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Journal of the Korean Physical Society, Vol. 60, No. 7, April 2012, pp. 993∼999 A Like-sign Dimuon Charge Asymmetry at Tevatron Induced by Anomalous Top Quark Couplings Jong Phil Lee Department of Physics and IPAP, Yonsei University, Seoul 120-749, Korea and Division of Quantum Phases & Devices, School of Physics, Konkuk University, Seoul 143-701, Korea Kang Young Lee∗ Division of Quantum Phases & Devices, School of Physics, Konkuk University, Seoul 143-701, Korea (Received 13 December 2011, in final form 15 February 2012) We show that the recently measured 3.9 σ deviations of the charge asymmetry of like-sign dimuon events from the standard model prediction by the D0 collaboration at Tevatron can be explained by introducing the anomalous right-handed top quark couplings. A combined analysis with the Bs − B̄s and the Bd − B̄d mixings, B → Xs γ decays and the time-dependent CP asymmetry in B → φK decays has been performed. The anomalous tsW couplings are preferred to explain the dimuon charge asymmetry together with other CP violating observables. PACS numbers: 12.90.+b, 13.20.He, 14.65.Ha Keywords: Dimuon charge asymmetry, CP violation, Bs mixing DOI: 10.3938/jkps.60.993 as more data are analyzed. If the deviation is confirmed with other experiments, it would indicate the existence of new physics beyond the SM. Many works are devoted to explaining the D0 dimuon asymmetry in and beyond the SM [2]. Although the charged currents are purely left-handed in the SM, the existence of right-handed charged currents is predicted in many new physics models beyond the SM. For instance, the variant SU(2)L ×SU(2)R ×U(1) model [3] and a dynamical electroweak symmetry breaking model [4] predict additional right-handed currents and some modification of the left-handed currents. In this work, we study the effects of anomalous right-handed top quark couplings on the D0 like-sign dimuon charge asymmetry. We introduce additional right-handed top quark couplings without specifying the underlying model and assume no effects of new particles and additional neutral currents interactions. The impacts of the anomalous top quark couplings have been studied in flavour physics and at colliders [5–7]. Here, we consider the anomalous top quark couplings and show that the measurement of the Absl can be explained by the anomalous tsW coupling, with accommodation of present data for Br(B → Xs γ), ∆Ms , ∆Md , and CP asymmetry in B → φK decays at 2-σ level. This paper is organized as follows. In Section II, we present the formalism for the dimuon charge asymmetry and neutral B meson system. In Section III, we present the contribution of the anomalous top quark couplings to I. INTRODUCTION Recently, the D0 collaboration has measured the CP violating like-sign dimuon charge asymmetry for b hadrons, defined as Absl ≡ Nb++ − Nb−− , Nb++ + Nb−− (1) of which value is reported to be [1] Absl = (−0.957 ± 0.172 (stat.) ± 0.093 (syst.))% (2) −1 of pp̄ data at for √ an integrated luminosity of 9.0 fb s = 1.96 TeV at Tevatron. In the definition of Eq. (1), Nb++ and Nb−− are the numbers of events where two b hadrons semileptonically decay into muons with charges of the same sign. Since the b quarks are produced as bb̄ pairs from pp̄ collisions at Tevatron, the like-sign dimuon events arises from a direct semileptonic decay of one of b hadrons and a semileptonic decay of the other b hadron following the B 0 − B̄ 0 oscillation. In the standard model (SM), the source of the CP violation in the neutral Bq0 system is the phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements involved