Yukawa Coupling Unification Research Articles

Asymptotic ultraviolet-safe unification of gauge and Yukawa couplings: The exceptional case

The ultimate dream of unification models consists in combining both gauge and Yukawa couplings into one unified coupling. This is achieved by using a supersymmetric exceptional E6 gauge symmetry together with asymptotic unification in compact five-dimensional space-time. The ultraviolet fixed point requires exactly three fermion generations: one in the bulk, and the two light ones localised on the SO(10) boundary in order to cancel gauge anomalies. A second option allows to preserve baryon number and to lower the compactification scale down to the typical scales of the intermediate Pati-Salam gauge theory.

Renormalization group evolution with scalar leptoquarks

Leptoquarks are theoretically well-motivated and have received increasing attention in recent years as they can explain several hints for physics beyond the Standard Model. In this article, we calculate the renormalisation group evolution of models with scalar leptoquarks. We compute the anomalous dimensions for all couplings (gauge, Yukawa, Higgs and leptoquarks interactions) of the most general Lagrangian at the two-loop level and the corresponding threshold corrections at one-loop. The most relevant analytic results are presented in the appendix, while the notebook containing the full expressions can be downloaded at https://github.com/SumitBanikGit/SLQ-RG. In our phenomenological analysis, we consider some exemplary cases with focus on gauge and Yukawa coupling unification.

Non-supersymmetric SO(10) models with Gauge and Yukawa coupling unification

We study a non-supersymmetric SO(10) Grand Unification Theory with a very high energy intermediate symmetry breaking scale in which not only gauge but also Yukawa coupling unification are enforced via suitable threshold corrections and matching conditions. For gauge unification, we focus on a few symmetry breaking patterns with the intermediate gauge groups text {SU}(4)_{textrm{C}} times text {SU}(2)_{textrm{L}} times text {SU}(2)_{textrm{R}} (Pati–Salam) and text {SU}(3)_{textrm{C}} times text {SU}(2)_{textrm{L}} times text {SU}(2)_{textrm{R}}times text {U}(1)_{{textrm{B}}-{textrm{L}}} (minimal left-right symmetry) assuming an additional global U(1) Peccei–Quinn symmetry, and having the Standard Model supplemented by a second Higgs doublet field at the electroweak scale. We derive the conditions as well as the approximate analytical solutions for the unification of the gauge coupling constants at the two-loop level and discuss the constraints from proton decay on the resulting high scale. Specializing to the case of the Pati–Salam intermediate breaking pattern, we then impose also the unification of the Yukawa couplings of third generation fermions at the high scale, again at the two-loop level. In the considered context, Yukawa unification implies a relation between the fermion couplings to the 10- and 126-dimensional scalar representations of the SO(10) group. We consider one such possible relation which is obtainable in an text {E}_6 model where the previous two scalar fields are part of a single multiplet. Taking into account some phenomenological features such as the absence of flavor changing neutral currents at tree-level, we derive constraints on the parameters of the low energy model, in particular on the ratio of the two Higgs doublets vacuum expectation values tan beta .

Yukawa coupling unification in non-supersymmetric SO(10) models with an intermediate scale

We discuss the possibility of unifying in a simple and economical manner the Yukawa couplings of third generation fermions in a non-supersymmetric SO(10) model with an intermediate symmetry breaking, focusing on two possible patterns with intermediate Pati-Salam and minimal left-right groups. For this purpose, we assume a minimal Yukawa sector at high energy, starting with two Higgs bi-doublets at the intermediate scale which then simply reduce to a two Higgs doublet model at the electroweak scale. We first enforce gauge coupling unification at the two-loop level by including the threshold corrections in the renormalization group running which are generated by the heavy fields that appear at the intermediate symmetry breaking scale. We then study the running of the Yukawa couplings of the top quark, bottom quark and tau lepton at two-loops in these two breaking schemes, when the appropriate matching conditions are imposed. We find that the unification of the third family Yukawa couplings can be achieved while retaining a viable spectrum, provided that the ratio of the vacuum expectation values of the two Higgs doublet fields is large, tan⁡β≈60.

