Matching conditions are universal ingredients that describe how fragmentation functions change when heavy-flavour thresholds are crossed during the factorisation scale evolution. They are the last missing piece for a consistent description of observables with identified final-state hadrons at next-to-next-to leading order accuracy in quantum chromodynamics. We present an analytical form of the matching condition for light-flavour to hadron fragmentation function at next-to-next-to leading order. The derivation is performed by extending the formalism employed in the extraction of the next-to leading order matching conditions to the subsequent order, making use of $e^+e^-$ annihilation cross sections. We obtain the first non-trivial heavy-quark effect in the light-quark fragmentation functions and provide results in Mellin space.
We report on our recent progress towards including the photon fragmentation contribution in next-to-next-to-leading order (NNLO) QCD predictions for photon production cross sections. This extension to previous NNLO calculations requires the identification of the photon in singular parton-photon collinear limits. We discuss how these limits can be subtracted within antenna subtraction using fragmentation antenna functions and we outline their integration.
An infrared and collinear (IRC) safe definition of the partonic flavour of a jet is vital for precision predictions of quantum chromodynamics at colliders. Jet flavour definitions have been presented in the literature, but they are typically defined through modification of the jet algorithm to be sensitive to partonic flavour at every stage of the clustering. While this does ensure that the sum of flavours in a jet is IRC safe, a flavour-sensitive clustering procedure is difficult to apply to realistic data. We introduce a distinct and novel approach to jet flavour that can be applied to any c…
We report on an update of the next-to-next-to-leading order (NNLO) ABKM09 parton distributions functions. They are obtained with the use of the combined HERA collider Run I inclusive deep-inelastic scattering (DIS) data and the partial NNLO corrections to the heavy quark electro-production taken into account. The value of the strong couplig constant $α^{\rm NNLO}_{\rm s}(M_{\rm Z})=0.1147(12)$ is obtained. The standard candle cross sections for the Tevatron collider and the LHC estimated with the updated PDFs are provided.
We present positivity bounds, derived from the principles of analyticity, unitarity and crossing symmetry, that constrain the low-energy constants of chiral perturbation theory. Bounds are produced for 2, 3 or more flavours with equal meson masses, up to and including next-to-next-to-leading order (NNLO), using the second and higher derivatives of the amplitude. We enhance the bounds by using the most general isospin combinations posible (or higher-flavour counterparts thereof) and by analytically integrating the low-energy range of the amplitude. In addition, we present a powerful and general…
We present positivity bounds, derived from the principles of analyticity, unitarity and crossing symmetry, that constrain the low-energy constants of chiral perturbation theory. Bounds are produced for 2, 3 or more flavours in meson-meson scattering with equal meson masses, up to and including next-to-next-to-leading order (NNLO), using the second and higher derivatives of the amplitude. We enhance the bounds by using the most general isospin combinations posible (or higher-flavour counterparts thereof) and by analytically integrating the low-energy range of the discontinuities. In addition, w…
We calculate the unpolarized transverse momentum dependent fragmentation function (TMDFF) at next-to-next-to-leading order (NNLO), evaluating separately TMD soft factor and TMD collinear correlator. For the first time the cancellation of spurious rapidity divergences in a properly defined individual TMD beyond the first non-trivial order is shown. This represents a strong check of the given TMD definition. We extract the matching coefficient necessary to perform the transverse momentum resummation at next-to-next-to-next-to-leading-logarithmic accuracy. The universal character of the soft func…
Isolated photon production at hadron colliders proceeds via direct production and fragmentation processes. Theory predictions for the isolated photon and photon-plus-jet cross section often impose idealised photon isolation criteria, eliminating the fragmentation contribution and introducing a systematic uncertainty in the comparison to data. We present NNLO predictions for the photon-plus-jet cross section with the experimental isolation including both, direct and fragmentation contributions. Predictions with two different parton-to-photon fragmentation functions are compared, allowing for an…
