A future $ e^+e^- $ collider could run at the $\textit{Z}$-pole to perform important electroweak (EW) precision measurements, but such a run may not be viable for a future muon collider. However, this can be compensated for by measuring other EW processes utilizing the high energy and large luminosity of the muon collider. In this paper, we consider the measurements of the vector boson fusion processes of $ WW/WZ/W\gamma $ to a pair of fermions (along with a $ \nu_{\mu}\bar{\nu}_{\mu} $ or $ \nu_{\mu}\mu^+/\bar{\nu}_{\mu}\mu^- $ pair) at a high-energy muon collider and study their potential for probing EW observables. We consider two run scenarios for the muon collider with center-of-mass energies of 10 and 30 TeV, respectively, and focus on the processes involving $ f=b,c,\tau $ and the dimension-6 operators that directly modify the corresponding fermions coupling to the $ Z/W $ bosons. The invariant mass distribution of the $ f\bar{f} $ pair helps to separate the events from the $ Z/W $ and high-energy resonances, whereas the polar angle of the outing fermion provides additional information. Through a chi-squared analysis on the binned distributions and combining the information from the $\textit{WW}$ and $ WZ/W\gamma $ fusion processes, all relevant Wilson coefficients can be constrained simultaneously. The precision surpasses the current EW measurement constraints and is even competitive with future $ e^+e^- $ colliders. Our analysis can be included in a more complete framework that is required to fully determine the potential of muon colliders in EW precision measurements.

China

Hao-Qiao Li

Hai-Ning Yan

Jiayin Gu

Germany

Xiao-Ze Tan

Probing $\textit{Z}$/$\textit{W}$ pole physics at high-energy muon colliders via vector-boson-fusion processes * Supported by the National Natural Science Foundation of China (NSFC) (12035008, 12375091, 12347171), and the Innovation Program for Quantum Science and Technology (2024ZD0300101). Xiao-Ze Tan also acknowledges the support from Helmholtz – OCPC (Office of China Postdoctoral Council) Postdoctoral Fellowship Program

We apply the QCD sum rule method to systematically study excited light meson operators and calculate their decay constants. These operators are constructed by explicitly adding one covariant derivative to the quark-antiquark pair. In total, twelve such operators are constructed, among which ten are subjected to detailed numerical analyses. The considered quark contents include <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>q</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mi>s</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mo>=</mo><mi>u</mi><mo>/</mo><mi>d</mi></math>), allowing the formation of various <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> flavor nonets. For instance, our results support the interpretation that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1320</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>f</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy="false">(</mo><mn>1525</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>2</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>1430</mn><mo stretchy="false">)</mo></math> states constitute a flavor nonet with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><msup><mn>2</mn><mrow><mo>+</mo><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></msup></math>. In addition, we predict several excited meson states, whose masses and decay constants are determined using the QCD sum rule method.

Wei-Han Tan

Wen-Ying Liu

Hong-Zhou Xi

Hua-Xing Chen

QCD sum rule study of excited light meson operators

Lepton flavor violation (LFV) offers a powerful probe of physics beyond the Standard Model, particularly in models addressing neutrino masses and the baryon asymmetry of the universe. In this study, we investigate LFV processes within the framework of type II seesaw leptogenesis, where the Standard Model is extended by an $S U(2)_L$ triplet Higgs field. We focus on key LFV processes, including $\mu^+\to e^+\gamma$ , $\mu^+ \to e^+e^-e^+$ , and $\mu \rightarrow e$ conversion in nuclei, deriving stringent constraints on the parameter space from current experimental data. We scan the 3$\textit{σ}$ range of neutrino oscillation parameters and identify the most conservative bounds consistent with existing measurements. Our results reveal that the MEG experiment currently provides the most stringent constraints in the normal ordering (NO) scenario, while the SINDRUM experiment offers comparable sensitivity in the inverted ordering (IO) case. Future experiments, such as MEG II, Mu3e, Mu2e, and COMET, are predicted to significantly improve the sensitivity, testing larger regions of the parameter space.

