Feynman-diagrammatic Approach Research Articles

Tools for NLO automation: Extension of the golem95C integral library

We present an extension of the program golem95C for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes, which supports tensor ranks exceeding the number of propagators. This extension allows various applications in Beyond the Standard Model physics and effective theories, for example higher ranks due to propagators of spin two particles, or due to effective vertices. Complex masses are also supported. The program is not restricted to the Feynman diagrammatic approach, as it also contains routines to interface to unitarity-inspired numerical reconstruction of the integrand at the tensorial level. Therefore, it can serve as a general integral library in automated programs to calculate one-loop amplitudes. New version program summaryProgram title: golem95-1.3.0Catalogue identifier: AEEO_v3_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEEO_v3_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 242036No. of bytes in distributed program, including test data, etc.: 1092837Distribution format: tar.gzProgramming language: Fortran95.Computer: any computer with a Fortran95 compiler.Operating system: Linux, Unix.RAM: RAM used per integral/form factor is insignificantClassification: 4.4, 11.1.External routines: some finite scalar integrals are called from OneLOop [1,2], the option to call them from LoopTools [3,4] is also implemented.Catalogue identifier of previous version: AEEO_v2_0Journal reference of previous version: Comput. Phys. Comm. 182(2011)2276Does the new version supercede the previous version?: yesNature of problem:evaluation of one-loop multi-leg integrals occurring in the calculation of next-to-leading order corrections to scattering amplitudes in particle physics. In the presence of particles with spin two in the loop, or effective vertices, or certain gauges, tensor integrals where the rank exceeds the number of propagators N are required.Solution method:extension of the reduction algorithm to rank r≤10 for N≤4 and r≤N+1 for N≥5, which is sufficient for most applications in Beyond the Standard Model Physics.Reasons for new version:the previous version was restricted to tensor ranks less than or equal to the number of propagators.Summary of revisions:tensor ranks >N are supported, an alternative reduction method for the case of infrared divergent triangles is implemented, numerical stability for the case of small mass differences has been improved.Running time:depends on the nature of the problem. A single call to a rank 6 five-point form factor at a randomly chosen kinematic point, using real masses, takes 10−3 s on an Intel Core 4 i7-3770 CPU with a 3.4 GHz processor.

Charged Higgs boson mass of the MSSM in the Feynman diagrammatic approach

The interpretation of the Higgs signal at \sim 126 GeV within the Minimal Supersymmetric Standard Model (MSSM) depends crucially on the predicted properties of the other Higgs states of the model, as the mass of the charged Higgs boson, MH+-. This mass is calculated in the Feynman-diagrammatic approach within the MSSM with real parameters. The result includes the complete one-loop contributions and the two-loop contributions of O(alpha_t alpha_s). The one-loop contributions lead to sizable shifts in the MH+- prediction, reaching up to \sim 8 GeV for relatively small values of M_A. Even larger effects can occur depending on the sign and size of the mu parameter that enters the corrections affecting the relation between the bottom-quark mass and the bottom Yukawa coupling. The two-loop O(alpha_t alpha_s) terms can shift MH+- by more than 2 GeV. The two-loop contributions amount to typically about 30% of the one-loop corrections for the examples that we have studied. These effects can be relevant for precision analyses of the charged MSSM Higgs boson.

