Hints for a low Bs ! �þ�� rate and the fourth generation

Wei-Shu Hou, Masaya Kohda, and Fanrong Xu

Department of Physics, National Taiwan University, Taipei, Taiwan 10617(Received 5 April 2012; published 14 May 2012)

With full 2011 LHC data analyzed, there is no indication for deviation from standard model in CP

violating phase for Bs ! J=c�, nor in the forward-backward asymmetry for B0 ! K�0�þ��. Standardmodel sensitivity, however, has been reached for the Bs ! �þ�� rate, and there may be some hint for a

suppression. We illustrate that, if a suppressedBðBs ! �þ��Þ bears out with 2012 data, it would imply a

lower bound on the fourth generation quark mixing product jV�t0sVt0bj.

DOI: 10.1103/PhysRevD.85.097502 PACS numbers: 14.65.Jk, 11.30.Er, 12.15.Hh, 13.20.He

I. INTRODUCTION

The winter conferences have brought forth a host of newexperimental results from the LHC. Continuing the 2011trend, the standard model (SM) stands tall, and there are nostrong hints of new physics beyond SM (BSM). On theflavor front, a fit [1] to Bs ! J=c� events by LHCb with1 fb�1 data yields ��s that is in good agreement with SM,while combining the �s � 2�Bs

(the CP violating phase

of �Bs ! Bs mixing) measurement with the result fromBs ! J=c�� gives

�s ¼ �0:002� 0:083� 0:027 rad ðLHCb 1 fb�1Þ¼ �0:002� 0:087 rad; (1)

which is fully consistent with the result of 0:03� 0:16�0:07 with 1=3 of the data set. Again with 1 fb�1 data,LHCb has advanced the measurement of forward-backward asymmetry in B0 ! K�0�þ��, giving a firstmeasurement [2] of the zero-crossing point

q20 ¼ ð4:9þ1:1�1:3Þ GeV2; ðLHCb 1 fb�1Þ; (2)

which is consistent with the SM expectation of4:0–4:3 GeV2 [3].

It is interesting then, that more apparent progress hasbeen made on the quest for the Bs ! �þ�� rare decaymode: SM sensitivity has genuinely been reached, and data[4,5] might be suggestive of a rate below SM expectations.Given that a decade long search for Bs ! �þ�� wasmotivated by the possible enhancement up to factors ofhundreds to thousands, by powers [6] of tan� in thesettings of supersymmetry or two Higgs doublet models,we are now at the juncture of a mindset change, switchingfrom possible huge enhancements of old, to SM-like oreven sub-SM values as it might emerge. It is in this contextthat we wish to explore in this paper the implications onrelevant flavor parameters involving a fourth generation ofquarks, t0 and b0 (SM4).

It should be noted that bounds on t0 and b0 masses havereached [7] the 600 GeV level by direct search at the LHC,hence we have nominally crossed the threshold ofthe unitarity bound (UB) of 500–550 GeV [8]. In the

following, we will proceed naively, extending our previouswork [9], and return to comment on UB and other issuestowards the end of our discussion.

II. LOW VERSUS SM-LIKE Bs ! �þ�� RATE

It is difficult to enhance Bs ! �þ�� in SM4 by morethan a factor of 2 or three, because it is constrained byB ! Xs‘

þ‘� (together with B ! Xs�), which is consis-tent with SM. Hence, this mode appeared less relevant forSM4, until recently. In contrast, the aforementioned tan�enhancement effect feeds scalar operators that do not enterb ! s� and b ! s‘þ‘� processes, hence were far lessconstrained. However, the scalar operators are now mutedby the prowess of the LHC (and previous searches at theTevatron).A dramatic turn of events were already played out in

2011, where the combined result [10] of LHCb and CMS,BðBs ! �þ��Þ< 11� 10�9 at 95% confidence level(CL), refuted the CDF result [11] of ð18þ11

�9 Þ � 10�9,

which was at the time itself hot off the press. Adding closeto 3 fb�1 data to the previous 7 fb�1 analysis, the CDFvalue dropped a bit to ð13þ9

