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1. Universal features of higher-form symmetries at phase transitions

   https://doi.org/10.21468/SciPostPhys.11.2.033  

   Wu, Xiao-Chuan; Jian, Chao-Ming; Xu, Cenke (January 2021, SciPost Physics)

   We investigate the behavior of higher-form symmetries at variousquantum phase transitions. We consider discrete 1-form symmetries, whichcan be either part of the generalized concept “categorical symmetry”(labelled as \tilde{Z}_N^{(1)} Z ̃ N ( 1 ) )introduced recently, or an explicit Z_N^{(1)} Z N ( 1 ) 1-form symmetry. We demonstrate that for many quantum phase transitionsinvolving a Z_N^{(1)} Z N ( 1 ) or \tilde{Z}_N^{(1)} Z ̃ N ( 1 ) symmetry, the following expectation value \langle \left( O_\mathcal{C}\right)^2 \rangle ⟨ ( O 𝒞 ) 2 ⟩ takes the form \langle \left( \log O_\mathcal{C} \right)^2 \rangle \sim - \frac{A}{\epsilon} P + b \log P ⟨ ( log O 𝒞 ) 2 ⟩ ∼ − A ϵ P + b log P , where O_\mathcal{C} O 𝒞 is an operator defined associated with loop \mathcal{C} 𝒞 (or its interior \mathcal{A} 𝒜 ),which reduces to the Wilson loop operator for cases with an explicit Z_N^{(1)} Z N ( 1 ) 1-form symmetry. P P is the perimeter of \mathcal{C} 𝒞 ,and the b \log P b log P term arises from the sharp corners of the loop \mathcal{C} 𝒞 ,which is consistent with recent numerics on a particular example. b b is a universal microscopic-independent number, which in (2+1)d ( 2 + 1 ) d is related to the universal conductivity at the quantum phasetransition. b b can be computed exactly for certain transitions using the dualitiesbetween (2+1)d ( 2 + 1 ) d conformal field theories developed in recent years. We also compute the"strange correlator" of O_\mathcal{C} O 𝒞 : S_{\mathcal{C}} = \langle 0 | O_\mathcal{C} | 1 \rangle / \langle 0 | 1 \rangle S 𝒞 = ⟨ 0 | O 𝒞 | 1 ⟩ / ⟨ 0 | 1 ⟩ where |0\rangle | 0 ⟩ and |1\rangle | 1 ⟩ are many-body states with different topological nature. 

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2. CHARACTERIZING THE CONTINUOUS DEGREES

   Andrews, Uri; Igusa, Gregory; Miller, Joseph S.; Soskova, Mariya I. (January 2019, Israel journal of mathematics)

   The continuous degrees measure the computability-theoretic content of elements of computable metric spaces. They properly extend the Turing degrees and naturally embed into the enumeration degrees. Although nontotal (i.e., non-Turing) continuous degrees exist, they are all very close to total: joining a continuous degree with a total degree that is not below it always results in a total degree. We call this property almost totality. We prove that the almost total degrees coincide with the continuous degrees. Since the total degrees are definable in the partial order of enumeration degrees, we see that the continuous degrees are also definable. Applying earlier work on the continuous degrees, this shows that the relation “PA above” on the total degrees is definable in the enumeration degrees. In order to prove that every almost total degree is continuous, we pass through another characterization of the continuous degrees that slightly simplifies one of Kihara and Pauly. We prove that the enumeration degree of A is continuous if and only if A is codable, meaning that A is enumeration above the complement of an infinite tree, every path of which enumerates A. 

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3. The effect of nonlinear drag on the rise velocity of bubbles in turbulence

   https://doi.org/10.1017/jfm.2021.556  

   Ruth, Daniel J.; Vernet, Marlone; Perrard, Stéphane; Deike, Luc (October 2021, Journal of Fluid Mechanics)

   We investigate how turbulence in liquid affects the rising speed of gas bubbles within the inertial range. Experimentally, we employ stereoscopic tracking of bubbles rising through water turbulence created by the convergence of turbulent jets and characterized with particle image velocimetry performed throughout the measurement volume. We use the spatially varying, time-averaged mean water velocity field to consider the physically relevant bubble slip velocity relative to the mean flow. Over a range of bubble sizes within the inertial range, we find that the bubble mean rise velocity $$\left \langle v_z \right \rangle$$ decreases with the intensity of the turbulence as characterized by its root-mean-square fluctuation velocity, $u'$ . Non-dimensionalized by the quiescent rise velocity $$v_{q}$$ , the average rise speed follows $$\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$$ at high $${\textit {Fr}}$$ , where $${\textit {Fr}}=u'/\sqrt {dg}$$ is a Froude number comparing the intensity of the turbulence to the bubble buoyancy, with $$d$$ the bubble diameter and $$g$$ the acceleration due to gravity. We complement these results by performing numerical integration of the Maxey–Riley equation for a point bubble experiencing nonlinear drag in three-dimensional, homogeneous and isotropic turbulence. These simulations reproduce the slowdown observed experimentally, and show that the mean magnitude of the slip velocity is proportional to the large-scale fluctuations of the flow velocity. Combining the numerical estimate of the slip velocity magnitude with a simple theoretical model, we show that the scaling $$\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$$ originates from a combination of the nonlinear drag and the nearly isotropic behaviour of the slip velocity at large $${\textit {Fr}}$$ that drastically reduces the mean rise speed. 

