Signals of Warped Top-Condensation in B-Decays

TL;DR

This paper explores the implications of a warped top-condensation model predicting a light radion, analyzing constraints and signals in B-decays and astrophysics, with potential for new physics discovery.

Contribution

It investigates the phenomenology of a light radion in warped top-condensation models, focusing on B-decay processes and astrophysical bounds, which is a novel application.

Findings

Constraints on radion properties from B-decay data

Potential signals of radion in b → s φ transitions

Astrophysical bounds on very light radions

Abstract

A recently proposed warped top-condensation model generally predicts a light radion \phi, with a mass of a few GeV or less, whose interactions are suppressed by a scale of order 100 TeV. In this talk, we present existing constraints and potential signals from the process b \to s \phi, in the context of such a model. Astrophysical bounds, applicable to very light radions, are also briefly discussed.

Equations

$${\Lambda }_{\varphi }=\sqrt{6M_5^3/k}{e}^{-kL},$$

$$m_{\varphi }\sim (35\mathrm{TeV}/{\Lambda }_{\varphi })4\mathrm{GeV}.$$

$$\frac{\mathrm{Br}(B\to X_s\varphi )}{\mathrm{Br}(B\to X_{c}e{\bar{\nu }}_e)}=\frac{27\sqrt{2}}{64{\pi }^2}\frac{G_{\varphi }{m}_b^2}{f(m_c/m_b)}{\left|\frac{V_{st}^{†}{V}_{tb}}{V_{cb}}\right|}^2{\left(\frac{m_t}{m_b}\right)}^4\times {\left(1-\frac{m_{\varphi }^2}{m_b^2}\right)}^2,$$

$$\mathrm{Br}(B\to X_s\varphi )\sim 10^{-5}(\mathrm{Loop}).$$

$${\mathcal{L}}_{FV}=\frac{\varphi }{{\Lambda }_{\varphi }}({\bar{d}}_L^i{d}_R^j{a}_{ij}\sqrt{m_i{m}_j}+h.c.);(i\ne j),$$

$$\frac{\mathrm{Br}(B\to X_s\varphi )}{\mathrm{Br}(B\to X_{c}e{\bar{\nu }}_e)}=\frac{6{\pi }^2{a}_{bs}^2}{{\Lambda }_{\varphi }^2{G}_F^2}\frac{(m_s/m_b^3)(1-m_{\varphi }^2/m_b^2{)}^2}{|V_{cb}{|}^{2}f(m_c/m_b)}$$

$$\mathrm{Br}(B\to X_s\varphi )\sim 10^{-2}(\mathrm{Tree}),$$

$${\Gamma }_{{\mu }^{+}{\mu }^{-}}:{\Gamma }_{\bar{s}s}:{\Gamma }_{gg}\simeq x_{\mu }^2{m}_{\mu }^2:3x_s^2{m}_s^2:{\left(\frac{b_4{\alpha }_s}{2\pi }\right)}^2{m}_{\varphi }^2,$$

$$\mathrm{Br}(b\to s\varphi \to sgg)\sim 10^{-2}(\mathrm{WTCM}),$$

$$\mathrm{Br}(b\to sgg)\sim 10^{-3}(\mathrm{SM})$$

$$|a_{bs}|/{\Lambda }_{\varphi }\text{raise}1.29167pt<\text{lower}4.30554pt\sim (10^4\mathrm{TeV}{)}^{-1}.$$

$${\tau }_{\varphi }\sim \frac{32{\pi }^3{\Lambda }_{\varphi }^2}{b_4^2{\alpha }_s^2{m}_{\varphi }^3}\sim 10^{-12}\mathrm{s}{\left(\frac{{\Lambda }_{\varphi }}{10^2\mathrm{TeV}}\right)}^2{\left(\frac{1\mathrm{GeV}}{m_{\varphi }}\right)}^3,$$

$${\Gamma }_{{\mu }^{+}{\mu }^{-}}:{\Gamma }_{\gamma \gamma }\simeq m_{\mu }^2:m_{\varphi }^2/(kL{)}^2.$$

$$\mathrm{Br}(B\to s{\mu }^{+}{\mu }^{-})=(4.3\pm 1.2)\times 10^{-6}(\mathrm{Data}).$$

$$|a_{bs}|/{\Lambda }_{\varphi }\text{raise}1.29167pt<\text{lower}4.30554pt\sim (2\times 10^5\mathrm{TeV}{)}^{-1}.$$

Full text

The following is based on a talk given at the SUSY 2009 conference, held at Northeastern University, Boston, MA, USA, June 5-10, 2009. The material for the talk is from Ref. Davoudiasl and Ponton (2009), where more details and references can be found.

