Fixed-order Perturbation Theory Research Articles

Form factor π0γ*γ in lightcone sum rules combined with renormalization-group summation vs experimental data.

We consider the lightcone sum-rule (LCSR) description of the pionphoton transition form factor in combination with the renormalization group of QCD. The emerging scheme represents a certain version of Fractional Analytic Perturbation Theory and significantly extends the applicability domain of perturbation theory towards lower momenta Q2 ≲ 1 GeV2. We show that the predictions calculated herewith agree very well with the released preliminary data of the BESIII experiment, which have very small errors just in this region, while the agreement with other data at higher Q2 is compatible with the LCSR predictions obtained recently by one of us using fixed-order perturbation theory.

Resummed transverse momentum distribution of pseudo-scalar Higgs boson at NNLOA+NNLL

In this article we have studied the transverse momentum distribution of the pseudo-scalar Higgs boson at the Large Hadron Collider (LHC). The small pT region which provides the bulk of the cross section is not accessible to fixed order perturbation theory due to the presence of large logarithms in the series. Using the universal infrared behaviour of the QCD we resum these large logarithms up to next-to-next-to-leading logarithmic (NNLL) accuracy. We observe a significant reduction in theoretical uncertainties due to the unphysical scales at NNLL level compared to the previous order. We present the pT distribution matched to NNLOA+NNLL, valid for the whole pT region and provide a detailed phenomenological study in the context of both 14 TeV and 13 TeV LHC using different choices of masses, scales and parton distribution functions which will be useful for the search of such particle at the LHC in near future.

Fiducial distributions in Higgs and Drell-Yan production at N3LL+NNLO

The perturbative description of certain differential distributions across a wide kinematic range requires the matching of fixed-order perturbation theory with resummation of large logarithmic corrections to all orders. We present precise matched predictions for transverse-momentum distributions in Higgs boson (H) and Drell-Yan pair (DY) production as well as for the closely related ϕη* distribution at the LHC. The calculation is exclusive in the Born kinematics, and allows for arbitrary fiducial selection cuts on the decay products of the colour singlets, which is of primary relevance for experimental analyses. Our predictions feature very small residual scale uncertainties and display a good convergence of the perturbative series. A comparison of the predictions for DY observables to experimental data at 8 TeV shows a very good agreement within the quoted errors.

Strong coupling from e+e−→hadrons below charm

We use a new compilation of the hadronic $R$-ratio from available data for the process $e^+e^-\to\mbox{hadrons}$ to determine the strong coupling, $\alpha_s$. We make use of all data for the $R$-ratio from threshold to a center-of-mass energy of 2 GeV by employing finite-energy sum rules. Data above 2 GeV, for which at present far fewer high-precision experimental data are available, do not provide much additional constraint but are fully consistent with the values for $\alpha_s$ we obtain. Quoting our results at the $\tau$ mass to facilitate comparison to the results obtained from analogous analyses of hadronic $\tau$-decay data, we find $\alpha_s(m_\tau^2)=0.298\pm 0.016\pm 0.006$ in fixed-order perturbation theory, and $\alpha_s(m_\tau^2)=0.304\pm 0.018\pm 0.006$ in contour-improved perturbation theory, where the first error is statistical, and the second error reflects our estimate of various systematic effects. These values are in good agreement with a recent determination from the OPAL and ALEPH data for hadronic $\tau$ decays.

Higher-order QCD corrections to hadronic \u03c4 decays from Pad\xe9 approximants

Perturbative QCD corrections to hadronic τ decays and e+e− annihilation into hadrons below charm are obtained from the Adler function, which at present is known in the chiral limit to five-loop accuracy. Extractions of the strong coupling, αs, from these processes suffer from an ambiguity related to the treatment of unknown higher orders in the perturbative series. In this work, we exploit the method of Padé approximants and its convergence theorems to extract information about higher-order corrections to the Adler function in a systematic way. First, the method is tested in the large-β0 limit of QCD, where the perturbative series is known to all orders. We devise strategies to accelerate the convergence of the method employing renormalization scheme variations and the so-called D-log Padé approximants. The success of these strategies can be understood in terms of the analytic structure of the series in the Borel plane. We then apply the method to full QCD and obtain reliable model-independent predictions for the higher-order coefficients of the Adler function. For the six-, seven-, and eight-loop coefficients we find c5,1 = 277 ± 51, c6,1 = 3460±690, and c7,1 = (2.02±0.72)×104, respectively, with errors to be understood as lower and upper bounds. Our model-independent reconstruction of the perturbative QCD corrections to the τ hadronic width strongly favours the use of fixed-order perturbation theory (FOPT) for the renormalization-scale setting.

