Implications of $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing for new physics

We provide a comprehensive, up-to-date analysis of possible new physics contributions to the mass difference $\Delta M_D$ in $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing. We consider the most general low-energy effective Hamiltonian and include leading-order QCD running of effective operators. We then explore an extensive list of possible new physics models that can generate these operators, which we organize as including extra fermions, extra gauge bosons, extra scalars, extra space dimensions and extra symmetries. For each model we place restrictions on the allowed parameter space using the recent evidence for observation of $D$ meson mixing. In many scenarios, we find strong constraints that surpass those from other search techniques and provide an important test of flavor-changing neutral currents in the up-quark sector. We also review the recent BABAR and Belle findings, and describe the current status of the standard model predictions of $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing.

Figure 1

Loop diagram for $D^0\to {\overline{D}}^0$.

Figure 2

Left: $x_{\mathrm{D}}$ in the four generation model as a function of the CKM mixing factor $|V_{c{b}^{\prime }}^{*}{V}_{u{b}^{\prime }}|$ for $b^{\prime }$-quark masses of 200, 300, 400, and 500 GeV from bottom to top. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded. Right: The present $1\sigma$ excluded region in the mass-mixing parameter plane, as well as possible future contours taking $x_{\mathrm{D}}<(15.0,8.0,5.0,3.0)\times {10}^{-3}$, corresponding to the blue (dark gray) dashed, red (gray) dashed, cyan (lightest gray) dotted, and green (light gray) dot-dashed curves, respectively.

Figure 3

Box contribution from heavy weak-isosinglet quarks.

Figure 4

Left: $x_{\mathrm{D}}$ in the singlet $Q=-1/3$ quark model as a function of the singlet quark mass for various values of the mixing angle $s_2=0.0001$, 0.0002, 0.0003 corresponding to the solid, dotted, and dashed curves, respectively. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded. Right: The present $1\sigma$ excluded region (short-dashed curve) in the mass $m_S$ and mixing angle $s_2$ parameter plane for the singlet $Q=-1/3$ quark in the model of Bjorken et al. [38] described in the text. Possible future contours are also shown, taking $x_{\mathrm{D}}<(15.0,8.0,5.0,3.0)\times {10}^{-3}$ from top to bottom, corresponding to the solid, medium-dashed, long-dashed, and longer-dashed curves, respectively.

Figure 5

Tree-level contribution from $Z^0$ exchange.

Figure 6

Value of $x_{\mathrm{D}}$ as a function of the mixing parameter ${\lambda }_{uc}$ in units of ${10}^{-2}$ in the $Q=+2/3$ quark singlet model. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded.

Figure 7

$x_{\mathrm{D}}$ in a generic $Z^{\prime }$ model as a function of the $Z^{\prime }$ boson mass (normalized by the flavor-changing coupling constant) for the case $C_L=C_R=C$. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded.

Figure 8

$x_{\mathrm{D}}^{(\mathrm{FS})}$ as a function of $m_1/f$ for the gauge boson mass ratios $m_1/m_2=0.01$, 0.5, 0.7 corresponding to the solid, dotted, and dashed curves, respectively. The $1\sigma$ region for $x_{\mathrm{D}}$ is also shown, with the yellow shaded region depicting the excluded region.

Figure 9

$x_{\mathrm{D}}$ in the left-right symmetric model with nonmanifest left-right symmetry as a function of the right-handed CKM mixing factor $|V_{ub}^R{V}_{cb}^{R*}|$ for $M_R=300$, 600, 1000, 1500 GeV from top to bottom. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded.

Figure 10

Left: $x_{\mathrm{D}}$ in the alternate left-right model as a function of the mass of the $W_R$ for various values of the singlet quark mass splittings, $\Delta /m=0.1$, 0.2, 0.5, 1.0 from bottom to top. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded. Right: The present $1\sigma$ excluded region in the $M_R$—mass splitting parameter plane, as well as possible future contours taking $x_{\mathrm{D}}<(15.0,8.0,5.0,3.0)\times {10}^{-3}$, corresponding to the blue (dark gray) dashed, red (gray) dashed, cyan (lightest gray) dotted, and green (light gray) dot-dashed curves, respectively. The mass of the first generation singlet quark $D_1$ is taken to be 500 and 2000 GeV as labeled.

Figure 11

Left: $x_{\mathrm{D}}$ in vector leptoquark models as a function of the vector leptoquark mass $M_{\mathrm{VLQ}}$, with ${\lambda }_{PP}=0.1$ (solid line), ${\lambda }_{PP}=0.07$ (short dash), and ${\lambda }_{PP}=0.05$ (long dash) for $P=L$ or $R$. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded. Right: The present $1\sigma$ excluded region in the vector leptoquark mass–coupling parameter plane, as well as possible future contours taking $x_{\mathrm{D}}<(15.0,8.0,5.0,3.0)\times {10}^{-3}$, corresponding to the blue (dark gray) dashed, red (gray) dashed, cyan (lightest gray) dotted, and green (light gray) dot-dashed curves, respectively.

Figure 12

Box diagrams with charged Higgs contributions to $D$ meson mixing.

