<p>We consider the theory of a higher-derivative (HD) real scalar field <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> coupled to a complex scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>, the coupling of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> being given by two types, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mrow><mi>σ</mi><mi>ϕ</mi></mrow></msub><msup><mi>σ</mi><mi>†</mi></msup><mi>σ</mi><msup><mi>ϕ</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ξ</mi><mrow><mi>σ</mi><mi>ϕ</mi></mrow></msub><msup><mi>σ</mi><mi>†</mi></msup><mi>σ</mi><msup><mrow><mo stretchy="false">(</mo><msub><mo>∂</mo><mi>μ</mi></msub><mi>ϕ</mi><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></math>. We evaluate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> one-loop corrections <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi><mi>V</mi><mo stretchy="false">(</mo><mi>σ</mi><mo stretchy="false">)</mo></math> to the effective potential of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>, both the contribution from the positive norm part of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ϕ</mi></math> and that from the <i>negative norm part</i> (ghost). We show that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi><mi>V</mi><mo stretchy="false">(</mo><msub><mi>σ</mi><mrow><mi>cl</mi></mrow></msub><mo stretchy="false">)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><mrow><mi>cl</mi></mrow></msub><mo stretchy="false">→</mo><mi>∞</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>σ</mi><mrow><mi>cl</mi></mrow></msub></math> is a classical value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>, is positive, implying the stability of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi><mi>V</mi><mo stretchy="false">(</mo><msub><mi>σ</mi><mrow><mi>cl</mi></mrow></msub><mo stretchy="false">)</mo></math> by the HD one-loop radiative corrections at high energy.</p>

Japan

Yugo Abe

Takeo Inami

Keisuke Izumi

UV stability of one-loop radiative corrections in higher-derivative scalar field theory

We obtain the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which has   <math> <msubsup> <mi>R</mi> <mi>μν</mi> <mn>2</mn> </msubsup> </math>  $$ {R}_{\mu \nu}^2 $$  term in the action. Unitarity bound is not satisfied because of the existence of negative norm states, while an analog of unitarity bound for S-matrix unitarity holds due to the cancelation among the positive norm states and negative norm ones in the unitarity summation in the optical theorem. The violation of unitarity bound is a counter example of Llewellyn Smith’s conjecture on the relation between tree-level unitarity and renormalizability. We have recently proposed a new conjecture that an analog of the unitarity bound for S-matrix unitarity gives the equivalent conditions to those for renormalizability. We show that the gravitational theory of quadratic curvature is a nontrivial example consistent with our conjecture.

High-energy properties of the graviton scattering in quadratic gravity

Abstract The flavor-changing gravitational process, d → s + graviton, is evaluated at the one-loop level in the standard electroweak theory with on-shell renormalization. The results that we present in the ’t Hooft–Feynman gauge are valid for on- and off-shell quarks and for all external and internal quark masses. We show that there exist non-decoupling effects of the internal heavy top quark in interactions with gravity. A naive argument taking account of the quark Yukawa coupling suggests that the amplitude of the process d → s + graviton in the large top quark mass limit would possibly acquire an enhancement factor , where m$_{t}$ and M$_{W}$ are the top quark and the W-boson masses, respectively. In practice this leading enhancement is absent in the renormalized amplitude due to cancellation. Thus the non-decoupling of the internal top quark takes place at the  level. The flavor-changing two- and three-point functions are shown to satisfy the Ward–Takahashi identity, which is used as a consistency check for the aforementioned cancellation of the  terms. Among the  non-decoupling terms, we sort out those that can be regarded as due to the effective Lagrangian in which quark bilinear forms are coupled to the scalar curvature.

