A Scale-invariant Higgs Sector and Structure of the Vacuum

In view of the current status of measured Higgs boson properties, we consider a question whether only the Higgs self-interactions can deviate significantly from the Standard-Model (SM) predictions. This may be possible if the Higgs effective potential is irregular at the origin. As an example we investigate an extended Higgs sector with singlet scalar(s) and classical scale invariance. We develop a perturbative formulation necessary to analyze this model in detail. The behavior of a phenomenologically valid potential in the perturbative regime is studied around the electroweak scale. We reproduce known results: The Higgs self-interactions are substantially stronger than the SM predictions, while the Higgs interactions with other SM particles are barely changed. We further predict that the interactions of singlet scalar(s), which is a few to several times heavier than the Higgs boson, tend to be fairly strong. If probed, these features will provide vivid clues to the structure of the vacuum. We also examine Veltman's condition for the Higgs boson mass.Comment: 26 pages, 14 figures, minor modification, version to appear in JHE

Probing Higgs self-coupling of a classically scale invariant model in e+e−→Zhhe^+e^- \to Zhh: Evaluation at physical point

A classically scale invariant extension of the standard model predicts large anomalous Higgs self-interactions. We compute missing contributions in previous studies for probing the Higgs triple coupling of a minimal model using the process $e^+e^- \to Zhh$. Employing a proper order counting, we compute the total and differential cross sections at the leading order, which incorporate the one-loop corrections between zero external momenta and their physical values. Discovery/exclusion potential of a future $e^+e^-$ collider for this model is estimated. We also find a unique feature in the momentum dependence of the Higgs triple vertex for this class of models.Comment: 14 pages, 7 figures; Version to appear in Phys. Lett.

Singularities and MZVs in Feynman Loop Integrals (Various aspects of multiple zeta values)

"Various aspects of multiple zeta values". July 23～26, 2013. edited by Kentaro Ihara. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.Feynman diagram is a theoretical tool for computing physical quantities in particle physics, and each diagram is given as a multiple integral. Often Feynman diagrams can be expressed by multiple zeta values (MZVs) and their generalizations. We discuss relations between singularities of diagrams and types of MZVs from a physicist's viewpoint. This provides a hint to a connection between topology of a diagram and its value in terms of MZVs. New technologies for computing complicated diagrams and unsolved problems are also discussed

On enhanced corrections from quasi-degenerate states to heavy quarkonium observables

It is well known that in perturbation theory existence of quasi-degenerate states can rearrange the order counting. For a heavy quarkonium system, naively, enhanced effects ($l$-changing mixing effects) could contribute already to the first-order and third-order corrections to the wave function and the energy level, respectively, in expansion in $\alpha_s$. We present a formulation and note that the corresponding (lowest-order) corrections vanish due to absence of the relevant off-diagonal matrix elements. As a result, in the quarkonium energy level and leptonic decay width, the enhanced effects are expected to appear, respectively, in the fifth- and fourth-order corrections and beyond.Comment: 9 page

Determination of mcm_c and mbm_b from quarkonium 1S energy levels in perturbative QCD

We update determination of the $\overline{\rm MS}$ masses of the charm and bottom quarks, from comparisons of the masses of the charmonium and bottomonium $1S$ states with their perturbative predictions up to next-to-next-to-next-to-leading order in $\varepsilon$ expansion and using the $\overline{\rm MS}$ masses. Effects of non-zero charm-quark mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain $\overline m_c=1246\pm 2 (d_3) \pm 4 (\alpha_s) \pm 23 (\text{h.o.} )~{\rm MeV}$ and $\overline m_b=4197\pm 2 (d_3) \pm 6 (\alpha_s) \pm 20 (\text{h.o.} )\pm 5 (m_c)~ {\rm MeV}$, which agree with the current Particle Data Group values.Comment: 12 pages, 5 figures, 1 table. v2: Typo corrected in Eq.(3); no change of final result

UV contribution and power dependence on ΛQCD\Lambda_\mathrm{QCD} of Adler function

We formulate a way to separate UV and IR contributions to the Adler function and discuss how $\Lambda_\mathrm{QCD}^2/Q^2$ dependence is encoded in the UV contribution within perturbative QCD.Comment: 10 pages, 5 figures. v3: minor modification