Figure 13

$x_{\mathrm{D}}^{(2\mathrm{HDM})}$ in the flavor-conserving two-Higgs-doublet model as a function of $\tan \beta$ for charged Higgs boson masses of $m_{H^{\pm }}=100$, 250, and 500 GeV, corresponding to the solid, dashed red (gray), and dashed-dot green (light gray) curves, respectively. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded region depicting the region that is excluded.

Figure 14

The dipenguin diagram with neutral Higgs exchange.

Figure 15

$x_{\mathrm{D}}$ as a function of $M_H/C$ in models with no natural flavor conservation in the Higgs sector. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded.

Figure 16

Left: $1\sigma$ excluded region in the effective neutral Higgs mass–coupling plane for the tree-level contribution to $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing in the Cheng-Sher ansatz. Right: $1\sigma$ excluded region in the effective neutral Higgs mass–coupling plane for the box diagram contribution to $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing in the Cheng-Sher ansatz. In both figures, possible future contours taking $x_{\mathrm{D}}<(15.0,8.0,5.0,3.0)\times {10}^{-3}$, corresponding to the blue (dark gray) dashed, red (gray) dashed, cyan (lightest gray) dotted, and green (light gray) dot-dashed curves, respectively, are also displayed.

Figure 17

$x_{\mathrm{D}}$ as a function of the new gauge boson mass $M$ in composite Higgs models for $g=0.1$ (solid line), $g=0.3$ (dash-dotted line), and $g=0.5$ (dashed line). The $1\sigma$ experimental bounds are as indicated, with the yellow shaded area depicting the region that is excluded.

Figure 18

Tree-level gauge KK exchange that mediates neutral meson oscillations.

Figure 19

Left: $x_{\mathrm{D}}$ in the split fermion model as a function of the separation between the left-handed $u$ and $c$ quark states in the extra dimension for various values of the compactification scale. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded region depicting the region that is excluded. Right: $1\sigma$ excluded region in the $u_L-c_L$ separation and compactification scale parameter plane, as well as possible future contours taking $x_{\mathrm{D}}<(15.0,8.0,5.0,3.0)\times {10}^{-3}$, corresponding to the blue (dark gray) dashed, red (gray) dashed, cyan (lightest gray) dotted, and green (light gray) dot-dashed curves, respectively.

Figure 20

The coupling strength, scaled to the SM strong coupling constant, of the zero-mode fermions to the first five gluon KK excitations (as labeled) as a function of the fermion bulk mass parameter $c_f$.

Figure 21

The contribution to $x_{\mathrm{D}}$ from a warped extra dimension with the SM fields in the bulk as a function of the mass for the first gluon KK excitation. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded region depicting the region that is excluded. The curves correspond to model I [dash-dotted, green (light gray)], model II [dashed, red (gray)], and model III (solid) as described in the text.

Figure 22

Contributions to $D$ mixing from mass insertions in the squark propagator in MSSM. $N$, $M$, $P$, and $Q$ label the helicity $(L,R)$.

Figure 23

The constraints on the absolute value of the mass insertions with different helicities as a function of the mass ratio $m_{\tilde{g}}/m_{\tilde{q}}$ for various values of the average squark mass. The $1\sigma$ excluded region, corresponding to $x_{\mathrm{D}}<11.7\times {10}^{-3}$, lies above the curves.

Figure 24

Contours, corresponding to $x_{\mathrm{D}}=15.0\times {10}^{-3}$, for the absolute value of the mass insertions with different helicities as a function of the mass ratio $m_{\tilde{g}}/m_{\tilde{q}}$ for various values of the average squark mass. The region above the curves corresponds to larger values of $x_{\mathrm{D}}$.

Figure 25

Contours, corresponding to $x_{\mathrm{D}}=3.0\times {10}^{-3}$, for the absolute value of the mass insertions with different helicities as a function of the mass ratio $m_{\tilde{g}}/m_{\tilde{q}}$ for various values of the average squark mass. The region above the curves corresponds to larger values of $x_{\mathrm{D}}$.

Figure 26

Contributions to $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing from the ${\lambda }^{\prime }$ superpotential terms in supersymmetric models with R-parity violation.

Figure 27

Left: $x_{\mathrm{D}}$ in supersymmetry with R-parity violation as a function of the product of R-parity violating couplings ${\tilde{\lambda }}_{i2k}^{\prime }{\tilde{\lambda }}_{i1k}^{\prime }$ taking $m_{{\tilde{d}}_{R,k}}=m_{{\tilde{\ell }}_{L,i}}$, with $m_{{\tilde{d}}_{R,k}}=300$, 500, 1000, and 2000 GeV corresponding to the solid, green (light gray) dashed, red (gray) dotted, and blue (dark gray) dash-dotted curves, respectively. The $1\sigma$ experimental bounds are as indicated, with the yellow shaded region depicting the region that is excluded. Right: $1\sigma$ excluded region in the R-parity violating coupling–squark mass plane, as well as possible future contours taking $x_{\mathrm{D}}<(15.0,8.0,5.0,3.0)\times {10}^{-3}$, corresponding to the blue (dark gray) dashed, red (gray) dashed, cyan (lightest gray) dotted, and green (light gray) dot-dashed curves, respectively.