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Comment on ‘‘New Physics Contributions to the Lifetime Difference in D0- D0 Mixing’’

The precision measurement on the oscillation of a neu- tral particle and its antiparticle is very important to probe the footprints of new physics (NP). Although so far no clear signal tells us the existence of NP, Golowich, Pakvasa, and Petrov [1] have recently shown that the NP effects could have significant contributions to the lifetime difference in the D0- D0 mixing, with the resultant form

y ’X

n

n

DASMn ASMn  2X

n

n

DANPn ASMn ; (1) where y  D=2D, DD is the decay rate (rate difference), n corresponds to the phase space of the charmless intermediate state n, and ASMANP denotes the decay amplitude for D0 ! n dictated by the standard model (SM) [NP] contributions. In their Letter, various NP models, including vectorlike, supersymmetry (SUSY) without (with) R parity, left-right (LR) and multi-Higgs models, on the Eq. (1) are analyzed. Their results display that except the SUSY models without R parity, y is typi- cally less than 104. However, we find that in the non- manifest LR model, an important LR mixing effect, illustrated in Fig.1, was not considered in Ref. [1].

Two charged gauge bosons WL;R in the LR model are mixed and described by W1  cosWL sinWR and W2   sinWL cosWR[2], where W1is the observed boson and  is the mixing angle between WL and WR. Interestingly,  of O102 is still allowed by current experimental data [2,3]. Using the small mixing angle, the charged current interaction associated with LR mixing is given by

LLRgR

2

p VabRubPRdaW1; (2) where ab is the flavor index. gR and VR are the right- handed gauge coupling and flavor mixing matrix, respec- tively. In the nonmanifest LR model, since the pattern for VRcould be VcsR VudR 0 and VusR VcdR O1 [4], it is clear that Fig. 1gives the dominant contribution. In terms of the leading results of the operator product expan- sion, only Oijk‘4  ukpc2cju1ci in Eq. (7) of Ref. [1] has the contribution, where i, j, k, ‘ denote the color indices,  PL, 2 PL, and 1  PR. Consequently, the effect for the lifetime difference is found to be

yLR CLRVcsLVusR K2hQ0i  K1h ~Q0i; (3) where K1  C1C1Nc C1C2 C1C2with Nc  3, K2  C2C2, hQ0i  h D0j uiPLciujPRcjjD0i, h ~Q0i  h D0j uiPLcjujPRcijD0i, and

CLR G2F

2mDDgm2cpxs

; (4)

with xs m2s=m2c, g gR=gL, and  being the Wolfsen- stein’s parameter. Here, C12 C12. From Eq. (4), we see clearly that the LR mixing contribution is at least 1= pxs

 mc=mslarger than that presented in Ref. [1].

With GF 1:166 105GeV2, ms 0:12 GeV, mc 1:4 GeV, mD  1:86 GeV, fD  0:23 GeV, g< 0:033, C1 0:55, and C2 1:3, we get the maximum value of yLR 1:4 103: (5) Recently, BABAR [5] and BELLE [6] Collaborations have reported the evidence for the D- D mixing with the combined 68% C.L. results of

x mD

D  5:5 2:2 103; y  5:4 2:0 103: (6) Clearly, our result in Eq. (5) based on the LR mixing mechanism in the nonmanifest LR model fits well with the data in Eq. (6).

Chuan-Hung Chen,1,2Chao-Qiang Geng,3,4and Soo-Hyeon Nam5

1Department of Physics

National Cheng-Kung University Tainan 701, Taiwan

2National Center for Theoretical Sciences, Taiwan

3Department of Physics National Tsing-Hua University Hsinchu 300, Taiwan

4Theory Group, TRIUMF 4004 Wesbrook Mall

Vancouver, British Columbia V6T 2A3, Canada

5Department of Physics National Central University Chung-Li 32054, Taiwan

Received 8 May 2007; published 2 July 2007 DOI:10.1103/PhysRevLett.99.019101

PACS numbers: 12.60.i, 13.25.Ft, 14.40.Lb, 14.65.Dw [1] E. Golowich, S. Pakvasa, and A. Petrov, Phys. Rev. Lett.

98, 181801 (2007).

[2] W. M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006).

[3] S. H. Nam, Phys. Rev. D 68, 115006 (2003).

[4] P. Langacker and S. U. Sankar, Phys. Rev. D 40, 1569 (1989).

[5] B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett.

98, 211802 (2007).

[6] M. Staricˇ et al. (Belle Collaboration), Phys. Rev. Lett. 98, 211803 (2007).

c

s s

u WL WR

FIG. 1. Feynman diagram for the left-right mixing.

PRL 99, 019101 (2007) P H Y S I C A L R E V I E W L E T T E R S week ending 6 JULY 2007

0031-9007= 07=99(1)=019101(1) 019101-1 © 2007 The American Physical Society

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