Circular Scale of Time as a Guide for the Schrodinger Perturbation Process of a Quantum-Mechanical System

We point out that a suitable scale of time for the Schrödinger perturbation process is a closed line having rather a circular and not a conventional straight-linear character. A circular nature of the scale concerns especially the time associated with a particular order N of the perturbation energy which provides us with a full number of the perturbation terms predicted by Huby and Tong. On the other hand, a change of the order N—connected with an increased number of the special time points considered on the scale—requires a progressive character of time. A classification of the perturbation terms is done with the aid of the time-point contractions present on a scale characteristic for each N. This selection of terms can be simplified by a partition procedure of the integer numbers representing N-1. The detailed calculations are performed for the perturbation energy of orders N=7 and N=8 .

Non-locality of Entangled Coherent States and Its Evolution in a Thermal Reservoir

Regarding the necessary and sufficient condition violating Bell-CHSH's inequality as criterion for nonlocality of entangled states, we present a perturbative calculation determining non-locality of evolving entangled states.Furthermore, by means of the perturbative calculation, the non-locality and its evolution of two kinds of entangled coherent states in a thermal reservoir are discussed.

Calculations on the hyperfine constants of the ground states for lithium-like system

In this paper a relativistic many-body perturbation calculation is performed to calculate the hyperfine constants of the ground states for lithium-like isoelectronic sequence. Zeroth-order hyperfine constants are calculated with DiracFock wavefunctions, and the finite basis sets of the Dirac Fock equations are constructed by B splines. With the finite basis sets, the core polarization and the correlation effect are evaluated.

Can Really Regularized Amplitudes Be Obtained as Consistent with Their Expected Symmetry Properties?

Through a very detailed investigation involving a set of simple perturbative amplitudes we show that the answer for the question put in the title of the present work is: undoubtedly NO! We are not restricting the sentence to the amplitudes which are considered as anomalous. The referred investigation is performed by using a procedure alternative to the traditional regularization methods. In the context of such a strategy the amplitudes are not modified in intermediary steps of the calculation, like traditional regularization procedures do, and only the validity of the linearity in the integration operation is assumed in the operations made in Feynman integrals typical of the perturbative calculations. The central point of the investigation is the question related to the consistent interpretation of the amplitudes. For these purposes, in all amplitudes having power counting indicating the possibility of divergences, the relations among Green functions, Ward identities and low energy limits are analyzed, in a model having different species of massive 1/2 spin fermions coupled to spin 0 and 1 (even and odd parity) boson fields, formulated in a space-time dimension D=1+1. We show that the maintenance of the linearity in operations involving Feynman integrals excludes the possibility of an anomalous term in the Ward identity relating the axial-vector and the pseudo-scalar-vector two point functions amplitudes. In addition, we show that it is not possible the maintenance of Ward identities and low energy limits in a consistent way if the amplitudes of the perturbative calculations are quantities to be regularized, just because there is no regularization method which is capable to give acceptable results for the divergent objects present in the calculations. This conclusion includes the Dimensional Regularization method which cannot give unique results if the linearity and the symmetric integration are simultaneously required in Feynman integrals. The qualitative conclusions apply in an equally-way in other space-time dimensions having, therefore, implications in many phenomenological consequences of quantum field theories stated through perturbative solutions.

Color-kinematics duality and dual conformal symmetry for a four-loop form factor in N=4 SYM

We obtain the integrand of full-color four-loop three-point form factor of the stress-tensor supermultiplet in N=4 SYM,based on the color-kinematics(CK)duality and generalized unitarity method.Our result not only manifests all dual Jacobi relations via CK duality but also contains 133 free parameters.This suggests the constructibility of the form factor at even higher loops via CK duality.We also find that the planar form factor has a hidden dual conformal symmetry in the lightlike limit of the operator momentum,which is checked up to four loops.

Next-to-leading-order relativistic and QCD corrections to prompt J/ψpair photoproduction at future e^(+)e^(−)colliders

Within the framework of nonrelativistic-QCD factorization,we calculate both the next-to-leading-order relativistic and QCD corrections to prompt J/ψpair production,with feed-down fromψ(2S)mesons,via photon-photon collisions at future e^(+)e^(−)colliders,including the Future Circular Lepton Collider(FCC-ee),the Circular Electron Positron Collider(CEPC),and the Compact Linear Collider(CLIC).We present total cross sections and distributions in single J/ψtransverse momentum and rapidity,as well as in J/ψpair invariant mass.The relativistic and QCD corrections both turn out to be large and negative.However,the production rates are large enough for useful experimental studies.

Quarksonic matter at high isospin density

Analogous to the quarkyonic matter at high baryon density in which the quark Fermi seas and the baryonic excitations coexist, it is argued that a ＂quarksonic matter＂ phase appears at high isospin density where the quark （antiquark） Fermi seas and the mesonic excitations coexist. We explore this phase in detail in both large Nc and asymptotically free limits. In the large Nc limit, we sketch a phase diagram for the quarksonic matter. In the asymptotically free limit, we study the pion superfluidity and thermodynamics of the quarksonic matter by using both perturbative calculations and an effective model.

