Box Diagram Contribution Research Articles

Electroweak box diagram contribution for pion and kaon decay from lattice QCD

Electroweak box diagram contribution for pion and kaon decay from lattice QCD

Dispersive analysis of neutral meson mixing

We analyze the neutral meson mixing by directly solving the dispersion relation obeyed by the mass and width differences of the two meson mass eigenstates. We solve for the parameters $x$ and $y$, proportional to the mass and width differences in the charm mixing, respectively, taking the box-diagram contributions to $x(s)$ and $y(s)$ at large mass squared $s$ of a fictitious $D$ meson as inputs. The SU(3) symmetry breaking is introduced through physical thresholds of different $D$ meson decay channels for $y(s)$. These threshold-dependent effects, acting like nonperturbative power corrections in QCD sum rules, stabilize the solutions of $y(s=m_D^2)$ with the $D$ meson mass $m_D$. We then calculate $x(s)$ through the dispersive integration of $y(s)$, and show that our predictions $x(m_D^2)\approx 0.21\%$ and $y(m_D^2)\approx 0.52\%$ are close to the data in both $CP$-conserving and $CP$-violating cases. It is observed that the channel containing di-kaon states provides the major source of SU(3) breaking, which enhances $x(m_D^2)$ and $y(m_D^2)$ by four orders of magnitude relative to the perturbative results. We also predict the coefficient ratio $q/p$ involved in the charm mixing with $|q/p|-1\approx 2\times 10^{-4}$ and $Arg(q/p)\approx 6\times 10^{-3}$ degrees, which can be scrutinized by precise future measurements. The formalism is extended to studies of the $B_{s(d)}$ meson mixing and the kaon mixing, and the small deviations of the obtained width differences from the perturbative inputs explain why the above mixing can be understood via short-distance dynamics. We claim that the puzzling charm mixing is attributed to the strong Glashow-Iliopoulos-Maiani suppression on perturbative contributions, instead of to breakdown of the quark-hadron duality, which occurs only at 15\% level.

Constraining active-sterile neutrino mixing via lepton flavor violating decays of mesons

As a hypothetic particle, a sterile neutrino can exist in types of new physics models. In this work by investigating flavor violating semileptonic and leptonic decays of K,D, and B mesons induced by the GeV scale sterile neutrino, we explore its allowed regions in parameter space. Analytically, we derive branching fractions of semileptonic decay M^{+}_{h}to M_{l}^{+}ell _{1}^{+}ell _{2}^{-} and leptonic decay M^{0}to ell _{1}^{-}ell _{2}^{+}, including the contribution from a new box diagram contribution due to the massive sterile neutrino. Imposing its mass ranges, we numerically analyze the active-sterile neutrino mixings in corresponding regions. We find that when the sterile neutrino mass is located in between pion and kaon mass, K+→π+e±μ∓ gives the strongest constraint while B+→π+e±μ∓ provides the dominated constraint when its mass in between of kaon and B meson. If the sterile neutrino is even heavier than Bmesons, the LHCb B^{0}_{s}to mu ^{pm } e^{mp } results gives the strongest constraint.

Parity-violating inelastic electron-proton scattering at low Q2 above the resonance region

We report the measurement of the parity-violating asymmetry for the inelastic scattering of electrons from the proton, at $Q^2 = 0.082$ GeV$^2$ and $ W = 2.23$ GeV, above the resonance region. The result $A_{\rm Inel} = - 13.5 \pm 2.0 ({\rm stat}) \pm 3.9 ({\rm syst})$~ppm agrees with theoretical calculations, and helps to validate the modeling of the $\gamma Z$ interference structure functions $F_1^{\gamma Z}$ and $F_2^{\gamma Z}$ used in those calculations, which are also used for determination of the two-boson exchange box diagram ($\Box_{\gamma Z}$) contribution to parity-violating elastic scattering measurements. A positive parity-violating asymmetry for inclusive $\pi^-$ production was observed, as well as positive beam-normal single-spin asymmetry for scattered electrons and a negative beam-normal single-spin asymmetry for inclusive $\pi^-$ production.

