B→a_0(1450)ρ(ω) Decays in Perturbative QCD Approach

In the two-quark model supposition for the meson ao（1450）, which can be viewed as either the first excited state （scenario I） or the lowest lying state （scenario II）, the branching ratios and the direct CP-violating asymmetries for decays B→a0（1450）ρ（ω） are studied by employing the perturbative QCD factorization approach. We find the following results： （a） For the decays B- B→a0（1450）ρ- andB→a0^＋（1450）ρ^-, their branching ratios have large difference between two scenarios. Although their branching ratios are larger than other considered decay modes, their direct CP-violating asymmetries in both scenarios are small. （b） For the decays B-→a0^-（1450）ρ0 and B0→ a0（1450）ρ＋, a0^0（1450）ρ0, a00 （1450）w, their branching ratios are dose to each other between two scenarios, respectively. （c） Comparing with the decays a0^0（1450）ρ0,π0ρ0 π0π0, the decay B-→a0^-（1450）ρ0 receives a larger branching ratio in each scenario, which is sensitive to the variation of the Cabibbo-Kobayashi-Maskawa angle α.

Approach to Perturbative QCD Results in Transition Amplitudes of NucleonNegative-Parity Resonances

The scaling behaviors of the nucleon resonance transition amplitudes from perturbative QCD (PQCD) are utilized to parametrize the amplitudes of the first negative-parity nucleon resonance . Our analysis indicates that the constraints of the transition amplitude for the resonance at the limit by QCD sum rule calculations are not applicable at a moderate range of compared with the present available data if the contribution of is dominant in the limit.

B→K0^＊（1430）K Decays in Perturbative QCD Approach

In this article, we calculate the branching ratios of B→K0^＊ （1430）K decays by employing the pertur-bative QCD （pQCD） approach at leading order. We perform the evaluations in the two scenarios for the scalar meson spectrum. We find that （i） The leading order pQCD predictions for the branching ratio Br（B^＋→K^＋K0^＊（1430）^0）are in good agreement with the experimental upper limit in both scenarios, while the pQCD predictions for other considered B→K0^＊（1430）K decay modes are also presented and will be tested by the LHC experiments; （ii） The annihilation contributions play an important role in these considered decays, for B^0→K0^＊（1430）^±K^± decays,for example,which are found to be （1-4）×10^-6.

Pure annihilation type D→PP(V) decays in the perturbative QCD approach

The annihilation type diagrams are difficult to calculate in any kind of model or method. Encouraged by the successful calculation of pure annihilation type B decays in the perturbative QCD factorization approach, we calculate the pure annihilation type D→ PP（V） decays in the perturbative QCD approach based on the kw factorization. Although the expansion parameter 1lind is not very small, our leading order numerical results agree with the existing experimental data for most channels. We expect more accurate observation from experiments, which can help us learn about the dynamics of D meson weak decays.

Space- and time-like kaon electromagnetic form factors in perturbative QCD

We present a phenomenological analysis of the space- and time-like charged kaon electromagnetic form factors in factorized perturbative QCD （pQCD） by employing an analytic model for αs （Q2 ） and an infrared （IR） finite gluon propagator. In the space-like region, due to the lack of available experimental data above Q2 ～ 0.2 GeV2 , we only give our results for intermediate energies and make no comparison. In the time-like region, our results agree reasonably well with the available experimental data at moderate energies, including the CLEO data and the J/ψ result.

B→(J/ψ,η_c)K decays in the perturbative QCD approach

In this paper,we calculated the B →（J/ψ,ηc） K decays in the perturbative QCD（pQCD） factorization approach with the inclusion of the partial next-to-leading order（NLO） contributions. With the inclusion of the significant enhancement from the NLO vertex corrections,the NLO pQCD predictions for the branching ratios agree with the data within 2σ errors：Br（B0 → J/ψK0） = 5.2-＋32..58×10-4,Br（B＋ → J/ψK＋） = 5.6-＋32..79×10-4,Br（B0 →ηcK0） = 5.5-＋22..30 × 10-4,Br（B＋ →ηcK＋） = 5.9-＋22..51 × 10-4.