�7Þ � 10�9, but the Tevatron hasrun out of steam. ATLAS has also turned out a bound of22� 10�9 based on 2:4 fb�1 data, which is not yet com-petitive even with summer 2011 results from LHCbor CMS. The highlight this winter was therefore theBs ! �þ�� results from CMS and LHCb.Let us first describe the LHCb result. Using a multi-

variate analysis, LHCb gave [5] the 95% CL bound of

BðBs ! �þ��Þ< 4:5� 10�9; ðLHCb 1 fb�1Þ; (3)

which is approaching rather close to the SM value [12] of

B ðBs ! �þ��Þ ¼ ð3:2� 0:2Þ � 10�9 ðSMÞ: (4)

In fact, LHCb gave a fitted number,

BðBs ! �þ��Þ ¼ ð0:8þ1:8�1:3Þ � 10�9; ðLHCb 1 fb�1Þ;

(5)

which naively implies a possibly negative branching ratio.The central value is from the maximum log-likelihood,

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while the errors correspond to varying the log-likelihoodby 0.5. The main upshot may be that LHCb does not reallysee any clear hint of an SM-strength signal. Either this is adownward fluctuation of the ‘‘true SM’’ value of Eq. (4), ornature has a sub-SM value in store for us. We caution, ofcourse, that statistics are still rather low.

The CMS result [4] is, at 95% CL,

B ðBs ! �þ��Þ< 7:7� 10�9; ðCMS5 fb�1Þ (6)

by a cut-based analysis. A mild deficit seems to be indi-cated when compared with the median expected limit of<8:4� 10�9. But the handful of events reveal some inter-esting pattern. In the Barrel detector region, one expects�2:7 signal events if SM were true, together with �0:8events from background. Only two events were observed,which are separated by �100 MeV, wider than the nomi-nal detector mass resolution. This suggests the presence ofbackground events. Whether this constitutes one eventeach for signal and background, or if both events arebackground, it seems to echo LHCb [5] in some‘‘downward’’ fluctuation from the SM value of Eq. (4).However, if both LHCb and CMS sense a downward signalfluctuation, then the likelihood that the actual signal mightbe lower would be enhanced.

In the Endcap detector region, the situation is a bitpuzzling. Here, signal and background are both expectedat 1.2 event level, while a total of 4 events were seen [4].But they all cluster within 50 MeV or less, inside a signalmass window of 150 MeV, which is set at twice thedetector mass resolution (poorer than in the Barrel detec-tor). However, since the Endcap is less sensitive than theBarrel, we refrain from further comment, except that the‘‘excess’’ events push up the bound of Eq. (6) slightly.Thus, by CMS Barrel detector alone, the ‘‘discrepancy’’with median expected is a little larger.

Although anything can happen at the present statisticslevel, LHCb expects to add �1 fb�1 in 2012, while CMSwould add �15 fb�1, both at the slightly higher collisionenergy of 8 TeV. We therefore like to emulate futureprospects as follows. For the indication of lower than SMrate, we shall take Eq. (5) at face value. Projecting to full2011–2012 data, besides the doubling of LHCb data, CMSdata should increase more than four fold (a multivariateanalysis approach should increase the effective luminos-ity). Although one cannot really project the combined

effective reduction of errors, we take the factorffiffiffi

6p � 2:5;

i.e. in our subsequent numerics, besides the 1� allowedrange for Eq. (5), we will show also the 1=2:5� range,which would give ð0:8þ0:7

�0:5Þ � 10�9. While this is rather

aggressive, it would illustrate a sub-SM result when LHCbcombined with CMS probes genuinely below SM values. Itis not impossible that, by end of the 2011–2012 run, wefind BðBs ! �þ��Þ to be consistent with zero, i.e. at10�9 or less. We note that ATLAS could also eventuallycontribute significantly to Bs ! �þ�� search.

