arXiv:hep-ph/9909349v1 13 Sep 1999 hne o UYa iheeg colliders. a energy high provide at mesino– fact SUSY for established, in channel is can once oscillations attempted antimesino of the be existence special- in only very could the violation a which sflavor representing measurement than of ized Rather probe sector. sensitive pro- squark very mesino– could and a neutral forbidden addition, vide not In are oscillations decay. antimesino angular with heavy jets jets displaced from displaced from of significantly to Decay differ rise which distributions give states. can bound states mesino these or sbaryon Squarks in phenomenology. novel hadronize very motivation, to leads theoretical super- scenario the this spontaneous Beyond to breaking. couplings symmetry messenger suppressed supersymme- interacting have strongly gauge-mediated the fields which of in theories breaking try in NLSP occur squark a can unconventional, perhaps While explored. supersymme- [1]. for deter- try signatures largely phenomenological and the model-dependent, mines is supersymmetric next-to-lightest (NLSP) the gravi- of the identity of The ton. supersymmetric the lightest is elec- the (LSP) the particle scales, between Planck intermediate and scale troweak a below is breaking present at remain breaking, spectrum, unknown. superpartner spontaneous underly- largely the this the as of well However, scale as and scale. mechanism be electroweak ing should the order ordinary masses the of of breaking superpartners the the for stability, main- to this Uni- order tain scale In Grand electroweak corrections. the the radiative stabilizing quadratic as by against such scales, Planck scales, or energy fied higher characterized much theories by fundamental more in embedded be uesmer raigadconserved and breaking supersymmetry LPi eatbe h nyaalbeculn o de- for coupling available only The metastable. is NLSP qakDcyadHadronization and Decay Squark are NLSP squark a of consequences the letter this In supersymmetry spontaneous of scale intrinsic the If to model standard the allows (SUSY) Supersymmetry ASnmes 48.y 26.vUDHP9-S1SU-ITP- UND-HEP-98-US01 12.60.Jv 14.80.Ly, t numbers: same-sign PACS squ a the with in events violation through sflavor supersymmetry up-type for of channel probe signatures. sensitive distinctive a with give rates observable at le occur oscillation can can mesino–antimesino collider b Neutral energy mesinos high parameter. a and impact at sbaryons superpa states model forming bound standard , supersymmetric lightest light the with as hadronize squark a and breaking h hnmnlgclipiain fsprymti theo supersymmetric of implications phenomenological The ( a ) eateto hsc,Uiest fNteDm,NteDame Notre Dame, Notre of University Physics, of Department ( b ) eateto hsc,Safr nvriy tnod A9 CA Stanford, University, Stanford Physics, of Department eio–Atmsn Oscillations Antimesino – Mesino —Wt o scale low With .— R r Sarid Uri prt,the -parity, discovery a n ct Thomas Scott and 1 ǫ Γ( expect by squarks given all is and in heavy are rate the NLSP decay the which three-body in The limit the suppressed. space phase he oydcytruhacagdcretinteraction, current charged t a through decay body Three n upesdmdst ih urs uhas such quarks, light to modes violat- flavor suppressed through kinemat- ing are only decays the stop- two-body quark, allowed a top For ically the nega- Yukawa. than top lighter and squark the like to repulsion, the proportional to both level contribution mass, evolution stop group renormalization left-right tive of because (s)quarks. down-type the for likewise r eae otegueegnttsby eigenstates gauge the to eigenstates related flavor-mass are quark up-type right-handed and tn.Tetobd ea aefra ptp squark up-type an for rate decay two-body NLSP, The itino. ewe h ur n qakms iesae,i given is eigenstates, mass squark by and quark the between a struhteGlsiocomponents, Goldstino the through is cay where qakms iesae r eae oflvreigenstates flavor to related by are eigenstates mass squark ( where and ˜ U ( 2 e N → h ihetsur slkl ob otystop-like mostly be to likely is squark lightest