We estimate \Delta Gamma_d/\Gamma_d, including 1/m_b contributions and part
of the next-to-leading order QCD corrections, and find it to be around 0.3%. We
show the methods to measure \Delta Gamma_d/\Gamma_d by using at least two
different final states on the untagged B_d decay. The nonzero width difference
can also be used to identify new physics effects and to resolve a twofold
discrete ambiguity in the B_d-\bar{B}_d mixing phase. With the high statistics
and accurate time resolution of the upcoming LHC experiment, the measurement of
\Delta Gamma_d seems to be possible. This measurement would be important for an
accurate measurement of \sin2\phi_1 at the LHC. We also derive an upper bound
on the value of \Delta Gamma_d/\Gamma_d in the presence of new physics.Comment: 3 pages, LaTeX, Presented at the 5th KEK Topical Conference(KEKTC5

A.S. Dighe

Beneke

C.S. Kim

Groom

Grossman

Hurth

T. Hurth

T. Yoshikawa

English

arXiv

Crossref

Measurement of the width difference of Bd mesons

We estimate &#916;&#915;d/&#915;d, including 1/mb contributions and part of the next-to-leading order QCD corrections, and find it to be around 0.3%. We show the methods to measure &#916;&#915;d/&#915;d by using at least two different final states on the untagged Bd decay. The nonzero width difference can also be used to identify new physics effects and to resolve a twofold discrete ambiguity in the Bd — B&#773;d mixing phase. With the high statistics and accurate time resolution of the upcoming LHC experiment, the measurement of &#916;&#915;d seems to be possible. This measurement would be important for an accurate measurement of sin 2&#966;1 at the LHC. We also derive an upper bound on the value of &#916;&#915;d/&#915;d in the presence of new physics

Dighe, A. S.

Hurth, T.

Kim, C. S.

Yoshikawa, T.

Indian Academy of Sciences

Measurement of the width difference of B<sub>d</sub> mesons

Publications of the IAS Fellows

We estimate \Delta Gamma_d/\Gamma_d, including 1/m_b contributions and part of the next-to-leading order QCD corrections, and find it to be around 0.3%. We show the methods to measure \Delta Gamma_d/\Gamma_d by using at least two different final states on the untagged B_d decay. The nonzero width difference can also be used to identify new physics effects and to resolve a twofold discrete ambiguity in the B_d-\bar{B}_d mixing phase. With the high statistics and accurate time resolution of the upcoming LHC experiment, the measurement of \Delta Gamma_d seems to be possible. This measurement would be important for an accurate measurement of \sin2\phi_1 at the LHC. We also derive an upper bound on the value of \Delta Gamma_d/\Gamma_d in the presence of new physics

