Eur. Phys. J. C (2017) 77:344 DOI 10.1140/epjc/s10052-017-4888-4 Regular Article - Theoretical Physics New physics effects in charm meson decays involving → + −( ∓ ± ) c ul l li l j transitions Suchismita Sahoo, Rukmani Mohantaa School of Physics, University of Hyderabad, Hyderabad 500046, India Received: 18 January 2017 / Accepted: 5 May 2017 © The Author(s) 2017. This article is an open access publication Abstract We study the effect of the scalar leptoquark and these branching fractions, the so-called R(D(∗)), defined as (∗) ¯ (∗) ¯ (∗) Z boson on the rare decays of the D mesons involving R(D ) = BR(B → D τντ )/BR(B → D lνl ), where → + −( ∓ ± ) = ,μ . σ flavour changing transitions c ul l li l j . We con- l e , exceed the SM prediction by 3 5 [6], thus opening strain the new physics parameter space using the branching an excellent window to search for new physics (NP) in the ratio of the rare decay mode D0 → μ+μ− and the D0 − D¯ 0 up quark sector. oscillation data. We compute the branching ratios, forward– Mixing between a neutral meson and its anti-meson with a backward asymmetry parameters and flat terms in D+(0) → specific flavour provides an useful tool to deal with problems π +(0)μ+μ− processes using the constrained parameters. The in flavour sector. For example, in the past the K 0 − K¯ 0 and branching ratios of the lepton flavour violating D meson B0 − B¯ 0 oscillations, involving mesons made of up- and decays, such as D0 → μe,τe and D+(0) → π +(0)μ−e+ down-type quarks, have provided information as regards the are also investigated. charm and top quark mass scale, much before the discovery of these particles in the collider. On the other hand, the D0 − 1 Introduction D¯ 0 system involves mesons with up-type quarks and in the SM the mixing rate is sufficiently small, so that the new The rare B and D meson decay processes driven by a flavour physics component might play an important role in this case. changing neutral current (FCNC) transitions constitute a sub- The mixing parameters required to describe the D0 − D¯ 0 ject of great interest in the area of electroweak interactions mixing are defined by x = M/ and y = /2, where and provide an excellent testing ground to look for new M () is the mass (width) difference between the mass physics beyond the standard model (SM). The FCNC decays eigenstates. are highly suppressed in the SM and occur only at one-loop In this paper, we focus on the analysis of rare charm meson + − ∓ ± level. Of particular interest among the FCNC decays are the decays induced by c → uμ μ and c → uμ e FCNC rare semileptonic B meson decays involving the transitions transitions. We calculate the branching ratios, forward– b → sl+l−, where several anomalies at the level of few backward asymmetry parameters and the flat terms in +( ) +( ) + − sigma have been observed recently in the LHCb experiment D 0 → π 0 μ μ processes both in the scalar lep- [1–4]. To complement these results, efforts should also be toquark (LQ) and the generic Z model. These processes made towards the search for new physics signal in the up suffer from resonance background through c → uM → + − () quark sector, mainly in the rare charm meson decays involv- ul l , where M denotes η (pseudoscalar), ρ,φ,ω(vector) ing c → ul+l− quark level transitions. Recently the LHCb mesons. However, to reduce the background coming from experiment has searched for the branching ratio of the lep- these resonances, we work in the low and high q2 regimes, ton flavour violating (LFV) D0 → μ∓e ± decays and put i.e., q2 ∈[0.0625, 0.275] GeV2 and q2 ∈[1.56, 4.00] GeV2, the limit as BR(D0 → μ∓e ± )<1.3 × 10−8 [5] at 90% which lie outside the mass square range of the resonant confidence level (CL). On the other hand, both the Belle and mesons. We also compute the branching ratios of lepton +( ) +( ) − + the BaBar experiments have reported significant deviations flavour violating D0 → μe,τe and D 0 → π 0 μ e ¯ (∗) on the measured branching fractions of B → D τντ pro- processes. These LFV processes have negligible contribu- cesses from the corresponding SM predictions. The ratio of tions from the SM, as they proceed through the box diagrams with tiny neutrino masses in the loop. However, they can a e-mail: [email protected] occur at tree level in the LQ and Z models and are expected 123 344 Page 2 of 16 Eur. Phys. J. C (2017) 77:344 to have significantly large branching