The notable feature across the board for the new physicssearch at the LHC, however, is that no cracks were found inSM’s armor. Thus, we offer a second case of SM-likebehavior. Here, we take the central value from SM, andmimic the current error bar by satisfying the 95% CLbound from CMS. We get from Eq. (6),

B ðBs ! �þ��Þ ¼ ð3:2� 2:7Þ � 10�9 ðSM-likeÞ:(7)

Again, we will discuss the 1� and 1=2:5� allowed range ofEq. (7) for projections into the future. Actual error reduc-tion would likely be more than 1=2:5 for SM-like centralvalues in Eq. (7).We follow our previous paper [9] and combine the above

scenarios for BðBs ! �þ��Þ with measurements of�s and AFBðB0 ! K�0�þ��Þ (we shorthand as AFB be-low). Our target physics is the flavor parameters of thefourth generation for b ! s transitions, namely V�

t0sVt0b �rsbe

i�sb . If the current hint for 125 GeV SM-like Higgsboson does not get substantiated by 2012 data, a veryheavy fourth generation could provide the mechanismfor electroweak symmetry breaking through its strongYukawa interaction [13]. We will find that a sub-SMBðBs ! �þ��Þ value would imply a lower bound onrsb ¼ jV�

t0sVt0bj, which would be rather interesting.

We had suggested that the three measurements of �s,BðBs ! �þ��Þ and AFB would help map out the pre-ferred V�

t0sVt0b, or ðrsb; �sbÞ parameter space. The main

measurements are �s and BðBs ! �þ��Þ, with AFB pro-viding further discrimination, both in its shape, and nowalso the q20 value [2]. Three cases were discussed. Case Awas for large and negative �s, where we used sin2�Bs

¼�0:3� 0:1, and enhanced 109BðBs ! �þ��Þ ¼5:0� 1:5. This was motivated by hints for large and nega-tive time-dependent CP violation in Bs ! J=c� fromTevatron studies. Although a �0:2� 0:1 value could stillbe entertained at the 2� level, there is not more to be saidbeyond our previous work, while the likelihood for en-hanced BðBs ! �þ��Þ is receding. Thus, we no longerpresent this case. Cases B and C were for sin2�Bs

taking

the SM value of �0:04� 0:01, while 109BðBs ! �þ��Þtakes the slightly enhanced or depressed values of5:0� 1:5 and 2:0� 1:5, respectively. By design, theoverlap between Case B and Case C is precisely whenBðBs ! �þ��Þ is SM-like. Thus, the three Cases of A, B,and C map out the foreseen parameter space in rsb and�sb

as data improves.With the present experimental situation for

BðBs ! �þ��Þ, which could either be sub-SM as inEq. (5), or SM-like, as in Eq. (7), we reinvestigate theimplications for the preferred region in the rsb-�sb plane.For both cases, we impose the �s � 2�Bs

constraint of

Eq. (1). The observed shape and q20 value from AFB are

further applied to constrain parameter space. We takemt0 ¼ 650 GeV for the sake of illustration.

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III. RESULTS

The �Bs � Bs mixing amplitude is

Ms12 ¼

G2FM

2W

12�2mBs

f2BsB̂Bs

�B�s12; (8)

with

�s12 ¼ ð�SM

t Þ2S0ðt; tÞ þ 2�SMt �t0�S

ð1Þ0 þ �2

t0�Sð2Þ0 ; (9)

where �q � V�qsVqb. With S0 and �SðiÞ0 as defined in

Ref. [14], Eq. (9) manifestly respects Glashow-Iliopoulos-Maiani [15]. The CP violation phase

�s ¼ 2�Bs� argMs

12 ¼ arg�s12 (10)

depends only on mt0 and �t0 ¼ V�t0sVt0b. Note that �SM

t ¼��c � �u ffi �0:04� V�

usVub. Although we take PDG[16] values for the phase of Vub, it is exciting that thephase of V�

usVub is starting to be directly measured viainterference of tree processes. For BðBs ! �þ��Þ, thef2Bs

dependence is largely removed [17] by taking the ratio

with �mBs=�mBs

jexp, which works for SM4 as in SM.

