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Baking Club

Publik·18 anggota
Jose Rodriguez
Jose Rodriguez

File: State Of Decay ... !EXCLUSIVE!

To address these considerations, several detector concepts are being considered. The baseline CODEX-b conceptual design makes use of Resistive Plate Chambers (RPC) tracking stations with \(\mathcal O(100)\) ps timing resolution. A hermetic detector, with respect to the LLP decay vertex, is needed to achieve good signal efficiency and background rejection. In the baseline design, this is achieved by placing six RPC layers on each surface of the detector. To ensure good vertex resolution five additional triplets of RPC layers are placed equally spaced along the depth of the detector, as shown in Fig. 3b. Other, more ambitious options are being considered, that use both RPCs as well as large scale calorimeter technologies such as liquid [10] or plastic scintillators, used in accelerator neutrino experiments such as NO\(\nu \)A [11], T2K upgrade [12] or Dune [13]. If deemed feasible, implementing one of these options would permit measurement of decay modes involving neutral final states, improved particle identification and more efficient background rejection techniques.

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The \(h A'_\mu A'^\mu \) operator, by contrast, is controlled by the mixing of the \(H'\) with the SM Higgs. This can arise from the kinetic term \(\left D_\mu H'\right ^2\), with \(\left\langle H'\right\rangle \ne 0\) and \(H-H'\) mixing. This induces the exotic Higgs decay \(h\rightarrow A'A'\). In the limit where the mixing with the photon is small, this becomes the dominant production mode for the \(A'\), which then decays through the kinetic mixing portal to SM states. CODEX-b would have good sensitivity to this mixing due to its transverse location, with high \(\sqrt\hats\). Importantly, the coupling to the Higgs and the mixing with the photon are independent parameters, so that the lifetime of the \(A'\) and the \(h\rightarrow A'A'\) branching ratio are themselves independent, and therefore convenient variables to parameterize the model. Figure 7 shows the reach of CODEX-b for two different values of the \(A'\) mass, as done in Ref. [8] (see commentary therein), as well as the reach of AL3X [24] and MATHUSLA [22].

The parameter \(A_S\) can be exchanged for the mixing angle, \(\sin \theta \), of the S with the physical Higgs boson eigenstate. In the mass eigenbasis, the new light scalar therefore inherits all the couplings of the SM model Higgs: Mass hierarchical couplings with all the SM fermions, as well couplings to photons and gluons at one loop. All such couplings are suppressed by the small parameter \(\sin \theta \). The couplings induced by Higgs mixing are responsible not only for the decay of S [51, 52, 52,53,54,55], but also contribute to its production cross-section. Concretely, for \(m_KS couples most strongly to the virtual top quark in the loop. If the quartic coupling \(\lambda \) is non-zero, the rate is supplemented by a penguin with an off-shell Higgs boson, shown in Fig. 8b [59], as well as direct Higgs decays, shown in Fig. 8c.

CODEX-b is expected to have a potentially interesting reach for all these cases. This is true with the nominal design provided the ALP has a sizable branching fraction into visible final states, while for ALPs decaying to photons one would require a calorimeter element, as discussed below in Sect. 5.3. In this section, we will present the updated reach plots for BC10 and BC11 and leave the ALP with photon couplings (BC9) and the photophobic case for future study.

We estimate these production mechanisms using Pythia 8, with the code modified to account for the production of ALPs during hadronization. We include ALP production in decays by extending its decay table in such a way that for each decay mode containing a \(\pi ^0,\eta ,\eta '\) meson in the final state, we add another entry with the meson substituted by the ALP. The branching ratio is rescaled by the ALP mixing factor and phase space differences.

where \(s = 1\) (\(s=2\)) for a Dirac (Majorana) HNL and the final state M corresponds to a single kinematically allowed (ground-state) meson. Specifically, M considers: charged pseudoscalars, \(\pi ^\pm \), \(K^\pm \); neutral pseudoscalars \(\pi ^0\), \(\eta \), \(\eta '\); charged vectors, \(\rho ^\pm \), \(K^*\pm \); and neutral vectors, \(\rho ^0\), \(\omega \), \(\phi \). For \(m_N > 1.5\) GeV, we switch from the exclusive meson final states to the inclusive decays widths \(\Gamma _\ell _i qq'\) and \(\Gamma _\nu _i qq\), which are disabled below 1.5 GeV. Expressions for each of the partial widths may be found in Ref. [82]; each is mediated by either the W or Z, generating long lifetimes for N once one requires \(U_\ell N \ll 1\). Apart from the \(3\nu \), and some fraction of the \(\nu M\) and \(\nu qq\) (e.g. \(\nu \pi ^0\pi ^0\)) decay modes, all the N decays involve two or more tracks, so that the decay vertex will be reconstructible in CODEX-b, up to \(\mathcal O(1)\) reconstruction efficiencies. We model the branching ratio to multiple tracks by considering the decay products of the particles produced. Below 1.5 GeV, we consider the decay modes of the meson M to determine the frequency of having 2 or more charged tracks; above 1.5 GeV where \(\nu qq\) production is considered instead of exclusive single meson modes, we conservatively approximate the frequency of having two or more charged tracks as 2/3.

