Effective theory of decay into gamma-ray lines Thomas Hambye Univ. of Brussels (ULB), Belgium Based on a collaboration with Michael Gustafsson and Tiziana Scarna DSU-SISSA-Trieste 4//03
95% CL Lim <v> Expected 68% Containment Expected 95% Containment Expected 68% Containment Expected 95% Containment Weniger [0] Limit -7-7 Search for smoking gun lines produced by annihilation or decay -8-9 FIG.. 95% CL σv γγ upper limits for each profile considered in the corresponding optimized ROI. bands show the 68% (95%) expected -8 containment derived from 00 single-power law (no ) MC simulatio lines show the median expected limits from those simulations. The solid gray line shows the limits derived by W independent search for spectral lines from 0 300 GeV) when comparable ROIs and identical density pro -9 many recent experimental progresses γ 95% CL Lim <v> -30 FERMI: bound on annihilation gamma line m (GeV) -30 FERMI: bound on decay lifetime to gamma line (GeV) m s - ) 3 95% CL Limit (cm <v> F I G. -3. 95% C L v γγ upper limits for each D M profile considered in the corresponding optimized R O I. Yellow (green) sr - ) s - - (95% CL) (m -5-6 -7-8 -9-30 -7-8 -9 3.7 year R4 NFW Profile Observed Upper Limit Expected Limit Expected 68% Containment Expected 95% Containment Weniger [0] Limit CGH MC detection CGH limits extragalactic limits HESS: bound on gamma line flux 95% CL Limit (s) 30 9 305.5597 m (GeV) E (TeV) s - ) 3 95% CL Limit (cm <v> 30.73-5 -6-8 -9-30 95% CL Limit (s) -7 $ 30 3.7 year R90 Isothermal Profile Observed Upper Limit Expected Limit Expected 68% Containment Expected 95% Containment 9 8 3.7 year R80 NFW Profile Observed Lower Limit Expected Limit Expected 68% Containment Expected 95% Containment m 305.5597 FIG.. 95% CL τ γν lower limits Many in R80 theoretical for an NFW studies profile. too: Yellow (green) bands show the 68% (95%) expect bands show the 68% (95%) expected containment derived fromderived 00 single-power from 00 single-power law (no ) law MC (nosimulations. D M) M C simulations. The dashedt he lines dashed show the median expected lim linesshow -4 the median expected limits from simulations. those simulations. T he solid gray Annihilation: line shows Bergstrom, the limits Ullio, derived 97 98 ;Bern, by Weniger Gondolo, [0] Perelstein (an 97 ; independent search for spectral lines from 0 300 GeV) when comparable R O Is and Bergstrom, identical DBringmann, M density Eriksson, profiles were Gustafsson used. 04, 05 ; Boudjema, Semenov, Temes 05 ; Dudas, Mambrini, Pokorski, Romagnoni 09 ; -5 Jackson, Servant, Shaughnessy, Tait, Taoso 09, 3; Ramajaran, Tait, Whiteson ; -6 Ramajaran, Tait, Wijangco ; Cotta, Hewett, Le, Rizzo ; Bringmann, Huang, Ibarra, Vogl, Weniger ;Weniger ;... (GeV) m (GeV) Decay: Buchmuller, Covi, Hamagushi, Ibarra, Tran 07 ; Ibarra, Tran 07 ; Ishiwata, Matsumoto, Moroi 08 ; Buchmuller, Ibarra, Shindou, Takayama, Tran 09 ; Choi, Lopez Fogliani, Munoz, de Austri 09 ; Garny, Ibarra, Tran, Weniger ; Ibarra Tran, Weniger 3
