The effect of both Z and Z '-mediated flavor-changing neutral currents on B
s+-* i^ \x~ decay
S Sahoo*1, L Maharana2 and B R Behera3
department of Physics, National Institute of Technology, Durgapur-713 209, West Bengal, India department of Physics, Utkal University, Bhubaneswar - 751 004, Onssa, India
JJawahar Navodaya Vidyalaya, Tarbod - 766 105, Nuapada, Onssa, India E-mail sukadevsahoo(a)yahoo com
Received 25 October 2006, accepted 23 May 2007
Abstract : We study the effect of both Z and Z-mediated flavor-changing neutral currents (FCNCs) on the Bs ->/zV~ rare decay process. Mixing between ordinary and exotic left-handed quarks induces Z-mediated FCNC whereas mixing of right-handed ordinary and exotic quarks induces Z' -mediated FCNC. We find the branching ratio is enhanced from its standard model (SM) value due to the effect of both Z and Z-mediated FCNCs.
Keywords : Z-boson, Z' -boson, decays of bottom mesons, models beyond the standard model PACS No*. : 14.70.Hp; 14.70.Pw; 13.20.He; 12.60.-i
1. Introduction
In recent years ©-physics has been a very active area of research both experimentally and theoretically [1] because it is one of the domains where new physics might very well reveal itself. Rare B decays [2] induced by flavor-changing neutral current (FCNC) transitions are very important to probe the flavor sector of the SM. In the SM they arise from one- loop diagrams and are generally suppressed in comparison to the tree diagrams.
Nevertheless, one-loop FCNC processes can be enhanced by orders of magnitude in
Corresponding Author
© 2 0 0 7 I A C S
598 S Sahoo, L Maharana and B R Behera some cases due to the presence of new physics. New physics comes into play in rare B decays in two different ways : (a) through a new contribution to the Wilson coefficients or (b) through a new structure in the effective Hamiltonian, which are both absent in the SM. In this paper, we study Bs -> y?if rare decay considering the effect of both Z and Z -mediated FCNCs that change the effective Hamiltonian and modify the branching ratio.
Z -bosons are known to exist naturally in well-motivated extensions of the SM [3]. In particular, they often occur in grand unified theories (GUTs), superstring theories and theories with large extra dimensions [4]. It is surprising that a Z -boson is predicted at the weak scale [5] in supersymmetric E6 models. However, there are stringent limits on the mass of an extra Z from the non-observation of direct production followed by decays into e*e~ or / /+/ T by CDF [6], while indirect constraints from the precision data also limit the Z mass (weak neutral current processes and LEP II) and severally constrain the Z-Z mixing angle e [7,8]. These limits are model-dependent, but are typically in the range Mz>500 GeV and |0|<1CT3 for standard GUT models; stringent strong constraints on Mz, of the order of 1 TeV, are obtained in models with nonuniversal flavor gauge interactions [9]. There is, thus, both theoretical and experimental motivation for an additional Z \ most likely in the range 500 GeV - 1 TeV. Also, in this mass range, it should be possible to carry out significant diagnostic probes of Z couplings at the LHC and at a future NLC [10], which would complement those from the precision experiments [8].
In the Z sector, there has been a great deal of investigation to understand the underlying physics beyond the SM [11]. It has been shown that a leptophobic Z -boson can appear in £6 gauge models due to mixing of gauge kinetic terms [12,13]. Flavor mixing can be induced at the tree level in the up-type and/or down-type quark sector after diagonalizing their mass matrices. Mixing between ordinary and exotic left-handed quarks induces Z-mediated FCNCs. The right-handed quarks dR,SR and bR have different U(1) quantum numbers than exotic qR and their mixing will induce Z -mediated FCNCs [12,14]
among the ordinary down quark types. Tree level FCNC interactions can also be induced by an additional Z -boson on the up-type quark sector [15]. In the Z model [16], the FCNC b-s-Z coupling is related to the flavor-diagonal couplings qqZ in a predictive way, which is then used to obtain upper limits on the leptonic etZ couplings. Hence, it is possible to predict the branching ratio for the muonic decay of the Bs. With FCNCs, both Z a n d Z-boson contributes at tree level, and its contribution will interfere with the SM contributions [14,17].
