⇦Chinese Physics Letters, 2020, Vol. 37, No. 10, Article code 101301 Anomalous $tq\gamma$ Couplings and Radiative ${\boldsymbol B}$ Meson Decays Ying Tan (谭莹) and Chong-Xing Yue(岳崇兴)* Affiliations Department of Physics, Liaoning Normal University, Dalian 116029, China Received 26 May 2020; accepted 24 August 2020; published online 29 September 2020 Supported by the National Natural Science Foundation of China (Grant Nos. 11875157 and 11947402).
*Corresponding author. Email: cxyue@lnnu.edu.cn Citation Text: Tan Y and Yue C X 2020 Chin. Phys. Lett. 37 101301    Abstract Motivated by the recent ATLAS results in terms of the branching ratios $ Br(t\rightarrow q\gamma)$, we consider the effects of the anomalous $tq\gamma$ couplings on the radiative $B$ meson decays $\bar{B}\rightarrow X_{D} \gamma$ and $B\rightarrow V\gamma$ with $V$ being light vector mesons $\rho,\omega,\phi$ and $K^{\ast}$. Comparing with the corresponding experimental measured data, we obtain the constraints on anomalous $tq\gamma$ couplings. DOI:10.1088/0256-307X/37/10/101301 PACS:13.20.He, 14.65.Ha, 11.10.Ef © 2020 Chinese Physics Society Article Text Top quark is the heaviest of ordinary particles and its flavor changing neutral current (FCNC) couplings are forbidden at tree level in the standard model (SM) and highly suppressed at loop level owing to the Glashow–Iliopoulos–Maiani mechanism. The SM predictions for the branching ratios of the top FCNC decays $t\rightarrow q x ~(x=g$, $\gamma$, $Z$, and $H)$ with $q$ being an up or charm quark at the order of $O (10^{-12}$–$10^{-17})$,[1] which are beyond the range of present and even future experimental sensitivity. Many new physics scenarios beyond the SM predict the existence of the top FCNC couplings and some of these models can make the branching ratios of the top FCNC decays be significantly larger than those predicted by the SM, e.g., see Ref. [2]. Thus, observation of anyone of the top FCNC couplings (or called the anomalous top quark couplings) at high-energy collider experiments would imply discovery of the new physics signals. Searching for the anomalous top couplings is one of the important goals of present and future collider experiments. Although any physical signature has not been detected, the experimental upper limits for some of these couplings are obtained. For example, the upper limits on the anomalous $tq\gamma$ couplings have been given by the CMS collaboration at $95\%$ confidence level (CL) and assuming equal left- and right-handed couplings, which induce the branching ratios $Br(t\rightarrow c\gamma) < 0.17\%$ and $Br(t\rightarrow u\gamma) < 0.013\%$.[3] The high energy and high luminosity collider experiments will be more sensitive to the anomalous top couplings. Furthermore, the anomalous top couplings can affect the low-energy loop level processes involving the top quark. If these processes can be precisely measured, they can also give constraints on these couplings. For example, some of the $K$ and $B$ meson decay processes can be used to constrain the anomalous top couplings $tqx$.