A. Maier, P. Maierhoefer, P. Marquard
The second moment of the heavy quark vector correlator at O(alpha_s^3) is presented. The implications of this result on recent determinations of the charm and bottom quark mass are discussed.
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We compute, for the first time, the absorptive part of the massless correlator of two quark scalar currents in five loops. As physical applications we consider the O(alpha_s^4) corrections to the decay rate of the Standard Model Higgs boson into quarks, as well as the constraints on the strange quark mass following from QCD sum rules.
We present the first 30 moments of the low energy expansions of the vector, axial-vector, scalar and pseudo-scalar heavy quark correlation functions at three-loop order, including the singlet contribution which appears for the first time at three loops. In addition we compare the behavior of the moments for large n with the prediction from threshold calculations.
We compare the quarkonia correlators from potential models and from lattice QCD.
Coefficient functions of the operator product expansion of correlators of HQET heavy--light quark currents are calculated up operators of dimension 4 up to to 3 loops.
We present analytical results both in momentum and position space for the massless correlators of the vector and scalar currents to order alpha_s^4 as well as for the tensor currents to order alpha_s^3. The evolution equations for the correlators together with all relevant anomalous dimensions are discussed in detail. As an application we present explicit conversion formulas relating the MSbar-renormalized vector, scalar and tensor currents to their counterparts renormalized in the X-space renormalization scheme more appropriate for lattice calculations.
An expansion scheme is developed for Feynman diagrams describing the production of one massive and one massless particle near the threshold. As an example application, we compute the correlators of heavy-light quark currents, (\bar b gamma_mu u) and (\bar b gamma_5 u), through O(alpha_s^2).
The relation between the quark-gluon description of QCD and the hadronic picture is studied up to order alpha_s. The analysis of the spin-1 correlators is developed within the large NC framework. Both representations are shown to be equivalent in the euclidean domain, where the Operator Product Expansion is valid. By considering different models for the hadronic spectrum at high energies, one is able to recover the alpha_s running in the correlators, to fix the rho(770) and a1(1260) couplings, and to produce a prediction for the values of the condensates. The Operator Product Expansion is impr…
Relations connecting various zero momentum correlators of interpolating fields for pseudoscalar and scalar channel, containing one heavy and one light quark field, are derived from the Euclidean space formulation of the QCD functional integral. These relations may serve as constraints on the phenomenological models or approaches motivated from QCD, and suggest a method to extract the chiral quark condensates. It is also found that the correlator for pseudoscalar channel differs from that for scalar channel even in the large heavy quark mass limit.
We consider moments of the non-diagonal vector, axial-vector, scalar and pseudo-scalar current correlators involving two different massive quark flavours up to three-loop accuracy. Expansions around the limits where one mass is zero and the equal-mass case are computed. These results are used to construct approximations valid for arbitrary mass values.
HQET currents with the quantum numbers of the ground-state baryons are discussed. One-loop anomalous dimensions are calculated, and exact one-loop matching to QCD currents is found. Two-point correlators of these currents are calculated taking into account $d\le9$ terms of the OPE. Sum rules for heavy baryons Lambda_Q and Sigma^(*)_Q are analyzed. Three-point correlators of two baryonic currents and a heavy-heavy velocity changing current are calculated with the same accuracy. The baryonic Isgur-Wise form factors are estimated from the corresponding sum rules.
We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the four-loop correction to the second and third physical moment in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using a Ward identity, we obtain the third and fourth moment for the pseudo-scalar correlator. We briefly discuss the impact of these results on the determination of the charm quark mass and the strong coupling constant using lattice simulations for the current correlators and of the…
We present the result for the first moment of the scalar and axial-vector current correlator in third order of the strong coupling constant alpha_s and give the details of a recent evaluation of the pseudo-scalar correlator. The results can be used to reduce the theoretical uncertainty due to higher order corrections for the determination of fundamental parameters of QCD in the context of lattice calculations.
