On-shell Scheme Research Articles

GM2Calc: precise MSSM prediction for $$(g-2)$$ ( g - 2 ) of the muon

We present GM2Calc, a public C++ program for the calculation of MSSM contributions to the anomalous magnetic moment of the muon, $(g-2)_\mu$. The code computes $(g-2)_\mu$ precisely, by taking into account the latest two-loop corrections and by performing the calculation in a physical on-shell renormalization scheme. In particular the program includes a $\tan\beta$ resummation so that it is valid for arbitrarily high values of $\tan\beta$, as well as fermion/sfermion-loop corrections which lead to non-decoupling effects from heavy squarks. GM2Calc can be run with a standard SLHA input file, internally converting the input into on-shell parameters. Alternatively, input parameters may be specified directly in this on-shell scheme. In both cases the input file allows one to switch on/off individual contributions to study their relative impact. This paper also provides typical usage examples not only in conjunction with spectrum generators and plotting programs but also as C++ subroutines linked to other programs.

Renormalization of Generalized Quantum Electrodynamics

In the present work we shall study the renormalizability of Generalized Quantum Electrodynamics (GQED4). The on-shell renormalization scheme is reviewed and applied to the theory and we calculate the explicit expressions for all the counter-terms of the GQED4.

Vacuum Stability and Two Loop Threshold Corrections to the Higgs Quartic Coupling

We review the vacuum stability problem in the Standard Model by studying the next-to-next-to-leading order (NNLO) shape of the renormalization group improved effective potential by including the threshold corrections of the SM couplings. For this purpose we computed the sum of the vacuum bubbles diagrams up two-loop level and the Higgs tadpoles contributions by two different methods in an on-shell renormalization scheme where the renormalized parameters are directly expressed in terms of physical observables.

Basis invariant measure of CP-violation and renormalization

We analyze, in the context of a simple toy model, for which renormalization schemes the CP-properties of bare Lagrangian and its finite part coincide. We show that this is the case for the minimal subtraction and on-shell schemes. The CP-properties of the theory can then be characterized by CP-odd basis invariants expressed in terms of renormalized masses and couplings. For the minimal subtraction scheme we furthermore show that in CP-conserving theories the CP-odd basis invariants are zero at any scale but are not renormalization group invariant in CP-violating ones.

Higgs mass determination in supersymmetry

AbstractWe present the state-of-the-art of the effective field theory computation of the MSSM Higgs mass, improving the existing ones by including extra threshold corrections. We show that, with this approach, the theoretical uncertainty is within 1 GeV in most of the relevant parameter space. We confirm the smaller value of the Higgs mass found in the EFT computations, which implies a slightly heavier SUSY scale. We study the large tan β region, finding that sbottom thresholds might relax the upper bound on the scale of SUSY. We present SusyHD, a fast computer code that computes the Higgs mass and its uncertainty for any SUSY scale, from the TeV to the Planck scale, even in Split SUSY, both in the \( \overline{\mathrm{DR}} \) and in the on-shell schemes. Finally, we apply our results to derive bounds on some well motivated SUSY models, in particular we show how the value of the Higgs mass allows to determine the complete spectrum in minimal gauge mediation.

Galilean-invariant effective field theory for theX(3872)

XEFT is a low-energy effective field theory for charm mesons and pions that provides a systematically improvable description of the X(3872) resonance. A Galilean-invariant formulation of XEFT is introduced to exploit the fact that mass is very nearly conserved in the transition D*0 --> D0 pi0. The transitions D*0 --> D0 pi0 and X --> D0 D0-bar pi0 are described explicitly in XEFT. The effects of the decay D*0 --> D0 gamma and of short-distance decay modes of the X(3872), such as J/psi --> pi+ pi-, can be taken into account by using complex on-shell renormalization schemes for the D*0 propagator and for the D*0 D0-bar propagator in which the positions of their complex poles are specified. Galilean-invariant XEFT is used to calculate the D*0 D0-bar scattering length to next-to-leading order. Galilean invariance ensures the cancellation of ultraviolet divergences without the need for truncating an expansion in powers of the ratio of the pion and charm meson masses.

Pole mass of theWboson at two-loop order in the pureMS¯scheme

I provide a calculation at full two-loop order of the complex pole squared mass of the W boson in the Standard Model in the pure MS-bar renormalization scheme, with Goldstone boson mass effects resummed. This approach is an alternative to earlier ones that use on-shell or hybrid renormalization schemes. The renormalization scale dependence of the real and imaginary parts of the resulting pole mass are studied. Both deviate by about $\pm 4$ MeV from their median values as the renormalization scale is varied from 50 GeV to 200 GeV, but the theory error is likely larger. A surprising feature of this scheme is that the 2-loop QCD correction has a larger scale-dependence, but a smaller magnitude, than the 2-loop non-QCD correction, unless the renormalization scale is chosen very far from the top-quark mass.