in the box diagram. The D0 measurement of Eq. (2) shows a deviation of 3.9 −4 . The σ from the SM prediction, Absl = (−2.3+0.5 −0.6 ) × 10 measured value of Eq. (2) is improved again by more data ∗ E-mail: kylee14214@gmail.com -993- -994- Journal of the Korean Physical Society, Vol. 60, No. 7, April 2012 B → Xs γ, B − B̄ mixings, and B → φK decays to obtain the possible parameter sets. In Section IV, we discuss the dimuon charge symmetry with the anomalous top quark couplings and future experiments. Finally we conclude in Section V. At the Tevatron experiment, both decays of Bd and Bs mesons contribute to the asymmetry. Assuming that Γ(Bd0 → µ+ X) = Γ(Bs0 → µ+ X) to a very good approximation, the like-sign dimuon charge asymmetry can be expressed in terms of aqsl as [8] Absl = II. DIMUON CHARGE ASYMMETRY IN THE NEUTRAL B MESON SYSTEM Since the like-sign dimuon events following bb̄ production arise through the B − B̄ oscillation, the dimuon charge asymmetry can be described in terms of the parameters of the B − B̄ mixings. The neutral B meson system is described by the Schrödinger equation  


i d Bq (t) Bq (t) , (3) = M− Γ i B̄q (t) dt B̄q (t) 2 where M is the mass matrix and Γ is the decay matrix with q = d, s. The ∆B = 2 transition amplitudes, q ∆B=2 |B̄q0  = M12 , Bq0 |Heff (4) lead to the following mass difference between the heavy and the light states of the B meson, q MH ∆Mq ≡ B MH q − MLq = q 2|M12 |, (5) B ML q and are the mass eigenvalues for the where heavy and the light eigenstates, respectively. The total decay width difference of the mass eigenstates is defined by ∆Γq ≡ ΓqL − ΓqH = 2|Γq12 | cos φq , = Γ(bb̄ → µ+ µ+ X) − Γ(bb̄ → µ− µ− X) Γ(bb̄ → µ+ µ+ X) + Γ(bb̄ → µ− µ− X) − − + Γ+ RS ΓW S − ΓRS ΓW S − , − + Γ+ RS ΓW S + ΓRS ΓW S (7) in which ΓRS denotes the direct semileptonic decay rate in the right-sign process and ΓW S the decay in the wrong-sign process, implying the semileptonic decay rate of the Bq0 (B̄q0 ) meson following the Bq0 − B̄q0 oscillation. The dimuon asymmetry implies CP violation in the B system. The asymmetry of dimuon events is derived from the charge asymmetry of semileptonic decays of neutral Bq0 mesons, with aqsl defined as aqsl ≡ Γ(B̄q0 (t) → µ+ X) − Γ(Bq0 (t) → µ− X) . Γ(B̄q0 (t) → µ+ X) + Γ(Bq0 (t) → µ− X) (9) where fq are the production fractions of Bq mesons, and Zq = 1/(1 − yq2 ) − 1/(1 + x2q ) with yq = ∆Γq /(2Γq ), xq = ∆Mq /Γq . These parameters are measured to be fd = 0.323±0.037, fs = 0.118±0.015, xd = 0.774±0.008, xs = 26.2±0.5, and yd = 0, ys = 0.046±0.027 [9]. With these values, Eq. (10) is rewritten as Absl = (0.506 ± 0.043)adsl + (0.494 ± 0.043)assl . (10) The charge asymmetry for wrong charge semileptonic decay in Eq. (9) is expressed as aqsl = ∆Γq |Γq12 | tan φq , q sin φq = |M12 | ∆Mq (11) for which the SM predictions are given by [10] −4 adsl = (−4.8+1.0 , −1.2 ) × 10 assl = (2.1 ± 0.6) × 10−5 . (12) In the SM, ∆Γd /Γd is less than 1% while ∆Γs /Γs ∼ 10% is rather large. The decay matrix element Γq12 is obtained from the tree level decays b → cc̄q. Since the anomalous top couplings affect Γq12 through loops only, we ignore the new physics effects on Γq12 in this work. (6) where the decay widths ΓL and ΓH correspond to the physical eigenstates BL and BH , respectively, and the q /Γq12 ). CP phase is φq ≡ arg (−M12 The like-sign dimuon events consist of a right-sign (RS) process and a wrong-sign (WS) process, Absl ≡   1 fd Zd adsl + fs Zs assl , fd Zd + fs Zs (8) III. ANOMALOUS TOP QUARK COUPLINGS AND B PHYSICS In this paper, we work with an effective Lagrangian in a model independent way to parameterize the new physics effects. After