The Generalized Sine Theorem for Mixed Vertex Angle of Two Simplices and Applications

Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.

New insights to old problems

From the history of the θ-τ puzzle and the discovery of parity non-conservation in 1956, we review the current status of discrete symmetry violations in the weak interaction. Possible origin of these symmetry violations are discussed.

Reduction of PDF uncertainty in the measurement of the weak mixing angle at the ATLAS experiment

We investigate the parton distribution function(PDF)uncertainty in the measurement of the effective weak mixing angle sin2θ^(l)_(eff)at the CERN Large Hadron Collider(LHC).The PDF-induced uncertainty is large in proton-proton collisions at the LHC due to the dilution effect.The measurement of the Drell-Yan forward-backward asymmetry(ApB)at the LHC can be used to reduce the PDF uncertainty in the sin2θ^(l)_(eff)measurement.However,when including the full mass range of lepton pairs in the AFB data analysis,the correlation between the PDF updating procedure and the sin2θ^(l)_(eff) extraction leads to a sizable bias in the obtained sin2θ^(l)_(eff)value.From our studies,we find that the bias can be significantly reduced by removing Drell-Yan events with invariant mass around the Z-pole region,while most of the sensitivity in reducing the PDF uncertainty remains.Furthermore,the lepton charge asymmetry in the^boson events as a function of the rapidity of the charged leptons,A±(ηl),is known to be another observable which can be used to reduce the PDF uncertainty in the sin2θ^(l)_(eff)measurement.The constraint from A±(ηl)is complementary to that from AFB,and thus no bias affects the sin2θ^(l)_(eff)extraction.The studies are performed using the error PDF Updating Method Package(ePump),which is based on Hessian updating methods.In this article,the CT14HERA2 PDF set is used as an example.

A proposal on complementary determination of the effective electro-weak mixing angles via doubly heavy-flavored hadron production at a super Z-factory

To test the standard model(SM)precisely and to look for the clues deviating from SM,a proposal for determining the effective electro-weak mixing angles sin2θefff(particularly f=lept,c,b)is proposed.It is via observing the asymmetries(the forward-backward one AFB,the left-right one ALR and the combined left-right forward-backward one ALRFB)of the doubly heavy-flavored hadrons in the production at a super Z-factory(an e+e-collider designed with a luminosity as high as possible for modernday techniques runs around the center-of-mass energy s1/2=mZ).To see the sensitivity,uncertainties as well as the event accumulation precisely,the observables for describing the asymmetries of the produced hadrons are computed numerically with varying effective mixing angles,and based on the result analyses,it is concluded that the proposal may offer an independent complement determination of the effective mixing angles.

Measurement of the effective weak mixing angle at the CEPC

We present a study of the measurement of the effective weak mixing angle parameter(sin^(2)θ^(l)_(eff))at the Circular Electron Positron Collider(CEPC).As a fundamental physics parameter,sin^(2)θ_(eff)^(l) plays a key role not only in the global test of the standard model electroweak sector,but also in constraining the potential beyond standard model new physics at the high energy frontier.CEPC proposes a two year running period around the Z boson mass pole at high instataneous luminosity,providing a large data sample with 4 × 10^(12)Z candidates generated in total.It allows a high precision measurement of sin^(2)θ^(l)_(eff) both in the lepton and quark final states,where the uncertainty can be one order of magnitude lower than any previous measurement at the LEP,SLC,Tevatron,and LHC.It will improve the overall precision of the sin^(2)θ^(l)_(eff) experimental determination to be comparable to the preicision of the theoretical calculation with two-loop radiative corrections,and it will also provide direct comparisons between different final states.In this paper,we also study the measurement of sin^(2)θ^(l)_(eff) in the high mass region.Taking data for one month,the precision of sin^(2)θ^(l)_(eff) measured at 130 GeV from b quark final state is 0.00010,which will be an important experimental observation on the energy-running effect of sin^(2)θ^(l)_(eff).

Can a non-unitary effect be prominent in neutrino oscillation measurements?

Subject to neutrino experiments, the mixing matrix of ordinary neutrinos can still have small vi-olation from unitarity. We introduce a quasi-unitary matrix to interpret this violation and propose a natural scheme to parameterize it. A quasi-unitary factor △QF is defined to be measured in neutrino oscillation exper-iments and the numerical results show that the improvement in experimental precision may help us figure out the secret of neutrino mixing.

Properties of the coupling constants of J/ψ→VP decays

Based on the branching fractions of J/ψ→VP from different experiments, we investigate the properties of the coupling constants of J/ψ→ VP decays using a model-dependent approach. We find that the octet coupling constant, gs, of strong interaction is about twice larger than that of the singlet coupling constant g1; the electromag- netic breaking parameters g_E^i are larger than the mass breaking parameters g_M^i, moreover, the three parameters of the electromagnetic effect are about equal, but the three parameters of the mass effect are obviously different and their uncertainties are also large; and the phase angle between strong and electromagnetic interactions is in the range of 700-80°. It deepens our understanding of the coupling constant of J/ψ→VP decays.

D^+→η(′)l+ν_l semileptonic decays in light-cone sum rules

We calculate the D → η transition form factor in light-cone sum rules by taking improved current correlators to avoid the pollution from the twist-3 wave function. We get consistent results of the D＋ → η^（＇）l＋νl decays with the experimental data. By comparing the difference between the results of the branching ratios of D＋ → η^（＇）l＋νl from a two-pole parameterization model and from a BZ parameterization model, we find that the two-pole model and the BZ model are comparably believable. One way is supposed for the determination of the η-η mixing angle from the dependence of the branching ratios of D＋ → η^（＇）l＋νl decays on the η-η mixing angle.

Strong decays of P-wave mixing heavy-light 1^+ states

Many P-wave mixing heavy-light 1^＋ states have not yet been discovered by experiment, while others have been discovered but without width information, or with large uncertainties on the widths. In this paper, the strong decays of the P-wave mixing heavy-light 1^＋ states D^0, D^±, D^±, B^0, B^±： and Bs are studied by the improved Bethe SMpeter （B-S） method with two conditions of mixing angle 0： one is 0 = 35.3°; the other is considering a correction to the mixing angle 0=35.3°＋θ1. Valuable predictions for the strong decay widths are obtained： F（D1^0）=232 MeV, r（D1^0）=21.5 MeV, F（D1^±）=232 MeV, F（D1^±）=21.5 MeV, F（Ds1^±）=0.0101 MeV,Г（Ds1^±l）=0.950 MeV, F（BГ^±＋）=263 MeV, F（B1^±=16.8 MeV, F（B′s1）=0.01987 MeV and F（B,1）=0.412 MeV. It is found that the decay widths of D~ and Bsl are very sensitive to the mixing angle. The results will provide theoretical assistance to future experiments.