and considered five benchmarks, corresponding to different choices for the matrix \(\lambda '_ijk\), each with a different phenomenology. We reproduce here their results for their benchmarks 1 and 4, and refer the reader to Ref. [107] for the remainder. The parameter choices, production modes and main decay modes are summarized in Table 1. The reach of CODEX-b is shown in Fig. 15. In both benchmarks, CODEX-b would probe more than 2 orders of magnitude in the coupling constants. For benchmark 4 the reach would be substantially increased if the detector is capable of detecting neutral final states by means of some calorimetry.

The Abelian hidden sector model in Sect. 2.3.1 has enough free parameters to set the mass (\(m_A'\)), the Higgs branching ratio (\(\text Br(h\rightarrow A'A')\)) and the width (\(\Gamma _A'\)) independently. It therefore allows for a very general parametrization of the reach for exotic Higgs decays in terms of the lifetime, mass and production rate of the LLP. The downside of this generality is that the model has too many independent parameters to be very predictive. In many models, however, the lifetime has a very strong dependence on the mass, favoring long lifetimes for low mass states. We therefore provide a second, more constrained example where the lifetime is not a free parameter.

where h is the physical Higgs boson and \(\alpha '_3\) the twin QCD gauge coupling. After mapping the gluon operator to the low energy glueball field, this leads to a very suppressed decay width of the \(0^++\) state, even for moderate values of \(m_t/m_T\). In particular, the lifetime is a very strong function of the mass, and can be roughly parametrized as

For simplicity we assume that the second Higgs is too heavy to be produced in large numbers at the LHC, as is typical in composite UV completions. However, even in this pessimistic scenario the SM Higgs has a substantial branching ratio to the twin sector. Specifically, this Higgs has a branching ratio of roughly \(\sim m_t^2/m_T^2\) for the \(h\rightarrow b'b'\) channel. The \(b'\) quarks subsequently form dark quarkonium states, which in turn can decay to lightest hadronic states in the hidden sector. While this branching ratio is large, the phenomenology of the dark quarkonium depends on the detailed spectrum of twin quarks (see e.g. Ref. [124]). There is however a smaller but more model-independent branching ratio of the SM Higgs directly to twin gluons, given by [125]

where \(\text BR(Z_D\rightarrow ee; \Delta m)\) is the branching ratio for a kinetically mixed dark vector of mass \(\Delta m\) into ee. This is done to approximate the inclusion of additional accessible final states, as splittings in this model are commonly \(\mathcal O\left( \text GeV\right) \). While a more thorough treatment would integrate over phase space for each massive channel separately, this approximation captures the leading effect to well within the precision desired here. Additionally, \(\chi _2\) pairs can be directly produced through an off-shell \(Z_D\). Because the \(Z_D\) is off-shell, this does not generate a large contribution unless \(m_\chi _2 \lesssim 10\) GeV. This model provides a scenario containing an exotic Z decay into long-lived particles.

More generally, if the dark sector has additional symmetries and multiple states in the GeV mass range, as occurs naturally in hidden valley models with asymmetric dark matter (see e.g. Refs. [119, 138]), these excited states often must decay to the DM plus some SM states. Such decays must necessarily occur through higher dimensional operators, and macroscopic lifetimes are therefore generic. As for previous portals, LLP searches in the GeV mass range are best suited to displaced, background-free detectors such as CODEX-b.

In co-decaying dark matter models [146,147,148], the dark matter state, \(\chi _1\), is kept in equilibrium with a slightly heavier dark state, \(\chi _2\), though efficient \(\chi _1\chi _1\leftrightarrow \chi _2\chi _2\) processes in the early universe, but the dark sector does not maintain thermal equilibrium with the SM. The \(\chi _2\) state is, however, unstable and decays back to the SM. Because both states remain in equilibrium, this also depletes the \(\chi _1\) number density once the temperature of the dark sector drops below the mass of \(\chi _2\). For this mechanism to operate, \(\chi _2\) should have a macroscopic lifetime. On the one hand, the heavier \(\chi _2\) could very well be produced at the LHC through a heavy portal, however this is not strictly required for the co-decaying dark matter framework to operate. On the other hand, if implemented in the context of e.g. neutral naturalness [149, 150], a production mechanism at the LHC is typically a prediction and the phenomenology is once again that of a hidden valley. 041b061a72


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