Studying the localized CP violation and the branching fraction of the B^0→K^-π^+π^+π^-decay

In this work,we study the localized CP violation and the branching fraction of the four-body decay^ˉB 0→K^−π^+π^−π^+by employing a quasi-two-body QCD factorization approach.Considering the interference of^ˉB 0→ˉK^∗0(700)ρ0(770)→K^−π^+π^−π^+and^ˉB 0→ˉK∗(892)f0(500)→K^−π^+π^−π^+channels,we predict ACP(^ˉB 0→K^−π^+π^−π^+)∈[0.15,0.28]and B(^ˉB 0→K^−π^+π^−π^+)∈[1.73,5.10]×10^−7,respectively,which shows that the interference mechanism of these two channels can induce the localized CP violation to this four-body decay.Meanwhile,within the two quark model framework for the scalar mesons f0(500)andˉK^∗0(700),we calculate the direct CP violations and branching fractions of the^ˉB 0→ˉK^∗0(700)ρ0(770)and^ˉB 0→ˉK∗(892)f0(500)decays,respectively.The corresponding results are ACP(^ˉB 0→ˉK^∗0(700)ρ0(770))∈[0.20,0.36],ACP(^ˉB 0→ˉK∗(892)f0(500))∈[0.08,0.12],B(^ˉB 0→ˉK^∗0(700)ρ0(770)∈[6.76,18.93]×10^−8 and B(^ˉB 0→ˉK∗(892)f0(500))∈[2.66,4.80]×10^−6,indicating that the CP violations of these two-body decays are both positive and the branching fractions quite different.These studies provide a new way to investigate the aforementioned four-body decay and can be helpful in clarifying the configuration of the structure of the light scalar meson.

Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes revisited

We provide a new proof of Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes.As a key step,we explicitly demonstrate the cancellation of spurious poles originating from the maximally helicity violating vertices in these rules.To achieve this,we introduce specially-defined two-off-shell-line sub-amplitudes and examine their residues at spurious poles.

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.

Next-to-leading order QCD corrections to the decay of Higgs to vector meson and Z boson

The exclusive decay of the Higgs boson to a vector meson （J/φ or γ（1S）） and Z boson is studied in this work. The decay amplitudes are separated into two parts in a gauge invariant manner. The first part comes from the direct coupling of the Higgs boson to the charm （bottom） quark and the other from the HZZ＊ or the loop-induced HZγ＊ vertexes in the standard model. While the branching ratios from the direct channel are much smaller than those of the indirect channel, their interference terms give nontrivial contributions. We further calculate the QCD radiative corrections to both channels, which reduce the total branching ratios by around 20% for both J/φ and γ（1S） production. Our results provide a possible chance to check the SM predictions of the Hcc（Hbb） coupling and to seek for hints of new physics at the High Luminosity LHC or future hadron colliders.

Impact of lepton pT threshold on charge asymmetry predictions for inclusive Wboson production in pp collisions at 13 TeV

This paper presents the impact of the lepton transverse momentum p^(l)_(T) threshold on the W boson charge asymmetry predictions in perturbative QCD for the inclusive W^(±)+X→l^(±)v+X production in proton-proton(pp)collisions.The predictions are obtained at various low-p^(l)_(T) thresholds p^(l)_(T)>20,25,30,and 40 GeV in a fiducial region encompassing both the central and forward detector acceptances in terms of the lepton pseudorapidity 0≤ηl≤<4.5.The predicted distributions for the lepton charge asymmetry,which is defined by ηl(Aηl),at the next-to-next-to-leading order(NNLO)accuracy are compared with the CMS and LHCb data at 8 TeV center-of-mass collision energy.The 8 TeV predictions reproduce the data fairly well within the quoted uncertainties.The predictions from the CT14 parton distribution function(PDF)model are in a slightly better agreement with the data over the other PDF sets that are tested.The 13 TeV predictions using various p^(l)_(T) thresholds are reported for An,and the charge asymmetries that are defined in terms of the differential cross sections in bins of the W boson rapidity yw(A_(yw))and transverse momentum(Apw).The NNLO predictions for the Ayw,and Apw distributions are assessed to be in close correlation with the plT value.The An,and A_(yw) distributions are particularly shown to be more correlated at a higher ^(l)_(T) threshold.The Apw distributions are also reported from the merged predictions with improved accuracy by the inclusion of the next-to-next-to-next-to-leading logarithm(N^(3)LL)corrections,i.e.,at NNLO+N^(3)LL.The predicted distributions from various ^(l)_(T) thresholds represent a finer probe in terms of the capability to provide more constraints on the ratio of u and d quark distribution functions in the parton momentum fraction range 10^(-4)<x<1.