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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 1 Non-factorization effects in vdM scans and their implications for ATLAS/CMS scans in 2015 Introduction: scan-to-scan irreproducibility & non-factorization biases Quantifying (and correcting for) non-factorization effects in ATLAS, using luminosity & beamspot information: this presentation in LHCb, by direct imaging of the 2-D beam-density distributions see C. Barschel’s presentation, next in this meeting Implications for the 2015 ATLAS/CMS vdM-scan request W. Kozanecki (CEA-Saclay)

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 2 Absolute- L calibration challenges in 2012 (and not only then...) Two very challenging issues in 2012 vdM scans Scan-to-scan irreproducibility and/or systematic trend: 2-3 % ( syst, ATL ~ 3.6 %, syst, CMS ~ 4.4 %) Baffling in Apr 2012, real bad in Jul 2012, better in Nov 2012 (why so ≠?) Breakdown of x-y factorization in the 3-d L distribution aka ‘non-linear x-y correlations’ observed during vdM scans by all of ATLAS, CMS, LHCb in 2012 – but also by ATLAS in 2011 scans These 2 issues are clearly beam-dynamics effects, time-dependent & different fill-to-fill (instrumental drifts ruled out) turned out to be related ATLAS ~ CMS Apr’12 vdM 2.1 % Factorization assumes that shape of vdM scan curve during an x (y) scan is independent of the separation y ( x) in the orthogonal plane if this assumption is satisfied, the combination of 1 x-scan and 1 y-scan is sufficient to characterize the entire distribution L ( x, y) if this is violated at a “significant” level, the vdM formalism could be generalized to 2-d by performing a full 2-D grid scan (but: impractical!)

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 3 Hindu goddess Durga, wife of Lord Shiva Hindu goddess Parvati, wife of Lord Shiva Avatar: in Hinduism, a manifestation of a deity or released soul in bodily form on earth; an incarnate divine teacher. an incarnation, embodiment, or manifestation of a person or idea

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 4 The “beam size” and its avatars NameSymbolMeasurable using 1-Gaussian limitComments Single-beam size x,b, y,b b = B1, B2 BSRT, WS LHCb SMOG - Projections only Full 2-d Transverse convolved beam size x, y vdM scans x = x,1 + x,2 y = y,1 + y,2 Very precise: < 1% Transverse luminous size x, L, y, L 3-d vertex distribution x, L = x,1 + x,2 y, L = y,1 + y,2 Aka ‘beamspot width’ Resolut’n-limited for * < 10-15 m Bunch length z,b BQM Luminous length z, L z-vertex distribution z, L = 0.5 * f( * ) z,1 + z,2 ) Aka ‘beamspot length’

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 5 Vertical luminous size L (beamspot width) Testing factorization of L ( x, y) during vdM scans Convolved beam size (width of vdM scan curve) 12 % July 2012 vdM scans Nov 2012 vdM scans 20 %

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 6 Vertical luminous size L (beamspot width) Testing factorization of L ( x, y) during vdM scans Convolved beam size (width of vdM scan curve) 12 % July 2012 vdM scans Nov 2012 vdM scans 20 % The large reduction in non-linear x-y correlations, between the July & Nov 2012 scans, was achieved mainly by careful preparation of highly gaussian beams in the injectors. The elimination of blowup by multiple scattering in a transfer line, and the reduction of the LHC octupole strength, may also have played a role. The beam-beam contribution to non- factorization effects has been calculated to be negligible by comparison.

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 7 Production of (more) gaussian beams in the injector chain SPS WS profiles 18 Jul 12 LHCb vdM fill SPS WS profiles 02 Nov 12 Injector MD Data g + p0 fit See H. Bartosik’s LBOC presentation of 26 Nov 2013

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 8 Comparison of vdM scan profiles in Jul & Nov 2012 ATLAS scans Fit functions: g + g + constant g + constant July 2012 scan Nov 2012 scan g+g+p0: 2 /DOF = 2.8 g+p0 : 2 /DOF = 84.5 g+g+p0 fit collapses into 2 identical gaussians, i.e. g+p0

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 9 Vertical luminous size L (beamspot width) Quantifying factorization of L ( x, y) during vdM scans Convolved beam size (width of vdM scan curve) 12 % July 2012 vdM scans 20 % Non-factorization manifests itself via: & L different in centered & off-axis scans y L varying w/ x during horizontal scan (and vice-versa) non factorizable single-beam distributions (LHCb beam-gas imaging) systematic scan-to-scan vis inconsistencies Non-factorization @ IP 1, 5, 8 can be studied quantitatively only * by fitting evolution of beamspot position & luminous width during scans in particular: variation of y L (resp. x L ) w/ x ( y) during horizontal (resp. vertical) scans (both centered & off-axis) possible only if the vertex resolution does not dominate the luminous width * LHCb: additional input from BGI, needs b >> vertexing

