Geneva, November 6, Outline

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1 Supersymmetry in Particle Physics and Cosmology Wim de Boer IEKP, University Karlsruhe http//home.cern.ch/ deboerw Geneva, November 6, 2 Outline Introduction CMSSM Constraints Positron fraction in the CMSSM Parameter Space Comparison with HEAT and AMS data Summary Wim de Boer Geneva, November 6th, 2 1

2 Fundamental Questions in Physics Particle Physics What is the origin of mass? Why is the hydrogen atom exactly neutral? Why do the electroweak and strong forces have such different strengths? Cosmology Why does matter(atoms, galaxies..) exist? How where galaxies formed? What is Dark Matter made off? Magic Solution SUPERSYMMETRY Wim de Boer Geneva, November 6th, 2 2

3 SUSY is a symmetry between fermions and bosons It can be realized in nature only by presupposing a spin j 1/2 partner for each spin j particle of the SM. Since e.g. spin 0 electrons have not been observed, these shadow particles must be heavier ( broken supersymmetry) Nomenclature for Sparticles gluinos, winos, zinos, photinos spin 1/2 gauge bosons selectrons, smuons, staus, sneutrinos spin 0 leptons stop, sbottom, squark,...spin 0 quarks Higgsinos spin 1/2 partners of Higgs bosons charginos 2 mass eigenstates mixture of winos and charged Higgsinos neutralinos 4 mass eigenstates mixture of neutral gauge bosons and Higgsinos Wim de Boer Geneva, November 6th, 2 3

4 Typical Fits to AMS+HEAT Data vs e + /(e + + e - ) fraction bg+22 signal χ 2 =24.2 bg (ep-scaling=0.91) bg only fit χ 2 =48.0 HEAT 94/95/0 AMS 01 tanβ= 1.6; m 0 = ; = 300 e + /(e + + e - ) fraction bg+15 signal χ 2 =25.1 bg (ep-scaling=0.86) bg only fit χ 2=48.0 HEAT 94/95/0 AMS 01 tanβ=50; m 0 = 500; = 500 W + W - b b b b τ + τ positron energy 10-3 τ + τ positron energy Wim de Boer Geneva, November 6th, 2 4

5 More Fits e + /(e + + e - ) fraction tot (boost = 95) χ 2 = 30. bg (ep-scaling = 0.84) bg only fit χ 2 = 56.0 TS 93 Golden(96) CAPRICE 94 Boezio(9) HEAT 94/95/00 AMS 01 tanβ = 50; m 0 = 300; = 500 e + /(e + + e - ) fraction t t bg+8400 signal χ 2 =28.99 bg (ep-scaling=0.83) bg only fit χ 2=48.0 HEAT 94/95/0 AMS 01 tanβ=1.6; m 0 = 500; = 500 b b positron energy positron energy Wim de Boer Geneva, November 6th, 2 5

6 4 * 1 Dark Matter Annihilation equals B-Physics at LEP WILL SHOW at large quark pairs PRESENT LIMITS ON the annihilation is predominantly into large enough for this to happen Therefore Dark Matter annihilates dominantly into b-quarks Energy of the b-quarks +-, * ) ( '&% "!$# /.0 23 B-meson decay WELL understood in Dark Matter energy range Stable particles from dark matter annihilation are will propagate in the universe # , which Hard positron spectrum from semileptonic B-decays allows separation from antimatter, produced by secondary processes in universe Much more difficult for soft antiprotons Impossible for matter particles Antimatter will NOT penetrate atmosphere. Need detectors in space Wim de Boer Geneva, November 6th, 2 6

7 k m i j k G ˆ ƒ ƒƒ Œ ur f i w u v p cd b Q s lo º o h g urh CMSSM Fitprocedure urr cco lo rts loqp k lnm my xqy{z w u v k ƒ }~ Žq w Choose the 10 GUT supergravity inspired parameters H DF Š }~ˆ G = CEDF AB <;>= Žq w Q OP RXW Q OP = RVU Q OP = RTS Q OP = N = JLKM I = Ž w Š }~ Œ Minimize the Higgs potential in order to determine HZY s loqp u r ž Ÿ rts w œ lš u v Calculate masses and couplings at low energies by integrating about 30 coupled RGE s and decoupling sparticles at thresholds u r Ÿ «ª s ln ce f, _`a O^ []\ u v calculate ur ḱ³ o²± k³ o ± ¹ u µ v Determine the best parameters by minimizing. r Å Ä Â Â Ã Á ¾@ À ¼½ ¼š uln» u s læç uéè v Ah = = strongly correlated. Repeat fits for all pairs of Ah and Wim de Boer Geneva, November 6th, 2