Dighe, A S

Hurth, Tobias

Kim, C S

Yoshikawa, T

CERN Document Server

arXiv:hep-ph/0202070 v1   7 Feb 20021MeasurementoftheWidthDierenceofBdMesonsA.S.Dighea,T.Hurthb,C.S.KimcandT.YoshikawadaMax-Planck-InstituteforPhysics,FohringerRing6,D-80805Munich,GermanybCERN,TheoryDivision,CH{1211Geneva23,SwitzerlandcDepartmentofPhysicsandIPAP,YonseiUniversity,Seoul120-749,KoreadDepartmentofPhysicsandAstronomy,UniversityofNorthCarolina,ChapelHill,NC27599-3255,USAWeestimate d= d,including1=mbcontributionsandpartofthenext-to-leadingorderQCDcorrections,andndittobearound0:3%.Weshowthemethodstomeasure d= dbyusingatleasttwodierentnalstatesontheuntaggedBddecay.ThenonzerowidthdierencecanalsobeusedtoidentifynewphysicseectsandtoresolveatwofolddiscreteambiguityintheBd Bdmixingphase.WiththehighstatisticsandaccuratetimeresolutionoftheupcomingLHCexperiment,themeasurementof dseemstobepossible.Thismeasurementwouldbeimportantforanaccuratemeasurementofsin21attheLHC.Wealsoderiveanupperboundonthevalueof d= dinthepresenceofnewphysics.TheneutralBdmesonsystemhastwomasseigenstateswhichhavethemassdierenceandlifetimedierence.Themassdierencehasbeenmeasuredwellbutthelifetimedierencehasnotbeendonebecauseitisverytiny.Withinthestandardmodel(SM),thedierenceinthede-caywidthsisCKM-suppressedwithrespecttothatintheBssystem.Aroughestimateleadsto d d s s20:5%;where=0:225isthesineoftheCabibboangle,andwehavetaken s= s15%[1](seealso[2,3]).Here d(s)=( L+ H)=2istheaveragedecaywidthofthelightandheavyBd(s)mesons(BLandBHrespec-tively).Wedenotethesedecaywidthsby L; Hrespectively,anddene d(s) L  H.Atthepresentaccuracyofmeasurements,thislifetimedierence dcanwellbeignored.Asaresult,themeasurementandthephenomenologyof dhavebeenneglectedsofar,ascomparedwiththelifetimedierenceintheBssystemforexample.However,withthepossibilityofexper-imentswithhightimeresolutionandhighstatis-tics,suchasattheLHC,thisquantityisbecom-ingmoreandmorerelevant.WiththepossibilityofexperimentswithhighPresentedbyT.YoshikawaatKEKTC5.timeresolutionandhighstatistics,itisworth-whiletohavealookatthisquantityandmakearealisticestimateofthepossibilityofitsmea-surement(seealso[4,5]).In[4]weestimated d= dincluding1=mbcontributionsandpartofthenext-to-leadingor-derQCDcorrections.Wendthataddingthelattercorrectionsdecreasesthevalueof d= dcomputedattheleadingorderbyafactorofal-most2.Thenalresultis d= d=(2:6+1:2 1:6)10 3:(1)ThetwomasseigenstatesoftheneutralBdsys-temhaveslightlydierentlifetimes.Usingan-otherexpansionofthepartialNLOQCDcorrec-tionsproposedin[7],weget d= d=(3:0+0:9 1:4)10 3;(2)wherewehaveusedthepreliminaryvaluesforthebagfactorsfromtheJLQCDcollaboration[8].Intheerrorestimation,theerrorsaretheuncertain-tiesonthevaluesoftheCKMparameters,ofthebagparameters,ofthemassofthebquark,andofthemeasuredvalueofxd.Furthersourcesoferroraretheassumptionofnaivefactorizationmadeforthe1=mbmatrixelements,thescaledepen-2dence and the missing terms in the NLO contri-bution. Although the latter error is decreased inthe second estimate by smallness of CKM factors,a complete NLO calculation is denitely desirablefor the result to be more reliable.The most obvious way of trying to measurethe width dierence is through the semileptonicdecays, however we can not extract the quan-tity which is linear in  d= d. The time mea-surements of an untagged Bddecay to single -nal state is sensitive only to quadratic terms in d= d. So this method would involve measur-ing a quantity as small as ( d= d)2 10 5,which is too small to measure.However, combining time measurements fromtwo dierent nal states can enable us to mea-sure quantities linear in  d= d. Indeed, we canmeasure the ratio of two untagged lifetimes fortwo nal states:b1b2= 1 +b2  b12 d d+O( d= d)2; (3)where the b is the quantity depend on the nalstate. This indicates the necessity of at least twodierent nal states to extract  d= d.A viable option, perhaps the most eÆcientamong the ones considered in [4], is to comparethe measurements of the untagged lifetimes ofthe semileptonic decay mode SLand of the CP-specic decay modes CP. For each nal states,bSL= 0 and bCP=  cos(21). The ratio be-tween the two lifetimes CPand SLisSLCP= 1cos(21)2 d d+O( d= d)2:(4)The measurement of these two lifetimes should beable to give us a value of j dj, since j cos(21)jwill already be known to a good accuracy by thattime.Since the CP-specic decay modes of Bd(e.g.J= KS(L); D+D ) have smaller branching ratiosthan the semileptonic modes, and the semilep-tonic data sample may be enhanced by includingthe self-tagging decay modes (e.g. D()+sD() )which also have large branching ratios, we ex-pect that the most useful combination will be themeasurement of SLthrough all self-tagging de-cays and that of CP+through the decay Bd!J= KS. After 5 years of LHC running, we shouldhave about 5  105events of J= KS([9] table3), whereas the number of semileptonic decays,at LHCb alone, that will be directly useful inthe lifetime measurements is expected to be morethan 106per year, even with conservative esti-mates of eÆciencies.At LHCb, the