γ This talk: the line decay production scenario unlike an annihilation the decay width is not limited by thermal freeze out cross section value (and possible loop suppressions) there exists a simple motivated framework for slow decay: if stability is accidental just as for the proton in Standard Model UV physics has a priori no reason to respect an accidental low energy symmetry UV physics is expected to cause a decay suppressed by powers of UV scale L = L dim=4 + O (5) i + Λ i UV Λ O (6) i +... i UV Eichler; Nardi, Sannino, Strumia; Chen, Takahashi,Yanagida; Arvanitaki, Dimopoulos et al.; Bae, Kyae; Hamagushi, Shirai, Yanagida; Arina, TH, Ibarra, Weniger;... if UV scale is large the decay lifetime is naturally very large kind of intriguing coincidence: dim 6 Λ UV Λ GUT m TeV τ 8π m5 if and Λ 4 GUT 8 sec ~ experimental sensitivity today
Effective theory of decay into line(s) γ fully justified since UV scale expected much larger than SM and scales is practically feasible: not too many operator structures even if we allow for decay to a γ and a new unknown particle as we will do to be fully general Many criteria an operator must fulfill: must contain the field in a linear way must contain the photon field strength must lead to a radiative body decay must not have a one to one correspondence with another operator already in the list
List of possible dim 5 and dim 6 radiative operators dimension 5 dimension 6 for a scalar candidate: for a fermion candidate: for a spin candidate: O (5)YY φ φ F Yµν F µν Y φ =(,0) O (5)YL φ φ F Lµν F µν Y φ =(3,0) O (5)LL φ φ F Lµν F µν L φ =(/3/5,0) O (5)YY φ φ F Yµν F µν Y φ =(,0) O (5)LY φ φ F Lµν F µν Y φ =(3,0) O (5)Y ψ ψσ µν ψ F µν Y ψ ψ =(,0) O (5)L ψ ψσ µν ψ F µν L ψ ψ =(3,0) O (5)Y V O (5)L V F µν F µν Y φ φ=(,0) F µν F µν L φ φ=(3,0) Oφ YY φ F Yµν F µν Y φ φ φ =(,0) Oφ YL φ F Lµν F µν Y φ φ φ =(3,0) Oφ LL φ F Lµν F µν L φ φ φ =(/3/5,0) Oφ YY φ F Yµν F µν Y φ φ φ =(,0) O LY φ φ F Lµν F µν Y φ φ φ =(3,0) Oφ Y D µ φ D ν φf µν Y φ φ =(,0) A Oφ L D µ φ D ν φf µν L φ φ =(3,0) C 6 fermion operators Oψ Y ψσ µν ψ F µν Y φ ψ ψ φ =(,0) Oψ L ψσ µν ψ F µν L φ ψ ψ φ =(3,0) Oψ Y D µ ψγ ν ψ F µν Y ψ ψ =(,0) Oψ L D µ ψγ ν ψ F µν L ψ ψ =(3,0) Oψ 3Y ψγ µ D ν ψ F µν Y ψ ψ =(,0) Oψ 3L ψγ µ D ν ψ F µν L ψ ψ =(3,0) C d to 5 vector operators O V F µν F µρ Y Fν Y ρ OV Y Fµν F µν Y φφ φ φ =(,0) OV L Fµν F µν L φφ φ φ =(3,0) OV 3YY O 3LY V D µ φd ν φ F µν Y φ φ =(,0) D µ φd ν φ F µν L φ φ =(3,0)
Relevant questions bound on γ line intensity for each operator? various correlated signals from each operator for a multichannel analysis? is an experimental operator discrimination possible? getting information on particle nature and UV physics at the origin of the decay γ from line features: their number, energy and intensity main ways: from associated non monochromatic cosmic ray production
Possible body radiative decays and ray line features γ γ/z γ/z φ ψ γ, Z, Z ψ γ/z V 3 categories of operators: γ, Z, Z, φ, φ ) F Y,Lµν F µν operators: give lines Y,L γ γγ γz E γ = m E γ = m ( m Z/m M ) energy of first peak fixes the energy of second peak intensity of peaks also predicted: Γ γγ /Γ γz = cos θ W sin θ W F, sin θ W cos θ W F, Y F = m 6 /(m m Z )3 sin is above but not too far θ W cos F θ W only for scalar F Yµν F µν Y F F Yµν F µν Lµν F µν L L
Possible body radiative decays and γ ray line features γ/z γ/z φ ψ γ, Z, Z ψ γ/z V γ, Z, Z, φ, φ 3 categories of operators: γ ) operators giving lines from decay to an unknown particle γz, γφ γz, γφ only for scalar or vector energy of peaks fixed by intensity of peaks fixed by masses and quantum numbers of or scalar vev values E γ = m ( ( m Z,φ,φ /m ) m mass of unknowm particle m Z,φ,φ ( g T3 m Γ γz /Γ γz = m Z cos θ W gy Y m m Z ( ) Γ γφ /Γ γφ = φ 3 m m Z φ m m Z ) 3