A subleading power operator basis for the scalar quark current

Factorization theorems play a crucial role in our understanding of the strong interaction. For collider processes they are typically formulated at leading power and much less is known about power corrections in the λ ≪ 1 expansion. Here we present a complete basis of power suppressed operators for a scalar quark current at mathcal{O}left({lambda}^2right) in the amplitude level power expansion in the Soft Collinear Effective Theory, demonstrating that helicity selection rules significantly simplify the construction. This basis applies for the production of any color singlet scalar in qoverline{q} annihilation (such as boverline{b}to H ). We also classify all operators which contribute to the cross section at mathcal{O}left({lambda}^2right) and perform matching calculations to determine their tree level Wilson coefficients. These results can be exploited to study power corrections in both resummed and fixed order perturbation theory, and for analyzing the factorization properties of gauge theory amplitudes and cross sections at subleading power.

Pseudoscalar couplings in tt¯H production at NLO+NLL accuracy

We study the production of a Higgs boson in association to a top-antitop pair at the Large Hadron Collider. We show how precise predictions for the differential distributions with respect to the transverse momentum of the Higgs boson, to the invariant mass of the top-antitop-Higgs system and to the invariant mass of the top-antitop pair can provide useful information on the possible presence of a pseudoscalar component in the coupling of the top quark with the Higgs boson. We evaluate the production of a top-antitop pair and a Higgs boson to next-to-leading order in fixed order perturbation theory and we carry out the resummation of soft emission corrections to next-to-leading-logarithmic accuracy for the LHC operating at a center of mass energy of $13$ TeV. We discuss how the shape of these distributions can be employed experimentally, making a physics case for the kinematic reconstruction of dilepton channels.

A subleading operator basis and matching for gg \u2192 H

The Soft Collinear Effective Theory (SCET) is a powerful framework for studying factorization of amplitudes and cross sections in QCD. While factorization at leading power has been well studied, much less is known at subleading powers in the λ ≪ 1 expansion. In SCET subleading soft and collinear corrections to a hard scattering process are described by power suppressed operators, which must be fixed case by case, and by well established power suppressed Lagrangians, which correct the leading power dynamics of soft and collinear radiation. Here we present a complete basis of power suppressed operators for gg → H, classifying all operators which contribute to the cross section at mathcal{O}left({lambda}^2right) , and showing how helicity selection rules significantly simplify the construction of the operator basis. We perform matching calculations to determine the tree level Wilson coefficients of our operators. These results are useful for studies of power corrections in both resummed and fixed order perturbation theory, and for understanding the factorization properties of gauge theory amplitudes and cross sections at subleading power. As one example, our basis of operators can be used to analytically compute power corrections for N -jettiness subtractions for gg induced color singlet production at the LHC.

QCD factorization for B \u2192 \u03c0\u03c0\u2113\u03bd decays at large dipion masses

We introduce a factorization formula for semi-leptonic b → u transitions in the exclusive decay mode {B}^{-}to {pi}^{+}{pi}^{-}{ell}^{-}{overline{nu}}_{ell } in the limit of large pion energies and large dipion invariant mass. One contribution can be described in terms of a universal B → π form factor and the convolution of a short-distance kernel TI with the respective light-cone distribution amplitudes (LCDAs) of the positively charged pion. The second contribution, at leading power, completely factorizes, with a short-distance kernel TII convoluted with the leading-twist LCDAs for both pions and the B-meson. We calculate the leading contributions to the short-distance kernels TI and TII in fixed-order perturbation theory, and discuss the approximate relations among the resulting B → ππ partial-wave form factors. Our results provide useful theoretical constraints for phenomenological models that aim to analyze the complete B → ππℓν phase space.

Vector boson production in joint resummation

We study the transverse momentum (QT ) distribution of an electro-weak vector boson produced via the Drell-Yan mechanism, in the context of joint resummation. This formalism allows for the simultaneous resummation of logarithmic contributions that are enhanced at small QT and at partonic threshold. We extend joint resummation to next-to-next-to leading logarithmic accuracy and we present resummed and matched results for three different phenomenological setups. In particular, we study the production of a Z boson at the Tevatron and at the Large Hadron Collider (LHC), as well as the production of a heavier Z′ at the LHC. We compare our findings to standard QT resummation, as well as to fixed-order perturbation theory. We find that joint resummation provides a moderate (but not flat) correction with respect to QT resummation and it leads to a reduction of the scale dependence of the results. However, our study also shows some limitations of this formalism. While the use of joint resummation for Z production at the Tevatron and Z′ production at the LHC appears to be justified, our implementation suffers from a stronger dependence on power corrections for processes which are further away from threshold, such as Z production at the LHC, for which we cannot claim an improvement over standard QT resummation.