[4,5,6] Thus, studying virtual effects of the anomalous top couplings on some low-energy processes can be seen as supplement to direct detection of high energy collider experiments. Recently, the ATLAS collaboration has announced the results at $95\%$ CL in terms of the branching ratios $Br(t\rightarrow q\gamma)$,[7] which are $Br(t\rightarrow u\gamma) \leq0.0061\% $ and $Br(t\rightarrow c\gamma) \leq0.022\%$ for only the right-handed (RH) or left-handed (LH) $tq\gamma$ couplings. The future high energy collider experiments are expected to give more accurate results. Motivated by the recent ATLAS results and coming results, in this Letter we model-independently consider the effects of the anomalous $tq\gamma$ couplings on the radiative $B$ meson decays $\bar{B}\rightarrow X_{D} \gamma$ and $B\rightarrow V\gamma$ with $D=d$ or $s$ quark and $V$ being light vector mesons $\rho, \omega, \phi$ and $K^{\ast}$. The SM predictions and experimental measurements for the branching ratios of these decays have both been improved greatly in recent years. Therefore, based on Ref. [5], we reconsider the contributions of the anomalous $tq\gamma$ couplings to these decay processes and update existing constraints on the anomalous $tq\gamma$ couplings from the recent theoretical experimental results. The Anomalous $tq\gamma$ Couplings and the Decays $\bar{B}\rightarrow X_{D} \gamma$. Many new physics scenarios beyond the SM can induce the anomalous top couplings, which can be uniformly described in a model-independent way by the effective Lagrangian without resorting to the detailed flavor structure of the specific new-physics model. Up to dimension-five operators, the general effective Lagrangian of the anomalous $tq\gamma$ couplings with $q$ being $u$ or $c$ quark can be written as[1,8] $$\begin{align} \mathcal{L}= -\frac{e}{\varLambda}\bar{q}\sigma_{\mu\nu}q^{\nu}(\lambda^{\rm L}_{tq\gamma}P_{\rm L}+\lambda^{\rm R}_{tq\gamma}P_{\rm R})t A^{\mu},~~ \tag {1} \end{align} $$ where $P_{\rm L, R}=(1\mp\gamma_{5})/2$ are chirality projection operators. $\varLambda$ is the new-physics scale, which is taken as $\varLambda=1$ TeV in our numerical calculation; $\lambda^{\rm L}_{tq\gamma} $ and $\lambda^{\rm R}_{tq\gamma}$ are the effective LH and RH couplings. In this study, we focus our attention on the effects of $tq\gamma$ couplings on the branching ratios for the radiative $B$ meson decays $\bar{B}\rightarrow X_{D}\gamma$ and $B\rightarrow V\gamma$, thus we assume that $\lambda^{\rm L}_{tq\gamma}$ and $\lambda^{\rm R}_{tq\gamma}$ are real numbers. Since the decay width of the top quark is dominated by the decay channel $t\rightarrow Wb$, the branching ratio of the decay $t\rightarrow q\gamma$ can be approximately expressed as $$\begin{align} Br(t\rightarrow q\gamma)=\frac{\varGamma(t\rightarrow q\gamma)}{\varGamma(t\rightarrow Wb)}.~~ \tag {2} \end{align} $$ As the SM prediction for the decay width $\varGamma(t\rightarrow q\gamma)$ is exceedingly small,[1] one need only consider that contributed by the anomalous top couplings $tq\gamma$. At leading order, the decay widths $\varGamma(t\rightarrow q\gamma)$ and $\varGamma(t\rightarrow Wb)$ are given by $$\begin{align} \varGamma(t\rightarrow q\gamma)=\frac{\alpha_{\rm e} m_{t}^{3}}{\varLambda^{2}}(|\lambda^{\rm L}_{tq\gamma}|^{2} + |\lambda^{\rm R}_{tq\gamma}|^{2}),~~ \tag {3} \end{align} $$ $$ \varGamma(t\rightarrow Wb)=\frac{G_{\rm F}m^{3}_{t}}{8\sqrt{2}\pi}|V_{tb}|^{2} \Big(1-\frac{m_{W}^{2}}{m_{t}^{2}}\Big)^{2} \Big(1+2\frac{m^{2}_{W}}{m^{2}_{t}}\Big).