In this paper we propose a generalised holographic framework to describe superconductors. We first unify the description of s-, p-, and d-wave superconductors in a way that can be easily promoted to higher spin. Using a semianalytical procedure to compute the superconductor properties, we are able to further generalise the geometric description of the hologram beyond the AdS-Schwarzschild Black Hole paradigm and propose a set of higher-dimensional metrics which exhibit the same universal behaviour. We then apply this generalised description to study the properties of the condensate and the scaling of the critical temperature with the parameters of the higher-dimensional theory, which allows us to reproduce existing results in the literature and extend them to include a possible description of the newly observed f-wave superconducting systems.

Spain

Fabian Esser

Andrea Donini

Víctor Enguita-Vileta

United Kingdom

Veronica Sanz

Generalising Holographic Superconductors

A correction to this paper has been published: https://doi.org/10.1007/JHEP01(2020)161

Miguel Folgado

Nuria Rius

Erratum to: Gravity-mediated scalar Dark Matter in warped extra-dimensions

We study the possibility that Dark Matter (DM) is made of Feebly Interacting Massive Particles (FIMP) interacting just gravitationally with the Standard Model particles in the framework of a Clockwork/Linear Dilaton (CW/LD) model. We restrict here to the case in which the DM particles are scalar fields. This paper extends our previous study of FIMP’s in Randall-Sundrum (RS) warped extra-dimensions. As it was the case in the RS scenario, also in the CW/LD model we find a significant region of the parameter space in which the observed DM relic abundance can be reproduced with scalar DM mass in the MeV range, with a reheating temperature varying from 10 GeV to 109 GeV. We comment on the similarities of the results in both extra-dimensional models.

Colombia

Nicolás Bernal

FIMP Dark Matter in Clockwork/Linear Dilaton extra-dimensions

We study the possibility that Dark Matter (DM) particles of spin 0, 1/2 or 1 may interact gravitationally with Standard Model (SM) particles within the framework of a warped Randall–Sundrum (RS) model. Both the Dark Matter and the Standard Model particles are assumed to be confined to the infra-red (IR) brane and only interchange Kaluza–Klein excitations of the graviton and the radion (adopting the Goldberger–Wise mechanism to stabilize the size of the extra-dimension). We analyze the different DM annihilation channels and find that the presently observed Dark Matter relic abundance,  $$\Omega _{\mathrm{DM}}$$  <math> <msub> <mi>Ω</mi> <mi>DM</mi> </msub> </math>  , can be obtained within the freeze-out mechanism for DM particles of all considered spins. This extends our first work concerning scalar DM in RS scenarios (Folgado et al., in JHEP 01:161.  https://doi.org/10.1007/JHEP01(2020)161  , 2020) and put it on equal footing with our second work in which we studied DM particles of spin 0, 1/2 and 1 in the framework of the Clockwork/Linear Dilaton (CW/LD) model (Folgado et al., in JHEP 20:036.  https://doi.org/10.1007/JHEP04(2020)036  , 2020). We study the region of the model parameter space for which  $$\Omega _{\mathrm{DM}}$$  <math> <msub> <mi>Ω</mi> <mi>DM</mi> </msub> </math>   is achieved and compare it with the different experimental and theoretical bounds. We find that, for DM particles mass  $$m_{\mathrm{DM}} \in [1,15]$$  <math> <mrow> <msub> <mi>m</mi> <mi>DM</mi> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>1</mn> <mo>,</mo> <mn>15</mn> <mo>]</mo> </mrow> </mrow> </math>   TeV, most of the parameter space is excluded by the current constraints or will be excluded by the LHC Run III or by the LHC upgrade, the HL-LHC. The observed DM relic abundance can still be achieved for DM masses  $$m_{\mathrm{DM}} \in [4,15]$$  <math> <mrow> <msub> <mi>m</mi> <mi>DM</mi> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>4</mn> <mo>,</mo> <mn>15</mn> <mo>]</mo> </mrow> </mrow> </math>   TeV and  $$m_{G_1} &lt; 10$$  <math> <mrow> <msub> <mi>m</mi> <msub> <mi>G</mi> <mn>1</mn> </msub> </msub> <mo>&lt;</mo> <mn>10</mn> </mrow> </math>   TeV for scalar and vector boson Dark Matter. On the other hand, for spin 1/2 fermion Dark Matter, only a tiny region with  $$m_{\mathrm{DM }} \in [4, 15]$$  <math> <mrow> <msub> <mi>m</mi> <mi>DM</mi> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>4</mn> <mo>,</mo> <mn>15</mn> <mo>]</mo> </mrow> </mrow> </math>   TeV,  $$m_{G_1} \in [5,10]$$  <math> <mrow> <msub> <mi>m</mi> <msub> <mi>G</mi> <mn>1</mn> </msub> </msub> <mo>∈</mo> <mrow> <mo>[</mo> <mn>5</mn> <mo>,</mo> <mn>10</mn> <mo>]</mo> </mrow> </mrow> </math>   TeV and  $$\Lambda &gt; m_{G_1}$$  <math> <mrow> <mi>Λ</mi> <mo>&gt;</mo> <msub> <mi>m</mi> <msub> <mi>G</mi> <mn>1</mn> </msub> </msub> </mrow> </math>   is compatible with theoretical and experimental bounds. We have also studied the impact of the radion in the phenomenology, finding that it does not modify significantly the allowed region for DM particles of any spin (differently from the CW/LD case, where its impact was quite significant in the case of scalar DM). We, eventually, briefly compare results in RS with those obtained in the CW/LD model.

