def weightavgLF(x):
#see mathematica notebook "g-2_comparison.nb" for discussion of the two methods shown here.
#L=0 #for weighted sum
LogL=0 #for weighted average
for PMi,deltaamui,damui in zip(PM,deltaamu,damu):
#Add the pieces of the likelihood function together
#L+=exp(LFs.lognormallike(x,deltaamui,sqrt(damuexp**2+damui**2)*1e-10)) #This assumes no uncertainty in the computed MSSM value, or that the SM uncertainty dominates.
#LogL=log(L)
#Multiply seperate likelihood contributions together (don't need PMi contributions in this case)
LogL+=LFs.lognormallike(x,deltaamui,sqrt(damuexp**2+damui**2)*1e-10) #This assumes no uncertainty in the computed MSSM value, or that the SM uncertainty dominates.
return LogL #return the Log-Likelihood value
def globlikefunc(obsdict):
"""Compute log likelihoods and global log likelihood
Output format:
likedict = {likename: (logL, uselike),...}
"""
likedict = {} #reset likelihood dictionary
#Extract individual observables dictionaries from container dictionary
specdict = obsdict['spectrum']
decadict = obsdict['decay']
if usemicrOmegas: darkdict = obsdict['darkmatter']
#===========================================================
# EFFECTIVE PRIOR
#===========================================================
#likedict['CCRprior'] = (CCRprior(specdict['BQ'],specdict['tanbQ'],specdict['muQ']), useCCRprior)
#===============================================================
# DEFINE LIKELIHOOD CONTRIBUTIONS
#===============================================================
#-----------MAIN CONTRIBUTORS TO LIKELIHOOD-----------------
# delta(a_mu)
likedict['deltaamu'] = (LFs.lognormallike(x=specdict['deltaamu'],
mean=33.53e-10, sigma=8.24e-10), usedeltaamu)
#1106.1315v1, Table 10, Solution B (most conservative)
#=====Electroweak precision, RELIC DENSITY and (g-2)_mu=============
if usemicrOmegas:
#Dark matter relic density
likedict['omegah2'] = (omegalikefunc(darkdict['omegah2'], \
0.1186, sqrt((0.0031)**2+(0.10*0.1186)**2)), useomegah2)
# 2013 Planck data release (http://arxiv.org/abs/1303.5076)
# From table 2. Three numbers are relevant:
# Best fit, 68% confidence intercal
# 0.12029, 0.1196 +/- 0.0031 : Planck temp. data
# 0.11805, 0.1186 +/- 0.0031 : + Planck lensing data
# 0.12038, 0.1199 +/- 0.0027 : + WMAP low multipole
# : polarisation data
# Giving our somewhat arbitrary 10% extra theory uncertainty
# it doesn't matter which we choose (they are all within 2%
# of each other). Even the WMAP result (0.1123 +/- 0.0035) is
# only about 6% different from the central Planck result. So
# let's just use the "Planck only" data.
#
# old WMAP reference:
# 2010, 1001.4538v2, page 3 table 1 (WMAP + BAO + H0 mean)
# theory (second component) uncertainty stolen from
# 1107.1715, need proper source.
#=====Higgs constraints=============================================
# We first need to find out which of the NMSSM Higgses is SM-like
# Check the reduced couplings? Use those which are closest on
# average to 1? Crude, but good enough for first quick scan.
Higgses = ['H1','H2','H3','A1','A2'] # Must match blockmap
# Compute summed squared difference of couplings from 1
rgsqdiff = {}
for Higgs in Higgses:
rgsqdiff[Higgs] = \
(specdict['rg_{0}_u'.format(Higgs)] - 1)**2 \
+ (specdict['rg_{0}_d'.format(Higgs)] - 1)**2 \
+ (specdict['rg_{0}_WZ'.format(Higgs)] - 1)**2 \
+ (specdict['rg_{0}_g'.format(Higgs)] - 1)**2 \
+ (specdict['rg_{0}_a'.format(Higgs)] - 1)**2 \
# Get key of entry of rqsqdiff containing the min squared difference
mostSMlike = min(rgsqdiff, key=rgsqdiff.get)
likedict['mh_SMlike'] = (LFs.lognormallike(\
x=specdict['M{0}'.format(mostSMlike)], \
mean=126., sigma=sqrt(1.**2)), useLHCHiggs)