8 Ì Ë Unification of the Coupling Constants in the SM and the minimal MSSM 1/α i /α i /α 1 MSSM /α /α log Q log Q CÊ C B = C? = U. Amaldi, W. de Boer, H. Fürstenau, PL B260(1991) coupling constants of electromagnetic, weak, and strong interactions BÒ Ñ Ï Ð Î CEÍ due to radiative corrections (LO) Wim de Boer Geneva, November 6th, 2 8

9 _ h I I CMSSM Sparticle Spectrum mass From RGE equations q ~ L t ~ L t ~ R l ~ L Bino ~ l R Wino Gluino m 1 m 2 tan β = 50 Y t = Y b = Y τ (µ 0 2+m 0 2) m log 10 Q Characteristic MSSM Features Squarks and gluinos heavy through strong rad. corr. Gaugino from U(1) (=Bino) Lightest Neutral SUSY Particle (LSP) (if Ah not too large w.r.t. ) Mass terms in Higgs potential driven negative by Yukawa couplings EWSB (determines ) Higgs mixing parameter usually large compared with Ah Consequently Pseudoscalar Higgs and higgsinos heavy light Higgs SM-higgs-like LSP bino-like, since no mixing with heavy higgsinos very good DARK MATTER candidate Wim de Boer Geneva, November 6th, 2 9

10 o Ó u o f s s f s OÚ Þ OÚ ß h O Ý I h z z â ž z z æ å è æì æë ç Gaugino Fraction of the LSP Neutralino Mass Mixing Matrix ØÖÙ o p o p s o²p s o²p o p o²p ÔÖÕ oqp s oqp 1 From RGE Ah Ý QÚÜ Ý QÚÜ gaugino fraction Ah Ah { ÚÜ Q â àqã á  à [â á  à g  Neutralino à ä h á  àqä á  Gaugino Fraction ì é ê ìîí é m0 éê gaugino fraction SMALL coupling to Higgs and gauge bosons! _ Â ï» Large Wim de Boer Geneva, November 6th, 2 10

11 ð Où Ç ø I b Anom. magn. moment Iand ñó ñò ô<õ vs 130 öh m µ > 0 µ < 0 µ > 0 µ < 0 m0 / 1000 / 1000 / tanβ strongly preferred from ce f cd = GeV û Þ ø Q ú Å = = Ah = < Wim de Boer Geneva, November 6th, 2 11

12 ^ _`a ø ÿ ø Ç s Q O û û Ý b f _`a ž ž û Experimental Limits on χ total a µ = 339(112) b sγ = 3.43(0.53) 10-4 m h > GeV 6 tan β > 6.5 (95% CL) tan β at 95% C.L., if new data from g-2 (E821 Coll., PRL 89(2)101804), (BaBAR, hep-ex/06) and Higgs limit GeV are included. Note 1 away from SM, if data is used for calculating vacuum polarization; only, if hadronic -decays are used (M. Davier et al., hep-ph/02081); looking forward to KLOE data. Note 2 new Babar data ( ) closer to SM ( ) than previous CLEO ( ) data ü ýþ s ^ [ \ s û û û Þ ž s ß ß û s û Wim de Boer Geneva, November 6th, 2 12

13 # % # ' ' ( ' ÿ =Yτ ÿ / ÿ /0 ÿ Yukawa Unification 220!"!" #$ 180 Mtop &%!" #$ µ(0) > 0 µ(0) < 0 160!" #$ Y t Yt/b (0) % 10-3 ü ýþ and )+* Relation between Y b Preferred χ 2 or.-, ü ýþ ü ýþ 1 20 scenario excluded by Higgs limit! ü ýþ Low 10 0 tan β 1 10 Wim de Boer Geneva, November 6th, 2 13

