Renormalization Group Evolution Research Articles

Resummation of rapidity logarithms in B meson wave functions

We construct an evolution equation for the B meson wave functions in the k T factorization theorem, whose solutions sum the double logarithms associated with the light-cone singularities, namely, the rapidity logarithms. The derivation is subtler than that of the Sudakov resummation for an energetic light hadron, due to the involvement of the effective heavy-quark field. The renormalization-group evolution in the factorization scale needs to be included in order to derive an ultraviolet-finite and scale-invariant kernel for resumming the rapidity logarithms. It is observed that this kernel is similar to that of the joint resummation for QCD processes in extreme kinematic regions, which combines the threshold and k T resummations. We show that the resummation effect maintains the normalization of the B meson wave functions, and strengths their convergent behavior at small spectator momentum. The resummation improved B meson wave functions are then employed in the leading-order analysis of the B → π transition form factors, which lead to approximately 25 % deduction in the large recoil region.

Mini-Split

AbstractThe lack of evidence for new physics beyond the standard model at the LHC points to a paucity of new particles near the weak scale. This suggests that the weak scale is tuned and that supersymmetry, if present at all, is realized at higher energies. The measured Higgs mass constrains the scalar sparticles to be below 105TeV, while gauge coupling unification favors Higgsinos below 100 TeV. Nevertheless, in many models gaugino masses are suppressed and remain within reach of the LHC. Tuning the weak scale and the renormalization group evolution of the scalar masses constrain Split model building. Due to the small gaugino masses, either the squarks or the up-higgs often run tachyonic; in the latter case, successful electroweak breaking requires heavy higgsinos near the scalar sparticles. We discuss the consequences of tuning the weak scale and the phenomenology of several models of Split supersymmetry including anomaly mediation, U(1)B−Lmediation, and Split gauge mediation.

Uncertainty in electroweak symmetry breaking in models with high scale supersymmetry breaking and its impact on interpretations of searches for supersymmetric particles

Some regions of parameter space of the minimal supersymmetric standard model (MSSM) with high scale supersymmetry breaking have extreme sensitivity of electroweak symmetry breaking (EWSB) to the top quark mass through renormalisation group evolution effects. This leads to uncertainties in the predictions which need to be taken into account in the interpretation of searches for supersymmetric particles in these regions. As an example, we provide estimates of the current uncertainties on the position in parameter space of the region which does not break electroweak symmetry in the constrained MSSM (CMSSM). The position of the boundary of EWSB can vary by up to 2 TeV in m_0 due to the uncertainties coming from the current measurement errors on the top quark mass and from higher order corrections. In this dangerous region, for fixed CMSSM parameters the neutralino lightest supersymmetric particle mass has an associated large uncertainty of order 100%. These uncertainties therefore have a profound effect on the interpretation of LHC supersymmetric particle searches in terms of the CMSSM. We also show how to ameliorate poor convergence of the iterative numerical algorithm that calculates the MSSM spectrum near the boundary of EWSB.

High-momentum tails from low-momentum effective theories

In a recent work \cite{Anderson:2010aq}, Anderson \emph{et al.} used the renormalization group (RG) evolution of the momentum distribution to show that, under appropriate conditions, operator expectation values exhibit factorization in the two-nucleon system. Factorization is useful because it provides a clean separation of long- and short-distance physics, and suggests a possible interpretation of the universal high-momentum dependence and scaling behavior found in nuclear momentum distributions. In the present work, we use simple decoupling and scale-separation arguments to extend the results of Ref. \cite{Anderson:2010aq} to arbitrary low-energy $A$-body states. Using methods that are reminiscent of the operator product expansion (OPE) in quantum field theory, we find that the high-momentum tails of momentum distributions and static structure factors factorize into the product of a universal function of momentum that is fixed by two-body physics, and a state-dependent matrix element that is the same for both and is sensitive only to low-momentum structure of the many-body state. As a check, we apply our factorization relations to two well-studied systems, the unitary Fermi gas and the electron gas, and reproduce known expressions for the high-momentum tails of each.

