Three-loop Corrections Research Articles

Three loop QCD corrections to the heavy-light form factors: fermionic contributions

We present analytic results for three-loop fermionic corrections to the heavy-light form factors in perturbative quantum chromodynamics. Specifically, we present all light quark contributions and contributions from two heavy quark loops. We use the method of differential equations to compute all relevant three-loop master integrals. The results for all these contributions are expressed in terms of harmonic polylogarithms and generalized harmonic polylogarithms.

Heavy-to-light form factors to three loops

We compute three-loop corrections of O(αs3) to form factors with one massive and one massless quark coupling to an external vector, axialvector, scalar, pseudoscalar, or tensor current. We obtain analytic results for the color-planar contributions, for the contributions of light-quark loops, and the contributions with two heavy-quark loops. For the computation of the remaining master integrals we use the “expand and match” approach which leads to semianalytic results for the form factors. We implement our results in a and a ortran code which allows for fast and precise numerical evaluations in the physically relevant phase space. The form factors are used to compute the hard matching coefficients in Soft-Collinear Effective Theory for all currents. The tensor coefficients at lightlike momentum transfer are used to extract the hard function in B¯→Xsγ to three loops. Published by the American Physical Society 2024

Three-loop corrections to Higgs boson pair production: reducible contribution

We compute three-loop corrections to the process gg → HH originating from one-particle reducible diagrams. This requires the computation of two-loop corrections to the gluon-gluon-Higgs vertex with an off-shell gluon. We describe in detail our approach to obtain semi-analytic results for the vertex form factors and present results for the two form factors contributing to Higgs boson pair production.

Analytic and numerical bootstrap for the long-range Ising model

We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and mean-field behaviour. We use the Lorentzian inversion formula to compute infinitely many three-loop corrections in the two-dimensional LRI near the mean-field end. We further exploit the exact OPE relations that follow from bulk locality of the LRI to compute infinitely many two-loop corrections near the mean-field end, as well as some one-loop corrections near SRI. By including such exact OPE relations in the crossing equations for LRI we set up a very constrained bootstrap problem, which we solve numerically using SDPB. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI.

Soft Photon Theorem in QCD with Massless Quarks.

Working to all orders in dimensionally regularized QCD with massless quarks, we study the radiation of a photon whose energy is much lower than that of external partons. The conventional soft photon theorem receives corrections at leading power in the photon energy, associated with soft virtual loops of massless fermions. These additive corrections give an overall factor times the nonradiative amplitude that is infrared finite and real to all orders in α_{s}. Based on recent calculations of the three-loop soft gluon current, we identify the lowest-order three-loop correction.

The Higgs-gluon form factor at three loops in QCD with three mass scales

We report on the complete three-loop corrections to the Higgs-gluon form factor in QCD. While previous calculations are based on QCD with a single heavy quark of arbitrary mass, we extend the study to QCD involving two different massive quark flavors. Thereby, the full set of possible Feynman diagrams at three-loop order is taken into account. Employing differential equations for the relevant master integrals, we determine the form factor in terms of analytic expansions. Outside the radii of convergence, we compute high-precision numerical samples over the two-dimensional physical parameter space. Our new findings will enter as virtual corrections the computation of the top-bottom interference in hadronic Higgs-boson production at next-to-next-to-leading order (NNLO) in QCD.

Single-soft emissions for amplitudes with two colored particles at three loops

We compute the three-loop correction to the universal single-soft emission current for the case of scattering amplitudes with two additional color-charged partons. We present results valid for QCD and N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super-symmetric Yang-Mills theory. To achieve our results we develop a new integrand expansion technique for scattering amplitudes in the presence of soft emissions. Furthermore, we obtain contributions from single final-state parton matrix elements to the Higgs boson and Drell-Yan production cross section at next-to-next-to-next-to-next-to leading order (N4LO) in perturbative QCD in the threshold limit.

Three-loop b → sγ vertex with current-current operators

We compute three-loop vertex corrections to b → sγ induced by current-current operators. The results are presented as expansions in mc/mb with numerical coefficients which allow to cover all relevant values for the heavy quark masses in different renormalization schemes. Moreover we provide for the first time analytic results for the next-to-leading order contribution. Our results present an important building block to the next-to-next-to-leading order interference contributions of the current-current operators Q1 and Q2 with the electric dipole operator Q7.

