In gauge theory on 5D orbifolds the magnitude of chiral anomalies of 4D gauge fields changes with the value of the Aharonov-Bohm (AB) phase <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>θ</mi><mi>H</mi></msub></math> in the fifth dimension. Anomaly flows with the AB phase. In particular in the Randall-Sundrum (RS) warped space gauge couplings of 4D fermions depend on bulk mass parameters of 5D fermion multiplets. We show that in the GUT-inspired <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> gauge-Higgs unification model in the RS warped space the total anomalies including contributions of all Kaluza-Klein excited modes of fermions become universal, being independent of the values of the bulk mass parameters of fermions and expressed in terms of the values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> wave functions at the ultraviolet and infrared branes in the RS space. It is shown that cancellation of gauge anomalies is achieved in each generation even for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>θ</mi><mi>H</mi></msub><mo>≠</mo><mn>0</mn></math>.

Japan

Yutaka Hosotani

Anomaly flow and anomaly cancellation

In the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> gauge-Higgs unification in the Randall-Sundrum (RS) warped space, neutrino oscillations and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> couplings originate from Majorana mass terms on the ultraviolet brane in the RS space. Tiny neutrino masses are generated by an inverse seesaw mechanism. The PMNS matrix in the normal ordering with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mrow><mi>CP</mi></mrow></msub><mo>=</mo><mi>π</mi></math> naturally arises consistently with the NuFit-6.0 analysis of neutrino oscillation data.

Neutrino oscillations and PMNS matrix in gauge-Higgs unification

In the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> gauge-Higgs unification in the Randall-Sundrum warped space the mixing in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> couplings in the quark sector is induced by masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></math> singlet fermions which are responsible for splitting masses of down-type quarks from those of up-type quarks in each generation. We show that the observed Cabibbo-Kobayashi-Maskawa matrix in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> couplings is reproduced within experimental errors. Further flavor-changing neutral currents in the quark sector are shown to be naturally suppressed.

Shuichiro Funatsu

Hisaki Hatanaka

Czechia

Yuta Orikasa

Naoki Yamatsu

Origin of CKM matrix and natural FCNC suppression in gauge-Higgs unification

The <math><mi>W</mi></math> boson mass <math><msub><mi>m</mi><mi>W</mi></msub></math> in the grand unified theory inspired <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>×</mo><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> gauge-Higgs unification in the Randall-Sundrum (RS) warped space is evaluated. The muon decay <math><msup><mi>μ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>e</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>e</mi></msub><msub><mi>ν</mi><mi>μ</mi></msub></math> proceeds by the exchange of not only the zero mode of the <math><mi>W</mi></math> boson <math><mrow><mo>(</mo><msup><mrow><mi>W</mi></mrow><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msup><mo>)</mo></mrow></math> but also Kaluza-Klein (KK) excited modes <math><msup><mi>W</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></math> and <math><msubsup><mi>W</mi><mi>R</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msubsup></math> (<math><mi>n</mi><mo>≥</mo><mn>1</mn></math>) at the tree level. The anti–de Sitter curvature of the RS space also affects the relationship among the gauge couplings and the ratio of <math><msub><mi>m</mi><mi>W</mi></msub></math> to the <math><mi>Z</mi></math> boson mass <math><msub><mi>m</mi><mi>Z</mi></msub></math>. The <math><mi>W</mi></math> couplings of leptons and quarks also change. With the given KK mass scale <math><msub><mi>m</mi><mrow><mi>KK</mi></mrow></msub></math> the range of the Aharonov-Bohm phase <math><msub><mi>θ</mi><mi>H</mi></msub></math> in the fifth dimension is constrained. For <math><msub><mi>m</mi><mrow><mi>KK</mi></mrow></msub><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, <math><mn>0.085</mn><mo>≲</mo><msub><mi>θ</mi><mi>H</mi></msub><mo>≲</mo><mn>0.11</mn></math> and <math><mn>80.381</mn><mo>≲</mo><msub><mi>m</mi><mi>W</mi></msub><mo>≲</mo><mn>80.407</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. The predicted value of <math><msub><mi>m</mi><mi>W</mi></msub></math> for <math><mn>13</mn><mo>≤</mo><msub><mi>m</mi><mrow><mi>KK</mi></mrow></msub><mo>≤</mo><mn>20</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> lies between <math><msubsup><mi>m</mi><mi>W</mi><mrow><mi>SM</mi></mrow></msubsup><mo>=</mo><mn>80.354</mn><mo>±</mo><mn>0.007</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> in the standard model and <math><msubsup><mi>m</mi><mi>W</mi><mrow><mi>CDF</mi></mrow></msubsup><mo>=</mo><mn>80.4335</mn><mo>±</mo><mn>0.0094</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, the value reported by the CDF Collaboration in 2022.

