Feynman-diagrammatic Approach Research Articles

Nonholomorphic soft-term contributions to the Higgs-boson masses in the Feynman diagrammatic approach

We study the effects of non-holomprphic soft SUSY-breaking terms added to the Minimal Supersymmetric Standard Model (MSSM) on the Higgs-boson masses. The calculation of the non-holomorphic contributions is perfromed at the one-loop level in the Feynman diagramatic approach. After generating a FeynArts model file with the help of SARAH, we calculate the renormalized Higgs-boson self-energies at the one-loop level using the FeynArts/FormCalc setup. The results obtained from FeynArts/FormCalc are fed to FeynHiggs to estimate the contributions to the neutral CP-even Higgs-boson masses, $M_{h,H}$, as well as to the charged Higgs-boson mass, $M_{H^{\pm}}$. For the specific set of parameter points that we choose for this study, the non-holomorphic soft-term contributions to the CP-even light Higgs boson mass $M_h$, contrary to claims in the literature, turn out to be very small. For the CP-even heavy Higgs boson mass, $M_{H}$, as well as for the charged Higgs boson mass, $M_{H^{\pm}}$, the contributions can be substantially larger for some parts of parameter space.

Complete one-loop structure of the type-(I+II) seesaw effective field theory

Besides the three canonical seesaw mechanisms, the hybrid scenario, i.e., the so-called type-(I+II) seesaw mechanism containing both the right-handed neutrinos NR and the triplet Higgs Φ is also an appealing extension of the Standard Model (SM) to account for tiny neutrino masses. Recently, the seesaw effective field theories (SEFTs) of the three canonical seesaw mechanisms have already been completely constructed up to one-loop level. In this work, we carry out the one-loop matching of the type-(I+II) seesaw mechanism onto the corresponding type-(I+II) SEFT, which is by no means the trivial combination of the type-I and type-II SEFTs and contains additional contributions even though the right-handed neutrinos and the triplet Higgs have no direct interactions. Employing the Feynman diagrammatic approach, we calculate all those additional contributions from the entangled effects of NR and Φ, and finally achieve the complete one-loop structure of the type-(I+II) SEFT. In the type-(I+II) SEFT, the number and content of dim-6 operators are exactly the same as those in the type-II SEFT, but the Wilson coefficients of the unique dim-5 and nine dim-6 operators as well as the quartic coupling constant of the SM Higgs gain some additional contributions, which are absent in the type-I and type-II SEFTs.

NLO deflections for spinning particles and Kerr black holes

We employ the “KMOC” formalism of [1] to compute classical momentum deflections of spinning bodies with arbitrary spin orientations up to next-to-leading order (one loop). We do this in electrodynamics and gravity. The final result, valid for generic masses, is true for all spins at tree level and up to second (fourth) spin order for the electromagnetic (gravity) case at one loop. Furthermore, emphasis is given to the probe limit scenario where our results extend to all spin orders in the heavy source, even at next-to-leading order. We carry out our computations both using a unitarity based framework and Feynman diagrammatic approach which relies on scattering amplitudes computed on fixed backgrounds.

Two-loop mathcal{O} ((\u03b1t + \u03b1\u03bb + \u03b1\u03ba)2) corrections to the Higgs boson masses in the CP-violating NMSSM

We present our computation of the mathcal{O} ((αt + αλ + ακ)2) two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum. We choose a mixed overline{mathrm{DR}} -on-shell (OS) renormalisation scheme for the Higgs sector and apply both overline{mathrm{DR}} and OS renormalisation in the top/stop sector. For the treatment of the infrared divergences we apply and compare three different regularisation methods: the introduction of a regulator mass, the application of a small momentum expansion, and the inclusion of the full momentum dependence. Our new corrections have been implemented in the Fortran code NMSSMCALC that computes the Higgs mass spectrum of the CP-conserving and CP-violating NMSSM as well as the Higgs boson decays including the state-of-the-art higher-order corrections. Our numerical analysis shows that the newly computed corrections increase with rising λ and κ, remaining overall below about 3% compared to our previously computed mathcal{O} (αt(αt + αs)) corrections, in the region compatible with perturbativity below the GUT scale. The renormalisation scheme and scale dependence is of typical two-loop order. The impact of the CP-violating phases in the new corrections is small. We furthermore show that the Goldstone Boson Catastrophe due to the infrared divergences can be treated in a numerically efficient way by introducing a regulator mass that approximates the momentum-dependent results best for squared mass values in the permille range of the squared renormalisation scale. Our results mark another step forward in the program of increasing the precision in the NMSSM Higgs boson observables.