The warped top-condensation model (WTCM) introduced in Ref. Bai et al. (2008) is based on the Randall-Sundrum (RS) model Randall and Sundrum (1999). The WTCM does not have a fundamental scalar Higgs field, but includes bulk Standard Model (SM) gauge and fermion fields, with the latter arranged such that the light fields are localized towards the UV-brane and the heavy ones are localized towards the IR-brane of the RS background. In particular, the top quarks are IR-localized.

The strong interactions of the KK gluons with the top quarks gives rise to quark condensation, and hence EWSB. If the potential for the radion scalar, associated with the size $L$ of the extra dimension, is dominated by top condensation, one can show that $kL\approx 30$, where $k$ is the 5D curvature scale. With $k$ near the 4D Planck mass $M_{P}\sim 10^{18}$ GeV, this setup gives rise to the appearance of the gauge Kaluza-Klein (KK) modes at $m_{KK}\sim 30$ TeV and a very light radion $\phi$ of mass $m_{\phi}\sim 1$ GeV. The coupling of $\phi$ to the trace of energy-momentum tensor is suppressed by the scale

[TABLE]

where $M_{5}$ is the 5D fundamental scale of the RS background and $M_{P}\simeq M_{5}^{3}/k$. Roughly, we have

[TABLE]

The WTCM model also predicts a heavy composite Higgs of mass $m_{H}\sim 500$ GeV and requires a color-charged state with a mass around 2 TeV to obtain the correct top mass Bai et al. (2008). However, here we are interested in the low energy signals associated with $\phi$, and in particular those from $B$-meson decays. We note that a similar setup, using a fourth generation quark to form the EWSB condensate, was introduced in Ref. Burdman and Da Rold (2007), in which m_{KK}\mathrel{\raise 1.29167pt\hbox{>\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}1 TeV and m_{H}\mathrel{\raise 1.29167pt\hbox{>\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}700 GeV.

Let us focus on the process $B\to X_{s}\,\phi$, with $\phi$ emitted on-shell. We will use the spectator approximation: ${\rm Br}(B\to X_{s}\,\phi)/{\rm Br}(B\to X_{c}\,e{\bar{\nu}_{e}})\approx{\rm Br}(b\to s\,\phi)/{\rm Br}(b\to c\,e{\bar{\nu}_{e}})$ throughout. We begin with the loop-level contribution. By adapting a similar computation for a light Higgs in Ref. Grinstein et al. (1988), we find

[TABLE]

where $G_{\phi}\equiv(\sqrt{2}\Lambda_{\phi}^{2})^{-1}$, and $f(m_{c}/m_{b})\simeq 0.5$. With $m_{\phi}\sim 1$ GeV and $\Lambda_{\phi}\sim 100$ TeV, we find

[TABLE]

Here, we note that bulk fermions have non-universal couplings to the radion Azatov et al. (2009). This gives rise to tree-level flavor changing neutral current (FCNC) effects that could mediate $b\to s\phi$. The radion-mediated FCNC interctions, after mass matrix diagonalization, are given by Azatov et al. (2009)

[TABLE]

where $a_{ij}$ are functions of 5D fermion profile parameters $c_{f}\equiv m_{5}^{f}/k$, with $m_{5}^{f}$ the 5D fermion mass, and $m_{i}$ are the SM fermion masses.

We find $a_{ij}\sim 0.05$ to be a good representative value Azatov et al. (2009). With $a_{bs}^{2}=|a_{23}|^{2}+|a_{32}|^{2}$ and ignoring terms of $\mathcal{O}{(m_{s}/m_{b})}$, we get

[TABLE]

For $m_{\phi}\sim 1$ GeV and $\Lambda_{\phi}\sim 100$ TeV, we obtain

[TABLE]

which is much larger than the loop effect in Eq. (4). Hence, we will focus on the much larger tree-level bulk effect for the rest of our discussion.

