QCD corrections to the gluino induced contribution to b --> s gamma are shown
to be important in order to extract reliable bounds on the off-diagonal
elements of the squark mass matrices.Comment: 4 pages including 2 postscript figure

Greub, C.

Hurth, T.

Wyler, D.

English

arXiv

QCD corrections to the gluino induced contribution to b --> s gamma are shown to be important in order to extract reliable bounds on the off-diagonal elements of the squark mass matrices.QCD corrections to the gluino induced contribution to b --> s gamma are shown to be important in order to extract reliable bounds on the off-diagonal elements of the squark mass matrices

Greub, Christoph

Hurth, Tobias

Wyler, Daniel

CERN Document Server

arXiv:hep-ph/9912420v1  20 Dec 1999CERN–TH/99-335BUTP–99/21MPI-PhT-99-52ZH-TH–27/99hep-ph/99mmnnnINDIRECT SEARCH FOR SUPERSYMMETRY IN RARE B DECAYSChristoph GreubInstitut fu¨r theoretische Physik, Universita¨t Bern, CH-3012 Bern, SwitzerlandTobias HurthTheory Division, CERN, CH-1211 Geneva 23, SwitzerlandandMax-Planck-Institut fu¨r Physik, D–80805 Mu¨nchen, GermanyDaniel WylerInstitut fu¨r theoretische Physik, Universita¨t Zu¨rich, CH-8057 Zu¨rich, SwitzerlandABSTRACTQCD corrections to the gluino induced contribution to b → sγ are shown to be important inorder to extract reliable bounds on the off-diagonal elements of the squark mass matrices.Talk presented by Tobias Hurth at the International Euroconferenceon High Energy Physics (EPS-HEP99), 15-21 July 1999, Tampere, Finland.Indirect Search for Supersymmetryin Rare B DecaysChristoph Greub a, Tobias Hurth b, c ,and Daniel Wyler da Institut fu¨r Theoretische Physik, Universita¨t Bern, CH–3012 Bern, Switzerlandb Theory Division, CERN, CH–1211 Geneva 23, Switzerlandc Max-Planck-Institut fu¨r Physik, D–80805 Mu¨nchen, Germanyd Institut fu¨r Theoretische Physik, Universita¨t Zu¨rich, CH–8057 Zu¨rich, SwitzerlandAbstractQCD corrections to the gluino induced contribution to b→ sγ are shown to be important inorder to extract reliable bounds on the off-diagonal elements of the squark mass matrices.Rare processes are an important tool for investi-gating new interactions. The standard model contribu-tions are usually small and new physics may manifestitself clearly. In particular, rare decays provide guide-lines for supersymmetry model building. The experi-mental observation of these Flavour Changing NeutralCurrents (FCNCs), or the upper limits set on them yieldstringent relations between the many parameters in thesoft supersymmetry-breaking terms. The processes in-volving transitions between first and second generationquarks, namely FCNC processes in the K system, areconsidered to be most efficient in shaping viable super-symmetric flavour models. Moreover, the tight experi-mental bounds on some flavour diagonal transitions suchas the electric dipole moment of the electron and of theneutron, as well as g − 2, help constrain soft terms in-ducing chirality violations.The severe experimental constraints on flavourviolations have no direct explanation in the structure ofthe minimal supersymmetric standard model (MSSM).This is the essence of the well-known supersymmetricflavour problem. There exist several supersymmetricmodels (within the MSSM) with specific solutions tothis problem. Most popular are the ones in which thedynamics of flavour sets in above the supersymmetrybreaking scale and the flavour problem is killedby the mechanisms of communicating supersymmetrybreaking to the experimentally accessible sector: In theconstrained minimal supersymmetric standard model(mSUGRA) supergravity is the mediator between thesupersymmetry breaking and the visible sector [1].In gauge-mediated supersymmetry breaking models(GMSBs) the communication between the two sectorsis realized by gauge interactions [2]. More recentlythe anomaly mediated supersymmetry breaking models(AMSBs) were proposed, in which the two sectors arelinked by interactions suppressed by the Planck mass[3]. Furthermore, there are other classes of models inwhich the flavour problem is solved by particular flavoursymmetries.Neutral flavour transitions involving third genera-tion quarks, typically in the B system, do not pose yetserious threats to these models. The rare decay b → sγhas already been detected, but the precision of the mea-surements is at the moment not very high [4]. Never-theless, it has already carved out some regions in thespace of free parameters of most of the models in theabove classes (see [5] and references therein). In partic-ular, it dangerously constrains several somewhat tunedrealizations of these models [6]. Once the experimen-tal precision is increased, this decay will undoubtedlyhelp selecting the viable regions of the parameter