Yukawa coupling unification in an SO(10) model consistent with Fermilab (g \u2212 2)\u03bc result

We investigate the Yukawa coupling unification for the third generation in a class of SO(10) unified models which are consistent with the 4.2 σ deviation from the standard model of the muon g − 2 seen by the Fermilab experiment E989. A recent analysis in supergravity grand unified models shows that such an effect can arise from supersymmetric loops correction. Using a neural network, we further analyze regions of the parameter space where Yukawa coupling unification consistent with the Fermilab result can appear. In the analysis we take into account the contributions to Yukawas from the cubic and the quartic interactions. We test the model at the high luminosity and high energy LHC and estimate the integrated luminosities needed to discover sparticles predicted by the model.

T \u2212 b \u2212 \u03c4 Yukawa unification in non-holomorphic MSSM

We show that in the CMSSM with the non-holomorphic soft SUSY breaking terms, the Yukawa coupling unification of the third family fermions at the GUT scale, called t − b − τ Yukawa unification (YU), is possible under the recent collider and Dark Matter results. The YU parameter can also be found Rtbτ≈ 1, called perfect unification. We find that the squark masses exceed 3 TeV while the stau can be considerably lighter. In the case of YU, the tan β is in the interval [46,55]. We obtain bino-like dark matter (DM) of mass in the range of 0.6 TeV ≲ {m}_{upchi_1^0} ≲ 1.3 TeV where the recent Dark Matter direct detection limits are also satisfied. We also identify A-resonance solutions which reduce the relic abundance of LSP neutralino down to the ranges compatible with the current Planck measurements.

A bottom-up approach to fermion mass hierarchy: a case with vector-like fermions

Abstract We propose a bottom-up approach in which a structure of high-energy physics is explored by accumulating existence proofs and/or no-go theorems in the standard model or its extension. As an illustration, we study fermion mass hierarchies based on an extension of the standard model with vector-like fermions. It is shown that the magnitude of elements of Yukawa coupling matrices can become $O(1)$ and a Yukawa coupling unification can be realized in a theory beyond the extended model, if vector-like fermions mix with three families. In this case, small Yukawa couplings in the standard model can be highly sensitive to a small variation of matrix elements, and it seems that the mass hierarchy occurs as a result of fine tuning.

Unification of gauge and Yukawa couplings

In this talk we describe how unification of gauge and Yukawa couplings can be obtained in gauge-Higgs unification models in extra-dimensions using a toy model. It is usually considered that such unification is difficult to obtain using simple group theory arguments. We consider a toy model based on the SU(3) symmetry and show that including the renormalisation group running at one loop for the couplings improve the result. The gauge couplings unify asymptotically at high energies, and this may result from the presence of an UV fixed point. The Yukawa coupling is enhanced at low energies, showing that a genuine unification of gauge and Yukawa couplings may be achieved. Some other arguments and directions of study are also mentioned to tackle the problem of producing a scalar potential allowing to accommodate the measured Higgs mass at 125 GeV.

Top-bottom-tau Yukawa coupling unification in the MSSM plus one vectorlike family and fermion masses as IR fixed points

In the MSSM extended by a complete vectorlike family, precise top, bottom and tau Yukawa coupling unification can be achieved assuming SUSY threshold corrections which are typical for comparable superpartner masses. Furthermore, the unification is possible with a large unified coupling, implying that all three fermion masses can be simultaneously close to their IR fixed points. Assuming unified Yukawa couplings of order one or larger, the preferred common scale of new physics (superpartners and vectorlike matter) is in the 3 TeV to 30 TeV range, with larger couplings favoring smaller scales. Splitting superpartner masses from masses of vectorlike fields, the preferred scales extend in both directions. The multi-TeV scale for superpartners is compatible with and independently suggested by the Higgs boson mass.

