More Like this

1. Search for exotic decays of the Higgs boson to a pair of pseudoscalars in the $$\upmu \upmu \text{ b } \text{ b } $$ and $$\uptau \uptau \text{ b } \text{ b } $$ final states

   https://doi.org/10.1140/epjc/s10052-024-12727-4  

   Hayrapetyan, A ; Tumasyan, A ; Adam, W ; Andrejkovic, J W ; Bergauer, T ; Chatterjee, S ; Damanakis, K ; Dragicevic, M ; Del_Valle, A Escalante ; Hussain, P S ; et al ( May 2024 , The European Physical Journal C)

   A search for exotic decays of the Higgs boson ($$\text {H}$$$\text{H}$) with a mass of 125$$\,\text {Ge}\hspace{-.08em}\text {V}$$$\text{Ge}\text{V}$to a pair of light pseudoscalars$$\text {a}_{1} $$${\text{a}}_1$is performed in final states where one pseudoscalar decays to two$${\textrm{b}}$$$\text{b}$quarks and the other to a pair of muons or$$\tau $$$\tau$leptons. A data sample of proton–proton collisions at$$\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V} $$$\sqrt{s}=13\text{Te}\text{V}$corresponding to an integrated luminosity of 138$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$recorded with the CMS detector is analyzed. No statistically significant excess is observed over the standard model backgrounds. Upper limits are set at 95% confidence level ($$\text {CL}$$$\text{CL}$) on the Higgs boson branching fraction to$$\upmu \upmu \text{ b } \text{ b } $$$\mu \mu \text{b}\text{b}$and to$$\uptau \uptau \text{ b } \text{ b },$$$\tau \tau \text{b}\text{b},$via a pair of$$\text {a}_{1} $$${\text{a}}_1$s. The limits depend on the pseudoscalar mass$$m_{\text {a}_{1}}$$$m_{{\text{a}}_1}$and are observed to be in the range (0.17–3.3) $$\times 10^{-4}$$$\times {10}^{-4}$and (1.7–7.7) $$\times 10^{-2}$$$\times {10}^{-2}$in the$$\upmu \upmu \text{ b } \text{ b } $$$\mu \mu \text{b}\text{b}$and$$\uptau \uptau \text{ b } \text{ b } $$$\tau \tau \text{b}\text{b}$final states, respectively. In the framework of models with two Higgs doublets and a complex scalar singlet (2HDM+S), the results of the two final states are combined to determine upper limits on the branching fraction$${\mathcal {B}}(\text {H} \rightarrow \text {a}_{1} \text {a}_{1} \rightarrow \ell \ell \text{ b } \text{ b})$$$B(\text{H}\to {\text{a}}_1{\text{a}}_1\to \ell \ell \text{b}\text{b})$at 95%$$\text {CL}$$$\text{CL}$, with$$\ell $$$\ell$being a muon or a$$\uptau $$$\tau$lepton. For different types of 2HDM+S, upper bounds on the branching fraction$${\mathcal {B}}(\text {H} \rightarrow \text {a}_{1} \text {a}_{1} )$$$B(\text{H}\to {\text{a}}_1{\text{a}}_1)$are extracted from the combination of the two channels. In most of the Type II 2HDM+S parameter space,$${\mathcal {B}}(\text {H} \rightarrow \text {a}_{1} \text {a}_{1} )$$$B(\text{H}\to {\text{a}}_1{\text{a}}_1)$values above 0.23 are excluded at 95%$$\text {CL}$$$\text{CL}$for$$m_{\text {a}_{1}}$$$m_{{\text{a}}_1}$values between 15 and 60$$\,\text {Ge}\hspace{-.08em}\text {V}$$$\text{Ge}\text{V}$.

    

   more » « less
2. Multipliers on bi-parameter Haar system Hardy spaces

   https://doi.org/10.1007/s00208-024-02887-9  

   Lechner, R. ; Motakis, P. ; Müller, P_F_X ; Schlumprecht, Th ( May 2024 , Mathematische Annalen)

