Renormalization Group Evolution Research Articles

Predictions from high scale mixing unification hypothesis

Starting with 'High Scale Mixing Unification' hypothesis, we investigate the renormalization group evolution of mixing parameters and masses for both Dirac and Majorana type neutrinos. Following this hypothesis, the PMNS mixing parameters are taken to be identical to the CKM ones at a unifying high scale. Then, they are evolved to a low scale using MSSM renormalization-group equations. For both type of neutrinos, the renormalization group evolution 'naturally' results in a non-zero and small value of leptonic mixing angle $\theta_{13}$. One of the important predictions of this analysis is that, in both cases, the mixing angle $\theta_{23}$ turns out to be non-maximal for most of the parameter range. We also elaborate on the important differences between Dirac and Majorana neutrinos within our framework and how to experimentally distinguish between the two scenarios. Furthermore, for both cases, we also derive constraints on the allowed parameter range for the SUSY breaking and unification scales, for which this hypothesis works. The results can be tested by present and future experiments.

Three Dimensional SRG Evolution of theNNInteractions Using Picard Iteration

The Similarity Renormalization Group (SRG) evolution of nucleon-nucleon (NN ) interactions is calculated directly as function of momentum vectors for realistic potentials. To overcome the stiffness of the SRG flow equations in differential form for far off diagonal matrix elements, the differential equation is transformed to an integral form without employing a partial wave decomposition.

Deuteron electrodisintegration with unitarily evolved potentials

Renormalization-group (RG) methods used to soften Hamiltonians for nuclear many-body calculations change the effective resolution of the interaction. For nucleon knockout processes, these RG transformations leave cross sections invariant, but initial-state wave functions, interaction currents, and final-state interactions are individually altered. This has implications for the factorization of nuclear structure and reactions. We use deuteron electrodisintegration as a controlled laboratory for studying how structure and reaction components are modified under RG evolution, without the complication of three-body forces or currents. The dependence of these changes on kinematics is explored.

Renormalization-group evolution and nonperturbative behavior of chiral gauge theories with fermions in higher-dimensional representations

We study the ultraviolet to infrared evolution and nonperturbative behavior of a simple set of asymptotically free chiral gauge theories with an SU($N$) gauge group and an anomaly-free set of $n_{S_k}$ copies of chiral fermions transforming as the symmetric rank-$k$ tensor representation, $S_k$, and $n_{\bar A_\ell}$ copies of fermions transforming according to the conjugate antisymmetric rank-$\ell$ tensor representation, $\bar A_\ell$, of this group with $k, \ \ell \ge 2$. As part of our study, we prove a general theorem guaranteeing that a low-energy effective theory resulting from the dynamical breaking of an anomaly-free chiral gauge theory is also anomaly-free. We analyze the theories with $k=\ell=2$ in detail and show that there are only a finite number of these. Depending on the specific theory, the ultraviolet to infrared evolution may lead to a non-Abelian Coulomb phase, or may involve confinement with massless composite fermions, or fermion condensation with dynamical gauge and global symmetry breaking. We show that $S_k \bar A_k$ chiral gauge theories with $k \ge 3$ are not asymptotically free. We also analyze theories with fermions in $S_k$ and $\bar A_\ell$ representations of SU($N$) with $k \ne \ell$ and $k, \ \ell \ge 2$.

Hard matching for boosted tops at two loops

Cross sections for top quarks provide very interesting physics opportunities, being both sensitive to new physics and also perturbatively tractable due to the large top quark mass. Rigorous factorization theorems for top cross sections can be derived in several kinematic scenarios, including the boosted regime in the peak region that we consider here. In the context of the corresponding factorization theorem for $e^+e^-$ collisions we extract the last missing ingredient that is needed to evaluate the cross section differential in the jet-mass at two-loop order, namely the matching coefficient at the scale $\mu\simeq m_t$. Our extraction also yields the final ingredients needed to carry out logarithmic resummation at next-to-next-to-leading logarithmic order (or N$^3$LL if we ignore the missing 4-loop cusp anomalous dimension). This coefficient exhibits an amplitude level rapidity logarithm starting at $\mathcal{O}(\alpha_s^2)$ due to virtual top quark loops, which we treat using rapidity renormalization group (RG) evolution. Interestingly, this rapidity RG evolution appears in the matching coefficient between two effective theories around the heavy quark mass scale $\mu\simeq m_t$.