We calculate three-loop corrections to correlation functions of heavy-quark currents in the low- and high-energy regions. We present 30 coefficients both in the low-energy and the high-energy expansion of the scalar and the vector correlator with non-diagonal flavour structure. In addition we compute 30 coefficients in the high-energy expansion of the diagonal vector, axial-vector, scalar and pseudo-scalar correlators. Possible applications of our new results are improvements of lattice-based quark-mass determinations and the approximate reconstruction of the full momentum dependence of the co…
The correlator of vector heavy-quark currents at small q^2 is considered in the large-beta_0 limit. The leading IR renormalon ambiguity of the sum of the perturbative series is canceled by the UV renormalon ambiguity of the gluon condensate. Asymptotic behaviour of the perturbative series is obtained in a model-independent way, up to a single unknown normalization factor. Gluon-virtuality distribution functions for the perturbative correction are calculated.
Correlator of heavy-light quark currents in HQET in the large $β_0$ limit
在大$β_0$极限下计算了HQET中两个重轻夸克流关联函数的微扰贡献，展开到轻夸克质量的二次项，并讨论了Wilson系数Borel像的紫外和红外重正化子极点。
We perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients involving the leading power of b, the first beta-function coefficient, is resummed. To avoid a renormalization scale dependence when we match the resummation to the exactly known NLO and NNLO results, we employ the Complete Renormalization Group Improvement (CORGI) approach. These fixed-order and resummed CORGI results are analytically continued by numerically performing a contour integral to obtain corresponding fixed and all-orders ``contour-improved''…
We construct approximate formulas for the O(α_s^3) QCD contributions to vector, axial-vector, scalar and pseudo-scalar quark current correlators, which are valid for arbitrary values of momenta and masses. The derivation is based on conformal mapping and the Pade approximation procedure and incorporates known expansions in the low energy, threshold and high energy regions. We use our results to estimate additional terms in these expansions.
Using the new non-analytic reconstruction method obtained from Mellin-Barnes properties, one can extract the value $m_c(\bar{\text{MS}}) = 1.12 \pm 0.08 \;\; \text{GeV}$ from experimental data of the radiation-corrected measured hadronic cross section to the calculated lowest-order cross section for muon pair production in the heavy-quark approximation.
Bound states of heavy quarks are considered. Using the path integral formalism we are able to rederive, in a gauge invariant way, the Leutwyler-Voloshin short distance analysis as well as a long distance linear potential. At all distances we describe the states in terms of nonperturbative field correlators, and we include radiative corrections at short and intermediate distances. For intermediate distance states (particularly $b\bar {b}$ with $n=2$) our results improve, qualitatively and quantitatively, standard analyses, thanks mostly to being able to take into account the finiteness of the c…
We present analytical next-to-leading order results for the correlator of baryonic currents at the three-loop level with one finite mass quark. We obtain the massless and the HQET limits of the correlator as particular cases from the general formula, we also give explicit expressions for the moments of the spectral density. Calculations have been performed with an extensive use of the symbolic manipulation programs MATHEMATICA and REDUCE.
We compute moments of non-diagonal correlators with two massive quarks. Results are obtained where no restriction on the ratio of the masses is assumed. Both analytical and numerical methods are applied in order to evaluate the two-scale master integrals at three loops. We provide explicit results for the latter which are useful for other calculations. As a by-product we obtain results for the electroweak $ρ$ parameter up to three loops which can be applied to a fourth generation of quarks with arbitrary masses.