~~ \tag {4} $$ Here $\alpha_{\rm e}$ and $G_{\rm F}$ are the fine structure constant and the Fermi coupling constant, $m_{t}$ and $m_{W}$ are the masses of the top quark and electroweak gauge boson $W$, respectively. In the above equations we have neglected the masses of the quarks $q$ and $b$. The decays $\bar{B}\rightarrow X_{D}\gamma$ with $D=d$ and $s$ quarks are the theoretically clean and interesting FCNC processes, which are mainly contributed by the processes $b\rightarrow D\gamma$ at the partonic level. The $b\rightarrow D\gamma$ processes can be expressed by the effective Lagrangian[9] $$ \mathcal{L}_{\rm eff}=-\frac{4G_{\rm F}}{\sqrt{2}}V_{tD}^{\ast}V_{tb} \Big[\sum\limits_{i=1}^8C_{i}Q_{i} +k_{D}\sum\limits_{i=1}^2C_{i}(Q_{i}-Q^{u}_{i})\Big].~~ \tag {5} $$ The Cabibbo–Kabayashi–Maskawa matrix element ratio $k_{D}=(V^{\ast}_{uD}V_{ub})/(V^{\ast}_{tD}V_{tb})$ is small for $D=s$, and it is not this case for $D=d$. $C_{i}$ are the Wilson coefficients (WCs), $Q_{i=1-6}$ are the general effective four fermion operators. The dipole operators $Q_{7}$ and $Q_{8}$ are given by $$\begin{align} Q_{7}=\frac{e}{16\pi^{2}}m_{b}(\bar{D}_{\rm L}\sigma^{\mu\nu}b_{\rm R})F_{\mu\nu},~~ \tag {6} \end{align} $$ $$\begin{align} Q_{8}=\frac{g_{s}}{16\pi^{2}}m_{b}(\bar{D}_{\rm L}\sigma^{\mu\nu}T^{a}b_{\rm R})G^{a}_{\mu\nu}.~~ \tag {7} \end{align} $$ The anomalous $tq\gamma$ couplings given by Eq. (1) can contribute to the FCNC processes $b\rightarrow D\gamma$ via two $\gamma $-penguin diagrams, one of which is proportional to $V^{\ast}_{qD}V_{tb}$ and the other is proportional to $V^{\ast}_{tD}V_{qb}$. Since $|V^{\ast}_{qD}V_{tb}|\gg |V^{\ast}_{tD}V_{qb}|$ with $q$ being $u$ and $c$ quarks, the dominant contributions come from the diagram proportional to $V^{\ast}_{qD}V_{tb}$, and the contributions from the other diagram can be safely neglected. Furthermore, the anomalous $tq\gamma$ couplings contribute to the processes $b\rightarrow D\gamma$ via two independent chirality-flipped operators $m_{q}\bar{q}_{\rm R}\sigma^{\mu\nu}t_{\rm L}A$ and $m_{t}\bar{q}_{\rm L}\sigma^{\mu\nu}t_{\rm R}A$. Since $m_{t}\gg m_{q}$, we only consider the contributions from $m_{t}\bar{q}_{\rm L}\sigma^{\mu\nu}t_{\rm R}A$. Specifically, the contributions of the $tq\gamma$ couplings to the radiative decays $\bar{B}\rightarrow X_{D}\gamma$ can be expressed as the modified WC $C_{7}$, which can be written as[5] $$\begin{align} C^{tc\gamma}_{7}&(\mu_{W})=\frac{\lambda^{\rm R}_{tc\gamma}m_{t}}{\varLambda} \frac{V^{\ast}_{cs}}{V^{\ast}_{ts}} \Big[-\ln\frac{\mu_{W}}{m_{W}}-\frac{1}{4}\\ &+\frac{1}{2(x_{c}-1)(x_{t}-1)} +\frac{x^{3}_{c}}{2(x_{c}-1)^{2}(x_{c}-x_{t})}\ln x_{c}\\ &+\frac{x^{3}_{t}}{2(x_{t}-1)^{2}(x_{t}-x_{c})}\ln x_{t}\Big]~~ \tag {8} \end{align} $$ for the $b\rightarrow s\gamma$ process, and $$\begin{align} C^{tu\gamma}_{7}&(\mu_{W})=\frac{\lambda^{\rm R}_{tu\gamma}m_{t}}{\varLambda} \frac{V^{\ast}_{ud}}{V^{\ast}_{td}} \Big[-\ln\frac{\mu_{W}}{m_{W}}-\frac{1}{4}\\ &+\frac{1}{2(x_{u}-1)(x_{t}-1)}+\frac{x^{3}_{u}}{2(x_{u}-1)^{2}(x_{u}-x_{t})}\ln x_{u}\\ &+\frac{x^{3}_{t}}{2(x_{t}-1)^{2}(x_{t}-x_{u})}\ln x_{t}\Big]~~ \tag {9} \end{align} $$ for the $b\rightarrow d\gamma$ process. $X_{q}=m^{2}_{q}(\mu_{W})/m^{2}_{W}$. Owing to the $tq\gamma$ couplings that do not bring any new operators, the renormalization group evolution of these WCs from the scale $\mu_{W}$ down to $\mu_{b}$ is just the same as that in the SM. It is necessary to note that, due to $|V_{cs}|>|V_{us}|$ and $|V_{ud}|>|V_{cd}|$, in the above equations we only consider the contributions of the anomalous $tc\gamma$ and $tu\gamma$ couplings to the decays $\bar{B}\rightarrow X_{s}\gamma$ and $\bar{B} \rightarrow X_{d}\gamma$, respectively. The branching ratios of the decays $\bar{B}\rightarrow X_{D}\gamma$ can be generally expressed as[10] $$\begin{align} &Br(\bar{B}\rightarrow X_{D}\gamma)_{E_{\gamma}>E_{0}}\\ ={}& Br(\bar{B}\rightarrow X_{c}e\bar{\nu})_{\exp}\frac{6\alpha_{\rm e}}{\pi C} \Big|\frac{V^{\ast}_{tD}V_{tb}}{V_{cb}}\Big|^{2}[P_{D}(E_{0})+N_{D}(E_{0})],~~ \tag {10} \end{align} $$ where $P_{D}(E_{0})$ and $N_{D}(E_{0})$ denote the perturbative and non-perturbative contributions, respectively. To regularize infrared-radiation divergence, the photon-energy cut $E_{0}$ must not be equal to zero. Considering the resolution of the detector, its value is phenomenologically taken as $1.6$ GeV in the $\bar{B}$–meson rest frame. The factor $C$ is $$\begin{align} C=\Big|\frac{V_{ub}}{V_{cb}}\Big|^{2}\frac{\varGamma(\bar{B}\rightarrow X_{c}e\bar{\nu})}{\varGamma(\bar{B}\rightarrow X_{u}e\bar{\nu})},~~ \tag {11} \end{align} $$ with the experimental value $C_{\exp}=0.568\pm 0.007\pm 0.010$.[11] Including the contributions of the anomalous $tq\gamma$ couplings, Eq. (10) can be simplified to[12] $$\begin{align} Br(\bar{B}\rightarrow X_{D}\gamma)= R\Big|\frac{V^{\ast}_{tD}V_{tb}}{V_{cb}}\Big| [|C_{7D}(\mu_{b})|^{2}+N_{D}(E_{\gamma})]~~ \tag {12} \end{align} $$ with $$\begin{align} C_{7D}(\mu_{b})=C^{\rm SM}_{7D}(\mu_{b})+C^{tq\gamma}_{7}(\mu_{b}).~~ \tag {13} \end{align} $$ The WC $C^{\rm SM}_{7D}(\mu_{b})$ can be determined by the next-next-leading order (NNLO) predictions for the decays $\bar{B}\rightarrow X_{D}\gamma$, while $C^{tq\gamma}_{7}(\mu_{b})=k_{7}C^{tq\gamma}_{7}(\mu_{W})$ with $k_{7}$ being assumed as 0.5696.[12] Then we have $$\begin{align} R&\Big|\frac{V^{\ast}_{tD}V_{tb}}{V_{cb}}\Big|^{2}[|C^{\rm SM}_{7D}(\mu_{b}) +k_{7}C^{tq\gamma}_{7}(\mu_{W})]|^{2}-|C^{\rm SM}_{7D}(\mu_{b})|^{2}] \\={}&Br^{\rm TH}(\bar{B}\rightarrow X_{D}\gamma)-Br^{\rm SM}(\bar{B}\rightarrow X_{D}\gamma).~~ \tag {14} \end{align} $$ In our numerical calculation, we use the recent experimental average values obtained by the HFLAV collaboration[13] for $Br^{\exp}(\bar{B}\rightarrow X_{D}\gamma)$, while the NNLO values of $Br^{\rm SM}(\bar{B}\rightarrow X_{D}\gamma)$ have been given in Ref. [14], which are $$\begin{alignat}{1} &Br^{\exp}(\bar{B}\rightarrow X_{s}\gamma)=(3.32\pm 0.15)\times 10^{-4},~~ \tag {15} \end{alignat} $$ $$\begin{alignat}{1} &Br^{\exp}(\bar{B}\rightarrow X_{d}\gamma)=(0.92\pm 0.30)\times 10^{-5},~~ \tag {16} \end{alignat} $$ $$\begin{alignat}{1} &Br^{\rm SM}(\bar{B}\rightarrow X_{s}\gamma)=(3.36\pm 0.23)\times 10^{-4},~~ \tag {17} \end{alignat} $$ $$\begin{alignat}{1} &Br^{\rm SM}(\bar{B}\rightarrow X_{d}\gamma)=(1.73^{+0.12}_{-0.22})\times 10^{-5},~~ \tag {18} \end{alignat} $$ for the minimum photon energy $E_{\gamma}=E_{0}=1.6$ GeV.
cpl-37-10-101301-fig1.png
Fig. 1. The branching ratios (a) $Br(\bar{B} \rightarrow X_{s}\gamma)$ and (b) $Br(\bar{B} \rightarrow X_{d}\gamma)$ versus the coupling constants $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$ for $\varLambda=1$ TeV.