The Q R e ) Q U ai a Γ( q tpmsn–nieiooclain would oscillations mesino–antimesino Stop bW r o obde yaysmer and symmetry any by forbidden not are s a R Ri † → = Q ) Q √ e = e r etr n a rvd discovery a provide can and sector, ark ǫ aj dt ipae eswt ag negative large with jets displaced to ad G = a ( ( q ǫ e F q L ptptopology. op-top → ( 2 i ( fr eaig rdcino these of Production decaying. squarks efore Such investigated. are rtner j sntsprse yflvrvoain u is but violation, flavor by suppressed not is , U iswt o cl supersymmetry scale low with ries → L W e ) U ) U ai ) Lai stesprymtybekn cl,and scale, breaking supersymmetry the is b L q ai † Rij G q e G D + e i + Q = ) G e nldn eea sflvrmisalignment (s)flavor general including , e L ( = q

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ai 2 a , . . . , ! =    h left- The . m ǫ m 4 ( ( t ˜ q R Q 2 e W 2 U j ) → ,and 6, a ) Lij ai , m m c q (2) (1) G Lj ′ e Q 2 = e q 2 . j a ! ∗ quark mixing matrix. The phase space integrals are Fig. 1(a) for u˜au¯i u˜aui . The tree level con- tribution to theM oscillation↔ M amplitude for a single linear 1 (1 x)4(x a)2 6x3(3a + x) I(a,b)= dx − − combination of the Weyl components of the light quark 12x3a (x b)2 in the color singlet channel is Za  − 1 g2m 2 ∗ 2 s g˜ 4x (4a x) 2 2 g˜(Qaqi Qaqi)= ǫ(N)ai 1 2 2 2 (4) + − + x +2xa +3a A → − Nc mg˜ m (x b)   − Qa −  e e 1 b(1 x)4(x a)2(2a + x) where ǫ(N)ai is the same flavor matrix which appears in J(a,b)= dx − − (3) the two-body decay (1), and N = 3 is the numbere of col- 2x2a(x b)2 c Za − ors. contributions are comparable depending on the precise spectrum. For a stop-like squark the three-body mode t˜ bW G dominates if the sflavor violation is very small, while→ the two-body mode(s) t˜ qiG, i =1, 2, dominate for largere → ~ ~ ~ sflavor violation. Numerically, for mt˜ = 150 GeV the uj ui uj W ui < ~ ~ three-body decay t˜R bWe G dominates for ǫ(R)i3 4 g dk dl 10−3. For a stop-like→ squark much heavier than the∼ top,× ~ ~ 2 2 2 ui uj ui W uj t˜ tG dominates t˜ qiG fore ǫ < (1 m /m ) . → → (N)i3 − t t˜ For either the two- or three-body∼ modes, decay of a (a) (b) squarke NLSP to the Goldstinoe can take place over macro- scopic distances [1], and easily exceeds the hadroniza- FIG. 1. Mesino oscillations arise (a) from tree-level gaug- tion length scale [2]. For example, with mt˜ = 150 GeV ino exchange and (b) from one-loop charged current– −1 4 Γ (t˜R bW G) 75 cm (√F/100 TeV) , while for box diagrams. Arrows indicate the flow of number → −1≃ 4 and crosses represent fermion number violating mass m˜ = 190 GeV Γ (t˜ tG) 0.75 cm (√F/100 TeV) . t insertions. (S)flavor violation may be isolated in the gaugino A NLSP squarke therefore→ always≃ hadronizes before de- and gauge interactions. Diagrams for other and caying. Hadronization withe a light antiquark leads to a charginos and those related by crossing are not shown. neutral or charged mesino , (Qq), MQq ≡ while hadronization with two light quarks leads to a neu- tral or charged sbaryon bound state (Qqq),e and One-loop box diagrams also allow charged current and BQqq ≡e likewise for the states. chargino contributions as illustrated in Fig. 1(b). In the A long lived mesino or sbaryon might providee an inter- pure SU(2)L Wino limit, and ignoring left-right mixing e esting system in which to study heavy (s)quark aspects in couplings for simplicity, the one-loop amplitude is of QCD. In this work we concentrate on the implications 8α2m for supersymmetric and sflavor phenomenology. ∗ 2 W (Qb) (qℓ) (Qaq Q qi)= ǫ ǫ Mesino Oscillations.