   Let$$(h_I)$$$\left(h_I\right)$denote the standard Haar system on [0, 1], indexed by$$I\in \mathcal {D}$$$I\in D$, the set of dyadic intervals and$$h_I\otimes h_J$$$h_I\otimes h_J$denote the tensor product$$(s,t)\mapsto h_I(s) h_J(t)$$$(s,t)\mapsto h_I\left(s\right)h_J\left(t\right)$,$$I,J\in \mathcal {D}$$$I,J\in D$. We consider a class of two-parameter function spaces which are completions of the linear span$$\mathcal {V}(\delta ^2)$$$V\left({\delta }^2\right)$of$$h_I\otimes h_J$$$h_I\otimes h_J$,$$I,J\in \mathcal {D}$$$I,J\in D$. This class contains all the spaces of the formX(Y), whereXandYare either the Lebesgue spaces$$L^p[0,1]$$$L^p[0,1]$or the Hardy spaces$$H^p[0,1]$$$H^p[0,1]$,$$1\le p < \infty $$$1\le p<\infty$. We say that$$D:X(Y)\rightarrow X(Y)$$$D:X\left(Y\right)\to X\left(Y\right)$is a Haar multiplier if$$D(h_I\otimes h_J) = d_{I,J} h_I\otimes h_J$$$D(h_I\otimes h_J)=d_{I,J}{h}_I\otimes h_J$, where$$d_{I,J}\in \mathbb {R}$$$d_{I,J}\in R$, and ask which more elementary operators factor throughD. A decisive role is played by theCapon projection$$\mathcal {C}:\mathcal {V}(\delta ^2)\rightarrow \mathcal {V}(\delta ^2)$$$C:V\left({\delta }^2\right)\to V\left({\delta }^2\right)$given by$$\mathcal {C} h_I\otimes h_J = h_I\otimes h_J$$$C{h}_I\otimes h_J=h_I\otimes h_J$if$$|I|\le |J|$$$\left|I\right|\le \left|J\right|$, and$$\mathcal {C} h_I\otimes h_J = 0$$$C{h}_I\otimes h_J=0$if$$|I| > |J|$$$\left|I\right|>\left|J\right|$, as our main result highlights: Given any bounded Haar multiplier$$D:X(Y)\rightarrow X(Y)$$$D:X\left(Y\right)\to X\left(Y\right)$, there exist$$\lambda ,\mu \in \mathbb {R}$$$\lambda ,\mu \in R$such that$$\begin{aligned} \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C})\text { approximately 1-projectionally factors through }D, \end{aligned}$$$\begin{array}{c}\lambda C+\mu (\text{Id}-C)\text{approximately 1-projectionally factors through}D,\end{array}$i.e., for all$$\eta > 0$$$\eta >0$, there exist bounded operatorsA, Bso thatABis the identity operator$${{\,\textrm{Id}\,}}$$$\text{Id}$,$$\Vert A\Vert \cdot \Vert B\Vert = 1$$$\Vert A\Vert ·\Vert B\Vert =1$and$$\Vert \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C}) - ADB\Vert < \eta $$$\Vert \lambda C+\mu (\text{Id}-C)-ADB\Vert <\eta$. Additionally, if$$\mathcal {C}$$$C$is unbounded onX(Y), then$$\lambda = \mu $$$\lambda =\mu$and then$${{\,\textrm{Id}\,}}$$$\text{Id}$either factors throughDor$${{\,\textrm{Id}\,}}-D$$$\text{Id}-D$.

    

   more » « less
3. Surface Houghton groups

   https://doi.org/10.1007/s00208-023-02751-2  

   Aramayona, Javier ; Bux, Kai-Uwe ; Kim, Heejoung ; Leininger, Christopher J. ( November 2023 , Mathematische Annalen)

   For every$$n\ge 2$$$n\ge 2$, thesurface Houghton group$${\mathcal {B}}_n$$$B_n$is defined as the asymptotically rigid mapping class group of a surface with exactlynends, all of them non-planar. The groups$${\mathcal {B}}_n$$$B_n$are analogous to, and in fact contain, the braided Houghton groups. These groups also arise naturally in topology: every monodromy homeomorphism of a fibered component of a depth-1 foliation of closed 3-manifold is conjugate into some$${\mathcal {B}}_n$$$B_n$. As countable mapping class groups of infinite type surfaces, the groups$$\mathcal {B}_n$$$B_n$lie somewhere between classical mapping class groups and big mapping class groups. We initiate the study of surface Houghton groups proving, among other things, that$$\mathcal {B}_n$$$B_n$is of type$$\text {F}_{n-1}$$${\text{F}}_{n-1}$, but not of type$$\text {FP}_{n}$$${\text{FP}}_n$, analogous to the braided Houghton groups.