Higgs boson masses in the complex NMSSM at one-loop level

Abstract The Next-to-Minimal Supersymmetric Extension of the Standard Model (NMSSM) with a Higgs sector containing five neutral and two charged Higgs bosons allows for a rich phenomenology. In addition, the plethora of parameters provides many sources of CP violation. In contrast to the Minimal Supersymmetric Extension, CP violation in the Higgs sector is already possible at tree-level. For a reliable understanding and interpretation of the experimental results of the Higgs boson search, and for a proper distinction of Higgs sectors provided by the Standard Model or possible extensions, the Higgs boson masses have to be known as precisely as possible including higher-order corrections. In this paper we calculate the one-loop corrections to the neutral Higgs boson masses in the complex NMSSM in a Feynman diagrammatic approach adopting a mixed renormalization scheme based on on-shell and $ \overline{\mathrm{DR}} $ conditions. We study various scenarios where we allow for tree-level CP-violating phases in the Higgs sector and where we also study radiatively induced CP violation due to a non-vanishing phase of the trilinear coupling A t in the stop sector. The effects on the Higgs boson phenomenology are found to be significant. We furthermore estimate the theoretical error due to unknown higher-order corrections by both varying the renormalization scheme of the top and bottom quark masses and by adopting different renormalization scales. The residual theoretical error can be estimated to about 10%.

Comparison of transient grating signals from spheroidene in an organic solvent and in pigment-protein complexes fromRhodobacter sphaeroides2.4.1

The concurrent dynamics of the electronic excitation and vibronic oscillations of spheroidene have been investigated by means of the transient grating (TG) spectroscopy. The third-order optical responses of spheroidene in an organic solvent, in the LH2 light-harvesting antenna complexes, and in chromatophores have been compared in order to investigate the influence of the environment surrounding this photosynthetic pigment. Vibronic coherent oscillations with a period of several tens of femtosecond have been clearly observed superimposed on a slowly varying background, which reflects the electronic dynamics. The dynamics of the coherent oscillations have been analyzed by means of the wavelet analysis. Within our experimental accuracy, the decay times of the $\text{C}\text{C}$ and $\text{C}\text{C}$ stretching modes and ${\text{C}\text{CH}}_{3}$ rocking mode of each specimen are very close. The experimental results have also been analyzed using a Brownian oscillator model. For these numerical calculations, the spectral density for the underdamped modes has been determined from the Raman spectrum of spheroidene. It was found that the low-frequency modes that reflect the influence of the protein environment can be approximated by the overdamped Brownian oscillator. The experimentally observed linear absorption spectra as well as the third-order optical responses, i.e., TG curves, are reproduced very well by these calculations. The close agreement between the experiments and calculations indicates that the Feynman-diagrammatic approach can be applied to express not only the internal conversion but also the intermolecular excitation energy-transfer processes. The vibronic decay rates of spheroidene in LH2 complexes and chromatophores are evaluated to be about 20% larger than in the organic solvent.

FeynHiggs: A program for the calculation of MSSM Higgs-boson observables – Version 2.6.5

FeynHiggs is a Fortran code for the calculation of physical observables in the field of high-energy physics. FeynHiggs calculates various observables in the Higgs sector of the Minimal Supersymmetric Standard Model (MSSM) for real or complex parameters. These observables comprise Higgs-boson masses, mixing angles, couplings, Tevatron/LHC production cross-sections, branching ratios, as well as some additional observables such as Δ ρ, M W , the effective leptonic weak mixing angle, ( g − 2 ) μ , BR( b → s γ ), electric dipole moments. New version program summary Program title: FeynHiggs v2.6.5 Catalogue identifier: ADKT_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADKT_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL No. of lines in distributed program, including test data, etc.: 156 455 No. of bytes in distributed program, including test data, etc.: 1 058 758 Distribution format: tar.gz Programming language: Fortran 77, C, Mathematica Computer: Intel/AMD, PowerPC, Alpha Operating system: Linux, Windows (Cygwin), Mac OS, Tru64 Unix RAM: insignificant (typically a few MB) Classification: 11.5 Catalogue identifier of previous version: ADKT_v1_0 Journal reference of previous version: Comput. Phys. Comm. 124 (2000) 76 Does the new version supersede the previous version?: Yes Nature of problem: The experimental searches for Higgs bosons have to be compared with theory predictions at a high level of accuracy. Radiative corrections are especially important in the Minimal Supersymmetric Standard Model (MSSM). Solution method: High-precision calculations (mostly based on the Feynman-diagrammatic approach) for various Higgs-boson observables in the MSSM are implemented. The program takes the basic model parameters as input and evaluates many MSSM Higgs-boson observables relevant for experimental Higgs-boson physics. Reasons for new version: Existing calculations have been refined (e.g., by the inclusion of complex parameters); many new observables have been implemented. Summary of revisions: Input parameters are now allowed to be complex, and non-minimal flavor violation is permitted. Besides the Higgs-boson masses also branching ratios and hadron-collider production cross-sections are calculated. Restrictions: Several observables are still missing and have to be implemented. Running time: The command-line frontend, which invokes essentially all FeynHiggs functions, takes 200 ms a single point in parameter space On a 3 GHz AMD CPU.