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4. Probing transverse momentum dependent structures with azimuthal dependence of energy correlators

   https://doi.org/10.1007/JHEP03(2024)153  

   Kang, Zhong-Bo; Lee, Kyle; Shao, Ding Yu; Zhao, Fanyi (March 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We study the azimuthal angle dependence of the energy-energy correlators$$\langle \mathcal{E}\left({\widehat{n}}_{1}\right)\mathcal{E}\left({\widehat{n}}_{2}\right)\rangle $$in the back-to-back region fore⁺e⁻annihilation and deep inelastic scattering (DIS) processes with general polarization of the proton beam. We demonstrate that the polarization information of the beam and the underlying partons from the hard scattering is propagated into the azimuthal angle dependence of the energy-energy correlators. In the process, we define the Collins-type EEC jet functions and introduce a new EEC observable using the lab-frame angles in the DIS process. Furthermore, we extend our formalism to explore the two-point energy correlation between hadrons with different quantum numbers$${\mathbb{S}}_{i}$$in the back-to-back limit$$\langle {\mathcal{E}}_{{\mathbb{S}}_{1}}\left({\widehat{n}}_{1}\right){\mathcal{E}}_{{\mathbb{S}}_{2}}\left({\widehat{n}}_{2}\right)\rangle $$. We find that in the Operator Product Expansion (OPE) region the nonperturbative information is entirely encapsulated by a single number. Using our formalism, we present several phenomenological studies that showcase how energy correlators can be used to probe transverse momentum dependent structures. 

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5. Observation of $$ {\Lambda}_b^0 $$ → D+pπ−π− and $$ {\Lambda}_b^0 $$ → D*+pπ−π− decays

   https://doi.org/10.1007/JHEP03(2022)153  

   Aaij, R.; Abdelmotteleb, A. S.; Abellán Beteta, C.; Abudinén, F.; Ackernley, T.; Adeva, B.; Adinolfi, M.; Afsharnia, H.; Agapopoulou, C.; Aidala, C. A.; et al (March 2022, Journal of High Energy Physics)

   Abstract The multihadron decays $$ {\Lambda}_b^0 $$ Λ b 0 → D + pπ−π− and $$ {\Lambda}_b^0 $$ Λ b 0 → D * + pπ−π− are observed in data corresponding to an integrated luminosity of 3 fb − 1 , collected in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV by the LHCb detector. Using the decay $$ {\Lambda}_b^0 $$ Λ b 0 → $$ {\Lambda}_c^{+} $$ Λ c + π + π − π − as a normalisation channel, the ratio of branching fractions is measured to be $$ \frac{\mathcal{B}\left({\Lambda}_b^0\to {D}^{+}p{\pi}^{-}{\pi}^{-}\right)}{\mathcal{B}\left({\Lambda}_b^0\to {\Lambda}_c^0{\pi}^{+}{\pi}^{-}{\pi}^{-}\right)}\times \frac{\mathcal{B}\left({D}^{+}\to {K}^{-}{\pi}^{+}{\pi}^{+}\right)}{\mathcal{B}\left({\Lambda}_c^0\to {pK}^{-}{\pi}^{-}\right)}=\left(5.35\pm 0.21\pm 0.16\right)\%, $$ B Λ b 0 → D + p π − π − B Λ b 0 → Λ c 0 π + π − π − × B D + → K − π + π + B Λ c 0 → pK − π − = 5.35 ± 0.21 ± 0.16 % , where the first uncertainty is statistical and the second systematic. The ratio of branching fractions for the $$ {\Lambda}_b^0 $$ Λ b 0 → D *+ pπ − π − and $$ {\Lambda}_b^0 $$ Λ b 0 → D + pπ − π − decays is found to be $$ \frac{\mathcal{B}\left({\Lambda}_b^0\to {D}^{\ast +}p{\pi}^{-}{\pi}^{-}\right)}{\mathcal{B}\left({\Lambda}_b^0\to {D}^{+}p{\pi}^{-}{\pi}^{-}\right)}\times \left(\mathcal{B}\left({D}^{\ast +}\to {D}^{+}{\pi}^0\right)+\mathcal{B}\left({D}^{\ast +}\to {D}^{+}\gamma \right)\right)=\left(61.3\pm 4.3\pm 4.0\right)\%. $$ B Λ b 0 → D ∗ + p π − π − B Λ b 0 → D + p π − π − × B D ∗ + → D + π 0 + B D ∗ + → D + γ = 61.3 ± 4.3 ± 4.0 % . 

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