K+ Λ and K 0Λ photoproduction with High-Spin Nucleón Resonances

A new model for photoproduction of KΛ, i.e. γ + p → K+ Λ and γ + n → K 0Λ has been constructed by using the Feynman diagrammatic approach. By using this approach, we have calculated the scattering amplitude analytically. In addition, we have also included a number of very-high-spin nucleon resonances, i.e. those with spins 11/2 and 13/2, which are listed by the Particle Data Group (PDG). The unknown parameters in the model, i.e., the hadronic coupling constants, were extracted by fitting the calculated observables to nearly 9000 experimental data points. The result of the model calculations is compared with those of previous investigations and experimental data. From the comparison we may conclude that the constructed model can nicely reproduce the experimental data.

The use of Feynman diagrammatic approach for well test analysis in stochastic porous media

Transient well test analysis provides valuable information about reservoir characteristics such as permeability and the hydraulic diffusivity coefficient. It is based on the solution of diffusivity equation, which describes mass transfer in porous media. On the whole, analytical solutions are used for interpreting well test data. However, all these solutions were obtained under the condition of reservoir homogeneity. In a heterogeneous reservoir with spatially variable permeability, the exact analytical solutions are not known. The heterogeneous permeability field can be represented as the sum of two terms. The first term is a constant mean permeability value and the second one is a random function with known statistical properties. The second term can be considered a perturbation. The possibility of evaluating geostatistical parameters from well test analysis was considered by various authors and is still a challenging problem. In a randomly heterogeneous reservoir, a flow equation is formulated for the pressure, which is averaged over all the permeability realizations. It can be solved using Green’s function techniques, where the ensemble-averaged pressure is represented as an infinite perturbation series. This series can be represented graphically using Feynman diagrams and its summation can be performed following the rules that are well known in the quantum theory of solid state. For the first time, this framework was introduced to reservoir simulation in King (J. Phys. A: Math. Gen. 20, 3935–3947, 1987), where the stochastic pressure equation was solved for the steady-state case. In this study, we use diagram approach to obtain the solution of the time-dependent stochastic pressure equation which is derived for a lognormal random permeability field under the assumption of the Gaussian correlation function. The expression for transient ensemble averaged pressure is obtained with respect to high-order corrections of permeability variance. In the limit of sufficiently small variance, analytical expressions for the pressure correction are presented. The two limiting cases were considered: (i) the distance between wells is much bigger than the permeability correlation length; (ii) the opposite case where the correlation length is the smallest length parameter. The resulting solution can be used for the analysis of drawdown, build-up, and interference tests in stochastic porous media. The possibility of estimating the parameters of a random permeability field based on well test data is discussed.

Partial wave analysis for KΣ photoproduction on the nucleon valid from threshold up to W = 2.8 GeV

We have simultaneously analyzed the available kaon photoproduction data for the , , , and channels by using an isobar model constructed from the Feynman diagrammatic approach for the background terms and multipoles formulation for the resonance terms. The unknown coupling constants in the background terms as well as the helicity amplitudes and the kaon branching ratios of the resonance terms were extracted by fitting the calculated observables to nearly 8000 data points from the latest experimental measurements, including the recent and data from MAMI A2 collaboration. During the fitting process we used the data listed in the Review of Particle Properties of Particle Data Group as a guidance for the resonance properties. Since in the previous study the kaon branching ratio of the N(1710)P11 state was found to be relatively large and, as a consequence, a sizable spike appeared in the K+Σ− cross section near the threshold, in the present work we propose two isobar models, i.e. with and without this state. We have found that both models can nicely fit the data. Extensive comparisons between the result of model calculation and experimental data are presented in this paper. To investigate the role of each resonance in the present work the significance of each resonance is calculated and discussed. The present work indicates that the N(1895)S11 and Δ(1900)S31 as the important resonances in the KΣ photoproduction. We also present two examples of application of the presented isobar models, i.e. investigation of the nucleon resonance N(1535)S11 coupling to the KΣ channels and the contribution of KΣ channels to the Gerasimov–Drell–Hearn sum rule.

Two-loop mathcal{O} ( {alpha}_t^2 ) corrections to the neutral Higgs boson masses in the CP-violating NMSSM

We present our calculation of the two-loop corrections of mathcal{O} ( {alpha}_t^2 ) to the neutral Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM). The calculation is performed in the Feynman diagrammatic approach in the gaugeless limit at vanishing external momentum. We apply a mixed overline{mathrm{DR}} -on-shell (OS) renormalization scheme for the NMSSM input parameters. Furthermore, we exploit a overline{mathrm{DR}} as well as an OS renormalization in the top/stop sector. The corrections are implemented in the Fortran code NMSSMCALC for the calculation of the Higgs spectrum both in the CP-conserving and CP-violating NMSSM. The code also provides the Higgs boson decays including the state-of-the-art higher-order corrections. The corrections computed in this work improve the already available corrections in NMSSMCALC which are the full one-loop corrections without any approximation and the two-loop mathcal{O} (αtαs) corrections in the gaugeless limit and at vanishing external momentum. Depending on the chosen parameter point, we find that the O(αtαs + {alpha}_t^2 ) corrections add about 4-7% to the one-loop mass of the SM-like Higgs boson for overline{mathrm{DR}} renormalization in the top/stop sector and they reduce the mass by about 6-9% if OS renormalization is applied. For an estimate of the theoretical uncertainty we vary the renormalization scale and change the renormalization scheme and show that care has to be taken in the corresponding interpretation.