Correlators of heavy-light quark currents in HQET: Perturbative contribution up to 4 loops and beyond
本文研究了HQET中重轻夸克电流相关函数的微扰贡献，计算到四重循环并考虑大β₀极限，揭示了系数函数的Borel图像中存在重整化子极点，同时指出非阿贝尔化方法在此类系数函数上表现不佳。
The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries mass $M$. We exploit the decoupling relations between the full theory and the heavy quark effective theory (HQET) in order to obtain the logarithmic parts of the leading threshold terms. With the help of conformal mapping and Padé approximation numerical estimates for the non-logarithmic terms are extracted which in turn lead to a prediction of the correlator in HQET at order $α_s^2$.…
We study charmonia correlators at finite temperature. We analyze to what extent heavy quarkonia correlators are sensitive to the effect of heavy quark transport and whether it is possible to constrain the heavy quark diffusion constant by lattice calculations. Preliminary lattice calculations of quarkonia correlators performed on anisotropic lattices show that they are sensitive to the effect of heavy quark transport, but much detailed calculations are required to constrain the value of the heavy quark diffusion constant.
In this paper the three-loop polarization functions Π(q^2) are calculated for the cases of an external vector, axial-vector, scalar or pseudo-scalar current. Results are presented for the imaginary part which directly leads to the cross section $σ(e^+e^- \to Z \to hadrons)$ and to the Higgs decay rates, respectively.
We present a concise summary of recent results for the vector correlator in massless QCD at order ${\cal O}(α_s^4)$, with all colour factors being given for a generic colour group. As a direct consequence we arrive at: (i) the full QCD contribution to the QED $β$--function of order $α^2\, α_s^4$ in the MSbar- and MOM-schemes; (ii) the full five-loop result of order $α^6$ for the $β$-function of QED with a generic number of single-charged fermions, again for the MSbar- and MOM-schemes.
The coefficient functions of the gluon condensate $<G^2>$, in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of $z=q^2/4m^2$. In the limiting cases $z\to0$, $z\to1$, and $z\to-\infty$, comparisons are made with previous partial results. Approximation methods, based on these limiting cases, are critically assessed, with a view to three-loop work. High accuracy is achieved using a few moments as input. A {\em single} moment, combined with only the {\em leading} threshold and asymptotic behaviours, gives the …
This talk explores the spin--1 correlators up to O(alpha_s) through a large NC resonance theory. The phenomenological analyses of this kind must take these corrections into account since they produce a larger impact than the first OPE condensates. It is also necessary to separate low and high energy regimes; fixing the parameters of the lightest multiplets through perturbative QCD arguments is unfair and introduces errors in the determination of the condensates and resonance parameters. This separation of regimes improves our understanding of the Minimal Hadronical Approximation. The study at …
We calculate the low-energy limit of heavy quark current correlators within an expansion in the inverse heavy quark mass. The induced low-energy currents built from the gluon fields corresponding to the initial heavy quark currents are obtained from an effective action for gauge fields in the one-loop approximation at the leading order of the 1/m expansion. Explicit formulae for the low-energy spectra of electromagnetic and tensor heavy quark current correlators are given. Consequences of the appearance of a nonvanishing spectral density below the two-particle threshold for high precision phen…
We present the results of the analytical evaluation of the massless four-loop O(alpha_s^3) correction to the correlator of the quark scalar currents and the Higgs decay rate into hadrons.
Factorization for energy-energy correlator in heavy ion collision
本文利用软共线有效理论建立了重离子碰撞中能量-能量关联函数的因子化框架，分离喷注动力学与介质物理，揭示了高阶辐射修正导致的DGLAP和BFKL演化，并评估了非微扰物理的普适性。
Here I review the temperature-dependence of heavy quarkonia correlators in potential models with three different screened potentials, and compare these to the results from lattice QCD. None of the potentials investigated yield results consistent with the lattice data, indicating that screening is likely not the mechanism for heavy quarkonia suppression. I also discuss a simple toy model, not based on temperature-dependent screening, that can reproduce the lattice results.
In the framework of nonrelativistic QCD, we compute the leading double-logarithmic corrections of order alpha_s^3 ln^2(1/alpha_s) to the heavy-quark-antiquark bound-state wave function at the origin, which determines the production and annihilation rates of heavy quarkonia. The phenomenological implications for the top-antitop and Upsilon systems are discussed.