# Just a rough guess at the measured mass of the SM-like Higgs.
# Replace this with a rigorous likelihood involving decay rates.
#print mostSMlike, specdict['M{0}'.format(mostSMlike)], \
# rgsqdiff[mostSMlike]
#===============Flavour constraints=========================
# Branching ratios:
# Switch on/off using "useBdecays" config option.
# "Theory error" taken to be the larger of the upper/lower errors
# returned by nmspec. ->UPDATE: now using LFs.logdoublenormal,
# models upper and lower errors by seperate Gaussians.
# BF(b->s gamma) (i.e. B_u/B_d -> X_s gamma)
bsgexperr2 = (0.26e-4)**2+(0.09e-4)**2
bsguperr2 = bsgexperr2+(specdict['bsgmo+eth']-specdict['bsgmo'])**2
bsglwerr2 = bsgexperr2+(specdict['bsgmo-eth']-specdict['bsgmo'])**2
likedict['bsgmo'] = (LFs.logdoublenormal(x=specdict['bsgmo'],
mean=3.55e-4, sigmaP=sqrt(bsguperr2), sigmaM=sqrt(bsglwerr2))
, useBdecays)
# HFAG, arXiv:1010.1589 [hep-ex], Table 129 (Average)
# 0.09e-4 contribution added in accordance with newer HFAG edition:
# HFAG, arXiv:1207.1158 [hep-ex], pg 203. (i.e. basically unchanged)
# BR(B+ -> tau+ + nu_tau)
btaunuexperr2 = (0.3e-4)**2
btaunuuperr2 = btaunuexperr2+(specdict['B+taunu+eth']-specdict['B+taunu'])**2
btaunulwerr2 = btaunuexperr2+(specdict['B+taunu-eth']-specdict['B+taunu'])**2
likedict['B+taunu'] = (LFs.logdoublenormal(x=specdict['B+taunu'],
mean=1.67e-4, sigmaP=sqrt(btaunuuperr2), sigmaM=sqrt(btaunulwerr2))
, useBdecays)
# HFAG 1010.1589v3 (updated 6 Sep 2011), retrieved 12 Oct 2011
# Table 127, pg 180
# HFAG, arXiv:1207.1158 [hep-ex], pg 204. table 144
# (basically unchanged from 2010 data, smaller uncertainity
# (0.39->0.3), mean unchanged.
# BR(Bs -> mu+ mu-)
# See comments where BsmumuLogLcurve is created from data files
likedict['bmumu'] = (Bsmumulikefunc(specdict['bmumu']), useBdecays)
#Folding theory error into this properly would be hard... need to
#convolve it in for every point. Can't think of a better way.
#Otherwise need to settle on something constant that can be
#computed at the beginning of the run.
#specdict['bmumu+eth']
#specdict['bmumu-eth']
#--------Effective prior factor-------------------------------------
likedict['logJew'] = (\
logJew(specdict['lambda_Qsusy'],
specdict['kappa_Qsusy'],
specdict['Alambda_Qsusy'],
specdict['Akappa_Qsusy'],
specdict['mueff_Qsusy']/
specdict['lambda_Qsusy'], # <S>=mueff/lambda
specdict['TanB'],
specdict['MHu^2_Qsusy'],
specdict['MHd^2_Qsusy'],
specdict['MZ'],
specdict['g`_Qsusy'],
specdict['g2_Qsusy'])
, False)
likedict['logJrge'] = (\
logJrge(specdict['mueff_Qsusy']/
specdict['lambda_Qsusy'], # <S>=mueff/lambda
specdict['TanB'],
specdict['MHu^2_Qsusy'],
specdict['MHd^2_Qsusy'],
specdict['lambda_Qsusy'],
specdict['kappa_Qsusy'],
specdict['yt_Qsusy'],
specdict['g`_Qsusy'],
specdict['g2_Qsusy'],
specdict['g3_Qsusy'],
specdict['lambda_QGUT'],
specdict['kappa_QGUT'],
specdict['yt_QGUT'],
specdict['g`_QGUT'],
specdict['g2_QGUT'],
specdict['g3_QGUT'])
, False)
# Total combined effective log prior factor (for easy removal during
# analysis)
effprior = 0.
