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1. Characterizing Schwarz maps by tracial inequalities

   https://doi.org/10.1007/s11005-023-01636-4  

   Carlen, Eric; Müller-Hermes, Alexander (February 2023, Letters in Mathematical Physics)

   Abstract Let$$\phi $$ $\varphi$be a positive map from the$$n\times n$$ $n\times n$matrices$$\mathcal {M}_n$$ $M_n$to the$$m\times m$$ $m\times m$matrices$$\mathcal {M}_m$$ $M_m$. It is known that$$\phi $$ $\varphi$is 2-positive if and only if for all$$K\in \mathcal {M}_n$$ $K\in M_n$and all strictly positive$$X\in \mathcal {M}_n$$ $X\in M_n$,$$\phi (K^*X^{-1}K) \geqslant \phi (K)^*\phi (X)^{-1}\phi (K)$$ $\varphi \left(K^{\ast }{X}^{-1}K\right)⩾\varphi {\left(K\right)}^{\ast }\varphi {\left(X\right)}^{-1}\varphi \left(K\right)$. This inequality is not generally true if$$\phi $$ $\varphi$is merely a Schwarz map. We show that the corresponding tracial inequality$${{\,\textrm{Tr}\,}}[\phi (K^*X^{-1}K)] \geqslant {{\,\textrm{Tr}\,}}[\phi (K)^*\phi (X)^{-1}\phi (K)]$$ $\text{Tr}\left[\varphi \left(K^{\ast }{X}^{-1}K\right)\right]⩾\text{Tr}\left[\varphi {\left(K\right)}^{\ast }\varphi {\left(X\right)}^{-1}\varphi \left(K\right)\right]$holds for a wider class of positive maps that is specified here. We also comment on the connections of this inequality with various monotonicity statements that have found wide use in mathematical physics, and apply it, and a close relative, to obtain some new, definitive results. 

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2. Search for the $$ {B}_c^{+} $$ → χc1(3872)π+ decay

   https://doi.org/10.1007/JHEP06(2025)013  

   Aaij, R; Abdelmotteleb, A_S W; Abellan_Beteta, C; Abudinén, F; Ackernley, T; Adefisoye, A A; Adeva, B; Adinolfi, M; Adlarson, P; Agapopoulou, C; et al (June 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> A search for the decay$$ {B}_c^{+} $$ $B_c^{+}$→ χ_c1(3872)π⁺is reported using proton-proton collision data collected with the LHCb detector between 2011 and 2018 at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb⁻¹. No significant signal is observed. Using the decay$$ {B}_c^{+} $$ $B_c^{+}$→ψ(2S)π⁺as a normalisation channel, an upper limit for the ratio of branching fractions$$ {\mathcal{R}}_{\psi (2S)}^{\chi_{c1}(3872)}=\frac{{\mathcal{B}}_{B_c^{+}\to {\chi}_{c1}(3872){\pi}^{+}}}{{\mathcal{B}}_{B_c^{+}\to \psi (2S){\pi}^{+}}}\times \frac{{\mathcal{B}}_{\chi_{c1}(3872)\to J/\psi {\pi}^{+}{\pi}^{-}}}{{\mathcal{B}}_{\psi (2S)\to J/\psi {\pi}^{+}{\pi}^{-}}}<0.05(0.06), $$ $R_{\psi \left(2S\right)}^{{\chi }_{c1}\left(3872\right)}=\frac{B_{B_c^{+}\to {\chi }_{c1}\left(3872\right){\pi }^{+}}}{B_{B_c^{+}\to \psi \left(2S\right){\pi }^{+}}}\times \frac{B_{{\chi }_{c1}\left(3872\right)\to J/\psi {\pi }^{+}{\pi }^{-}}}{B_{\psi \left(2S\right)\to J/\psi {\pi }^{+}{\pi }^{-}}}<0.05\left(0.06\right),$ is set at the 90 (95)% confidence level. 

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3. More accurate $$ \sigma \left(\mathcal{GG}\to h\right),\Gamma \left(h\to \mathcal{GG},\mathcal{AA},\overline{\Psi}\Psi \right) $$ and Higgs width results via the geoSMEFT

   https://doi.org/10.1007/JHEP01(2024)170  

   Martin, Adam; Trott, Michael (January 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We develop Standard Model Effective Field Theory (SMEFT) predictions ofσ($$ \mathcal{GG} $$ $\mathrm{GG}$→h), Γ(h→$$ \mathcal{GG} $$ $\mathrm{GG}$), Γ(h→$$ \mathcal{AA} $$ $\mathrm{AA}$) to incorporate full two loop Standard Model results at the amplitude level, in conjunction with dimension eight SMEFT corrections. We simultaneously report consistent Γ(h→$$ \overline{\Psi}\Psi $$ $\overline{\Psi }\Psi$) results including leading QCD corrections and dimension eight SMEFT corrections. This extends the predictions of the former processes Γ, σto a full set of corrections at$$ \mathcal{O}\left({\overline{v}}_T^2/{\varLambda}^2{\left(16{\pi}^2\right)}^2\right) $$ $O\left({\overline{v}}_T^2/{\Lambda }^2{\left(16{\pi }^2\right)}^2\right)$and$$ \mathcal{O}\left({\overline{v}}_T^4/{\Lambda}^4\right) $$ $O\left({\overline{v}}_T^4/{\Lambda }^4\right)$, where$$ {\overline{v}}_T $$ ${\overline{v}}_T$is the electroweak scale vacuum expectation value and Λ is the cut off scale of the SMEFT. Throughout, cross consistency between the operator and loop expansions is maintained by the use of the geometric SMEFT formalism. For Γ(h→$$ \overline{\Psi}\Psi $$ $\overline{\Psi }\Psi$), we include results at$$ \mathcal{O}\left({\overline{v}}_T^2/{\Lambda}^2\left(16{\pi}^2\right)\right) $$ $O\left({\overline{v}}_T^2/{\Lambda }^2\left(16{\pi }^2\right)\right)$in the limit where subleadingm_Ψ→ 0 corrections are neglected. We clarify how gauge invariant SMEFT renormalization counterterms combine with the Standard Model counter terms in higher order SMEFT calculations when the Background Field Method is used. We also update the prediction of the total Higgs width in the SMEFT to consistently include some of these higher order perturbative effects. 