ratios. Leptoquarks transitions can be investigated well theoretically. The change are hypothetical colour triplet bosonic particles, which cou- in charm quantum number for rare FCNC charm meson ple to quarks and leptons simultaneously and contain both decays is either of two units or one unit, and hence, they baryon and lepton quantum numbers. It is interesting to study involve either C = 2orC = 1 transitions. The D0 − D¯ 0 flavour physics with leptoquarks as they allow quark–lepton mixing takes place via a C = 2 transition and the decay transitions at tree level, thus explaining several observed processes with C = 1 transitions are c → ul+l− and anomalies, e.g., the lepton non-universality (LNU) parameter c → uγ . | = ( → μ+μ−)/ ( → + −) RK q2∈[1,6] GeV2 BR B K BR B Ke e If we integrate out the heavy degrees of freedom associated in rare B decays. The existence of the scalar leptoquark is with the new interactions at a scale M, an effective Hamilto- predicted in the extended SM theories, such as grand unified nian in the form of a series of operators of increasing dimen- theory [7–11], the Pati–Salam model, the extended techni- sions can be obtained. However, the operators of dimension colour model [12,13] and the composite model [14]. In this d = 6 have important contributions to charm meson decays work, we consider the model which conserves baryon and or mixing. In general, one can write the complete basis of lepton numbers and does not allow proton decay. Here we these effective operators in terms of chiral quark fields for would like to see how this model affects the leptonic and both D0 − D¯ 0 mixing and the process D0 → l+l− as [52,53] semieptonic decays of the D0 meson induced by c → ul+l− |H| = (μ) | | (μ), transitions. The phenomenology of scalar leptoquarks and f i G Ci f Qi i (1) their implications to the B and D sector has been extensively i=1 studied in the literature [15–51]. where G has inverse-mass squared dimensions, Ci are the The Z boson is a colour singlet vector gauge boson and it Wilson coefficients.1 is electrically neutral in nature. By adding an additional U(1) The effective operators for D0 − D¯ 0 mixing at the heavy gauge symmetry, the new Z gauge boson could be naturally mass scale M are given by [52,53] derived from the extension of electroweak symmetry of the = ( γ )( γ μ ), = ( σ )( σ μν ), SM, such as superstring theories, grand unified theories and Q1 uL μcL uL cL Q5 u R μνcL u R cL μ μ theories with large extra dimensions. The processes mediated Q2 = (uL γμcL )(u Rγ cR), Q6 = (u RγμcR)(u Rγ cR), via c → u FCNC transitions could be induced by the generic Q3 = (uL cR)(u RcL ), Q7 = (uL cR)(uL cR), Z model at tree level. The theoretical framework of the heavy = ( )( ), = ( σ )( σ μν ), new Z gauge boson has been studied in the literature [52, Q4 u RcL u RcL Q8 uL μνcR uL cR 53,56,57]. In this paper, we investigate the Z contribution (2) to the rare D0 meson decay processes within the parameter + − q ( ) = L(R)q space constrained by D0 − D¯ 0 mixing and D0 → μ μ where L R are the chiral quark fields with L(R) = ( ∓γ )/ processes. 1 5 2 as the projection operators. The paper is organized as follows. In Sect. 2, we discuss In the standard model, the effective weak Hamiltonian for c → u μ = m the effective Hamiltonian describing C = 1 transitions the transitions at the scale c can be written as i.e., c → ul+l−, and C = 2 transition, which is respon- the sum of three contributions [49,54,55], 0 − ¯ 0 d s peng sible for D D mixing. The new physics contribution to Heff = λd H + λsH + λbH , (3) c → u transitions and the constraint on leptoquark couplings ∗ 0 ¯ 0 0 + − λ = from the D − D oscillation and the process D → μ μ where q VuqVcq is the product of Cabibbo–Kobayashi– are discussed in Sect. 3. We calculate the constraint on Z Maskawa (CKM) matrix elements. The explicit form of peng + − couplings from D0 − D¯ 0 mixing and leptonic D0 → μ+μ− H , which basically is responsible for the c → ul l decays in Sect. 4. In Sect. 5, we compute the branching ratios, transition is given by ⎛ ⎞ forward–backward asymmetry parameters and the flat terms +(0) → π +(0)μ+μ− 4G F of the process D in both these mod- Hpeng =− √ ⎝ C O + C O ⎠ , +(0) → π +(0)μ− + i i i i els. The lepton flavour violating D e and 2 i=3,...10,S,P i=7,...10,S,P D0 → μe,τe processes are discussed in Sects. 6 and 7. (4) Finally we summarize our findings in Sect.