fixing the phases of quarks so that VtqSM are the CKM matrix elements of the SM, we introq q duce the new tqW couplings gL and gR to redefine the effective CKM matrix elements and right-handed couplings:  g  L = −√ VtqSM t̄γ µ PL qWµ+ 2 q=b,s,d  q q +t̄γ µ (gL PL + gR PR )qWµ+ + H.c. g  = −√ Vtqeff t̄γ µ (PL + ξq PR )qWµ+ + H.c., 2 q=b,s,d (13) q gL ), q VtqSM gR . where Vtqeff = VtqSM (1 + and Vtqeff ξq = Since q q we set gL and gR to be complex, Vtqeff and ξq involve new phases and will predict new CP violating processes in B physics. For simplicity, we assume that only one of A Llike-sign Dimuon Charge Asymmetry at Tevatron Induced · · · – Jong Phil Lee and Kang Young Lee the anomalous tsW or tbW couplings is nonzero in this analysis. Then, the other CKM matrix elements are the same as those in the SM, and the phases of quarks are fixed with them. The matrix elements of the third row of the CKM matrix have not been directly measured yet, but just indirectly constrained by loop-induced processes and the unitarity of the CKM matrix. In our framework, the constraints should be applied to the effective CKM matrix elements Vtqeff instead of VtqSM . The additional Vtqeff ξq terms measure the anomalous right-handed top couplings. 1. B → Xs γ Decays Contributions of the right-handed top quark couplings to the penguin diagram for b → s transition are enhanced by a factor of mt /mb . Thus, the radiative B → Xs γ decays are sensitive to the anomalous right-handed tbW and tsW couplings and provide strong constraints on Br(B → Xs γ) = Br SM  ∗ |Vtseff Vtbeff | 0.0404 = q,SM M12  them while the anomalous tdW coupling is irrelevant in this analysis. The ∆B = 1 effective Hamiltonian for the B → Xs γ process with the right-handed couplings is given by 8  4GF ∗ ∆B=1 √ (Ci (µ)Oi (µ) V = − Hef V tb ts f 2 i=1 +Ci′ (µ)Oi′ (µ)) , (14) where the dimension 6 operators Oi are given in Ref. [11], and Oi′ are their chiral conjugate operators. The SM Wilson coefficients are shifted by C7 (mW ) = F (xt ) + ξb (mt /mb )FR (xt ) and C8 (mW ) = G(xt ) + ξb (mt /mb )GR (xt ) while the new Wilson coefficients are formed as C7′ (mW ) = ξs (mt /mb )FR (xt ) and C8′ (mW ) = ξs (mt /mb )GR (xt ) in the leading order of ξq . The InamiLim loop functions F (x) and G(x) are given in Refs. [11, 12], and the new loop functions FR (x) and GR (x) can be found in Refs. 5, 6, and 13. The branching ratio of the B → Xs γ decays including ξs and ξb effects is given by 2  
GR (xt ) mt FR (xt ) + 0.07 (B → Xs γ) 1 + Re(ξb ) 0.68 mb F (xt ) G(xt ) 
G2 (xt ) FR (xt )GR (xt ) m2 F 2 (xt ) +(|ξb |2 + |ξs |2 ) t2 0.112 R2 + 0.002 R2 + 0.025 , (15) mb F (xt ) G (xt ) F (xt )G(xt ) where the numerical values are obtained by using the RG evolution in Ref. 14. The SM prediction for the branching ratio is given by Br(B → Xs γ) = (3.15 ± 0.23) ×10−4 [15] and the current world average value of the measured branching ratio given by Br(B → Xs γ) −4 [16] for the photon = (3.55 ± 0.24+0.09 −0.10 ± 0.03) × 10 energy cut Eγ > 1.6 GeV. q M12 -995- ∗ Vtqeff Vtbeff ∗ VtqSM VtbSM 2  S3 (xt ) 1+ S0 (xt )  2. B − B̄ Mixings q The transition amplitude M12 for Bq − B̄q mixing is obtained from the box diagrams in the SM. In our model, the top quark couplings in the box diagram are modified to include the right-handed couplings. Since the loop integral including an odd number of right-handed couplings vanishes, the leading contribution of ξq to M12 is s,d as of quadratic order. We write M12 ξq2 B̄q0 |(b̄PR q)(b̄PR q)|Bq0  4 B̄q0 |(b̄γ µ PL q)(b̄γµ PL q)|Bs0  ξb∗ 2 B̄q0 |(b̄PL q)(b̄PL q)|Bq0  ξ ∗ ξq B̄q0 |(b̄PL q)(b̄PR q)|Bq0  + + b 2 B̄q0 |(b̄γ µ PL q)(b̄γµ PL q)|Bs0  4 B̄q0 |(b̄γ µ PL q)(b̄γµ PL q)|Bq0  where the Inami-Lim loop functions for new box diagrams are given by 