Spin-dependence of gravity-mediated dark matter in warped extra-dimensions

We study for the first time the case in which Dark Matter (DM) is made of Feebly Interacting Massive Particles (FIMP) interacting just gravitationally with the standard model particles in an extra-dimensional Randall-Sundrum scenario. We assume that both the dark matter and the standard model are localized in the IR-brane and only interact via gravitational mediators, namely the graviton, the Kaluza-Klein gravitons and the radion. We found that in the early Universe DM could be generated via two main processes: the direct freeze-in and the sequential freeze-in. The regions where the observed DM relic abundance is produced are largely compatible with cosmological and collider bounds.

Kaluza-Klein FIMP dark matter in warped extra-dimensions

We study the scaling of kaon decay amplitudes with the number of colours, $$N_c$$ <math><msub><mi>N</mi><mi>c</mi></msub></math> , in a theory with four degenerate flavours, $$N_f=4$$ <math><mrow><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></mrow></math> . In this scenario, two current-current operators, $$Q^\pm $$ <math><msup><mi>Q</mi><mo>±</mo></msup></math> , mediate $$\Delta S=1$$ <math><mrow><mi>Δ</mi><mi>S</mi><mo>=</mo><mn>1</mn></mrow></math>  transitions, such as the two isospin amplitudes of non-leptonic kaon decays for $$K\rightarrow (\pi \pi )_{I=0,2}$$ <math><mrow><mi>K</mi><mo>→</mo><msub><mrow><mo>(</mo><mi>π</mi><mi>π</mi><mo>)</mo></mrow><mrow><mi>I</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></math> , $$A_0$$ <math><msub><mi>A</mi><mn>0</mn></msub></math>  and $$A_2$$ <math><msub><mi>A</mi><mn>2</mn></msub></math> . In particular, we concentrate on the simpler $$K\rightarrow \pi $$ <math><mrow><mi>K</mi><mo>→</mo><mi>π</mi></mrow></math>  amplitudes, $$A^\pm $$ <math><msup><mi>A</mi><mo>±</mo></msup></math> , mediated by these two operators. A diagrammatic analysis of the large-$$N_c$$ <math><msub><mi>N</mi><mi>c</mi></msub></math>  scaling of these observables is presented, which demonstrates the anticorrelation of the leading $${{\mathcal {O}}}(1/N_c)$$ <math><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub><mo>)</mo></mrow></math>  and $${{\mathcal {O}}}(N_f/N_c^2)$$ <math><mrow><mi>O</mi><mo>(</mo><msub><mi>N</mi><mi>f</mi></msub><mo>/</mo><msubsup><mi>N</mi><mi>c</mi><mn>2</mn></msubsup><mo>)</mo></mrow></math>  corrections in both amplitudes. Using our new $$N_f=4$$ <math><mrow><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></mrow></math>  and previous quenched data, we confirm this expectation and show that these corrections are naturally large and may be at the origin of the $$\Delta I=1/2$$ <math><mrow><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>  rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, $$g^\pm $$ <math><msup><mi>g</mi><mo>±</mo></msup></math> , can be determined. A NLO estimate of the $$K \rightarrow (\pi \pi )_{I=0,2}$$ <math><mrow><mi>K</mi><mo>→</mo><msub><mrow><mo>(</mo><mi>π</mi><mi>π</mi><mo>)</mo></mrow><mrow><mi>I</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></math>  isospin amplitudes can then be derived, which is in good agreement with the experimental value.

Pilar Hernández

Carlos Pena

Fernando Romero-López

Dissecting the $$\Delta I=1/2$$ <math><mrow><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>  rule at large $$N_c$$ <math><msub><mi>N</mi><mi>c</mi></msub></math>

We study for the first time the possibility that Dark Matter (represented by particles with spin 0 1 2 or 1) interacts gravitationally with Standard Model particles in an extra-dimensional Clockwork/Linear Dilaton model. We assume that both, the Dark Matter and the Standard Model, are localized in the IR-brane and only interact via gravitational mediators, namely the Kaluza-Klein (KK) graviton and the radion/KK-dilaton modes. We analyse in detail the Dark Matter annihilation channel into Standard Model particles and into two on-shell Kaluza-Klein towers (either two KK-gravitons, or two radion/KK- dilatons, or one of each), finding that it is possible to obtain the observed relic abundance via thermal freeze-out for Dark Matter masses in the range ∈ [1 15] TeV for a 5- dimensional gravitational scale ranging from 5 to a few hundreds of TeV, even after taking into account the bounds from LHC Run II and irrespectively of the DM particle spin.

Gravity-mediated dark matter in clockwork/linear dilaton extra-dimensions

We revisit the case of scalar Dark Matter interacting just gravitationally with the Standard Model (SM) particles in an extra-dimensional Randall-Sundrum scenario. We assume that both, the Dark Matter and the Standard Model, are localized in the TeV brane and only interact via gravitational mediators, namely the graviton Kaluza-Klein modes and the radion. We analyze in detail the dark matter annihilation channel into two on-shell KK-gravitons, and contrary to previous studies which overlooked this process, we find that it is possible to obtain the correct relic abundance for dark matter masses in the range [1, 10] TeV even after taking into account the strong bounds from LHC Run II. We also consider the impact of the radion contribution (virtual exchange leading to SM final states as well as on-shell production), which does not significantly change our results. Quite interestingly, a sizeable part of the currently allowed parameter space could be tested by LHC Run III and by the High-Luminosity LHC.