Two-loop contributions of the order O α t α s $$ \mathcal{O}\left({\alpha}_t{\alpha}_s\right) $$ to the masses of the Higgs bosons in the CP-violating NMSSM

We provide the two-loop corrections to the Higgs boson masses of the CP-violating NMSSM in the Feynman diagrammatic approach with vanishing external momentum at $$ \mathcal{O}\left({\alpha}_t{\alpha}_s\right) $$ . The adopted renormalization scheme is a mixture between $$ \overline{\mathrm{DR}} $$ and on-shell conditions. Additionally, the renormalization of the top/stop sector is provided both for the $$ \overline{\mathrm{DR}} $$ and the on-shell scheme. The calculation is performed in the gaugeless limit. We find that the two-loop corrections compared to the one-loop corrections are of the order of 5-10%, depending on the top/stop renormalization scheme. The theoretical error on the Higgs boson masses is reduced due to the inclusion of these higher order corrections.

The m W − m Z interdependence in the Standard Model: a new scrutiny

The m W − m Z interdependence in the Standard Model is studied in the $$ \overline{M\ S} $$ scheme at the two-loop level, including the known higher-order contributions. The relevant radiative parameters, $$ \varDelta \widehat{\alpha}\left(\mu \right) $$ , $$ \varDelta {\widehat{r}}_W $$ , $$ \widehat{\rho} $$ are computed at O(α 2) taking into account higherorder QCD corrections and the resummation of the reducible contributions. We obtain m W = 80.357 ± 0.009 ± 0.003 GeV where the errors refer to the parametric and theoretical uncertainties, respectively. A comparison with the known result in the On-Shell scheme gives a difference of ≈ 6 MeV. As a byproduct of our calculation we also obtain the $$ \overline{M\ S} $$ electromagnetic coupling and the weak mixing angle at the top mass scale, $$ \widehat{\alpha}\left({M}_t\right)={(127.73)}^{-1}\pm 0.0000003 $$ and $$ { \sin}^2{\widehat{\theta}}_W\left({M}_t\right)=0.23462\pm 0.00012 $$ .

Fingerprinting the extended Higgs sector using one-loop corrected Higgs boson couplings and future precision measurements

We calculate radiative corrections to a full set of coupling constants for the 125 GeV Higgs boson at the one-loop level in two Higgs doublet models with four types of Yukawa interaction under the softly-broken discrete Z2 symmetry. The renormalization calculations are performed in the on-shell scheme, in which the gauge dependence in the mixing parameter which appears in the previous calculation is consistently avoided. We first show the details of our renormalization scheme, and present the complete set of the analytic formulae of the renormalized couplings. We then numerically demonstrate how the inner parameters of the model can be extracted by the future precision measurements of these couplings at the high luminosity LHC and the International Linear Collider.

Two-loop electroweak threshold corrections in the Standard Model

We study the relationships between the basic parameters of the on-shell renormalization scheme and their counterparts in the MS¯ scheme at full order O(α2) in the Standard Model. These enter as threshold corrections the renormalization group analyses underlying, e.g., the investigation of the vacuum stability. To ensure the gauge invariance of the parameters, in particular of the MS¯ masses, we work in Rξ gauge and systematically include tadpole contributions. We also consider the gaugeless-limit approximation and compare it with the full two-loop electroweak calculation.

Quark mass relations to four-loop order in perturbative QCD.

We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS[over ¯]) scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS[over ¯] quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS[over ¯] heavy quark masses.

Differential distributions for top-quark hadro-production with a running mass

We take a look at how the differential distributions for top-quark production are affected by changing to the running mass scheme. Specifically we consider the transverse momentum, rapidity and pair-invariant mass distributions at next-to-leading order for the top-quark mass in the $$\overline{\hbox {MS}}$$ scheme. It is found that, similar to the total cross section, the perturbative expansion converges faster and the scale dependence improves using the mass in the $$\overline{\hbox {MS}}$$ scheme as opposed to the on-shell scheme. We also update the analysis for the total cross section using the now available full next-to-next-to-leading order contribution.

Indirect measurement ofsin2θW(orMW) usingμ+μ−pairs fromγ*/Zbosons produced inpp¯collisions at a center-of-momentum energy of 1.96 TeV

Drell-Yan lepton pairs are produced in the process $p\bar{p} \rightarrow \mu^+\mu^- + X$ through an intermediate $\gamma^*/Z$ boson. The forward-backward asymmetry in the polar-angle distribution of the $\mu^-$ as a function of the invariant mass of the $\mu^+\mu^-$ pair is used to obtain the effective leptonic determination $\sin^2 \theta^{lept}_{eff}$ of the electroweak-mixing parameter $\sin^2 \theta_W$, from which the value of $\sin^2 \theta_W$ is derived assuming the standard model. The measurement sample, recorded by the Collider Detector at Fermilab (CDF), corresponds to 9.2 fb-1 of integrated luminosity from $p\bar{p}$ collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF Run II data set. The value of $\sin^2 \theta^{lept}_{eff}$ is found to be 0.2315 +- 0.0010, where statistical and systematic uncertainties are combined in quadrature. When interpreted within the context of the standard model using the on-shell renormalization scheme, where $\sin^2 \theta_W = 1 - M_W^2/M_Z^2$, the measurement yields $\sin^2 \theta_W$ = 0.2233 +- 0.0009, or equivalently a W-boson mass of 80.365 +- 0.047 GeV/c^2. The value of the W-boson mass is in agreement with previous determinations in electron-positron collisions and at the Tevatron collider.