Yukawa unification with four Higgs doublets in supersymmetric GUT

We discuss the Yukawa coupling unification, which can emerge in the grand unified theory, in the context of scenarios with more than one pair of Higgs doublet since the current LHC constraint has become a problem for the Yukawa unification scenarios with just one pair of Higgs doublet. More than one pair of Higgs doublets can easily arise in missing partner mechanism which solves the doublet-triplet splitting problem. In such a scenario, the Yukawa unification occurs at a medium tan⁡β value, e.g., ∼ 30, which corresponds to much smaller threshold corrections compared to usual large tan⁡β scenario for t−b−τ unification in the context of SO(10) and b−τ unification in the context of SU(5) models. Further, we show that an additional Higgs doublet pair lowers the sensitivity of the radiative symmetry breaking of the electroweak vacuum.

Effective field theory approach to trans-TeV supersymmetry: covariant matching, Yukawa unification and Higgs couplings

Dismissing traditional naturalness concerns while embracing the Higgs boson mass measurement and unification motivates careful analysis of trans-TeV supersymmetric theories. We take an effective field theory (EFT) approach, matching the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model (SM) EFT by integrating out heavy superpartners, and evolving MSSM and SMEFT parameters according to renormalization group equations in each regime. Our matching calculation is facilitated by the recent covariant diagrams formulation of functional matching techniques, with the full one-loop SUSY threshold corrections encoded in just 30 diagrams. Requiring consistent matching onto the SMEFT with its parameters (those in the Higgs potential in particular) measured at low energies, and in addition requiring unification of bottom and tau Yukawa couplings at the scale of gauge coupling unification, we detail the solution space of superpartner masses from the TeV scale to well above. We also provide detailed views of parameter space where Higgs coupling measurements have probing capability at future colliders beyond the reach of direct superpartner searches at the LHC.

Unification of gauge and Yukawa couplings

The unification of gauge and top Yukawa couplings is an attractive feature of gauge-Higgs unification models in extra-dimensions. This feature is usually considered difficult to obtain based on simple group theory analyses. We reconsider a minimal toy model including the renormalisation group running at one loop. Our results show that the gauge couplings unify asymptotically at high energies, and that this may result from the presence of an UV fixed point. The Yukawa coupling in our toy model is enhanced at low energies, showing that a genuine unification of gauge and Yukawa couplings may be achieved.

Masses of third family vectorlike quarks and leptons in Yukawa-unifiedE6

In supersymmetric $E_6$ the masses of the third family quarks and charged lepton, $t-b-\tau$, as well as the masses of the vector-like quarks and leptons, $D-\bar{D}$ and $ L-\bar{L}$, may arise from the coupling $27_3$ x $27_3$ x $27_H$, where $27_3$ and $27_H$ denote the third family matter and Higgs multiplets respectively. We assume that the SO(10) singlet component in $27_H$ acquires a TeV scale VEV which spontaneously breaks U(1)$_\psi$ and provides masses to the vector-like particles in $27_3$, while the MSSM doublets in $27_H$ provide masses to $ t, b$ and $\tau$. Imposing Yukawa coupling unification $h_t=h_b=h_{\tau}=h_D=h_L$ at $M_{GUT}$ and employing the ATLAS and CMS constraints on the $Z'_\psi$ boson mass, we estimate the lower bounds on the third family vector-like particles $D-\bar{D}$ and $L-\bar{L}$ masses to be around 5.85 TeV and 2.9 TeV respectively. These bounds apply in the supersymmetric limit.