That is,

B ðBs ! ���Þ ¼ CBs

�2Y

B̂Bs�B

j�SMt Y0ðxtÞ þ �t0�Y0j2j�s

12j=�mBsjexp ; (11)

where C ¼ 3g4Wm2�=2

7�3M2W , and �Y ¼ �YðxtÞ ¼ �Yðxt0 Þ

is taken.We plot, in Fig. 1(a), the contours for �s within 1� and

1=ffiffiffi

2p

� range of Eq. (1), in the rsb � jV�t0sVt0bj, �sb �

argV�t0sVt0b plane, for mt0 ¼ 650 GeV. Here, LHCb holds

a monopoly, and statistics are expected only to doubleduring 2012. Similarly for BðBs ! �þ��Þ, we plot thecontours within 1� and 1=2:5� range of Eq. (5), which issub-SM in strength. The mt0 value used is beyond the550 GeV nominal UB bound [8], and one is no longersure of the numerical accuracy of Eqs. (9) and (11), i.e. the

perturbative computation of the functions �SðiÞ0 and �Y0

would become questionable. However, some form such asEq. (9) should continue to hold even above the UB, and weshall continue to use existing formulas.The overlap between the �s and BðBs ! �þ��Þ con-

tours now favor �sb in the 4th quadrant with j sin�sbjsmall, where the darker regions are for more aggressiveerror projections towards the future. It should be clear thata precise determination of �sb depends much more on theprecision of �s measurement.We remark that Fig. 1(a) is a much more stringent

version of Case C presented in our previous paper, wherewe now have BðBs ! �þ��Þ considerably below SMexpectation. Thus, the most notable feature is that, evenat 1� error level, rsb is now bounded from below. This isbecause the (current LHCb [5]) central value of Eq. (5) ismore than 1� below the SM expectation of 3:2� 10�9.Thus, it calls for a finite t0 effect to subtract, or destruc-tively interfere, against the SM amplitude from top quark.That this might become the picture for flavor parametersinvolving 4th generation, if a lower than SM value forBðBs ! �þ��Þ is found at the LHC, is the main pointof this short note. It should be stressed that this is a naturalconsequence for SM4, since we know from existing con-straints that t0-induced amplitudes must be subdominant instrength compared with top-induced amplitudes, while thesign of the real part of V�

t0sVt0b can precisely be correlated

with what experiments observe.The SM-like case of Eq. (7) is less interesting, but given

the continued success of the SM into the LHC era, it shouldbe viewed as more probable. We illustrate in Fig. 1(b) formt0 ¼ 650 GeV the overlap of the contours for �s inEq. (1) and BðBs ! �þ��Þ in Eq. (7). Besides somehigh rsb region for modest j�sj values, the generic featureis relatively small rsb, with �sb undetermined by thepresent precision of �sb measurement. This small rsbcase is rather intuitive, that of subdued 4th generationeffect. We shall see that the larger rsb values are ruledout by the observation of SM-like behavior for AFB, as wehave seen in our previous paper.

0 90 180 270 3600

0.004

0.008

0.012

sb arg Vt' s Vt' b

r sb

Vt'

sV

t'b s 0.002 0.087

109 Bs

0.8 1.31.8

0 90 180 270 3600

0.004

0.008

0.012

sb arg Vt' s Vt' b

r sb

Vt'

sV

t'b

s 0.002 0.087

109 Bs

3.2 2.72.7

FIG. 1 (color online). Overlap region for contours of �s ¼ �0:002� 0:087, where dashed line is for 1=ffiffiffi

2p

the error, and109BðBs ! �þ��Þ ¼ (a) 0:8þ1:8

�1:3 (we allow only positive definite values), and (b) 3:2� 2:7, where the dashed line is for 1=2:5the error. For illustration, mt0 ¼ 650 GeV has been used.