Erratum: charm quark contribution to $ {K^{+}}\to {\pi^{+}}\nu \overline{\nu} $ at next-to-next-to-leading order

Abstract We correct the treatment of anomalous triangle diagrams occuring in the effective theory in which the heavy top quark is integrated out. To this end we determine the initial conditions and anomalous dimensions of the operator describing the Z-mediated coupling of neutrinos to quarks and further rectify the bilocal renormalization group evolution. Our changes affect the charm-quark contribution P c(X) at the next-to-leading and next-to-next-to-leading orders, but are numerically negligible as they amout to relative shifts below a permille.

Minimal flavor violation in the minimalU(1)B−Lmodel and resonant leptogenesis

We investigate the resonant leptogenesis scenario in the minimally $U(1)_{B-L}$ extended standard model with minimal flavor violation. In our model, the $U(1)_{B-L}$ gauge symmetry is broken at the TeV scale and standard model singlet neutrinos gain Majorana masses of order TeV. In addition, we introduce a flavor symmetry on the singlet neutrinos at a scale higher than TeV. The flavor symmetry is explicitly broken by the neutrino Dirac Yukawa coupling, which induces splittings in the singlet neutrino Majorana masses at lower scales through renormalization group evolutions. We call this setup "minimal flavor violation". The mass-splittings are proportional to the tiny Dirac Yukawa coupling, and hence they automatically enhance the CP asymmetry parameter necessary for the resonant leptogenesis mechanism. In this paper, we calculate the baryon number yield by solving the Boltzmann equations, including the effects of $U(1)_{B-L}$ gauge boson that also has TeV scale mass and causes washing-out of the singlet neutrinos in the course of thermal leptogenesis. The Dirac Yukawa coupling for neutrinos is fixed in terms of neutrino oscillation data and an arbitrary $3 \times 3$ complex-valued orthogonal matrix. We show that the right amount of baryon number asymmetry can be achieved through thermal leptogenesis in the context of the minimal flavor violation with singlet neutrinos and $U(1)_{B-L}$ gauge boson at the TeV scale. These particles can be discovered at the LHC in the near future.

Higgs boson mass and new physics

We discuss the lower Higgs boson mass bounds which come from the absolute stability of the Standard Model (SM) vacuum and from the Higgs inflation, as well as the prediction of the Higgs boson mass coming from asymptotic safety of the SM. We account for the 3-loop renormalization group evolution of the couplings of the Standard Model and for a part of two-loop corrections that involve the QCD coupling alpha_s to initial conditions for their running. This is one step above the current state of the art procedure ("one-loop matching--two-loop running"). This results in reduction of the theoretical uncertainties in the Higgs boson mass bounds and predictions, associated with the Standard Model physics, to 1-2 GeV. We find that with the account of existing experimental uncertainties in the mass of the top quark and alpha_s (taken at 2sigma level) the bound reads M_H>=M_min (equality corresponds to the asymptotic safety prediction), where M_min=129+-6 GeV. We argue that the discovery of the SM Higgs boson in this range would be in agreement with the hypothesis of the absence of new energy scales between the Fermi and Planck scales, whereas the coincidence of M_H with M_min would suggest that the electroweak scale is determined by Planck physics. In order to clarify the relation between the Fermi and Planck scale a construction of an electron-positron or muon collider with a center of mass energy ~200+200 GeV (Higgs and t-quark factory) would be needed.

Postcards from oases in the desert: phenomenology of SUSY with intermediate scales

The presence of new matter fields charged under the Standard Model gauge group at intermediate scales below the Grand Unification scale modifies the renormalization group evolution of the gauge couplings. This can in turn significantly change the running of the Minimal Supersymmetric Standard Model parameters, in particular the gaugino and the scalar masses. In the absence of new large Yukawa couplings we can parameterise all the intermediate scale models in terms of only two parameters controlling the size of the unified gauge coupling. As a consequence of the modified running, the low energy spectrum can be strongly affected with interesting phenomenological consequences. In particular, we show that scalar over gaugino mass ratios tend to increase and the regions of the parameter space with neutralino Dark Matter compatible with cosmological observations get drastically modified. Moreover, we discuss some observables that can be used to test the intermediate scale physics at the LHC in a wide class of models.