Box diagram contribution to the axial two-nucleon current

Recently, we have worked out the axial two-nucleon current operator to leading one-loop order in chiral effective field theory using the method of unitary transformation. Our final expressions, however, differ from the ones derived by the JLab-Pisa group using time-ordered perturbation theory (Phys. Rev. C 93, no. 1, 015501 (2016) Erratum: [Phys. Rev. C 93, no. 4, 049902 (2016)] Erratum: [Phys. Rev. C 95, no. 5, 059901 (2017)]). In this paper we consider the box diagram contribution to the axial current and demonstrate that the results obtained using the two methods are unitary equivalent at the Fock-space level. We adjust the unitary phases by matching the corresponding two-pion exchange nucleon-nucleon potentials and rederive the box diagram contribution to the axial current operator following the approach of the JLab-Pisa group, thereby reproducing our original result. We provide a detailed information on the calculation including the relevant intermediate steps in order to facilitate a clarification of this disagreement.

Pair production of the Elementary Goldstone Higgs boson at the LHC**Supported by National Natural Science Foundation of China (11275088, 11545012) and Natural Science Foundation of the Liaoning Scientific Committee (2014020151)

The Elementary Goldstone Higgs (EGH) model is a perturbative extension of the standard model (SM), which identifies the EGH boson as the observed Higgs boson. In this paper, we study pair production of the EGH boson via gluon fusion at the LHC and find that the resonant contribution of the heavy scalar is very small and the SM-like triangle diagram contribution is strongly suppressed. The total production cross section mainly comes from the box diagram contribution and its value can be significantly enhanced with respect to the SM prediction.

Implications ofB(μ→eγ)andΔaμon muonic lepton flavor violating processes

We study the implications of the experimental results on the $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ decay rate and the muon anomalous magnetic moment on muonic lepton flavor violating processes, such as $\ensuremath{\mu}\ensuremath{\rightarrow}3e$ and $\ensuremath{\mu}N\ensuremath{\rightarrow}eN$. We use a model-independent approach in this analysis, where these processes are considered to be loop induced by exchanging spin-$1/2$ and spin-0 particles. We explore two complementary cases---those with no cancellation mechanism in amplitudes and those with an internal (built-in) cancellation mechanism. Our main results are as follows: (a) Bounds from rates are used to constrain parameters, such as coupling constants and masses. These constraints can be easily updated by simple scalings, if the experimental situations change. (b) The muon $g\ensuremath{-}2$ data favors nonchiral interactions. (c) In $\ensuremath{\mu}\ensuremath{\rightarrow}3e$ and $\ensuremath{\mu}N\ensuremath{\rightarrow}eN$ processes, $Z$-penguin diagrams may play some role, while box diagram contributions to $\ensuremath{\mu}\ensuremath{\rightarrow}3e$ are usually highly constrained. (d) In the first case (without any built-in cancellation mechanism), using the recent $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ bound, we find that $\ensuremath{\mu}\ensuremath{\rightarrow}3e$ and $\ensuremath{\mu}N\ensuremath{\rightarrow}eN$ rates are usually bounded below the present experimental limits by two to three orders of magnitude in general. Furthermore, by comparing $\ensuremath{\Delta}{a}_{\ensuremath{\mu}}$ and $\mathcal{B}(\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma})$ data, the couplings of $\ensuremath{\mu}$ and $e$ are found to be highly hierarchical. Additional suppression mechanisms should be called for. (e) In the second case (with a built-in cancellation mechanism), mixing angles can provide additional suppression factors to satisfy the $\ensuremath{\Delta}{a}_{\ensuremath{\mu}}$ and $\mathcal{B}(\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma})$ bounds. While the $\ensuremath{\mu}\ensuremath{\rightarrow}3e$ rate remains suppressed, the bounds on $\ensuremath{\mu}N\ensuremath{\rightarrow}eN$ rates, implied from the latest $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ bound, can be relaxed significantly and can be just below the present experimental limits.

COUPLED CHANNEL EFFECTS IN ππ S-WAVE INTERACTION

We study coupled channel effects upon isospin I=2 and I=0 ππ S-wave interaction. With introduction of the ππ→ρρ→ππ coupled channel box diagram contribution into ππ amplitude in addition to ρ and f2(1270) exchange, we reproduce the ππ I =2 S-wave and D-wave scattering phase shifts and inelasticities up to 2 GeV quite well in a K-matrix formalism. For I=0 case, the same ππ→ρρ→ππ box diagram is found to give the largest contribution for the inelasticity among all possible coupled channels including ππ→ωω→ππ, [Formula: see text]. We also show why the broad σ appears narrower in production processes than in ππ scattering process.

