We examine the prospects for the detection of Higgs mediated lepton flavor
violation at LHC and at a photon collider in the minimal supersymmetric
standard model with large lepton flavor violating mass insertions in the
$\mu-\tau$ sector constraining the parameter space with several experimental
bounds. We find rates probably too small to be observed at future experiments
if models have to accommodate for a neutralino relic density as measured by
WMAP and explain the $(g-2)_{\mu}$ anomaly: better prospects are found if these
two constraints are applied only as upper bounds. The spin-independent
neutralino-nucleon cross section in the studied constrained parameter space is
just below the present CDMS limit while gamma rates from neutralino
annihilation in the halo are strongly suppressed.Comment: 6 pages, 2 figures, Prepared for the proceedings of the workshop:
  "LC09: $e^+ e^-$ Physics at the TeV Scale and the Dark Matter Connection",
  21-24 September 2009, Perugia, Ital

Cannoni, M.

Panella, O.

English

arXiv

We examine the prospects for the detection of Higgs-mediated lepton flavor violation at LHC and at a photon collider in the minimal supersymmetric standard model with large lepton flavor violating mass insertions in the μ − τ Sector constraining the parameter space with several experimental bounds. We find rates probably too small to be observed at future experiments if models have to accommodate for a neutralino relic density as measured by WMAP and explain the (g − 2)μ anomaly: better prospects are found if these two constraints are applied only as upper bounds. The spin-independent neutralino-nucleon cross-section in the studied constrained parameter space is just below the present CDMS limit while gamma rates from neutralino annihilation in the halo are strongly suppressed