Assuming the gluon field is well approximated by instanton configurations we derive a partition function and calculate the specific correlators. Namely, the heavy quark propagator and heavy quark-aniquark correlator with the account of the light quark determinant and QCD instanton vacuum properties. With these knowledge we calculate the light quark contribution to the interaction between heavy quarks, which might be essential for the properties of a few heavy quarks systems like oniums and double-heavy baryons.
We calculate the O(alpha_s^3 ln(alpha_s)) contributions to the heavy-quarkonium production and annihilation rates. Our result sheds new light on the structure of the high-order perturbative corrections and opens a new perspective for a high-precision theoretical analysis. We also determine the three-loop anomalous dimensions of the nonrelativistic vector and pseudoscalar currents.
Lattice study of correlators of chromoelectric fields for heavy quarkonium dynamics in the quark-gluon plasma
本文在非零温度下格点计算伴随表示色电场关联函数，发现卡西米尔因子重标度可将伴随重夸克扩散及八重态跃迁关联函数与基本表示关联函数相联系。
Assuming the gluon field is well approximated by instanton configurations we derive a light quarks determinant and calculate its contribution to the specific heavy quarks correlators -- namely, the heavy quark propagator and heavy quark-aniquark correlator, receiving the instanton generated light-heavy quarks interaction terms contributions. With these knowledge we calculate the light quark contribution to the interaction between heavy quarks, which might be essential for the properties of a few heavy quarks systems.
We estimate the couplings in the Heavy Hadron Chiral Theory (HHCT) lagrangian from the QCD sum rules in an external axial field. We take into account the perturbative correction to the meson correlator in the infinite mass limit. With the perturbative correction and three successive power corrections, the meson correlator in an axial field becomes one of the best known correlators. In spite of this, the corresponding sum rule is not very stable. It yields the result g_1 F^2/(380MeV)^3 = 0.1 - 0.2, where F^2 = f_M^2 m/4 = (380MeV)^3 is the central value of the heavy meson decay constant with th…
The heavy quark effective field theory (HQEFT) provides an effective way to deal with the heavy meson decays. In the paper, we adopt two different correlators to derive the light-cone sum rules of the $B \to π$ transition form factors (TFFs) within the framework of HQEFT. We label those two LCSR results as LCSR-${\cal U}$ and LCSR-${\cal R}$, which are for conventional correlator and right-handed correlator, respectively. We observe that the correlation parameter $|ρ_{\rm RU}|$ for the branching ratio ${\cal B}(B \to πl ν_{l})$ is $\sim 0.85$, implying the consistency of the LCSRs under differ…
We report the first systematic analysis of the off-light-cone effects in sum rules for heavy-to-light form factors. These effects are investigated in a model based on scalar constituents, which allows a technically rather simple analysis but has the essential features of the analogous QCD calculation. The correlator relevant for the extraction of the heavy-to-light form factor is calculated in two different ways: first, by adopting the full Bethe-Salpeter amplitude of the light meson and, second, by performing the expansion of this amplitude near the light cone $x^2=0$. We demonstrate that the…
Recently an electric and magnetic field correlator appearing in the description of the heavy quarkonium system was evaluated on the lattice. Here, we give a nonperturbative analytical evaluation of this field correlator using a dual description of long distance Yang--Mills theory and using the stochastic vacuum model. The two predictions are both compatible with lattice data but show a different dependence on the quark separation. We discuss the analytic results in relation to the lattice data.