Pseudo-scalar Higgs boson production at N[Formula: see text]LO[Formula: see text]+N[Formula: see text]LL[Formula: see text

We consider the production of a pseudo-scalar particle A at the LHC, and present accurate theoretical predictions for its inclusive cross section in gluon fusion. The prediction is based on combining fixed-order perturbation theory and all-order threshold resummation. At fixed order we include the exact next-to-next-to-leading order (NNLO) plus an approximate next-to-next-to-next-to-leading order (N^3LO_mathrm{A}) which is based on the recent computation at this order for the scalar case. We then add threshold resummation at next-to-next-to-next-to leading logarithmic accuracy (N^3LL^prime ). Various forms of threshold resummation are considered, differing by the treatment of subleading terms, allowing a robust estimate of the theoretical uncertainties due to missing higher orders. With particular attention to pseudo-scalar masses of 200 and 750 GeV, we also observe that perturbative convergence is much improved when resummation is included. Additionally, results obtained with threshold resummation in direct QCD are compared with analogous results as computed in soft-collinear effective theory, which turn out to be in good agreement. We provide precise predictions for pseudo-scalar inclusive cross section at 13 TeV LHC for a wide range of masses. The results are available through updated versions of the public codes ggHiggs and TROLL.

Tau hadronic spectral function moments: perturbative expansion and αs extractions

In the extraction of αs from hadronic τ decays different moments of the spectral functions have been used. Furthermore, the two mainstream renormalization group improvement (RGI) frameworks, namely Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT), lead to conflicting values of αs. In order to improve the strategy used in αs determinations, we have performed a systematic study of the perturbative behaviour of these spectral moments in the context of FOPT and CIPT. Higher order coefficients of the perturbative series, yet unknown, were modelled using available knowledge of the renormalon content of the QCD Adler function. We conclude that within these RGI frameworks some of the moments often employed in αs extractions should be avoided due to their poor perturbative behaviour. Finally, under reasonable assumptions about higher orders, we conclude that FOPT is the preferred method to perform the renormalization group improvement of the perturbative series.

State-of-the-Art Predictions for C-parameter and a Determination of αs

The C-parameter event-shape distribution for e+e− annihilation into hadrons is computed in the framework of SCET including input from fixed-order perturbation theory. We calculate all missing ingredients for achieving N3LL resummation accuracy in the cross section, which is then matched onto O(αs3) fixed-order results. Hadronization power corrections are incorporated as a convolution with a nonperturbative shape function. Wide-angle soft radiation effects introduce an O(ΛQCD) renormalon ambiguity in the cross section, which we cure by switching to the Rgap short-distance scheme. We also include hadron mass effects, but find their effect is rather small. Performing fits to the tail of the C-parameter distribution for many center of mass energies we find that the strong coupling constant is αs(mZ)=0.1121±0.0015, with χ2/dof=0.99.

αs from the updated ALEPH data for hadronic τ decays

We extract the strong coupling αs(mτ2) from the recently updated ALEPH non-strange spectral functions obtained from hadronic τ decays. We apply a self-consistent analysis method, first tested in the analysis of OPAL data, to extract αs(mτ2) and non-perturbative contributions. The analysis yields αsFO(mτ2)=0.296±0.010, using Fixed Order Perturbation Theory (FOPT), and αsCI(mτ2)=0.310±0.014, using Contour Improved Perturbation Theory (CIPT). The weighted average of these results with those previously obtained from OPAL data give αsFO(mτ2)=0.303±0.009 and αsCI(mτ2)=0.319±0.012, which gives, after evolution to the Z boson mass scale, αsFO(mZ2)=0.1165±0.0012 and αsCI(mZ2)=0.1185±0.0015, respectively. We observe that non-perturbative effects limit the accuracy with which αs can be extracted from τ decay data.

Formula omitted] from the (revised) ALEPH data for τ decay

We present a new analysis of αs from hadronic τ decays based on the recently revised ALEPH data, employing a strategy previously applied to the OPAL data. We examine critically the approach traditionally used, comparing it to our strategy, and commenting on the main differences between the two. Our analysis yields the values αs(mτ2)=0.296±0.010 using fixed-order perturbation theory, and αs(mτ2)=0.310±0.014 using contour-improved perturbation theory. Averaging these values with our previously obtained values from the OPAL data, we find αs(mτ2)=0.303±0.009, respectively, αs(mτ2)=0.319±0.012, as the most reliable results for αs from τ decays currently available.