The hMSSM approach for Higgs self-couplings revisited

We compare the decay of the heavy Higgs boson into two SM-like Higgs bosons, Hrightarrow hh, calculated in a Feynman-diagrammatic approach at the one-loop level based on the one hand on the full effective potential involving the top quark and stops in the Minimal Supersymmetric Standard Model (MSSM) accompanied by the matched Two-Higgs-Doublet Model (2HDM) as its low-energy limit and on the other hand on the hMSSM approximation. We identify missing contributions due to the top quark in the Higgs self-couplings of the hMSSM, that – when taken into account – lead to a good agreement between the hMSSM and a full MSSM calculation, at least in the limit of the Higgsino mass parameter mu being small compared to the stop spectrum. We also thoroughly analyze momentum-dependent and kinetic corrections intrinsic to the Feynman-diagrammatic approach and the matching to the effective Lagrangian, respectively, for both our calculation in the MSSM and the hMSSM and for the latter suggest to include additional corrections from the top quark, which are independent of the unknown supersymmetric spectrum.

Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters

Higher-order corrections to the MSSM Higgs-boson masses are desirable for accurate predictions currently testable at the LHC. By comparing the prediction with the measured value of the discovered Higgs signal, viable parameter regions can be inferred. For an improved theory accuracy, we compute all two-loop corrections involving the strong coupling for the Higgs-boson mass spectrum of the MSSM with complex parameters. Apart from the dependence on the strong coupling, these contributions depend on the weak coupling and Yukawa couplings, leading to terms of mathcal {O}{left( alpha alpha _sright) } and mathcal {O}{left( sqrt{alpha _{q_1}}sqrt{alpha _{q_2}}alpha _sright) }, (q_{1,2}=t,b,c,s,u,d). The full dependence on the external momentum and all relevant mass scales is taken into account. The calculation is performed in the Feynman-diagrammatic approach which is flexible in the choice of the employed renormalization scheme. For the phenomenological results presented here, a renormalization scheme consistent with higher-order corrections included in the code FeynHiggs is adopted. For the evaluation of the results, a total of 513 two-loop two-point integrals with up to five different mass scales are computed fully numerically using the program SecDec. A comparison with existing results in the limit of real parameters and/or vanishing external momentum is carried out, and the impact on the lightest Higgs-boson mass is discussed, including the dependence on complex phases. The new results will be included in the public code FeynHiggs.

Two-loop top and bottom Yukawa corrections to the Higgs-boson masses in the complex MSSM

Results for the two-loop corrections to the Higgs-boson masses of the MSSM with complex parameters of {mathcal {O}}{left( alpha _t^2+alpha _talpha _b+alpha _b^2right) } from the Yukawa sector in the gauge-less limit are presented. The corresponding self-energies and their renormalization have been obtained in the Feynman-diagrammatic approach. The impact of the new contributions on the Higgs spectrum is investigated. Furthermore, a comparison with an existing result in the limit of the MSSM with real parameters is carried out. The new results will be included in the public code FeynHiggs.

The Light CP-Even Higgs Boson Mass of the MSSM at Three-Loop Accuracy

In this paper we are going to discuss the relevant aspects related to the calculation of the higher order corrections to the lightest CP-even Higgs boson mass of the minimal supersymmetric standard model with real parameters (rMSSM). We have computed these corrections using the Feynman diagrammatic approach with a precision of three-loop in the SUSYQCD sector. The renormalization scheme adopted in this work is based on a variant of dimensional regularization where the so called dimensional reduction is performed in order to preserve supersymmetry to all perturbative orders. The calculation will extend the region of validity of previous studies to the whole parameters space. The emerging loop integrals have been computed by exploiting new proposed approaches based on the dispersion relation techniques for the numerical calculation of three-loop vacuum integrals with arbitrary mass scales.

Finite remainders of the Konishi at two loops in mathcal{N}=4 SYM

We present three point form factors (FF) in mathcal{N}=4 Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the ‘t Hooft coupling using Feynman diagrammatic approach. We have chosen on shell final states consisting of gϕϕ and ϕλλ, where ϕ, λ, g are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani’s IR subtraction operators. Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them. We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. However, surprisingly, the leading transcendental terms for gϕϕ agree with that of the half-BPS. We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.

