New physics at a Super Flavor Factory

The potential of a Super Flavor Factory (SFF) for searches of new physics is reviewed. While very high luminosity $B$ physics is assumed to be at the core of the program, its scope for extensive charm and $\tau$ studies are also emphasized. The possibility to run at the ${\rm Y}\left(5S\right)$ is also discussed; in principle, this could provide very clean measurements of $B_s$ decays. The strength and reach of a SFF are most notably due to the possibility of examining an impressive array of very clean observables. The angles and the sides of the unitarity triangle can be determined with unprecedented accuracy. These serve as a reference for new physics (NP) sensitive decays such as $B^{+}\to {\tau }^{+}{\nu }_{\tau }$ and penguin dominated hadronic decay modes, providing tests of generic NP scenarios with an accuracy of a few percent. Besides very precise studies of direct and time dependent $\mathit{CP}$ asymmetries in radiative $B$ decays and forward-backward asymmetry studies in $B\to X_s{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ and numerous null tests using $B$, charm, and $\tau$ decays are also likely to provide powerful insights into NP. The dramatic increase in luminosity at a SFF will also open up entirely new avenues for probing NP observables, e.g., by allowing sensitive studies using theoretically clean processes such as $B\to X_s\nu \overline{\nu }$. The SFF is envisioned to be a crucial tool for essential studies of flavor in the CERN Large Hadron Collider era and will extend the reach of the Large Hadron Collider in many important ways.

Figure 1

(Color online) 95% confidence level constraints on parameters $\overline{\rho }$ and $\overline{\eta }$ in the Wolfenstein parametrization of the CKM matrix. Left, present constraints: right, with errors shrunk to the size expected at a SFF while tuning central values to have compatible constraints. From 201.

Figure 2

(Color online) Sample diagrams contributing to the matching for $b\to s{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ at one loop order.

Figure 3

(Color online) Expectations for bounds on ${\Lambda }_{NP}$ for $\left({\overline{Q}}_L{Y}_U^{†}{Y}_U{\gamma }_{\mu }{Q}_L\right)\left({\overline{L}}_L{\gamma }_{\mu }{L}_L\right)$ that would follow from relative experimental precision ${\sigma }_{\mathrm{rel}}$, with currently expected theoretical uncertainties. From 267.

Figure 4

Contribution to the $B\to \tau {\overline{\nu }}_{\tau }$ decay mediated by $W,H^{\pm }$ exchange in 2HDM.

Figure 5

(Color online) Exclusion region in $(M_{H^{+}},\tan \beta )$ due to present data on $B\to \tau \nu$ and $R=\mathcal{B}(B\to D\tau \nu )∕\mathcal{B}(B\to De\nu )$. Dashed lines represent percentage deviation from the SM prediction of $R$ in the presently allowed region. From 439.

Figure 6

(Color online) Flavor changing coupling of the up Higgs boson $H_u$ to the down type quarks. From 494.

Figure 7

Example of squark-gluino $\Delta S=1$ penguin diagram with $h,k=L,R$.

Figure 8

(Color online) Constraints from $B$ physics observables and ${(g-2)}_{\mu }$ in the $(M_{H^{\pm }},\tan \beta )$ plane, with fixed $\mu =0.5\mathrm{TeV}$ and $A_U=0$. From 430.

Figure 9

(Color online) The standard CKM unitarity triangle.

Figure 10

(Color online) Statistical error on $\gamma$ $\left({\varphi }_3\right)$ as a function of the number of reconstructed $B^{\pm }\to D{K}^{\pm }$ decays and $D_{\mathit{CP}}$ decays as given by toy Monte Carlo study with $r_B=0.2$, $\gamma =70°$, ${\delta }_B=180°$, and $4\times {10}^5$ $D_{\mathit{CP}}$ decays (187). Dotted line shows the error on $\gamma$ from model dependent unbinned Dalitz plot fit with the same input parameters.

Figure 11

(Color online) Summary of the present constraints from isospin (blue/dark) and SU(3) flavor symmetry (red/light) on the $P∕T$ ratio in the $c$ convention. Only statistical errors are shown.