Possible body radiative decays and γ ray line features γ/z γ/z φ ψ γ, Z, Z ψ γ/z V γ, Z, Z, φ, φ 3 categories of operators: γ 3) operators giving only one line: only for scalar, fermion or vector E γ = m ( m Z,φ,φ,ψ/m ) N.B.: a same particle can in principle give several lines from appearing in several operators
Cosmic ray production associated to a line γ each operator must be gauge invariant: involves F µν Y or F µν L Z channel is there if E γ >> m Z W + W,...... as we will consider here channels are there by gauge invar. sometimes cosmic rays: p, γ D,e +, ν,... upper bounds on γ line intensity from CR constraints
γ Absolute upper bound on line intensity from CR constraint from a single operator (for several oper. see below) n γ n Z cos θ W sin θ W R γ/cr n γ n CR cos θ W sin θ W n CR/Z can be saturated only for a few operators (e.g. some with a F µν Y ) other operators can only give a smaller ratio many possibilities one can nevertheless have a simple global picture in steps
step procedure to classify the γ to CR ratio predictions ) first write down the maximum ratio a given structure can give in full generality there are only 5 maximum ratios: A : n γ n Z = cos θ W sin θ W or R γ/cr n γ n CR = cos θ W sin θ W n CR/Z characteristic of oper. with only F µν Y B : R γ/cr = n CR/Z C : R γ/cr = D,E : R γ/cr = with c sin θ W cos θ W n CR/Z sin θ W cos θ W n CR/Z + c W (n CR/W + + n CR/W ) 4 for D and E, respectively. Signal c W =/4, ratio characteristic of oper. with F µν Y F Lµν characteristic of some oper. with only F µν L characteristic of some oper. with only F µν L ) see for each structure how the ratio can be reduced: 3 ways: the ratio can depend on the multiplet considered: can reduce n γ /n CR by a few the ratio can depend on the unknown CR amount produced by new particle the ratio can depend on the unknown value of vev of new scalar can give very suppressed F cases
Classification of operators along the n γ /n CR ratio they give O (5)YY φ φ F Yµν F µν Y φ =(,0) A O (5)YL φ φ F Lµν F µν Y φ =(3,0) B O (5)LL φ φ F Lµν F µν L φ =(/3/5,0) D m O (5)YY φ φ F Yµν F µν Y φ =(,0) A x O (5)LY φ φ F Lµν F µν Y φ =(3,0) C x O (5)Y ψ ψσ µν ψ F µν Y ψ ψ =(,0) A x O (5)L ψ ψσ µν ψ F µν L ψ ψ =(3,0) C x,m O (5)Y V O (5)L V φ F µν F µν Y φ φ=(,0) A x F µν F µν L φ φ=(3,0) E x ψ m label: multiplet dependence, x label: CR from new particle v label: vev of new scalar dependence Oφ YY φ F Yµν F µν Y φ φ φ =(,0) A Oφ YL φ F Lµν F µν Y φ φ φ =(3,0) B Oφ LL φ F Lµν F µν L φ φ φ =(/3/5,0) C x,m Oφ YY φ F Yµν F µν Y φ φ φ =(,0) A x O LY φ φ F Lµν F µν Y φ φ φ =(3,0) C x Oφ Y D µ φ D ν φf µν Y φ φ =(,0) A x,m,v Oφ L D µ φ D ν φf µν L φ φ =(3,0) C x,m,v fermion operators Oψ Y ψσ µν ψ F µν Y φ ψ ψ φ =(,0) A x,m Oψ L ψσ µν ψ F µν L φ ψ ψ φ =(3,0) C x,m Oψ Y D µ ψγ ν ψ F µν Y ψ ψ =(,0) A x Oψ L D µ ψγ ν ψ F µν L ψ ψ =(3,0) C x,m Oψ 3Y ψγ µ D ν ψ F µν Y ψ ψ =(,0) A x Oψ 3L ψγ µ D ν ψ F µν L ψ ψ =(3,0) C x,m to 5 vector operators O V F µν F µρ Y Fν Y ρ OV Y Fµν F µν Y φφ φ φ =(,0) A x OV L Fµν F µν L φφ φ φ =(3,0) D x,m OV 3YY O 3LY V D µ φd ν φ F µν Y A x φ φ =(,0) A x,m D µ φd ν φ F µν L φ φ =(3,0) D x,m.
