We compare the fixed-order NLO QCD predictions for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mo>+</mo><mi>X</mi></math> process in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mo>ℓ</mo></math> decay channel with the parton-shower-based results obtained with the powheg and mc@nlo matching methods. In the first case, NLO QCD corrections are consistently included in both the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover></math> production step and the decays of the four top quarks, preserving all spin correlations. In the second approach, higher-order effects in top-quark decays with approximate spin correlations are simulated in the pythia parton-shower framework. Additionally, we analyze the impact of including the so-called matrix element corrections in top-quark decays in both parton-shower matched predictions. The comparison is performed at the integrated and differential fiducial cross-section level for the LHC center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13.6</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>.

Germany

Manal Alsairafi

Nikolaos Dimitrakopoulos

Malgorzata Worek

Modeling top-quark decays in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>t</mi><mover accent="true"><mrow><mi>t</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mi>t</mi><mover accent="true"><mrow><mi>t</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> production at the LHC

We perform a theoretical study of the decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> in search of the doubly heavy tetraquark states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>d</mi><mo stretchy="false">¯</mo></mover></math>. These <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states are assumed to be dynamically generated molecular states from the S-wave interactions between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msubsup><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msubsup></math> meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> or vectors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi></math>), they are labeled as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math>, respectively. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states arising from final-state interactions. Our results reveal a clear peak structure in the 7415–7425 MeV region, which is attributed to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state. Additionally, a distinct dip structure appears near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mrow><mo>*</mo><mn>0</mn></mrow></msup><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> threshold, characteristic of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>2</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> as a hadronic molecular state. A near-threshold enhancement associated with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>P</mi><mi>P</mi></mrow></msubsup></math> state and a dip arising from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow><mrow><mn>0</mn><mo>,</mo><mi>V</mi><mi>V</mi></mrow></msubsup></math> state are also identified, though the manifestation of these features depends sensitively on model parameter fine-tuning. Therefore, with increased experimental statistics, the decay channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math> offers a promising avenue for discovering and characterizing the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states.

China

Wen-Ying Liu

Hua-Xing Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>c</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> states in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup></math>

The particle origin of dark matter (DM) remains elusive despite decades of direct, indirect, and collider searches. Several groups have reported a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math>-ray excess toward the Galactic Center commonly referred to as the Galactic Center excess (GCE). Its spectrum is consistent with annihilation of weakly interacting massive particles (WIMPs) of mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>10</mn><mo>−</mo><mn>100</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> and a thermal-relic cross section. Although many concrete WIMP models reproduce the GCE spectrum, most are now excluded by direct detection experiments that are approaching the neutrino floor. We investigate a class of anomaly-free extensions of the Standard Model featuring gauged differences of lepton number, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math>, and gauged baryon minus lepton number, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math>. We show that these models can reproduce the GCE while remaining compatible with the observed relic abundance. We then impose collider and direct detection constraints, accounting for both tree-level and loop-induced kinetic mixing. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>e</mi></msub></math> model gives the best fit to the GCE: a DM mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>χ</mi></mrow></msub><mo>∼</mo><mn>40</mn><mo>−</mo><mn>50</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> remains consistent with the muon and electron magnetic moment anomalies, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mrow><mi>μ</mi><mo>,</mo><mi>e</mi></mrow></msub></math>, as well as current collider and direct detection limits, for mediator masses in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>∼</mo><mn>70</mn><mo>−</mo><mn>86</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> and a DM mediator coupling of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mn>5</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math>. By contrast, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>e</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> models yield poorer fits; satisfying both the relic density and experimental bounds forces the DM mass to lie very close to resonance (i.e. approximately half the mediator mass). Finally, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>−</mo><mi>L</mi></math> model also matches the GCE well, its parameter space is almost entirely ruled out by strong direct detection limits, except for the narrow resonance region where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>χ</mi></msub></math> should be equal to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><msup><mi>A</mi><mo>′</mo></msup></msub><mo>/</mo><mn>2</mn></math> requiring a fine-tuning at the few-percent level.