Two-Loop Corrections to the Charged Higgs-Boson Mass in the MSSM

We review the numerical effects of the leading two-loop corrections to the mass of the charged Higgs boson, M H ± , in the MSSM. They consist of the contributions of O ( α t α s ) and are calculated in the Feynman-diagrammatic approach. In the numerical analysis we investigate the variation of M H ± as a function of M A , tan β and the Higgs mixing parameter μ . The two-loop corrections can change M H ± up to 5 GeV for positive values μ and large tan β .

Precise predictions for LHC using a GOLEM

In this talk we present recent next-to-leading order results relevant for LHC phenomenology obtained with the GOLEM method. After reviewing the status of this Feynman diagrammatic approach for multi-leg one-loop calculations we discuss three applications: the loop-induced process gg -> Z^*Z^* and the virtual corrections to the five and six point processes qq -> ZZg and u ubar -> s sbar c cbar. We demonstrate that our method leads to representations of such amplitudes which allow for efficient phase space integration. In this context we propose a reweighting technique of the leading order unweighted events by local K-factors.

Precise predictions for [formula omitted] decays in the complex MSSM

Complete one-loop results for the decay widths of neutral Higgs bosons (ha) into lighter neutral Higgs bosons (hb,hc) are presented for the MSSM with complex parameters. The results are obtained in the Feynman-diagrammatic approach, taking into account the full dependence on the spectrum of supersymmetric particles and all complex phases of the supersymmetric parameters. The genuine triple-Higgs vertex contributions are supplemented with two-loop propagator-type corrections, yielding the currently most precise prediction for this class of processes. The genuine vertex corrections turn out to be very important, yielding a large increase of the decay width compared to a prediction based on the tree-level vertex. The new results are used to analyse the impact of the experimental limits from the LEP Higgs searches on the parameter space with a very light MSSM Higgs boson. It is found that a significant part of the parameter space of the CPX benchmark scenario exists where channels involving the decay h2→h1h1 have the highest search sensitivity, and the existence of an unexcluded region with Mh1≈45 GeV is confirmed.

The Higgs sector of the complex MSSM at two-loop order: QCD contributions

Results are presented for the leading two-loop contributions of O(αtαs) to the masses and mixing effects in the Higgs sector of the MSSM with complex parameters. They are obtained in the Feynman-diagrammatic approach using on-shell renormalization. The full dependence on all complex phases is taken into account. The renormalization of the appropriate contributions of the Higgs-boson sector and the scalar top and bottom sector is discussed. Our numerical analysis for the lightest MSSM Higgs-boson mass is based on the new two-loop corrections, supplemented by the full one-loop result. The corrections induced by the phase variation in the scalar top sector are enhanced by the two-loop contributions. We find that the corresponding shift in Mh1 can amount to 5 GeV.