14 2 2 2 > = ;? C = Electroweak precision data in MSSM and SM SM χ 2 /d.o.f = 33.1/1 MSSM χ 2 /d.o.f = 22.4/13 CMSSM χ 2 /d.o.f = 29.2/18 LEP SLC M Z Γ Z σ had R l l A FB R b R c b A FB c A FB M t sin 2 lept Θ eff M W (LEP) sin 2 Θ lept (A LR ) eff b X s γ SM fit has prob. 1.1%, i.e. excluded at 99% C.L.? Rescale errors from and NO significant change in parameters, but probability 8%, because of anomalous magne- and MSSM reduced tic moment, 3546 ;< 89 MSSM results from MSSM-Fitter (see WdB, W. Hollik et al., Z.Phys. C5(199) 62 and hepph/ ) SM results obtained with ZFITTER6.11 (see D. Bardin et al., hep-ph/ ) a µ SUSY pulls=(data-theo)/error Wim de Boer Geneva, November 6th, 2 14

15 E C = LK C J = D Mass W-Boson Mass M W pp -colliders ± LEP ± MSSM m t LEP2+pp F =19.4 GeV Average ± χ 2 /DoF 0.0 / 1 NuTeV ± LEP1/SLD ± SM GeV LEP1/SLD/m t ± m W m susy Direct measurements of ( above SM prediction from ). CNMPO C+Q O = ; < 8 9 CSR O GIH data Better agreement between direct and indirect measurements, if radiative corrections include SUSY contributions. Wim de Boer Geneva, November 6th, 2 15

16 Y UV Z X W ^ ws ^ L `_ `_ a a g l l f h f f T and [] [\ b) 10-4 Br(b X s γ m a µ SUSY m MSSM Contributions Combined Data on from ALEPH, BaBar, CLEO, BEL- LE slightly BELOW SM prediction, if one uses running c-quark mass s prq B > mon (Gambino and Misiak, hep-ph/ ) tvu z { J tyx cji ced c i c d cek c d Data on anomalous magnetic moment from E-821 slightly ABO- VE SM prediction, after correcting sign error in SM prediction from light-by-light scattering Wim de Boer Geneva, November 6th, 2 16

17 ws Œ u } } ƒ } } ƒ Dark Matter Density Physics Input Flat universe, if total density equals critical density, or Reacceleration of universe, as measured by redshift from Supernova Ia, depends on DIFFERENCE of and, while position of first acoustic peak in the CMB is sensitive to the flatness of the universe, i.e. SUM of and. QQ L ƒ Q } Q~ QQ QQ ˆ Š J Q Wim de Boer Geneva, November 6th, 2 1

18 Dark Matter Density Composition of the Universe % Vacuumenergy, 20% non-baryonic dark matter, 3% baryonic. Wim de Boer Geneva, November 6th, 2 18

19 z J J ) / J ˆ 0 š J š J ½ W J Repulsive Gravity? A simple example ž šœ J * *, Q Ÿ Q~ Differentiate with respect to t and use m M v «ª Two solutions for acceleration w if O J if O ² ± µ W { ³ J º¹ * ± J INFLATION, since Solution 2 at GUT ener- with gies Radius of Universe doubles every w¼0 /, J» s after phase transition! ½ /, 0À J ª ¾ 9» Wim de Boer Geneva, November 6th, 2 19

20 Á  Dark Matter Å Ã Ä Æ Ã Ä z Ë J É Ç È 9 ËÊ J É ÇœÈ < Ω h 2 < < Ω h 2 < Ωh 2 m 0 Ωh 2 m 0 Light regions preferred by Boomerang and SN Ia Wim de Boer Geneva, November 6th, 2 20

21 Ñ Ð ÑÓ ÑÓ Ì Ì Ì Ì ÑÓ ÒÑ Ì Ì Ü ë ë è ç á á è ç â â sá á ì ë ë ì s á á ð ð ë ë á á Main Diagrams for Neutralino Annihilation Gauge Bosons Fermions Ò ÑÓ Ö Ô Õ ÒÚÙ ÍÏÎ Ì ÍÏÎ Ì ÒÑ ÑÓ Ò Î ÍÏÎ Ì ÍÏÎ Ì Í Î Í Î ÍØÎ ÍØÎ To Note 1. Light fermion pairs suppressed due to Pauli-Principle (neutralinos are Majorana particles and fermions Pauli-Principle at zero momentum p-wave fermion mass!) 2. at 3. Ç ÈÝ L à à L à à ï à à Ë ÉßÞ á fermion pairs dominate ãåäæ æ sîí í s Þ Þ ëë ï à à ï à à sêé L à à á ã äæ æ (Neg. interference with t-channel) (Pos. interference with t-channel) ) 4. RESULT dominates over (for ÇœÈÝ ) Ë É Þ Wim de Boer Geneva, November 6th, 2 21