The antenna subtraction formalism allows to calculate QCD corrections to jet observables. Within this formalism, the subtraction terms are constructed using antenna functions describing all unresolved radiation between a pair of hard radiatior partons. In this paper, we focus on the subtraction terms for double real radiation contributions to jet observables in hadron-hadron collisions evaluated at NNLO. An essential ingredient to these subtraction terms are the four-parton antenna functions with both radiators in the initial state. We outline the construction of the double real subtraction te…
We extend the antenna subtraction method to include hadron fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD in $e^+e^-$ collisions. To handle collinear singularities associated with the fragmentation process, we introduce fragmentation antenna functions in final-final kinematics with associated phase space mappings. These antenna functions are integrated over the relevant phase spaces, retaining their dependence on the momentum fraction of the fragmenting parton. The integrated antenna functions are cross-checked against the known NNLO coefficient functions for identif…
We carry out a global QCD analysis of parton-to-pion fragmentation functions at next-to-next-to-leading order (NNLO) accuracy by performing a fit to the combined set of single-inclusive electron-positron annihilation and, for the first time, semi-inclusive deep-inelastic scattering (SIDIS) multiplicity data. For the latter, we utilize the approximate NNLO QCD corrections that were derived recently within the threshold resummation formalism. We explore the impact of the NNLO corrections on the description of the SIDIS data sets in various kinematic regimes and on the resulting pion fragmentatio…
We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through ${\cal O}(ε^2)$ in dimensional regulator (finding discrepancy for the linearly polarized gluon TMDPDFs with a previous result in the literature). We find a nontrivial momentum conservation sum rule for the linearly polarized compo…
We consider QCD radiative corrections to the associated production of a heavy-quark pair ($Q{\bar Q}$) with a generic colourless system $F$ at hadron colliders. We discuss the resummation formalism for the production of the $Q{\bar Q}F$ system at small values of its total transverse momentum $q_T$. The perturbative expansion of the resummation formula leads to the explicit ingredients that can be used to apply the $q_T$ subtraction formalism to fixed-order calculations for this class of processes. We use the $q_T$ subtraction formalism to perform a fully differential perturbative computation f…
We revisit the calculation of perturbative quark transverse momentum dependent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator provides a consistent framework for the calculation of various ingredients in transverse momentum dependent factorization. Compared to existing regulators in the literature, the exponential regulator has a couple of advantages which we explain in detail. As a result, the calculation is greatly simplified and we are able to obtain the next-to-next-to-leading order …
We apply the recently proposed flavoured anti-$k_{\text{T}}$ jet algorithm to $Wb\bar{b}$ production at the Large Hadron Collider at $\sqrt{s}=8$ TeV. We present results for the total cross section and differential distributions at the next-to-next-to-leading order (NNLO) in QCD. We discuss the effects of the remaining parametric freedom in the flavoured anti-$k_{\text{T}}$ prescription, and compare it against the standard flavour-$k_{\text{T}}$ algorithm. We compare the total cross section results against the CMS data, finding good agreement. The NNLO QCD corrections are significant, and thei…
We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark-flow techni…
The QCD coupling $α_s$ is extracted from the energy evolution of the first two moments (multiplicity and mean) of the parton-to-hadron fragmentation functions at low fractional hadron momentum $z$. Comparisons of the experimental $e^+e^-$ and deep-inelastic $e^\pm$p jet data to our NNLO$^*$+NNLL predictions, allow us to obtain $α_s(m_{_{\rm Z}})$ = 0.1205$\pm$0.0010$^{+0.0022}_{-0.0000}$, in excellent agreement with the current world average determined using other methods at the same level of accuracy.
I consider variations in the definition of a General-Mass Variable Flavour Number Scheme (GM-VFNS) for heavy flavour structure functions, both at next-to-leading order (NLO) and at next-to-next-to leading order (NNLO). I also define a new "optimal" scheme choice improving the smoothness of the transition from one flavour number to the next. At both NLO and NNLO I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the distributions when a new MSTW-type global fit to data is performed for each GM-VFNS. At NLO the par…
We discuss an NNLO realization of the general mass scheme S-ACOT-$χ$ for treatment of heavy-flavour production in neutral current deep-inelastic scattering. Practical implementation of the NNLO calculation is illustrated on the example of semi-inclusive structure functions $F_{2 c}(x,Q)$ and $F_{L c}(x,Q)$.