Konishi form factor at three loops in N=4 supersymmetric Yang-Mills theory

We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in ${\cal N}=4$ supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction ($\overline {DR}$) scheme. We show that it satisfies KG equation in $\overline {DR}$ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in ${\cal N}=4$.

More on the bending of light in quantum gravity

We reconsider the long-range effects of the scattering of massless scalars and photons from a massive scalar object in quantum gravity. At the one-loop level, the relevant quantum mechanical corrections could be sorted into the graviton double-cut contributions, massless-scalar double-cut contributions and photon double-cut contributions. In arXiv:1410.7590 and 1609.07477 N.E.J. Bjerrum-Bohr et al. have considered explicitly the implications of the graviton double-cut contributions on the gravitational bending of light and some classical formulations of the equivalence principle, using the modern double-copy constructions and on-shell unitarity techniques. In this article, instead we consider all three contributions and redo the analysis using the traditional Feynman diagrammatic approach. Our results on the graviton double-cut contributions agree with the aforementioned references, which acts as a nontrivial check of previous computations. Furthermore, it turns out that the massless-scalar double-cut contributions and the photon double-cut contributions do leave non-vanishing quantum effects on the scattering amplitudes and the gravitational bending of light. Yet, we find that the general structure of the gravitational amplitudes and the quantum discrepancy of the equivalence principle suggested in the aforementioned references remain intact.

Precise predictions for the Higgs-boson masses in the NMSSM

The particle discovered in the Higgs-boson searches at the LHC with a mass of about 125 , mathrm{GeV} can be identified with one of the neutral Higgs bosons of the Next-to-Minimal Supersymmetric Standard Model (NMSSM). We calculate predictions for the Higgs-boson masses in the NMSSM using the Feynman-diagrammatic approach. The predictions are based on the full NMSSM one-loop corrections supplemented with the dominant and sub-dominant two-loop corrections within the Minimal Supersymmetric Standard Model (MSSM). These include contributions at mathcal {O}{(alpha _t alpha _s, alpha _b alpha _s, alpha _t^2,alpha _talpha _b)}, as well as a resummation of leading and subleading logarithms from the top/scalar top sector. Taking these corrections into account in the prediction for the mass of the Higgs boson in the NMSSM that is identified with the observed signal is crucial in order to reach a precision at a similar level as in the MSSM. The quality of the approximation made at the two-loop level is analysed on the basis of the full one-loop result, with a particular focus on the prediction for the Standard Model-like Higgs boson that is associated with the observed signal. The obtained results will be used as a basis for the extension of the code FeynHiggs to the NMSSM.

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.

Higgs boson masses and mixings in the complex MSSM with two-loop top-Yukawa-coupling corrections

Results for the leading two-loop corrections of $\mathcal{O}{\left(\alpha_t^2\right)}$ from the Yukawa sector to the Higgs-boson mass spectrum of the MSSM with complex parameters are presented, with details of the analytical calculation performed in the Feynman-diagrammatic approach using a mixed $\left.\text{on-shell}\middle/\,\overline{\text{DR}}\right.$ scheme that can be directly matched onto the higher-order terms in the code ${\tt FeynHiggs}$. Numerical results are shown for the masses and mixing effects in the neutral Higgs-boson sector and their variation with the phases of the complex parameters. Furthermore, the analytical expressions of the two-loop self-energies and the required renormalization constants are recorded. The new results can consistently be implemented in ${\tt FeynHiggs}$.

Momentum-dependent two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM

Results are presented for the momentum dependent two-loop contributions of O(alpha_t alpha_s) to the masses and mixing effects in the Higgs sector of the MSSM. They are obtained in the Feynman-diagrammatic approach using a mixed on-shell/DRbar renormalization that can directly be matched onto the higher-order corrections included in the code FeynHiggs. The new two-loop diagrams are evaluated with the program SecDec. The combination of the new momentum dependent two-loop contribution with the existing one- and two-loop corrections in the on-shell/DRbar scheme leads to an improved prediction of the light MSSM Higgs boson mass and a correspondingly reduced theoretical uncertainty. We find that the corresponding shifts in the lightest Higgs-boson mass M_h are below 1 GeV in all scenarios considered, but can extend up to the level of the current experimental uncertainty. The results are included in the code FeynHiggs.

Two-loop top-Yukawa-coupling corrections to the Higgs boson masses in the complex MSSM

Results for the leading two-loop corrections of O(αt2) from the Yukawa sector to the Higgs-boson masses of the MSSM with complex parameters are presented. The corresponding self-energies and their renormalization have been obtained in a Feynman-diagrammatic approach. A numerical analysis of the new contributions is performed for the mass of the lightest Higgs boson, supplemented by the full one-loop result and the O(αtαs) terms including complex phases. In the limit of the real MSSM a previous result is confirmed.