– The mesino bound states are AW i → a 3m2 (C)ia (C)ia Q b,ℓ spin 1 Dirac . A neutral mesino and antimesino a X 2 e e e e differ by two units of (s)flavor, fermion number, F , and e 2 2 2 2 2 2 2 2 f(m /m ,mqℓ /mQ˜ ,m /m ,mW /m ) (5) R-charge. All of these quantum numbers are, how- × Qb Qa a We Qa Qa ever, manifestly violated in any supersymmetric the- (d˜b) † † (dℓ) ory. (S)quark flavor is violated by Yukawa couplings and where ǫ(Ce)ia =e (ULDL)ib(DeLUL)eba and ǫ(eC)ia = † † squark flavor may also be violated by scalar tri-linear (ULDL)iℓ(DLUL)ℓa and the loop function f(a,b,c,d) is couplings and possibly the scalar mass-squared matri- e e e 1 x y ces. Fermion number and R-symmetry are violated by e (1 y2) 2 dx dy dz − + (6) gaugino masses. So hadronization of squarks into neu- [D(a,b,c,d)]2 D(a,b,c,d) Z0 Z0 Z0   tral mesino bound states allows for the interesting phe- 2 nomenon of particle–antiparticle oscillations which is im- where D(a,b,c,d)= y +(b c 1)y+(c a)x+(d b)z+a. −(dℓ−) − − possible for an isolated charged particle. Operators which Ignoring quark masses ℓ ǫia = ǫ(L)ia. The box contri- violate the above symmetries appear as Majorana mass bution is intrinsically suppressed compared with the tree terms which mix the mesino and antimesino states. In- by at least 10−3 evenP without significant squark GIM cluding these effects, mesinos are therefore pseudo-Dirac suppression. So for up-type squarks the tree-level sflavor fermions. violating contributions through gluino exchange domi- Mesino oscillations are analogous to oscillations. nate unless up-type sflavor violation is highly suppressed At the microscopic level the ∆Q˜ = ∆q = ∆F = ∆R =2 compared with down-type. Quark flavor mixing effects in amplitudes which mix mesino and antimesino arise from charged current interactions represent an irreducible con- tree-level gluino and neutralino exchange as illustrated in tribution to mesino oscillations through the box diagram,

2 2 2 but are GIM suppressed by (m /m ) and numerically large transverse energy (ET ) and large missing trans- O b Q unimportant for oscillations which could be observed in verse energy (/ET ). For sufficiently long squark de- flight. cay lengths, these may be distinguished from analogous e The mesino–antimesino oscillation frequency is related heavy quark decays by large beam axis impact parame- to the short distance amplitudes given above by ters. In addition, since the massive mesinos and sbaryons are non-relativistic, the decay products are not signifi- Nc 2 ∗ cantly boosted in the lab frame and are therefore roughly ω = ∆m = ψ(0) (Qaq Q qi) (7) MM 2m | | A i → a uniformly distributed in cos ϕ, where ϕ is the angle be- Q e e tween the reconstructed momentum vector of the dis- The light (anti)quark wave function at the origin in placed jet and the unit normal between the beam axis e the (anti)mesino is defined here in terms of the ma- and the origin of the displaced jet. In contrast, the distri- trix element of the Dirac scalar bilinear, ψ(0) 2 bution of high E displaced jets from direct heavy quark | | ≡ T ( qqδ3(r) / )V , where V is the normaliza- production and decay is peaked near cos ϕ 1 since the hM| |Mi hM|Mi tion volume. This may be related to the mesino de- visible decay products are boosted in a direction∼ away 2 2 cay constant by ψ(0) = fM m /(4Nc). In the heavy from the production vertex. Mesino or sbaryon decay | | Q (s)quark limit, this is a purely QCD quantity which may therefore be distinguished by high ET jets with large may be approximated using the B-meson decay constant E/T and with large negative impact parameters (LNIPs), 2 e 3 fB 160 MeV giving ψ(0) (220 MeV) [3], indepen- cos ϕ < 0. These observables result if the visible decay ≃ | | ≃ products∼ recoil against the invisible Goldstino in a di- dent of mQ and Nc in the heavy (s)quark and large Nc limits. rection towards, rather than away from the production Numerically, the gluino contribution to the ˜ vertex. LNIPs provide an efficient means to search for ex- e Mtu ↔ t˜∗u oscillation wavelength is βγλ where λ 2π/ω is otic massive metastable particles which decay to hadronic M ≡ final states [6]. m 2 λ (4 nm) g˜ y (1 y2) ǫ−2 (8) Neutral mesino–antimesino oscillations present the ≃ 250 GeV − (N)13 possibility of another novel experimental signature, even   for decay lengths which are too short to be resolved in where y = mt˜/mg˜ and by assumption y < 1 so 0 < 3 real space. Oscillations may be revealed in any decay y(1 y2) < 2/3 0.38. Oscillations on the scale of a mode which tags the sign of the (anti)squark in a neutral detector− could occur≃ for ǫ as small as 5 10−5. Up- p (N)13 (anti)mesino. Squark–antisquark production events in type sflavor violation involving the third generation× is combination with mesino–antimesino oscillation can then essentially unconstrained by present data, so extremely lead to same-sign events. For example, the antisquark rapid oscillations compared with the decay length and may hadronize as a neutral antimesino which oscillates scale of a detector are conceivable. to a mesino before decaying, while the squark hadronizes The time integrated probability for a mesino to decay as a charged mesino or sbaryon which can not oscillate. as an antimesino depends on the oscillation frequency Summing over all possibilities, the time-integrated ratio and decay rate of same- to opposite-sign events is x2 N + N−− 2 f (1 f ) ( )= 2 2 (9) ++ 0 0 2 2 P M → M 2(1 + δ + x ) R = P −P 2 2 2 f0 +2 f0 ≡ N − + N− 1 2 f +2 f ≃ P P + + − P 0 P 0 where x = ∆mMM/Γ, and δ = (mM mM)/Γ allows for (10) a possible diagonal flavor-conserving− splitting discussed below. Rapid oscillations, x 1, yield ( )= 1 , where ( ), and f is the neutral mesino ≫ P M → M 2 P ≡P M → M 0 while for slow oscillations, x 1, ( ) 1 x2. hadronization fraction (the finite mass im- ≪ P M → M → 2 1 < < 1 > Experimental Signatures.— Since a squark NLSP is plies 3 f0 2 for up-type squarks). Thus, for x 1 a strongly interacting it is likely to be the most abundantly significant∼ fraction∼ of squark–antisquark events will∼ yield produced SUSY particle at a collider. The ex- same-sign events. perimental signatures depend on the decay length. For The feasibility of determining the sign of an a decay length of order or larger than a meter, non- (anti)squark at decay depends on the decay products. relativistic squarks which hadronize as charged mesinos For stop-like squark decays t˜ bW G or t˜ tG with and sbaryons appear as highly-ionizing tracks (HITs) in t bW , the W - reliably→ tag the sign→ of the → a tracking chamber. Using the stop production cross sec- (anti)squark. The W -bosons signs maye in turne be de- tion [4] and preliminary results of a CDF search for HITs termined with the leptonic decay mode W ℓν where in Run I at the Tevatron [5] we estimate a current bound ℓ = e,µ. This requires isolating these primary→ on the mass of long lived stops of roughly 150 GeV. from any secondary leptons arising from b-quark decay. Mesino or sbaryon decay lengths shorter than roughly Such distinctive, essentially background free events have a meter can lead to observably displaced jets with both the topology of same-sign top-top events, and provide

3 a possible discovery mode for SUSY. The largest back- splitting. Using the chiral quark value for the mesino 2 ground is probably from top-antitop production with the magnetic moment, µM 3 µp, gives δλ (2π/ω)(x/δ) very small probability of misidentification of the primary 10.5 m/[B/Tesla]. Forward≃ scattering off≡ nuclei in ≃ 2 µ leptons or mismeasurement of the charges. At the Fer- through operators of the form (4π/Λχ) γ NγµN −1 M M milab Tevatron Run IIa with 2 fb of integrated lu- where Λχ 1.1 GeV is the chiral symmetry breaking minosity, a 175 GeV stop squark with dominant decay scale, give δλ≃ 1.2 m/[ρ/(gm cm−3)]. So for oscillations t˜ bW G and oscillation parameter x 1 would yield which could be≃ observed in flight through the (low den- →10 same-sign dilepton top-top events,∼ while x 1 sity) tracking region of a detector, these effects do not ∼ ≫ would yielde 20 events. A detection acceptance times dominate, δλ > λ or δ/x < 1 [8]. efficiency > ∼30% should give a detectable signal for these Conclusions∼.– A squark∼ NLSP can give rise to novel parameters.