We present FEYNCALC 9.3, a new stable version of a powerful and versatile MATHEMAT-ICA package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages, automatic extraction of the ultraviolet divergent parts of 1-loop integrals, support for amplitudes with Majorana fermions and γ-matrices with explicit Dirac indices are explained in detail. Furthermore, we discuss some common problems and misunderstandings that may arise in the daily usage of the package, providing explanations and workarounds.

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The energy-energy correlation (EEC) between two detectors in e þ e − annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.

The energy-energy correlation (EEC) function in e + e − annihilation is currently the only QCD event shape observable for which we know the full analytic result at the next-to-leading order (NLO). In this work we calculate the EEC observable for gluon initiated Higgs decay analytically at NLO in the Higgs Effective Field Theory (HEFT) framework and provide the full results expressed in terms of classical polylogarithms, including the asymptotic behavior in the collinear and back-to-back limits. This observable can be, in principle, measured at the future e + e − colliders such as CEPC, ILC, FCC-ee or CLIC. It provides an interesting opportunity to simultaneously probe our understanding of the strong and Higgs sectors and can be used for the determinations of the strong coupling.

We present a new interface called FeynHelpers that connects FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and calculations in quantum field theory (QFT) to Package-X and FIRE. The former provides a library of analytic results for scalar 1-loop integrals with up to 4 legs, while the latter is a general-purpose tool for reduction of multi-loop scalar integrals using Integration-by-Parts (IBP) identities. With this add-on many types of calculations that were difficult or hardly feasible with FeynCalc previously, can now be done in a much simpler way. This is demonstrated with four different examples from QED, QCD and Higgs physics.Comment: 39 pages, 1 figure. Accompanying Mathematica notebooks are bundled with the source files of this document. To obtain the program, see https://github.com/FeynCalc/feynhelper

We consider two-loop QCD corrections to the element $$ {\Gamma}_{12}^q $$ Γ 12 q of the decay matrix in Bq−$$ {\overline{B}}_q $$ B ¯ q mixing, q = d, s, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference ∆Γs matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in mc/mb up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase ∆Γs.

We calculate in the nonrelativistic QCD (NRQCD) factorization framework all leading relativistic corrections to the exclusive production of χ cJ þ γ in e þ e − annihilation. In particular, we compute for the first time contributions induced by octet operators with a chromoelectric field. The matching coefficients multiplying production long distance matrix elements (LDMEs) are determined through perturbative matching between QCD and NRQCD at the amplitude level. Technical challenges encountered in the nonrelativistic expansion of the QCD amplitudes are discussed in detail. The main source of uncertainty comes from the not so well known LDMEs. Accounting for it, we provide the following estimates for the production cross sections at ffiffi ffi s p ¼ 10.6 GeV: σðe þ e − → χ c0 þ γÞ ¼ ð1.4 AE 0.3Þ fb, σðe þ e − → χ c1 þ γÞ ¼ ð15.0 AE 3.3Þ fb, and σðe þ e − → χ c2 þ γÞ ¼ ð4.5 AE 1.4Þ fb.

Van der Waals interactions between two neutral but polarizable systems at a separation R much larger than the typical size of the systems are at the core of a broad sweep of contemporary problems in settings ranging from atomic, molecular and condensed matter physics to strong interactions and gravity. In this paper, we reexamine the dispersive van der Waals interactions between two hydrogen atoms. The novelty of the analysis resides in the usage of nonrelativistic effective field theories of quantum electrodynamics. In this framework, the van der Waals potential acquires the meaning of a matching coefficient in an effective field theory, dubbed van der Waals effective field theory, suited to describe the low-energy dynamics of an atom pair. It may be computed systematically as a series in R times some typical atomic scale and in the fine-structure constant α. The van der Waals potential gets short-range contributions and radiative corrections, which we compute in dimensional regularization and renormalize here for the first time. Results are given in d space-time dimensions. One can distinguish among different regimes depending on the relative size between 1/R and the typical atomic bound-state energy, which is of order mα 2 . Each regime is characterized by a specific hierarchy of scales and a corresponding tower of effective field theories. The shortdistance regime is characterized by 1/R ≫ mα 2 and the leading-order van der Waals potential is the London potential. We compute also next-to-next-to-next-to-leading order corrections. In the long-distance regime we have 1/R ≪ mα 2 . In this regime, the van der Waals potential contains contact terms, which are parametrically larger than the Casimir-Polder potential that describes the potential at large distances. In the effective field theory, the Casimir-Polder potential counts as a next-to-next-to-next-to-leading-order effect. In the intermediate-distance regime, 1/R ∼ mα 2 , a significantly more complex potential is obtained. We compare this exact result with the two previous limiting cases. We conclude bz commenting on the van der Waals interactions in the hadronic case.