2 1+x S3 (x) = 4x2 + log x , (17) (1 − x)2 (1 − x)3  , (16) and the SM loop function S0 (x) can be found elsewhere [11,12]. We let the CKM matrix elements in the SM be ∗ ∗ VtsSM VtbSM = 0.404 and VtdSM VtbSM = 0.0082ei2β , where β is the weak phase of the CKM matrix. The hadronic -996- Journal of the Korean Physical Society, Vol. 60, No. 7, April 2012 matrix elements for the four-quark operators are param- B̄q0 |(b̄γ µ PL q)(b̄γµ PL q)|Bq0  = B̄q0 |(b̄PL q)(b̄PL q)|Bq0  = B̄q0 |(b̄PL q)(b̄PR q)|Bq0  = eterized as [17] 8 2 f B̂B m2 , 3 B q q Bq B̄q0 |(b̄PR q)(b̄PR q)|Bq0  7 2 2 mq f m , 3 B q Bq mb 5 = − fB2 q B̂Bq m2Bq 3
mB q mb + mq 2 , (18) where B̂Bq is the Bag parameter and fB2 q the decay constant. The SM predictions for the mass differences are ∆Md = 0.53 ± 0.02 ps−1 and ∆Ms = 19.30 ± 6.74 ± 0.07 ps−1 [10]. The measurements are ∆Md = 0.509 ± 0.006 ps−1 [16] and ∆Ms = 17.77 ± 0.10 ± 0.07 ps−1 [10]. 3. CP Asymmetries in B → φK Decays The b → ss̄s transition responsible for the B → φK decays arises at the one-loop level in the SM, where the gluon penguin contribution dominates. Since VtsSM involves no complex phase to leading order in the SM, the weak phase sin 2β measured in B → φK decays should agree with that measured in B → J/ψK decays, and the direct CP asymmetry of B → φK decays should vanish up to small pollution. The decay amplitude of B → φK decays with anomalous top couplings are given in Ref. 6. We define the parameter λ as λ= d ∗ Ā M12 , d A M12 (19) d where A = A(B 0 → φK 0 ), Ā = A(B̄ 0 → φK̄ 0 ) and M12 is given in Eq. (18). The time-dependent CP asymmetry in B → φK decays is written in terms of λ as Γ(B̄ 0 (t) → φK̄ 0 ) − Γ(B 0 (t) → φK 0 ) , Γ(B̄ 0 (t) → φK̄ 0 ) + Γ(B 0 (t) → φK 0 ) (20) = SφK sin ∆mB t − CφK cos ∆mB t, aφK (t) ≡ Fig. 1. (Color online) Allowed parameters (|ξs |, |Vtseff |) under the B physics constraints and D0 dimuon asymmetry. The whole band of the green (grey) + black + yellow (light grey) regions is allowed by Br(B → Xs γ) only. The green (grey) + black regions are allowed by Br(B → Xs γ) and ∆Ms . The black region is allowed by both constraints of Br(B → Xs γ) and ∆Ms , and satisfies Absl measured by D0. The red (dark grey) dots denote points additionally allowed by CP asymmetries in B → φK decays. The confidence level is at 95% C.L. IV. RESULTS where the coefficients 2Imλ , 1 + |λ|2 1 − |λ|2 = −AφK , = 1 + |λ|2 SφK = CφK (21) are measured in the Belle and BaBar. The average values of the measurements are −ηSφK = 0.44+0.17 −0.18 , and CφK = −0.23 ± 0.15 [16]. First, we consider the nonzero anomalous tsW couplings. The Bd − B̄d mixing is not affected in this case, and we get constraints on the tsW couplings from B → Xs γ decays, ∆Ms , and CP asymmetry in B → φK decays. Figure 1 shows the allowed parameters of |ξs | and |Vtseff | at the 95% C.L. In the B → Xs γ decays of Eq. (17), the contribution of the right-handed couplings involves the enhancement factor mt /mb and leads to a substantial change in the amplitude. Since the measure- A Llike-sign Dimuon Charge Asymmetry at Tevatron Induced · · · – Jong Phil Lee and Kang Young Lee Fig. 2. (Color online) Allowed parameters (ReVtseff , ImVtseff ) under the B physics constraints and D0 dimuon asymmetry. The whole circle of the yellow (light grey) + green (grey) + black regions is allowed by Br(B → Xs γ) only, the ring shape of the green (grey) + black regions allowed by Br(B → Xs γ) and ∆Ms . The black regions allowed by both constraints of Br(B → Xs γ) and ∆Ms , and satisfies