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 10 Luminous-region modelling x y L Aim: reproduce the evolution, during vdM scans, of the luminosity-scan curves L ( x, y) the beamspot position,, the luminous widths ( x L, y L ) and length ( z L ) Procedure Assumption: each beam (1, 2) = non- factorizable double gaussian (or other model) 1,2 (x, y, z) = w 1,2 G A (x, y, z)+ (1-w 1,2 ) G B (x, y, z) described (in this case) by ~ 11 parameters/beam Fit these beam parameters to the measured beam-separation ( x, y) dependence of: L,,,, x L, y L, z L Beam Parameters for each of B1, B2 σ x,a = narrow gaussian x-width σ y,a = narrow gaussian y-width σ z,a = narrow gaussian z-width κ a = x-y correlation in narrow gaussian w a = weight of narrow gaussian σ x,b = broad gaussian x-width σ y,b = broad gaussian y-width σ z,a = broadgaussian z-width κ b = x-y correlation in broad gaussian α xz beam crossing angle in x-z plane α yz beam crossing angle in y-z plane

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 11 Luminous-region observables during a (symmetric) vdM scan The evolution of the beamspot position and luminous width during a scan gives information on the shape of the beams Example 1: different x widths Example 2: same x and y widths, but with opposite x-y correlation The luminous region moves in the same direction as the narrower of the two beams The luminous region moves in the direction transverse (y) to the scan direction (x)

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 12 Luminous-region observables during a (symmetric) vdM scan (2) Example 3: evolution of the shape of the luminous region each beam is modelled as a double gaussian Luminous region (x projection) Beam 1 Beam 2

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 13 For each scan (x & y) and each [available] colliding bunch [3-4/30], the fit results are compared to the measurements this example: F 2855 (July 2012), BCID 1, horizontal scan 6 Typical result of combined fit to L & luminous-region scan data L (a.u.) Beamspot x-positionBeamspot y-positionBeamspot z-position x luminous width y luminous width Luminous length x-y correlation coeff.

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 14 For the set of single beam parameters output by the fit: define the non-factorization correction R the “true” luminosity (i.e. not assuming factorization) is determined by computing numerically the 4-d overlap integral: the “vdM” luminosity (assuming factorization) is computed from the integral under the x- & y- scan curves (which is proportional to 1/ x y ) Quantifying (non-)factorization – at last!

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 15 Consistency of L calibrations, before factorization correction Jul 2012 F 2855 Jul 2012 F 2856 Apr 2012 F 2520 Nov 2012 F 3311 Nov 2012 F 3316

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 16 Consistency of L calibrations, before & after factorization correction Jul 2012 F 2855 Jul 2012 F 2856 Apr 2012 F 2520 Nov 2012 F 3311 Nov 2012 F 3316

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 17 Consistency of L calibrations, before & after factorization correction Jul 2012 F 2855 Jul 2012 F 2856 Apr 2012 F 2520 Nov 2012 F 3311 Nov 2012 F 3316 ? ? The best correction is... no correction at all!

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 18 Parameters for first vdM scans @ IP1 at √s = 13 TeV ParameterNov 2012Apr-May ‘15Comments * [m] / E b [TeV] 11 / 415-20 / 6.5 Optimum btwn L & statistics Transverse phase-space tailoring in injector chain + LHC Gaussian (no tails!) minimize NLC Gaussian (no tails!) minimize NLC No screens Minimize LHC octupoles N ( m-rad) 2.5 – 3.5~ 3 L beam-beam Luminous size L ( m) 57- 67~ 57 RQ same L as in 2012 Vertex resolution ( m) 30-50 Bunch pattern ~ 40-50 b > 1 s sep’rtn No trains ~ 40-50 b > 1 s sep’rtn No trains No parasitic crossings Weaker tails Bunch intensities0.7 – 1.0 10 11 0.6 - 0.8 10 11 beam-beam Nominal crossing angle0Negotiable Review after 1st scan session

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 19 Conclusions One of the most challenging issues in vdM scans is the control of non- factorization biases only known countermeasure: beam-tailoring in injector chain quantitative understanding (if only to set a systematic uncertainty) entirely dependent on luminous-region (aka beamspot) analysis imperatively requires that vertexing << L The reduction in x/y beam size (during vdM scans) brought about by the higher beam energy in 2015 the envisaged lower * after ramp/queeze the lower emittances (that also exacerbate beam-beam corrections) very severely impacts the ability to exploit beamspot information very severely impacts the ability to exploit beamspot information ATLAS & CMS request scan conditions instrumentally equivalent to those in Nov 2012 maintaining the same luminous size L implies increasing * to 15-20 m tailoring transverse phase space in the injectors need the scans (vdM + LSC) asap in 2015 (for ATLAS, need BCM stabilized) luminometer diamonds must have ‘seen’ > 10 pb -1 shortly before scan (pumping) for 1 st scan of 2015, Xing angle at IP1 OK for ATLAS (compatibility w/ LHCf)