spacein the above class of models and/or discriminate amongthese or other possible models. It is important to calcu-late the rate of this decay with theoretical uncertaintiesreduced as much as possible, and general enough forgeneric supersymmetric models. In the standard model,the rate for b → sγ is known up to next-to-leading or-der (NLL) in QCD [7]. The NLL calculation reducesthe large scale dependence present at the LL (±25%)to a mere percent uncertainty. This accuracy is how-ever somewhat fortuitous as it is obtained through largeaccidential cancellations among different contributionsto the NLL corrections [8, 9]. Indeed, the accuracy forthe NLL calculation of the b → sγ rate in a two-Higgsmodel is substantially worse [8].The calculation of this decay rate within supersym-metric models is still far from this level of sophistica-tion. There are several contributions to the decay ampli-tude: Besides the W− − t-quark and the H− − t-quarkcontributions, there are also the chargino, gluino andneutralino contributions. All these contributions werecalculated in [10] within the mSUGRA model; their an-alytic expressions apply naturally also to the GMSB,2and AMSB models. The inclusion of QCD correctionsneeded for the calculation of the rate, was in [10] as-sumed to follow the SM pattern. A calculation takinginto account solely the gluino contribution has been per-formed in [11] for a generic supersymmetric model, butno QCD corrections were included.An interesting NLL analysis of b→ sγ was recentlyperformed [12, 13] in a specific class of models wherethe only source of flavour violation at the electroweakscale is that of the SM, encoded in the Cabibbo-Kobayashi-Maskawa (CKM) matrix. This calculation,however, cannot be used in particular directions of theparameter space of the above listed models in whichquantum effects induce a gluino contribution as largeas the chargino or the SM contributions. Nor it can beused as a model-discriminator tool, able to constrain thepotentially large sources of flavour violation typical ofgeneric supersymmetric models.Among these, the flavour non-diagonal vertexgluino-quark-squark induced by the flavour violatingscalar mass term and trilinear terms is particularlyinteresting. This is generically assumed to induce thedominant contribution to quark flavour transitions, asthis vertex is weighted by the strong coupling constantgs. Therefore, it is often taken as the only contributionto these transitions and in particular to the b → sγdecay, when attempting to obtain order-of-magnitudeupper bounds on flavour violating terms in the scalarpotential [11, 14]. Once the constraints coming from theexperimental measurements are imposed, however, thegluino contribution is reduced to values such that theSM and the other supersymmetric contributions cannotbe neglected anymore. Any LL and NLL calculationof the b → sγ rate in generic supersymmetric models,therefore, should then include all possible contributions.The gluino contribution, however, presents somepeculiar features related to the implementation of theQCD corrections. In ref. [15] this contribution to thedecay b → sγ is therefore investigated in great detailfor supersymmetric models with generic soft terms. Itis shown that the relavant operator basis of the SMeffective Hamiltonian gets enlarged to contain magneticand chromomagnetic operators with an extra factor ofαs and weighted by a quark mass mb or mc, andalso magnetic and chromomagnetic operators of lowerdimensionality, as well as additional scalar and tensorialfour-quark operators. A few results of our analysisin ref. [15] are given in the following, showing theeffect of the LL QCD corrections on constraints onsupersymmetric sources of flavour violation.To understand the sources of flavour violation whichmay be present in supersymmetric models in addition tothose enclosed in the CKM matrix, one has to considerthe contributions to the squark mass matricesM2f =(m2f,LL m2f,LRm2f,RL m2f,RR)+ (1)(Ff,LL +Df,LL Ff,LRFf,RL Ff,RR +Df,RR), (2)where f stands for up- or down-type squarks. In thesuper CKM basis where the quark mass matrices arediagonal and the squarks are rotated in parallel to theirsuperpartners, the F terms from the superpotential andthe D terms turn out to be diagonal 3×3 submatrices ofthe 6× 6 mass matricesM2f . This is in general not truefor the additional terms (1), originating from the softsupersymmetric breaking potential. As a consequence,gluino contributions to the decay b → sγ are inducedby the off-diagonal elements of the soft terms m2f,LL,m2f,RR, m2f,RL.It is convenient to select one possible source offlavour violation in the squark sector at a time andassume that all the remaining ones are vanishing.Following ref. [11], all diagonal