This paper is organized as follows: in Section 2, we discuss the B$ - » ^yT decay in the standard model. In Section 3, we give a brief account of the model and explain why it implies FCNC at the tree level. Then, we evaluate the effective Hamiltonian for
Bs - » / i+/ T decay considering the Feynman diagram and the contribution comes from both the Z a n d Z-bosons. In Section 4, we calculate the branching ratio for Bs ~> ju+/T
decay. Then we discuss the results, so obtained, and compare our results with that of others.
2. Bs --> JU+/T decay in the standard model
Let us consider the Bs ~> / / V ~ decay process. Ijjn the standard model, this process is loop-suppressed. However, it is potentially sensitive to new physics beyond the SM. This decay involves b -> s transitions. The effective Hamiltonian [2] describing the process
B8->f+r(t = n)9 is
Heff=^*t[cf (s^P,b)(7yV) + C1 0(s^PLb)(7y^5^)
" ^^(sPY*PRb)(lY»Ys')\ (1)
• J
where GF is the Fermi coupling constant, A, = VtbVJ6, PRX = — (1 ± y5 ), p= p+ + p„ the sum of the momenta of the t and r , and C7, Cg* and C10 are Wilson coefficients [18]
evaluated at the b quark mass scale.
We use the Vacuum Insertion Method (VIM) [19] for the evaluation of matrix elements as :
( 0 | s ^ y5b | £ £ ) = ifByB, (2)
(0|sy5to|fl£) = ifBsmBsf (3)
0\s<T»vPRb\BZ) = 0 . (4)
and
Let us consider the contribution of each term in equation (1). pg = p£ + p ^ , hence the contribution from C9 term in equation (1) will vanish upon contraction with the lepton bilinear, C7 will also give zero by equation (4) and the remaining C10 term will get a factor of 2me. Using the above results, we can write the transition amplitude for this process as
M( BS - > t r ) = / ^ £ £ A, fBC,0 m, (7y5*) , ( 5) and the corresponding branching ratio [18] is given by
B(B, ->?C ) . | £ «><f. m
B. m° 11{, Vif Cf„ l ^
(6)600 S Sahoo, L Maharana and B R Behera The value of the branching ratio in the standard model is predicted as
e ( es~ > / i V ) = 4.2x10-9[16],
a ( es~ > / / V ) = (5.t±3.3)x10~9 [18, 20],
e ( Bs- * / i V ) = = ( 3 . 5 ± 1 . 0 ) x 1 0 -9 [21]. (7) Recently, this branching ratio has been constrained by the D0 Collaboration [22] with
an upper bound :
S(SS ->A*+AT ) < 5.0x10~7 (95% C.L). (8)
3. The model
In extended quark sector model [17,23], besides the three standard generations of the quarks, there is an SU(2)L singlet of charge - 1/3. This model allows for Z-mediated FCNCs. The up quark sector interaction eigenstates are identified with mass eigenstates but down quark sector interaction eigenstates are related to the mass eigenstates by a 4x 4 unitary matrix, which is denoted by K. The charged-current interactions are described by
C - ^ ( ^
+^ ) . (9)
J""= VijUiLY"djL. (10)
The charged-current mixing matrix V is a 3 x 4 submatrix of K :
Vu = Kfj for / « 1,....3, / . 1 4. (11)
Here, V is parametrized by six real angles and three phases, instead of three angles and one phase in the original CKM matrix.
The neutral-current interactions are described by
w
J"3 = - \ uP^PLYMdqL + 1 Si,uiLy>iuiL. (13)
In neutral-current mixing, the matrix for the down sector is i7 = 1/* 1/. Since in this case V is not unitary, U * 1. Its nondiagonal elements do not vanish :
Upq - - KAp KAq for P * 9- (14)
Since the various Upq are non-vanishing, they allow for flavor-changing neutral currents that would be a signal for new physics.