Mass-splitting between haves and have-nots — symmetry vs. Grand Unified Theory

We revisit the long-standing problem of supersymmetric grand unified theory (GUT), the doublet-triplet splitting problem. We discuss whether symmetry which controls the {\mu} term in the minimal supersymmetric standard model is compatible with GUT. We find that the symmetry must be broken at the GUT scale. A similar argument also shows that the R symmetry, which is important for low energy supersymmetry, must be broken down to a Z2R symmetry at the GUT scale. We propose a new prescription to achieve the doublet-triplet splitting by symmetry. There, the symmetry which controls the {\mu} term is spontaneously broken at the GUT scale by order parameters which are charged under other symmetries. Bilinear terms of triplet Higgses are charged under the other symmetries, while those of doublet Higgses are not. Then triplet Higgses directly couple to the order parameters and hence obtain GUT scale masses, while doublet Higgses obtain suppressed masses. The broken R symmetry can be also effectively preserved by a similar prescription. As a demonstration, we construct an SU(5)$\times$SU(5) GUT model. We also comment on unification of yukawa couplings.

Yukawa unification and sparticle spectroscopy in gauge mediation models

We explore the implications of t-b-tau (and b-tau) Yukawa coupling unification condition on the fundamental parameter space and sparticle spectroscopy in the minimal gauge mediated supersymmetry breaking (mGMSB) model. We find that this scenario prefers values of the CP-odd Higgs mass m_A > 1 TeV, with all colored sparticle masses above 3 TeV. These predictions will be hard to test at LHC13 but they may be testable at HE-LHC 33 TeV or a 100 TeV collider. Both t-b-tau and b-tau Yukawa coupling unifications prefer a relatively light gravitino with mass < 30 eV, which makes it a candidate hot dark matter particle. However, it cannot account for more than 15 % of the observed dark matter density.

Exact SU(5) Yukawa matrix unification in the general flavour violating MSSM

We investigate the possibility of satisfying the $SU(5)$ boundary condition $\mathbf{Y}^d=\mathbf{Y}^{e\,T}$ at the GUT scale within the renormalizable $R$-parity conserving Minimal Supersymmetric Standard Model (MSSM). Working in the super-CKM basis, we consider non-zero flavour off-diagonal entries in the soft SUSY-breaking mass matrices and the $A$-terms. At the same time, the diagonal $A$-terms are assumed to be suppressed by the respective Yukawa couplings. We show that a non-trivial flavour structure of the soft SUSY-breaking sector can contribute to achieving precise Yukawa coupling unification for all the three families. However, large non-zero values of the flavour-violating parameter $(m^2_{dl})_{12}$ lead to a strong tension with the Lepton Flavour Violating (LFV) observables. Nevertheless, the LFV problem does not arise when the Yukawa coupling unification requirement is restricted to the second and third families only. We demonstrate that such a scenario is consistent with a wide set of experimental constraints, including flavour and electroweak observables, Higgs physics and the LHC bounds. We also point out that in order to provide a proper value for the relic density of dark matter, the lightest neutralino needs to be almost purely bino-like and with mass in the range of 200$\div$600 GeV. Such a clear experimental prediction makes the flavour-violating $SU(5)$ Yukawa unification scenario fully testable at the LHC 14 TeV.

Fermion hierarchy from sfermion anarchy

We present a framework to generate the hierarchical flavor structure of Standard Model quarks and leptons from loops of superpartners. The simplest model consists of the minimal supersymmetric standard model with tree level Yukawa couplings for the third generation only and anarchic squark and slepton mass matrices. Agreement with constraints from low energy flavor observables, in particular Kaon mixing, is obtained for supersymmetric particles with masses at the PeV scale or above. In our framework both the second and the first generation fermion masses are generated at 1-loop. Despite this, a novel mechanism generates a hierarchy among the first and second generations without imposing a symmetry or small parameters. A second-to-first generation mass ratio of order 100 is typical. The minimal supersymmetric standard model thus includes all the necessary ingredients to realize a fermion spectrum that is qualitatively similar to observation, with hierarchical masses and mixing. The minimal framework produces only a few quantitative discrepancies with observation, most notably the muon mass is too low. We discuss simple modifications which resolve this and also investigate the compatibility of our model with gauge and Yukawa coupling Unification.