if useJew: effprior += likedict['logJew'][0]
if useJrge: effprior += likedict['logJrge'][0]
likedict['effprior'] = (effprior, True)
#===============GLOBAL LOG LIKELIHOOD=======================
LogL = sum( logl for logl,uselike in likedict.itervalues() if uselike )
return LogL, likedict
def globlikefunc(obsdict):
"""Compute log likelihoods and global log likelihood
Output format:
likedict = {likename: (logL, uselike),...}
"""
likedict = {} #reset likelihood dictionary
#Extract individual observables dictionaries from container dictionary
specdict = obsdict['spectrum']
if usemicrOmegas: darkdict = obsdict['darkmatter']
if useSuperISO: flavdict = obsdict['flavour']
#NO HDECAY STUFF IN HERE
#if useHDecay: decadict = obsdict['decay']
#===========================================================
# EFFECTIVE PRIOR
#===========================================================
likedict['CCRprior'] = (CCRprior(specdict['BQ'], specdict['tanbQ'],
specdict['muQ']), useCCRprior)
#===============================================================
# DEFINE LIKELIHOOD CONTRIBUTIONS
#===============================================================
#Note: some things left commented in old pysusy2 format because
#they contain useful information and I can't be bothered
#reformatting it.
#-----------STANDARD MODEL DATA ------------
# this is used to constrain the nuisance parameters
# -NB-REMOVED -> USING GAUSSIAN PRIORS INSTEAD.
#ialphaemL = Observable(slhafile=setupobjects[SPECTRUMfile], block="SMINPUTS",
# index=1, average=127.918, sigma=0.018,likefunc=LFs.lognormallike)
# #Jun 2009 hep-ph/0906.0957v2, they reference PDG 2008, but I can't find the value myself.
#alphasL = Observable(slhafile=setupobjects[SPECTRUMfile], block="SMINPUTS",
# index=3, average=0.1184, sigma=0.0007,likefunc=LFs.lognormallike)
# #PDG 2010 pg 101 - Physical Constants
#MZL = Observable(slhafile=setupobjects[SPECTRUMfile], block="SMINPUTS",
# index=4, average=91.1876, sigma=0.0021,likefunc=LFs.lognormallike)
# #PDG 2010 pg 101 - Physical Constants
#MtopL = Observable(slhafile=setupobjects[SPECTRUMfile], block="SMINPUTS",
# index=6, average=173.3, sigma=1.1,likefunc=LFs.lognormallike)
# #1007.3178, tevatron, 19 Jul 2010
#MbotL = Observable(slhafile=setupobjects[SPECTRUMfile], block="SMINPUTS",
# index=5, average=4.19, sigma=0.18,likefunc=LFs.lognormallike)
# #PDG 2010 quark summary - http://pdg.lbl.gov/2010/tables/rpp2010-sum-quarks.pdf (NOTE - lower uncertainty is 0.06 not 0.18, altered distribution to make it symmetric for simplicity)
likedict['MW'] = (LFs.lognormallike(
x=specdict['MW'], mean=80.399,
sigma=sqrt(0.023**2 + 0.015**2)), useMW)
#PDG 2010, 2011 and partial 2012 update
#from
#http://lepewwg.web.cern.ch/LEPEWWG/ - extracted Apr 8 2011 (Jul 2010 average value)
#theory (second component) uncertainty stolen from 1107.1715, need proper source (they
#do not give one)
#-----------MAIN CONTRIBUTORS TO LIKELIHOOD-----------------
#=====Electroweak precision, RELIC DENSITY and (g-2)_mu========
if usemicrOmegas:
# delta rho parameter, describes MSSM corrections to electroweak observables
likedict['deltarho'] = (LFs.lognormallike(
x=darkdict['deltarho'], mean=0.0008, sigma=0.0017),
usedeltarho)
#PDG Standard Model Review: Electroweak model and constraints on new physics, pg 33 eq 10.47.