Now consider the Bs - » \ £ \ f decay process |n the presence of Z-mediated flavor- changing neutral current [17] at tree level (Figurp 1). The Zbs FCNC coupling, which affects B -decays, is parameterized by one independent parameter Usb and this parameter is constrained by branching ratio of the process 6S -> ju*/T. Given that the Z-boson contributes to Bs -» l*r(( = /u), one can write the effective Hamiltonian [2] as
Heff(Z) = ^ ^ [ s y " ( 1 - yGF 5) b ] [ 7 ( ^ y , - c ; y , y5) ^ ] (15)
Figure 1. Feynman diagram for Bs~* ii* n~ in a model with tree level FCNC transitions, where the blob ( • ) represents the tree level flavor- changing vertex.
C£ = - ± + 2 s i n20w . C'A = -1.
where C£ and C*A are the vector and axial vector ZtC couplings and are given as (16) The transition amplitude is given as
M(B
s->tr) = - i^u^f
Btc^2m
t(lr
se)
t and the corresponding branching ratio is given as(17)
4*-'a-^i^4^i«rJH?
(18)602 S Sahoo, L Maharana andB R Behera The same idea can be applied to a Z -boson Le.9 mixing among particles which have different Z quantum numbers will induce FCNCs due to Z exchange [24,14] and surprisingly these effects can be just as large as Z-mediated FCNCs. Since the U* are generated by mixing that breaks weak isospin, they are expected to be at most 0(M,/M2), where M,{M2) is typical light (heavy) fermion mass. On the other hand, the Z-mediated coupling yz' can be generated via mixing of particles with same weak isospin and, so, suffer no suppression. Even though Z -mediated interactions are suppressed relative to Z, these are compensated by the factor Upq/Upq ~(M2/M,). Thus the effect of Z - mediated FCNCs are comparable to that of Z-mediated FCNCs. If we assume
\^
b\Av
tbv
tsx , then it is possible to write U$b instead of U%b, which gives significant contributions to the Bs - » i i * i T decay process. The new contributions from Z -boson are exactly the same as in the Z-boson. Therefore, we write the general effective Hamiltonian [14] that contribute to es -> t f (^ = iu), in the light of equation (15) as :Herri?) = ^Usb[sY"(^Y5)b][f(C^y,-C^Xs )<]
9 Mz (19) where g= e/(s\r\6wcos6w) and g' is the gauge coupling associated with the L/(1)' group. The absence of the suppression in the mixing for the Z -mediated FCNC can compensate for /wf/Mj* suppression of the Z amplitude relative to the Z amplitude, which implies that the coefficients describing the Z and Z flavor-changing effective interactions can be comparable in size. Hence we assume g'lg * 10. The net effective Hamiltonian can be written, from equation (15) and (19), as Heff = Heff(2T)+Heff(Z) and
Heff = ^UBb[sy''('\-Y8)b][t(clYll-CrAYl.Y*)l]
and the corresponding branching ratio is given as
1+ g Mz (20)
g M
r-i2
(21)
We use this formula for the calculation of branching ratio for the rare decays Bs -*tC{t = n, t). In the next section we will calculate for £~n only.
4. Results and discussions
In this section, we calculate the branching ratio for Bs -> / i V ~ decay process using all
the recent data [25]: m^ =105.658369 MeV, n ^ = 5.3696 ± 0.0024 GeV, average Bs
lifetime rBs =(1.461±0.057)x10""12 s, decay constant fBs =0.24 GeV, M2 = 91.1876 GeV, GF = 1.16639 x1(T5 GeV2, sin2 0^=0.2$ and \Usb\ = W'3 [26]. Since the Z has not yet been discovered, its mass is unknown However, the Z mass is constrained by direct searches at Fermilab, weak neutral cu^ent data and precision studies at LEP and the SLC [6,8], which give a model-dependent lower bound around 500 GeV. More strong constraints on M^ , of the order of 1 TeV, £re obtained in models with nonuniversal flavor gauge interactions [9]. In a study of B njeson decays with Z -mediated flavor- changing neutral currents [27], they study the *T -boson in the mass range of a few hundred GeV to 1 TeV. Our investigations in both the left-right symmetric model [28] and potential model [29] give a lower bound of M^ > 500 GeV. There are thus good motivations for Z -boson with a mass range 500 GeV - 1 TeV [30].