For 1~{}{\rm GeV}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}4 GeV, which is in the natural WTCM range, the $b$ quark decays are on-shell and perturbative QCD can be used to calculate hadronic decay rates of $\phi$. For 3.7~{}{\rm GeV}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}4 GeV, $\phi$ decays mostly into $\tau^{+}\tau^{-}$ and $c{\bar{c}}$. For m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}3.7 GeV, $\mu^{+}\mu^{-},{\bar{s}}s$, and $gg$ are the most relevant decay modes. We find for the partial widths

[TABLE]

where $m_{s}\simeq 104$ MeV, $b_{4}=25/3$ is the QCD $\beta$-function for 4 flavors, and $\alpha_{s}/\pi\simeq 0.1$. Here $x=(c_{L}+c_{R})_{f}$, where $f=\mu,\,s$, and $c_{L,R}$ parametrize the localization of $f$ left- and right-handed chiralities; we typically expect $x\approx 1$. Thus, in this range of $m_{\phi}$, the radion nearly always decays into gluons. We get the branching fraction

[TABLE]

which compared to that expected from the SM Simma and Wyler (1990); Liu and Yao (1990)

[TABLE]

implies

[TABLE]

The lifetime of $\phi$ is estimated to be

[TABLE]

roughly corresponding to a displaced vertex of $\mathcal{O}{(0.3)}$ mm that could be a distinct signature. For 2m_{\pi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}1 GeV we are in the non-perturbative regime and do not have reliable estimates. However, the main signal is expected to be $X_{s}\pi\pi$, with displaced $\pi\pi$ vertices.

Over the range $2m_{\mu}<m_{\phi}<2m_{\pi}$, the partial widths will be given by

[TABLE]

With $m_{\phi}\approx 2m_{\mu}$ and $kL\simeq 30$ in the WTCM, the di-muon final state dominates in this range. Experimental data Amsler et al. (2008) give

[TABLE]

Demanding that the effect from $\phi$ be within the error on this measurement, we then get

[TABLE]

For radion masses 15~{}{\rm MeV}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}2m_{\mu}, the dominant decay channel is into di-photons and \tau_{\phi}\mathrel{\raise 1.29167pt\hbox{>\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}10^{-6} s . Hence, the signal will be $b\to sE\!\!\!\!\!/$, for this range of $m_{\phi}$; we find that the experimental bounds on $B\to X_{s}\,\nu{\bar{\nu}}$ Amsler et al. (2008) do not yield a severe constraint on the model parameters.

Finally, we would like to mention that for m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}30 MeV, $\phi$ is light compared to the supernova core temperature $T\sim 30$ MeV and its emission can over cool the star. Here, bounds from SN 1987A, based on energy loss in nucleon $N$ scattering $NN\to NN\phi$, imply \Lambda_{\phi}\mathrel{\raise 1.29167pt\hbox{>\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}10^{6} TeV, corresponding to m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}100 keV. Hence, roughly, the interval 0.1~{}{\rm MeV}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}30 MeV (corresponding to 10^{6}{\rm~{}TeV}\mathrel{\raise 1.29167pt\hbox{>\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}\Lambda_{\phi}\mathrel{\raise 1.29167pt\hbox{>\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}10^{4} TeV) is disfavored by the SN 1987 A data.

In summary, the WTCM provides a mechanism to obtain the weak scale from a scale $\Lambda_{\phi}\sim 100$ TeV. This model typically predicts m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}4 GeV, which suggests that $B$-decays may provide signals of the light radion. We focused on the process $b\to s\phi$. Here, the tree-level FCNC effects from non-universality dominate over loop-induced contributions. We derived a number of bounds on WTCM parameters, using $B$-decay constraints and pointed out that the subsequent $\phi$ decays can lead to measurable displaced vertex signals. We briefly discussed SN 1987A constraints and estimated that they disfavor the mass range 0.1~{}{\rm MeV}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}m_{\phi}\mathrel{\raise 1.29167pt\hbox{<\kern-7.5pt\lower 4.30554pt\hbox{\sim}}}30 MeV.

We thank the SUSY 2009 organizers. Work supported by the US Department of Energy under Grant Contract DE-AC02-98CH10886.