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Chris Quigg Fermi National Accelerator Laboratory CDF Derek Leinweber Theoretical Perspectives Chris Quigg Fermi National Accelerator Laboratory CDF Derek Leinweber Derek XLVI Rencontres de Moriond (EW)· 20 mars 2011 1 Two New Laws of Nature + 18 Pointlike (r 10− m) quarks and leptons ≤ oR i3 +R i2 eR i1 bR tR sR cR i3 dR i2 uR i1 oL +L eL tL cL uL bL sL dL Interactions: SU(3) SU(2) U(1) gauge symmetries c ⊗ L ⊗ Y 2 Highly idealized 3 Many tensions, puzzles, outstanding questions Lots of new ideas Beautiful experiments: mature / new / dreams 4 Quantum Chromodynamics Asymptotically free theory Many successes in perturbation theory to 1 TeV Growing understanding: nonperturbative regime Quarks & gluons confined: evidence, no proof No structural defects, but strong CP problem 5 Evolution of the strong coupling “constant” 11 10 9 8 7 s 6 _ 1/ 5 4 3 2 1 100 101 102 103 Q [GeV] 6 REPORTS mud,correspondingtoMp ≅ 135 MeV,are difficult. vector meson (r, K*) octets that do not require (25, 26)andforoursetup(27)], simulating di- They need computationally intensive calculations, the calculation of disconnected propagators. rectly at physical mud in large enough volumes, with Mp reaching down to 200 MeV or less. Typical effective masses are shown in Fig. 1. which would be an obvious choice, is still ex- 5) Controlled extrapolations to the contin- 3) Shifts in hadron masses due to the finite tremely challenging numerically. Thus, the stan- uum limit, requiring that the calculations be size of the lattice are systematic effects. There dard strategy consists of performing calculations performed at no less than three values of the are two different effects, and we took both of at a number of larger mud and extrapolating the lattice spacing, in order to guarantee that the them into account. The first type of volume de- results to the physical point. To that end, we use scaling region is reached. pendence is related to virtual pion exchange be- chiral perturbation theory and/or a Taylor expan- Our analysis includes all five ingredients tween the different copies of our periodic system, sion around any of our mass points (19). listed above, thus providing a calculation of the and it decreases exponentially with Mp L.Using 5) Our three-flavor scaling study (27)showed light hadron spectrum with fully controlled sys- MpL > 4 results in masses which coincide, for that hadron masses deviate from their continuum tematics as follows. all practical purposes, with the infinite volume values by less than approximately 1% for lattice 1) Owing to the key statement from renor- results [see results, for example, for pions (22) spacings up to a ≈ 0.125 fm. Because the sta- malization group theory that higher-dimension, and fore baryons (23, 24)]. Nevertheless, for one tistical errors of the hadron masses calculated in local operators in the action are irrelevant in the of our simulation points, we used several vol- the present paper are similar in size, we do not continuum limit, there is, in principle, an un- umes and determined the volume dependence, expect significant scaling violations here. This is limited freedom in choosing a lattice action. which was included as a (negligible) correction at confirmed by Fig. 2. Nevertheless, we quantified There is no consensus regarding which action all points (19). The second type of volume de- and removed possible discretization errors by a would offer the most cost-effective approach to pendence exists only for resonances. The cou- combined analysis using results obtained at three the continuum limit and to physical mud.Weuse pling between the resonance state and its decay lattice spacings (19). an action that improves both the gauge and products leads to a nontrivial-level structure in We performed two separate analyses, setting fermionic sectors and heavily suppresses non- finite volume. Based on (20, 21), we calculated the scale with MX and MW.Theresultsofthese physical, ultraviolet modes (19). We perform a the corrections necessary to reconstruct the reso- two sets are summarized in Table 1. The X set is series of 2 + 1 flavor calculations; that is, we nance masses from the finite volume ground- shown in Fig. 3. With both scale-setting proce- include degenerate u and d sea quarks and an state energy and included them in the analysis dures, we find that the masses agree with the additional s sea quark. We fix ms to its approxi- (19). hadron spectrum observed in nature (28). mate physical value. To interpolate to the phys- 4) Though important algorithmic develop- Thus, our study strongly suggests that QCD ical value, four of our simulations were repeated ments have taken place recently [for example is the theory of the strong interaction, at low on November 29, 2008 with a slightly different ms.Wevarymud in a range that extends down to Mp ≈ 190 MeV. Table 1. Spectrum results in giga–electron volts. The statistical (SEM) and systematic uncertainties 2) QCD does not predict hadron masses in on the