In general, the value of g'lg is undetermined [31]. However, generically, one expects that g'lg « 1 if both U(1) groups have the same origin from some grand unified theory. If we take gig = 1 and (MzIMrf < (91 / 500)2 ~ 0.033, the contribution of Z will be very small; which can be neglected with comparison to Z contribution. In order to get significant contribution due to Z -mediated FCNCs, we have taken the ratio g'Ig equal to first power of 10 i.e. g'lg * 10 in our calculations.
Using the lower limit for the mass of Z -boson, M^ = 500 GeV, we get
8 ( ss- » / i V ) = 39.30x10~8. (22)
Again using the mass of Z-boson, M^ = 1000 GeV, we get
S ( 0s^Ju V )z + r=7.O4x1O-8. (23)
From equation (22) and (23), it is clear that depending on the precise value of M^ , the Z -mediated FCNCs gives sizable contributions to es -»ju+/T d e c ay process. Thus, the branching ratio for Bs -> y?n~ decay process depends upon the range for g'lg and for M^ . Our estimation gives the value of the branching ratio for Bs -> //+/T decay process in the range o f :
B ( & - > / i V ) = 7.04x10~8 - 39.30 x 10~8. (24) The author of Ref. [2] predicts the value e ( Ba -» M > ~ ) = 2.1 x 10*8 • Our result is
higher because the author in Ref. [2] considered only the effect of Z-boson whereas we have considered the effect of both Zand Z-mediated FCNCs on es - » / /+/ T decay
604 S Sahoo, L Maharana and B R Behera process. It is also shown that in supersymmetric (SUSY) models with large values of
tan p (the ratio of the vacuum expectation values of the two Higgs fields), the branching ratio for Bs -> M+M~ decay can be as large as - K T6 [32]. From equation (24), it is clear that our estimated branching ratio for B$ —> \i*if decay process is enhanced from its standard model value [equation (7)] and also satisfies the experimental upper limit [equation (8)]. Hence, the B$ -* ^/LI~ decay process could provide signals for new physics beyond the standard model. These facts lead to enrichment in the phenomenology of both the Z and Z -mediated FCNCs and Bs -> / / V ~ decay; and the physics beyond the standard model will be known after the discovery of the Z -boson.
Acknowledgments
We would like to thank R. Mohanta for fruitful discussions and suggestions. We also thank Hara Prasanna Lenka, Surendra Kumar Martha, Kartik Senapati, Paltu Burman, Debidas Sarkar and Ashok Mondal for their kind help for the preparation of the manuscript.
We thank the referee for suggesting valuable improvements of the manuscript.
References
[1] A K Giri and R Mohanta Eur. Phys. J. C45 151 (2006); J A Aguilar-Saavedra Acta Phys. Polon.
B35 2695 (2004)
[2] R Mohanta, arXiv: hep-ph/0503225 v1 23 Mar 2005 [3] P Langacker, arXiv: hep-ph/0308033
[4] M Masip and A Pamarol Phys. Rev. D60 096005 (1999) [hep-ph/9902467]
[5] J Hewett and T Rizzo Phys. Rep. 183 193 (1989)
[6] F Abe et al [CDF Collaboration] Phys. Rev. Lett. 67 2418 (1991); Phys. Rev. 79 2192 (1997) [7] J Erler and P Langacker Phys. Lett. B456 68 (1999); Phys. Rev. Lett. 84 212 (2000) [8] The LEP Electroweak Working Group and SLD Heavy Flavour Group, hep-ex/0212036
[9] C T Hill Phys. Lett. B345 483 (1995); R S Chivukula, E H Simmons and J Terning Phys. Lett. B331 383 (1994); H Georgi, E E Jenkis and E H Simmons Phys. Rev. Lett. 62 2789 (1989); Nud. Phys.