Study of the B_c→B_sπ decay with the perturbative QCD approach

The Bc → Bsπ decay is studied with the perturbative QCD approach. Three types of wave functions for Bs meson are considered. The transition form factor F0Bc → Bsπ （0） and the branching ratio IBr（Bc → Bsπ） are sensitive to the model of the Bs meson wave functions. With appropriate inputs, our estimate on 23r（Bc → Bsπ） is comparable with the recent LHCb measurement. A clear signal of Bc → Bsπ decay should be easily observed at the Large Hadron Collider.

Reinvestigating B→PV decays by including contributions from Φ_(B2) with the perturbative QCD approach

Considering the B mesonic wave function φ_(B2),B→PV decays are re studied in the leading order for three scenarios using the perturbative QCD approach within the standard model,where P=π and K,and V denotes the ground SU(3) vector mesons.It is found that contributions from φ_(B2) can enhance most branching ratios and are helpful for improving the overall consistency of branching ratios between the updated calculations and available data,although there are still several discrepancies between the experimental and theoretical results.

Quasi-two-body B_((s))→K^(*)γ→Kπγ decays in the perturbative QCD approach

In this study,we investigate quasi-two-body B_((s))→K^(*)γ→Kπγ decays in the perturbative QCD approach.Two-meson distribution amplitudes are introduced to describe the final state interactions of the Kπpair,which involve time-like form factors and Gegenbauer polynomials.We calculate the CP averaged branching ratios of the B_((s))→K^(*)γ→Kπγ decays.Our results are in agreement with newly updated data measured by Belle Ⅱ.This suggests that it is more appropriate to analyze these quasi-two-body B decays in the three-body framework than the two-body framework.We also predict direct CP asymmetries for the considered decay modes and find that A_CP(B_(u,d)→K^(*)γ→Kπγ) is small and less than 1% in magnitude,whereas A_CP(B_(s)→K^(*)γ→Kπγ)is larger and can reach a few percent.Our predictions can be tested in future B meson experiments.

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.

Studies of B_s^O→η′η′ Decays in pQCD Approach

We calculate the CP averaged branching ratios and CP-violating asymmetries for Bs^0 → η＇η＇ and η＇η＇ decays in the perturbative QCD （pQCD） approach here. The pQCD predictions for the C P-averaged branching ratios are Br（Bs^0 → ηη）=（14.2-7.5^＋18.0） ×10^-6,Br（Bs^0 → ηη＇）=（12.4-7.0^＋18.2）×10^-6,and Br（Bs^0 → η＇η＇） =（9.2-4.9^＋15.3）×10^-6, which agree well with those obtained by employing the QCD factorization approach and also be consistent with available experimental upper limits. The gluonic contributions are small in size： less than 7% for Bs →ηηand ηη＇ decays, and around 18% for Bs →η＇η＇ decay. The CP-violating asymmetries for three decays are very small： less than 3% in magnitude.

Role of Electromagnetic Dipole Operator in the Electroweak Penguin Dominated Vector Meson Decays of B Meson

The pure annihilation type decays Dd^0→Фγand Bs→ργ receive only colour suppressed penguin contributions with a very small branching ratio in the standard model. When we include the previously neglected electromagnetic dipole operator, the branching ratios can be enhanced to R（^-Bd^0→Фγ）≈ 1×10^-11 and R（^-Bs→ργ）～（6 - 16） ×10^-10, which are one order magnitude larger than previous study using the QCD factorization approach. The new effect can also give a large contribution, of order 10^-9, to transverse polarization of B→Фρ and B →ωФ, which is comparable to the longitudinal part. These effects can be detected in the LHCb experiment and the super-B factories.

