Amsterdam, December 13, Outline

Transcription

1 Unification Scale Physics Wim de Boer IEKP, University Karlsruhe deboerw Amsterdam, December 13, 2 Outline Introduction MSSM Constraints Positron fraction in the CMSSM Parameter Space Comparison with HEAT and AMS data Summary Wim de Boer Amsterdam, December 13th, 2 1

2 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 Amsterdam, December 13th, 2 2

3 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 U. Amaldi, W. de Boer, H. Fürstenau, PL B260(1991) coupling constants of electromagnetic, weak, and strong interactions due to radiative corrections (LO) Wim de Boer Amsterdam, December 13th, 2 3

4 ) (% % '&% % * * " % 0 Running Coupling Constants Electric Charge q Colour Charge Quantum Fluctuations around pointlike charge create energy-dependent (running) effective charge. (Allowed by Einstein (E=mc ) and Heisenberg ( )) QED: Shielding of bare charge by pairs. Reduced charge at large distance (or low energy.) At LEP instead of at low energy "$# QCD: In contrast to photons, GLUONS carry (colour) charge THEMSELVES Not only splitting into pairs, but into gluons as well Gluons enhance charge Antishielding (which dominates over shielding) opposite running At LEP instead of at the proton mass.,+ "$# &% -/. Wim de Boer Amsterdam, December 13th, 2 4

5 A < C B Running of strong coupling constant jet fraction / % a) y cut = 0.0 AMY JADE MARK II TASSO VENUS LEP 3-jet fraction 9;: 2 24 QCD, α s (m Z ) = 0.11 µ 2 = 0.0 s =>@? From: T. Hebbeker, Phys. Rep. 217(1992) s / GeV Wim de Boer Amsterdam, December 13th, 2 5

6 KL J I 9 G E KKWW V U P P cbww a S P P P S _ Q Which CC needed for unification? values (calc. up ): 9HG Most precise to sin 2 θw from (m 0 MON : 9HG, )F (100,100) (Higgs) WYX PRQ S U TS PRQ WWWW WYX from (,) (300,300) ^ [ Z\[ ] 9 G (500,500) 0,b A FB (Higgs) WYX PRQ ` _S S PRQ (1000,1000) WWWW WYX world avg. A LR (SLD) Larger value of clearly preferred for unification with SUSY masses below a few TeV. 9HG 0.23 (Note: small value of from sensitive to theoretical error on luminosity ) 9HG world avg. [ Z\[ ] L Kgf Jed α s Wim de Boer Amsterdam, December 13th, 2 6

7 h Triple Yukawa Unification Y t Y b Y τ Infrared Fixed Points for all Yukawas at large i.e. values of Yukawa couplings at low energy largely independent of starting values at the GUT scale m l ikj Low energy values consistent with top, bottom and tau mass log E Wim de Boer Amsterdam, December 13th, 2 7

8 o s o s o n =Yτ ˆ Œ. Š ŠŽ ˆ Œ ˆ Yukawa Unification 220 prs = prq o m l ikj } xzy{ ql q t 10 Mtop Ju w t p v } xzy{ s ql Ju µ(0) > 0 µ(0) < w ~ p v q~ } xzy{ s ql } xzy{ s w Ju p v q Y t Yt/b (0) 10-3 w o w ~ 10-4 Y b r and ƒ Relation between Preferred: χ 2 or Š. ˆ # r 20 r Ž 10 scenario excluded by Higgs limit r Low 0 tan β 1 10 Wim de Boer Amsterdam, December 13th, 2

9 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 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 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 Amsterdam, December 13th, 2 9

10 Ÿ " µ µ µ µ š " š ³ Ÿ µ µ µ µ ± Ÿ ˆ Ÿ & & ½ - # # ¼ ¼ # ¼ ¼ Å - Ž & Ÿ Ž Higgs mechanism predicted in MSSM & $œ š ): # The MSSM requires two Higgs doublets ( ª «" # ž ª " # ž The tree level potential for the neutral sector can be written as: ² ² ¹ š.. ² ² ² ³ š ² ³ ² " # ² Note: Couplings are GAUGE couplings, not arbitrary as in SM Electroweak Symmetry Breaking, if potential has minimum with non-zero v.e.v. r Æ ÃÀÄ ÂÁ ¾À ËÍÌ ÇÉÈÊ one can derive easily: º» º º» º From - Ž At GUT scale:, but at due to loop corrections from heavy top mass Only works for # # # GeV - Ð% Ž3Ï Î - % Wim de Boer Amsterdam, December 13th, 2 10