China

<math><mrow><mi>W</mi></mrow></math> boson mass in gauge-Higgs unification

We examine <math><mi>W</mi></math> and <math><mi>Z</mi></math> boson pair production processes at electron-positron collider experiments in the <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>C</mi></mrow></msub><mo>×</mo><mi>S</mi><mi>O</mi><mo>(</mo><mn>5</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>W</mi></mrow></msub><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>X</mi></mrow></msub></mrow></math> gauge-Higgs unification (GHU) model. We find that the deviation of the total cross section for the <math><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><mo>→</mo><msup><mi>W</mi><mo>−</mo></msup><msup><mi>W</mi><mo>+</mo></msup></math> process from the Standard Model (SM) in the GHU model with parameter sets, which are consistent with the current experiments, is about 0.5% to 1.5% and 0.6% to 2.2% for <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>250</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and 500 GeV, respectively, depending on the initial electron and positron polarization. We find that for the <math><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><mo>→</mo><mi>Z</mi><mi>Z</mi></math> process the deviation from the SM in the GHU model is at most 1%. We find that unitarity bound for the <math><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup><mo>→</mo><msup><mi>W</mi><mo>−</mo></msup><msup><mi>W</mi><mo>+</mo></msup></math> process is satisfied in the GHU model as in the SM, as a consequence of the relationship among coupling constants.

<math><mrow><mi>W</mi></mrow></math> and <math><mi>Z</mi></math> boson pair production at electron-positron colliders in gauge-Higgs unification

Abstract In grand-unified-theory-inspired SO(5) × U(1)$_{X}$ × SU(3)$_{C}$ gauge-Higgs unification (GHU) in the Randall–Sundrum warped spacetime, the W- and Z-couplings of all 4D fermion modes become nontrivial. The W- and Z-couplings of zero-mode quarks and leptons slightly deviate from those in the SM, and the couplings take the matrix form in the space of Kaluza–Klein (KK) states. In particular, the 4D couplings and mass spectra in the KK states depend on the Aharonov–Bohm phase θ$_{H}$ in the fifth dimension. Nevertheless there emerge three astonishing sum rules among those coupling matrices, which guarantees the finiteness of certain combinations of corrections to vacuum polarization tensors. We confirm by numerical evaluation that the equality in the sum rules holds with 5- to 7-digit accuracy. Based on the sum rules we propose improved oblique parameters in GHU. Oblique corrections due to fermion 1-loop diagrams are found to be small.

Taiwan

Coupling sum rules and oblique corrections in gauge-Higgs unification

We examine effects of <math><msup><mi>Z</mi><mo>′</mo></msup></math> bosons in gauge-Higgs unification (GHU) models at <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> Bhabha scatterings. We evaluate differential cross sections in Bhabha scatterings including <math><msup><mi>Z</mi><mo>′</mo></msup></math> bosons in two types of <math><mi>SO</mi><mo>(</mo><mn>5</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>×</mo><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> GHU models. We find that deviations of differential cross sections in the GHU models from those in the SM can be seen at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>250</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. With 80%-longitudinally polarized electron and 30%-longitudinally polarized positron beams, the left-right asymmetries in the GHU A and B models are resolved at more than <math><mn>3</mn><mi>σ</mi></math> at <math><msub><mi>L</mi><mrow><mi>int</mi></mrow></msub><mo>=</mo><mn>250</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. We also show that Bhabha scattering with scattering angle less than 100 mrad can be safely used as luminosity measurements at <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders since the effects of <math><msup><mi>Z</mi><mo>′</mo></msup></math> bosons are well suppressed for small scattering angle. We propose a new observable which can be measured at future TeV-scale <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> linear colliders.