New study of the isotensor ππ interaction

With t-channel ρ, f 2(1270) exchange and the ππ→ ρρ→ ππ box diagram contribution, we reproduce the ππ isotensor S-wave and D-wave scattering phase shifts and inelasticities up to 2.2 GeV quite well in a K-matrix formalism. The t-channel ρ exchange provides repulsive negative phase shifts while the t-channel f 2(1270) gives an attractive force to increase the phase shifts for ππ scattering above 1 GeV, and the coupled-channel box diagram causes the inelasticities. The implication to the isoscalar ππ S-wave interaction is discussed.

Higgs boson couplings to quarks with supersymmetric CP and flavor violations

In minimal supersymmetric model (SUSY) with a light Higgs sector, explicit CP violation and most general flavor mixings in the sfermion sector, integration of the superpartners out of the spectrum induces potentially large contributions to the Yukawa couplings of light quarks via those of the heavier ones. These corrections can be sizeable even for moderate values of tanβ, and remain nonvanishing even if all superpartners decouple. When the SUSY breaking scale is close to the electroweak scale, the Higgs exchange effects can compete with the gauge boson and box diagram contributions to rare processes, and their partial cancellations can lead to relaxation of the existing bounds on flavor violation sources. In this case there exist sizeable enhancements in flavor-changing Higgs decays. When the superpartners completely decouple, however, the Higgs mediation becomes the dominant SUSY contribution to rare processes the saturation of which, without a strong suppression of the flavor mixings, prefers large tanβ and certain ranges for the CP-odd phases. The decay rate of the lightest Higgs into light down quarks becomes comparable with that into the bottom quark. Moreover, the Higgs decay into the up quark is significantly enhanced. There are observable implications for rare processes, atomic electric dipole moments, and collider searches for Higgs bosons.

Polarized virtual photon structure functiong2γand twist-3 effects in QCD

We investigate the twist-3 effects in the polarized virtual photon structure. The structure functions $g_1^\gamma$ and $g_2^\gamma$ of polarized photon could be experimentally studied in the future polarized $ep$ or $e^+e^-$ colliders. The leading contributions to $g_1^\gamma$ are the twist-2 effects, while another structure function $g_2^\gamma$, which only exists for the virtual photon target, receives not only the twist-2 but also twist-3 contributions. We first show that the twist-3 effects actually exist in the box-diagram contributions and we extract the twist-3 part, which can also be reproduced by the pure QED operator product expansion. We then calculate the non-trivial lowest moment ($n=3$) of the twist-3 contribution to $g_2^\gamma$ in QCD. For large $N_c$ (the number of colors), the QCD analysis of the twist-3 effects in the flavor nonsinglet part of $g_2^\gamma$ becomes tractable and we can obtain its moments in a compact form for all $n$.

Effects of an extra Z' in the heavy-quark sector

In the light of the recent experimental result of the ARGUS Collaboration at DESY on \(B^0 \bar B^0 \) mixing, we examine its implication on the mass of the extra Z'-boson in theSpL (6)×UY (1) extension of the standard electroweak theory by considering the contributions of the tree level diagrams mediated by this extra Z'-boson. It is found that for the calculated bound onmZ', large values ofxs can be explained. In addition, it is found that the tree level contributions to ΔmD for the \(D^0 \bar D^0 \) system is at least an order of magnitude higher than the standard-model box diagram contributions.

Semi-leptonic flavour-changing neutral-current decays of the fourth generation b′-quark

We study the decay modes b′ → bℓ +ℓ −, b′ → bν ν for min b′ ⪅M Z including virtual γ, Z 0, and box diagram contributions, the latter complicating the computation considerably. Due to the effect of the Z 0 propagator and the finite Z 0 width, these decay rates are substantial. The box diagram is subleading but also not negligible. As a consequence, the lepton pair mass distribution is rather flat and high mass ℓ +ℓ − or ν ν pairs are much more abundant than suggested from phase space. It is found that b′ → bZ ∗ (loosely denoting the sum of if b′ → bℓ +ℓ −, b′ → ν ν and b′ → bq q ) is of similar order as the b′ → bg decay mode, and is likely to dominate in case m t′ is very heavy. With three light neutrinos, the decay b′ → bν ν is similar order as b′ → b γ, however, the b′ → bℓ +ℓ − mode are relatively suppressed. The flavour-changing neutral-current b′ decay scenario is thus shown to be quite rich. A comprehensive, but theoretical, discussion is given regarding b′ discovery potentials at present and future colliders.