B331 541 (1990)
[10] A Leike Phys. Rev. 317C 143 (1999) [hep-ph/9805494]
[11] S Sahoo Indian J. Phys. 80 (2) 191 (2006); X-G He and G Valencia, hep-ph/0605202; D Feldman, Z Liu and P Nath Phys. Rev. Lett. 97 021801 (2006) [hep-ph/0603039]; B B Deo and L Maharana Phys. Lett. B461 105 (1999); F Abe et al [CDF Collaboration] Phys. Rev. Lett. T7 438 (1996); The LEP Collaboration and LEP Electroweak Working Group, CERN-PPE / 95 / 172.
[12] K S Babu, C Kolda and J March-Russell Phys. Rev. D54 4635 (1996) [hep-phV 9603212]; Phys. Rev.
D57 6788 (1998) [hep-ph/9710441]
[13] T G Rizzo Phys. Rev. D59 015020 (1998) [hep-ph/9806397]; F del Aguila, J Moreno and M Quiros Nud. Phys. B372 3 (1992); B361 45 (1991)
[14] S Sahoo and L Maharana Phys. Rev. D69 115012 (2004); V Barger, C- W Chiang, J Jiang and P Langacker Phys. Lett. BS96 229 (2004); V Barger, C-W Chiang, P Langacker and H S Lee Phys.
Lett. B598 218 (2004); Phys. Lett. B580 186 (2004)
[15] A Arhrib, K Chung, C- W Chiang and T- C Yuan, hep-ph/0602175 [16] K Cheung, C- W Chiang, N G Deshpande and J Jiang, hep-ph/0604223
[17] Y Nir and D Silverman Phys. Rev. D42 1477 (1990); D Silverman Phys. Rev. D45 1800 (1992); V Barger, M S Berger and R J N Phillips Phys. Rev. 062 166 (1995)
[18] G Buchalla, A J Buras and M E Lautenbacher Rev. $fod. Phys. 68 1125 (1996) [hep-ph/9512380];
A Ali and C Greub Phys. Rev. D57 2996 (1998) [hep-fih/ 9707251]; M Bauer, B Stech and M Wirbel Z. Phys. C34 103 (1987); G Altarelli, G Curci, G Mftinelli and S Petrarca Nucl. Phys. B187 461 (1981); M Beneke, Th Fledmann and D Seidel Nucl. Phys. B612 25 (2001)
[19] M K Gaillard and B W Lee Phys. Rev. D10 897 (19754)
[20] J Kroll et al "Search for the decay 6s- > / i V / fermilab preprint, FERMILAB-CONF-95/229-E (1995)
[21] A Ali, DESY Report No. DESY 96-106, hep-ph/9606324
[22] V M Abazov et al [DO Collaboration] Phys. Rev. Lett. 94 071802 (2005) [23] M Gronau and D London Phys. Rev. D55 2845 (1997)
[24] E Nardi Phys. Rev. DAB 1240 (1993); J Bernabeu, E Nardi and D Tommasini NucL Phys. B409 69 (1993) [hep-ph/9306251]
[25] W-M Yao et al. [Particle Data Group] J. Phys. G: Nucl. Part. Phys. 33 1 (2006) [ http://pdg.lbl.gov]
[26] A K Giri and R Mohanta Phys. Rev. D68 014020 (2003)
[27] V Barger, C-W Chiang, P Langacker and H - S Lee Phys. Lett. B580 186 (2004) [hep-ph/0310073]
[28] S Sahoo, L Maharana, S Acharya and A Roul Int. J. Mod. Phys. A20 2625 (2005) [29] S Sahoo, A K Meikap and L Maharana Mod. Phys. Lett. A21 275 (2006)
[30] A Cordero-Cid, G Tavares-Velasco and J J Toscano, hep-ph/0507135 [31] M Cvetic and B W Lynn Phys. Rev. D35 51 (1987)
[32] S R Choudhury and N Gaur Phys. Lett. B451 86 (1999) [hep-ph/9810307]