Bhabha scattering in the gauge-Higgs unification

The minimal <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> extension of the Standard Model (SM) is a well-motivated new physics scenario, where anomaly cancellation dictates new neutral gauge boson (<math><msup><mi>Z</mi><mo>′</mo></msup></math>) couplings with the SM fermions in terms of the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> charges of the new scalar fields. We investigate the SM charged fermion pair-production process for different values of these <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> charges at future <math><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math> colliders: <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>f</mi><mover><mi>f</mi><mo>¯</mo></mover></math>. Apart from the standard <math><mi>γ</mi></math> and <math><mi>Z</mi></math>-mediated processes, this model features additional <math><mi>s</mi></math>-channel (or both <math><mi>s</mi></math> and <math><mi>t</mi></math>-channel when <math><mi>f</mi><mo>=</mo><msup><mi>e</mi><mo>−</mo></msup></math>) <math><msup><mi>Z</mi><mo>′</mo></msup></math> exchange which interferes with the SM processes. We first estimate the bounds on the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> coupling <math><mo>(</mo><msup><mi>g</mi><mo>′</mo></msup><mo>)</mo></math> and the <math><msup><mi>Z</mi><mo>′</mo></msup></math> mass <math><mo>(</mo><msub><mi>M</mi><msup><mi>Z</mi><mo>′</mo></msup></msub><mo>)</mo></math> considering the latest dilepton and dijet constraints from the heavy resonance searches at the LHC. Then using the allowed values of <math><msup><mi>g</mi><mo>′</mo></msup></math>, we study the angular distributions, forward-backward <math><mo>(</mo><msub><mi>A</mi><mi>FB</mi></msub><mo>)</mo></math>, left-right <math><mo>(</mo><msub><mi>A</mi><mi>LR</mi></msub><mo>)</mo></math>, and left-right forward-backward <math><mo>(</mo><msub><mi>A</mi><mrow><mi>LR</mi><mo>,</mo><mi>FB</mi></mrow></msub><mo>)</mo></math> asymmetries of the <math><mi>f</mi><mover><mi>f</mi><mo>¯</mo></mover></math> final states. We find that these observables can show substantial deviations from the SM results in the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> model, thus providing a powerful probe of the multi-TeV <math><msup><mi>Z</mi><mo>′</mo></msup></math> bosons at future <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders.

South Korea

Arindam Das

United States

P. S. Bhupal Dev

Spain

Sanjoy Mandal

Probing the minimal <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>X</mi></msub></math> model at future electron-positron colliders via fermion pair-production channels

By projecting the partition function on the “color”-singlet state, we investigate the Hosotani mechanism in the fermion-gauge boson plasma. The present toy-model analysis of the one-loop effective potential at finite temperature shows that the critical temperature of gauge symmetry breaking increases at higher temperature in the smaller volume.

Nahomi Kan

Koichiro Kobayashi

Kiyoshi Shiraishi

Hosotani Mechanism in the “Color”-singlet Plasma

Abstract Universality in anomaly flow by an Aharonov–Bohm phase θ$_{H}$ is shown in the flat M$^{4}$ × (S$^{1}$/Z$_{2}$) spacetime and in the Randall–Sundrum (RS) warped space. We analyze the SU(2) gauge theory with doublet fermions. With orbifold boundary conditions the U(1) part of the gauge symmetry remains unbroken at θ$_{H}$ = 0 and π. Chiral anomalies smoothly vary with θ$_{H}$ in the RS space. It is shown that the anomaly coefficients associated with this anomaly flow are expressed in terms of the values of the wave functions of the gauge fields at the UV and IR branes in the RS space. The anomaly coefficients depend on θ$_{H}$, the warp factor of the RS space, and the orbifold boundary conditions for fermions, but not on the bulk mass parameters of fermions.