2. rész
Kozmológia a 21. században
A táguló Világegyetem Ha a Világegyetem valóban tágul, akkor régen „kisebb”, ezért melegebb volt • A hőmérséklet a mérettel fordítottan arányos az elegendően forró VE-t elektromágneses plazma töltötte ki, amelynek hűlése során kialakultak az atomok és a mindent kitöltő
! kozmikus elektromágneses háttérsugárzás
A kozmikus sugárzás felfedezése • 1965: A. Penzias és R. Wilson (Bell Lab) érzékeny mikrohullámú antennája
A kozmikus sugárzás • 1965: A. Penzias és R. Wilson érzékeny mikrohullámú antennája – iránytól – napszaktól, évszaktól független elektromágneses sugárzást észleltek • Az antenna hibáját kizárták Mi lehet a titokzatos sugárzás forrása? • Mi már sejtjük: A VE-t az első perceiben elektromágneses sugárzás töltötte ki, ami azóta is ott van, csak hullámhossza a tágulás arányában megnőtt Penzias és Wilson mérése szerint a sugárzás hőmérséklete 3,5 K (11. kérdés: Mit jelent ez?)
intenzitás
A hőmérsékleti sugárzás intenzitásának hullámhosszfüggése
hullámhossz ~10cm alatt a légkör átlátszatlan Földről csak az eloszlás maximumától jobbra eső rész mérhető
Irány a világűr:
A Cosmic Background Explorer űrszonda FIRAS = Far Infrared Absolute Spectrophotometer DMR = Differential Microwave Radiometer DIRBE = Diffuse Infrared Background Experiment
!
A FIRAS spektrum
Valaha látott legtökéletesebb hőmérsékleti sugárzási spektrum
A CoBE által mért sugárzási görbe
sugárzás intenzitása
hullámhossz
Planck-görbe
frekvencia
A FIRAS spektrum A hőmérsékleti sugárzás spektrumát a Planckféle eloszlás írja le
(kT )4 x3 dx d"(f, T ) = 8⇡ 3 ex (hc) 1 Z 1
" (T ) = n (T ) =
Z
hf x= kT
d"(f, T ) = cT Stefan-Boltzmann 4
0
1
0
3
d"(f, T ) (kT ) = 8⇡ hf (hc)3
Z
1 0
x2 dx = x e 1
12. kérdés: Mekkora a nukleáris részecske/foton arány?
Izotrópnak látta-e a COBE VE-t?
A Tejút hatását le kell vonni
Izotrópnak látta-e a COBE VE-t?
A dipólus anizotrópia a Föld mozgásának következménye (szintén le kell vonni)
A COBE felfedezése
A piros és kék tartományok hőmérséklet különbsége 10-5K (0,01mm-es hullámok az uszodában)
Multipólus sorfejtés
∑l
l=1
T ( , ⇥) =
a ,m
mY m(
, ⇥)
Egy dia a 2009-es előadásomból A kozmikus zene „hangszíne” (a háttérsugárzás hatványspektruma) Az első csúcs helye Ω-tól függ
A magasság ΩB függvénye
ℓ∑ a 2ℓm m
T (ϑ, ϕ ) = ∑ aℓmYℓm (ϑ, ϕ ) ℓm
14
A CMB hatványspektruma
a2m m
T ( , ⇥) =
a ,m
mY m(
, ⇥)
Felső légköri kísérletek
BOOMERanG
Maxima EPSHEP Cocconi-prize 2011: ,,a kozmikus háttérsugárzás anizotrópiájának tanulmányozásában elért kimagasló eredményeikért’’
Kísérlet a világűrben
PLANCK
Kísérletek az Antarktiszon
SOUTH DASI POLE ACBAR QUAD BICEP SPUD
Tiszta égbolt
További kísérletek: Andok tetején (Atacama, Cerro Toco)
Vonzó tiszta égbolt
ACT
Az újszülött VE egyre szebb képe COBE 1992
WMAP 2003
PLANCK 2013
~7°
ACT, SPT ...