#Taking larger of the 1 sigma confidence internal values
#(likelihood function is actually highly asymmetric, PDG gives
#1 sigma: 1.0008 +0.0017,-0.0007
#2 sigma: 1.0004 +0.0029,-0.0011
#We are ignoring these complexities. The 0.0017 sigma should be quite on the conservative
#side, and contributions seem to only be positive, so the weird lower sigmas are essentially
#irrelevant anyway, in the CMSSM at least. I do not know if other MSSM models will be different,
#I assume probably not.
#In ISAJET have sin**2(thetaw), consider replacing deltarho with this. Values in different schemes
#in same part of pdg, pg 30, Table 10.8.
#Dark matter relic density
likedict['omegah2'] = (omegalikefunc(
darkdict['omegah2'], 0.1123,
sqrt((0.0035)**2 + (0.10 * 0.1123)**2)), useomegah2)
#Jan 2010, 1001.4538v2, page 3 table 1 (WMAP + BAO + H0 mean)
#theory (second component) uncertainty stolen from 1107.1715, need proper source
#Anomalous muon magnetic moment
likedict['deltaamu'] = (LFs.lognormallike(
x=darkdict['deltaamu'], mean=33.53e-10, sigma=8.24e-10),
usedeltaamu)
#1106.1315v1, Table 10, Solution B (most conservative)
#=====FLAVOUR OBSERVABLES FROM DARKMATTERfile======
# Note: Ditching these for now. Don't use them and they just make the output confusing.
# micrOmegas computes some of these essentially 'for free', so we may
# as well record them for comparison.
# NOTE: See equivalent flavour file observables definitions for references.
#
#bsgmoM = Observable(slhafile=setupobjects[DARKMATTERfile], block="CONSTRAINTS",
#index=2, average=3.55e-4, sigma=sqrt((0.26e-4)**2+(0.30e-4)**2),likefunc=LFs.lognormallike, uselike=False)
#
#bmumuM = Observable(slhafile=setupobjects[DARKMATTERfile], block="CONSTRAINTS",
#index=3, average=4.3e-8, sigma=0.14*4.3e-8,likefunc=CMSLHCbBsmumulikefunc(CLscurve,minBR,maxBR), uselike=False)
#
#obsorder += ['bsgmoM','bmumuM']
#=====DARK MATTER DIRECT DETECTION========
# LSP-nucleon cross sections # uncertainty in LSP-proton SI cross-section
# Note, this is based on uncertainties in hadronic scalar coefficients, currently hardcoded into micromegas.
# These uncertainties are propagated through a modified version of micromegas alongside the amplitude calculation.
# LSP-proton SI cross-section
likedict['sigmaLSPpSI'] = (xenonlikefunc(
darkdict['sigmaLSPpSI'], specdict['Mneut1'],
darkdict['dsigmaLSPpSI']), useDMdirect)
#likelihood function built from information in fig 5 of 1104.2549, 100 days of Xenon100 data (Apr 2011)
#=====FLAVOUR OBSERVABLES=============
if useSuperISO:
#Branching ratios
# BF(b->s gamma) - USING SUPERISO VALUE FOR LIKELIHOOD. Micromegas value recorded for comparison
likedict['bsgmo'] = (LFs.lognormallike(
x=flavdict['bsgmo'], mean=b2sg[0], sigma=b2sg[1]), True)
# BF(Bs -> mu+mu-) - USING SUPERISO VALUE FOR LIKELIHOOD. Micromegas value recorded for comparison
#likedict['bmumu'] = (Bsmumulikefunc(flavdict['bmumu']), True) #previous fancy version, using simplified likelihood for now
likedict['bmumu'] = (LFs.logerfupper(
x=flavdict['bmumu'], limit=b2mumu[0], sigma=b2sg[1]), True)