The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box

We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g_GF, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g_GF. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g^2_GF ~ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansatz a'la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g^2_GF ~ 6 is still not governed by possible infrared conformality.

Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision.

We perform a manifestly gauge-independent analysis of the vacuum stability in the standard model including two-loop matching, three-loop renormalization group evolution, and pure QCD corrections through four loops. All these ingredients are exact, except that light-fermion masses are neglected. We in turn apply the criterion of nullifying the Higgs self-coupling and its beta function in the modified minimal-subtraction scheme and a recently proposed consistent method for determining the true minimum of the effective Higgs potential that also avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we derive an upper bound on the pole mass of the top quark by requiring that the standard model be stable all the way up to the Planck mass scale and conservatively estimate the theoretical uncertainty. This bound is compatible with the Monte Carlo mass quoted by the Particle Data Group at the 1.3σ level.

Baryon chiral perturbation theory extended beyond the low-energy region.

We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is, we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants, which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.

Large trilinear At soft supersymmetry breaking coupling from 5D MSSM

The possibility of generating a large trilinear At soft supersymmetry breaking coupling at low energies through renormalisation group evolution in the 5D MSSM is investigated. Using the power law running in five dimensions and a compactification scale in the 10-103 TeV range, we show that gluino mass may drive a large enough At to reproduce the measured Higgs mass and have a light stop superpartner below ∼ 1 TeV, as preferred by the fine tuning argument for the Higgs mass.

Competition between the Haldane insulator, superfluid and supersolid phases in the one-dimensional Bosonic Hubbard Model

We use quantum Monte Carlo (QMC), density matrix renormalization group (DMRG) and time evolution block decimation (TEBD) to study the competition between several exotic quantum phases in the one-dimensional extended bosonic Hubbard model and map its phase diagram. Of particular interest is the Haldane insulating phase which we show to be present only for density p = 1. We also show that the supersolid phase is present for a wide range of parameters including commensurate densities.

Non-global logarithms, factorization, and the soft substructure of jets

An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and resummed down to an unresolved infrared scale by making sufficiently many measurements on a jet or other restricted phase space region. Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors. To connect with the NGLs of more inclusive measurements, we present a novel perturbative expansion which is controlled by the volume of the allowed phase space for unresolved emissions. Arbitrary accuracy can be obtained by making more and more measurements so to resolve lower and lower scales. We find that even a minimal number of measurements produces agreement with Monte Carlo methods for leading-logarithmic resummation of NGLs at the sub-percent level over the full dynamical range relevant for the Large Hadron Collider. We also discuss other applications of our factorization theorem to soft jet dynamics and how to extend to higher-order accuracy.

Focus point gauge mediation with incomplete adjoint messengers and gauge coupling unification

As the mass limits on supersymmetric particles are gradually pushed to higher values due to their continuing non-observation at the CERN LHC, looking for focus point regions in the supersymmetric parameter space, which shows considerably reduced fine-tuning, is increasingly more important than ever. We explore this in the context of gauge mediated supersymmetry breaking with messengers transforming in the adjoint representation of the gauge group, namely, octet of color SU(3) and triplet of weak SU(2). A distinctive feature of this scenario is that the focus point is achieved by fixing a single combination of parameters in the messenger sector, which is invariant under the renormalization group evolution. Because of this invariance, the focus point behavior is well under control once the relevant parameters are fixed by a more fundamental theory. The observed Higgs boson mass is explained with a relatively mild fine-tuning Δ=60–150. Interestingly, even in the presence of incomplete messenger multiplets of the SU(5) GUT group, the gauge couplings still unify perfectly, but at a scale which is one or two orders of magnitude above the conventional GUT scale. Because of this larger unification scale, the colored Higgs multiplets become too heavy to trigger proton decay at a rate larger than the experimentally allowed limit.