~0.3° ~0.1°
~0.02°
Temperature distribution of CMB
Hatványspektrum aPlanck Planck szerint Planck Collaboration: The mission Angular scale 90
18
2
10
1
0.2
0.1
0.07
6000 5000
D [µK2]
4000 3000 2000 1000 0
50
500
1000
1500
2000
2500
Multipole moment, Fig. 19. The temperature angular power spectrum of the primary CMB from Planck, showing a precise measurement of seven acoustic peaks, that are well fit by a simple six-parameter ⇤CDM theoretical model (the model plotted is the one labelled [Planck+WP+highL] in Planck Collaboration XVI (2013)). The shaded area around the best-fit curve represents cosmic variance, including the sky cut used. The error bars on individual points also include cosmic variance. The horizontal axis is logarithmic up to ` = 50, and linear beyond. The vertical scale is `(` + 1)Cl /2⇡. The measured spectrum shown here is exactly the same as the one shown in Fig. 1 of Planck Collaboration XVI (2013), but it has been rebinned to show better the low-` region.
Az ismert hatványspektrum Planck Collaboration: The Planck mission 104 Planck WMAP9 ACT SPT
D [µK2]
103
102
2 100
500
1000
1500
2000
2500
3000
Fig. 25. Measured angular power spectra of Planck, WMAP9, ACT, and SPT. The model plotted is Planck’s best-fit model including Planck temperature, WMAP polarization, ACT, and SPT (the model is labelled [Planck+WP+HighL] in Planck Collaboration XVI (2013)). Error bars include cosmic variance. The horizontal axis is `0.8 .
Modelljóslatok hatványspektrumra (ΛCDM: hat-paraméteres illesztés)
Győztes
A hatványspektrumból nyerhető adatok Az első csúcs helye Ω-tól függ
A magasság ΩΛ függvénye
A magasság ΩB függvénye
A magasságok Ωm függvényei
Hatványspektrum aPlanck Planck szerint Planck Collaboration: The mission Angular scale 90
18
1
0.2
6000
0.1
0.07
6 paraméterrel illesztett ΛCDM model
5000
D [µK2]
4000 3000 2000 1000 0
2
10
50
500
1000
1500
2000
2500
Multipole moment, Fig. 19. The temperature angular power spectrum of the primary CMB from Planck, showing a precise measurement of seven acoustic peaks, that are well fit by a simple six-parameter ⇤CDM theoretical model (the model plotted is the one labelled [Planck+WP+highL] in Planck Collaboration XVI (2013)). The shaded area around the best-fit curve represents cosmic variance, including the sky cut used. The error bars on individual points also include cosmic variance. The horizontal axis is logarithmic up to ` = 50, and linear beyond. The vertical scale is `(` + 1)Cl /2⇡. The measured spectrum shown here is exactly the same as the one shown in Fig. 1 of Planck Collaboration XVI (2013), but it has been rebinned to show better the low-` region.
A három nagyágyú: SNIa, CMB, BAO
Mi a sötét energia? • A sötét energia a VE gyorsuló tágulásának egy lehetséges és népszerű magyarázata. • Két változatát képzelik – Kozmológiai állandó, ami a teret mindenütt kitöltő homogén energiasűrűség – Mindent kitöltő homogén skalármező (nem a Higgs!) • Állapotegyenlet (nyomás ∝ energiasűrűség) p=wε – 13. kérdés: Mekkora w nem-relativisztikus ideális gáz esetén? – Relativisztikus ideális gáz: w=1/3 – Kozmológiai állandó: w=-1
A három nagyágyú: SNIa, CMB, BAO
Hubble Hubblediagram diagram (740SN SNIa)Ia) 2015: (740 Hubble-tv
Betoule et al.et2014 (JLA) Betoule al. 2014 (JLA)
w-Ωm diagram
DarkDark Energy equation of state Energy equation of state W= W= pressure/density pressure/density (cosmological constant W=-1) (cosmological constant W=-1)6
6
Kozmológiai paraméterek mennyiség
2003
2015 (Planck+…)
H
71
67.74±0.46 km/s/Mpc
Ω
1.02±0.02
1.000±0.009
Ω
0.27±0.04
0.3089±0.0062
Ω
0.044±0.004
0.0501±0.0003
Ω
0.73±0.04
0.6911±0.0062
T
(13.7±0.2) Gév
(13.799±0.021) Gév
T
(379±8) ezer év
Mi lehet a sötét anyag? VE-ben keressük: • Barionos: önálló kutatási területek – bolygók – fehér törpék – MACHO-k (Massive Compact Halo Object): barna, fekete törpék, neutroncsillagok, fekete lyukak – gázfelhők • WIMP-ek
Laboratóriumban keressük: • Nem barionos (ismeretlen), gyengén hat kölcsön a barionos anyaggal – „forró” (közel fénysebességű, HDM): neutrínók (kevés) – „hideg” (lassú, CDM): Weakly Interacting Massive Particle (WIMP) Részecskefizikusok kedvence, de egyelőre nem sikerült találni
Netalán a gravitáció módosul nagy skálán?