11 Fundamental Questions in Physics: Particle Physics Cosmology Why do the electroweak and strong forces have such different strengths? What is the origin of mass? Why is the hydrogen atom exactly neutral? What is Dark Matter made off? Why does matter(atoms, galaxies..) exist? How where galaxies formed? Possible Solution to all questions simultaneously: SUPERSYMMETRY Wim de Boer Amsterdam, December 13th, 2 11

12 ãâ ã è ãâû Typical Fits to AMS+HEAT Data vs ÑÒ Ó e + /(e + + e - ) fraction bg+22 signal χ 2 =24.2 bg (ep-scaling=0.91) bg only fit χ 2 =4.0 HEAT 94/95/0 AMS 01 tanβ= 1.6; m 0 = ; = 300 e + /(e + + e - ) fraction bg+175 signal χ 2 =25.1 bg (ep-scaling=0.6) bg only fit χ Ô2=4.0 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 ç ä å à Ù á ã Þ ØÚÙ rö ç äæå à Ù á ÝßÞ Û/Ü ØÚÙ rö Wim de Boer Amsterdam, December 13th, 2 12

13 ãâ ã è More Fits e + /(e + + e - ) fraction tot (boost = 95) χ 2 = 30.7 bg (ep-scaling = 0.4) bg only fit χ 2 = 56.0 TS 93 Golden(96) CAPRICE 94 Boezio(97) HEAT 94/95/00 AMS 01 tanβ = 50; m 0 = 300; = 500 e + /(e + + e - ) fraction t t bg+400 signal χ 2 =2.99 bg (ep-scaling=0.3) bg only fit χ Ô2=4.0 HEAT 94/95/0 AMS 01 tanβ=1.6; m 0 = 500; = 500 b b positron energy positron energy ç ä å ãâ ã à Ù á ÝßÞ Û/Ü Ø Ù rö ç ä å à Ù á ã Þ ØÚÙ rö Wim de Boer Amsterdam, December 13th, 2 13

14 í í ì ì ÿ ø ø þ Dark Matter Annihilation equals B-Physics at LEP WILL SHOW: at large quark pairs PRESENT LIMITS ON ékêë é êë the annihilation is predominantly into large enough for this to happen Therefore: Dark Matter annihilates dominantly into b-quarks Energy of the b-quarks: öõôó îðïòñ ùúú îüûý B-meson decay WELL understood in Dark Matter energy range Stable particles from dark matter annihilation are: will propagate in the universe ñ, 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 Amsterdam, December 13th, 2 14

15 à à à à Ü % Ü ' < 6; Gaugino Fraction of the LSP Neutralino Mass Mixing Matrix: 1 From RGE: # Þ $% ã " ã " gaugino fraction & Þ $% Þ " $% 2 0 (1, *.- % (/0, *.- à+* Ù () Neutralino: à ( 3 %, *.- à (3, * Gaugino Fraction: < 9 : <>= 9 m0 9: 6 7 gaugino fraction SMALL coupling to Higgs and gauge *? Large Wim de Boer Amsterdam, December 13th, 2 15

16 l jj c c ¾ h i j ¾ h f á g - h x y r M x y z ut uu x y j f o à s j o j à s o b ¾ % o ) o Ø Þ Þ Þ à Þ CMSSM Fitprocedure ¾i in mn k h xw uv t pqrso l Choose the 10 GUT supergravity inspired parameters: N JL xw {} ~ pqzso M D IKJL $H D AGF ACBED ƒ l xw T UZY T D U.X T D UWV T D S Ø D OQPR ' D l t pq so Minimize the Higgs potential in order to determine N\[ ¾ l k j 42Ž 2 l Œ ¾Š ¾Ĝ k Calculate masses and couplings at low energies by integrating about 30 coupled RGE s and decoupling sparticles at thresholds 22Ž ¾ ce _ /^] šœ k calculate žhÿ j žh Ÿ k Determine the best parameters by minimizing. j * * Gª «Š ¾ oá j %à ¾ ± ³² k rö $% D strongly correlated. Repeat fits for all pairs of $% à D and Wim de Boer Amsterdam, December 13th, 2 16

17 ¼ ¾ ã½ ' Þ Ù ± Þ b Anom. magn. moment 'and µ µ ǹ vs ºÒ Ó 130»h m µ > 0 µ < 0 µ > 0 µ < 0 m0 / 1000 / 1000 / tanβ strongly preferred from ce cd à D Þ GeV À # Û Û Ü ½ à D Ø Þ D rö $% D Wim de Boer Amsterdam, December 13th, 2 17

18 ½ Ø Û Û ½ ± Þ Û âû Å À ÄÀ à " å È 4 Û 4 Û è 4 Û À ã Ü Experimental Limits on ºÂÁ Ó 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 (E21 Coll., PRL 9(2)10104), (BaBAR, hep-ex/ ) 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/020177); looking forward to KLOE data. Note 2: new Babar data ( ) closer to SM ( ) than previous CLEO ( ) data rö ã è Ý Ü Ù b _ / ] Û ã ÀÇÆ ÝÇÆ Û/Ü Ù Ü ãå Û âàü ã À # Ü Ü ãå & & À Ü ã o å Å É À Ü Wim de Boer Amsterdam, December 13th, 2 1