Figure 12

(Color online) Measurement of $\alpha$ from $B\to \pi \pi$. Left: The isospin triangle relations due to 358, with the notation $A_{ij}\equiv A(B^0\to {\pi }^i{\pi }^j)$. Only one of four possible triangle orientations is shown. Right: Constraints on $\alpha$ from isospin analysis of $B\to \pi \pi$ (231). Note that solutions at $\alpha \approx 0$ need large values of $T,P$ with fine-tuned cancellation and are thus excluded. From 182.

Figure 13

(Color online) HFAG compilation of $\sin \left(2{\beta }^{\mathrm{eff}}\right)\equiv -{\eta }_f{S}_f$ measurements in $b\to s$ penguin dominated decays (122) compared to $\sin \left(2\beta \right)$ from $b\to c\overline{c}s$ decays to charmonia such as $B^0\to J∕\psi K^0$. Not included is the recent BaBar result on $B^0\to f_0{K}_S^0$ from the time dependent Dalitz plot analysis of $B^0\to {\pi }^{+}{\pi }^{-}{K}_S^0$ (100), which has highly non-Gaussian uncertainties.

Figure 14

Typical contributions to the weak annihilation amplitude in $B\to K^{*}\gamma$ (a) and $B\to \rho \gamma$ (b) weak radiative decays. Additional diagrams with the photon attaching to the final state quarks are not shown.

Figure 15

Diagram with insertion of the operator $O_2^c$ which contributes to right-handed photon emission. The wavy line denotes a photon and the curly line a gluon.

Figure 16

Parametrization of the final state in the rare decay $B\to K^{*}(\to K\pi ){\mathcal{l}}^{+}{\mathcal{l}}^{-}$.

Figure 17

(Color online) Differential decay rate $d\mathcal{B}(B^0\to {K^{*}}^0{\mathcal{l}}^{+}{\mathcal{l}}^{-})∕d{q}^2$ and the forward-backward asymmetry $A_{\mathrm{FB}}(B^0\to K^{*0}{\mathcal{l}}^{+}{\mathcal{l}}^{-})$. The dashed line denotes leading-order approximation (including some tree level $1∕m_b$ corrections) and the solid line denotes the next-to-leading order result. The band reflects all theoretical uncertainties from parameters and scale dependence combined (on left figure the thin band is without errors on the form factors and CKM input). From 147.

Figure 18

(Color online) Predictions for the forward-backward in $B\to X_s{\mathcal{l}}^{+}{\mathcal{l}}^{-}$. Left: The full NNLO prediction for $B\to X_s{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ forward-backward asymmetry normalized to the dilepton mass distribution (dashed line) and the total—parametric and perturbative—error band (shaded area). From 420. Right: $d{A}_{FB}∕d{q}^2$ in SM (solid line), with sign of $C_{10}$ opposite to SM (line 1), with reversed $C_{7\gamma }$ sign (line 2), both $C_{7\gamma }$ and $C_{10}$ signs reversed (line 3). From 33.

Figure 19

(Color online) Isospin asymmetry $\Delta \left(\rho \gamma \right)$ as a function of the CKM angle $\alpha$. The band displays the total theoretical uncertainty which is mainly due to weak annihilation. The vertical dashed lines limit the range of $\alpha$ obtained from the CKM unitarity triangle fit.

Figure 20

(Color online) Correlation between $\mathcal{B}(\mu \to e\gamma )$ and $\mathcal{B}(\tau \to \mu \gamma )$, and the dependence on the heaviest right-handed neutrino mass $m_{N_3}$ and the neutrino mixing angle ${\theta }_{13}$ in constrained MSSM with three right-handed neutrinos (40). For three values of $m_{N_3}$, the range of predicted values for the lepton flavor violating branching fractions are illustrated for different values of ${\theta }_{13}$ by scanning over other model parameters. Horizontal and vertical dashed lines denote experimental bounds, with dotted lines showing estimated future sensitivities [note that these are almost one order of magnitude too conservative with regard to the SFF sensitivity for $\mathcal{B}(\tau \to \mu \gamma )$] (26; 183).

Figure 21

The LHC reach for $196{\mathrm{fb}}^{-1}$ in the ${\tilde{\theta }}_{ij}\text{−}\Delta {\tilde{m}}_{ij}$ plane, and the line of the constant $\mathcal{B}(\mu \to e\gamma )$ in cMSSM with $\tan \beta =10$, $A=0$, $M_0=90\mathrm{GeV}$, and $M_{1∕2}=250\mathrm{GeV}$. From 410.