Strong coupling from the revised ALEPH data for hadronicτdecays

We apply an analysis method previously developed for the extraction of the strong coupling from the OPAL data to the recently revised ALEPH data for non-strange hadronic $\tau$ decays. Our analysis yields the values $\alpha_s(m_\tau^2)=0.296\pm 0.010$ using fixed-order perturbation theory, and $\alpha_s(m_\tau^2)=0.310\pm 0.014$ using contour-improved perturbation theory. Averaging these values with our previously obtained values from the OPAL data, we find $\alpha_s(m_\tau^2)=0.303\pm 0.009$, respectively, $\alpha_s(m_\tau^2)=0.319\pm 0.012$. We present a critique of the analysis method employed previously, for example in analyses by the ALEPH and OPAL collaborations, and compare it with our own approach. Our conclusion is that non-perturbative effects limit the accuracy with which the strong coupling, an inherently perturbative quantity, can be extracted at energies as low as the $\tau$ mass. Our results further indicate that systematic errors on the determination of the strong coupling from analyses of hadronic $\tau$-decay data have been underestimated in much of the existing literature.

Jet vetoes for Higgs boson production at future hadron colliders

We study Higgs boson production in exclusive jet bins at possible future 33 and 100 TeV proton-proton colliders. We compare the cross sections obtained using fixed-order perturbation theory with those obtained by also resuming large logarithms induced by the jet-binning in the gluon-fusion and associated production channels. The central values obtained by the best-available fixed-order predictions differ by $10-20\%$ from those obtained after including resummation over the majority of phase-space regions considered. Additionally, including the resummation dramatically reduces the residual scale variation in these regions, often by a factor of two or more. We further show that in several new kinematic regimes that can be explored at these high-energy machines, the inclusion of resummation improvement is mandatory.

The strong coupling from tau decays without prejudice

We review our recent determination of the strong coupling αs from the OPAL data for non-strange hadronic tau decays. We find that αs(mτ2)=0.325±0.018 using fixed-order perturbation theory, and αs(mτ2)=0.347±0.025 using contour-improved perturbation theory. At present, these values supersede any earlier determinations of the strong coupling from hadronic tau decays, including those from ALEPH data.

Multiparticle Higgs and vector boson amplitudes at threshold

In a spontaneously broken gauge theory we consider (sub)-processes in which one virtual intermediate state (it can be a Higgs or a gauge field) produces many on-shell Higgses and massive vector bosons. In the kinematic regime where all final states are produced on their mass threshold, we show how to compute iteratively all tree-level amplitudes $$ {\mathcal{A}}_{1\to n+ m} $$ involving an arbitrary number n of Higgs bosons and m of longitudinal vector bosons in the final state, and list the amplitudes coefficients for up to n=32 and m=32. Wefindthattheseamplitudesexhibitfactorialgrowthnotonlyinthenumberof scalar fields, but also in the number of longitudinal gauge fields, $$ {\mathcal{A}}_{1\to n+ m} $$ ~ n! m!. This growth is not expected to disappear at loop-level in the fixed-order perturbation theory. We conclude that at energies accessible at the next generation of hadron colliders, such as the 50-100 TeV FCC, where $$ \sqrt{\widehat{s}} $$ is sufficient to produce ≫1/α W of W, Z and H, perturbation theory breaks down when applied to the multiparticle electroweak production, at least near the kinematic multiparticle mass threshold where the electroweak gauge-Higgs sector becomes strongly coupled.

Transverse-momentum spectra of electroweak bosons near threshold at NNLO

We obtain the next-to-next-to-leading order corrections to transverse-momentum spectra of W, Z and Higgs bosons near the partonic threshold. In the threshold limit, the electroweak boson recoils against a low-mass jet and all radiation is either soft, or collinear to the jet or the beam directions. We extract the virtual corrections from known results for the relevant two-loop four-point amplitudes and combine them with the soft and collinear two-loop functions as defined in Soft-Collinear Effective Theory. We have implemented these results in a public code PeTeR and present numerical results for the threshold resummed cross section of W and Z bosons at next-to-next-to-next-to-leading logarithmic accuracy, matched to next-to-leading fixed-order perturbation theory. The two-loop corrections lead to a moderate increase in the cross section and reduce the scale uncertainty by about a factor of two. The corrections are significantly larger for Higgs production.