More Like this

1. Lieb–Thirring Inequality for the 2D Pauli Operator

   https://doi.org/10.1007/s00220-024-05177-2  

   Frank, Rupert L; Kovařík, Hynek (February 2025, Communications in Mathematical Physics)

   Abstract By the Aharonov–Casher theorem, the Pauli operatorPhas no zero eigenvalue when the normalized magnetic flux$$\alpha $$ $\alpha$satisfies$$|\alpha |<1$$ $\left|\alpha \right|<1$, but it does have a zero energy resonance. We prove that in this case a Lieb–Thirring inequality for the$$\gamma $$ $\gamma$-th moment of the eigenvalues of$$P+V$$ $P+V$is valid under the optimal restrictions$$\gamma \ge |\alpha |$$ $\gamma \ge \left|\alpha \right|$and$$\gamma >0$$ $\gamma >0$. Besides the usual semiclassical integral, the right side of our inequality involves an integral where the zero energy resonance state appears explicitly. Our inequality improves earlier works that were restricted to moments of order$$\gamma \ge 1$$ $\gamma \ge 1$. 

   more » « less
2. An Allard-type boundary regularity theorem for $2d$ minimizing currents at smooth curves with arbitrary multiplicity

   https://doi.org/10.1007/s10240-024-00144-y  

   De Lellis, Camillo; Nardulli, Stefano; Steinbrüchel, Simone (February 2024, Publications mathématiques de l'IHÉS)

   Abstract We consider integral area-minimizing 2-dimensional currents$$T$$ $T$in$$U\subset \mathbf {R}^{2+n}$$ $U\subset R^{2+n}$with$$\partial T = Q\left [\!\![{\Gamma }\right ]\!\!]$$ $\partial T=Q〚\Gamma 〛$, where$$Q\in \mathbf {N} \setminus \{0\}$$ $Q\in N\setminus \left\{0\right\}$and$$\Gamma $$ $\Gamma$is sufficiently smooth. We prove that, if$$q\in \Gamma $$ $q\in \Gamma$is a point where the density of$$T$$ $T$is strictly below$$\frac{Q+1}{2}$$ $\frac{Q+1}{2}$, then the current is regular at$$q$$ $q$. The regularity is understood in the following sense: there is a neighborhood of$$q$$ $q$in which$$T$$ $T$consists of a finite number of regular minimal submanifolds meeting transversally at$$\Gamma $$ $\Gamma$(and counted with the appropriate integer multiplicity). In view of well-known examples, our result is optimal, and it is the first nontrivial generalization of a classical theorem of Allard for$$Q=1$$ $Q=1$. As a corollary, if$$\Omega \subset \mathbf {R}^{2+n}$$ $\Omega \subset R^{2+n}$is a bounded uniformly convex set and$$\Gamma \subset \partial \Omega $$ $\Gamma \subset \partial \Omega$a smooth 1-dimensional closed submanifold, then any area-minimizing current$$T$$ $T$with$$\partial T = Q \left [\!\![{\Gamma }\right ]\!\!]$$ $\partial T=Q〚\Gamma 〛$is regular in a neighborhood of $$\Gamma $$ $\Gamma$. 

   more » « less
3. Measurement of the inclusive isolated-photon production cross section in pp collisions at $$\mathbf {\sqrt{\textit{s}}=13}$$ TeV

   https://doi.org/10.1140/epjc/s10052-024-13506-x  

   Acharya, S; Adamová, D; Agarwal, A; Aglieri_Rinella, G; Aglietta, L; Agnello, M; Agrawal, N; Ahammed, Z; Ahmad, S; Ahn, S U; et al (January 2025, The European Physical Journal C)