Upper bound on γ line intensity the most stringent constraints are from from p γ D below ~TeV above ~TeV 6 7 A B C D E F Y p γ D p constraint with MIN setup F L Γγ[s ] 8 9 FERMI HESS 30 NFW, MIN 3 3 4 m [GeV] bounds from CR relatively close to direct search bounds less stringent for A and B by orders of magnitudes less stringent for C, D, E cases by a factor of a few
Upper bound on γ line intensity the most stringent constraint are from from p γ D below ~TeV above ~TeV 6 7 A B C D E F Y p γ D p constraint with MIN setup F L Γγ[s ] 8 9 FERMI HESS 30 NFW, MIN if a γ 3 3 4 m [GeV] line is found around the corner: A >E are possible for C >E this would imply associated CR flux excess around the corner conversely observation of CR excess around the corner not compatible with A, B
Upper bound on γ line intensity the most stringent constraint are from from p γ D below ~TeV above ~TeV 6 7 A B C D E F Y p γ D p constraint with MIN setup F L Γγ[s ] 8 9 FERMI HESS 30 NFW, MIN 3 3 4 m [GeV] future: better knowledge of CR flux would lower A E lines by up to one order of magnitude CTA, HESS,...: direct search improvement by ~ order of magnitude example: if MED instead of MIN: C >E go below direct constraint
Upper bound on γ line intensity for operators with only SM and fields A h γ + h (with F µν Y ) 7 G I Y G IR Y C h γ + h (with F µν L ) E µ Ee Γγ[s ] 8 E τ G I L G IR L 9 NFW, MIN 3 4 m [GeV]
What if UV physics generates several operators in correlated way? in most situations it marginally changes the CR constraints example: L a Λ UV φ φf Yµν F µν Y + b Λ UV φ φf Yµν F µν L + c Λ UV to reduce CR emission one needs to suppress several channels: γz, ZZ, W + W,... φ φf Lµν F µν L impossible or at the price of several fine tunings
An explicit example of accidental symmetry setup: hidden vector if is a massive gauge boson, abelian or non abelian TH 08 ; TH, Tytgat 09 Arina, TH, Ibarra, Weniger Hidden vector : accidental custodial symmetry a gauged SU() + SSB from a scalar doublet φ L = 4 F µνa F a µν + (D µ φ) (D µ φ) µ φφ φ λ φ (φ φ) φ gets a vev v φ 3 massive gauge bosons V + a real scalar i η m V = g φv φ m η = λ φ v φ stable due to residual SU() custodial sym. + communication with the SM through Higgs portal: V i ηη,... (V µ, V µ, V µ 3 ) = singlet η = forbidden: triplet L Higgs portal = λ m φ φh H relic density, direct detection,...
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Summary A systematic study of γ-line production and associated multichannel CR production can be done in principle and in practice for a decay: - use of effective theory fully justified - not too many operator structures bounds from basically unavoidable CR emission are in most cases slightly less stringent than direct γ-line search bounds real possibilities of operator discrimination do exist: γ - observing both a -line and associated CR s - from number, energy and intensity of -lines γ
FERMI: bound on decay lifetime to gamma line