A realistic intersecting D6-brane model after the first LHC run

With the Higgs boson mass around 125 GeV and the LHC supersymmetry search constraints, we revisit a three-family Pati-Salam model from intersecting D6-branes in Type IIA string theory on the T 6/(ℤ2 × ℤ2) orientifold which has a realistic phenomenology. We systematically scan the parameter space for μ < 0 and μ > 0, and find that the gravitino mass is generically heavier than about 2 TeV for both cases due to the Higgs mass low bound 123 GeV. In particular, we identify a region of parameter space with the electroweak fine-tuning as small as Δ EW ~ 24-32 (3-4%). In the viable parameter space which is consistent with all the current constraints, the mass ranges for gluino, the first two-generation squarks and sleptons are respectively [3, 18] TeV, [3, 16] TeV, and [2, 7] TeV. For the third-generation sfermions, the light stop satisfying 5σ WMAP bounds via neutralino-stop coannihilation has mass from 0.5 to 1.2 TeV, and the light stau can be as light as 800 GeV. We also show various coannihilation and resonance scenarios through which the observed dark matter relic density is achieved. Interestingly, the certain portions of parameter space has excellent t-b-τ and b-τ Yukawa coupling unification. Three regions of parameter space are highlighted as well where the dominant component of the lightest neutralino is a bino, wino or higgsino. We discuss various scenarios in which such solutions may avoid recent astrophysical bounds in case if they satisfy or above observed relic density bounds. Prospects of finding higgsino-like neutralino in direct and indirect searches are also studied. And we display six tables of benchmark points depicting various interesting features of our model. Note that the lightest neutralino can be heavy up to 2.8 TeV, and there exists a natural region of parameter space from low-energy fine-tuning definition with heavy gluino and first two-generation squarks/sleptons, we point out that the 33 TeV and 100 TeV proton-proton colliders are indeed needed to probe our D-brane model.

Split sfermion families, Yukawa unification and muon g − 2

We consider two distinct classes of Yukawa unified supersymmetric SO(10) models with non-universal and universal soft supersymmetry breaking (SSB) gaugino masses at M GUT. In both cases, we assume that the third family SSB sfermion masses at M GUT are different from the corresponding sfermion masses of the first two families (which are equal). For the SO(10) model with essentially arbitrary (non-universal) gaugino masses at M GUT, it is shown that t-b-τ Yukawa coupling unification is compatible, among other things, with the 125 GeV Higgs boson mass, the WMAP relic dark matter density, and with the resolution of the apparent muon g − 2 anomaly. The colored sparticles in this case all turn out to be quite heavy, of order 5 TeV or more, but the sleptons (smuon and stau) can be very light, of order 200 GeV or so. For the SO(10) model with universal gaugino masses and NUHM2 boundary conditions, the muon g − 2 anomaly cannot be resolved. However, the gluino in this class of models is not too heavy, ≲ 3 TeV, and therefore may be found at the LHC.

Top quark and Higgs boson masses in supersymmetric models

We study the implications for bounds on the top quark pole mass m t in models with low scale supersymmetry following the discovery of the Standard Model-like Higgs boson. In the minimal supersymmetric standard model, we find that m t ≥ 164 GeV, if the light CP even Higgs boson mass m h = 125 ± 2 GeV. We also explore the top quark and Higgs boson masses in two classes of supersymmetric SO(10) models with t-b-τ Yukawa coupling unification at M GUT. In particular, assuming SO(10) compatible non-universal gaugino masses, setting m h = 125 GeV and requiring 5% or better Yukawa unification, we obtain the result 172 GeV ≤ m t ≤ 175 GeV. Conversely, demanding 5% or better t-b-τ Yukawa unification and setting m t = 173.2 GeV, the Higgs boson mass is predicted to lie in the range 122 GeV ≤ m h ≤ 126 GeV.