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4. Polarized fragmenting jet functions in inclusive and exclusive jet production

   https://doi.org/10.1007/JHEP03(2024)142  

   Kang, Zhong-Bo; Xing, Hongxi; Zhao, Fanyi; Zhou, Yiyu (March 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this work, we present a complete theoretical framework for analyzing the distribution of polarized hadrons within jets, with and without measuring the transverse momentum relative to the standard jet axis. Using soft-collinear effective theory (SCET), we derive the factorization and provide the theoretical calculation of both semi-inclusive and exclusive fragmenting jet functions (FJFs) under longitudinal and transverse polarization. With the polarized FJFs, one gains access to a variety of new observables that can be used for extracting both collinear and transverse momentum dependent parton distribution functions (PDFs) and fragmentation functions (FFs). As examples, we provide numerical results for the spin asymmetry$$ {A}_{TU,T}^{\cos \left({\phi}_S-{\hat{\phi}}_{S_h}\right)} $$ $A_{\mathrm{TU},T}^{cos\left({\varphi }_S-{\hat{\varphi }}_{S_h}\right)}$from polarized semi-inclusive hadron-in-jet production in polarizedppcollisions at RHIC kinematics, where a transversely polarized quark would lead to the transverse spin of the final-state hadron inside the jet and is thus sensitive to the transversity fragmentation functions. Similarly, another spin asymmetry,$$ {A}_{TU,L}^{\cos \left({\phi}_q-{\phi}_S\right)} $$ $A_{\mathrm{TU},L}^{cos\left({\varphi }_q-{\varphi }_S\right)}$from polarized exclusive hadron-in-jet production in polarizedepcollisions at EIC kinematics would allow us to access the helicity fragmentation functions. These observables demonstrate promising potential in investigating transverse momentum dependent PDFs and FFs and are worthwhile for further measurements. 

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5. Measurement of exclusive $$J/\psi$$ and $$\psi(2S)$$ production at $$\sqrt{s}=13$$ TeV

   https://doi.org/10.21468/SciPostPhys.18.2.071  

   Collaboration, LHCb; Aaij, Roel; Abdelmotteleb, Ahmed_Sameh Wagih; Abellan_Beteta, Carlos; Abudinèn, Fernando Jesus; Ackernley, Thomas; Adefisoye, Ayomide Matthew; Adeva, Bernardo; Adinolfi, Marco; Adlarson, Patrik Harri; et al (January 2025, SciPost Physics)

   Measurements are presented of the cross-section for the central exclusive production ofJ/\psi\to\mu^+\mu^- $J/\psi \to {\mu }^{+}{\mu }^{-}$and\psi(2S)\to\mu^+\mu^- $\psi \left(2S\right)\to {\mu }^{+}{\mu }^{-}$processes in proton-proton collisions at\sqrt{s} = 13 \ \mathrm{TeV} $\sqrt{s}=13TeV$with 2016–2018 data. They are performed by requiring both muons to be in the LHCb acceptance (with pseudorapidity2<\eta_{\mu^±} < 4.5 $2<{\eta }_{{\mu }^{\pm }}<4.5$) and mesons in the rapidity range2.0 < y < 4.5 $2.0<y<4.5$. The integrated cross-section results are\sigma_{J/\psi\to\mu^+\mu^-}(2.0 ${\sigma }_{J/\psi \to {\mu }^{+}{\mu }^{-}}(2.0<y_{J/\psi }<4.5,2.0<{\eta }_{{\mu }^{\pm }}<4.5)=400\pm 2\pm 5\pm 12pb,{\sigma }_{\psi \left(2S\right)\to {\mu }^{+}{\mu }^{-}}(2.0<y_{\psi \left(2S\right)}<4.5,2.0<{\eta }_{{\mu }^{\pm }}<4.5)=9.40\pm 0.15\pm 0.13\pm 0.27pb,$where the uncertainties are statistical, systematic and due to the luminosity determination. In addition, a measurement of the ratio of\psi(2S) $\psi \left(2S\right)$andJ/\psi $J/\psi$cross-sections, at an average photon-proton centre-of-mass energy of1\ \mathrm{TeV} $1TeV$, is performed, giving$ = 0.1763 ± 0.0029 ± 0.0008 ± 0.0039,$$ where the first uncertainty is statistical, the second systematic and the third due to the knowledge of the involved branching fractions. For the first time, the dependence of theJ/\psi$ $J/\psi$and\psi(2S) $\psi \left(2S\right)$cross-sections on the total transverse momentum transfer is determined inpp $pp$collisions and is found consistent with the behaviour observed in electron-proton collisions. 

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