entries in m2d, LL,m2d, RR, and m2u, RR are set to be equal and theircommon value is denoted by m2q˜ . The branching ratiocan then be studied as a function ofδLL,ij =(m2d, LL)ijm2q˜, δRR,ij =(m2d, RR)ijm2q˜, (3)δLR,ij =(m2d, LR)ijm2q˜, (i 6= j). (4)The remaining crucial parameter needed to determinethe branching ratio is x = m2g˜/m2q˜ , where mg˜ isthe gluino mass. In the following, we concentrate onthe LL QCD corrections to the gluino contribution.In Figs. 1 and 2, the solid lines show theFigure 1. Gluino-induced branching ratio BR(B → Xsγ) asa function of x = m2g˜/m2q˜ , obtained when the only source offlavour violation is δLR,23 (see text).QCD corrected branching ratio, when only δLR,23 orδLL,23 are non vanishing. The branching ratio is3Figure 2. Same as in Fig. 1 when only δLL,23 is non-vanishing.plotted as a function of x, using mq˜ = 500 GeV.The dotted lines show the range of variation of thebranching ratio, when the renormalization scale µ variesin the interval 2.4–9.6 GeV. Numerically, the scaleuncertaintly in BR(B → Xsγ) is about ±25%. Anextraction of bounds on the δ quantities more precisethan just an order of magnitude, therefore, wouldrequire the inclusion of next-to-leading logarithmicQCD corrections. It should be noticed, however, thatthe inclusion of the LL QCD corrections has alreadyremoved the large ambiguity on the value to be assignedto the factor αs(µ) in the gluino-induced operators.Before adding QCD corrections, the scale in this factorcan assume all values from O(mb) to O(mW ): thedifference between BR(B → Xsγ) obtained whenαs(mb) or when αs(mW ) is used, is of the same orderas the LL QCD corrections. The corresponding valuesfor BR(B → Xsγ) for the two extreme choices of µare indicated in Figs. 1 and 2 by the dot-dashed lines(µ = mW ) and the dashed lines (µ = mb). The choiceµ = mW gives values for the non-QCD correctedBR(B → Xsγ) relatively close to the band obtainedwhen the LL QCD corrections are included, if onlyδLL,23 is non-vanishing. Finding a corresponding valueof µ that minimizes the QCD corrections in the casestudied in Fig. 1, when only δLR,23 is different fromzero, depends strongly on the value of x. In the contextof the full LL result, it is important to stress that theexplicit αs factor has to be evaluated - like the Wilsoncoefficients - at a scale µ = O(mb).In spite of the large uncertainties which thebranching ratio BR(B → Xsγ) still has at LL inQCD, it is possible to extract indications on the sizethat the δ-quantities may maximally acquire withoutinducing conflicts with the experimental measurements(see [15]).Acknowledgment: This work was partially supported bySchweizerischer Nationalfonds.References[1] A.H. Chamseddine, R. Arnowitt and P. Nath,Phys. Rev. Lett. 49 (1982) 970; R. Barbieri, S.Ferrara, and C.A. Savoy, Phys. Lett. B119(1982) 343; L.J. Hall, J. Lykken, and S.Weinberg, Phys. Rev. D27 (1983) 2359.[2] M. Dine, W. Fischler, and M. Srednicki, Nucl.Phys. B189 (1981) 575; S. Dimopoulos and S.Raby, Nucl. Phys. B192 (1981) 353; M. Dineand A.E. Nelson, Phys. Rev. D49 (1993) 1277;M. Dine, A.E. Nelson, and Y. Shirman, Phys.Rev. D51 (1995) 1362; M. Dine, A.E. Nelson,Y. Nir and Y. Shirman, Phys. Rev. D53 (1996)2658.[3] M. Leurer, Y. Nir, and N. Seiberg, Nucl. Phys.B398 (1993) 319 and Nucl. Phys. B420 (1994)468.[4] M.S. Alam et al. Phys. Rev. Lett. 74, 2885(1995); CONF 98-17, ICHEP98 1011; R. Barateet al. Phys. Lett. B429, 169 (1998).[5] T. Goto, Y. Okada and Y. Shimizu, Phys. Rev.D58 (1998) 094006.[6] F.M. Borzumati, M. Olechowski andS. Pokorski, Phys. Lett. B349 (1995) 311;F.M. Borzumati, hep-ph/9702307.[7] A. Ali and C. Greub, Z. Phys. C49, 431 (1991);Phys. Lett. B259, 182 (1991); Phys. Lett. B361,146 (1995); N. Pott, Phys. Rev. D54, 938 (1996);C. Greub, T. Hurth and D. Wyler, Phys. Lett.B380, 385 (1996); Phys. Rev. D54, 3350 (1996);K. Adel and Y. Yao, Phys. Rev. D49, 4945(1994); C. Greub and T. Hurth, Phys. Rev. D56,2934 (1997); K. Chetyrkin, M. Misiak andM. Munz, Phys. Lett. B400, 206 (1997).[8] F.M. Borzumati and C. Greub, Phys. Rev. D58(1998) 074004; D59 (1999) 057501.M. Ciuchini et al., Nucl. Phys. B527 (1998) 21.[9] A.L. Kagan and M. Neubert, Eur. Phys. J. C7(1999) 5.[10] S. Bertolini, F. Borzumati, A. Masiero, and G.Ridolfi, Nucl. Phys. B353 (1991) 591.[11] F. Gabbiani, E. Gabrielli, A. Masiero, and L.Silvestrini, Nucl. Phys. B477 (1996) 321[12] M. Ciuchini, G. Degrassi, P. Gambino andG.F. Giudice, Nucl. Phys. B534 (1998) 3[13] C. Bobeth, M. Misiak and J. Urban,hep-ph/9904413.[14] J.S. Hagelin, S. Kelley, and T. Tanaka, Nucl.Phys. B415 (1994) 293.[15] F.M. Borzumati, C. Greub, T. Hurth andD. Wyler, hep-ph/9911245.

Indirect search for supersymmetry in rare B decays

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