Heavy and light meson wavefunctions

We present a short review on the properties of heavy and light mesons’light-cone wavefunctions(LCWFs),and their distribution amplitudes(DAs).The B meson LCWFs can be treated by taking the heavy quark limit(mb!1)and by using the heavy quark effective theory.Furthermore,we propose a simple model for the B meson wavefunctions with 3-particle Fock states’contributions,whose behaviors are controlled by two parameters K and d.Using such model,the form factors FB!p t;0;Tand FB!K t;0;Tin large recoil region are studied up to Oe1=m2bT within the kTfactorization approach.On the other hand,we adopt BrodskyHuang-Lepage(BHL)prescription for constructing the WFs of the lighter pseudoscalars as gc;D-meson,pion,kaon,ge0T and etc.Such BHL-like model can be conveniently extended to construct the LCWFs for light scalar or vector mesons.Within such model the longitudinal distributions of those WFs are basically determined by a parameter B,whose value can be determined via a global fit of experimental data.

Properties of the decay H→γγ using the approximate α_s^4 corrections and the principle of maximum conformality

The decay channel H→γγis an important channel for probing the properties of the Higgs boson.In this paper,we analyze its decay width by using the perturbative QCD corrections up to theα4s order with the help of the principle of maximum conformality(PMC).PMC has been suggested in literature for eliminating the conventional renormalization scheme-and-scale ambiguities.After applying PMC,we observe that an accurate renormalization scale independent decay widthΓ(H→γγ)up to the N4LO level can be achieved.Taking the Higgs mass,MH=125.09±0.21±0.11 GeV,given by the ATLAS and CMS collaborations,we obtainΓ(H→γγ)|LHC=9.364+0.076-0.075 KeV.

Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders

In this study,we investigate in detail the generalized Crewther Relation(GCR)between the Adler function(D)and the Gross-Llewellyn Smith sum rules coefficient(C^(GLS))using the newly proposed single-scale approach of the principle of maximum conformality(PMC).The resultant GCR is scheme-independent,with the residual scale dependence due to unknown higher-order terms highly suppressed.Thus,a precise test of QCD theory without renormalization schemes and scale ambiguities can be achieved by comparing with data.Moreover,a demonstration of the scheme independence of the commensurate scale relation up to all orders is presented.Additionally,for the first time,the Pade approximation approach has been adopted for estimating the unknown 5th-loop contributions from the known four-loop perturbative series.

Importance of proper renormalization scale-setting for QCD testing at colliders

A primary problem affecting perturbative quantum chromodynamic （pQCD） analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality （PMC） eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set orderby-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant as to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the Nc → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the ＂increasing-decreasing＂ behavior observed by the DO collaboration for increasing tt invariant mass. At lower energies, the angular distributions of heavy quarks can be used to obtain a direct determination of the heavy quark potential. A discussion of the angular distributions of massive quarks and leptons is also presented, including the fermionic component of the two-loop corrections to the electromagnetic form factors. These results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing collider sensitivity to possible new physics beyond the Standard Model.

Total decay width of H → gg using the infinite-order scale-setting approach based on intrinsic conformality

We conducted a detailed study on the properties of the total decay width of the Higgs decay channel H→gg up toα_(s)^(6)-order QCD corrections by using the newly suggested infinite-order scale-setting approach,which is based on both the principle of maximum conformality and intrinsic conformality.This approach is called PMC_(∞) By using the PMC_(∞)approach,we observed that the conventional renormalization scale ambiguity in perturbative QCD calculation is eliminated,and the residual scale dependence due to unknown higher-order terms can also be highly suppressed.We then obtained an accurate perturbative QCD prediction on the total decay width,e.g.,Г(H→gg)|PMC_(∞)=336.42_(-6.92)^(+7.01)keV,where the errors are squared averages of those from all the mentioned error sources.

Reanalysis of the top-quark pair hadroproduction and a precise determination of the top-quark pole mass at the LHC

In this study,we calculate the tt pQCD production cross-section at the NNLO and determine the top-quark pole mass from recent measurements at the LHC at the center-of-mass energy √S=13 TeV to a high precision by applying the principle of maximum conformality(PMC).The PMC provides a systematic method that rigorously eliminates QCD renormalization scale ambiguities by summing the nonconformalβcontributions into the QCD coupling constant.The PMC predictions satisfy the requirements of renormalization group invariance,including renormalization scheme independence,and the PMC scales accurately reflect the virtuality of the underlying production subprocesses.By using the PMC,an improved prediction for the tt production cross-section is obtained without scale ambiguities,which in turn provides a precise value for the top-quark pole mass.Moreover,the prediction of PMC calculations that the magnitudes of higher-order PMC predictions are well within the error bars predicted from the known lower-order has been demonstrated for the top-quark pair production.The resulting determination of the top-quark pole mass,m^(pole)_(t)=172.5±1.4 GeV,from the LHC measurement at √S=13 TeV agrees with the current world average cited by the Particle Data Group(PDG).The PMC prediction provides an important high-precision test of the consistency of pQCD and the SM at √S=13 TeV with previous LHC measurements at lower CM energies.