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 20 Additional material

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 21 A key assumption of the vdM scan method as currently applied is that the luminosity factorizes in x & y: factorizes in x & y: This is equivalent to assuming that the shape of the scan curve during an x (y) scan is independent of the separation y ( x) in the orthogonal plane if this is the case, the combination of 1 x-scan and 1 y-scan is sufficient to characterize the entire distribution L ( x, y) if this is violated at a “significant” level, the vdM formalism can be generalized to 2 dimensions by performing a grid scan (impractical!) Although linear x-y coupling does violate this assumption, the induced bias is typically very small ( L / L ~ 0.1%) with present LHC optics (small x-y coupling coeff., x ~ y, x ~ y ) A fundamental assumption: x-y factorization of L ( x, y)

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 22 To estimate (roughly) the magnitude of a potential NLC-induced bias, ATLAS routinely compared the visible cross-sections (i.e. the L calibration scales) obtained by fitting the x- & y- vdM-scan curves using either an uncorrelated model (= baseline): g+g (can simplify to g, or to g+p0) a correlated double-gaussian model (naïve & by no means unique) that reduces to the uncorrelated model at x = y = 0 (but with f x = f y ) Observed impact on visible cross-sections at √s = 7 TeV (ATLAS) vis / vis ~ 3%, 2%, 0.9%, 0.5 % for Apr ’10, May ’10, Oct ’10, May ’11 The more single-gaussian the scan curves, the smaller the potential bias (a property of this model – but probably not a general property?) As the effect looked small for the two main 7 TeV scan sessions, and for lack of manpower, didn’t look much further until large 2012 signal A complementary approach: correlated fits to vdM scan curves L (x,y)

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 23 Comparison of uncorrelated & correlated fits to vdM scan curves 0.4 % 1.8 % 1.6 % 3.0 % 2.8 % Uncorrelated (= factorizable) L ~ G 1 (x) G 2 (y) Correlated (non-factorizable) L ~ g N (x, y) + (1 – g W (x,y)

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 24 Comparison of uncorrelated & correlated fits to vdM scan curves 0.4 % 1.8 % 1.6 % 3.0 % 2.8 % Uncorrelated (= factorizable) L ~ G 1 (x) G 2 (y) Correlated (non-factorizable) L ~ g N (x, y) + (1 – g W (x,y) Notes the true bias may be larger than the difference between uncorrelated & correlated fits (coupling-model dependence?) there may be other coupling models which also yield a stable central value, but significantly different from the present one.

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 25 A detour: beam-gas & luminous-region imaging Measured ( 1,2 ~ 90 for m, E b = 4 TeV) Vertex resolution ~ 30 Beam-gas imaging (LHCb only) measure 1 x,y, 2 x,y separately independent absolute L calibration Luminous-region ima ging msre L x,y + their dependence on x,y during vdM scan Resolution systematics critical: 10% on resolution 1.2 % on 1, 2 2.4 % on L with 2012 conditions The basic problem... b scales like sqrt ( * /E b ) with 2012 (2015) conditions, a 10% uncertainty on the vertexing resolution implies a 2-3 % (4 – 5%) error on L (for the same ) the vertex resolution won’t get any better!

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W. KozaneckiLHC Beam Operations Committee, 3 Dec 2013 Slide 26 Do’s and don’t ‘s: some of the lessons learnt from 2012 scans Don’t... use small * reconstructed luminous width L (= beamspot width) becomes resolution-dominated and very difficult to analyze ~ 5 too high for comfort: potential detector non-linearities push for small emittances the smaller , the more L is resolution-dominated set nominal crossing angle complicates measurement/characterization of satellites notable exception: LHCb needs large Xing-angle for beam-gas enhanced ghost-charge measurement use nominal bunch intensities beam-beam corrections: 2% for Nov 2012 @ N ~ 0.9 p/bunch ! Do favor... large * make L ALAP ( resolution) * = 11, = 3 optimal @ 8 TeV “nominal LHC” emittances make L ALAP ( resolution) BUT avoid anything that creates non-gaussian tails (e.g. blowup by screen in transfer line) Large enough L critical for (a) non-factorization systematics (b) L calibration by beam-gas imaging zero crossing angle optimize satellite reconstruction beams as gaussian as possible in SPS + LHC (+ moderate bunch N) tailor injected phase space (still an art more than a science...) avoid strong octupoles

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