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DOI 10.1393/ncc/i2010-10605-2Colloquia: LC09IL NUOVO CIMENTO Vol. 33 C, N. 2 Marzo-Aprile 2010Higgs sector of the MSSM: Lepton flavor violation at colliders andneutralino dark matterM. Cannoni(1) and O. Panella(2)(1) Departamento de Fisica Aplicada, Universidad de Huelva - Campus de El Carmen21071 Huelva, Spain(2) INFN, Sezione di Perugia - Via A. Pascoli, 06129 Perugia, Italy(ricevuto il 18 Febbraio 2010; approvato il 25 Marzo 2010; pubblicato online il 18 Giugno 2010)Summary. — We examine the prospects for the detection of Higgs-mediated lep-ton flavor violation at LHC and at a photon collider in the minimal supersymmetricstandard model with large lepton flavor violating mass insertions in the μ − τ sec-tor constraining the parameter space with several experimental bounds. We findrates probably too small to be observed at future experiments if models have toaccommodate for a neutralino relic density as measured by WMAP and explain the(g − 2)μ anomaly: better prospects are found if these two constraints are appliedonly as upper bounds. The spin-independent neutralino-nucleon cross-section in thestudied constrained parameter space is just below the present CDMS limit whilegamma rates from neutralino annihilation in the halo are strongly suppressed.PACS 11.30.Pb – Supersymmetry.PACS 14.80.Da – Supersymmetric Higgs bosons.PACS 95.35.+d – Dark matter (stellar, interstellar, galactic, and cosmological).1. – IntroductionThe Higgs sector of the minimal supersymmetric standard model (MSSM) [1], es-pecially the heavy neutral Higgses A and H, play a prominent role in the physics ofneutralino dark matter [2]. In some region of the supersymmetric (SUSY) parameterspace neutralinos yield the desired amount of relic density by annihilating into fermionsthrough the s-channel resonant exchange of neutral Higgs bosons h, H, A, the so-calledfunnel region where mA  2mχ; besides, as dark matter is expected to be distributedin a halo surrounding our galaxy, neutralinos can scatter off nuclei in terrestrial detec-tors: the coherent scattering is mediated by scalar interactions through the s-channelexchange of squarks and t-channel exchange of the CP -even neutral Higgs bosons h andH. These effects become sizable when squarks are heavy and tan β is large in reason ofthe enhanced Higgs bosons coupling to down-type fermions, especially for the b quarkc© Societa` Italiana di Fisica 183184 M. CANNONI and O. PANELLAwhich has the largest Yukawa coupling receiving large radiative SUSY-QCD correctionsat large tanβ.Once a source of lepton flavor violation (LFV) is present in the slepton mass ma-trix, for example the MSSM with the seesaw mechanism for generation of small neu-trino masses [3], non-holomorphic LFV Yukawa couplings of the type L¯iRLjLH∗u areinduced at loop level and become particularly sizable at large tanβ giving rise to en-hanced Higgs-mediated LFV effects [4]. The LFV mass insertions δijLL = (m2L)ij/m2L,δijRR = (m2R)ij/m2R, where (m2L,R)ij are the off-diagonal flavor changing entries of theslepton mass matrix, are free parameters which allow for a model-independent study ofLFV signals. We introduce LFV in the model through the mass insertions δ32LL,RR = 0.5.This value ensures the largest rates in LFV processes and allows us to study the moreoptimistic scenarios for LFV detection; higher values contradict the mass insertion ap-proximation as an expansion of propagators in these small parameters.Higgs-mediated effects become interesting at large μ and tanβ and low mA; further,if SUSY-QCD particles are heavy, Higgs effects are dominant also for neutralino darkmatter. We thus consider the following real MSSM parameter space: 100GeV ≤ mA ≤1TeV, 20 ≤ tanβ ≤ 60, 500GeV ≤ μ ≤ 5TeV, (the sign of μ is taken positive, aspreferred by the SUSY explanation of the (g − 2)μ anomaly), 150GeV ≤ M1, M2 ≤1.5TeV (we do not impose any relation but let them vary independently allowing forgaugino non-universality at the weak scale), 1TeV ≤ M3 ≤ 5TeV (to have large massesfor gluinos), 1TeV ≤ mU3 , mD3 , mQ3 ≤ 5TeV (for the first and the second generationthe soft masses are set to be equal, mUi = mDi = mQi = mq˜, where i = 1, 2 and mq˜ isanother free parameter which varies in the same range), 300GeV ≤ mL3 , mE3 ≤ 2.5TeV(for the first and the second generation the slepton soft masses are set to be equal,mLi = mEi = m˜, where i = 1, 2 and m˜), −2 ≤AU3mU3, AD3mD3 ,AE3mE3≤ 2 while for the firstand the second generation the trilinear scalar couplings are set to zero.We impose on the parameter space several experimental limits: 1) LEP, TEVATRONbounds on sparticle masses and the LEP bound on light Higgs; 2) present bounds onB-physics observables B(B → Xsγ), B(Bs → μ+μ−), ΔmBs , B(B → τν); 3) the presentexperimental upper bounds on LFV processes