22 ö õ õ þ! * ) ( '! & û ü 3 / þÿ þý < ; ; ; ËÊ ë á ç p-wave suppression at low momentum for light final states at low neutralino momenta òôó t Ü ñ üú ù ü ùøyú û ø öê ,.0/ þ! $ þ þ! %$ ý þú!" þú #!" þ HE E ðgf < = ç ËÊ E E ðcb < = ç <>= ç Ë D D? ò Wim de Boer Geneva, November 6th, 2 22

23 K áá ð à à ëë ð à à v lr { z y b a ` x _ w ^ ] U[ u lr t lr \ U[ s lr ml VU lk UT q Z É ëë ð à à 5 5 IJ Pseudoscalar Higgs exchange vs j i i g h g d c dfe c S R R P Q P M L MON L n6op W6XY. ÇœÈÝ dominates at large Wim de Boer Geneva, November 6th, 2 23

24 K ëë áá } ½ ¼ µ» º ¾ ÉË ÇÄ ƒ ƒ ëë áá Ï ËÊ IJ s,t-channel Interferences at large final state final state Higgs small, Z large for Higgs large, Z small for ««ª }~ µ ¹ ƒ Ä À Á  Ã «¾ É ÇÈ Ä À Á  Ã «fæ «Å µ œ š ž Ÿž ƒ Ž œ š ž Ÿž µ ƒ ƒ Ž À Ê À Á  ÃÂ Æ ¾ µ ƒœ µ œ š ž Ÿž ƒœ ±ˆ²³ Š ƒ ˆ (t-ch, Higgs) Interf. POS, (t-ch, Z) Interf. NEG ) final states suppressed (enhanced) due to interferences! ( ÌÎÍÝ final state dominates at large HE E ë á Ë D ðgf ËÊ E E D ð B? Ðò Wim de Boer Geneva, November 6th, 2 24

25 K þ Ý Ñ Ñ ô ó ò ñ î æê ð çæ æå é ï ëë áá è à à ï ëë áá ç à à ëë à à 5 5 IJ x-section vs ýþ ÿ üû û øöú øôù äã â Þàßá á ÙÚÜ Ø ÒÖÕ ÒÔÓ ï æê ü ü ØÚöõ Øõ Ú í æê ì æê ë æê þ è ßá ( ) æ ãåäæ â B ñ B ) á D ( DOMINANT! Ï Þ ÌÎÍÝ For Wim de Boer Geneva, November 6th, 2 25

26 #"! ñ E HE E E Ï A) ) $ % % % /ò /ò E E.. /ò E., + 3ò 3ò E E E E.. 66 Comparison of X-sections in CalcHEP and darksusy cm s GeV ðgf D ð B GeV 4(' &% ÌÎÍÝ D GeV GeV Ðò CalcHEP darksusy * ë ë 0, ) + E-, )&+ /ò. E * á á HE+ ), + ), $&+. 1 E, 0&+ E-, ! Feynarts agrees with CalcHEP concerning Wim de Boer Geneva, November 6th, 2 26

27 8 K ë ë 6 6 Neutralino Annihilation X-sections for IJ <σv> [cm 3 s -1 ] sigv_bb m 0 <σv> [cm 3 s -1 ] sigv_tt m 0 Wim de Boer Geneva, November 6th, 2 2

28 8 K Neutralino Annihilation X-sections for IJ <σv> [cm 3 s -1 ] sigv_tau m 0 <σv> [cm 3 s -1 ] sigv_ww m 0 Wim de Boer Geneva, November 6th, 2 28

29 98 K ë ë 6 6 Neutralino Annihilation X-sections for IJ <σv> [cm 3 s -1 ] sigv_bb m 0 <σv> [cm 3 s -1 ] sigv_tt m 0 Wim de Boer Geneva, November 6th, 2 29

30 98 K Neutralino Annihilation X-sections for IJ <σv> [cm 3 s -1 ] sigv_tau m 0 <σv> [cm 3 s -1 ] sigv_ww m 0 Wim de Boer Geneva, November 6th, 2 30

31 98 8 K Ï Ï Neutralino Annih. total X-sections for IJ and <σv> [cm 3 s -1 ] sigmav m 0 <σv> [cm 3 s -1 ] sigmav m 0 ÌÎÍ ÌÎÍ Wim de Boer Geneva, November 6th, 2 31