In Figs. 1(a) and 1(b) we plot the branching ratios $Br (\bar{B}\rightarrow X_{s}\gamma)$ and $Br (\bar{B}\rightarrow X_{d}\gamma)$ contributed by both the SM and $tq\gamma $ couplings versus the coupling constants $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$ in the case of assuming the SM predictions within $1\sigma$ (dashed line) and $2\sigma$ (dotted line) ranges. The red solid lines correspond to the values of $Br^{\rm SM}[\bar{B}\rightarrow X_{d(s)}\gamma]$ taking their cental values. The horizontal solid and dotted lines represent the experimental cental value and deviations from it at $\pm 1\sigma$ error bars, respectively. One can see from Fig. 1 that the constraint from the experimental value of $Br(\bar{B}\rightarrow X_{s}\gamma) $ on the coupling $\lambda^{\rm R}_{tc\gamma}$ is stronger than that for the coupling $\lambda^{\rm R}_{tu\gamma}$ from $Br (\bar{B} \rightarrow X_{d}\gamma) $. If one demands that the theoretical predictions for $Br (\bar{B} \rightarrow X_{s}\gamma)$ and $Br (\bar{B} \rightarrow X_{d}\gamma)$ are consistent with the corresponding experimental values in the $1\sigma$ error range, then the values of $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$ must be in the ranges of $- 0.018 \sim 0.014$ and $-0.024 \sim -0.0001$, respectively, and there are $|\lambda^{\rm R}_{tc\gamma}| \leq 0.018$ and $|\lambda^{\rm R}_{tu\gamma}| \leq 0.024$. The predicted upper limits on $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$ are both lower than those from the recent ATLAS results.[7] Our results for the anomalous $tc\gamma $ coupling are compatible with those from $Br(\bar{B}\rightarrow X_{s}\gamma) $ given in Ref. [5].
Table 1. The SM predictions and current experimental averages of the branching ratios $Br(B\rightarrow V\gamma)$, given in units of $10^{-6}$.
Decay channel SM Experiment
$B^{+}\rightarrow K^{\ast+}\gamma$ $35.1\pm7.8$ $39.2\pm1.3$
$B^{0}\rightarrow K^{\ast}\gamma$ $34.9\pm7.8$ $41.7\pm1.2$
$B_{s}\rightarrow \phi\gamma$ $43.3\pm7.7$ $35.2\pm3.4$
$B^{0}\rightarrow \rho^{0}\gamma$ $0.65\pm0.12$ $0.86^{+0.15}_{-0.14}$
$B^{+}\rightarrow \rho^{+}\gamma$ $1.37\pm0.26$ $0.98^{+0.25}_{-0.24}$
The Anomalous $tq\gamma $ Couplings and the Decays $B \rightarrow V\gamma $. The exclusive decays $B \rightarrow V\gamma $ with $V$ being light vector meson $K^{\ast}, \rho, \omega$ and $\phi $ are the same as the inclusive decays $B \rightarrow X_{D}\gamma $ at partonic level, which can be described by the processes $b \rightarrow D\gamma$. The relevant effective Lagrangian has been given in Eq. (5). Unlike the inclusive decays $B \rightarrow X_{D}\gamma $, which can be calculated perturbatively with high precision, the exclusive decays $B \rightarrow V\gamma $ become complicated due to considerable hadronic uncertainties.