Measurements in heavy-flavour azimuthal angular correlation provide insight into the production, propagation, and hadronization of heavy-flavour jets in ultra-relativistic hadronic and heavy-ion collisions. These measurements across different particle species help to isolate the possible modification in particle production and fragmentation due to different mass and quark contents. Jet correlation studies give direct access to the initial parton dynamics produced in these collisions. \\ This article studies the azimuthal angular correlations of heavy-flavour hadrons (charm and beauty mesons an…
The theoretical description of photon production at particle colliders combines direct photon radiation and fragmentation processes, which can not be separated from each other for definitions of photon isolation used in experimental measurements. The theoretical description of these processes must account for collinear parton-photon configurations, retaining the dependence on the photon momentum fraction, and includes the parton-to-photon fragmentation functions. We extend the antenna subtraction method to include photon fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD…
Beam and jet functions in Soft-Collinear Effective Theory describe collinear initial- and final-state radiation (jets), and enter in factorization theorems for N-jet production, the Higgs pT spectrum, etc. We show that they may directly be calculated as phase-space integrals of QCD splitting functions. At NLO all computations are trivial, as we demonstrate explicitly for the beam function, the transverse-momentum-dependent beam function, the jet function and the fragmenting jet function. This approach also highlights the role of crossing symmetry in these calculations. At NNLO we reproduce the…
The current paper presents a determination of $K^0_S$ and $Λ/\barΛ$ fragmentation functions (FFs) from QCD analysis of single-inclusive electron-positron annihilation process (SIA). Our FFs determinations are performed at next-to-leading order (NLO), and for the first time, at next-to-next-to-leading order (NNLO) accuracy in perturbative Quantum Chromodynamics (pQCD) which is designated as {\tt SAK20} FFs. Each of these FFs is accompanied by their uncertainties which are determined using the `Hessian' method. Considering the hadron mass corrections, we clearly investigate the reliability of ou…
We present the first open-source analysis of fragmentation functions (FFs) of charged pions (entitled IPM-xFitter) computed at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy in perturbative QCD using the xFitter framework. This study incorporates a comprehensive and up-to-date set of pion production data from single-inclusive annihilation (SIA) processes, as well as the most recent measurements of inclusive cross-sections of single pion by the BELLE collaboration. The determination of pion FFs along with their theoretical uncertainties is performed in the Zero-Ma…
The width difference $ΔΓ$ among the two mass eigenstates of the $B_s$-$\bar B_s$ system is measured with a precision of 7%. The theory prediction has a larger uncertainty which mainly stems from unknown perturbative higher-order QCD corrections. I discuss the subset of next-to-next-to-leading order diagrams proportional to $α_s^2\, N_f$, where $N_f=5$ is the number of quark flavours. The results are published in [1].
We discuss the theory prediction of epsilon_K and the rare K -> pi nu nu-bar decays and review the structure and current status of higher-order contributions to these flavour changing processes in the standard model in some detail. This includes the next-to-next-to-leading order QCD calculation to the charm quark contribution to K+ -> pi+ nu nu-bar and to the charm-top quark contribution to epsilon_K. Electroweak corrections to the rare kaon decays are also discussed.
We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange structure functions in deep inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top lim…
Charm-quark fragmentation with an effective coupling constant
我们使用最近提出的一个非微扰模型，基于一个有效的强耦合常数和自由的可调参数，研究e+e-湮灭中的c味强子产生。在微扰碎裂函数的框架下描述了粲夸克的产生，包括NLO系数函数、NLL非单重态的DGPs演化和NNLL大尺度的再确认。我们通过在NNLO近似下的有效耦合常数来模拟强子化效应，并将我们的结果与在Z 0极点和Upperdance（4S）共振下的实验数据进行了比较。我们发现，在实验和理论的不确定性范围内，当x<1-Lambda/m_c时，我们的模型能够给出ALEPH D ~*~+介子谱的合理描述。当与BELLE和CLEO在x空间中的D和D^* 数据进行比较时，出现了更严重的差异。在误差范围内，我们的模型仍然能够再现所有考虑的数据集的前十个梅林时刻。然而，相当大的理论不确定性要求一个完整的NNLO/NNLL分析。