Chengcheng Han

Yijun Han

Sihui Huang

Zhanhong Lei

Probing type II seesaw leptogenesis through lepton flavor violation * Chengcheng Han acknowledges supports from the National Key R&D Program of China (2023YFA1606100), the Sun Yat-Sen University Science Foundation, the Fundamental Research Funds for the Central Universities at Sun Yat-sen University (24qnpy117) and the Key Laboratory of Particle Astrophysics and Cosmology (MOE) of Shanghai Jiao Tong University

General one-loop formulas for loop-induced processes $gg/\gamma \gamma \rightarrow \phi_i\phi_j$ with $\phi_i\phi_j = hh,~hH,~HH$ are presented in this paper. The analytic expressions evaluated in this study are valid for a class of Higgs Extensions of the Standard Model, $\textit{e.g.,}$ Inert Doublet Higgs, Two Higgs Doublet, Zee-Babu, and Triplet Higgs Models$\textit{.}$ Analytic expressions for one-loop form factors are expressesd in terms of the basic scalar one-loop two-, three-, and four-point functions following the output format of the packages $ {\tt LoopTools}$ and $ {\tt Collier}$ . Hence, physical results can be evaluated numerically using one of these packages. The analytic results are tested using several checks such as the ultraviolet finiteness and infrared finiteness of the one-loop amplitudes. Furthermore, the amplitudes obey the ward identity due to massless gauge bosons in the initial states. This identity is also verified numerically. Regarding applications, we present the phenomenological results for the investigated processes in the Zee-Babu model as a typical example. In particular, production cross-sections for the processes $\gamma \gamma\rightarrow hh$ are scanned over the parameter space of the Zee-Babu Model.

Vietnam

Khiem Hong Phan

Dzung Tri Tran

Thanh Huy Nguyen

One-loop analytical expressions for $\textit{gg}$/$\textit{γγ}$ → ϕ$_{i}$ϕ$_{j}$ in Higgs extensions of the standard model and their applications * This research is supported by Vietnam National Foundation for Science and Technology Development (103.01-2023.16). Khiem Hong Phan and Dzung Tri Tran express their gratitude to all the valuable support from Duy Tan University, for the 30th anniversary of establishment (Nov. 11, 1994 - Nov. 11, 2024) towards ''Integral, Sustainable and Stable Development''

We study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave bottom baryons of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> flavor antitriplet and systematically calculate their strong decay properties, including their <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-wave decays into ground-state bottom baryons with light pseudoscalar mesons and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave decays into ground-state bottom baryons with light vector mesons. Together with [W. H. Tan et al., Predicted <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy="false">(</mo><mn>6087</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and further predictions, <a href="http://dx.doi.org/10.1140/epjc/s10052-024-12717-6">Eur. Phys. J. C 84, 382 (2024)</a>., H. M. Yang et al., Decay properties of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave bottom baryons within light-cone sum rules, <a href="http://dx.doi.org/10.1140/epjc/s10052-020-7637-z">Eur. Phys. J. C 80, 80 (2020)</a>., H. M. Yang and H. X. Chen, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave bottom baryons of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> flavor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mn mathvariant="bold">6</mn><mi>F</mi></msub></math> <a href="http://dx.doi.org/10.1103/PhysRevD.101.114013">Phys. Rev. D 101, 114013 (2020)</a>., and X. Luo, H. M. Yang, and H. X. Chen, Radiative decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave bottom baryons from light-cone sum rules, <a href="http://arXiv.org/abs/2407.04433">arXiv:2407.04433</a>.], a rather complete investigation has been performed to study their mass spectra and strong/radiative decay properties, through the methods of quantum chromodynamics (QCD) sum rules and light-cone sum rules within the framework of heavy quark effective theory. Among various possibilities, we identify four <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>b</mi></msub></math> and four <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>b</mi></msub></math> baryons, with limited decay widths and so capable of being observed in experiments. Their masses, mass splittings within the same multiplets, and strong/radiative decay widths are summarized in Table II for future experimental searching.