SOME TWO-LOOP CONTRIBUTIONS TO MUON MAGNETIC DIPOLE MOMENT IN THE CP-VIOLATING MSSM

In the CP-violating minimal supersymmetric extension of the Standard Model (MSSM), we study the two-loop diagrams without the one-loop self-energy, and they are composed of virtual neutralino–slepton-Z. We obtain electroweak corrections to the anomalous magnetic dipole moment (MDM) of muon. With electromagnetic gauge invariance, the Wilson coefficients of dimension-5 operators contributing to the MDM of muon are deduced. To remove the ultra-violet divergences induced by the divergent sub-diagrams, we use the on-shell scheme. The numerical results are about 8.8×10-11, i.e. at the same order of present experimental precision, which indicates these two-loop diagrams are important.

Indirect measurement ofsin2θW(MW) usinge+e−pairs in theZ-boson region withpp¯collisions at a center-of-momentum energy of 1.96 TeV

Drell-Yan lepton pairs are produced in the process $p\bar{p} \rightarrow e^+e^- + X$ through an intermediate $\gamma^*/Z$ boson. The lepton angular distributions are used to provide information on the electroweak-mixing parameter $sin^2\theta_W$ via its observable effective-leptonic $sin^2\theta_W$, or $sin^2\theta^{lept}_{eff}$. A new method to infer $sin^2\theta_W$, or equivalently, the W-boson mass M_W in the on-shell scheme, is developed and tested using a previous CDF Run II measurement of angular distributions from electron pairs in a sample corresponding to 2.1 fb-1 of integrated luminosity from $p\bar{p}$ collisions at a center-of-momentum energy of 1.96 TeV. The value of $sin^2\theta^{lept}_{eff}$ is found to be 0.2328 +- 0.0010. Within a specified context of the standard model, this results in $sin^2\theta_W$ = 0.2246 +- 0.0009 which corresponds to a W-boson mass of 80.297 +- 0.048 GeV/c^2, in agreement with previous determinations in electron-position collisions and at the Tevatron collider.

Estimating two-loop radiative effects in the MOLLER experiment

Within the on-shell renormalization scheme, two-loop electroweak corrections to the parityviolating polarization asymmetry in the reaction e−e− → e−e−(γ, γγ) were estimated for the MOLLER experiment at JLab. The infrared divergence and the imaginary part of the amplitude were taken completely under control. Relevant compact expressions obtained by using asymptotic methods are free from unphysical parameters and are convenient for analysis and for numerical estimations. A numerical analysis revealed a significant scale of two-loop effects and the need for taking them into account in the MOLLER experiment.

One-loop on-shell renormalization of MSSM vertexes

The on-shell renormalization scheme for electroweak theory is well studied in the standard model (SM), but a consistent on-shell renormalization scheme for the minimal supersymmetric standard model (MSSM) is still unknown. In the MSSM, we study the on-shell scheme for three vertexes: and , with virtual SUSY particles (chargino, sneutrino, neutralino and slepton) at one-loop order. Instead of the amplitude of a single triangle diagram, the sum of the amplitude of triangle diagrams belonging to one suit can be renormalized in the on-shell scheme. One suit points out that the internal virtual particles are consistent. The zero-momentum scheme is also used for the renormalization. The two schemes can make the renormalized results decoupled, and in the MSSM some of the special characters of the on-shell scheme are shown. This work is propitious in completing the on-shell renormalization scheme in the MSSM.

One-loop electroweak corrections for polarized Møller scattering at different renormalization schemes and conditions

Using two different approaches, we perform detailed calculations of the one-loop (Next-to-Leading Order (NLO)) electroweak radiative corrections to the parity violating e − e − → e − e −(γ) scattering asymmetry. First approach, more classical, relies on calculations “by hand” with reasonable approximations, second approach relies on program packages FeynArts, FormCalc, LoopTools, and FORM. The detailed numerical analysis of the various contributions is provided for a wide range of energies relevant for the ultraprecise 11 GeV MOLLER experiment planned at the JLab, as well as future experiments at the International Linear Collider (ILC). The numerical results obtained within the on-shell renormalization scheme using two different sets of renormalization conditions are in excellent agreement. We also calculate the total NLO correction in the Constrained Differential Renormalization (CDR) scheme. Analysis of the results, along with the increasing experimental precision, shows that it is feasible that the corrections at the Next-to-Next-to-Leading Order (NNLO) level may be important for the next generation of experiments.

Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment

We compute the eighth-order fermionic corrections involving two and three closed massless fermion loops to the anomalous magnetic moment of the muon. The required four-loop on-shell integrals are classified and explicit analytical results for the master integrals are presented. As further applications we compute the corresponding four-loop QCD corrections to the mass and wave function renormalization constants for a massive quark in the on-shell scheme.