Absl measured by D0. The red (dark grey) dots denote points additionally allowed by CP asymmetries in B → φK decays. The confidence level is at 95% C.L. ments of Br(B → Xs γ) agree with the SM predictions, a substantial change in the amplitude due to ξs should be compensated for by a large shift of Vtseff , as we can see in s Fig. 1. On the other hand, the contribution of ξs to M12 s does not involve such an enhancement factor, and M12 is governed merely by Vtseff . The like-sign dimuon charge s . Thus we find that asymmetry is affected through M12 b the deviation of Asl from the SM value leads to a deviation of Vtseff and to a nonzero ξs . Finally, these values satisfy the CP asymmetry in B → φK decays in most region. We have allowed values of Vtseff and ξs 0.01 < |ξs | < 0.03, 0.022 < |Vtseff | < 0.029, (22) from all experimental constraints. We find our results show a sizable deviation from the value of |Vts | = 0.0403 for a global fit of the unitary triangle in the SM [9]. Note that this result does not mean that the CKM unitarity is violated but that an “effective” parameter Vtseff extracted from Bs − B̄s mixing looks different from the SM value. We show the allowed region of the complex parameter Vtseff at the 95% C.L. in Fig. 2. The sizable phase eff eff < 22◦ and 194◦ < θts < 202◦ , is predicted, 14◦ < θts b from the measured Asl value in this plot while it is very small, ∼2◦ , in the SM. Note that this phase is essential to explain the dimuon charge asymmetry. Since new -997- Fig. 3. (Color online) Allowed parameters (|ξb |, |Vtbeff |) under the B physics constraints and D0 dimuon asymmetry. The whole band of the black + green (grey) + yellow (light grey) regions is allowed by Br(B → Xs γ) only. The black + green (grey) regions are allowed by Br(B → Xs γ), ∆Ms and ∆Md . The black region is allowed by all constraints of Br(B → Xs γ), ∆Ms , ∆Md , SφK , CφK , and satisfies Absl measured by D0. The confidence level is at 95% C.L. effects on Γq12 have been ignored in this work, our CP eff , comes only from the Bs − B̄s mixphase, φs = −2θts ing. Our results are consistent with the 2010 results, +59 ◦ ◦ φs (CDF) = (−29+44 −49 ) [18] and φs (D0) = (−44−51 ) [19], from Bs → J/ψφ decays and with the recent best-fit ◦ value φs = (−52+32 −25 ) at 2-σ level [20]. Such agreements are understood by that all observed CP asymmetries at present in the Bs system can be explained by the indirect CP violation through modified Bs − B̄s mixing. In our case, the modified Bs mixing is due to Vtseff . Considering the anomalous tbW couplings to explain Absl , we have constraints from B → Xs γ decay, ∆Ms , ∆Mb , and the CP asymmetry in B → φK decays. In Fig. 3, we show the allowed parameters of |ξb | and |Vtbeff | at the 95% C.L. In this case, the SM value of |Vtbeff | = 1 is still consistent with the dimuon charge asymmetry. Instead, we require a new phase of Vtbeff to explain the Absl shown in Fig. 4, although Vtb is real in the SM. We used the SM value of the CP violating phase = −0.091+0.026 φSM −0.038 [10]. Figure 4 allows the phase and gle ranges −66o < θtb < −21o and 114o < θtb < 159o at 95% C.L. The CP phase of the Bd system is described by the weak phase sin 2βeff = sin 2(β + θtb ), which is precisely measured in B → J/ψKs decays to be sin 2βeff = 0.676 ± 0.020 [16], which agrees with the SM predictions very well. This implies that the large -998- Journal of the Korean Physical Society, Vol. 60, No. 7, April 2012 Fig. 4. (Color online) Allowed parameters (ReVtbeff , ImVtbeff ) constraints and D0 dimuon asymmetry. The whole circle of the yellow (light grey) + green (grey) + magenta (dark grey) + black