Yi-Jie Wang

Xuan Luo

Er-Liang Cui

Zhi-Yong Zhou

Strong decay properties of P-wave single bottom baryons of the SU(3) flavor antitriplet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mover accent="true"><mrow><mn>3</mn></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi mathvariant="normal">F</mi></mrow></msub></mrow></math>

We apply the QCD sum rule method to study the light single-gluon hybrid states with various (exotic) quantum numbers. We construct 24 single-gluon hybrid currents and use 18 of them to calculate the masses of 44 single-gluon hybrid states with the quark-gluon contents <math><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi></math> (<math><mi>q</mi><mo>=</mo><mi>u</mi><mo>/</mo><mi>d</mi></math>) and <math><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi><mi>g</mi></math>. We concentrate on the hybrid states with the exotic quantum number <math><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math>, whose masses and widths are calculated to be <math><msub><mi>M</mi><mrow><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mo>;</mo><msup><mn>1</mn><mo>−</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>1.6</mn><msubsup><mn>7</mn><mrow><mo>−</mo><mn>0.17</mn></mrow><mrow><mo>+</mo><mn>0.15</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math><msub><mi>Γ</mi><mrow><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mo>;</mo><msup><mn>1</mn><mo>−</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>53</mn><msubsup><mn>0</mn><mrow><mo>−</mo><mn>330</mn></mrow><mrow><mo>+</mo><mn>540</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, <math><msub><mi>M</mi><mrow><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mo>;</mo><msup><mn>0</mn><mo>+</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>1.6</mn><msubsup><mn>7</mn><mrow><mo>−</mo><mn>0.17</mn></mrow><mrow><mo>+</mo><mn>0.15</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math><msub><mi>Γ</mi><mrow><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mo>;</mo><msup><mn>0</mn><mo>+</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mspace></mspace><mn>12</mn><msubsup><mn>0</mn><mrow><mo>−</mo><mn>110</mn></mrow><mrow><mo>+</mo><mn>160</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, <math><msub><mi>M</mi><mrow><mo>|</mo><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi><mi>g</mi><mo>;</mo><msup><mn>0</mn><mo>+</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>1.8</mn><msubsup><mn>4</mn><mrow><mo>−</mo><mn>0.15</mn></mrow><mrow><mo>+</mo><mn>0.14</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, and <math><msub><mi>Γ</mi><mrow><mo>|</mo><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi><mi>g</mi><mo>;</mo><msup><mn>0</mn><mo>+</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>10</mn><msubsup><mn>0</mn><mrow><mo>−</mo><mn>80</mn></mrow><mrow><mo>+</mo><mn>110</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Our results support the interpretations of the <math><msub><mi>π</mi><mn>1</mn></msub><mo>(</mo><mn>1600</mn><mo>)</mo></math> and <math><msub><mi>η</mi><mn>1</mn></msub><mo>(</mo><mn>1855</mn><mo>)</mo></math> as the hybrid states <math><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mo>;</mo><msup><mn>1</mn><mo>−</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></math> and <math><mo>|</mo><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi><mi>g</mi><mo>;</mo><msup><mn>0</mn><mo>+</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></math>, respectively. Considering the uncertainties, our results suggest that the <math><msub><mi>π</mi><mn>1</mn></msub><mo>(</mo><mn>1600</mn><mo>)</mo></math> and <math><msub><mi>η</mi><mn>1</mn></msub><mo>(</mo><mn>1855</mn><mo>)</mo></math> may also be interpreted as the hybrid states <math><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mo>;</mo><msup><mn>1</mn><mo>−</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></math> and <math><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mo>;</mo><msup><mn>0</mn><mo>+</mo></msup><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></math>, respectively. To differentiate these two assignments and to verify whether they are hybrid states or not, we propose to examine the <math><msub><mi>a</mi><mn>1</mn></msub><mo>(</mo><mn>1260</mn><mo>)</mo><mi>π</mi></math> decay channel in future experiments.