Italy

Jordan Koechler

Mattia Di Mauro

Leptophilic dark matter in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><msub><mi>L</mi><mi>i</mi></msub><mo>−</mo><msub><mi>L</mi><mi>j</mi></msub></mrow></msub></math> models: A solution to the Fermi-LAT Galactic Center excess consistent with cosmological and laboratory observations

Under chiral effective field theory, we study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> interactions up to second chiral order at one-loop level, which contain full contact, one-pion-exchange (OPE) and two-pion-exchange (TPE) contributions. Here, we adopt a new subtraction scheme of the two-particle-reducible contributions and attempt different regularization schemes uniquely for the TPE contributions since they are highly divergent on the momentum transfer. Under these schemes, we conclude that, in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> channel, the TPE contribution is repulsive, then the competition between this powerful repulsing TPE and the other two (contact and OPE) results in a quite weak attraction. This explains why <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> has an extremely small binding energy if treated as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>0</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> bound state. This feature resembles that of hidden charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> as we investigated in previous work [<a href="http://dx.doi.org/10.1103/PhysRevD.105.034013">Phys. Rev. D 105, 034013 (2022)</a>], which also interpreted the extremely near-threshold phenomenon of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math>. In addition, we also solve the Bethe-Salpeter equation with the chiral interactions for a consistency check.

Hao Xu

Li-Xiang Ren

Investigating the two-pion exchange of the double charm <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> chiral interactions and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>

We present a comprehensive QCD analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math> form factors within the framework of light-cone sum rules, employing two-pion light-cone distribution amplitudes (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>π</mi><mi>DA</mi></math>s). For the first time, we derive the twist-three <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>π</mi><mi>DA</mi></math>s explicitly by exploiting the conformal symmetry of massless QCD. This breakthrough enables the first systematic calculation of higher-power corrections to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math>-type transitions. Leveraging the recently measured partial decay fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>l</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>l</mi></msub></math> by the Belle detector, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>4.27</mn><mo>±</mo><mn>0.49</mn><msub><mo stretchy="false">|</mo><mrow><mi>data</mi></mrow></msub><mo>±</mo><mn>0.55</mn><msub><mo stretchy="false">|</mo><mtext>LCSRs</mtext></msub><mo stretchy="false">)</mo></mrow><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> within the dominant region of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi></math> resonance. We clarify that the relatively small value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> extracted from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>ρ</mi><mi>l</mi><mi>ν</mi></math>, when compared to the golden channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>l</mi><mi>ν</mi></math>, arises due to the finite width and nonresonant effects. We anticipate future measurements of purely isovector and isoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mi>l</mi><mn>4</mn></mrow></msub></math> decays, which will aid in reducing uncertainties by enhancing our understanding of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> phase shifts in the two-pion distribution amplitudes through heavy flavor decays.

Shan Cheng

QCD analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi></math> form factors and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></mrow></math> extraction from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mrow><mi>l</mi><mn>4</mn></mrow></msub></math> decays