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The SM-like shape for AFB as observed by LHCb pro-vides a powerful discriminant against larger rsb values.Note that data prior to summer 2011 had suggested adeviation from SM behavior [16], which, besides a hintfor sizable deviation in sin2�Bs

, was part of the motivation

for Case A in our previous paper. The SM-like shape forAFB is further affirmed with 1 fb�1 data from LHCb [2],while the first measurement for zero-crossing point,Eq. (2), is offered. We have checked the allowed parameterspace of Fig. 1 and find generically that rsb * 0:004 wouldgenerate significant deviations in shape for AFB. The dropfrom roughly 0.008 [9] to 0.004 is due to the higher mt0 ¼650 GeV taken to satisfy direct search bounds [7], as wellas the tighter experimental constraints towards SM. Wenote with interest that, for the sub-SM BðBs ! �þ��Þcase, the slightly larger than SM central value of q20 ¼4:9 GeV2 in Eq. (2) also prefers �sb in the 4th quadrant.

IV. DISCUSSION AND CONCLUSION

After some hints for BSM physics for some years, bothin AFBðB0 ! K�0�þ��Þ and in sin2�Bs

[18], SM is re-

affirmed by 2011 data from LHC. Interestingly, now theremight be a hint for BðBs ! �þ��Þ below SM expecta-tions. It is of course too early to tell. However, this modehas always been looked upon as possibly greatly enhancedby the less constrained scalar operators. We are at least atthe turning point, where no large enhancement is observed,but now whether it is SM-like, or sub-SM, can be distin-guished with full 2011–2012 data. The 4th generation t0quark offers the natural toolbox in this domain, as it isconstrained to be subdominant by b ! s� and b ! s‘þ‘�data for a decade, while providing a destructive mechanismin the unknown phase of V�

t0sVt0b. In contrast, adjusting the

scalar interactions to the SM strength is like training a bighammer on a small nail.

We note that, to have BðBs ! �þ��Þ near the centralvalue of Eq. (5), the C10 Wilson coefficient would beconsiderably smaller than SM value, such that one wouldworry aboutBðB ! Xs‘

þ‘�Þ. It is then interesting to notethat LHCb data does seem to indicate that the

dBðB0 ! K�0�þ��Þ=dq2 differential rate could be alittle lower than the SM expectations [2]. Althougha vanishing BðBs ! �þ��Þ is unlikely [more likelywithin ð1–2Þ � 10�9], it would be interesting to watchthis mutually supporting trend of somewhat lower BðBs!�þ��Þ and BðB!K�‘þ‘�Þ [or BðB!Xs‘

þ‘�Þ]. Thedarker region in Fig. 1(a) is just to stress the point.We have used mt0 ¼ 650 GeV to satisfy direct search

bounds, which is now beyond the nominal unitarity bound.To probe much further, the 13–14 TeV run would benecessary. However, with the Yukawa coupling turningnonperturbative, the phenomenology may change [19].Fortunately, the leading production mode of gg ! Q �Q isnot affected. The usage of such large mt0 values is becom-ing dubious, and nonperturbative studies should be per-formed. The nonperturbative, strong Yukawa couplingcould actually be the source of electroweak symmetrybreaking [13]. It is interesting that, with full 2011–2012data, we would learn whether a 125 GeV Higgs boson issubstantiated, as well as whether Bs ! �þ�� is belowSM expectations.In conclusion, we illustrate what LHC data might tell us

about 4th generation flavor parameters. Assuming 2011–2012 data would give �s ¼ �0:002� 0:062 and takingmt0 ¼ 650 GeV, we mocked the low Bs ! �þ�� ratecase with ð0:8þ0:7

�0:5Þ � 10�9, which would imply jV�t0sVt0bj �

0:0015� 0:004, with �40� & argV�t0sVt0b & 15�. On the

other hand, if an SM-like Bs ! �þ�� rate emerges, itwould imply small jV�

t0sVt0bj at a couple per mille, while

argV�t0sVt0b would require more precise measurement of �s

to determine. The B0 ! K�0�þ�� forward-backwardasymmetry provides a further discriminant that rules outjV�

t0sVt0bj * 0:004 for the discussed allowed regions.

ACKNOWLEDGMENTS

W.S.H. is grateful to U. Langenegger, S. Stone, andD. Tonelli for communications, and thanks the NationalScience Council for the Academic Summit Grant No. NSC100-2745-M-002-002-ASP. M.K. and F.X. are supportedby the NTU Grant No. 10R40044 and the Laurel program.

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