Wide range of parameters!
Direct generally ...dedetection van soksearches más javaslat is optimised for W
Legnépszerűbb WIMP: LSP • D = R = (-1)3B+2S+L R-paritás – 13+1. kérdés: Mekkora az u-kvark és a muon R-paritása? – R = -1 s-fermionokra • Ha a legkönnyebb s-részecske semleges (neutralínó), akkor SA jelölt • Az ilyen s-részecske közvetve felfedezhető az LHC-n (hiányzó energia a jele)
Egy minimális lehetőség: inert Higgs • A SM Higgs-mechanizmus minimális kiterjesztése feltételezett D-szimmetriával – A D = -1-es Higgs-részecske az SA jelölt (fermionokkal nem hat kölcsön)
O operat SM χ we will this study are, 2q) SM O = (¯ q γ 1 jof 1 we paper, we willmainly assume a dark matter parti will study are i g g (possibly mediated by light mediators) O = HighPT Selectio 2 µ O = HighPT Selection r of (Z ⇤⇤) + and (W ⇤) + j final states. In t χ q 4 jets in 1 fb data, although we will also 36 pb of integrated luminosity. Th we Throughout will study are, 4 spectrum, and conclude. Throughout this pap for(possibly dark searches at hadron c 2 2 mediated 2Experimental i gχ matter gtheq superscript 2q by lig qvetoe − are O = (¯ q γ q) ( χγ ¯ are vetoed ifS q − M 1 ofby as indicated “inv”. stud Describe DM interactions as 2 µ Olost, = (¯ q q) ( χχ) ¯ , 36 pb integrated luminosity. The ATL Dark matter pair production through a related relat 1 successively penergy cuts,[24, W 2CMS 2TATLAS iqgCDF gplus /maj 2χ − 2harder /T of jets missing (jthe +SI,⌅(j E )/< ⌅(j ,mostly E q[22], , )E by [23] and 25], q − M M q Probes o scalar O 2 weOperators mono-jets will study are, and Here O1performed = (¯ q q) ( χχ) ¯ , 3 3 successively harder p cuts, the major sele We hm for dark matter searches at hadron collider Figure 1: Dark matter produc T SM i (possibly mediated by light 2for Ourtake analysis will, the most part, be based on the ATLA We hop analysis are given below. SM we qiwe = u, d, s and turn on each o i g g will study are, q 2q− M mainly of (Z ⇤⇤) + j and (W Probes of D Here we take = u, d, s and turn on each veryHighPT Select Probes of DM χ q 3 Th WIMP-ek keresése gdata, ggiven veryHighPT ggweµby gthe / T ) events χ missing qi gi jets in 1jets fb plus ofare although will also compare to theSe eT analysis below. of energy (j µ + E Limits in direct detection plane χ q 4 χ q events are ve (¯ q γ γ O = O = (¯ q γ q) ( χγ ¯ χ) , DM-nu S i g g lost, as indicated superscript “ 2 χ= qHere 5 3 2 events ar 36 pb of integrated luminosity. The search contai invµ Limits in direct detection plane µ ATLAS 2 2γ⇤⇤) we take q = O (¯ q q) ( χ ¯ 2 mainly of (Z + j and (W ⇤) + operator will be easy to deduce). q is the (¯ q γ γ q) (χ O = 2 2 / DM-nucle / or ⌅(j , E O = (¯ q q) ( χγ ¯ χ) , q − M 1 SI, vecto LowPT Selection requires E > 120 G O µ 5 3 2 µ 2 Operators and mono-jets DM-nucleu scenar operator will easy to deduce). q[23] is4⌅(j Here we take qT criteria = u, g− gthe − successively harder p2 by cuts, major from hope to pr 2be or 2χthe 2>3.1. Figure 1: Dark matter production int 2iq 2M /selection qWe LowPT Selection requires E 120 GeV, o performed CDF [22], and qas − M scen T CMS Comp q − M q M lost, indicated by superscript “inv”. We hope to probe d We hope to probe dark analysis are given below. q ¯ are vetoed if they contain a sec O = (¯ q q) ( χχ) ¯ i g g In all cases events a, χ q2 1 the related to mass of the particle whose exc µ Throughout this paper, we will assume a dark matter p are vetoed if they contain a second je i g g Limits in direct detection plane 2 Our analysis will, for the most par In all cases even Operat χ q vector performed by CDF CMS and ATLA (¯ qγ[22], γg γ(= q)qu, ¯[23] γ χ) =Here µ(χγ DM-nucleus scat and ps >SD, 20,Ge related to the mass of the particle whose e) µ 5GeV, 5and 3 = q(¯ − M Limits in direct detection plane i • gyorsítóval: SM WIMP ax we take qχ d, tu q21γE/g q) χγ ¯g γone χ) ,(e) OO3LowPT 2DM-nucleus operator will be DM-nucleus scatterin Selection requires >= 120 jet with pused (j20 i g µ 5g 5DM Now convert the high‐energy scattering vect DM Here we take q u, d, s and turn on operator will be eas q − M i g SM and p (e) > χ q 2 2 The cuts Describe DM interactio χ qmost SM jets in 1if Selection fb of data, although we w 3.1. Comparing Our analysis will, for the part, be bbo qvetoed − M DM exc Dark matter pair production thr This is a representative set of operators / Now convert the high‐energy O = (¯ q γ q) HighPT E > 220 are they contain arequires second jet with p (j ) > 30 / limit on into limits on , O = (¯ q γ q) ( χγ ¯ HighPT Selection requires E > 220 GeV, T 4 5 The cuts us are (¯ selected byq) req T2 436 5 Section O = q γ 1g of 1χ a Throughout this paper, we will assume dark matter parti i g g 2 This is a representative set of operato i g 2 µ 2 2 χ q jets in 1 fb data, although we will also operator will be easy to deduc q pb of integrated luminosity. Th weesemények will studyhiányzó are, i g g limit on into limits on , qc DM by converting quark‐level to operator will be easy to deduce). SM χ q q − M DM for dark matter searches at hadron | (j )| < 2.4. A se 2 2 q − M DM are selected by are vetoed if there isjetaq) second SM DM are vetoed ifq) there isχγ aq,one second jet w ¯ (possibly mediated by lig DM Sect /(¯ = q γ q) ( ¯ χ) , Selection requires E > 220 GeV, with p (j Sm = (¯ γ ( χγ ¯ OO4HighPT = (¯ q γ ( χγ ¯ χ) SD and q − M scenarios. Majorana dark matter will yield sAao 1 4O 5 5 Describe DM interactions as 5 5 to 2are µ to the mass related the ma Nucleon‐level matrix elements: 2related 2harder the leading jet is 36 pb of integrated luminosity. The ATL by converting quark‐level to 2q− 2M Dark matter pair production through | (j )| < 2.4. successively p cuts, the maj W 2 2 − q M / and H T vetoed if⌅(j there is a second jet with | (j )| < 4.5 / of jets plus missing energy (j + E ) / ⌅(j , E ) < 0.5. Any further jets w E < 0.5. Any further psu psuedo-sca 2q Twa − T, the 2dark scenarios. for Majorana matter will yield T )M related to the mass of the particle related to mass of the part vetoed, as are even we will study are, Nucleon‐level matrix elements: the leading jeth 3 successively harder p cuts, the major sele We / dark matter searches at hadron collider ⌅(j , E ) <are 0.5. Any further jets with | (jlight )| hop < 4.5 m T below. i (possibly mediated by We vector interactions). Initially we will assume analysis given and SM observed events inm i g g mainly of (Z ⇤⇤) + j and (W energiával SM WIMP SM χ q 3 SM vetoed, as are e SM Here we take q = u, d, s and turn on each operator one at i g g we leav /time Here =Limits in direct detection plane u, d,s and turn onon each operator one at a300 time (but resu analysis are given below. of jets plus missing energy (j + )>jet events /E Here weHere take qtake =q q=u, d, and turn on each operator one veryHighPT Selection requires E 300 G i g g wewetake u, d, ss vector and turn each operator one at a (bu χ q This is a represe T This is a representative set of o T / / χ q veryHighPT Selection requires E > GeV, one with interactions). Initially we will assu veryHighPT Selection requires E > q This is a representative set q q (¯ q γ γ O = This is a rep q DM-nu Nucleon Nucleon Tq q⇤⇤) qq observed events lost, as indicated by the superscript “ qaDM-nucle Nucleo µ 5 3 q inv Limits