Japan

Niu Su

Light single-gluon hybrid states with various exotic quantum numbers

The methods of QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory have been widely applied to study the singly heavy baryons, and especially, we have applied these methods to predict not only the mass and width of the $$\varXi _b(6087)^0$$ <math> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>6087</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math> recently discovered by LHCb, but also its observation channel and its mass difference from the $$\varXi _b(6100)^-$$ <math> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>6100</mn> <mo>)</mo> </mrow> <mo>-</mo> </msup> </mrow> </math> . We apply the same approach to perform a complete study on the P-wave bottom baryons of the SU(3) flavor $${\bar{\textbf{3}}}_F$$ <math> <msub> <mover> <mrow> <mn>3</mn> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>F</mi> </msub> </math> and investigate their fine structure. Besides the $$\varLambda _b(5912)^0$$ <math> <mrow> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>5912</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math> , $$\varLambda _b(5920)^0$$ <math> <mrow> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>5920</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math> , $$\varXi _b(6087)^0$$ <math> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>6087</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math> , and $$\varXi _b(6100)^-$$ <math> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>6100</mn> <mo>)</mo> </mrow> <mo>-</mo> </msup> </mrow> </math> , our results suggest the existence of the other two $$\varLambda _b$$ <math> <msub> <mi>Λ</mi> <mi>b</mi> </msub> </math> and two $$\varXi _b$$ <math> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> </math> baryons, whose widths are limited. They are the $$\varLambda _b(J^P = 3/2^-)$$ <math> <mrow> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>=</mo> <mn>3</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math> with the mass and width about $$(5.93^{+0.13}_{-0.13}~\textrm{GeV},\,0.0^{+12.0}_{-~0.0}~\textrm{MeV})$$ <math> <mrow> <mo>(</mo> <mn>5</mn> <mo>.</mo> <msubsup> <mn>93</mn> <mrow> <mo>-</mo> <mn>0.13</mn> </mrow> <mrow> <mo>+</mo> <mn>0.13</mn> </mrow> </msubsup> <mspace width="3.33333pt"></mspace> <mtext>GeV</mtext> <mo>,</mo> <mspace width="0.166667em"></mspace> <mn>0</mn> <mo>.</mo> <msubsup> <mn>0</mn> <mrow> <mo>-</mo> <mspace width="3.33333pt"></mspace> <mn>0.0</mn> </mrow> <mrow> <mo>+</mo> <mn>12.0</mn> </mrow> </msubsup> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> <mo>)</mo> </mrow> </math> , the $$\varLambda _b(5/2^-)$$ <math> <mrow> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>5</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math> with $$(5.94^{+0.13}_{-0.13}~\textrm{GeV},\,\approx 0~\textrm{MeV})$$ <math> <mrow> <mo>(</mo> <mn>5</mn> <mo>.</mo> <msubsup> <mn>94</mn> <mrow> <mo>-</mo> <mn>0.13</mn> </mrow> <mrow> <mo>+</mo> <mn>0.13</mn> </mrow> </msubsup> <mspace width="3.33333pt"></mspace> <mtext>GeV</mtext> <mo>,</mo> <mspace width="0.166667em"></mspace> <mo>≈</mo> <mn>0</mn> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> <mo>)</mo> </mrow> </math> , the $$\varXi _b(3/2^-)$$ <math> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math> with $$(6.10^{+0.15}_{-0.10}~\textrm{GeV},\, 1.4{^{+11.6}_{-~1.4}}~\textrm{MeV})$$ <math> <mrow> <mo>(</mo> <mn>6</mn> <mo>.</mo> <msubsup> <mn>10</mn> <mrow> <mo>-</mo> <mn>0.10</mn> </mrow> <mrow> <mo>+</mo> <mn>0.15</mn> </mrow> </msubsup> <mspace width="3.33333pt"></mspace> <mtext>GeV</mtext> <mo>,</mo> <mspace width="0.166667em"></mspace> <mn>1.4</mn> <msubsup> <mrow></mrow> <mrow> <mo>-</mo> <mspace width="3.33333pt"></mspace> <mn>1.4</mn> </mrow> <mrow> <mo>+</mo> <mn>11.6</mn> </mrow> </msubsup> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> <mo>)</mo> </mrow> </math> , and the $$\varXi _b(5/2^-)$$ <math> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>5</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </math> with $$(6.11^{+0.15}_{-0.10}~\textrm{GeV},\,1.0{^{+7.4}_{-1.0}}~\textrm{MeV})$$ <math> <mrow> <mo>(</mo> <mn>6</mn> <mo>.</mo> <msubsup> <mn>11</mn> <mrow> <mo>-</mo> <mn>0.10</mn> </mrow> <mrow> <mo>+</mo> <mn>0.15</mn> </mrow> </msubsup> <mspace width="3.33333pt"></mspace> <mtext>GeV</mtext> <mo>,</mo> <mspace width="0.166667em"></mspace> <mn>1.0</mn> <msubsup> <mrow></mrow> <mrow> <mo>-</mo> <mn>1.0</mn> </mrow> <mrow> <mo>+</mo> <mn>7.4</mn> </mrow> </msubsup> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> <mo>)</mo> </mrow> </math> . Their mass splittings are calculated to be $$M_{\varLambda _b(5/2^-)} - M_{\varLambda _b(3/2^-)} = 17\pm 7~\textrm{MeV}$$ <math> <mrow> <msub> <mi>M</mi> <mrow> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>5</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mi>M</mi> <mrow> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </msub> <mo>=</mo> <mn>17</mn> <mo>±</mo> <mn>7</mn> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> </mrow> </math> and $$M_{\varXi _b(5/2^-)} - M_{\varXi _b(3/2^-)} = 14\pm 7~\textrm{MeV}$$ <math> <mrow> <msub> <mi>M</mi> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>5</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mi>M</mi> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> <mo>)</mo> </mrow> </mrow> </msub> <mo>=</mo> <mn>14</mn> <mo>±</mo> <mn>7</mn> <mspace width="3.33333pt"></mspace> <mtext>MeV</mtext> </mrow> </math> . All these baryons are explained as the P-wave bottom baryons of the $$\rho $$ <math> <mi>ρ</mi> </math> -mode, where the orbital excitation is between the two light quarks. However, the existence of this mode is still controversial, so their experimental searches can verify both our approach and the existence of the $$\rho $$ <math> <mi>ρ</mi> </math> -mode, which can significantly improve our understanding on the internal structure of hadrons.