proper time resolution is ex-pected to be as good as   0:03 ps. Thisindeed is a very small fraction of the Bdlifetime(Bd 1:5 ps [10]), so the time resolution is nota limiting factor in the accuracy of the measure-ment, and the statistical error plays the dominantrole. Taking into account the estimated numberof Bdproduced the measurement of the lifetimedierence does not look too hard at rst glance.One may infer that if the number of relevantevents with the proper time of decay measuredwith the precision  is N , then the value of d= dis measured with an accuracy of 1=pN .With a suÆciently large number of events N , itshould be possible to reach the accuracy of 0.5%or better.We also point out the interlinked nature ofthe accurate measurements of 1and  d= dthrough the conventional gold-plated decay[4,6].In the future experiments that aim to measure1to an accuracy of 0.005 or better, the correc-tions due to  dwill form a major part of thesystematic error, which can be taken care of by asimultaneous t to sin(21), dand an eectiveparameter  that comes from the CP violation inK  K and B  B systems, and also takes careof small theoretical uncertainties.The calculations of the width dierence in Bdand in the Bssystem (as in [1]) run along similarlines. However, there are some subtle dierencesinvolved, due to the values of the dierent CKMelements involved, which have signicant conse-quences. In particular, whereas the upper boundon the value of  s(including the eects of newphysics) is the value of  s(SM) [11], the up-per bound on  dinvolves a multiplicative fac-tor in addition to  d(SM). Using the deni-tions q Arg( 21)q;q Arg(M21)q, whereq 2 fd; sg, we can write q=  2j 21jqcos(q  q) : (5)3Since the contribution to  21comes only fromtree diagrams, we expect the eect of new physicson this quantity to be very small. We there-fore take j 21jqand qto be unaected by newphysics. On the other hand, the mixing phaseqappears from loop diagrams and can thereforebe very sensitive to new physics. The eect ofnew physics on  scan be bounded by giving anupper bound on  s: s s(SM)cos(2)  s(SM) ; (6)with 2 =  Arg[(VcbVcs)2=(VtbVts)2]   0:03.Thus, the value of  scan only decrease in thepresence of new physics[11].In the Bdsystem, an upper bound for  d,based on the additional assumption of three-generation unitarity, can be derived: d d(SM)cos[Arg(1 + Æf)]: (7)We can calculate the bound (7) in terms of theextent of the higher order NLO corrections. In [4],we got jArg(1 + Æf)j < 0:6, so that we have thebound  d< 1:2  d(SM). A complete NLOcalculation will be able to give a stronger bound.We have seen that the ratio of two eectivelifetimes can enable us to measure the quantity obs(d) cos(21) d= d. In the presence ofnew physics, this quantity is in fact (see eq. (5)) obs(d)=  2(j 21jd= d) cos(d) cos(d  d).In SM, we get obs(d)(SM) = 2(j 21jd= d) cos(21) cos[Arg(1 + Æf)] :(8)If jÆf j < 1:0, we have cos[Arg(1 + Æf)] > 0(in fact, from the t in [12] and our error esti-mates, we have cos[Arg(1 + Æf)] > 0:8). Then obs(d)(SM) is predicted to be positive. Newphysics is not expected to aect d, but it mayaect din such a way as to make the combina-tion cos(d) cos(d d) change sign. A negativesign of  obs(d)would therefore be a clear signalof such new physics.It is well known, that the Bd{Bdmixing phasedis eÆciently measured through the decaymodes J= Ksand J= KL. If we take the newphysics eects into account, the time-dependentasymmetry is ACP=   sin(Mdt) sin(d); in theSM, we have d=  21. The measurementof sin(d) still allows for a discrete ambiguityd$  d. It is clear that, if dcan be deter-mined independently of the mixing in the Bdsys-tem, then measuring  obs(d), which is propor-tional to cos(d) cos(d  d), resolves the dis-crete ambiguity in principle. We note that thesefeatures are unique to the Bdsystem.ACKNOWLEDGMENTSThe work of C.S.K. was supported by GrantNo. 2001-042-D00022 of the KRF. The work ofT.Y. was supported in part by the US Depart-ment of Energy under Grant No.DE-FG02-97ER-41036.REFERENCES1. M. Beneke, G. Buchalla, C. Greub, A. Lenzand U. Nierste, Phys. Lett. B 459 (1999) 631.2. M. Beneke and A. Lenz, J.Phys.G G27(2001) 1219 and references therein.3. D. Becirevic, hep-ph/0110124 and referencestherein.4. A.S. Dighe, T. Hurth, C.S. Kim andT. Yoshikawa, hep-ph/0109088, accepted forpublication in Nucl.Phys.B.5. T. Hurth et al., J. Phys. G 27 (2001) 1277.6. A.S. Dighe, T. Hurth, C.S. Kim andT. Yoshikawa, hep-ph/0112067.7. Report of Workshop on B Physics atthe Tevatron: Run II and Beyond, hep-ph/0201701.8. S. Hashimoto and N. Yamada [JLQCD col-laboration], hep-ph/0104080.9. P. Ball et al., hep-ph/0003238.10. Particle Data Group, D.E. Groom et al., Eur.Phys. J. C15 (2000) 1.11. Y. Grossman, Phys. Lett. B 380 (1996) 99.12. S. Mele, hep-ph/0103040.

Measurement of the Width difference of $B_{d}$ mesons

Measurement of the Width Difference of B_d Mesons

Measurement of the Width Difference of B_d Mesons

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