in direct detection plane Nucleon Nu SectionO 43events we will discuss the effect of aq) light Here we take q = O = (¯ ( χ ¯ 4 mainly of (Z + j and (W ⇤) + Nu (¯ q γ γ q) (χ = 2 2 events are vetoed if there is a second 2 are vetoed if there is second jet with | (j )| < / we le 1 LowPT Selection requires E > 120 G µ 5 DM-nucleu T Here we take q = u, 2performed g/are gvetoed operatorwill willbe beeasy easy to to deduce). q LowPT is isthe exchanged momentum the − 2χ direct 2>with 2the events if there is aan 2iq 2M Op /momentum qdirect Selection requires E 120|and GeV, os by CDF [22], CMS [23] and Majorana dark matter wil operator deduce). qscenarios. /is TAny or ⌅(j ,E ) exchanged < 0.5. Any further jets (j )|mo < 4.5 q − M q − M 2 operator will be easy to deduce). q the exchanged lost, as indicated by the superscript “inv”. † •operator közvetlenül: or ⌅(j , E ) < 0.5. further jets scenarios. Majorana dark matt Section 4 we will discuss the effect of a ligh direct 2 T /ifto are vetoed they contain afurth sec = (¯ qthe q) (second χχ) ¯fermion and HO H1χχ ¯ Our appearing the dimension s, scenarios. Majorana will deduce). q is the exchanged d orvetoed ⌅(j ,[22], E < 0.5. are if2up they contain aAny jeO dire T )CMS 2 2 analysis will, for most par related be to theeasy mass ofto theq¯particle whose exchange generates the four scenarios. Major performed by CDF [23] and ATLA all cases events are ifgenerates contain any hard leptons, qvetoed −iiχare M of as ggthey ggInitially vector interactions). we wilaf related to the mass of theq particle whose exchange the four operator will be χ qq(µ)| †In i g g DM 1for operator will be eas ¯ SM q Now convert the high‐energy In all cases events vetoed if they contain vector interactions). Initially w DM and H H χχ ¯ appearing up to the dimension and p (e) > 20 GeV and muons as | < 2.4 and p (µ) χ SM we leave their study and the study of operato jets in 1 fb of data, although we w Our analysis will, for the most part, be b DM related toszórás the ismass ofNow convert the high‐energy the particle whose exchange generate /(¯ O = q γ q) rugalmas WIMP WIMP HighPT Selection requires E > 220 This a representative set of O operators that will generate a variety of / = (¯ q γ q) ( χγ ¯ HighPT Selection requires E > 220 GeV, T 4 5 limit on into limits on , In all cases events are vetoed if they co T 4 5direct The cuts by1we CMS are similar to those of the vector interactions). O = (¯ q γ q) 14 Section will discuss the effect ofd i g g and ppb (e) > 20 GeV and for muons asof |LowPT (µ 2 2 as related to This the ismass of the particle whose exchange gene Opera 2 µ 2 2 Tused Focus on χ q a representative set of operators that will generate a vari jets in 1 fb of data, although we will also 36 of integrated luminosity. Th Focus on direct det limit on into limits on , q − M by converting quark‐level to 2by qused − M /20 vetoed ifCMS there isone aon second are vetoed if there is(¯ aq2γ second jet areO selected by requiring E >GeV 150 GeV and jet with pwa Now convert the high‐energy ¯study Operator O leads to spin-independent co vector interaction Section 4>and we will discuss the eff leave their the study of opera 1are and p1similar (e) and for muons = q) ( χγ ¯ q − M Focus dir scenarios. Majorana darkwe matter will yield result (though for a Majo T The cuts similar to t1 Dark matter pair production through a are diagram like figure 2 µ related to the mass o related to the ma † Nucleon‐level matrix elements: 36 pb of integrated luminosity. The ATL by converting quark‐level to (a similar game can | (j of )|and < 2.4. A⌅(j second jet with psimilar (j ) >cuts, 30 GeV is can allowed successively harder p the maj W 2 2 This is a representative set operators that will gene (a game be H H χχ ¯ appearing up to the dim atommagon mélyen T / Now convert the high‐energy / , E ) < 0.5. Any further jets w ⌅(j , E ) < 0.5. Any further 2 could limit on into limits on for will dark matter searches hadron colliders [3, 4]. The signal w q, at2, Tjthe −mediator M scenarios. Majorana dark matter yield similar (though for a Ope /CMS The cuts used by are simila ‐Nucleon are selected by requiring E > 150 GeV an †⌅(j Nucleon‐level matrix elements: the leading jet is )
of 10 χrequires 3gqwith | ofwe (jas < 2.4. A second jet pwith (j > 3G /Focus leave their and the study Here we take q = u, d, s and turn on each operator one ‐Nucleon are selected by requiring E 150 G 1 )| 2In T> atommag analysis are given ¯ mainly (Z ⇤⇤) + j and (W ⇤) + j final the la /states. Section 4 we will T Here we take q = u, d, s and turn on each one veryHighPT Selection E > 300 i g Limits in direct detection plane This is a represe DM co vector interactions). Initially we will assume that the mediator is heav q T / χ q F ascenarios. felszín alatt atommag atommag Majorana dark matter will yield similar result (th veryHighPT Selection requires E > observed events in the various searches is shown in table I. (¯ qγradians. γsecond O = This is aNucleo rep qa>the DM-nu coul Tγ is)| generated through axial-vecto Section 4 we will by converting quark‐level to discuss the Operator effect aindicated light mediator. There are two additio µ 5G 3we †⌅(j q Nucleon‐level matrix elements: lost,of as by the superscript “inv”. Experimental studies Limits in direct detection plane 3= the leading jet is vetoed j2there )(¯ < 2.0 E q Here we take q = 1 ,DM-nucle leave their study and stu (a 4 |O (j < 2.4. A second jet with p (j Nu q γ q) (χ O 2 2 events are if is / of as arising from exchange of a scalar of m 1 T (a sim and H H χχ ¯ appeari LowPT Selection requires E 120 µ 5 3 DM-nucleu Operator O leads to spin-indepen T Here we take q = u, performed by CDF [22], CMS [23] and ATLAS [24, 25], mostly in t q − M 1 2Selection events are vetoed is alep 2events 2E/ T if>there scenarios. Majorana dark matter yield similar resul LowPT requires 120 GeV, vetoed, as are containing charged under Section 4† Hwe will discuss the effect of awill light mediator. There are two aos q − M 2 operator will be easy to deduce). q is the exchanged mo † / Nucleon‐level matrix elements: and H χχ ¯ appearing up to the dimension six level. While they are less cons or ⌅(j , E ) < 0.5. Any further jets the leading jet is ⌅(j , j ) < 2.0 rad could arise from exchange of a pseudo-scalar Our analysis will, for the most part, be based on the ATLAS se 2 1 2 T are vetoed if they contain a sec DM scenarios. will† be easy toOperator deduce). qarising is⌅(jfrom exchanged vector interactions). Initially weO will assume that the medi /will and H H χχ ¯ app or ,the E )also <Majorana 0.5. Any furth Operator O leads to spin-in vetoed if2 we they contain aaxial-ve second je dire events inthe searches is d sh 1various T is generated through exchange of a scala •operator közvetve: WIMP SM jets in observed 1of fb3 as ofare data, although compare to the earlie scenarios. Major vetoed, as are events containing char i g g operator will be andweHleave H χχ ¯their appearing up the36coupling. dimension six While they are les we leave study χ q ifDM study and the study of operators involving the three heavy quar ilevel. gχcombinations DM pb In ofall integrated luminosity. The ATLAS search contains t operator will be eas qq¯toparticle SM