High scale mixing unification for Dirac neutrinos

Starting with high scale mixing unification hypothesis, we investigate the renormalization group evolution of mixing parameters and masses for Dirac type neutrinos. Following this hypothesis, the PMNS mixing angles and phase are taken to be identical to the CKM ones at a unifying high scale. Then, they are evolved to a low scale using renormalization-group equations. The notable feature of this hypothesis is that renormalization group evolution with quasi-degenerate mass pattern can explain largeness of leptonic mixing angles even for Dirac neutrinos. The renormalization group evolution "naturally" results in a non-zero and small value of leptonic mixing angle $\theta_{13}$. One of the important predictions of this work is that the mixing angle $\theta_{23}$ is non-maximal and lies only in the second octant. We also derive constraints on the allowed parameter range for the SUSY breaking and unification scales for which this hypothesis works. The results are novel and can be tested by present and future experiments.

Dark matter and gauge coupling unification in nonsupersymmetric SO(10) grand unified models

Unlike minimal SU(5), SO(10) provides a straightforward path towards gauge coupling unification by modifying the renormalization group evolution of the gauge couplings above some intermediate scale which may also be related to the seesaw mechanism for neutrino masses. Unification can be achieved for several different choices of the intermediate gauge group below the SO(10) breaking scale. In this work, we consider in detail the possibility that SO(10) unification may also provide a natural dark matter candidate, stability being guaranteed by a leftover $Z_2$ symmetry. We systematically examine the possible intermediate gauge groups which allow a non-degenerate, fermionic, Standard Model singlet dark matter candidate while at the same time respecting gauge coupling unification. Our analysis is done at the two-loop level. Surprisingly, despite the richness of SO(10), we find that only two models survive the analysis of phenomenological constraints, which include suitable neutrino masses, proton decay, and reheating.

Connecting dark matter UV complete models to direct detection rates via effective field theory

Direct searches for WIMPs are sensitive to physics well below the weak scale. In the absence of light mediators, it is fruitful to apply an Effective Field Theory (EFT) approach accounting only for dark matter (DM) interactions with Standard Model (SM) fields. We consider a singlet fermion WIMP and effective operators up to dimension 6 which are generated at the mass scale of particles mediating DM interactions with the SM. We perform a one-loop Renormalization Group Evolution (RGE) analysis, evolving these effective operators from the mediators mass scale to the nuclear scales probed by direct searches. We apply our results to models with DM velocity-suppressed interactions, DM couplings only to heavy quarks, leptophilic DM and Higgs portal, which without our analysis would not get constrained from direct detection bounds. Remarkably, a large parameter space region for these models is found to be excluded as a consequence of spin-independent couplings induced by SM loops. In addition to these examples, we stress that more general renormalizable models for singlet fermion WIMP can be matched onto our EFT framework, and the subsequent model-independent RGE can be used to compute direct detection rates. Our results allow us to properly connect the different energy scales involved in constraining WIMP models, and to combine information from direct detection with other complementary searches, such as collider and indirect detection.

The Higgs mass and the scale of new physics

In view of the measured Higgs mass of 125 GeV, the perturbative renormalization group evolution of the Standard Model suggests that our Higgs vacuum might not be stable. We connect the usual perturbative approach and the functional renormalization group which allows for a straightforward inclusion of higher-dimensional operators in the presence of an ultraviolet cutoff. In the latter framework we study vacuum stability in the presence of higher-dimensional operators. We find that their presence can have a sizable influence on the maximum ultraviolet scale of the Standard Model and the existence of instabilities. Finally, we discuss how such operators can be generated in specific models and study the relation between the instability scale of the potential and the scale of new physics required to avoid instabilities.

Standard Model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements

Models of Weakly Interacting Massive Particles (WIMPs) specified at the electroweak scale are systematically matched to effective theories at hadronic scales where WIMP-nucleus scattering observables are evaluated. Anomalous dimensions and heavy quark threshold matching conditions are computed for the complete basis of lowest-dimension effective operators involving quarks and gluons. The resulting QCD renormalization group evolution equations are solved. The status of relevant hadronic matrix elements is reviewed and phenomenological illustrations are given, including details for the computation of the universal limit of nucleon scattering with heavy $SU(2)_W\times U(1)_Y$ charged WIMPs. Several cases of previously underestimated hadronic uncertainties are isolated. The results connect arbitrary models specified at the electroweak scale to a basis of $n_f=3$ flavor QCD operators. The complete basis of operators and Lorentz invariance constraints through order $v^2/c^2$ in the nonrelativistic nucleon effective theory are derived.

Renormalization group evolution of neutrino parameters in presence of seesaw threshold effects and Majorana phases

We examine the renormalization group evolution (RGE) for different mixing scenarios in the presence of seesaw threshold effects from high energy scale (GUT) to the low electroweak (EW) scale in the Standard Model (SM) and Minimal Supersymmetric Standard Model (MSSM). We consider four mixing scenarios namely Tri–Bimaximal Mixing, Bimaximal Mixing, Hexagonal Mixing and Golden Ratio Mixing which come from different flavor symmetries at the GUT scale. We find that the Majorana phases play an important role in the RGE running of these mixing patterns along with the seesaw threshold corrections. We present a comparative study of the RGE of all these mixing scenarios both with and without Majorana CP phases when seesaw threshold corrections are taken into consideration. We find that in the absence of these Majorana phases both the RGE running and seesaw effects may lead to θ13<5° at low energies both in the SM and MSSM. However, if the Majorana phases are incorporated into the mixing matrix the running can be enhanced both in the SM and MSSM. Even by incorporating non-zero Majorana CP phases in the SM, we do not get θ13 in its present 3σ range. The current values of the two mass squared differences and mixing angles including θ13 can be produced in the MSSM case with tan⁡β=10 and non-zero Majorana CP phases at low energy. We also calculate the order of effective Majorana mass and Jarlskog Invariant for each scenario under consideration.

Renormalization-group evolution of chiral gauge theories

We calculate the ultraviolet to infrared evolution and analyze possible types of infrared behavior for several asymptotically free chiral gauge theories with gauge group SU($N$) and massless chiral fermions transforming according to a symmetric rank-2 tensor representation $S$ and $N+4$ copies (flavors) of a conjugate fundamental representation $\bar F$, together with a vectorlike subsector with chiral fermions in higher-dimensional representation(s). We construct and study three such chiral gauge theories. These have respective vectorlike subsectors comprised of (a) $p$ copies of fermions in the adjoint representation, (b) $N = 2k$ even and $p$ copies of fermions in the antisymmetric rank-$k$ tensor representation, and (c) $p$ copies of $\{S + \bar S\}$ fermions. Results are presented for beta functions, their infrared zeros, and predictions from the most-attractive-channel approach for the formation of bilinear fermion condensates. Importantly, we show that for these theories, the expected ultraviolet to infrared evolution obeys a conjectured inequality concerning the field degrees of freedom for all values of the parameters $N$ and $p$ characterizing each theory.

Bottom-tau unification by neutrinos in a nonsupersymmetric SU(5) model

We show that Yukawa couplings of bottom quarks and tau leptons can be unified in a non-supersymmetric SU(5) model. We introduce an arbitrary number of right-handed neutrinos. Their masses and Yukawa couplings that satisfy the unification condition by renormalization group evolution are shown. In the case that the grand unification scale is $10^{15.5}$GeV and three right-handed neutrinos have the same mass, the upper bound on their mass is $\sim 10^{14.1}$GeV.