last digits are given in the first and second set of parentheses, respectively. Experimental physical units: Only dimensionless combinations masses are isospin-averaged (19). For each of the isospin multiplets considered, this average is (such as mass ratios) can be calculated. To set the within at most 3.5 MeV of the masses of all of its members. As expected, the octet masses are more overall physical scale, any dimensionful observ- accurate than the decuplet masses, and the larger the strange content, the more precise is the able can be used. However, practical issues in- result. As a consequence, the D mass determination is the least precise. fluence this choice. First of all, it should be a quantity that can be calculated precisely and X Experimental (28) MX (X set) MX (W set) www.sciencemag.org whose experimental value is well known. Sec- r 0.775 0.775 (29) (13) 0.778 (30) (33) ond, it should have a weak dependence on mud, K* 0.894 0.906 (14) (4) 0.907 (15) (8) so that its chiral behavior does not interfere with N 0.939 0.936 (25) (22) 0.953 (29) (19) that of other observables. Because we are con- L 1.116 1.114 (15) (5) 1.103 (23) (10) sidering spectral quantities here, these two con- S 1.191 1.169 (18) (15) 1.157 (25) (15) ditions should guide our choice of the particle X 1.318 1.318 1.317 (16) (13) whose mass will set the scale. Furthermore, the D 1.232 1.248 (97) (61) 1.234 (82) (81) particle should not decay under the strong in- S* 1.385 1.427 (46) (35) 1.404 (38) (27) Downloaded from teraction. On the one hand, the larger the strange X* 1.533 1.565 (26) (15) 1.561 (15) (15) content of the particle, the more precise the mass W 1.672 1.676 (20) (15) 1.672 determination and the weaker the dependence on Light hadron spectrum with dynamical fermions mud.ThesefactssupporttheuseoftheW baryon, the particle with the highest strange content. On Fig. 3. The light hadron the other hand, the determination of baryon dec- spectrum of QCD. Hori- uplet masses is usually less precise than those of zontal lines and bands are the octet. This observation would suggest that the experimental values the X baryon is appropriate. Because both the with their decay widths. W and X baryon are reasonable choices, we Our results are shown by carry out two analyses, one with MW (the W set) solid circles. Vertical error and one with MX (the X set). We find that for all bars represent our com- three gauge couplings, 6/g2 =3.3,3.57,and3.7, bined statistical (SEM) and both quantities give consistent results, namely systematic error estimates. a ≈ 0.125, 0.085, and 0.065 fm, respectively. To p, K,andX have no error fix the bare quark masses, we use the mass ratio bars, because they are pairs M /M ,M /M or M /M ,M /M .We used to set the light quark p W K W p X K X mass, the strange quark determine the masses of the baryon octet (N, S, mass and the overall L, X)anddecuplet(D, S*, X*, W)andthose scale, respectively. members of the light pseudoscalar (p, K)and BMW 1226 21 NOVEMBER 2008 VOL 322 SCIENCE www.sciencemag.org 7 How Might QCD Crack? (Breakdown of factorization) Free quarks / unconfined color New kinds of colored matter Quark compositeness Larger color symmetry containing QCD 8 Electroweak Theory To good approximation … 3-generation V–A GIM suppresses FCNC CKM quark-mixing matrix describes CPV Gauge symmetry validated in e+e- → W+W– Tested as quantum field theory at per-mille level 9 QuiggFig02.pdf 6/16/09 1:29:27 PM Gauge symmetry (group-theory structure) tested in + + e e− W W − → 30 No ZWW vertex Only υe exchange 20 (pb) WW σ 10 LEP data Standard model 02/17/2005 0 160 180 200 √s (GeV) 10 Electroweak Theory Survives Many Tests 11 Electroweak Theory Anticipates Discoveries 240 200 160 120 Top Mass (GeV) 80 40 1990 1995 2000 2005 2010 Year 12 Large Hadron Collider CMS LHCb ALICE ATLAS ➲ 13 19.3.2011 14 CMS 15 15 CMS 16 ATLAS 17 Hector Berlioz· Les Troyens· Valencia 18 Wonderful progress … … but miles to go: Beam energy x 2 Luminosity x 100 19 Ratios of Parton Luminosities 100 qq gg – 10-1 ud gq 10-2 [7 TeV] / [14 TeV] [14 / TeV] [7 10-3 10-2 10-1 100 101 W [TeV] 20 An unknown agent hides electroweak symmetry ✴ A force of a new character, based on interactions of an elementary scalar ✴ A new gauge force, perhaps acting on undiscovered constituents ✴ A residual force that emerges from strong dynamics among electroweak gauge bosons ✴ An echo of extra spacetime dimensions 21 Spontaneous Breaking of Gauge Symmetry (1964) Higgs (then) Kibble Guralnik Hagen Englert Brout 22 The Importance of the 1-TeV Scale EW theory does not predict Higgs-boson mass Thought experiment: conditional upper bound W+W –, ZZ, HH, HZ satisfy s-wave unitarity, _ 1/2 provided MH ≤ (8π√2/3GF) ≈ 1 TeV • If bound is respected, perturbation theory is “everywhere” reliable • If not, weak interactions among W±, Z, H become strong on 1-TeV scale New phenomena are to be found around 1 TeV 23 Where the SM Higgs Boson Is Not 2 Direct searches $! = -2ln(Q) LHC: H%WW only.
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