Towards gg → HH at next-to-next-to-leading order: Light-fermionic three-loop corrections

We consider light-fermion three-loop corrections to gg→HH using forward scattering kinematics in the limit of a vanishing Higgs boson mass, which covers a large part of the physical phase space. We compute the form factors and discuss the technical challenges. The approach outlined in this letter can be used to obtain the full virtual corrections to gg→HH at next-to-next-to-leading order.

Three-loop matching coefficients for heavy flavor-changing currents and the phenomenological applications

Within the framework of non-relativistic QCD (NRQCD) factorization, we compute the matching coefficients between full Quantum Chromodynamics (QCD) and NRQCD for the heavy flavor-changing vector, axial-vector, scalar and pseudo-scalar currents up to next-to-next-to-next-to-leading order (N3LO). We accomplish the analytical expressions for the three-loop renormalization constants and the corresponding anomalous dimensions for all of the four NRQCD currents with two different heavy flavors. The three-loop QCD corrections to the matching coefficients turn out to be significantly larger than lower order corrections. By employing the scale relation, we approximately simulate the N3LO correction to the wave functions at the origin for the vector {B}_c^{ast } meson and the pseudo-scalar Bc meson from the known result for the equal-mass heavy quarkonium in potential NRQCD (pNRQCD). We find large cancellations at the third order between the matching coefficients and the wave functions at the origin, and obtain the convergent decay constants of {B}_c^{ast } and Bc up to N3LO. We present the complete perturbative QCD predictions for the decay constants, leptonic decay widths, and branching ratios of the beauty-charmed mesons.

Massive three-loop form factors: Anomaly contribution

We compute three-loop corrections to the singlet form factors for massive quarks using a semi-analytic method which provides precise results over the whole kinematic range. Particular emphasis is put on the anomaly contribution originating from an external axial-vector current. We also discuss in detail the contribution for a pseudoscalar current and verify the chiral Ward identity to three-loop order. Explicit results are presented for the low- and high-energy regions and the expansions around threshold.

Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark

We compute the matching coefficient between the quantum chromodynamics (QCD) and the non-relativistic QCD (NRQCD) for the flavor-changing scalar current involving the heavy charm and bottom quark, up to the three-loop order within the NRQCD factorization. For the first time, we obtain the analytical expressions for the three-loop renormalization constant tilde{Z}_s(x,R_f) and the corresponding anomalous dimension tilde{gamma }_s(x,R_f) for the NRQCD scalar current with the two heavy bottom and charm quark. We present the precise numerical results for those relevant coefficients (C_{FF}(x_0), ldots , C_{FBB}(x_0)) with an accuracy of about thirty digits. The three-loop QCD correction turns out to be significantly large. The obtained matching coefficient C_s(mu _f,mu ,m_b,m_c) is helpful to analyze the threshold behaviours when two different heavy quarks are close to each other and form the double heavy B_c meson family.

New determination of |Vcb| using the three-loop QCD corrections for the B → D⁎ semi-leptonic decays

We present a new determination of the Cabibbo-Kobayashi-Maskawa matrix element |Vcb| by using the three-loop perturbative QCD corrections for the B→D⁎ semi-leptonic decay. The decay width of B→D⁎ semi-leptonic decay can be factorized as perturbatively calculable short-distance part and the non-perturbative but universal long-distance part. We adopt the principle of maximum conformality (PMC) single-scale setting approach to deal with the perturbative series so as to achieve a precise fixed-order prediction for the short-distance parameter ηA. By applying the PMC, an overall effective αs value is achieved by recursively using the renormalization group equation, which inversely results in a precise scale-invariant pQCD series. Such scale-invariant series also provides a reliable basis for predicting the contributions from uncalculated perturbative terms. We then obtain ηA=0.9225−0.0168+0.0117, where the error is the squared average of those from Δαs(MZ)=±0.0010 and the uncertainties caused by the uncalculated higher-order perturbative terms. By using the data of B→D⁎ℓν¯ℓ, we finally obtain |Vcb|PMC=(40.60−0.57+0.53)×10−3, which is consistent with the PDG value within errors.