Local projections of low-momentum potentials

Nuclear interactions evolved via renormalization group methods to lower resolution become increasingly nonlocal (off-diagonal in coordinate space) as they are softened. This inhibits both the development of intuition about the interactions and their use with some methods for solving the quantum many-body problem. By applying ``local projections'', a softened interaction can be reduced to a local effective interaction plus a nonlocal residual interaction. At the two-body level, a local projection after similarity renormalization group (SRG) evolution manifests the elimination of short-range repulsive cores and the flow toward universal low-momentum interactions. The SRG residual interaction is found to be relatively weak at low energy, which motivates a perturbative treatment.

Renormalization group evolution of the non-unitary operator

Integrating out a heavy field gives rise to effective Lagrangian containing higher-dimensional operators. In the context of Type-I seesaw mechanism, integrating out the heavy right-handed neutrino field leads to unique dimension-five operator which gives the tree level neutrino mass term. Apart from these there are dimension-six operators that can have important implications. A linear combination of two such operators gives rise to the non-unitarity in the lepton mixing matrix, UPMNS. In this paper, we discuss the origin of non-unitarity at the high scale and its evolution through renormalization group running.

QCD analysis of double parton scattering: Spin and color correlations, interference effects, and evolution

We derive a factorization formula for the double Drell-Yan cross section in terms of double parton distribution functions (dPDFs). Diparton flavor, spin and color correlations and parton-exchange interference terms contribute, even for unpolarized beams. Soft radiation effects are nontrivial for the color correlation and interference contributions and are described by nonperturbative soft functions. We provide a field-theoretic definition of the quark dPDFs and study some of their basic properties, including discrete symmetries and their interpretation in a nonrelativistic quark model. We calculate the renormalization group evolution of the quark dPDFs and of the soft functions. The evolution receives contributions from both ultraviolet and rapidity divergences. We find that color correlation and interference effects are Sudakov suppressed, greatly reducing the number of dPDFs needed to describe double parton scattering at high-energy experiments.

Erratum: Renormalization group evolution in the type I and type II seesaw model [Phys. Rev. D76, 073010 (2007)

We carefully analyze the renormalization group equations in the type I + II seesaw scenario in the extended standard model (SM) and minimal supersymmetric standard model (MSSM). Furthermore, we present analytic formulae of the mixing angles and phases and discuss the RG effect on the different mixing parameters in the type II seesaw scenario. The renormalization group equations of the angles have a contribution which is proportional to the mass squared difference for a hierarchical spectrum. This is in contrast to the inverse proportionality to the mass squared difference in the effective field theory case.

Constraining general two Higgs doublet models by the evolution of Yukawa couplings

We study how general two Higgs doublet models can be constrained by considering their properties under renormalization group evolution of the Yukawa couplings. We take into account both the appearance of a Landau pole as well as off-diagonal Yukawa couplings leading to flavour changing neutral currents in violation with experimental constraints at the electroweak scale. We find that the latter condition can be used to limit the amount of Z2 symmetry breaking allowed in a given model.

Vacuum stability, neutrinos, and dark matter

Motivated by the discovery hint of the Standard Model (SM) Higgs mass around 125 GeV at the LHC, we study the vacuum stability and perturbativity bounds on Higgs scalar of the SM extensions including neutrinos and dark matter (DM). Guided by the SM gauge symmetry and the minimal changes in the SM Higgs potential we consider two extensions of neutrino sector (Type-I and Type-III seesaw mechanisms) and DM sector (a real scalar singlet (darkon) and minimal dark matter (MDM)) respectively. The darkon contributes positively to the $\beta$ function of the Higgs quartic coupling $\lambda$ and can stabilize the SM vacuum up to high scale. Similar to the top quark in the SM we find the cause of instability is sensitive to the size of new Yukawa couplings between heavy neutrinos and Higgs boson, namely, the scale of seesaw mechanism. MDM and Type-III seesaw fermion triplet, two nontrivial representations of $SU(2)_{L}$ group, will bring the additional positive contributions to the gauge coupling $g_{2}$ renormalization group (RG) evolution and would also help to stabilize the electroweak vacuum up to high scale.