   Abstract The production cross section of inclusive isolated photons has been measured by the ALICE experiment at the CERN LHC in pp collisions at centre-of-momentum energy of$$\sqrt{s} =13$$ $\sqrt{s}=13$ TeV collected during the LHC Run 2 data-taking period. The measurement is performed by combining the measurements of the electromagnetic calorimeter EMCal and the central tracking detectors ITS and TPC, covering a pseudorapidity range of$$|\eta ^{\gamma }|<0.67$$ $|{\eta }^{\gamma }|<0.67$and a transverse momentum range of$$7 $7<p_{\text{T}}^{\gamma }<200$GeV/$$c$$ $c$. The result extends to lower$$p_\textrm{T}^{\gamma }$$ $p_{\text{T}}^{\gamma }$and$$x_\textrm{T}^{\gamma } = 2p_\textrm{T}^{\gamma }/\sqrt{s} $$ $x_{\text{T}}^{\gamma }=2p_{\text{T}}^{\gamma }/\sqrt{s}$ranges, the lowest$$x_\textrm{T}^{\gamma }$$ $x_{\text{T}}^{\gamma }$of any isolated photon measurements to date, extending significantly those measured by the ATLAS and CMS experiments towards lower$$p_\textrm{T}^{\gamma }$$ $p_{\text{T}}^{\gamma }$at the same collision energy with a small overlap between the measurements. The measurement is compared with next-to-leading order perturbative QCD calculations and the results from the ATLAS and CMS experiments as well as with measurements at other collision energies. The measurement and theory prediction are in agreement with each other within the experimental and theoretical uncertainties. 

   more » « less
4. Proton capture on $$^{90}$$Zr revisited

   https://doi.org/10.1140/epja/s10050-025-01521-9  

   Simon, A; Koros, J; Olivas-Gomez, O; Kelmar, R; Churchman, E; Clark, A M; Harris, C; Henderson, S L; Kelly, S E; Millican, P; et al (March 2025, The European Physical Journal A)

   Abstract The$$^{90}$$ $_{}^{90}$Zr(p,$$\gamma $$ $\gamma$)$$^{91}$$ $_{}^{91}$Nb reaction is one of the important reactions in the$$A\approx 90$$ $A\approx 90$mass region and part of the nucleosynthesis path responsible for production of$$^{92}$$ $_{}^{92}$Mo during the$$\gamma $$ $\gamma$-process. Discrepant data in the literature provide a cross section that varies up to 30% within the Gamow window for the$$^{90}$$ $_{}^{90}$Zr(p,$$\gamma $$ $\gamma$)$$^{91}$$ $_{}^{91}$Nb reaction. Thus, the cross section measurements of$$^{90}$$ $_{}^{90}$Zr(p,$$\gamma $$ $\gamma$)$$^{91}$$ $_{}^{91}$Nb reaction were revisited using the$$\gamma $$ $\gamma$-summing technique. The results are consistent with the lower-value cross sections found in the literature. Based on the new data an updated reaction rate for$$^{90}$$ $_{}^{90}$Zr(p,$$\gamma $$ $\gamma$)$$^{91}$$ $_{}^{91}$Nb is provided that is up to 20% higher than that obtained from thenon-smokercode. 

   more » « less
5. Toward extracting $$\gamma $$ from $$B\rightarrow DK$$ without binning

   https://doi.org/10.1140/epjc/s10052-023-12057-x  

   Backus, Jeffrey V; Freytsis, Marat; Grossman, Yuval; Schacht, Stefan; Zupan, Jure (September 2023, The European Physical Journal C)

   Abstract $$B^\pm \rightarrow DK^\pm $$ $B^{\pm }\to D{K}^{\pm }$transitions are known to provide theoretically clean information about the CKM angle$$\gamma $$ $\gamma$, with the most precise available methods exploiting the cascade decay of the neutralDintoCPself-conjugate states. Such analyses currently require binning in theDdecay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of$$\gamma $$ $\gamma$, with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to$$\gamma $$ $\gamma$, its conceptually novel approach opens the door to new strategies for$$\gamma $$ $\gamma$extraction. More studies are required to see if these can be competitive with the existing methods. 

   more » « less