qtheir DM Various of these cases events areg vetoed they contain SM vector interactions). Initially we will assume that the m DM related to the mass of the whose exchange generate / unde O = (¯ q γ q) HighPT Selection requires E > 220 /(¯ observed events in the various search as from exchange successively harder parising cuts, therequires major selection criteria from eac Operator O is generated ax OHighPT = qmuons γ>through q) (5aχγ ¯ofnu Selection GeV, o Tif Ther 4of 3events In all cases are vetoed they ca T 4 5220 could arise from exchange of aE pseudo-sca Section we willutaló the effect of a light mediator. vector interactions). and p (e) > 20 GeV and for as | (µ 2 2 related to the mass of the particle whose exchange gene 2 2 T Operator Odiscuss to the spin-independent coupling between the DM and we 4 leave their study and study of operators involving the three heav 1 leads analysis are given below. szétsugárzásra we leave their stu Both ATLAS and CMS impose isolatio q20− − M under theand SMare such as squarks supersymm qused M are vetoed ifCMS there issimilar amuons second vetoed ifby there isin aadditional second jettowa Now convert the high‐energy vector interaction p (e) > GeV and for Operator O lead T The cuts are t could arise from exchange of a pseud related to the mass 1 related to the ma since they would not have a large impact on ouro Operator O is generated throu 3 This is a representative set operators that will gene /TO † / LowPT of Selection requires E > 120 GeV, one jet withoccurs p of (j ) th >w 1 DM coupling. Various combinations Now convert the high‐energy / of as arising from exchange of a scalar of mass M , is similar but t ⌅(j , E ) < 0.5. Any further jets Section 4 we will discuss the effect of a light mediator. T ⌅(j , E ) < 0.5. Any further 2 2 limit on into limits on , 2 Tbetween Operator O1 leads to spin-independent coupling the DM an / The cuts used by CMS are simila ‐Nucleon and H H χχ ¯ appearing up to the dimension six level. While are selected by requiring E > 150 GeV an Section 4 we will disc T Figure 1: Dark matter production in association with a single jet in a hadron collider. Both ATLAS and CMS impose additional areof vetoedoperators if SM they contain a second that jet with p (jwill ) > 30 Ge jel a világűrből WIMP Foc This isOperator a representative set SM DM coupling. Various combinations Focus limit on into limits on , SM by converting quark‐level to Operator O could arise from exchange of aG | (j )| < 2.4. A second jet with p (j )one > 3G / O is generated through axial-vector exchange and gives a spin-dep Here we take q = u, d, s and turn on each operator one at ‐Nucleon 1 are selected by requiring E > 1 2150 T> since they would not have awe large impact 3 of as arising from ex ¯ / Section 4 will T Here we take q = u, d, s and turn on each operator under the SM such as squarks in supersym veryHighPT Selection requires E 300 This is a represe / T of as arising from exchange of a scalar of mass M , O is similar but oc † / HighPT Selection requires E > 220 GeV, one jet with p (j ) > F scenarios. Majorana dark matter will yield similar result (th veryHighPT Selection requires E > 2 This is a rep q Tq 2E Nucleo † q Nucleon‐level matrix elements: the leading jet is ⌅(j , j ) < 2.0 radians. andweHleave ¯their appearing theare dimension six level. W 1 2 studyby converting quark‐level to andup thetostudy of operators involving the under the SM such as squarks in sup (a(jw 4 H χχ | vetoed (j1events )|if < 2.4. A second jet Nu there is avetoed second jet | (jiswith )| a<(a 4.5pand are if with there second T sim