Hui-Min Yang

Predicted $$\varXi _b(6087)^0$$ <math> <mrow> <msub> <mi>Ξ</mi> <mi>b</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>6087</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math> and further predictions

We apply the QCD sum rule method to study the double-gluon hybrid states with the quark-gluon contents <math><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mi>g</mi></math> (<math><mi>q</mi><mo>=</mo><mi>u</mi><mo>/</mo><mi>d</mi></math>) and <math><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi><mi>g</mi><mi>g</mi></math>. We construct twenty-eight double-gluon hybrid currents, eleven of which are found to be zero due to some internal symmetries between the two gluons fields. We concentrate on the nonvanishing currents with the exotic quantum numbers <math><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> and <math><msup><mn>3</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math>. Their masses are calculated to be <math><msub><mi>M</mi><mrow><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mi>g</mi><mo>;</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>4.3</mn><msubsup><mn>5</mn><mrow><mo>−</mo><mn>0.30</mn></mrow><mrow><mo>+</mo><mn>0.26</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math><msub><mi>M</mi><mrow><mo>|</mo><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi><mi>g</mi><mi>g</mi><mo>;</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>4.4</mn><msubsup><mn>9</mn><mrow><mo>−</mo><mn>0.30</mn></mrow><mrow><mo>+</mo><mn>0.25</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math><msub><mi>M</mi><mrow><mo>|</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mi>g</mi><mi>g</mi><mo>;</mo><msup><mn>3</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>3.0</mn><msubsup><mn>2</mn><mrow><mo>−</mo><mn>0.31</mn></mrow><mrow><mo>+</mo><mn>0.24</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, and <math><msub><mi>M</mi><mrow><mo>|</mo><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi><mi>g</mi><mi>g</mi><mo>;</mo><msup><mn>3</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup><mo>⟩</mo></mrow></msub><mo>=</mo><mn>3.1</mn><msubsup><mn>6</mn><mrow><mo>−</mo><mn>0.28</mn></mrow><mrow><mo>+</mo><mn>0.22</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. The decay behaviors of the <math><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>3</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> states are studied, and we propose to search for them in the <math><mi>π</mi><msub><mi>a</mi><mn>1</mn></msub><mo>(</mo><mn>1260</mn><mo>)</mo><mo>/</mo><mi>ρ</mi><mi>ω</mi><mo>/</mo><mi>ϕ</mi><mi>ϕ</mi></math> channels in future particle experiments.

