numbers ◽  
The Standard Model

We use a new approach to study string scale gauge coupling unification systematically, allowing both the possibility of noncanonical U (1)Y normalization and the existence of vector-like particles whose quantum numbers are the same as those of the Standard Model (SM) fermions and their Hermitian conjugates and the SM adjoint particles. We first give all the independent sets (Yi) of particles that can be employed to achieve SU (3)C and SU (2)L string scale gauge coupling unification and calculate their masses. Second, for a noncanonical U (1)Y normalization, we obtain string scale SU (3)C × SU (2)L × U (1)Y gauge coupling unification by choosing suitable U (1)Y normalizations for each of the Yi sets. Alternatively, for the canonical U (1)Y normalization, we achieve string scale gauge coupling unification by considering suitable combinations of the Yi sets or by introducing additional independent sets (Zi), that do not affect the SU (3)C × SU (2)L unification at tree level, and then choosing suitable combinations, one from the Yi sets and one from the Zi sets. We also briefly discuss string scale gauge coupling unification in models with higher Kac–Moody levels for SU (2)L or SU (3)C.

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