The proposed Large Hadron electron Collider (LHeC), with a center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>≈</mo><mn>1.3</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, provides a clean and sensitive environment to probe the top quark’s neutral current interactions with the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><mi>p</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>−</mo></msup><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover></math>. We investigate the precision with which the Standard Model (SM) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>Z</mi></math> couplings—the vector and axial-vector components (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>C</mi><mrow><mn>1</mn><mi>V</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">Δ</mi><msub><mi>C</mi><mrow><mn>1</mn><mi>A</mi></mrow></msub></math>) can be measured, along with possible new physics effects parametrized by higher-dimensional operators inducing weak electric and magnetic dipolelike interactions (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mrow><mn>2</mn><mi>V</mi></mrow></msub><mo>,</mo><msub><mi>C</mi><mrow><mn>2</mn><mi>A</mi></mrow></msub></math>). Focusing on the semileptonic decay channel, where either the top quark decays leptonically to a positively charged lepton (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mo>ℓ</mo><mo>+</mo></msup><mo>=</mo><msup><mi>e</mi><mo>+</mo></msup><mo>,</mo><msup><mi>μ</mi><mo>+</mo></msup></math>) and the antitop hadronically, or vice versa, we utilize the azimuthal angle difference <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mrow><msup><mi>e</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>±</mo></msup></mrow></msub></math> between the scattered electron and the charged lepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mo>ℓ</mo><mo>±</mo></msup></math> as the key observable to derive projected constraints. Using a one-parameter multibin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup></math> analysis of the differential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>ϕ</mi><mrow><msup><mi>e</mi><mo>−</mo></msup><msup><mo>ℓ</mo><mo>±</mo></msup></mrow></msub></math> distribution, the constraints on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>C</mi><mrow><mn>1</mn><mi>A</mi></mrow></msub></math> improve from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>50</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, while the improvement for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><msub><mi>C</mi><mrow><mn>1</mn><mi>V</mi></mrow></msub></math> remains within the same order of magnitude, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">)</mo></math>. These results correspond to average relative precisions of approximately 8% and 68%, respectively, with respect to their SM values. The anomalous tensor couplings <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mrow><mn>2</mn><mi>V</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mrow><mn>2</mn><mi>A</mi></mrow></msub></math> are constrained at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy="false">)</mo></math> level even at low luminosity and improve moderately with increasing luminosity. While the two-parameter analysis broadens the allowed regions due to parameter correlations, it maintains competitive sensitivity, particularly for the SM-like couplings. Throughout, we assume a systematic uncertainty of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>δ</mi><mi>s</mi></msub><mo>=</mo><mn>5</mn><mo>%</mo></math> in all analyses, and all results are quoted at the 95% confidence level. These results demonstrate the LHeC’s potential to provide complementary and competitive sensitivity to top-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> couplings compared to current and future hadron and lepton collider capabilities.

South Africa

Katlego Machethe

India

Pramod Sharma

Mukesh Kumar

Brazil

Rafiqul Rahaman

Bruce Mellado

Analyzing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>Z</mi></math>-couplings at the future <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>−</mo></msup><mi>p</mi></math> collider

We study an alternative $$U(1)_{B-L}$$ model with singlet chiral fermions which can act as WIMP and FIMP type DM, which is anomaly-free by constructions in contrast to the well studied $$B-L$$ extension where three right handed neutrinos are needed for gauge anomaly cancellation. Fermion dark matter masses are generated after the $$U(1)_{B-L}$$ is broken spontaneously, so the Yukawa couplings for WIMP and FIMP components can be distinguished by the hierarchical values of the vacuum expectation values of the singlet scalar fields. Moreover, the $$U(1)_{B-L}$$ gauge boson receives a TeV-scale mass for a tiny extra gauge coupling, so it goes out of equilibrium from the rest of the model content in the early Universe. Both the $$U(1)_{B-L}$$ gauge boson and FIMP component are produced from the decays of the bath particles, and the former can decay into FIMP DM and/or WIMP DM before BBN. The WIMP component can reside in the resonance region of the Higgs bosons or dominantly annihilate into a pair of singlet-like scalars. Thus, there is a flexibility to choose a small mixing between the visible and dark sectors, thereby evading all the current direct and indirect detection bounds. Furthermore, we show that WIMP and FIMP components can coexist in suitable fractions, depending on the choice of model parameters, allowing for additional protection for WIMP DM against various experimental bounds. Finally, we identify the dimension-6 and dimension-7 operators for Majorana neutrino masses in our model, being consistent with the $$U(1)_{B-L}$$ gauge symmetry, and provide a possibility of extending the model with additional singlet fermions for neutrino masses.