Takahiro Kubota

Heavy particle non-decoupling in flavor-changing gravitational interactions

We investigate several phenomena related to FCNCs in the  $$\text {3-3-1-1}$$  <math> <mtext>3-3-1-1</mtext> </math>   model. The sources of FCNCs at the tree-level from both the gauge and Higgs sectors are clarified. Experiments on the oscillation of mesons most stringently constrain the tree-level FCNCs. The lower bound on the new physics scale is imposed more tightly than in the previous,  $$\text {M}_{\text {new}}&gt;12 $$  <math> <mrow> <msub> <mtext>M</mtext> <mtext>new</mtext> </msub> <mo>&gt;</mo> <mn>12</mn> </mrow> </math>   TeV. Under this bound, the tree-level FCNCs make a negligible contribution to the  $$\text {Br}(B_s \rightarrow \mu ^+ \mu ^-)$$  <math> <mrow> <mtext>Br</mtext> <mo>(</mo> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo>→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> </math>  ,  $$\text {Br}(B \rightarrow K^{*} \mu ^+ \mu ^-)$$  <math> <mrow> <mtext>Br</mtext> <mo>(</mo> <mi>B</mi> <mo>→</mo> <msup> <mi>K</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> </math>   and  $$\text {Br}(B^{+}\rightarrow K^{+}\mu ^{+}\mu ^{-})$$  <math> <mrow> <mtext>Br</mtext> <mo>(</mo> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> </math>  . The branching ratio of radiative decay  $$b \rightarrow s \gamma $$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <mi>γ</mi> </mrow> </math>   is enhanced by the ratio  $$\frac{v}{u}$$  <math> <mfrac> <mi>v</mi> <mi>u</mi> </mfrac> </math>   via diagrams with the charged Higgs mediation. In contrast, the charged currents of new gauge bosons significantly contribute to the decay process  $$\mu \rightarrow e \gamma $$  <math> <mrow> <mi>μ</mi> <mo>→</mo> <mi>e</mi> <mi>γ</mi> </mrow> </math>  .

Vietnam

Duy Nguyen Tuan

Huong Do Thi

Physical constraints derived from FCNC in the 3-3-1-1 model

Abstract We investigate the relation between -matrix unitarity () and renormalizability in theories with negative-norm states. The relation has been confirmed in many field theories, including gauge theories and Einstein gravity, by analyzing the unitarity bound, which follows from the -matrix unitarity and the norm positivity. On the other hand, renormalizable theories with a higher-derivative kinetic term do not necessarily satisfy the unitarity bound because of the negative-norm states. In these theories it is not known whether the -matrix unitarity provides a nontrivial constraint related to the renormalizability. In this paper, by relaxing the assumption of norm positivity we derive a bound on scattering amplitudes weaker than the unitarity bound, which may be used as a consistency requirement for -matrix unitarity. We demonstrate in scalar field models with a higher-derivative kinetic term that the weaker bound and the renormalizability imply identical constraints.

Tomotaka Kitamura

Toshifumi Noumi

-matrix Unitarity and Renormalizability in Higher-derivative Theories

We investigate the ultraviolet (UV) behavior of two-scalar elastic scattering with graviton exchanges in higher-curvature gravity theory. In Einstein gravity, matter scattering is shown not to satisfy the unitarity bound at tree level at high energy. Among some of the possible directions for the UV completion of Einstein gravity, such as string theory, modified gravity, and inclusion of high-mass/high-spin states, we take gravity coupled to matter. We show that matter scattering with graviton interactions satisfies the unitarity bound at high energy, even with negative norm states due to the higher-order derivatives of metric components. The difference in the unitarity property of these two gravity theories is probably connected to that in another UV property, namely, the renormalizability property of the two.

South Korea

Matter scattering in quadratic gravity and unitarity

We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability conditions are modified from those in relativistic theories. We show that for renormalizability, an extended version of the power-counting condition is required in addition to the conventional one. The unitarity bound for S-matrix elements also gives stronger constraints on interaction terms because of the reference frame dependence of scattering amplitudes. We prove that both unitarity and renormalizability require identical conditions as in the case of conventional relativistic theories.

Toshiaki Fujimori

Taiwan

Spain

Tree-level unitarity and renormalizability in Lifshitz scalar theory

To define a free string by the Nambu–Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric . In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.

Pei-Ming Ho

Geometry of area without length

We study whether inflation is realized based on the radion gauge-Higgs potential obtained from the one-loop calculation in five-dimensional gravity coupled to a gauge theory. We show that the gauge-Higgs can give rise to inflation in accord with the astrophysical data and the radion plays a role in fixing the values of physical parameters. We clarify the reason why the radion dominated inflation and the hybrid inflation cannot occur in our framework.

Yoshiharu Kawamura

Yoji Koyama

Inflation from radion gauge-Higgs potential at Planck scale

There has been a proposal that infrared quantum effects of massless interacting field theories in de Sitter space may provide time-dependent screening of the cosmological constant. As a concrete model of the proposal, we study the three loop corrections to the energy–momentum tensor of massless $\lambda \phi ^4$ theory in the background of classical Liouville gravity in $D=2$ dimensional de Sitter space. We find that the cosmological constant is screened, in sharp contrast to the massless $\lambda \phi ^4$ theory in $D=4$ dimensions due to the sign difference between the cosmological constant of the Liouville gravity and that of the Einstein gravity. To argue for the robustness of our prediction, we introduce the concept of time-dependent infrared counter-terms and examine if they recover the de Sitter invariance in the $\lambda \phi ^4$ theory in comparison with the Sine–Gordon model, where it was possible.