∼ experimental signatures including HITs or LNIPs. The Observation of stop mesino oscillations requires, and possibility of mesino–antimesino oscillations provides a very sensitively probes, up-type squark sflavor violation. discovery channel for SUSY through same-sign dilepton −1 For example, for a stop decay length Γ 10 cm, events in association with high ET heavy flavor jets and > ∼ maximal t˜u¯ t˜∗u mixing, x 1, occurs for all largeE /T . Oscillations are most easily observed for a > M −↔5 M −1 ǫ(N)13 5 10 . Evenfor Γ 2 µ∼m (which could not stop-like squark in same-sign top-top events, or same sign be resolved∼ × as a displaced vertex),∼ maximal mixing occurs charm-jets in a sample of LNIPs. Mesino oscillations > −2 for any ǫ(N)13 10 . The magnitude of squark sflavor would provide a very sensitive probe of sflavor violation. violation depends∼ on the scale at which (s)quark flavor is If the mesino decay length is macroscopic and the oscil- broken. If the flavor scale is not too much larger than the lation length is fortuitously of the same order, x 1, messenger scale for transmitting supersymmetry break- mesino oscillations could be observed in real space in∼ the ing, interesting levels of sflavor mixing are expected, and signed decay length distributions. observable mesino oscillations can occur. We thank I. Bigi, R. Demina, Y. Grossman, and The flavor violating two-body decay t˜ cG can dom- N. Uraltsev for useful discussions. The work of U.S. was inate if sflavor violation is large enough,→ as discussed supported in part by the US National Science Foundation above. This mode also dominates if the NLSPe squark under grant PHY98-02483, and that of S.T. by the US is scharm-like,c ˜ cG. Semi-leptonic decay of the c- National Science Foundation under grant PHY98-70115, quarks hadronized→ in D0,±- could then be used to the Alfred P. Sloan Foundation, and Stanford University tag same-sign events ine high ET charm-jets with large through the Frederick E. Terman Fellowship. 0 0 E/T . D D oscillation is negligible and would not contaminate↔ a mesino oscillation signal at the discovery level in a relatively clean sample of LNIPs. However, squark decays in this mode with a decay length that is too short to resolve using LNIPs would be contaminated [1] S. Dimopoulos, M. Dine, S. Raby, and S. Thomas, by production of b-jets which are not eas- hep-ph/9601367, Phys. Rev. Lett. 76 (1996) 3494; hep- ily distinguished from charm-jets. This standard model ph/9607450, Nucl. Phys. Proc. Suppl. A 52 38 (1997). 0 background could be significant since B0 B oscilla- [2] Metastable squarks which hadronize and decay over tions are non-negligible. Self-tagging of the↔ heavy flavor macroscopic distances can also arise with suppressed but at production to determine its sign [7], or measuring total non-vanishing renormalizable R-parity violation. jet charge after decay to isolate D± mesons which do not [3] For a recent lattice calculation, see S. Aoki et al. (the 63 oscillate could reduce this background, but requires large JLQCD Collab.), Nucl. Phys. Proc. Suppl. , 356 (1998). B515 statistics, and is probably not applicable at the discovery [4] W. Beenakker et al., Nucl. Phys. , 3 (1998); M. Spira, hep-ph/9812407. level. [5] “Search for Stable Charged Particles at CDF,” D. Stuart, Observing oscillations for a squark NLSP which decays LBL Research Progress Seminar, July 14, 1998. to other flavors is more problematic. For a sbottom-like [6] A search for LNIPs would also be sensitive to a squark which decays by ˜b bG, the B0-meson back- → NLSP which decays to a Higgs and Goldstino, with grounds discussed above are important. Decays to lighter the decaying to a pair of b-jets, K. Matchev quarks, Q (u,d,s)G, are difficulte to sign using self and S. Thomas, hep-ph/9908482, SU-ITP-99-35. tagging. So→ a stop-like NLSP squark provides the best [7] M. Gronau , A. Nippe, and J.L. Rosner, Phys. Rev. D 47, opportunitye to observee mesino oscillations. 1988 (1993); M. Gronau and J.L. Rosner, Phys. Rev. D Charge conjugate non-invariant environmental effects 49, 254 (1994). give rise to flavor conserving diagonal mesino–antimesino [8] Matter effects would however suppress analogous oscilla- splitting, indicated by δ = 0 in (9), and could poten- tions in the case of a spositronium bound state of an elec- tron and a NLSP antislepton stopped in matter. tially suppress oscillations.6 The mesino spin couples to the ambient magnetic field, B, and induces a diagonal

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