regions is allowed by Br(B → Xs γ) only. The thick ring of the green (grey) + magenta (dark grey) + black regions allowed by Br(B → Xs γ) and ∆Ms , and the thin ring of the magenta (dark grey) + black regions allowed by Br(B → Xs γ), ∆Ms , and ∆Md . The black region is allowed by all constraints of Br(B → Xs γ), ∆Ms , ∆Md , SφK , CφK , and satisfies Absl measured by D0. The confidence level is at 95% C.L. additional phase of Vtb is not consistent with the measured sin 2β. Such disagreement implies that the dimuon charge asymmetry and the B → J/ψK decay are hardly explained simultaneously only with the modification of Vtbeff . The anomalous tdW coupling contributes to only the Bd − B̄d mixing and to only adsl . As in the case of the tbW couplings, the additional phase of Vtd is constrained by the measured sin 2βeff = sin 2(β − θtd ), where θtd is the additional phase of Vtd . Thus, adsl cannot be changed much as the anomalous tdW coupling varies due to strong ∆Md constraint. s Since the anomalous tsW couplings contribute to M12 d s and not to M12 , only asl is shifted as ξs varies. Means d and M12 are affected by the anomawhile, both M12 lous tbW couplings, and both assl and adsl are modified as ξb varies. Finally, only adsl are modified but negligible, as ξd varies. We show the variations of assl and absl in Fig. 5 with the allowed parameter sets of (ξs , Vtseff ) and (ξb , Vtbeff ) given in Figs. 1 – 4. Thuss we conclude that the dimuon charge asymmetry favors anomalous tsW couplings rather than tbW and tdW couplings. Fig. 5. The thick black lines are our predictions of adsl and assl varying the anomalous tbW and tsW couplings with the measurements of Absl (inclined band) by D0 [1], adsl (vertical band) at B factory [16] and assl (horizontal band) by D0 [21]. The crossing point of thick lines denotes the SM prediction. The 1 − σ error bands are shown. V. CONCLUDING REMARKS We have studied the effects of the anomalous tqW couplings to explain the recently measured deviation of likesign dimuon charge asymmetry at Tevatron. Our new complex couplings are able to explain the D0 dimuon charge asymmetry at the 95% C.L. under constraints from the precisely measured Br(B → Xs γ), ∆Md , ∆Ms , SφK , and CφK data. However, the additional phase of Vtbeff is not consistent with the CP violation in the B → J/ψK decay while the anomalous tsW couplings agree with those in the B → J/ψφ decays at 2-σ level. The effect of the anomalous tdW coupling is very small due to strong constraints on sin 2β in the B → J/ψK decay and ∆Md . We conclude that the dimuon charge asymmetry favors a new top coupling in Bs − B̄s mixing rather than in Bd − B̄d mixing, and we show that the anomalous tsW couplings satisfy the constraints of B physics. ACKNOWLEDGMENTS This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education, Science and Technology (2009-0088395). KYL is supported in part by WCU program through A Llike-sign Dimuon Charge Asymmetry at Tevatron Induced · · · – Jong Phil Lee and Kang Young Lee the KOSEF funded by the MEST (R31-2008-000-100570) and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education, Science and Technology (2009-0076208). REFERENCES [1] V. M. Abazov et al. [D0 collaboration], Phys. Rev. D 84, 052007 (2011); V. M. Abazov et al. [D0 collaboration], Phys. Rev. Lett. 105, 081801 (2010); V. M. Abazov et al. [D0 collaboration], Phys. Rev. D 82, 032001 (2010). [2] H. Ishimori, Y. Kajiyama, Y. Shimizu and M. Tanimoto, Prog. Theor. Phys. 126, 703 (2012); K. Y. Lee and S.h. Nam, Phys. Rev. D 85, 035001 (2012); R. Fleischer and R. 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