#might as well leave the other limits in unenforced
# BF(B_u -> tau nu) / BF(B_u -> tau nu)_SM
# ButaunuButaunuSM = MultiIndexObservable(setupobjects[LOWENERGYfile],LOWENERGYblock,(521,2,0,2,-15,16),
# average=1.28, sigma=0.38,likefunc=LFs.lognormallike)
# #copying 1107.1715, need to find proper source.
#REPLACING THE ABOVE RATIO, it is more straightforward to impose constraints directly on the branching ratio itself
#BF(B_u -> tau nu)
likedict['Butaunu'] = (LFs.lognormallike(
x=flavdict['Butaunu'], mean=1.67e-4, sigma=0.39e-4), False)
#Heavy Flavour Averaging Group (HFAG)
#1010.1589v3 (updated 6 Sep 2011), retrieved 12 Oct 2011
#Table 127, pg 180
# Delta0(B->K* gamma) (hope this is the same as Delta0-, seems like it might be)
# (isospin asymmetry)
likedict['Delta0'] = (LFs.lognormallike(
x=flavdict['Delta0'],
mean=0.029,
sigma=sqrt(0.029**2 + 0.019**2 + 0.018**2)), False)
# BaBAR, 2008 - 0808.1915, pg 17. No theory error included, pieces are different aspects of experimental error.
# BR(B+->D0 tau nu)/BR(B+-> D0 e nu)
likedict['BDtaunuBDenu'] = (LFs.lognormallike(
x=flavdict['BDtaunuBDenu'], mean=0.416, sigma=0.128),
False)
# BaBAR, 2008 - 0709.1698, pg 7, Table 1 (R value). No theory error included.
# R_l23: involves helicity suppressed K_l2 decays. Equals 1 in SM.
likedict['Rl23'] = (LFs.lognormallike(
x=flavdict['Rl23'], mean=1.004, sigma=0.007), False)
# FlaviaNet Working Group on Kaon Decays
# 0801.1817v1, pg 29, Eq. 4.19. No theory error included (meaning SuperISO error, as for other observables)
# BR(D_s->tau nu)
likedict['Dstaunu'] = (LFs.lognormallike(
x=flavdict['Dstaunu'],
mean=0.0538,
sigma=sqrt((0.0032)**2 + (0.002)**2)), False)
#Heavy Flavour Averaging Group (HFAG)
#1010.1589v3 (updated 6 Sep 2011), retrieved 12 Oct 2011
#Figure 68, pg 225. Theory error stolen from 1107.1715, need to find proper source.
# BR(D_s->mu nu)
likedict['Dsmunu'] = (LFs.lognormallike(
x=flavdict['Dsmunu'],
mean=0.00581,
sigma=sqrt((0.00043)**2 + (0.0002)**2)), False)
#Heavy Flavour Averaging Group (HFAG)
#1010.1589v3 (updated 6 Sep 2011), retrieved 14 Oct 2011
#Figure 67, pg 224. Theory error stolen from 1107.1715, need to find proper source.