[15] However, various technical methods have been developed to study these decay processes and are not reviewed here. The branching ratios of the decays $B \rightarrow V\gamma $ can be generally written as[16] $$\begin{align} Br(B\rightarrow V\gamma)={}&\frac{G^{2}_{\rm F}\alpha_{\rm e}m^{3}_{B}m^{2}_{b}\tau_{B}}{32\pi^{4}}s \Big(1-\frac{m^{2}_{V}}{m^{2}_{B}}\Big)^{3}|V^{\ast}_{tD}V_{tb}|^{2}\\ &\cdot [T^{V}_{1}(0,\mu_{b})]^{2}|C^{t}_{7}(\mu_{b})+k_{D}C^{u}_{7}(\mu_{b})|^{2}\\ ={}&R^{V}_{D}|C^{t}_{7}(\mu_{b})+k_{D}C^{u}_{7}(\mu_{b})|^{2},~~ \tag {19} \end{align} $$ where $\tau_{B}$ is the lifetime of the meson $B$; $m_{B}$, $m_{b}$ and $m_{V}$ are the masses of the mason $B$, bottom quark $b$ and light vector mason $V$, respectively. $T^{V}_{1}(0, \mu_{b})$ is the process dependent form factor at $q^{2}=0$ and the scale $\mu_{b}$. The factor $s=1/2$ for $\rho^{0}$ and $\omega$, while $s=1$ for other light vector mesons. To consider the contributions of the anomalous $tq\gamma$ couplings to the decays $B \rightarrow V\gamma$, we define the relative correction parameter $A^{V}$ as $$\begin{align} A^{V}=\frac{|C^{t}_{7}(\mu_{b})+k_{D}C^{u}_{7}(\mu_{b})|^{2}}{|C^{t,{\rm SM}}_{7}(\mu_{b})+ k_{D}C^{u,{\rm SM}}_{7}(\mu_{b})|^{2}},~~ \tag {20} \end{align} $$ where $C^{i}_{7}(\mu_{b})$ contains the contributions from both the SM and the anomalous $tq\gamma$ couplings. It is obvious that, for the parameter $A^{V}$, most of the high-order corrections and hadronic uncertainties cancel between numerator and denominator, making $A^{V}$ sensitive to new-physics effects. Using the relation $A^{V} \leq Br^{\exp}(B\rightarrow V\gamma) / Br^{\rm SM}(B \rightarrow V\gamma)$, we can obtain the constraints on the anomalous $tq\gamma$ couplings. In our numerical estimation, we will take the values of $Br^{\exp}(B \rightarrow V\gamma)$ as the current experimental averages,[13] which are collected in Table 1. The corresponding SM predictions are also listed in Table 1, which are given in Ref. [17] and references therein. The branching ratio of the decay $B_{s} \rightarrow \phi\gamma$ is the time-integrated $\bar{Br}(B_{s} \rightarrow \phi\gamma)$. Although the SM predictions and experimental measurements for $Br(B \rightarrow V\gamma)$ have not reached the expected precision, they agree with each other at the level of $1\sigma$. Thus we expect that these decay processes can also give constraints on the anomalous $tq\gamma$ couplings. Our numerical results are summarized in Table 2. For comparison, the upper bounds on the couplings $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$ from the recent ATLAS results[7] are also shown. One can see from Table 2 that the experimental measured values of $Br(B \rightarrow V\gamma)$ can indeed give constraints on the coupling constants $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$, which are comparable to those from the decays $B \rightarrow X_{D}\gamma$ and lower than the ATLAS results. The SM predictions and experimental measurements for $Br(B \rightarrow V\gamma)$ in this study and Ref. [5] differ from each other, so our results are slightly different from those given in Ref. [5].
Table 2. Constraints on the couplings $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$ from the decays $B \rightarrow V\gamma$ for $\varLambda=1$ TeV.