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.

Emergence of mass in the gauge sector of QCD

It is currently widely accepted that gluons,while massless at the level of the fundamental QCD Lagrangian,acquire an effective mass through the non-Abelian implementation of the classic Schwinger mechanism.The key dynamical ingredient that triggers the onset of this mechanism is the formation of composite massless poles inside the fundamental vertices of the theory.These poles enter the evolution equation of the gluon propagator and nontrivially affect the way the Slavnov-Taylor identities of the vertices are resolved,inducing a smoking-gun displacement in the corresponding Ward identities.In this article,we present a comprehensive review of the pivotal concepts associated with this dynamical scenario,emphasizing the synergy between functional methods and lattice simulations and highlighting recent advances that corroborate the action of the Schwinger mechanism in QCD.

Pure annihilation decays of B^(s)_(0)→a^(+)_(0)a^(−)_(0)and B^(0)_(d)→K^(∗+)_(0)K^(∗−)_(0)in the PQCD approac

We study the CP-averaged branching fractions and the CP-violating asymmetries in the pure annihilation decays of B^(s)_(0)→a^(+)_(0)a^(−)_(0)and B^(0)_(d)→K^(∗+)_(0)K^(∗−)_(0),where a_(0)[K^(∗)_(0)]denotes the scalar a_(0)(980)and a_(0)(1450)[K^(∗)_(0)(800)(orκ)and K^(∗)_(0)(1430)],with the perturbative QCD factorization approach under the assumption of two-quark structure for the a_(0)and K^(∗)_(0)states.The numerical results show that the branching ratios of the B^(0)_(d)→K^(∗+)_(0)K^(∗−)_(0)decays are in the order of 10^(−6),while the decay rates of the B^(s)_(0)→a^(+)_(0)a^(−)_(0)modes are in the order of 10−5.In light of the measured modes with the same quark components in the pseudoscalar sector,namely,B^(0)_(d)→K^(+)k_(-)and B^(0)_(s)→π^(+)π_(−),the predictions for the considered decay modes in this work are expected to be measured at the Large Hadron Collider beauty and/or Belle-Ⅱexperiments in the(near)future.Meanwhile,it is of great interest to find that the twist-3 distribution amplitudesφ^(S)andφ^(T)with inclusion of the Gegenbauer polynomials for the scalar a_(0)(1450)and K^(∗)_(0)(1430)states in scenario 2 contribute slightly to the branching ratios while significantly to the CP violations in the B^(0)_(d)→K^(∗)_(0)(1430)+K^(∗)_(0)(1430)−and B^(0)_(s)→a_(0)(1450)+a_(0)(1450)−decays,which indicates that,compared to the asymptoticφ^(S)andφ^(T),these Gegenbauer polynomials could change the strong phases evidently in these pure annihilation decay channels.These predictions await for the future confirmation experimentally,which could further provide useful information to help explore the inner structure of the scalars and shed light on the annihilation decay mechanism.

B→K_0~*(1430)η^(') decays in the pQCD approach

Based on the assumption of two-quark structure of the scalar meson K0^＊（1430）, we calculate the CP-averaged branching ratios for B→K0^＊（1430）η（＇） decays in the framework of the perturbative QCD （pQCD） approach here. We perform the evaluations in two scenarios for the scalar meson spectrum. We find that： （a） the pQCD predictions for Br（B→K0^＊（1430）η（＇）） which are about 10^-5 10^-6, basically agree with the data within large theoretical uncertainty; （b） the agreement between the pQCD predictions and the data in Scenario Ⅰ is better than that in Scenario Ⅱ, which can be tested by the forthcoming LHC experiments; （c） the annihilation contributions play an important role for these considered decays.