19 Ê Ê Ê Î Ñ Ö Ù Øa Ó Electroweak precision data in MSSM and SM SM: χ 2 /d.o.f = 33.1/17 MSSM: χ 2 /d.o.f = 22.4/13 CMSSM: χ 2 /d.o.f = 29.2/1 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 %, because of anomalous magne- and MSSM reduced tic moment, Ë ÌÍ ÑŽÒÔÓ ÏÐ MSSM results from MSSM-Fitter (see WdB, W. Hollik et al., Z.Phys. C75(1997) 627 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 Amsterdam, December 13th, 2 19

20 Û Ù Ó âá Ù à Ó Ú Mass 0.55 W-Boson Mass M W pp -colliders ± LEP ± MSSM m t LEP2+pp Ü =179.4 GeV Average ± χ 2 /DoF: 0.0 / 1 NuTeV ± 0.04 LEP1/SLD ± SM GeV LEP1/SLD/m t ± m W m susy Direct measurements of ( above SM prediction from ). Ù\ãåä ÙWæ ä ÑÒ Ó Ï ÎÐ Ùèç ä ÝßÞ data Better agreement between direct and indirect measurements, if radiative corrections include SUSY contributions. Wim de Boer Amsterdam, December 13th, 2 20

21 î êë ï í ì ó â õô õô ó à ö ö û ú ü ú ú é and ðò ðñ ) 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 a â (Gambino and Misiak, hep-ph/ ) øþý øeù ø ý ø ù øeÿ ø ù Data on anomalous magnetic moment from E-21 slightly ABO- VE SM prediction, after correcting sign error in SM prediction from light-by-light scattering Wim de Boer Amsterdam, December 13th, 2 21

22 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. ææ â æ æ ææ ææ à æ Wim de Boer Amsterdam, December 13th, 2 22

23 Dark Matter Density Composition of the Universe: 77% Vacuumenergy, 20% non-baryonic dark matter, 3% baryonic. Wim de Boer Amsterdam, December 13th, 2 23

24 ' & ' & % &( &( &( &( &( ' & 0 7 â Ö Ö ; ; Ý Ö Ö â Ë Ö Ö â Ë Ö Ö â 7 Main Diagrams for Neutralino Annihilation Gauge Bosons Fermions + )* "$# "$# "$# "$# ",# ",# '/. ' # "-# "-# 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. for Ð 132 :9 fermion pairs dominate :9 Ö Ö â B <>= Ý Ö Ö â C C 5 5 < = (Neg. interference with t-channel) (Pos. interference with t-channel) ) 4. RESULT: dominates over (for 4 5 Ð 1 2 ) Wim de Boer Amsterdam, December 13th, 2 24

25 J I H G H G c d c PW _ ^ jr { z ] \ W y [ x r w ` ab M N PQ PO jk ji V à p-wave suppression at low momentum for light final states at low neutralino momenta ÑFE 0 D N L K N KJL,M hg g dfe ƒ ~} W P Y r j u W P PZY r j jvu O PW L i rjs t rjs X PW L q ljmonp RPSTU à9 Ë Š 7 Œ à9 Ë æ Š Ž 7 Œ à ó Š 7 à Ñ à Þ Wim de Boer Amsterdam, December 13th, 2 25

26 ¾ º à  Á ª À œ ½ º ¼ º œ» º µ œ ³ œ ¹ 4 Ð f Pseudoscalar Higgs exchange vs Ë Ö Þ Ö Þ Ë Ö Þ Ö Þ ² ± ± ««š ž Ÿ. 1 2 dominates at large Ë Ö Þ Ö Þ Wim de Boer Amsterdam, December 13th, 2 26

27 ð ï ï Å Ä Ä üõ Ü Û Ó Ú Ù ü íì éç ç õö õô ËÌ ËÊ 7 à f s,t-channel Interferences at large final state final state Higgs small, Z large for Higgs large, Z small for óò ò ðçñ ÉÈ È ÅÇÆ ÓËØ ò ò ò Ý ÝßÞ ü õ ÿ ãëê ãä â å æå èà Ýáà Ó Ë Ö ãä â å æå ü õ õ ÿ Ó Ë Ë Ö ô üõý Ê ÓËÔ þ üõý í éî ç ãä â å æå èà ÓËÔ û õøðùú Ò ÍËÎÐÏÑ (t-ch, Higgs) Interf. POS, (t-ch, Z) Interf. NEG ) final states suppressed (enhanced) due to interferences ( final state dominates at large 7 Œ à9 7 Œ à9 æ Ž à ó à à Þ Wim de Boer Amsterdam, December 13th, 2 27