We develop an effective field theory (EFT) framework to perform an analytic calculation for energy correlator observables computed on groomed heavy-quark jets. A soft-drop grooming algorithm is applied to a jet initiated by a massive quark to minimize soft contamination effects such as pile-up and multi-parton interactions. We specifically consider the two-particle energy correlator as an initial application of this EFT framework to compute heavy quark jet substructure. We find that there are different regimes for the event shapes, depending on the size of the measured correlator observable, t…
We derive the initial condition for the perturbative fragmentation function of a heavy quark through order O(alpha_s^2) in the MS-bar scheme. This initial condition is useful for computing heavy quark (or lepton, in case of QED) energy distributions from calculations with massless partons. In addition, the initial condition at O(alpha_s^2) can be used to resum collinear logarithms ln(Q^2/m^2) in heavy quark energy spectrum with next-to-next-to-leading logarithmic accuracy by solving the DGLAP equation.
Heavy quark production in high-energy proton-nucleus (pA) collisions is described in the framework of the Color Glass Condensate. kT factorization is broken even at leading order albeit a more general factorization in pA holds at this order in terms of 2, 3 and 4 point correlators of Wilson lines in the nuclear target. The x-evolution of these correlators is computed in the large A and large N mean field limit of the Balitsky-Kovchegov equation. We show results for heavy quark production at RHIC and LHC energies.
In the present work we consider the influence on the heavy quark correlators due to the instanton background in the framework of instanton liquid model (ILM) of QCD vacuum by taking into account also the perturbative gluon effects. For a single heavy quark this leads to the mass shift due to the direct-instanton nonperturbative and ILM modified perturbative contributions, respectively. In the heavy quark-antiquark ($Q\bar{Q}$) sector we obtain the potential consisting the direct instanton induced part and the one-gluon exchange (OGE) perturbative part which is screened at large distances due t…
Meson Green's functions and decay constants $f_Γ$ in different channels $Γ$ are calculated using the Field Correlator Method. Both, spectrum and $f_Γ$, appear to be expressed only through universal constants: the string tension $σ$, $α_s$, and the pole quark masses. For the $S$-wave states the calculated masses agree with the experimental numbers within $\pm 5$ MeV. For the $D$ and $D_s$ mesons the values of $f_{\rm P} (1S)$ are equal to 210(10) and 260(10) MeV, respectively, and their ratio $f_{D_s}/f_D$=1.24(3) agrees with recent CLEO experiment. The values $f_{\rm P}(1S)=182, 216, 438$ MeV …
Minimizing Selection Bias in Inclusive Jets in Heavy-Ion Collisions with Energy Correlators -- arXiv note
本文作为配套注释，将新提出的基于能量关联器的观测量应用于CMS首次重离子碰撞能量关联器测量，以最小化能量损失导致的选择偏差。
We examine the O(alpha_s) forward-backward asymmetries for the production process e+ e- --> gamma,Z --> q qbar (g), tagging the outgoing heavy-quark jet at center-of-momentum energies off the Z-peak. The complicated analytic results are reduced to simple polynomial forms that provide excellent approximations. For charm and bottom quark, a full dynamical cancellation gives O(alpha_s) zeros in the forward-backward asymmetry close to the Z-peak. We conclude with a detailed numerical analysis of our results.
Mechanism of di-pion transitions $nS\to n'Sππ(n=3,2; n'=2,1)$ in bottomonium and charmonium is studied with the use of the chiral string-breaking Lagrangian allowing for the emission of any number of $π(K,η),$ and not containing fitting parameters. The transition amplitude contains two terms, $M=a-b$, where first term (a) refers to subsequent one-pion emission: $Υ(nS)\toπB\bar B^*\toπΥ(n'S)π$ and second term (b) refers to two-pion emission: $Υ(nS)\toππB\bar B\toππΥ(n'S)$. The one-parameter formula for the di-pion mass distribution is derived, $\frac{dw}{dq}\sim$(phase space) $|η-x|^2$, where $…
We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-$β_0$ limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our results are used to study the higher-order behaviour of dimensionless ratios of vector and pseudo-scalar moments used for the precise extraction of the strong coupling, $α_s$, from relativistic quarkonium sum rules and lattice data, respectively. We show that these ratios benefit from a partial cancellation of the leading renormalon singularities. Our results can gu…
We investigate the quarkonia correlators in QCD with no light quarks within a potential model with different screened potentials. Our results for the temperature dependence of the charmonium and bottomonium correlators are qualitatively consistent with existing and preliminary lattice results. We identify however, a much reacher structure in the correlators than the one seen on the lattice.