Wei Chen

Shi-Lin Zhu

Light double-gluon hybrid states with the exotic quantum numbers <math><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> and <math><msup><mn>3</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math>

Current interpretations of the LHC results on two Higgs doublet models (2HDM) underestimate the sensitivity due to neglecting higher order effects. In this work, we revisit the impact of these effects using the current cross-section times branching ratio limits of the $$A\rightarrow hZ, H \rightarrow VV$$ <math> <mrow> <mi>A</mi> <mo>→</mo> <mi>h</mi> <mi>Z</mi> <mo>,</mo> <mi>H</mi> <mo>→</mo> <mi>V</mi> <mi>V</mi> </mrow> </math> and $$H\rightarrow hh$$ <math> <mrow> <mi>H</mi> <mo>→</mo> <mi>h</mi> <mi>h</mi> </mrow> </math> channels. With a degenerate heavy Higgs mass $$m_\varPhi $$ <math> <msub> <mi>m</mi> <mi>Φ</mi> </msub> </math> , we find that the LHC searches gain sensitivity to the small $$\tan \beta $$ <math> <mrow> <mo>tan</mo> <mi>β</mi> </mrow> </math> region after including loop corrections, even close to $$\cos (\beta -\alpha )=0$$ <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math> which is not reachable at tree level for all types of 2HDM. For a benchmark point with $$m_\varPhi =300$$ <math> <mrow> <msub> <mi>m</mi> <mi>Φ</mi> </msub> <mo>=</mo> <mn>300</mn> </mrow> </math> GeV, $$\tan \beta &lt;1.8(1.2)$$ <math> <mrow> <mo>tan</mo> <mi>β</mi> <mo>&lt;</mo> <mn>1.8</mn> <mo>(</mo> <mn>1.2</mn> <mo>)</mo> </mrow> </math> can be probed for the Type-I(II) 2HDM model for $$\cos (\beta -\alpha )=0$$ <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math> . When the deviation from $$\cos (\beta -\alpha )=0$$ <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math> is larger, the region for which current searches have exclusion potential becomes larger.

Australia

Wei Su

Martin White

Anthony Williams

Canada

Yongcheng Wu

Exploring the low $$\tan \beta $$ <math> <mrow> <mo>tan</mo> <mi>β</mi> </mrow> </math> region of two Higgs doublet models at the LHC

Reliably computing the free energy in a gauge theory like QCD is a challenging and resource-demanding endeavor. We explore the possibility to obtain the associated thermodynamic anomaly from two-point functions based on a conjectured relation. This conjecture is triggered by the relation to the Tan contact in condensed matter systems. For this investigation we use state-of-the-art results for the Yang-Mills gluon two-point function from the lattice and the functional renormalization group, as well as novel Dyson-Schwinger results at finite temperature computed in the present work. This allows for a first, qualitative, test of this conjecture. The results from all methods reveal the same nontrivial temperature behavior of the subleading large momentum dependence of the gluon propagator relevant for the conjectured relation. The comparison with the expected behavior for SU(2) Yang-Mills theory is encouraging to further pursue this approach.