A new search for the doubly charmed baryon ■ at the LHC

The standard quark model is capable of predicting the existence of doubly heavy baryons.Similar to doubly heavy mesons,doubly heavy baryons may allow the QCD-inspired potential model,the nonrelativistic QCD(NRQCD)factorization theory[1],etc.,to work on them well,while serving as a fruitful“laboratory”for testing these theories when a greatly enough collection of relevant data is available.Many attempts have been made to observe doubly heavy baryons,yet none of them succeeded due to the difficulties in producing such baryons either at the e^+e^- colliders or at the hadronic colliders.Noticeably,the running of the large hadronic collider(LHC)with a large centre-of-mass protonproton collision energy and a much higher luminosity provides a good opportunity for experimentalists to realize the aforementioned observation.

Gauge dependence of the perturbative QCD predictions under the momentum-space subtraction scheme

The momentum-space subtraction(MOM) scheme is one of the most frequently used renormalization schemes in perturbative QCD(pQCD) theory.In this paper,we discuss in detail the gauge dependence of the pQCD predictions obtained under the MOM scheme.Conventionally,a renormalization scale ambiguity exists for the fixedorder pQCD predictions;this assigns an arbitrary range and error for the fixed-order pQCD prediction and makes the discussions on the issue of the gauge dependence much more involved.The principle of maximum conformality(PMC) adopts the renormalization group equation to determine the magnitude of the coupling constant;hence,it determines the effective momentum flow of the process,which is independent of the choice of renormalization scale.Thus,no renormalization scale ambiguity exists in PMC predictions.To focus our attention on the MOM scheme’s gauge dependence,we first apply the PMC to deal with the pQCD series.As an explicit example,we adopt the Higgs boson decay width Γ(H→gg) up to its five-loop QCD contribution,to demonstrate the behavior of the gauge dependence before and after applying the PMC.Interaction vertices are chosen to define five different MOM schemes:mMOM,MOMh,MOMq,MOMg,and MOMgg.Under these MOM schemes,we obtain Γ(H →gg)|PMC(m(MOM)=332.8-3.711.6±7.3 keV,Γ(H→gg)|PMCMOMh=332.8-34.6+27.5±7.3 keV,Γ(H→gg)|PMCMOMq=332.934.727.4±7.3 keV,Γ(H→gg)|PMCMOMg=332.734.627.5±7.3 keV,and Γ(H→gg)|PMCMOMgg=337.9-1.7+1.2±7.7 keV;here,the central values correspond to the Landau gauge with the gauge parameter ξMOM=0,the first errors correspond to ξMOM ∈ [-1,1],and the second ones arise through taking △αsMS(MZ)=±0.0011.The uncertainty of the Higgs mass △MH=0.24 GeV causes an extra error of ~±1.7(or ~±1.8) keV for all the aforementioned MOM schemes.It is found that the Higgs decay width Γ(H→gg) depends very weakly on the choice of MOM scheme,which is consistent with renormalization group invariance.It is found that the gauge dependence of Γ(H→ gg) under the MOMgg scheme is less than ±1%,which is the smallest gauge dependence among all the aforementioned MOM schemes.

Precise determination of the top-quark on-shell mass Mt via its scale-invariant perturbative relation to the top-quark MS mass m_(t)(m_(t))

The principle of maximum conformality(PMC)provides a systematic approach to solve the conventional renormalization scheme and scale ambiguities.Scale-fixed predictions of physical observables using the PMC are independent of the choice of renormalization scheme–a key requirement for renormalization group invariance.In this paper,we derive new degeneracy relations based on the renormalization group equations that involve both the usualβ-function and the quark mass anomalous dimensionγm-function.These new degeneracy relations enable improved PMC scale-setting procedures for correct magnitudes of the strong coupling constant and MS¯-running quark mass to be determined simultaneously.By using these improved PMC scale-setting procedures,the renormalization scale dependence of the MS¯-on-shell quark mass relation can be eliminated systematically.Consequently,the top-quark on-shell(or MS¯)mass can be determined without conventional renormalization scale ambiguity.Taking the top-quark MS¯mass m¯t(m¯t)=162.5+2.1−1.5 GeV as the input,we obtain Mt≃172.41+2.21−1.57 GeV.Here,the uncertainties arise from errors combined with those fromΔαs(MZ)and the approximate uncertainty resulting from the uncalculated five-loop terms predicted through the Padéapproximation approach.