The perturbative $$K^0 - \bar K^0 $$ amplitude

In the standard model of weak interactions the\(K^0 - \bar K^0 \) transition amplitude is the sum of three contributions: the box diagram, the double penguin and the dispersive terms. Recent data onB-meson decays is used to determine the magnitude of the box diagram contribution. When the hadronic matrix element of the box diagram is given byB ∼ 1.2, this contribution alone reproduces the observedKL-KS mass difference δm. The double penguin amplitude is shown to give a significant contribution to δm. A lower bound on thet-quark mass is obtained including the effect of the double penguin amplitude. The result is significantly lower than the result obtained using the box diagram alone.

Deep-inelastic photon-neutrino scattering

The moments of the structure functions ${\mathcal{F}}_{T}^{(N)}$, ${\mathcal{F}}_{3}^{(N)}$, and ${\mathcal{F}}_{L}^{(N)}$ in deep-inelastic photon-neutrino scattering have been calculated. Exactly calculable leading-order QCD corrections to the boxdiagram contributions are large for ${\mathcal{F}}_{T}^{(N)}$ and ${\mathcal{F}}_{3}^{(N)}$ increasing with $N$. For ${\mathcal{F}}_{L}^{(N)}$ the corrections are very small except for small $N$. Dependence of the results on the number of flavors of quarks is very small.

Effective lagrangian for ΔS = 1 and ΔS = 2 transition in the Higgs boson exchange model of CP violation

Using standard renormalization group technique, strong interaction corrections to ΔS = 1 and ΔS = 2 transitions are calculated in the Higgs-boson exchange model of CP violation. It is shown that the box diagram contribution to the ratio ϵ′ ϵ is not modified in any significant way with respect to lowest order calculation.

Virtual photon structure to non-leading order in QCD

We investigate the virtual photon structure functions for Λ 2 ⪡ P 2 ⪡ Q 2, where − Q 2 (− P 2) is the mass squared of the probe (target) photon. We do this to next-to-leading order in QCD. The non-leading corrections significantly modify the leading log result, in particular at large x. Also, the perturbatively calculated structure function is positive at low x even for P 2 ≈ 1 GeV 2. (For a real photon target it becomes negative at low x.) For large P 2 the QCD result approaches the box diagram (Born) structure function also when non-leading contributions are included. It is, however, important to include the large non-leading box diagram contributions in making this comparison.

Phonon splitting in the magnetised vacuum

An explicit result for the quadratic vacuum polarisation tensor in a static uniform magnetic field is derived using the Gehenian representation of the electron propagator. The formalism of relativistic-quantum plasma physics is used to calculate the probability for a photon to split into two photons in the magnetised vacuum, without approximation in the magnetic field strength or in the photon frequency or wavenumber. The exact effect of photon dispersion on photon splitting is included. It is shown that the probability for photon splitting in both the weak-field and low-frequency limits is greatest when the energy of the initial photon is divided equally between the two final photons. Errors are indicated in earlier results for the box-diagram contribution to photon splitting in the magnetised vacuum.

Long-range perturbing forces and the N/D method

It is suggested that the inclusion of box-diagram contributions to the lefthand cut, permits the removal of infra-red divergences in perturbation methods in an unambigous way. The method is applied to potential models and yields satisfactory results.

More Integral Representations for Scattering Amplitudes with Complex Singularities

Previous work is generalized in order to achieve a better understanding of the role of complex singularities in connection with integral representations. The most general conditions under which the box-diagram contribution to a scattering amplitude satisfies a representation with real integration contours are derived. Explicit representations are derived in several special cases. It is frequently found possible to obtain representations that are essentially of the Mandelstam type, although the more general Bergman-Oka-Weil representation must be invoked in general. One example of a three-dimensional representation is given, which exhibits the analytic structure in one of the external masses in addition to the kinematical variables. The significance of the ``physical sheet'' is discussed.