32 K < ; 0 Ï < ; Ï 0 E ç ç Typical Fits to AMS+HEAT Data vs IJ e + /(e + + e - ) fraction bg+22 signal χ 2 =24.2 bg (ep-scaling=0.91) bg only fit χ 2 =48.0 HEAT 94/95/0 AMS 01 tanβ= 1.6; m 0 = ; = 300 e + /(e + + e - ) fraction bg+15 signal χ 2 =25.1 bg (ep-scaling=0.86) bg only fit χ ;2=48.0 HEAT 94/95/0 AMS 01 tanβ=50; m 0 = 500; = 500 W + W - b b b b τ + τ positron energy 10-3 τ + τ positron energy 5 4 < ÌÎÍ 5 4 < H E+ ÌÎÍ Wim de Boer Geneva, November 6th, 2 32

33 0 K Ï Ï IJ contr. for AMS+HEAT Data vs = Ì Í ÌÎÍ χ 2 - term 30 χ 2 - term m0 m0 χ 2 χ 2 Wim de Boer Geneva, November 6th, 2 33

34 Ï Ï Boost factor for combined AMS and HEAT Data ÌÎÍ Ì Í boost factor boost m boost factor boost m Wim de Boer Geneva, November 6th, 2 34

35 What about antiprotons? p flux [GeV -1 cm -2 s -1 sr -1 ] tanβ = 50 m 0 = 300 GeV = 500 GeV Φ F = 500 MeV tot (boost = 1) χ 2 = 13.3 signal(dsusy) bg (SMR) χ 2 = 12.9 MASS 91 Basini(99) IMAX 92 Mitchell(96) CAPRICE 94 Boezio(9) BESS 95/9 Orito(00) CAPRICE 98 Boezio(00) p flux [GeV -1 cm -2 s -1 sr -1 ] tanβ = 50 m 0 = 300 GeV = 500 GeV Φ F = 900 MeV tot (boost = ) χ 2 = 12.9 signal(dsusy) bg (SMR) χ 2 = 14.8 MASS 91 Basini(99) IMAX 92 Mitchell(96) CAPRICE 94 Boezio(9) BESS 95/9 Orito(00) CAPRICE 98 Boezio(00) antiproton energy Solar Modulation 500 GeV antiproton energy Solar Mod. 900 GeV Wim de Boer Geneva, November 6th, 2 35

36 AMS02 is a state of the art detector to separate matter from antimatter High resolution spectrometer based on silicon sensors in a superconducting 0.9 T Magnet, Transition Radiation Detector, RICH counter and calorimeter to identify particles. Wim de Boer Geneva, November 6th, 2 36

37 Expected Flight Date 5 Wim de Boer Geneva, November 6th, 2 3

38 Wim de Boer Geneva, November 6th, 2 38

39 @ 0 Ï Possible AMS-02 Data in 6 one year AMS one year AMS e + /(e + + e - ) fraction 10-1 exp. data by DarkSUSY bg Mosk-Strong (e + -scale=0.86) generated dummy data tanβ= 50; m 0 = 500; = 500 e + /(e + + e - ) fraction 10-1 exp. data by DarkSUSY bg Mosk-Strong (e + -scale=0.89) generated dummy data tanβ= 50; m 0 =1000; = positron energy positron energy < ; > 5 4 < < ;?> 5 4 < ÌÎÍ Wim de Boer Geneva, November 6th, 2 39

40 0 0 Ï Possible after one year AMS excl. LSP 90 % CL 99 % CL tanβ=50; m 0 =500; = excl. LSP 90 % CL 99 % CL tanβ=50; m 0 =1000; = χ 2 m χ 2 m 0 < ; > 5 4 < < ;?> 5 4 < ÌÎÍ Wim de Boer Geneva, November 6th, 2 40

41 I LM KJ NO P M M Q S S R Q M M R S S Summary Low values of ( LEP Higgs Limit and FHG E D ) excluded by electroweak data (g-2, ) At larger values of DM M A DOMINANT FINAL STATE FINAL STATE has orders of magnitude larger x-section than final states and also larger than final states for large D A FINAL STATE fits the AMS+HEAT data as well as the final states or Space experiments AMS-02 and PAMELA offer good prospects for studying in detail DM annihilation by precise measurement of positron and antiproton spectra. Wim de Boer Geneva, November 6th, 2 41