South Korea

Sarif Khan

Hyun Lee

WIMP-FIMP option and neutrino masses via a novel anomaly-free $$B-L$$ symmetry

The near-singularity BKL dynamics of five dimensional gravity and supergravity (and also an extended four-dimensional supergravity) is known to be given by the billiard problem of a particle within a fundamental domain of the Bianchi groups PSL(2, 𝒪) ⊂ PSL(2, ℂ), acting on ℍ . Here 𝒪 are the Gaussian or Eisenstein integers, which define a square or triangular lattice in ℂ. The Wheeler-DeWitt wavefunctions near the singularity are, correspondingly, automorphic Maaß forms of PSL(2, 𝒪). We show how these wavefunctions are associated to certain $\textit{L}$-functions evaluated along their critical axis. Each of these $\textit{L}$-functions admits an Euler product representation over the complex primes 𝒫 ⊂ 𝒪. From this fact we write the $\textit{L}$-function as the trace over an auxiliary Hilbert space of charged harmonic oscillators, labeled by the complex primes 𝒫 . In this way we have constructed a ‘dual’ primon gas partition function for the wavefunction of the universe close to a five dimensional cosmological singularity.

United Kingdom

Marine Clerck

Sean Hartnoll

Ming Yang

Wheeler-DeWitt wavefunctions for 5d BKL dynamics, automorphic $\textit{L}$-functions and complex primon gases

<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>We investigate a classical model of coupled harmonic oscillators (CHO) as the classical counterpart of the Lee model. In this classical model, the divergence of the fundamental frequency and its renormalization precisely reproduce the divergence and renormalization of the physical mass of the particle, revealing that mass divergence in the Lee model is not solely a quantum phenomenon.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>We derive the necessary conditions that any renormalization must satisfy for the two-oscillator system corresponding to the single-mode Lee model.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>We examine the classical analog of the <italic>N</italic>-<italic>&#952;</italic> scattering process in the Lee model and demonstrate that the cutoff-dependent behavior of the scattering strength parallels the quantum scenario, indicating that the suppression of scattering also has a classical origin.</para></list-item></list>

Kang Xu

C.P. Sun

Classical analog of the T. D. Lee model for renormalization

There is lattice evidence that the QCD matter above the chiral restoration temperature $$T_{ch}$$ and below the deconfinement temperature $$T_d$$ , called stringy fluid, is characterized by approximate chiral spin symmetry, which is a symmetry of confinement in QCD with light quarks. The energy density, pressure and entropy density in the stringy fluid scale as $$N_c^1$$ , which is in contrast to the $$N_c^0$$ scaling in the hadron gas and to the $$N_c^2$$ scaling in the quark-gluon plasma. Here we clarify the origin of the $$N_c^1$$ scaling. We employ a solvable field-theoretical large $$N_c$$ chirally symmetric and confining model. In vacuum the confining potential induces a spontaneous breaking of chiral symmetry. The mesons are spatially localized states of quarks and antiquarks. Still in the confining regime the system undergoes the chiral restoration phase transition at $$T_{ch}$$ because of Paili blocking of the quark levels required for the existence of the quark condensate, by the thermal excitation of quarks and antiquarks. The same Paili blocking leads to a delocalization of the color singlet low-spin meson-like states that become infinitely large in the chiral limit. Consequently the stringy fluid represents a very dense medium of the overlapping huge color-singlet low-spin quark-antiquark systems. The Bethe–Salpeter equation that determines the rest-frame excitation energies of the color-singlet quark-antiquark system is $$N_c$$ -independent both in vacuum and in the medium in the confining regime. The excitation energy of the quark-antiquark color-singlet systems scales as $$N_c^0$$ , i.e. as meson mass in vacuum. The $$N_c^1$$ scaling of the energy density in the stringy fluid is provided by the fluctuations of the color-singlet quark-antiquark systems.

Austria

L. Glozman

On the origin of the $$N_c^1$$ scaling in the confined but chirally symmetric phase at high T