Decay channel $|\lambda^{\rm R}_{tc\gamma}|$ $|\lambda^{\rm R}_{tu\gamma}|$
$B^{+}\rightarrow K^{\ast+}\gamma$ $0.0143$
$B^{0}\rightarrow K^{\ast}\gamma$ $0.0209$
$B_{s}\rightarrow \phi\gamma$ $0.0275$
$B^{0}\rightarrow \rho^{0}\gamma$ $0.0103$
$B^{+}\rightarrow \rho^{+}\gamma$ $0.0111$
ATLAS results $0.0902$ $0.0475$
In summary, radiative $B$ meson decay plays an important role in precision of testing the SM and detecting the virtual effects of new physics beyond the SM. We reconsider the impacts of the anomalous $tq\gamma$ couplings on the radiative $B$ meson decays $B \rightarrow X_{d(s)}\gamma$ and $B \rightarrow V\gamma$ in a model-independent way. It is found that the anomalous top couplings $tc\gamma$ and $tu\gamma$ can generate significant contributions to the decays $B \rightarrow X_{s}\gamma[B \rightarrow K^{*}(\phi)\gamma]$ and $B \rightarrow X_{d}\gamma(B \rightarrow \rho\gamma)$, respectively. With the current experimental average values of the branching ratios, the constraints on the couplings $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$ are obtained. The $1\sigma$ upper bounds on $\lambda^{\rm R}_{tc\gamma}$ and $\lambda^{\rm R}_{tu\gamma}$ from the decay $\bar{B} \rightarrow X_{s(d)}\gamma$ are 0.018 and 0.024, respectively. The decays $B \rightarrow V\gamma$ can also generate strict constraints on these couplings, which are comparable to those from the decays $B \rightarrow X_{D}\gamma$. References Rare decays of the top quark in the standard and two-Higgs-doublet modelsFlavour-changing top decays in the aligned two-Higgs-doublet modelProbing flavor-changing top-charm-scalar interactions in e + e − collisionsTop-quark decay via the anomalous coupling t ¯ c γ at hadron collidersNew supersymmetric contributions to t → cV Rare top decays t→cγ, t→cg and CKM unitarityFlavor structure of warped extra dimension modelsOn the flavor structure of the littlest Higgs modelSupersymmetry-induced flavor-changing neutral-current top-quark processes at the CERN Large Hadron ColliderScalar flavor changing neutral currents and rare top quark decays in a two Higgs doublet model “for the top quark”Next-to-Leading-Order QCD Corrections to the Top-Quark Decay via Model-Independent Flavor-Changing Neutral-Current CouplingsSM Higgs boson and t → c Z decays in the 2HDM type III with C P violation$t \rightarrow cg$ and $t \rightarrow cZ$ in universal extra-dimensional modelsSearch for anomalous single top quark production in association with a photon in pp collisions at s = 8 $$ \sqrt{s}=8 $$ TeVAnomalous couplings of the third generation in rare B decaysCP violation in B→ργ decay with anomalous right-handed top quark couplingsDeciphering top flavor violation at the CERN LHC with B factoriesImplications of the anomalous top quark couplings in B s − B ¯ s mixing, B → X s γ and top quark decays B ¯ → X s γ constraints on the top quark anomalous t → c γ couplingAnomalous tqγ coupling effects in exclusive radiative B-meson decaysAnomalous tqZ coupling effects in rare B- and K-meson decaysConstraints on anomalous tcZ coupling from $ \overline{\mathrm{B}}\to {{\overline{\mathrm{K}}}^{*}}{\mu^{+}}{\mu^{-}} $ and B s →μ + μ − decaysTop-quark flavor-changing tqZ couplings and rare $$\Delta F=1$$ processesFlavor signatures of complex anomalous tcZ couplingsSearch for flavour-changing neutral currents in processes with one top quark and a photon using 81 fb−1 of pp collisions at s = 13 TeV with the ATLAS experimentTop-quark physics at the LHCA minimal set of top anomalous couplingsWeak decays beyond leading logarithmsWeak radiative B-meson decay beyond leading logarithmsTwo Higgs doublet model predictions for B ¯ → X s γ in NLO QCDQuark mass effects inUntagged CP asymmetry as a probe for new physicsNNLO QCD corrections to the matrix elements using interpolation inFactorization at subleading power and irreducible uncertainties in $ \bar{B} \to {X_s}\gamma $ decayPrecision Determination of the Cabibbo-Kobayashi-Maskawa Element V c b The impact of flavour changing neutral gauge bosons on $ \bar{B} \to {X_s}\gamma $ B → X d γ and constraints on new physicsAverages of $b$-hadron, $c$-hadron, and $τ$-lepton properties as of 2018Updated Next-to-Next-to-Leading-Order QCD Predictions for the Weak Radiative B -Meson DecaysTowards $$ \overline{B}\to {X}_s\gamma $$ at the NNLO in QCD without interpolation in mcRadiative and Electroweak Penguin Decays of B MesonsExclusive radiative and electroweak $b\to d$ and $b\to s$ penguin decays at NLO B → V γ beyond QCD factorizationConstraints on new physics from radiative B decaysRare B-meson decays at the crossroads
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