B(τ → μγ), B(τ → μη), B(τ → μμμ), 4)the exclusion limits on the neutralino-nucleus spin-independent cross-section from theCDMS experiment [5]; 5) the CDF exclusion limits in the (mA, tanβ)-plane [6]. All ofthem are applied at the same time with the exception of the WMAP 3σ interval [7] onrelic density and (g− 2)μ anomaly for which we also relax the lower bounds: thus in thefollowing figures the light gray (turquoise) points have only Ωχh2 ≤ 0.13 and aMSSMμ ≤4× 10−9, the plus-shaped points dark-gray (indigo) points satisfies 0.09 ≤ Ωχh2 ≤ 0.13and aMSSMμ ≤ 4 × 10−9, finally, the squared points satisfy 0.09 ≤ Ωχh2 ≤ 0.13 and1×10−9 ≤ aMSSMμ ≤ 4×10−9. For numerical computations we use the codeDarkSusy [8]and the code FeynHiggs [9], while for the explicit formulas and further details on theexperimental constraints we refer the reader to ref. [10].2. – Higgs-mediated LFV at LHC and at a photon colliderAt high tanβ the dominant production mechanisms for A, H at LHC is bb¯ fusion dueto the mb tanβ enhanced bb¯Φ couplings. We calculate the cross-section with FeynHiggswhich uses the approximation σMSSM(bb¯ → Φ) = σSM(bb¯ → Φ)Γ(Φ→bb¯)MSSMΓ(Φ→bb¯)SM , whereσSM(bb¯ → Φ) is the total SM cross-section for production of Higgs boson with mass mΦvia bb¯ fusion: to obtain the value in the MSSM it is rescaled with the ratio of the decayHIGGS SECTOR OF THE MSSM ETC. 185Fig. 1. – (Colour on-line) Left: scatter plot of the inclusive production cross-section pp→ Φ+Xtimes the branching ratio of Φ → τμ at LHC vs. mA (Φ = A,H). Right: scatter plot for thecross-section of the process γγ → τμbb¯ in photon-photon collision at √sγγ = 600GeV. Thelight gray (turquoise) points have only Ωχh2 ≤ 0.13 and aMSSMμ ≤ 4 × 10−9, the plus-shapeddark-gray (indigo) points satisfy 0.09 ≤ Ωχh2 ≤ 0.13 and aMSSMμ ≤ 4×10−9, finally, the squaredpoints satisfy 0.09 ≤ Ωχh2 ≤ 0.13 and 1× 10−9 ≤ aMSSMμ ≤ 4× 10−9.width of the inverse process in the MSSM over the SM decay width [9]. We calculate foreach random model the product σ(pp → Φ+X)×B(Φ→ τμ). As masses and couplingsof A and H are practically identical as discussed above, we have σ(pp → A+X)+σ(pp →H + X)  2σ(pp → A + X). The scatter plot σ(pp → Φ + X) × B(Φ → τμ) is shownin fig. 1, left panel. We see that with the nominal integrated luminosity of 100 fb−1 peryear models which satisfy both the relic density abundance and Δaμ can give up to 10events per year (squared points), up to 40 if we relax the condition on the lower limitof Δaμ (plus-shaped points) and up to 200-300 relaxing both the lower limits (turquoise(light-gray) points).In γγ collisions the main production mechanism for Φ = A,H is ττ fusion while thebb¯ is suppressed by a factor 3(1/3)4(mb/mτ )2  0.1 which cannot be compensated bycorrections to the b Yukawa coupling. In ref. [11] we studied in detail the μτ fusionprocess γγ → μτbb¯ where the Higgs boson is produced in the s-channel via a virtual μτpair and can be detected from its decay mode A → bb¯. There we have shown that a goodanalytical approximation for the cross-section is obtained using the equivalent particleapproximation wherein the colliding real photons split, respectively, into τ and μ pairswith the subsequent μτ fusion into the Higgs boson and that the effect of photons spectracan be neglected. We thus consider monochromatic photons with √sγγ = 600GeV, andphoton-photon luminosity 500 fb−1 y−1 [11]. The scatter plot of the signal cross-sectionversus mA is shown in fig. 1, right panel. Here the models which satisfy both the relicdensity abundance and Δaμ (squared points) have maximal cross-section 10−3 fb, whichis too small. Relaxing the lower limits cross-sections up to 2×10−2 fb are possible, giving10 events/year.186 M. CANNONI and O. PANELLAFig. 2. – (Colour on-line) Left: scatter plot for the spin-independent neutralino-nucleon cross-section vs. the neutralino mass. The area above the solid line is excluded by the CDMS finalresults; the area above the dotted line is excluded by the 2008 CDMS search. The dashed anddot-dashed lines give the sensitivity reach of two phases of the XENON experiment. Right:scatter plot for the particle physics factor entering the formula of the flux of gamma-rays fromneutralino annihilation in the halo, see the text. The light gray (turquoise) points have onlyΩχh2 ≤ 0.13 and aMSSMμ ≤ 4 × 10−9, the plus-shaped dark-gray (indigo) points satisfy 0.09 ≤Ωχh2 ≤ 0.13 and aMSSMμ ≤ 4× 10−9, finally, the squared points satisfy 0.09 ≤ Ωχh2 ≤ 0.13 and1× 10−9 ≤ aMSSMμ ≤ 4× 10−9.3. – Neutralino dark matter direct and indirect detectionThe spin-independent neutralino-nucleon cross-section in the limit of heavy squarksand large tanβ can be approximated as [12] σSI  g′2g2|N11|2|N13|2m4N4πm2W m4Atan2 β×Kf , whereN11 and N13 are the lightest neutralino unitary mixing matrix elements, mN the nucleonmass (neglecting the mass difference between the neutron and the proton) and Kf afactor which depends on nucleon form factors. The left panel of fig. 2 shows the scatterplot for the spin-independent neutralino-nucleon cross-section as a function of mχ and theregion excluded by CDMS [5]. We emphasize that CDF and CDMS limits are very mildconstraints: the region excluded by CDF is practically excluded by the other constraintswhile the CDMS limit excludes only one plus-shaped point leaving untouched the regionspreferred by WMAP and the (g− 2)μ anomaly. The XENON100 experiment [13] shouldreach the sensitivity corresponding to the dashed gray (red) line in fig. 1, left panel.Such sensitivity is able to cover the region with the highest cross-section, mχ ≥ 300GeV,where there is a large higgsino component. On the other hand, the region preferred by(g − 2)μ anomaly cannot be covered. We also report the prospected sensitivity goal ofthe XENON experiment with 1 ton detector mass [13], dot-dashed gray (red) line, whichis 10−11–10−10 pb for neutralino mass in the range 100–1000GeV: practically all of theparameter space can be probed.We also present the effect of our constrained parameter space on the flux of photonscoming from neutralino annihilation in the halo which is a very active field in indirectdark matter detection. The flux of gammas expected from neutralino annihilation isgenerally given by F = ΦPP × Φastro where the second factor contains the astrophysi-HIGGS SECTOR OF THE MSSM ETC. 187cal information and is given by the integral of the squared of the dark matter densityalong the direction of observation, while ΦPP is the particle physics factor given byΦPP (Eγ > Eth) = 〈σv〉/(2m2χ)∫ mχEthdE(dNγ/dE), where 〈σv〉 is the thermal averagedcross-section annihilation times the velocity of neutralinos and the dNγ/dE is the pho-ton spectrum which is integrated over energies greater than Eth. Here we are interestedmainly in the evaluation of the particle physics factor and in comparing it with otherstudies in the literature in the framework of the MSSM. We present ΦPP as a functionof the neutralino mass in fig. 2, right panel, with threshold energy Eth = 1GeV. Formodels with a relic density inside the WMAP interval the maximum value of the particlephysics factor is 2× 10−32 photons GeV−2 cm3 s−1 for neutralino mass around 200GeV:this value is two orders of magnitude smaller than the typical values found in similarstudies without the constraints from lepton flavor violation and the updated B physicsand (g− 2)μ constraints, see refs. [14]. We remark that most of the models which satisfythe WMAP bounds, the plus-shaped and squared points in the figures, satisfy the Higgsfunnel condition mA  2mχ (see fig. 2, left panel of ref. [10]): the main annihilationchannel is χχ → bb¯/τ τ¯ through s-channel heavy Higgs exchange which is strongly con-strained in our scenario and thus it is natural to have a reduction of photon emission.A reduction of the gamma-ray flux in the funnel region is also found in ref. [3] in thestudy of the minimal supergravity (mSUGRA) plus right-handed neutrinos for see-sawgeneration of neutrino masses respect to the case of pure mSUGRA.4. – ConclusionsIn the framework of the MSSM with heavy SUSY-QCD particles and large tanβwe have studied lepton flavor violation in τ − μ sector mediated by the heavy neutralHiggs Φ = A, H at high-energy colliders through the production and decay at LHC,pp → Φ + X, Φ→ τμ and the μ− τ fusion at a photon collider, γγ → τμbb¯.We have found that in models with 0.09 ≤ Ωχh2 ≤ 0.13 and 1 ≤ aMSSMμ × 109 ≤ 4:at LHC the cross-section for pp → Φ + X, Φ → τμ can reach O(10−1–10−2) fb in therange mA = 400–1000GeV giving up to 10 events with 100 fb−1; the cross-section ofγγ → τμbb¯ reaches O(10−3) fb, thus too small even for the large value of the expectedluminosity of 500 fb−1. Prospects are somewhat more encouraging if we relax the lowerlimits, imposing only Ωχh2 ≤ 0.13 and aMSSMμ × 109 ≤ 4: the cross-section at LHC isabout 2 fb for low mA masses and around 2×10−2 fb in γγ collisions. On the other hand,to observe such effects, in any case, the full luminosity of the machine is needed.We have also studied the spin-independent neutralino nucleus cross-section: we haveshown that in models that satisfy 0.09 ≤ Ωχh2 ≤ 0.13 and 1 ≤ aMSSMμ × 109 ≤ 4, thecross-section lies just below the sensitivity of XENON100 which should report resultssoon. The full XENON 1 ton is needed to cover all the parameter space. 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Higgs sector of the MSSM: Lepton flavor violation at colliders and neutralino dark matter

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Higgs sector of the MSSM: lepton flavor violation at colliders and neutralino dark matter

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