The Higgs boson masses and mixings of the complex MSSM in the Feynman-diagrammatic approach

New results for the complete one-loop contributions to the masses and mixing effects in the Higgs sector are obtained for the MSSM with complex parameters using the Feynman-diagrammatic approach. The full dependence on all relevant complex phases is taken into account, and all the imaginary parts appearing in the calculation are treated in a consistent way. The renormalization is discussed in detail, and a hybrid on-shell/DRbar scheme is adopted. We also derive the wave function normalization factors needed in processes with external Higgs bosons and discuss effective couplings incorporating leading higher-order effects. The complete one-loop corrections, supplemented by the available two-loop corrections in the Feynman-diagrammatic approach for the MSSM with real parameters and a resummation of the leading (s)bottom corrections for complex parameters, are implemented into the public Fortran code FeynHiggs2.5. In our numerical analysis the full results for the Higgs-boson masses and couplings are compared with various approximations, and CP-violating effects in the mixing of the heavy Higgs bosons are analyzed in detail. We find sizable deviations in comparison with the approximations often made in the literature.

Functional determinants for radial operators

We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of Gel'fand and Yaglom to higher dimensions. We use the zeta function formalism, and the results agree with what one would obtain using the angular momentum cutoff method based on radial WKB. The final expression is numerically equal to an alternative expression derived in a Feynman diagrammatic approach, but is considerably simpler.

Implications of the Higgs boson searches on different soft SUSY-breaking scenarios

We investigate the Higgs boson sector of the Minimal Supersymmetric Standard Model (MSSM) in the framework of the three most prominent soft SUSY-breaking scenarios, mSUGRA, mGMSB and mAMSB. For each scenario, we determine the parameters at the electroweak scale from the set of input variables at higher energy scales (depending on the specific scenario) and evaluate the Higgs boson properties. The latter are based on results obtained within the Feynman-diagrammatic approach by taking into account the complete one-loop and the dominant two-loop contributions. The maximum value of the mass of the lightest neutral CP -even MSSM Higgs boson, m h , is determined in the three scenarios, and the behavior of the Higgs couplings to fermions and gauge bosons is investigated. Restrictions on tan β and on the set of higher-energy scale parameters are derived from the lower limits arising from the Higgs search at LEP2. We furthermore discuss the regions of parameter space in the three scenarios compatible with interpreting the excess observed at LEP2 as a Higgs signal, m h =115 +1.3 −0.9 GeV. The case where the events observed at LEP2 could originate from the production of the heavier neutral CP -even Higgs boson is also considered. The implications of a possible Higgs signal at 115 GeV for SUSY searches at future colliders are briefly discussed for each of the three scenarios.

The Higgs boson sector of the complex MSSM in the Feynman-diagrammatic approach

In the Minimal Supersymmetric Standard Model with complex parameters (cMSSM) we calculate higher order corrections to the Higgs boson sector in the Feynman-diagrammatic approach using the on-shell renormalization scheme. The application of this approach to the cMSSM, being complementary to existing approaches, is analyzed in detail. Numerical examples for the leading fermionic corrections, including the leading two-loop effects, are presented. Numerical agreement within 10% with other approaches is found for small and moderate mixing in the scalar top sector. The leading fermionic corrections, supplemented by the full logarithmic one-loop and the leading two-loop contributions are implemented into the public Fortran code FeynHiggsFastC.

Calculation of 1-loop hexagon amplitudes in the Yukawa model

We calculate a class of one-loop six-point amplitudes in the Yukawa model. The construction of multi-particle amplitudes is done in the string inspired formalism and compared to the Feynman diagrammatic approach. We show that there exists a surprisingly efficient way of calculating such amplitudes by using cyclic identities of kinematic coefficients and discuss in detail cancellation mechanisms of spurious terms. A collection of formulas which are useful for the calculation of massless hexagon amplitudes is given.