28 LK E & \ [ = < Z ; Y : V NR X 7 /3 9 ON 0/ NM /. A ` aa ` 7 f x-section vs FGIH GIJ CD AB -, + ')(* * "#%$ W NR /3 E] ] E^^ #?> > # U NR 6 /3 T NR 5 /3 S NR 4 /3 Q P GIJ 2 1(* âa a ( )? <>= ; ( âa a æ D æ ) _ Þ _ Þ 9 _ Þ _ Þ DOMINANT _ Þ _ Þ : For Wim de Boer Amsterdam, December 13th, 2 2

29 d b kj i h g D f e c n 7 7 n x x t aa x x u { { wy z y Þ} Þ} Comparison of X-sections in CalcHEP and darksusy cm s GeV 9 l q n 9 sr l GeV Žq l Ïp 7on Œ 4ml 1 2 GeV l GeV lþ CalcHEP darksusy Iw u q Iw vu q q u t w w w q u w q u Œ Iw u Iw vu w z Feynarts agrees with CalcHEP concerning Wim de Boer Amsterdam, December 13th, 2 29

30 ~ a a Neutralino Annihilation X-sections for f <σv> [cm 3 s -1 ] sigv_bb m 0 <σv> [cm 3 s -1 ] sigv_tt m 0 Wim de Boer Amsterdam, December 13th, 2 30

31 ~ z y y Neutralino Annihilation X-sections for f <σv> [cm 3 s -1 ] sigv_tau m 0 <σv> [cm 3 s -1 ] sigv_ww m 0 w Wim de Boer Amsterdam, December 13th, 2 31

32 ~ a a Neutralino Annihilation X-sections for f <σv> [cm 3 s -1 ] sigv_bb m 0 <σv> [cm 3 s -1 ] sigv_tt m 0 Wim de Boer Amsterdam, December 13th, 2 32

33 ~ z y y Neutralino Annihilation X-sections for f <σv> [cm 3 s -1 ] sigv_tau m 0 <σv> [cm 3 s -1 ] sigv_ww m 0 w Wim de Boer Amsterdam, December 13th, 2 33

34 ~ Neutralino Annih. total X-sections for f and <σv> [cm 3 s -1 ] sigmav m 0 <σv> [cm 3 s -1 ] sigmav m 0 l ƒ l ƒ Wim de Boer Amsterdam, December 13th, 2 34

35 ˆ contr. for AMS+HEAT Data vs f l ƒ l ƒ χ 2 - term χ 2 - term χ m χ m Wim de Boer Amsterdam, December 13th, 2 35

36 Boost factor for combined AMS and HEAT Data l ƒ l ƒ boost factor boost m boost factor boost m Wim de Boer Amsterdam, December 13th, 2 36

37 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(97) BESS 95/97 Orito(00) CAPRICE 9 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 = 7) χ 2 = 12.9 signal(dsusy) bg (SMR) χ 2 = 14. MASS 91 Basini(99) IMAX 92 Mitchell(96) CAPRICE 94 Boezio(97) BESS 95/97 Orito(00) CAPRICE 9 Boezio(00) antiproton energy Solar Modulation 500 GeV antiproton energy Solar Mod. 900 GeV Wim de Boer Amsterdam, December 13th, 2 37

38 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 Amsterdam, December 13th, 2 3

39 Expected Flight Date: 5 Wim de Boer Amsterdam, December 13th, 2 39

40 Wim de Boer Amsterdam, December 13th, 2 40

41 Š Š Possible AMS-02 Data in 6 one year AMS one year AMS e + /(e + + e - ) fraction 10-1 DarkSUSY (boost = 90) bg Mosk-Strong (e + -scale=0.5) MonteCarlo tanβ= 50; m 0 = 300; = 500 e + /(e + + e - ) fraction 10-1 DarkSUSY (boost = 250) bg Mosk-Strong (e + -scale=0.) MonteCarlo tanβ= 50; m 0 =1000; = positron energy positron energy Ž Œ Þ l Ž Œ% Þ l ml ƒ Wim de Boer Amsterdam, December 13th, 2 41

42 ˆ Š Š 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 Ž Œ Þ l Ž Œ% Þ l ml ƒ Wim de Boer Amsterdam, December 13th, 2 42

43 š ž œ Ÿ ž ž ž ž Summary Low values of ( LEP Higgs Limit and ) excluded by electroweak data (g-2, ) At larger values of ž ž DOMINANT FINAL STATE FINAL STATE has orders of magnitude larger x-section than final states and also larger than final states for large 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 Amsterdam, December 13th, 2 43