#=================Direct sparticle search limits=============================
nmass = np.abs(
specdict['Mneut1']
) #get abs because spectrum generator returns negative values sometimes
smass = np.abs(specdict['MseL'])
likedict['MseL'] = (LFs.logsteplower(
x=smass,
limit=99 if nmass < 84 else 96 if smass - nmass > 6 else 73),
useDSL) #Phys. Lett. B544 p73 (2002)
smass = np.abs(specdict['MsmuL'])
likedict['MsmuL'] = (LFs.logsteplower(
x=smass, limit=94.4 if smass - nmass > 6 else 73),
useDSL) #Phys. Lett. B544 p73 (2002)
smass = np.abs(specdict['Mstau1'])
likedict['Mstau1'] = (LFs.logsteplower(
x=smass, limit=86 if smass - nmass > 8 else 73),
useDSL) #Phys. Lett. B544 p73 (2002)
smass = np.abs(specdict['MesnuL'])
likedict['MesnuL'] = (LFs.logsteplower(
x=smass, limit=43 if smass - nmass < 10 else 94),
useDSL) #Phys. Lett. B544 p73 (2002)
smass = np.abs(specdict['Mchar1'])
likedict['Mchar1'] = (
LFs.logsteplower(
x=smass, limit=97.1 if (smass - nmass) > 3 else 45), useDSL
) #45 GeV limit from PDG 2010, unconditional limit from invisible Z width, other limit from Eur. Phys. J. C31 p421 (2003)
#NOTE: USING SAME LIMITS FOR L AND R SQUARKS, CHECK THAT THIS IS FINE.
smass = np.abs(specdict['Mstop1'])
likedict['Mstop1'] = (
LFs.logsteplower(
x=smass, limit=95 if smass - nmass > 8 else 63), useDSL
) #? Damn don't seem to have written down where this comes from. Need to find out.
smass = np.abs(
specdict['Msbot1']
) #NOTE: stop2 heavier than stop1 by definition so only need to bother applying limit to stop1. (1 and 2 are the mass eigenstates, mixtures of L and R interaction eigenstates). Same for sbot2
likedict['Msbot1'] = (LFs.logsteplower(
x=smass, limit=93 if smass - nmass > 8 else 63), useDSL)
#NOTEL USING SAME LIMITS FOR REST OF SQUARKS, CHECK THIS ABOVE, 'squarklikefunc'.
#likelihood function defined above, usage: squarklikefunc(smassIN,nmassIN) (smass - THIS sparticle mass, nmass - neutralino 1 mass)
#NOTE: L and R states are same as 1 and 2 states for other squarks because off diagonal terms in the mixing matrices are
#negligible. This is not true for the third generation squarks which is why we are sure to label them 1 and 2 above (1=lightest)
for Msquark in [
'MsupL', 'MsupR', 'MsdownL', 'MsdownR', 'MsstrangeL',
'MsstrangeR', 'MscharmL', 'MscharmR'
]:
likedict[Msquark] = (squarklikefunc(specdict[Msquark], nmass),
useDSL)
likedict['Mgluino'] = (
LFs.logerflower(x=specdict['Mgluino'], limit=289,
sigma=15), useDSL
) #from 08093792 - not well checked, probably need to update with LHC data.
# ---------------NOTE: LEP HIGGS MASS LIMIT-------------------. Using digitized LEP limit from hep-ph/0603247 (2006), fig 3a
# Using digitized curve to compute m_h bound appropriate to g_ZZh coupling for each model point with estimated 3 GeV sigma for m_h returned by SoftSusy
# Need the following observables to be extracted to compute Higgs likelihood function:
# alpha,tanbetaQ #RGE running of tanb is slow so tanbQ should be approximately the EW tanb value
# Likelihood function for this is written above (needs to return a lower limit erf likelihood depending on g_ZZh):
#higgs=lightest higgs mass;alpha=higgs scalar mixing angle;tanbeta=tan(higgs VEV ratio)
mhiggs = np.abs(specdict['Mh0'])
#likedict['Mh0'] = (LFs.logerflower(x=mhiggs, limit=higgslimitfunc(specdict['alpha'],specdict['tanbQ'],mHlimitcurve), sigma=3), useHiggs)
#now using LHC measured higgs mass
#NOTE! SET TO TRUE! IGNORES WHATEVER IS SPECIFIED IN CONFIG FILE!
likedict['Mh0'] = (LFs.lognormallike(
x=mhiggs, mean=mh[0], sigma=mh[1]), True)
#No fancy HDecay stuff in here.
#===============GLOBAL LOG LIKELIHOOD=======================
LogL = sum(
logl for logl, uselike in likedict.itervalues() if uselike)
return LogL, likedict