Neutral MSSM Higgs-boson production at $\mathrm{e^+e^-}$ colliders in the Feynman-diagrammatic approach

We calculate the cross sections for the neutral Higgs-boson production at e+e- colliders in the Minimal Supersymmetric Standard Model (MSSM) using the Feynman-diagrammatic approach and the on-shell renormalization scheme. We incorporate the Higgs-boson propagator corrections, evaluated up to two-loop order, into the prediction of the cross sections for the Higgs-boson production mechanism e+e- -> hZ, hA. The propagator corrections consist of the full one-loop contribution, including the effects of non-vanishing external momentum, and at the two-loop level of the dominant corrections of O(alpha alpha_s) and further sub-dominant contributions. The results are supplemented with the complete set of one-loop vertex and box corrections. The effects of the two-loop propagator corrections are investigated in detail. We briefly discuss also the effect of the box contributions for high $\sqrt{s}$. We compare our results with the case where only the corrections to the effective mixing angle, evaluated within the renormalization-group-improved one-loop Effective Potential approach, are taken into account. We find agreement better than 10% for LEP2 energies and deviations larger than 20% for $\sqrt{s}$ = 500 GeV.

Novel approach to pion and eta production in proton-proton collisions near threshold

We evaluate the threshold matrix-element for the reaction $pp \to pp\pi^0$ in a fully relativistic Feynman diagrammatic approach. We employ a simple effective range approximation to take care of the S-wave $pp$ final-state interaction. The experimental value for the threshold amplitude ${\cal A} = (2.7 - i 0.3)$ fm$^4$ can be reproduced by contributions from tree level chiral (long-range) pion exchange and short-range effects related to vector meson exchanges, with $\omega$ exchange giving the largest individual contribution. Pion loop effects appear to be small. We stress that the commonly used heavy baryon formalism is not applicable in the NN-system above the pion production threshold due to the large external momentum, $|\vec p | \simeq \sqrt {Mm_\pi}$, with $M$ and $m_\pi$ the nucleon and the pion mass, respectively. We furthermore investigate the reaction $pp\to p n \pi^+$ near threshold within the same approach. We extract from the data the triplet threshold amplitude as ${\cal B}= (2.8 -i 1.5)$ fm$^4$. Its real part can be well understood from (relativistic) tree level meson-exchange diagrams. In addition, we investigate the process $pp \to pp \eta$ near threshold. We use a simple factorization ansatz for the $pp\eta$ final-state interaction and extract from the data the modulus of the threshold amplitude, $|{\cal C}| = 1.32 $fm$^4$. With $g_{\eta N}=5.3$, this value can be reproduced by (relativistic) tree level meson-exchange diagrams and $\eta$-rescattering, whose strength is fixed by the $\eta N$ scattering length. We also comment on the recent near threshold data for $\eta'$-production.

A non-diagrammatic method for perturbative calculations in field theory

Feynman's diagrammatic approach to perturbative quantum field theory is not easily applied unless the interactions have simple power series expansions. In particular, when the interaction involves non-integer powers of the field, as happens when carrying out the so-called delta -expansion, the diagrammatic approach must be supplemented with some prescription for the analytic continuation of the exponents. Here the authors propose a new approach to perturbative field theory when bypasses Wick's theorem, and uses instead the fact that the joint probability distribution function for the fields at a finite set of points can be determined exactly from their expectation values, variances and mutual covariances. One can then calculate expectation values for products of operators at these points, or at least express them as finite-dimensional definite integrals. This technique is illustrated by calculating expectation values for non-polynomial O(n)-invariant operators.

Correlations and fluctuations in reflection coefficients for coherent wave propagation in disordered scattering media.

The relation between the reflection coefficients and the Green's function for a coherent wave propagation in a disordered elastic-scattering medium is derived. The sum rule of the reflection and transmission coefficients corresponding to probability conservation is shown rigorously for an arbitrary scattering potential. The correlation function of the reflection coefficients is then calculated by using a Feynman-diagrammatic approach in the weak-localized multiple-scattering regime (L\ensuremath{\gg}l\ensuremath{\gg}\ensuremath{\lambda}). The result is in agreement with recent experiments on the so-called ``memory effect'' in reflection coefficients. A more general condition under which the memory effect can occur is derived. Differences between the the correlation functions for reflection and that for transmission are discussed.