The light stop scenario from gauge mediation

In this paper we embed the light stop scenario, a MSSM framework which explains the baryon asymmetry of the universe through a strong first order electroweak phase transition, in a top-down approach. The required low energy spectrum consists in the light SM-like Higgs, the right-handed stop, the gauginos and the Higgsinos while the remaining scalars are heavy. This spectrum is naturally driven by renormalization group evolution starting from a heavy scalar spectrum at high energies. The latter is obtained through a supersymmetry-breaking mix of gauge mediation, which provides the scalars masses by new gauge interactions, and gravity mediation, which generates gaugino and Higgsino masses. This supersymmetry breaking also explains the \mu\ and B_\mu\ parameters necessary for electroweak breaking and predicts small tri-linear mixing terms A_t in agreement with electroweak baryogenesis requirements. The minimal embedding predicts a Higgs mass around its experimental lower bound and by a small extension higher masses m_H\lesssim 127 GeV can be accommodated.

Travels on the squark-gluino mass plane

Soft supersymmetry breaking appears in the weak-scale effective action but is usually generated at higher scales. For these models, the structure of the renormalization group evolution down to the electroweak scale leaves only part of the squark-gluino and slepton-gaugino mass planes accessible. Our observations divide these physical mass planes into three wedges: the first can be reached by all models of high-scale breaking; the second can only be populated by models with a low mediation scale; in the third, wedge squarks and gluinos would have to be described by an exotic theory. All usual benchmark points reside in the first wedge, even though an LHC discovery in the third wedge would arguably be the most exciting outcome.

Radiatively Generated Leptogenesis inS4Flavor Symmetry Models

We study how leptogenesis can be implemented in the seesaw models withS4flavor symmetry, which lead to the tri-bimaximal neutrino mixing matrix. By considering renormalization group evolution from a high-energy scale of flavor symmetry breaking (the GUT scale is assumed) to the low-energy scale of relevant phenomena, the off-diagonal terms in a combination of Dirac Yukawa-coupling matrix can be generated and the degeneracy of heavy right-handed neutrino Majorana masses can be lifted. As a result, the flavored leptogenesis is successfully realized. We also investigate how the effective light neutrino mass|〈mee〉|associated with neutrinoless double beta decay can be predicted along with the neutrino mass hierarchies by imposing the experimental data on the low-energy observables. We find a link between the leptogenesis and the neutrinoless double beta decay characterized by|〈mee〉|through a high-energy CP phase ϕ, which is correlated with the low-energy Majorana CP phases. It is shown that the predictions of|〈mee〉|for some fixed parameters of the high-energy physics can be constrained by the current observation of baryon asymmetry.

Improving the tunings of the MSSM by adding triplets and singlet

We study an extension of the minimal supersymmetric standard model (MSSM) which includes both new $SU(2)$ triplets with hypercharge $\ifmmode\pm\else\textpm\fi{}1$ and a standard model gauge singlet (\`a la the next-to-minimal supersymmetric standard model [NMSSM]) which are coupled to each other. We are motivated by the little hierarchy problem, as well as by the $\ensuremath{\mu}$ problem of the MSSM. We show that the NMSSM and the triplet-extended MSSM can successfully solve problems of one another: while triplets are responsible for large correction to the lightest physical Higgs mass, the singlet's vacuum expectation value (VEV) explains why the $\ensuremath{\mu}$ terms (for the Higgs doublets and the new triplets) are naturally of order the electroweak (EW) scale. We also show that singlet-triplet coupling significantly changes the renormalization group evolution of the singlet mass squared, helping to render this mass squared negative, as required for the singlet to acquire a VEV. We analyze constraints on this scenario from EW precision measurements and find that a relatively large region of the parameter space of this model is viable, especially with the triplet fermions (including doubly charged) being light.

SIMILARITY RENORMALIZATION GROUP EVOLUTION OF NUCLEAR FORCES

In this work we study the similarity renormalization group (SRG) evolution of chiral effective field theory (ChEFT) nucleon-nucleon (NN) interactions derived within the framework of the subtracted kernel method (SKM) approach. We apply the SRG transformation to evolve the leading-order (LO) ChEFT NN potential in the 1S0 and the 3S1-3D1 partial-wave channels and calculate the corresponding phase-shifts.

Renormalization Group Functions in the Broken Symmetry Phase

We investigate the renormalization group(RG) evolution for the neutral scalar field theory in the broken symmetry phase. By using the minimum condition of the vacuum expectation value(VEV), we show that the RG evlution of the effective potential in the broken symmetry phase is governed by the same RG functions in case of the symmetric phase.