We calculate the leading mass-suppressed two-loop contribution, proportional to alpha_s^3/(m_q r^2), to the potential of a heavy quark-antiquark system. This contribution originates in the nonabelian nature of quantum chromodynamics (QCD) and has no analogue in quantum electrodynamics (QED). For this purpose, we elaborate a technique based on the implementation of the threshold expansion within the effective theory of nonrelativistic QCD (NRQCD). We discuss phenomenological implications of our result for heavy-quarkonium physics. We also confirm a previous result for the two-loop O(alpha_s^2) …
Heavy Quark Pair Energy Correlators: From Profiling Partonic Splittings to Probing Heavy-Flavor Fragmentation
本文提出重味能量关联子作为新观测量，通过共线因子化和重求和刻画重夸克对劈裂与重味碎裂，并进一步用于探测介质对劈裂函数的修正及介质空间结构。
Probing Local Charm Hadronization Dynamics with Hadron-Anchored Energy Correlators
本文提出强子锚定能量关联器（HAEC）用于重味喷注，发现Λc+相对D0存在局部能量流抑制及标度转变，可区分重夸克质量与碎裂顶点起源。
It is demonstrated how perturbative O(alpha_s^2) relativistic corrections to the non-relativistic stable heavy quark-antiquark production cross section in e^+e^- annihilation based on a Coulombic QCD potential can be systematically calculated using the concept of effective field theories. The O(alpha_s^2) corrections from the relativistic energy-momentum relation, the relativistic phase space corrections and the O(alpha_s^2) corrections involving the group theoretical factors C_F^2 and C_F T are determined explicitly. For the case of $t\bar t$ production the sum of these corrections amounts to…
Recently it has been shown that in the large-recoil limit new symmetries emerge which impose various relations on form factors that parametrise the decay of heavy B mesons into light mesons. These symmetry relations are broken by radiative QCD corrections. We show that these corrections are perturbatively calculable, and present results to first order in the strong coupling constant alpha_s.
Unraveling QCD dynamics with heavy quark energy correlators
该研究利用重夸克能量关联器，结合有效场论分析，探究QCD动力学中夸克质量对喷注子结构的影响，表明其可用于测试核介质中喷注的修正效应。
Flavor Flux Correlators, Forward-Backward Asymmetries, and Anomalies
本文提出味通量关联函数，利用重味量子数的能隙特性实现干净的微扰可观测量，并揭示重夸克前后不对称性与电弱反常的联系，为高精度检验标准模型提供新探针。
We study the diffusion of heavy quarks in the Quark Gluon Plasma using the Langevin equations of motion and estimate the contribution of the transport peak to the Euclidean current-current correlator. We show that the Euclidean correlator is remarkably insensitive to the heavy quark diffusion coefficient and give a simple physical interpretation of this result using the free streaming Boltzmann equation. However if the diffusion coefficient is smaller than $\sim 1/(πT)$, as favored by RHIC phenomenology, the transport contribution should be visible in the Euclidean correlator. We outline a pro…
Brambilla, Escobedo, Soto, and Vairo have derived an effective description of quarkonium with two parameters; a momentum diffusion term and a real self-energy term. We point out that there is a similar real self-energy term for a single open heavy flavor and that it can be expressed directly in terms of Euclidean electric field correlators along a Polyakov line. This quantity can be directly studied on the lattice without the need for analytical continuation. We show that Minkowski-space calculations of this correlator correspond with the known NLO Euclidean value of the relevant electric fiel…
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