Narrow-width approximation beyond the Standard Model

Transcription

1 Narrow-widh approximaion eyond he Sandard Model Chrisoph Uhlemann Insiu für Theoreische Physik und Asrophysik Universiä Würzurg Maria Laach 2007 Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

2 Ouline narrow-widh approximaion (NWA) explained feaures of MSSM - why we expec prolems a sysemaic analysis applicaion o specific MSSM scenarios improvemen of NWA Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

3 NWA explained The NWA For Γ m = 1 2mΓ 1 (q 2 m 2 ) 2 +m 2 Γ 2 π mγ δ(q2 m 2 ) for Γ 0 se inermediae paricle on-shell for Γ 0 drop off-shell effecs, spin correlaion o oain σ NWA = σ prod BR wih BR = Γ par /Γ oal reduces phasespace-dimension, calculaion of separae producion and decay relaively simple, loop calculaions feasile Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

4 NWA explained An example For measuring g a e +, consider he following processes for producion (Kolodziej, 2006) e + e + γ, Z (a) e + γ, Z () e + Z Z (c) wihou conriuion of hird diagram, σ g 2 and are unsale, herefore we end up wih diagrams like Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

5 e + γ, Z (a) W + d u W µ ν µ NWA explained e + γ, Z () 8 paricle final sae diagrams conriuing o his final sae a leading order W + W u d ν µ µ e + Z (c) Z d W + ū W ν µ µ Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

6 e + γ, Z (a) W + d u W µ ν µ NWA explained e + γ, Z () 8 paricle final sae diagrams conriuing o his final sae a leading order In NWA, he cross secion is W + W u d ν µ µ e + Z (c) Z d W + ū W ν µ µ σ NWA = σ(e + ) Γ W Γ Γ W µ ν µ Γ W Γ W + Γ Γ W + u d Γ W Γ Γ diagrams easy o calculae, a mos 3-paricle phasespace Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

7 NWA explained NWA and he SM NWA error elieved o e of O(Γ/m), wihou proof we developed a proof addiional assumpions needed, Γ m no enough O(Γ/m) jusifies expansion of he error in Γ/m i does no mean error Γ/m error Γ/m seems o rely on specific feaures of he sandard model: 1 masses of decay producs small compared o unsale paricles e.g. firs wo generaion fermions vs. W and Z, vs., vs. 2 limied se of paricles and couplings (no VSS and SSS a all) Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

8 NWA explained NWA eyond he SM New physics expeced a TeV, will e accessile a LC well sudied, heoreically appealing candidae: MSSM nearly degenerae masses in decay chains possile many new paricles and couplings, e.g. VSS and SSS sparicles cascade-decay ino LSP and SM paricles long decay chains increase complexiy NWA would e helpful, u is i safe? hese feaures migh also e found in oher SM exensions Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

9 sysemaic check A sysemaic check Therefore a sysemaic check would e nice. i s no possile o check all complicaed processes if his was feasile, he NWA would e superfluous smalles piece of decay chains conaining producion and decay of unsale paricle: 1 3 processes q P p 1 ypically occur in decays of susy-paricles occur in he diagrams for g, menioned efore can e checked sysemaically, giving hins on where o e careful p 3 p 2 Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

10 sysemaic check 50 processes in MSSM calculaed and checked relaive error indeed Γ/m generally, NWA fails if sum of daugher masses approaches paren mass in producion or decay NWA can fail for m i 85% of m, or work up o 98% someimes dependence on coupling parameers αp L + βp R cerain verices produce large deviaions, ohers do no no spin-correlaion effecs a all Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

11 sysemaic check m3 M m M s ss ssv: simple marix elemen no spin correlaion sill large deviaions plo for m 1 = m 2 = 0 lue - error 10% red - error 25% marix elemen produces (q 2 m 2 3 )2, having wo effecs: 1 asympoic ehaviour for large q 2 is q 4, compensaing he q 4 decrease of he Brei-Wigner shape (q 2 m 2 3 )2 (q 2 m 2 ) 2 +m 2 Γ 2 cons > 0 2 for m 3 m he peak of he Brei-Wigner shape is suppressed Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

12 specific MSSM scenarios NWA in he MSSM 105 free parameers in he unconsrained MSSM even wih fixed susy-reaking scheme oo many parameers o scan he full MSSM 10 specific poins wih aached model lines Snowmass Poins and Slopes commied as enchmark poins for phenomenology for he SPS poins all possile resonan 1 3 decays generaed and compared NWA o off-shell half of he chain pars wih large deviaions don occur in MSSM (no heavy vecor osons, herefore no resonan...-vss ec) Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

13 specific MSSM scenarios examples wih sale final saes and large R := (σ ofs σ nwa )/σ nwa, normalized o Γ/m process a SPS R Γ/m in % g d d L dd χ 0 1 1a g uũ L uu χ χ + 1 ν eẽ L ν e e χ χ 0 2 eẽ L ee χ χ 0 3 eẽ R ee χ χ 0 4 e ẽ R ee χ g uũ L ud χ g d d L du χ Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

14 improving NWA Modified NWA formulas 1 maximum of he Brei-Wigner a q 2 = m 2 phase space facors can shif his maximum include his effec y using q 2 = m 2 eff insead of q2 = m PS(m 2 ) (q 2 m 2 ) 2 +m 2 Γ 2 vs. PS(q 2 ) (q 2 m 2 ) 2 +m 2 Γ q 1 improves NWA ehaviour a kinemaic ounds 2 does no change very much in he inner of he parameer space 3 no process-dependen Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

15 improving NWA Threshold-improved NWA (Kauer, 2007) facors like β(m, M) = 1 m 2 /M 2 in phasespace facors addiional β-like facors in ampliude amplify hreshold effecs inegrae β facors wih Brei-Wigner insead of seing hem on-shell which facors depends on he process and parameers inegrals can no e calculaed analyically in general large improvemens, error Γ m, insead of jus O(Γ/m) Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15

16 conclusion Conclusion proof ha NWA error is of O( Γ m ) generally, i is no Γ/m general 1 3 processes in MSSM checked all resonan 1 3 decays for SPS poins generaed and checked unexpeced large NWA errors occur under cerain condiions NWA safe in he middle of he parameer space improved NWA formulas developed and applied Chrisoph Uhlemann (Würzurg) NWA eyond he SM Maria Laach / 15