for dark matter searches at hadron colliders inv[3, 4]. The signal would m / T ) events over the Standard Model b of jets plus missing energy (j + E inv ⇤) + j final states. In the latter c mainly of (Z ⇤⇤) + j and (W 2 of 2T j + lost, as indicated by the superscript “inv”. Experimental studies performed by CDF [22], CMS [23] and ATLAS [24, 25], mostly in the co Our analysis1will, for the most part, be based on the ATLAS search [ 1 1 of data, although we will also compare to the earlier CM jets in 1 fb 1 2 T 36 pb of integrated luminosity. The ATLAS search contains three T 2s 3 major selection criteria from each ana successively harder pT cuts, the analysis are given below.3
Ope
P Pro Prob 33
T
T 1 T GeV, one jet with p (jT ) > 120 / T > 120 LowPT Selection requires E G T 1 2 T are vetoed if they contain a second jet with pT (j2 ) ‐Nucleon > 30 GeV an
‐Nucleon
1
/ T > 220 1 T G HighPT Selection requires E T GeV, one jet with pT (j1 ) > 250 1 2 and with e are vetoed if there is a second jet with | (j2 )| < 4.5 /2T )
P Pro Prob
/ T > 300 GeV, one jet with pT (j1 ) > veryHighPT Selection requires E T events are vetoed if there is a second jet with3 | (j2 )| < 4.5 and w ATLAS2and C / T ) < 0.5. Any further jets with | (jBoth or ⌅(j2 , E 2 )| < 4.5 must ha
4
2
since they 2would no
T
3
Dark matter production in association a single Bothwith ATLAS an In all casesFigure events1:are vetoed if they contain any hard leptons, defined fo since they would and pT (e) > 20 GeV and for muons as | (µ)| < 2.4 and pT (µ) > 10 GeV T The Tcuts used by CMS are similar to those of the LowPT ATLAS 3.1. Comparing Various Mono-Jet An / T > 150 GeV and one jet with pT (j1 ) > 110 ‐Nucleon are selected by requiring E | (j1 )| <‐Nucleon 2.4. A second jet with TpT (j2 ) > 30 GeV is allowed if the azi T the leading jet is ⌅(j1 , j2 ) < 2.0 radians. Events with more than two 1 T 2 vetoed, as are events containing charged leptons with pT > 10 GeV. Th 1 2 observed events in the various searches T is shown in table I. T
inv
3
Both ATLAS and CMS impose additional isolation cuts, which we do not mimic i since they would not have a large impact on our results.
3 Figure 1: Dark matter production in association a single in a impose hadron additional collider. isolation cuts, which we do n Bothwith ATLAS andjet CMS David Berge ‐ CERN since they1would not have a large impact on our results.
3.1.
1
Comparing Various Mono-Jet Analyses T
3
David B
3
Dark matter pair production through a diagram like figure 1 is one of the leading channels for dark matter searches at hadron colliders [3, 4]. The signal would manifest itself as an excess T / T ) events over the Standard of jets plus missing energy (j + E Model background, which consists 3 inv ⇤) + j final states. In the latter case the charged lepton is mainly of (Z ⇤⇤) + j and (W / T final states have been lost, as indicated by the superscript “inv”. Experimental studies of j + E T Extra Dimensions. performed by CDF [22], CMS [23] and ATLAS [24, 25], mostly in the context of
T
T
T
2
1
2
1
Felfedezésre ítélve? We are living in a privileged decade
The Decade of the WIMP
Rocky Kolb University of Chicago
MPIK-Heidelberg November 2012
majd meglátjuk...
Értjük-e ezeket a kérdéseket? • Vannak-e eddig fel nem fedezett természeti törvények? • Hogyan érthetjük meg a sötét energia rejtélyét? • Létezik-e több mint három tér-dimenzió? • Egyesülnek-e az alapvető kölcsönhatások? • Miért van oly sokfajta elemi részecske? Van-e esetleg több? • Mi a sötét anyag, elő tudjuk-e állítani laboratóriumban? • Mit mondanak a neutrínók? • Hogyan keletkezett fejlődött a Világegyetem? • Hová tűnt az antianyag?
Vége