    

   more » « less
4. Measurement of non-prompt $${{\textrm{D}}^{0}}$$-meson elliptic flow in Pb–Pb collisions at $$\sqrt{s_{\textrm{NN}}} = 5.02$$ TeV

   https://doi.org/10.1140/epjc/s10052-023-12259-3  

   Acharya, S ; Adamová, D ; Aglieri_Rinella, G ; Agnello, M ; Agrawal, N ; Ahammed, Z ; Ahmad, S ; Ahn, S U ; Ahuja, I ; Akindinov, A ; et al ( December 2023 , The European Physical Journal C)

   The elliptic flow$$(v_2)$$$\left(v_2\right)$of$${\textrm{D}}^{0}$$${\text{D}}^0$mesons from beauty-hadron decays (non-prompt$${\textrm{D}}^{0})$$${\text{D}}^0)$was measured in midcentral (30–50%) Pb–Pb collisions at a centre-of-mass energy per nucleon pair$$\sqrt{s_{\textrm{NN}}} = 5.02$$$\sqrt{s_{\text{NN}}}=5.02$ TeV with the ALICE detector at the LHC. The$${\textrm{D}}^{0}$$${\text{D}}^0$mesons were reconstructed at midrapidity$$(|y|<0.8)$$$\left(\right|y|<0.8)$from their hadronic decay$$\mathrm {D^0 \rightarrow K^-\uppi ^+}$$$D^0\to K^{-}{\pi }^{+}$, in the transverse momentum interval$$2< p_{\textrm{T}} < 12$$$2<p_{\text{T}}<12$ GeV/c. The result indicates a positive$$v_2$$$v_2$for non-prompt$${{\textrm{D}}^{0}}$$${\text{D}}^0$mesons with a significance of 2.7$$\sigma $$$\sigma$. The non-prompt$${{\textrm{D}}^{0}}$$${\text{D}}^0$-meson$$v_2$$$v_2$is lower than that of prompt non-strange D mesons with 3.2$$\sigma $$$\sigma$significance in$$2< p_\textrm{T} < 8~\textrm{GeV}/c$$$2<p_{\text{T}}<8\text{GeV}/c$, and compatible with the$$v_2$$$v_2$of beauty-decay electrons. Theoretical calculations of beauty-quark transport in a hydrodynamically expanding medium describe the measurement within uncertainties.

    

   more » « less
5. Finding solutions with distinct variables to systems of linear equations over $$\mathbb {F}_p$$

   https://doi.org/10.1007/s00208-022-02391-y  

   Sauermann, Lisa ( April 2022 , Mathematische Annalen)

   Let us fix a primepand a homogeneous system ofmlinear equations$$a_{j,1}x_1+\dots +a_{j,k}x_k=0$$$a_{j,1}{x}_1+\cdots +a_{j,k}{x}_k=0$for$$j=1,\dots ,m$$$j=1,\cdots ,m$with coefficients$$a_{j,i}\in \mathbb {F}_p$$$a_{j,i}\in F_p$. Suppose that$$k\ge 3m$$$k\ge 3m$, that$$a_{j,1}+\dots +a_{j,k}=0$$$a_{j,1}+\cdots +a_{j,k}=0$for$$j=1,\dots ,m$$$j=1,\cdots ,m$and that every$$m\times m$$$m\times m$minor of the$$m\times k$$$m\times k$matrix$$(a_{j,i})_{j,i}$$${\left(a_{j,i}\right)}_{j,i}$is non-singular. Then we prove that for any (large)n, any subset$$A\subseteq \mathbb {F}_p^n$$$A\subseteq F_p^n$of size$$|A|> C\cdot \Gamma ^n$$$\left|A\right|>C·{\Gamma }^n$contains a solution$$(x_1,\dots ,x_k)\in A^k$$$(x_1,\cdots ,x_k)\in A^k$to the given system of equations such that the vectors$$x_1,\dots ,x_k\in A$$$x_1,\cdots ,x_k\in A$are all distinct. Here,Cand$$\Gamma $$$\Gamma$are constants only depending onp,mandksuch that$$\Gamma $\Gamma <p$. The crucial point here is the condition for the vectors$$x_1,\dots ,x_k$$$x_1,\cdots ,x_k$in the solution$$(x_1,\dots ,x_k)\in A^k$$$(x_1,\cdots ,x_k)\in A^k$to be distinct. If we relax this condition and only demand that$$x_1,\dots ,x_k$$$x_1,\cdots ,x_k$are not all equal, then the statement would follow easily from Tao’s slice rank polynomial method. However, handling the distinctness condition is much harder, and requires a new approach. While all previous combinatorial applications of the slice rank polynomial method have relied on the slice rank of diagonal tensors, we use a slice rank argument for a non-diagonal tensor in combination with combinatorial and probabilistic arguments.

    

   more » « less