Singlet and nonsinglet three-loop massive form factors

We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet contributions as well as those singlet contributions where the external current couples to a massive quark loop. We apply a semi-numerical method which is based on expansions around singular and regular kinematical points. They are matched at intermediate values of the squared partonic center-of-mass energy $s$ which allows to cover the whole kinematic range for negative and positive values of $s$. Our method permits a systematic increase of the precision by varying the expansion depth and the choice of the intermediate matching points. In our current set-up we have at least seven significant digits for the finite contribution of all form factors. We present our results as a combination of series expansions and interpolation functions which allows for a straightforward use in practical applications.

Three-loop QCD corrections to the electroweak boson masses

I find the three-loop corrections at leading order in QCD to the physical masses of the Higgs, $W$, and $Z$ bosons in the Standard Model. The results are obtained as functions of the $\overline{\mathrm{MS}}$ Lagrangian parameters only, using the tadpole-free scheme for the vacuum expectation value. The dependences of the computed masses on the renormalization scale are found to be smaller than present experimental uncertainties in each case. In the case of the Higgs boson mass, the new result is the state of the art, while the results for $W$ and $Z$ are in good numerical agreement with corresponding results in the on-shell and hybrid schemes. These results are now included in the Standard Model in Dimensional Regularization computer code.

Towards two- and three-loop QCD corrections to the width difference in $B_s-\bar{B}_s$ mixing

In this work we address the issue of large perturbative uncertainties in the theory prediction for \Delta \Gamma_sΔΓs, the width difference in the B^0_s - \bar{B}^0_sBs0−B‾s0 mixing process. To this aim we complete important steps towards the full analytic result for the previously unknown Wilson coefficients from the matching between |\Delta B|=1|ΔB|=1 and |\Delta B|=2|ΔB|=2 effective Hamiltonians at next-to-next-leading order (NNLO) in the strong coupling constant. We provide a thorough discussion of technical and conceptual difficulties behind this computation and give an outlook regarding the availability of the new NNLO theory prediction for \Delta \Gamma_sΔΓs.

Leading fermionic three-loop corrections to W-boson mass and Z-pole observables

In this proceeding, we highlight the computation of leading fermionic three-loop corrections to electroweak precision observables (EWPOs) accomplished recently. We summarize the numerical analysis and provide an outlook.

Massive Vector Form Factors to Three Loops.

We compute the three-loop nonsinglet corrections to the photon-quark form factors taking into account the full dependence on the virtuality of the photon and the quark mass. We combine the method of differential equations in an effective way with expansions around regular and singular points. This allows us to obtain results for the form factors with an accuracy of about eight to twelve digits in the whole kinematic range.

Renormalized ε -finite master integrals and their virtues: The three-loop self-energy case

Loop diagram calculations typically rely on reduction to a finite set of master integrals in $4 - 2\epsilon$ dimensions. It has been shown that for any problem, the masters can be chosen so that their coefficients are finite as $\epsilon \rightarrow 0$. I propose a definition of renormalized $\epsilon$-finite master integrals, which incorporate ultraviolet divergence subtractions in a specific way. A key advantage of this choice is that in expressions for physical observables, expansions to positive powers in $\epsilon$ are never needed. As an example, I provide the subtractions for general three-loop self-energy integrals. The differential equations method is used to compute numerically the renormalized $\epsilon$-finite master integrals for arbitrary external momentum invariant, in special cases with internal masses equal to a single scale or zero. These include the ones necessary for the three-loop QCD corrections to the self-energies of the W, Z, and Higgs bosons. In principle, the same method should provide for numerical computation of general three-loop self energies with any masses.

Multiloop corrections for collider processes using auxiliary mass flow

With a key improvement, the auxiliary mass flow method is now able to compute Feynman integrals encountered in cutting-edge collider processes. We have successfully applied it to compute some integrals involved in two-loop electroweak corrections to $e^+e^-\to HZ$, two-loop QCD corrections to $3j$, $W/Z/H+2j$, $t\bar{t}H$ and $4j$ production at hadron colliders, and three-loop QCD corrections to $t\bar{t}$ production at hadron colliders, all of which are crucial for precision frontier in collider physics in the following decade. Our results are important building blocks and benchmarks for future studies of these processes.