Scheme-scale ambiguity in analysis of QCD observable

The scheme-scale ambiguity that has plagued perturbative analysis in QCD remains on obstacle to making precise tests of the theory.Many attempts have been done to resolve the scale ambiguity.In this regard the BLM,EC,PMS and CORGI approaches are more distinct.We try to employ these methods to fix the scale ambiguity at NLO,NNLO and even in more higher order approximations.By optimizing the renormalization scale,there will be a possibility to predicate higher order terms.We present general results for predicted terms at any order,using different optimization methods.Some observable as specific examples will be used to indicate the validity of scale fixing to predicate the higher order terms.

NNLO QCD predictions of electron charge asymmetry for inclusive pp→W+X production in forward region at 13 and 14 TeV

This paper presents perturbative QCD predictions of the electron charge asymmetry for inclusive W^(±)X→e^(±)v+X production in proton-proton(pp)collisions.Perturbative QCD calculations are performed at next-to-next-to-leading order(NNLO)accuracy using different parton distribution function(PDF)modelsat 8,13,and 14 TeV center-of-mass energies of CERN LHC pp collisions.NNLO calculations are performed for electrons with transverse momenta above 20 GeV in the forward electron pseudorapidity region 2.0≤ne≤4.25.NNLO predictions are first compared at 8 TeV with the measurements of the LHCb experiment at the LHC for the W^(±)/W^(-)cross section ratio and charge asymmetry distributions.The 8 TeV predictions using NNPDF3.1,CT14,and MMHT2014 PDF sets are reported to be in good agreement with the LHCb data for the entire ne region,justifying the extension of the calculations to 13 and 14 TeV energies.The charge asymmetry predictions at NNLO accuracy are reported in the forward ne bins at 13 and 14 TeV and compared among NNPDF3.1,CTI4,and MMHT2014 PDF sets.Overall,the predicted W^(±)differential cross-section and charge asymmetry distributions based on different PDF scts are found to be consistent with each other for the entire ne region.The charge asymmetry distributions are shown to be more sensitive to discriminate among different PDF models in terms of the 14 TeV predictions.

Investigation of proton structure function F_(2)^(p)at HERA in light of an analytical solution to the Balitsky–Kovchegov equation

In this paper,the proton structure function F_(2)^(p)(x,Q^(2))at small-x is investigated using an analytical solution to the Balitsky–Kovchegov(BK)equation.In the context of the color dipole description of deep inelastic scattering(DIS),the structure function F_(2)^(p)(x,Q^(2))is computed by applying the analytical expression for the scattering amplitude N(k,Y)derived from the BK solution.At transverse momentum k and total rapidity Y,the scattering amplitude N(k,Y)represents the propagation of the quark-antiquark dipole in the color dipole description of DIS.Using the BK solution we extracted the integrated gluon density xg(x,Q^(2))and then compared our theoretical estimation with the LHAPDF global data fits,NNPDF3.1sx and CT18.Finally,we have investigated the behavior of F_(2)^(p)(x,Q^(2))in the kinematic region of 10^(-5)≤x≤10^(-2)and 2.5 GeV^(2)≤Q^(2)≤60 GeV^(2).Our predicted results for F_(2)^(p)(x,Q^(2))within the specified kinematic region are in good agreement with the recent high-precision data for F_(2)^(p)(x,Q^(2))from HERA(H1 Collaboration)and the LHAPDF global parametrization group NNPDF3.1sx.

Properties of the free energy density using the principle of maximum conformality

We present a detailed study on the properties of the free energy density at high temperature by applying the principle of maximum conformality（PMC）scale-setting method within effective field theory.The PMC utilizes the renormalization group equation recursively to identify the occurrence and pattern of the non-conformal{βi}-terms,and determines the optimal renormalization scale at each order.Our analysis shows that a more accurate free energy density up to gs^5-order level without renormalization scale dependence can be achieved by applying the PMC.We also observe that by using a smaller factorization scale around the effective parameter m E,the PMC prediction is consistent with the lattice QCD prediction derived at low temperature.